What is the value of -27-8
A.-35
B.-19
C.19
D.35

Answer:

a) Value T's and More

b) y = 8x

c) 8; cost per t-shirt

d) $25

e) Value T's and More for orders of fewer than 25 t-shirts.
    Print-o-Rama for larger orders of more than 25 t-shirts.

Step-by-step explanation:

We are given that Allison’s middle school team has designed t-shirts featuring their team name and color. Allison and her friend Nicole have volunteered to call local stores to get an estimate of the total cost of purchasing the t-shirts.

[tex]\dotfill[/tex]

A proportional relationship is a linear relationship between two variables where the ratio of one variable to the other is constant, and the graph of this relationship passes through the origin (0, 0).

Value T's and More represents a proportional relationship because the cost per t-shirt is constant at $8, and the graph modelling the data for this company passes through the origin (0, 0), meaning that when no t-shirts are purchased, the cost is $0.

Print-o-Rama does not represent a proportional relationship because although they charge a fixed amount per t-shirt, there is an additional set-up fee. This makes the cost function in the form y = mx + b (where b is the set-up fee), resulting in a graph that does not pass through the origin (0, 0).

[tex]\dotfill[/tex]

A proportional relationship can be expressed as y = kx, where k is the constant of proportionality.

Since the cost per t-shirt at Value T's and More is constant at $8, the constant of proportionally is k = 8, so the equation relating cost (y) and shirts (x) for Value T's and More is y = 8x.

[tex]\dotfill[/tex]

As discussed in part b, the constant of proportionality for ValueT's and More is 8. This represents the cost per t-shirt (in dollars).

[tex]\dotfill[/tex]

To find the set-up fee, let's use the given points (10, 95) and (50, 375) for Print-o-Rama and assume the cost model is y = mx + b, where m is the cost per shirt, and b is the set-up fee.

Substitute both points into y = mx + b to set up two equations:

[tex]95=10m + b\\\\375=50m+b[/tex]

Subtract the first equation from the second equation to eliminate b, then solve for m:

[tex]375-95=(50m+b)-(10m+b) \\\\280=40m\\\\m=7[/tex]

This means that the cost per t-shirt is $7.

Substitute m = 7 back into one of the equations and solve for b. Let's use 95 = 10m + b:

[tex]95 = 10(7) + b \\\\95=70+b\\\\b=95-70\\\\b=25[/tex]

Therefore, the set-up fee for Print-o-Rama is $25.

[tex]\dotfill[/tex]

To determine the most cost-effective supplier, we need to equate the cost equations of Value T's and More and Print-o-Rama to identify the exact number of t-shirts at which the costs for both companies are equal:

[tex]8x=7x+25\\\\8x-7x=25\\\\x=25[/tex]

Solving 8x = 7x + 25 for x gives us x = 25, meaning that for an order of 25 t-shirts, the total cost from both suppliers is the same. For orders of fewer than 25 t-shirts, Value T's and More is cheaper, but for orders of more than 25 t-shirts, Print-o-Rama is more cost-effective due to its lower per-shirt cost despite the set-up fee.

Therefore, after analysing the pricing models of both Value T’s and More and Print-o-Rama, it is recommended to use:

a. The graph shows a proportional relationship

b. The proportional equation is  y = 8k

c. The constant of proportionality is 8

d. Print-o-Rama's set up fee is 25

a. A linear graph that intercepts the origin has a proportional relationship.

b. The equation is written in the form y = kx, using point (10, 80)

80 = 10k

k = 8

The equation is written as y = 8k

c. The constant of proportionality is k which is equal to 8

d. The set up fee is the y-intercept (b). The equation is written in the form y = mx + b

m = (375 - 95) / (50 - 10)

m = 280 / 40

m = 7

Using point slope formula

y - 95 = 7 (x - 10)

y = 7x - 70 + 95

y = 7x + 25

The y-intercept, b is 25

Final answer:

To find the number of new games rented, set up an equation using the given information. Assume all 6 games rented were new games, and solve for the number of new games.

