Shade above the line if the symbol ≥ or > is used.
What is linear inequality?
A linear inequality in mathematics is an inequality involving a linear function. One of the symbols for inequality is found in a linear inequality. It displays non-equal data in graph form.If < or > is used to denote that the border is not a component of the solution, use a dashed line. Shade the relevant area. The sign of the inequality will let you know which half-plane to shade unless you are graphing a vertical line.
Shade above the line if the symbol ≥ or > is used.
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Which of the following statements are true for triangle A B C ? Select all that apply.
Triangle DEF is congruent to triangle GHI is correct.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. A triangle having vertices A, B, and C is known as triangle ABC. Any three points in Euclidean geometry that are not collinear result in a distinct triangle and a distinct plane.
A triangle is a polygon with three edges and three vertices. A triangle's total number of angles equals 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
Equilateral, scalene, isosceles, and other triangles are used.
Given are three triangles ΔABC, ΔDEF, ΔIHG.
ΔDEF is congruent to ΔGHI as -
EF = IH (given)
∠E = ∠H (right angle)
FD = IG (given)
Using SAS congruent rule, ΔDEF ≅ ΔGHI
Therefore, triangle DEF is congruent to triangle GHI is correct.
The complete question is : Which of the following statements are correct?
Select all that apply.
Triangle ABC is congruent to triangle DEF.
Triangle DEF is congruent to triangle GHI.
All three triangles are congruent.
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Solve similar triangles (advanced)
Solve for x
For the given similar triangles the value of x is 16/7.
What is similar triangles?
If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be comparable. To put it another way, similar triangles have the same shape but may differ in size. In addition, if the corresponding sides of the triangles are identical in length, the triangles are congruent.
Let the triangles ΔABD and ΔADE are similar.
Since ratios of sides of similar triangles are in proportion.
⇒
[tex]\frac{AB}{AD} = \frac{BC}{DE}\\ \frac{4}{7} =\frac{x}{4} \\16 = 7x\\x = \frac{16}{7}[/tex]
Hence, the value of x is 16/7.
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How do you find equivalent in math?
To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
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How much must be deposited today into the following account in order to have $25,000 in 7 years for a down payment on a house? Assume no additional deposits are made.
$___ should be deposited today.
$14587.5 should be deposited today
What is Compound interest?Compound interest, also called "compounding interest," is the interest on the initial investment as well as the accrued interest on that investment.
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited.
From the information given,
A = 25000
r = 8% = 8/100 = 0.08
n = 1 because it was compounded once in a year.
t = year
Therefore, substituting the values into the formula
25000 = P(1 + 0.08/1)^1 × 7
25000 = P(1.08)^7
25000 = 1.7138P
P = 25000/1.7138
P = $14587.5
Hence, the amount that should be deposited is $14587.5
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On Tuesday, the Soto Salad restaurant served 6 ½ cups of Italian salad dressing. If the restaurant serves ¼ cup of dressing with each salad, how many salads were ordered with Italian dressing?
Group of answer choices
26
22
24
28
Answer:
26
Answer choice 1.
Step-by-step explanation:
6 1/2 ÷ 1/4 is our equation.
6 1/2 as an improper fraction is 13/2
Our new equation is 13/2÷1/4
flip the divisor into a reciprocal and multiply:
13/2×4/1
simplify:
13/1×2/1
26/1
=26
PLEASE MARK BRAINLIESTAnswer: The answer is A or 26
Step-by-step explanation: I have my ways ;>
A small toy rocket is launched from a 18-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t^2 + 3t+18. How long will it take the rocket to hit the
ground?
The time it would take the rocket to hit the ground upon launch is; 3 seconds.
At what time does the rocket hit the ground?It follows from the task content that the time taken for the rocket in discuss to hit the ground upon launch is to be determined.
Since the given formula for the height in terms of time, t is;
h = - 3t² + 3t + 18
It follows that ; when the rocket hits the ground; the height; h = 0.
Therefore;
0 = - 3t² + 3t + 18
0 = -3t² + 9t - 6t + 18
0 = -3t ( t - 3 ) - 6 ( t - 3)
-3t - 6 = 0 OR. t - 3 = 0.
t = -2. OR. t = 3.
Therefore, since the time after launch can only be positive; the time taken for the rocket to hit the ground is; 3 seconds.
