The required range is [0,∞]
All values, or inputs, constitute a function's domain, while all values, or outputs, constitute its range.
When examining a graph, the range of the function is from up to down, and the domain refers to all of the values on the graph from right to left.
Therefore , the range of the function on the graph of all real numbers extends from zero to positive infinity.
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1. The unit price of an item is how much it costs for one item. It's useful to know the unit price when buying in bulk. If we're buying 100 items, then you'll save quite a bit of money if you buy the unit priced item that costs $10 per item compared to the unit price of $12 per item!
You can calculate a unit price by dividing the total amount of money you spent for items by the number of items you purchased. For instance: $7.99 per oz of goldfish is $ 7.99 / 30= 0.26$ per ounce.
Which purchase has the lower unit price - $\$ 200$ for 15 flower arrangements, or $70 for 5 flower arrangements?
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a problem sum of division
Cost of 15 flowers = $200
Cost of 1 flower = $200 [tex]\div[/tex] 15 = $13.33
Cost of 5 flowers = $70
Cost of 1 flower = $70 [tex]\div[/tex] 5 = $14
So unit price of 15 flower arrangement of $200 is lower than unit price of 5 flower arrangement of $70
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What would the answer be? I tried 4 and -4 and a lot more.
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
What is a prime multiple?
The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime
What are Prime Numbers ?
A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.
This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.
Numbers that have more than 2 factors are known as composite numbers.
For example :
The factors of 3 are 1 and 3.
Therefore, the prime multiples of 3 are 1 and 3.
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When one of the coordinates is zero, the point will be on
an axis. True or False?
How do you make a 10 in first grade math?
We make a ten in first grade by taking 1 from the next left digit of the number in which we are doing the indicated operation.
According to the question,
We have the following information:
Making a ten in first grade
We consider that in making a ten we take 1 from the next left digit of the number from which we are subtracting any other number. Or it is often said to be taking a carry.
Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.
For example, 24-16 can be performed when we add a ten to 4 by taking 1 from 2. Now, 6 can be easily subtracted from 14.
Hence, we make a ten in first grade by taking 1 from the next left digit of the number in which we are doing the indicated operation.
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Think back to our discussion on Negative Exponents. Why do we follow the steps that we do, specifically, why do we flip the number (reciprical)? Use the other laws of exponents to help gauge your thinking, but I want you to try to determine the meaning behind the process instead of just memorizing the steps. This might be a tough question to answer, so just do your best and we can discuss this again in class.
By using the law of exponents, it has been proved that
[tex]a^{-n} = \frac{1}{a^n}[/tex]
What are exponent?
Exponent tells us how many times a number is multiplied by itself.
For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]
Here, 2 is multiplied by itself 4 times.
If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),
a is the base and m is the index.
The laws of exponents are
[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]
We know this law
[tex]a^p \times a^q = a^{p + q}[/tex]
Putting p = n and q = -n
[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]
So,
[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]
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Problem:
The perpendicular bisector of line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB
What is an equation for the perpendicular bisector of the line segment joining (1,2) and (-5,12) ? Write your equation in point-slope form, standard form, or slope-intercept form.
The equation of the perpendicular bisector, in slope-intercept form, is: y = 3/5x + 7/5.
How to Find the Equation of a Perpendicular Line?The equation of a line can be expressed:
In slope-intercept form is y = mx + b.In point-slope form is y - b = m(x - a).In standard form, it is Ax + By = C.First, find the slope of the line that is bisected perpendicularly that passes through (1, 2) and (-5, 12):
Slope (m) = change in y / change in x = (12 - 2) / (-5 - 1) = 10/-6
Slope (m) = -5/3
The negative reciprocal or -5/3 is 3/5. Therefore, the slope (m) of the perpendicular bisector would be: 3/5.
To write the equation of the line in point-slope form, substitute m = 3/5 and (a, b) = (1, 2) into y - b = m(x - a):
y - 2 = 3/5(x - 1)
Rewrite in slope-intercept form:
y - 2 = 3/5x - 3/5
y = 3/5x - 3/5 + 2
y = 3/5x + 7/5
Rewrite the equation in standard form:
-3/5x + y = 7/5.
