According to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
What is co-ordinate geometry ?Coordinate geometry, also known as analytic geometry, is a branch of mathematics that deals with the study of geometric shapes using algebraic principles. It involves the use of coordinates to represent points, lines, curves, and other geometric figures on a plane or in space.
According to the given information:we need to know the coordinates of its foci, co-vertices, and the center. We can start by finding the center of the ellipse, which is the midpoint of the line segment joining the foci:
Center = ( (-8 + (-8))/2 , (14 + (-16))/2 ) = (-8,-1)
Next, we can find the distance between the foci, which is given by:
[tex]distance between foci = 2c = sqrt[(14 - (-16))^2 + (-8 - (-8))^2] = 30[/tex]
where c is the distance from the center to either focus.
We also know that the distance between the co-vertices is given by:
distance between co-vertices = 2a = |-16 - 0| = 16
where a is the distance from the center to either co-vertex.
Finally, we can use the standard form equation for an ellipse centered at the origin:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
where b is the distance from the center to either vertex.
To find b, we can use the Pythagorean theorem:
[tex]b^2 = c^2 - a^2 \\b^2 = 30^2 - 16^2\\b^2 = 784\\b = 28[/tex]
Now we have all the information we need to write the equation of the ellipse:
[tex](x+8)^2/16^2 + (y+1)^2/28^2 = 1[/tex]
Therefore, according to the given information, the equation of the ellipse is [tex](x+8)^2/256 + (y+1)^2/784 = 1.[/tex]
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if the sum of a number and eight is doubled, the result is seven less than the number. Find the number.
Answer:
Step-by-step explanation:
Let's call the number we're looking for "x".
The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:
2(x+8) = x-7
Now let's solve for x:
2x + 16 = x - 7
2x - x = -7 - 16
x = -23
Therefore, the number we're looking for is -23.
What is the limit of (n!)^(1/n) as n approaches infinity?
Note: n! means n factorial, which is the product of all positive integers up to n.
Answer:
Step-by-step explanation:
To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:
n! ≈ (n/e)^n √(2πn)
where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.
Using this approximation, we can rewrite (n!)^(1/n) as:
(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)
Taking the limit as n approaches infinity, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)
Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:
lim [√(2πn)]^(1/n) = 1
For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:
lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1
Therefore, combining the two terms, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1
Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.
Answer:1
Step-by-step explanation:
I will mark you brainiest!
Determine the MOST PRECISE name for the quadrilateral below.
A) rhombus
B) parallelogram
C) square
D) trapezoid
E) kite
The answer is A, rhombus.
Mason earns $8.10 per hour and worked 40 hours. Noah earns $10.80 per hour. How many hours would Noah need to work to equal Mason’s earnings over 40 hours?
Answer:
Noah would need to work 30 hours to equal Mason's earning for 40 hours
Step-by-step explanation:
Mason;
8.10 x 40 = 324
324 ÷ 10.80 = 30 hours.
Helping in the name of Jesus.
Answer:
30 hours
Step-by-step explanation:
40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours
3. Factor 72x³ +72x² +18x.
The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
Factored value is what?Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.
What is a factored expression example?Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.
We can factor out [tex]18x[/tex] from each term to simplify the expression:
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]
An expression enclosed in parentheses can now be calculated by grouping or factoring.
[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]
The expression's properly factored version has the following result,
[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]
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After solving the problem Is the statement true or false
Answer:
True
Step-by-step explanation:
Since x = 3 since we are given that f(3) = 16, x = 3.
The equation is:
[tex]f(x) = x^{2} + 2x + 1[/tex]
and x = 3, we can easily sustitute x with 3. When we do so, our equation will look like:
[tex]f(3) = 3^{2} + 2(3) + 1[/tex]
Now, we will solve.
3^2 is = 9
2(3) = 6
Now, we will plug into the equation:
[tex]f(3) = 9 + 6 + 1[/tex]
Combine like terms (constants)
[tex]f(3) = 16[/tex]
Please check the image for directions, Five stars, and like. Thank you
The measure of HI based on the given diagram is 70 units.
What is a triangle mid segment?A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.