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The physician has ordered testosterone 170 mg IM weekly for hormone replacement. The medication is supplied in 200 mg/ml. How many milliliters will the nurse administer? (Round to nearest tenth)
0.85 millimeter the nurse will administer
What is division ?
One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.
The act of dividing anything into equal parts is called a division. As an illustration, we could divide a group of 20 people into 4 groups of 5, 5 groups of 4, and so on.
1 ml contain 200 mg of hormone
200 mg = 1 ml
1 mg = 1 / 200 ml
1 mg contain 1/200 ml of hormone
170 mg = 1/200 * 170 ml
= 170 / 200
170 mg = 0.85 ml
The nurse will administer 0.85 ml
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Help Please!
3. An exercise equipment company is producing 45 lb. weights. To ensure the quality of their weights, they randomly select 60 weights and find that the mean weight of their sample is 45.07 lbs. with a standard deviation of 0.09 lbs. Create a 95% confidence interval and interpret the answer in context.
A. (45.0509, 45.0891); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0509 and 45.0891 lbs.
B. (44.8423, 45.2977); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.8423 and 45.2977 lbs.
C. (44.9772, 45.0228); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.9772 and 45.0228 lbs.
D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0472 and 45.0928 lbs.
4. Raul is analyzing a set of data he collected and creating a confidence interval. If he chose to reduce the size of the sample and increase the level of confidence, how would that affect the confidence interval? Explain.
A. The size of the confidence interval would decrease because Raul would be dividing by a larger z-score and multiplying by a smaller sample size.
B. The size of the confidence interval would increase because Raul would be dividing by a smaller z-score and multiplying a larger sample size.
C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
D. The size of the confidence interval would decrease because Raul would be multiplying by a smaller z-score and dividing by a smaller sample size
The responses for the confidence intervals of the 45 lbs weight and the set of data are;
3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928
4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
What is a confidence interval?The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.
3. The confidence interval can be found using the formula;
[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]
Where;
[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs
s = The standard deviation of the sample = 0.09 lbs
n = The sample size
z = The confidence level = 1.96 at 95% confidence level
Therefore;
[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]
45.0472 < μ < 45.0928
The correct option is therefore, option D
Therefore;
The company can be 95% sure that the mean of the population of the 45 lb weights are between 45.0472 and 45.0928 lbs4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.
Increasing the level of confidence will increase z, thereby also increasing the confidence interval.
The correct option is therefore, option C.
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Please help will mark Brainly
Answer:
neither narrower or broader
Step-by-step explanation:
if you look at your problem it says identical so that means exactly the same so it would be the second choice neither narrower or broader
What are the examples of ASA congruence?
ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.
What does a congruence mean in mathematics?
If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.
Describe ASA congruence through an example.
ASA (Angle-Side- Angle)
According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.
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7. What is Mrs. Dudley's waming to the guests regarding her leaving the property at night?
a. If they do not clear the dinner table, she will not "wait on people" the following moming
(b.) If they get into trouble, she wouldn't be able to hear them "in the night"
c. If they decide they want to leave, no one will be there to "open the gate" for them
d. If they experience anything, not to "confront" it
8. Which statement best embodies Eleanor's feelings about Hill House?
a. "There is a comforting calmness that accompanies the silence that fills these halls"
b. "My confidence grew that my journcy will end with lovers mecting" "It's awful and I don't want to stay...get away from here, get away"
a. "I am finally starting to feel wanted because of these three people I can call friends"
9. The second guest claims that Eleanor is like his/her...
a. Best friend
b. Sister
(c) Cousin
d. mother
10. Which of the following statements does NOT describe Hill House or how it made its inhabitants feel?
a. "Hill House gave its guests a false sense of comfort and security"
b. "Hill House seemed awake"
c. "Hill House would stay as it was until it was destroyed"
d. "I am like a small creature swallowed whole by a monster [Hill House]"
In the end, Hill House stands for the enigmas of the human mind, whether it is "sane" or not, as well as the horror that the mind's intrinsic weirdness can arouse. Hill House is intricate, convoluted, and appears to be unknowable, just like the mind.
How does Dr Montague describe Hill House?The history of Hill House is first described by Doctor Montague.
He asserts that "the concept of certain houses as filthy or banned" is an old one, much like the idea that some places on earth are fundamentally good and good, while others are sacred or holy.