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Solve for m.
m+14<−125
Responses
m>−11320
m is greater than negative 1 and 13 over 20
m<−1320
m is less than negative 1 and 3 over 20
m<−11320
m is less than negative 1 and 13 over 20
m>−1320
The value of m in the inequality expression given as m + 14 < −125 is m < -139
How to calculate the value of m?In the question, the inequality expression is given as
m+14<−125
Express the inequality properly
So, we have the following representation
m + 14 < −125
To start with, we subtract 14 from both sides
This gives
m + 14 - 14 <−125 - 14
Evaluate the difference
m < -139
Hence, the solution is m < -139
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A certain forest covers an area of 2,000 square kilometers. Suppose that each year, this area decreases by 6%. What is the equation that best represents the area of the forest each year?
Hint: Use the formula y = P(1 + r)x.
y = 2,000(0.94)x
y = 2,000(1.06)x
y = 2,000(0.06)x
y = 2,000(1.94)x
The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.
The equation will be:
= 2000(1 - 6%)^x
= 2000(0.94)^x
In conclusion, the correct option is A.
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Fing
the lowest torm of the following fraction
1. 6-42
2. 14-28
The lowest form of 6/42 is 1/7 and,
the lowest form of 14/28 is 1/2.
What is the lowest form of fraction?
When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form. This is also known as its Lowest form.
In fraction 6/42, both denominator and numerator have common factor as 6, So we divide the denominator and numerator by 6.
Hence, we get 1/7.
Similarly, In fraction 14/28, both denominator and numerator have common factor as 14, So we divide the denominator and numerator by 14.
Hence, we get 1/2.
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Please help will mark Brainly
The rate of change in the given interval would be 1.25 ft/s.
What is the rate of change?
The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.
By observation, we can take the points from the graph in between the given interval.
The points would be (3, 2.5) and (5, 4)
Then the rate of change = y2 - y1/ x2 - x1
= 4 - 2.5/5 - 3
= 2.5/2
= 1.25 ft/s.
Hence, the rate of change in the given interval would be 1.25 ft/s.
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How do you know if a triangle is ASA or AAS?
The difference between 2 parts of congruency is as follows.
What is congruent?
Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’
Main Body:
ASA vs AAS:
ASA stands for “Angle, Side, Angle”,
AAS means “Angle, Angle, Side”
ASA ===
two triangles are congruent if they need associate equal aspect contained between corresponding equal angles. If the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the enclosed aspect of 1 triangle are congruent, severally, to the 2 angles and therefore the enclosed aspect of the second triangles, then it satisfies the condition that the triangles are congruent.
AAS===
two angles and an opposite facet. AAS is one amongst the 5 ways that to see if 2 triangles are congruent. It states that if the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the facet opposite to at least one of them in one triangle are congruent to the corresponding angles and therefore the non-included facet of the second triangle, then the triangles are congruent.
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What is the upfront cost to secure this apartment?
A) $1,876
B) $1,225
C) $2,105
D) $1,025
B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)
1000 + 25 + 200 = 1225
When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
at a field trip for every 8 students there is 1 chaperone. if the teacher purchased 108 total tickets, how many tickets were for students?
First, 108/9=12
This means that are 12 groups of people.
If there are 8 students in each group, 12 x 8 = 96.
96 should be your answer.
What are the 5 ways triangles are congruent?
The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.
Two triangles are congruent if and only if they have the same three sides and angles.
SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.
ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.
AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.
HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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What is the inverse of f(x) = 2x2 -4?
y= ±√x+4/2
f⁻¹(x)=x-4/2
y= ±√x+2/4
f⁻¹(x)=±√2x-4
The inverse of the function f(x) = [tex]2x^2 - 4[/tex] is
[tex]f^{-1}(x) = \pm \sqrt{\frac{x + 4}{2}}[/tex]
First option is correct
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here, f(x) = [tex]2x^2 - 4[/tex]
Let f(x) = y
[tex]2x^2 - 4[/tex] = y
[tex]2x^2 = y + 4\\x^2 = \frac{y + 4}{2}\\x = \pm \sqrt{\frac{y + 4}{2}}[/tex]
[tex]f^{-1}(x) = \pm \sqrt{\frac{x + 4}{2}}[/tex]
First option is correct
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How do you find a polynomial?