HI = 3x + 5
EF = -3x + 55
So,
HI = 1/2(EF)
3x + 5 = 1/2(-3x + 55)
3x + 5 = (-3x + 55) / 2
cross product
2(3x + 5) = -3x + 55
open parenthesis
6x + 10 = - 3x + 55
6x + 3x = 55 - 10
9x = 45
divide both sides by 9
x = 45/9
x = 5
Therefore, the measure of HI and EF are;
HI = 3x + 5
= 3(5) + 55
= 15 + 55
= 70
EF = -3x + 55
= -3(5) + 55
= -15 + 55
= 40
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What are inequalities?
Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
Just needing help here
Based on the graph given, the function is not continuous at x = 1.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. A function is typically represented using functional notation as f(x), which means that the output value of the function f corresponds to the input value x. Functions can take many forms and can be represented graphically or algebraically. They are used to describe many real-world phenomena, including physical systems, economic trends, and social behavior. Functions are important in mathematics because they provide a framework for understanding relationships between variables and for solving problems in various areas of mathematics, science, and engineering.
Here,
At x = 1, there is a "hole" or a point of discontinuity in the graph where the function is undefined. This is because the function has a removable discontinuity at x = 1, meaning that the limit of the function exists at x = 1 but the function is not defined at that point.
Therefore, the value of x at which the function is not continuous is: 1
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Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down.
Answer:
gdiduusuehfuehvv
Step-by-step explanation:
bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it
GUYS PLEASE HELP MATH!!
Answer:
4.3
Step-by-step explanation:
Question 15 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:
Standard deck of 52 cards
4 suits (CLUBS SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
DIAMONDS
If a card is drawn at random from the deck, what is the probability it is a jack or ten?
0
4/52- 1/13
8/52 = 2/13
48/52- 12/13
Answer: 2/13
Step-by-step explanation:
There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:
P(Jack or Ten) = 8/52 = 2/13
So the answer is 2/13.
Step-by-step explanation:
a probability is airways the ratio
desired cases / totally possible cases
in each of the 4 suits there is one Jack and one 10.
that means in the whole deck of cards we have
4×2 = 8 desired cases.
the totally possible cases are the whole deck = 52.
so, the probability to draw a Jack or a Ten is
8/52 = 2/13
for a given positive integer n, output all the perfect numbers between 1 and n, one number in each line.
Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.
A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.
Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).
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The complete question is:
What are all the perfect numbers between 1 and n (where n is a positive integer)?
right triangle that i’m confused on please help
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
determine, without actually computing the z transform, the rocs for the z transform of the following signals:
The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.
Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.
In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.
However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.
So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.
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The complete question is :
Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.
Jane has been practicing sewing, and she wants to make a rectangular blanket to give as a gift to her best friend. So that the blanket is not too small, Jane decides the blanket will have an area of approximately 40 square feet, or 5,760 square inches. She also wants the blanket to be 18 inches longer than it is wide to have room to embroider her friend's name along one edge.
To the nearest tenth of an inch, what is the width of the blanket?
The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
What is width in rectangle ?
In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.
Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.
The area of the blanket is given by:
Area = Length x Width
5760 sq inches = (x + 18) inches * x inches
Expanding the right-hand side and solving for x, we get:
[tex]x^2 + 18x - 5760 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a[/tex]
where a = 1, b = 18, and c = -5760. Plugging in these values, we get:
[tex]x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)[/tex]
[tex]x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2[/tex]
x ≈ 67.42 or x ≈ -85.42
Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.
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-6(4p+5) > 34-8p HELP ASAP
Answer:
p < -4
Step-by-step explanation:
-6(4p+5) > 34 - 8p
-24p - 30 > 34 - 8p
-16p - 30 > 34
-16p > 64
p < -4
Question 1: 10 pts
A triangle has a base length of 2ac² and a height 6 centimeters more than the base
length. Find the area of the triangle if a = 4 and c = 2.
608 cm²
224 cm²
1,216 cm²
576 cm²
The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²
What is the Area of a Triangle?Area = 1/2(base)(height).