Explanation:

To find the number of new games rented, we can set up an equation using the information given.

Let x represent the number of new games rented and y represent the number of older games rented.

We know that the total cost of renting 6 games is $22. Therefore, we can write the equation:

4x + 2y = 22

To find the number of new games rented, we want to solve for x. We can do this by substituting a value for y and solving for x.

Let's assume all 6 games rented were new games, so y = 0.

Substituting this value into the equation gives:

4x + 2(0) = 22

Simplifying, we get:

4x = 22

Dividing both sides by 4, we find that x = 5.5.

Since we can't rent a fractional number of games, the student rented 5 new games.

Answer:

(1, - 8 )

Step-by-step explanation:

We have P(- 2, 3 ) → P'(- 6, - 4 )

The image coordinates are 4 less than the original x- coordinate and 7 less than the original y- coordinate, thus the translation rule is

T : (x, y ) → (x - 4, y - 7 ), thus

(5, - 1 ) → (5 - 4, - 1 - 7 ) → (1, - 8 )

Answer: 0.6666666

Step-by-step explanation:

Answer:

0.6 repeatedly. as a fraction is 2/3

Answer:

5 (3x - 5) (x + 2 )

Answer: 5 (3x-5)(x+2)

Final answer:

To simplify the expression [tex]5^2 \times 5^4[/tex] , add the exponents to get [tex]5^{(2+4)}[/tex], which simplifies to 5^6, resulting in a final value of 15,625.

Explanation:

The question involves simplifying an expression with exponential terms. When multiplying exponents with the same base, we add the exponents according to the product of powers property. The base in this question is 5, and we have two exponential expressions:[tex]5^2[/tex] and [tex]5^4.[/tex]To simplify 5^2 x 5^4, you add the exponents since the bases are the same. This gives you[tex]5^{(2+4)} = 5^6[/tex] .

To simplify [tex]5^2 \times 5^4[/tex], we add the exponents 2 and 4, which gives us [tex]5^{(2+4).[/tex] simplifies to [tex]5^6.[/tex] Calculating this, we get [tex]5 \times 5 \times 5 \times 5 \times 5 \times 5,[/tex]  which equals 15,625.

Answer:

The Correct answer:

CORRECT (SELECTED)

14x+23=14x-23

Step-by-step explanation:

We are given four equations and are asked to identify which has no solutions. By isolating the variable 'x' in each equation, we can see that the only equation without a solution is Choice C: 14x+23=14x-23 because it results in an incorrect statement.

The subject of this question is about identifying which equations have no solutions. To find the solution of an equation, you need to isolate the variable, here, it is 'x'. Let's evaluate the provided choices:

Thus, only equation Choice C: 14x+23=14x-23 has no solutions.

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Answer: 15

Step-by-step explanation:

3x5 is 15

To find the total number of squares in 5 rows, multiply the number of squares in each row, which is 3, by the number of rows, which is 5.

To find the total number of squares in 5 rows, we need to multiply the number of squares in each row by the number of rows. Since there are 3 squares in each row, we can multiply 3 by 5 to get the answer.

Step 1: Multiply the number of squares in each row, which is 3, by the number of rows, which is 5: 3 x 5 = 15.

Step 2: Therefore, there are 15 squares in 5 rows.

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Answer:

the answer is 1.

Step-by-step explanation:

2+2=4x2=8 8 divided by 8 = 1

Answer:

first = 21 - 5 = 16

second  = 21

Third = 21*2 = 42

Step-by-step explanation:

first + second + third = 79

Let the second number = x

third = 2*x

first = x - 5

So we get

x - 5 + x + 2x = 79

4x - 5 = 79                  Add 5

4x - 5 + 5 = 79 + 5     Combine

4x= 84                         Divide by 4

4x/4 = 84/4

x = 21

Final answer:

Using algebraic methods, the three numbers are determined to be 16, 21, and 42. The values are obtained by setting up an equation based on the given relationships and solving for the variable.