Possibly "evil from the start," the Hill House has been uninhabitable for more than twenty years.
Instead of being malicious, Doctor Montague sees the home as sick or "deranged."
Doctor Montague learned about the rental from a previous tenant a year ago.
After researching it, he found that no renter had kept it for more than a few days.
Even finding a short-term lease, according to Montague, was challenging.
10) "Hill House provided its visitors with a false sense of security and comfort"
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Need help pls on maths question
Answer please anyone help same doubht
Step-by-step explanation:
Answer:
Refer to the photos taken.
Step-by-step explanation:
help please the function f(x) = 3x -8 , solve f(x) = 7
Answer:
f(x) = 13
Step-by-step explanation:
f(x) = 7 means that x = 7
Plug this in:
3(7) - 8
21 - 8
13
f(x) = 13
Determine which set of ordered pairs represent a
Function and justify your selection.
{(-1,4), (2, 4), (8,4), (10,4)}
{(0, -2), (3, 7), (0, 2), (18,2))
{(-1,3), (-1,-1), (-1,-12), (-1,0)}
{(1, 2), (2, 3), (3, 4), (3,5)}
Justification: (What is your reasoning?)
Answer:
{(-1,4), (2, 4), (8,4), (10,4)}
all of the x-values are different
Step-by-step explanation:
The other three options have duplicate x-values with different y-values.
What are the steps in solving rational expressions?
The steps in solving two rational numbers is using the cross multiplication method and then do the arithmetic operation on the numerator
The rational expression is defined as the expression with both numerator and denominator has polynomials.
Consider two rational expressions
Add two expression using cross multiplication
a/b + c/d
Cross multiply the expression
a/b + c/d = (ad + cb) / bd
Subtract two expression using cross multiplication
a/b - c/d
Cross multiply the expression
a/b + c/d = (ad - cb) / bd
Therefore, the two rational expression can be solved by using the cross multiplication method and do the arithmetic operation
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HELPPP FOR 100 points plsss
Answer:
a. YES
b. YES
c. NO
d. YES
Step-by-step explanation:
[tex]\frac{7^6}{7^3}[/tex] simplifies to [tex]7^3[/tex]
a:
Let's simplify this:
([tex]7^9[/tex])([tex]\frac{1}{7^6}[/tex])
Now:
[tex]\frac{7^9}{7^6}[/tex]
Which equals:
[tex]7^3[/tex]
So, YES
b:
Simplify this one:
[tex]\frac{1}{7^8} / \frac{1}{7^1^1}[/tex]
Or:
[tex](\frac{1}{7^8})(7^1^1)[/tex]
Which simplifies to:
[tex]7^3[/tex]
So, YES
c:
Simplifies to:
[tex]\frac{7^8}{7^4}[/tex]
Which equals:
[tex]7^4[/tex]
So, NO
d:
This simplifies to:
[tex]\frac{1}{7^3} * 7^6\\\\ \frac{7^6}{7^3} \\\\7^3[/tex]
So, YES
Determine the solution to the system of equations
x - 6y + 4z = -12
x + y = 0
2x + 2y = 0
Answer:
x = 0 , y = 0 , z = -3
Step-by-step explanation:
Solve the following system:
{x - 6 y + 4 z = -12 | (equation 1)
x + y - 4 z = 12 | (equation 2)
2 x + 2 y + 5 z = -15 | (equation 3)
Swap equation 1 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
x + y - 4 z = 12 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - (13 z)/2 = 39/2 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Multiply equation 2 by 2/13:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
x - 6 y + 4 z = -12 | (equation 3)
Subtract 1/2 × (equation 1) from equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 7 y + (3 z)/2 = -9/2 | (equation 3)
Multiply equation 3 by 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+0 y - z = 3 | (equation 2)
0 x - 14 y + 3 z = -9 | (equation 3)
Swap equation 2 with equation 3:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y - z = 3 | (equation 3)
Multiply equation 3 by -1:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y + 3 z = -9 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 3 × (equation 3) from equation 2:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x - 14 y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 2 by -14:
{2 x + 2 y + 5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{2 x + 0 y+5 z = -15 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{2 x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Divide equation 1 by 2:
{x+0 y+0 z = 0 | (equation 1)
0 x+y+0 z = 0 | (equation 2)
0 x+0 y+z = -3 | (equation 3)
Collect results:
Answer: {x = 0 , y = 0 , z = -3
Step-by-step explanation:
please I need help on question 5
The value of x is 19 and the measure of angles in triangle ABC are 75°, 75° and 30° respectively.