Given the parameters:
Base length = 2ac² cmHeight = 2ac² + 6 cmIf a = 4 and c = 2, then:
Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)
Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)
Area = 1/2(32)(38)
Area = 608 cm²
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What is the value of 2/2 exponent -3
Answer:1
Step-by-step explanation:
2/2=1
1^-3=1
1/1times1times1
Answer:
1
Step-by-step explanation:
[tex]\frac{2}{2}[/tex] = 1
[tex]1^{-3}[/tex] To make a negative exponent positive, put it under one.
[tex]\frac{1}{1^{3} }[/tex] = [tex]\frac{1}{1}[/tex] = 1
Helping in the name of Jesus.
You run 3 laps around a rectangular field. The field is 100 meters long and 97 meters wide. How many meters do you run?
LI Annexure A shows Rhandzu's grade 11 school timetable for 2023. Learners are given 5 minutes to change from one lesson to the other. Use ANNEXURE A to answer the questions that follow. 1.1.1 Determine how l
ong the second break is. 1.1.2 How many subjects is Rhandzu doing? 1.1.3 Determine the number of days in an eight-day cycle that Rhandzu has Mathematical Literacy. Explain why it is important to schedule breaks on the time-table. 1.1.4
The answer of the given question based on determining the second break in the break is 1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , 1.1.2 Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.
What is Sepedi Home Language?Sepedi is Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in northern parts of country, like Limpopo, Gauteng, and Mpumalanga provinces.
Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to study of Sepedi as first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.
1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.
1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.
1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.
It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.
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The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.
What is Sepedi Home Language?Sepedi is Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in northern parts of country, like Limpopo, Gauteng, and Mpumalanga provinces.
Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to study of Sepedi as first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.
1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.
1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.
1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.
It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.
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two random vectors follow the same distribution does this mean every marginalized variables have to follow the same distribution
Yes. they can in fact, more than two independent variables can have the same distribution. Two random vectors follow the same distribution, which means that each marginalized variable must follow the same distribution.
In probability theory and statistics, the marginal distribution of a subset of a set of random variables is the probability distribution of the variables contained in that subset. It gives the probability of different values of variables in the subset without reference to the values of other variables. This contrasts with conditional distributions, which give probabilities based on the values of other variables.
The marginal variables are the variables of the subset of variables which are retained. These concepts are "marginal" because they can be found by adding the values of the rows or columns of a table and writing the sum in the blank space of the table.
The distribution of the marginal variable (marginal distribution) is obtained by marginalizing the distribution of the suppressed variable (that is, focusing on the sum in the margin), and the suppressed variable is called marginalized.
Complete Question:
If two random variables have the same PDF/PMF, then does this mean they have the same distribution?
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Distance in the coordinate plane iready
Answer:
Distance in the coordinate plane iready
Step-by-step explanation:
Sure, I can help with distance in the coordinate plane!
The distance between two points (x1, y1) and (x2, y2) in the coordinate plane can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Here's an example:
Let's say we want to find the distance between the points (3, 4) and (6, 8).
We can plug these coordinates into the distance formula:
d = √((6 - 3)^2 + (8 - 4)^2)
Simplifying the expression inside the square root:
d = √(3^2 + 4^2)
d = √(9 + 16)
d = √25
d = 5
Therefore, the distance between the points (3, 4) and (6, 8) is 5 units.
i need the answer to this question
The measure of angle BAC is 55°, which is closest to option B (50°).
What is a tangent angle?The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:
[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]
[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]
Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:
[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]
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It is most similar to option B (50°) when the angle BAC is 55°.
What is a tangent angle?
The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.
This property can only be found in triangles with straight angles.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD
Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.
Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).
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Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4
Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m
The correct matches are: 4 in. → 10.2 cm , 7 kg → 15.4 lb
6 gal → 22.7 L and 65 ft → 19.8 m.
What are conversions?Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.
For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.
Here are the conversions:
1 inch = 2.54 cm (approx.)
1 kg = 2.205 lb (approx.)
1 gal = 3.785 L (approx.)
1 ft = 0.3048 m (approx.)