Explanation:

We are tasked with determining the values of three numbers where the sum is 79, the third number is twice the second, and the first number is 5 less than the second. Let's define the second number as x. Therefore, the third number would be 2x and the first number would be x - 5. Setting up the equation based on these relationships, we have:

(x - 5) + x + (2x) = 79

Combining like terms, we get:

4x - 5 = 79

Adding 5 to both sides to isolate the variable, we find:

4x = 84

Dividing by 4 gives us:

x = 21

Now we can find the first and third numbers:

First number: x - 5 = 21 - 5 = 16

Second number: x = 21

Third number: 2x = 2(21) = 42

The numbers are 16, 21, and 42.

Answer:

40.7m^2

Step-by-step explanation:

Base×Height= 5.2m×3=15.6m2

Area of semicircle= Pie r^2= Pie×4^2=16×pie

pie×16÷2=8×pie

8×3.14=25.12m2

15.6m2+25.12m2=40.72m2

rounded to nearest tenth=40.7m2

Answer: [tex]40.7\ m^2[/tex]

Step-by-step explanation:

Given : A parallelogram has base 5.2 meters and height 3 meters, and a semicircle with a radius of 4 meters.

Area of parallelogram is given by :-

[tex]A_p=b\times h[/tex] , where b is base and h is height of parallelogram.

[tex]=5.2\times3=15.6\ m^2[/tex]   (1)

Area of semicircle :-

[tex]A_s=\dfrac{\pi r^2}{2}[/tex], where r is radius.

[tex]=\dfrac{3.14\times4^2}{2}=25.12[/tex]     (2)

Now from (1) and (2),. the area of the combined figure will be :-

[tex]A=A_p+A_s\\\\=15.6+25.12=40.72\approx40.7\ m^2[/tex]

Answer:

The inequality  is 9(t+5) < 6

Step-by-step explanation:

Let

t -----> the number

we know that

The phase "5 more than a number t" is equal to adds the number t and 5

(t+5)

The phase "the product of 9 and the quantity 5 more than a number t" is equal to multiply 9 by (t+5)

9(t+5)

less ----> represent the symbol "<"

therefore

The inequality that represent this problem is

9(t+5) < 6

The IQR is a measure of data distribution and used in outlier detection. The IQR is calculated by subtracting Q1 from Q3. After calculating the IQR, the lower and upper cut-offs can be calculated and data points below or above these cut-offs are considered as outliers.

The interquartile range (IQR) is a measure of statistical dispersion, and it can be useful in identifying 'outliers' in data. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) in a data set.

For the provided data set, to find the IQR, it should be sorted in ascending order and then Q1 and Q3 should be calculated. In your case, the sorted data set is: 12.8, 13.0, 13.5, 15.0, 15.0, 15.1, 15.2, 15.5, 15.6, 16.4, 16.6, 17.7, 18.3, 19.1, 19.3, 19.6, 20.5, 21.0, 26.2, 27.8, 33.5.

After finding Q1 and Q3, subtract Q1 from Q3 to get IQR (a.). Then, find the lower and upper cut-offs by subtracting 1.5 times of IQR from Q1 (b.) and adding 1.5 times of IQR to Q3 (c.), respectively. Any data points below the lower cut-off or above the upper cut-off are considered as outliers (d.).

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The function g(x) = f(-x) represents a reflection of the graph of f(x) across the y-axis. This transformation swaps the values of the function for positive and negative x values, creating a mirror image.  So since the max of f was when x = 2, the max of g will be when x = -2.

Understanding the Transformation of Function g(x) = f(-x)

function g(x) = f(-x).

This indicates a transformation where the function f(x) is reflected across the y-axis.

To put it simply, the graph of y = f(-x) is the mirror image of the graph of y = f(x) across the y-axis.

f g(x) = f(-x), the graph of g looks like a mirror image of f, where the y-axis is the mirror.  

For example, g(1) will be what f's value at -1 was (-1).  g(2) = f(-2) = -3.  g(3) = f(-3) = -1.  etc.  