What is a triangle?triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.
The sum of ∠A + ∠B + ∠C = 180°( sum of angles in a triangle )
3x + 18 + 7x - 58 + 2x - 8 = 180°
12x -48° = 180°
12x = 228
x = 228/12
x = 19
but ∠A = 3x + 18, but x = 19
∠A = 3(19) + 18 which is 75°
Also ∠B = 7x -58
∠B = 7(19) - 58 which is 75°
∠C = 2x -8
∠C = 2(19) - 8 which is 30°
In conclusion, the value of x = 19, ∠A = 75°, ∠B = 75° ∠C = 30°
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The table shows Tonya's homework assignment. Tonya's teacher instructed the class to simplify each expression by dividing the numerator and denominator by the GCF.
Complete the table by simplifying each expression and then finding the value.
Divide the numerator and denominator by the GCF to reduce a fraction. (This is also referred to as "writing a fraction in the simplest terms.") The common factors are sometimes shown to be "cancelled." It is worth noting that the result is an equivalent fraction in its simplest form.
How do you divide the numerator to the denominator by GCF?To put it simply, we must divide the numerator (x) by the denominator (y) to simplify it. For example, after simplifying 3 6, represent it as a fraction and identify the numerator and denominator. 3 6 can be written as 3/6. Further simplification yields 1/2.
Let's pretend the fraction is a proper fraction. The denominator is the numerator. We want to reduce the fraction to its simplest form.
a) Use Numerator =Remainder* as the denominator.
Now Numerator >Remainder* b)Numerator Remainder*=Remainder** c) ••• (keep going until Remainder =0)
d) When the Remainder equals zero, the Divisor is the GCD (or GCF, as you say). GCF is a misnomer because it only deals with numbers. Only the term GCF applies to variables (with numerical values, as in algebraic expression).
Let us look at an example.
407/3367 is the fraction.
As evident, the numbers407 ,3367 does not appear to have share Divisors 2 or 3 or 5 or 7 or 11 from prima facie considerations. So we may take recourse of successive division method.
3367 ÷407 =Remainder 111 (quotient 8)
407 ÷ 111 =Remainder 74 (quotient 3)
111 ÷74=Remainder 37 (quotient 1)
74 ÷37 =Remainder 0 (ZERO )
Here 37 divides leaving Remainder zero. Therefore the GCD is 37
Fraction 407 /3367 =(407 ÷37)/(3367÷37)=11/91
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Find the inverse of f(x)=1/2 (3x+4). Show your work step-by-step.
Answer: f(-1)= 2/3x-4/3
Step-by-step explanation:
Solve normally and then do the inverse not to hard.
HELP ME OUT PLEASE ITS DUE IN 5 MINS
The equation that can be used to find the number of wolves in the state on January 1 is w - 23 = 84
How to represent a situation with an equation?A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier.
The equation that can be used to find the number of wolves in the state on January 1 can be calculated as follows:
where
w = number of wolves in the state January 1.Therefore, the equation to represent the situation is as follows:
w - 23 = 84
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y.y^3.y^2 pleas help me and spread the gospel of God
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]y^{1+3+2[/tex]
2) Simplify 1 + 3 to 4.
[tex]y^{4+2}[/tex]
3) Simplify 4 + 2 to 6.
[tex]y^6[/tex]
Thank you,
Eddie
Tony bought a shirt for a friend's birthday for $27.00. He liked the shirt so much that he returned to the store a week later to buy a shirt for himself. Tony found the price of the shirt had changed to $32.13. Rounded to the nearest whole percent, what is the percent increase in the price of the shirt?
You have to divide 27 by 100 and that gives you .27.
If you multiply until you reach 32.13 with different numbers you get 19. It is a 19% increase.
Tom's growth chart
categorical
discrete
continuous
Tom's growth chart is a continuous graph.