Using these conversions, we can find the equivalent measures:
4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm
7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb
6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L
65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m
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main Street tea company blends black tea that sells for $3.45 a pound with Earl Gray tea that sells for $2.15 a pound to produce 80 lb of mixture that they sell for $2.75 a pound how much of each kind of tea does the mixture contain rounding to the nearest pound
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
Let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively:
x+y=80....................eq 1
3.45x+2.15y=2.75(80)......eq 2
:
rewrite eq 1 to x=80-y and plug that value into eq 2
:
3.45(80-y) +2.15y=2.75(80)
:
276-3.45y+2.15y=220
:
-1.3y=56
:
y=43.07 pounds of $2.15 tea
:
28x=80-43.07=36.93 pounds of $3.45 tea
Let a= the pounds of the more expensive tea needed
Let b= the pounds of the less expensive tea needed
(1) a+%2B+b+=+80
(2) 345a+%2B+215b+=+80%2A275 (in cents)
--------------------------
In words, (2) says.
(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =
(lbs of mixture x price/lb of mixture)
-------
Multiply both sides of (1) by 215 and then.
subtract from (2)
345a+%2B+215b+=+80%2A275
-215a+-+215b+=+-80%2A215
130a+=+80%2A60
130a+=+4800
a+=+36.92
and, from (1)
(1) a+%2B+b+=+80
36.92+%2B+b+=+80
b+=+80+-+36.92
b+=+43.08
36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.
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The mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations.
Let's denote the amount of black tea in pounds by "x" and the amount of Earl Gray tea in pounds by "y".
Since the total amount of mixture is 80 lb, we have:
x + y = 80 ----(1)
We also know that the mixture sells for $2.75 a pound, so the total revenue from selling 80 lb of mixture is:
80 x $2.75 = $220
On the other hand, the cost of the mixture is the sum of the costs of the black tea and the Earl Gray tea, which is:
3.45x + 2.15y
Since the company wants to make a profit, the revenue must be greater than the cost, so we have:
3.45x + 2.15y < $220
We can simplify this inequality by dividing both sides by 0.1:
34.5x + 21.5y < 2200 ----(2)
Now we have two equations with two unknowns (equations (1) and (2)), which we can solve using substitution or elimination.
Substitution method:
From equation (1), we have:
y = 80 - x
Substituting this into equation (2), we get:
34.5x + 21.5(80 - x) < 2200
Simplifying and solving for x, we get:
x < 34.5
Rounding x to the nearest pound, we get x = 34.
Substituting this value into y = 80 - x, we get y = 46.
Therefore, the mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.
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The sides of a triangle have lengths
7.5,11
, and
x
. If
x
is an integer, what is the least possible value of
x
? A. 1 B. 2 C. 3 D. 4 E. 5
If x is an integer, the least possible value of x is 4. So the option D is correct.
The triangle's third side should be less than the sum of the other two sides and more than the difference of the other two sides.
11 - 7.5 < x < 11 + 7.5
Simplify
3.5 < x < 18.5
So the value of the x is between 3.5 and 18.5.
From the option the value 4 and 5 lies between 3.5 and 18.5.
As we have to determine the least possible value of x, so the value of x should be 4. So the option D is correct.
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The complete question is:
The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x?
A. 1
B. 2
C. 3
D. 4
E. 5
How do I solve? I don’t understand
Step-by-step explanation:
Use the 110 to find the 70 degree angle (they form a straight line = 180°)
then 70 + 64 + R angle = 180° ( sum of angles of a triangle)
then : R angle = 46°
then the R angle + 2x-10 = 90° ( because the two lines are perpendicular)
(2x -10)° + 46 ° = 90 °
x = 27
Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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Find the x intercepts. Show all possible solutions.
For the function f(x) = 7/8x² - 14, the x-intercepts are x = -4 and x = 4.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find the x-intercepts of the function f(x), we need to solve the equation f(x) = 0.
f(x) = 7/8x² - 14
Substitute f(x) with 0 -
0 = 7/8x² - 14
Add 14 to both sides -
7/8x² = 14
Multiply both sides by 8/7 -
x² = 16
Take the square root of both sides -
x = ±4
Therefore, the x-intercepts of the function f(x) are x = -4 and x = 4.
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