So since the max of f was when x = 2, the max of g will be when x = -2.

Here’s an example to illustrate:

Suppose f(x) = x².

The graph of y = f(x) is a parabola facing upwards.

For y = f(-x), or y = (-x)²,

the graph will still be a parabola facing upwards.

Since g(x) = f(-x), the absolute values are not changed but the sign change in x reflects each point across the y-axis.

This reflection happens because negating the independent variable x means we swap the values of the function at positive and negative x values.

Question:

If the function g is defined so that g(x)=f(-x), then for what value of x does g attain its maximum value?

Answer:

5/3 hours

Step-by-step explanation:

2/3 hour = 40 minutes

You can solve it by proportion:

40 minutes = 2/5 room

x minutes = 1 room

[tex]x=\frac{40}{\frac{2}{5} }[/tex]

100 minutes = 5/3 hours

Answer: 1 hour 40 minute

Step-by-step explanation:

If it take 2/3 of an hour to paint 2/5 of a room

1Hour = 60min

2/3 of 60min

2/3 × 60min

=120min / 3

= 40min

That is it take 40min to paint 2/5 of a room

So using proportion

2/5 room = 40min

1room = X min

We cross multiply

2/5 × X = 40min

2X / 5 = 40min

We cross multiply again

2X = 200min

Divide bothside by 2

x = 100 min

But 1hour =60min

Therefore 100min = 1 hour 40min.

The measure of an angle being equal to itself is an example of the Reflexive Property, which states that any quantity is equal to itself.

The statement "The measure of an angle is equal to itself" is true because of the Reflexive Property. This property states that any quantity is equal to itself, which is a fundamental idea in mathematics and logic. In the context of geometry and angles, it means that an angle is always equal to its measure. So, if θ represents the measure of an angle, then we could say θ = θ, which demonstrates the Reflexive Property.

The other properties listed—the Property of Equality, Symmetric, and Transitive—are also important in the realms of algebra and geometry but do not directly apply to the fact that an entity is equal to itself. Instead, these properties involve the relationship between different entities or the equality between them derived from other equalities.

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Final answer:

To find the side length of the original square, we formed a quadratic equation based on the given information and solved it to get a side length of 5 meters.

Explanation:

The question asks us to find the length of a side of the original square when the sides are increased by 3 meters and the new area becomes 64 square meters. First, let's denote the side length of the original square as x. If each side of the square is increased by 3 meters, then the new side length is x + 3 meters. The area of the new square is given to be 64 m², which can be represented as the square of the new side length, so the equation becomes:

(x + 3)²= 64

This simplifies to:

x² + 6x + 9 = 64

Subtracting 64 from both sides:

x² + 6x - 55 = 0

This is a quadratic equation that we can solve by factoring or using the quadratic formula. In this case, the equation factors to:

(x + 11)(x - 5) = 0

This gives us two possible solutions for x: -11 or 5. Since a side length cannot be negative, we disregard the -11 and conclude that the side length of the original square is 5 meters.

Answer:

x = [tex]\frac{1}{12}[/tex] y²

Step-by-step explanation:

Any point (x, y ) on the parabola is equidistant from the focus and the directrix

Using the distance formula, then

[tex]\sqrt{(x-3)^2+(y-0)^2}[/tex] = | x + 3 |

Squaring both sides

(x - 3)² + y² = (x + 3)² ← expanding both sides

x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides

- 12x + y² = 0 ( subtract y² from both sides )

- 12x = - y² ( divide both sides by - 12 )

x = [tex]\frac{1}{12}[/tex] y²

Answer:

y²-12x = 0

Step-by-step explanation:

The formula for calculating the equation of a parabola is y² = 4ax

and x = a

To find the equation of the parabola with focus (3, 0) and directrix x = –3,

The point given (x,y) = (3,0) and x = -3

From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3

Similarly, x = 3 from the given point.