What is a continuous graph ?Continuous graphs are those in which every single value of x has a corresponding value of y, and the line of the graph is always uninterrupted.This is because every point is situated adjacent to the one on either side of it. The graph is continuous if the line is continuous, in other words. If a function's graph is a continuous curve with no breaks, holes, or gaps, then the function is considered continuous.One with dispersed points is a discrete graph and a direction or trend for it could be present or not. Categorical data is visualized using bar charts and pie charts. According to the visual, both sorts of graphs have variances.To learn more about continuous graph , refer:
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A rectangular yard measuring 35 ft by 55 ft is bordered (and surrounded) by a fence. Inside, a walk that is 3 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of walk is 504 square feet
Area of rectangleThe area of rectangle is define as a product of length L and width w
calculate the area of rectangle yard
Area = L x W,
where A equal the Area, L equals the length and W equal width.
A = 35 x 55
A= 1925 square feet
Area of the rectangular yard is 1925 square feet
From the question, we have 3ft wide goes all the way along the fence inside.
Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .
Area = L x W
A = 29 x 49
A = 1421 square feet
Area of new rectangle formed by allowing for three foot walk is 1421 square feet
Area of Walk
To get the area walk; we subtract area of new rectangular formed from area of rectangular yard
Area of Walk = Area of Rectangular yard - Area of new rectangle
Area of Walk = 1925 - 1421
Area of Walk = 504 square feet.
Therefore, the area of walk is 504 square feet.
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help me out thanks so much please help
The solution is Option D.
The equation is w - 23 = 84
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of wolves on January 1 = w
Now , after 1 year
The number of wolves in the state is = 84
And , number of wolves in the state after 1 year = 23 less than previous year
So ,
84 = 23 less than w
84 = w - 23 be equation (1)
Adding 23 on both sides of the equation , we get
w = 107
Therefore , the value of w = 107
And the equation is w - 23 = 84
Hence , The equation is w - 23 = 84
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In which quadrant is the number 5i located on the complex plane?
The number 5i located on the complex plane in I Quadrant.
What is Complex Plane?
The real axis and the imaginary axis are the graph's horizontal and vertical axes, which are orthogonal (or perpendicular). The labels Re and Im are typically present. The complex plane is the plane defined by these coordinates.
We are aware that in a two-dimensional plane, an ordered pair's x- and y-coordinates are treated as the real and imaginary parts of the complex number, respectively.
i.e., a+bi=(a,b) -- Quadrant I,
-a+bi=(-a,b) -- Quadrant II,
a-bi=(a,-b) -- Quadrant III
and
-a-bi=(-a,-b) -- Quadrant IV
The complex number that is being presented is 5i, aland it is located in quadrant I.
As a result, the complex number in question belongs in Quadrant I.
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Describe the function‘s end behavior. f(x)=−10+2x^5−9x^3
as x→∞,f(x)→
as x→−∞,f(x)→
The function‘s end behavior is falls to the left and rises to the right.
The given function is [tex]f(x)=-10+2x^5-9x^3[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Use the degree and the leading coefficient to determine the behavior.
Falls to the left and rises to the right.
Find where the first derivative is equal to 0 to find the local maxima and minima.
x =−3√30/10 is a local maximum
x = 3√30/10 is a local minimum
Therefore, the function‘s end behavior is falls to the left and rises to the right.
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Question 3 (2 points)
Find the area of the composite figure. Show work to get bonus points.
The required area of shaded region is 495 square feet.
What is parallelogram?A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Given that,
The length of square = 25 ft.
The area of square = 25 x 25 = 625 square ft.
The length of internal parallelogram = 13 ft.
And the height of parallelogram = 10 ft.
The area of parallelogram = 13 x 10 = 130 square ft.
The area of shaded region = 625 - 130 = 495 square feet.
The required area of shaded region is 495 square feet.
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Which of the following measures would create an infinite number of triangles? three sides: 3 cm, 5 cm, and 7 cm three angles: 62°, 34°, and 84° two sides of 4 cm and 7 cm with an angle of 54° between them three sides: 3 cm, 5 cm, and 10 cm
An infinite number of triangle will be created by angles: 62°, 34°, and 84°
How to know when infinite number of triangles are formedInfinite number of triangles are formed when no side is given
The three angles will produce an unlimited number of similar triangles if side lengths are not provided.
the option that correspond to this condition is the option that gave only angles and no sides which is angles: 62°, 34°, and 84°
Other options has sides or a side given and not in accordance to form infinite number of triangles
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