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
How do you solve an isosceles triangle problem?
Isosceles triangle problem can be solved by given steps
what is isosceles triangle ?
An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.
explanation:
In isosceles triangle
1. Two sides of the triangle are congruent
2. The angle opposite those sides are congruent
x + 72 +72 = 180
x = 180 -144
x = 36
Hence the isosceles triangle problem can be solved by above steps and explanation
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Select the correct answer.
What is the approximate solution to this equation?
19 + 2 ln x= 25
Answer:
3
Step-by-step explanation:
Hope this helps..
Toby created a sculpture for art class using different-sized cubes. The smallest cube is 1.5 inches along each edge. The largest cube is 7.5 inches along each edge.
How many of the smallest cubes would it take to fill the largest cube?
Write your answer as a whole number or decimal. Do not round.
There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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In Exercises 13-16, find the area of the polygon with the given vertices. (See Example 3.)
13. E(3,1), F(3,-2), G(-2,-2)
14. J(-3,4), K(4,4), L(3,-3)
The area of the polygon EFG with given vertices is, 7.5 units.
What is area of triangle?
The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.
Let the given vertices are,
E(3, 1), F(3, -2), G(-2, -2)
There are three vertices, so the polygon is a triangles.
Since,
Area of triangle = 1/2 x base x height.
If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.
Now to find the lengths of side FG and EF.
By using the distance formula,
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]
⇒ Area = 1/2 x 5 x 3
= 1/2 x 15
Area = 7.5
Hence, the area of the polygon EFG is 7.5 units.
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How do you find the range on a graph?
The range of a graph can be found using the values depicted on the y-axis.
According to the question,
We have the following information:
We have a graph and we need to know how do we find the range of that graph.
We know that the domain of a graph is the collection or in other words set of input values depicted on x -axis and the range of a graph is the set of possible output values portrayed on y-axis of the graph.
In noting down the range of a graph, we first list down the down value and then the up value or in other words we move from down to up in order to find the range of a graph.
Hence, the range of a graph can be found using the values depicted on the y-axis.
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Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
A x
B x + 1
C x + 2
D 2x
Answer:
B) x + 1
Step-by-step explanation:
Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.
Eg: 5 , 6 , 7 ,.....
6 = 5 + 1
7 = 6 + 1
So, if first number is x, then the next number will be x + 1
A rectangular piece of paper with length 25 cm and width 12 cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².
What is a rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
To caluculate the area of the paper that remains, we use the formula below.
Formula:
Ar = lb-π(b/2)²............ Equation 1Where:
Ar = Area of the paper that remainl = Length of the rectangular paperb = width of the rectangular paperr = Radius of the semi circleFrom the question,
Given:
l = 25 cmb = 12 cmr = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
Ar = (25×12)-(3.14×6²)Ar = 300-113.04Ar = 186.96 cm²Hence, the area of the paper left is 186.96 cm².
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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write 3/5 as a fraction or as a whole or mixed number
Answer:
Step-by-step explanation:
1) 4 1/4 + 5 1/2
= 9 3/4
2) 10 4/5 - 6 1/5
= 4 3/5
3) 3 1/4 - 1 3/4
= 1 1/2
4) 3 2/5 + 7 7/10
= 11 1/10
5 ) 10 3/13 + 2 10/13
= 13
Answer:
1
Step-by-step explanation:
Its for sure 1
How do you make an exponential decay model?
The exponential decay formula can take one of three forms:
f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]
Where,
a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality
What is Exponential Decay ?
Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.
The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:
f (x) = abx
f (x) = a (1 – r)x
P = P0 e-k t
Where,
a (or) P0 = Initial amount
b = decay factor
e = Euler’s constant
r = Rate of decay (for exponential decay)
k = constant of proportionality
x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as
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(1 point)
Solve this inequality, and write your answer in interval notation.
|x|>-5
Please type:
- int for oo,
- no solution if there are no real solutions
- U for the union symbol U
You have attempted this problem 8 times.
Your overall recorded score is 0%
You have unlimited attempts remaining.
Answer: [tex](-\infty, \infty)[/tex]
Step-by-step explanation:
Absolute value is always non-negative.