Substituting the value of x = -3 in the formula for equation of a parabola gives;

y² = 4(-3)x

y²= -12x

y²-12x = 0

Answer:

1. -6 3/5 + 2 = -4 3/5

2. -9 3/5 + 5 = -4 3/5

3. 33

Hope it helps

The answer to the addition problems are as follows;

For the first question;

An addition problem that has a sum of -4 3/5 may take different forms one of which is the answer supplied where; -5 3/5 is added to 1 and the result is; -4 3/5.

Fir the second question;

Fir the third question;

Therefore, x = 51 -18

x = 33

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Answer:

f of x equals 7 times one eighth to the x power

Step-by-step explanation:

Given phrase,

function f of x equals 7 times one half to the 3 times x power,

[tex]\implies f(x) = 7(\frac{1}{2})^{3x}[/tex]

By the power to power property of exponent,

That is,

[tex](a^m)^n=a^{m.n}[/tex]

[tex]f(x) = 7((\frac{1}{2})^3)^x[/tex]

[tex]f(x) = 7(\frac{1}{8})^x[/tex]

= f of x equals 7 times one eighth to the x power

Answer:

1

Step-by-step explanation:

Starting from the y-intercept of [0, 1], you do rise\run by either moving one block south over one block west or one block north over one block east. Either way, you will still get a rate of change [slope] of 1.

I am joyous to assist you anytime.

Answer:

1.25 gallons per second

Step-by-step explanation:

To figure this out divide 50 by 40

I don't know how to explain this further, hope this is good enough.

- Que

Answer:

It use 1.25 gallons of water per  second

Step-by-step explanation:

Amount of water used for car wash in 40 seconds = 50 gallons

Amount of water used for car wash in 1 seconds = [tex]\frac{50}{40}[/tex]

Amount of water used for car wash in 1 seconds = [tex]1.25[/tex]

So, Amount of water used in 1 second is 1.25 gallons

So, Unit rate = 1.25 gallons per second

Hence it use 1.25 gallons of water per  second

Answer:

66 km ÷ 24 km/h = 2 3/4 hours =

2 hours, 45 minutes

Answer:

first one. Just simply calculate it :/

Answer: 257

Step-by-step explanation:

|-143 + 400| = 257

The hiker starts 143 feet below sea level (-143). After climbing 400 feet, the hiker is now 257 feet above sea level.

The hiker's initial elevation is 143 feet below sea level, which we represent as -143. The hiker then climbs 400 feet, so we add this to the initial elevation. Therefore, the calculation is: -143 + 400 = 257.

This means that the hiker's new elevation, relative to sea level, is 257 feet above sea level.

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Answer:

AB=15 BC=60

Step by step:

AB+BC=AC

AC=75

Plug in AC to the equation: AB+BC=75

BC=4(ab)

Plug in BC into the equation: AB+4(AB)=75

Simplify: 5AB=75

Divide each side by 5: AB=15

BC=4(15)=60

Answer:  AB = 60, BC = 15

Step-by-step explanation:

AB is 4 times bigger than BC ⇒    AB = 4BC

Use the Segment Addition Property: AB + BC = AC

and substitution (replace AB with 4BC) and (AC with 75) to solve for BC

4BC + BC = 75

        5BC = 75

          BC = 15

AB = 4BC

    = 4(15)

    = 60

Answer: 5/6

Step-by-step explanation: if you were to say the probability would be choosing 3 then it would be 1/6 because you have 1 chance of choosing 3 and 5 others of choosing anything else but 3 this applies for the same thing your asking just opposite sides

Answer:

Step-by-step explanation:

[tex]y=2^x\\\\\text{Put}\ x=5\ \text{to the equation of the function:}\\\\y=2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]

The output, or the result when we input x=5 into the function y=2^x, is 32. This is found by substituting the given input into the function.

The function you've provided is y=2 to the power of x . It is an exponential function. The output for a function is simply the result you get when you substitute a given input into the function. In this case, the function is defined as y = 2^x. To find the output when x=5, replace x in the function with 5. So y = 2^5 = 32. Therefore, the output for an input of x=5 in your function is 32.

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