Match each problem to its solution. 8 8.2 9 56.25 Jonah earns $12.50 per hour as a marketing intern. If he works for 4.5 hours, how many dollars does he earn? arrowRight Jessica purchased items worth $41.23 at the local grocery store. The cashier made a mistake while ringing up her items, and Jessica ended up paying $50.23. How many extra dollars did she pay? arrowRight Josie has 20 meters of cloth. She needs to make long-sleeved blouses with that cloth. If one long-sleeved blouse requires 2.5 meters of cloth, how many blouses can she make with the material? arrowRight Jeremy bought 3.2 pounds of potatoes, 2.3 pounds of oranges, and 2.7 pounds of onions. How many pounds does his purchase weigh? arrowRight

Answer:

The volume of the box is

V(x) = 4x^3 -72x^2+320x

Step-by-step explanation:

Here, we are interested in calculating the volume of the box

From what we can see, the shape of the box is a cuboid

Mathematically, the volume of a cuboid is l * b * h

Thus, what we have will be;

x * 20-2x * 16-2x

= x ( 20(16-2x) -2x(16-2x))

= x(320-40x-32x + 4x ^2)

= x(320-72x+4x^2)

= 320x-72x^2 + 4x^3

the volume v(x) will be;

V(x) = 4x^3 -72x^2+320x

Based on the single letter that Peter picks and the single digit, the expected value in one turn for Star One is $-0.296262

First, find the probability that Peter picks the correct letter and the correct digit:
= Probability of picking letter x Probability of picking digit

= 1/26 x 1/10

= 0.3846%

The expected value per turn for Star One s:

= (0.3846% x 700) + ( (1 - 0. 3846%) x -3)

= $-0.296262

In conclusion, the expected value for a turn of Star One is $-0.296262.

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Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

Answer:

(e^3 / e^2n)

Step-by-step explanation:

isn't this the same question

Answer:

M(3.5 , 3.5)

J(3.5 , 14)

K(21 , 14)

L(21 , 3.5)

Step-by-step explanation:

M(1,1)

J(1,4)

K(6,4)

L(6,1)

multiply the coordinates by the scale factor of 3.5

M(3.5 , 3.5)

J(3.5 , 14)

K(21 , 14)

L(21 , 3.5)

Answer:

2 (x-5) = 10

2x-10 = 10

2x = 10 + 10

x = 20/2

x = 10

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

x = -5 and y = 3

Step-by-step explanation:

There are two equations :

3x − 2y = −21 ....(1)

2x + 5y = 5 ......(2)

Multiply equation (1) by 2 and equation (2) by 3.

6x - 4y = -42 ...(3)

6x + 15y = 15 ....(4)

Subtract equation (4) from (3) :

6x - 4y - (6x + 15y) = -42 -15

-4y -15y = -57

-19y = -57

y = 3

Put y = 3 in equation (2) :

2x + 5(3) = 5

2x = 5-15

2x = -10

x = -5

So, the value of x is (-5) and y = 3.

The required surface area would be A= 2πr² + 710/r which represents area A as a function of its radius r, where r is measured in centimeters.

The can's surface area A and volume V are determined by the equation if the container has a radius of r and a height of h.

A= 2πr² + 2πrh and V = πr²h

The volume V of a 12 oz cola can is 355 cm³

Given that cola can is approximately cylindrical.

V = πr²h = 355 cm³

h = 355 / πr²

Substitute the value of h in the can's surface area A, we get

A= 2πr² + 2πr(355 / πr²)

A= 2πr² + 2(355/r)

A= 2πr² + 710/r

Therefore, the required surface area would be A= 2πr² + 710/r which represents area A as a function of its radius r, where r is measured in centimeters.

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−24x+16

Hope this helps!

Answer:

-24× + 16

Step-by-step explanation:

hope this helps :D

Answer:

D. .................... . . . . . . . . . . . . .... . . . . . . . . .

Answer:

answer D 4.500..........

Answer:

AC=44

Step-by-step explanation:

Two triangles are congruent

So the equation is

3z+17=6z-10

6z-3z=17+10

3z=27

z=9

So AC =

6.9-10

54-10

44

Answer:

y = 5

Step-by-step explanation:

when the slope of a line is 0 because it does not incline

it is y = wherever the y value is

so in this case

it is

y = 5

Answer:

9.

Step-by-step explanation:

The top triangle is half in measurements then the bottom

Answer:

self replicate

cloning site

lower molecular weight

selectable marker gene

Answer:

A. magnitude of 8 and direction angle equal to 0 degrees

Step-by-step explanation:

EDGE 2020

Answer:

9 cups of yellow paint

Step-by-step explanation:

A mixture of paint calls for 1/3 cups of red paint and 3/4 cups of yellow paint.

From the above question

1/3 cups of red paint = 3/4 cups of yellow paint

1 cup of red paint = x cups of yellow paint

Cross Multiply

1/3 × x = 3/4 × 1

x = 3/4 ÷ 1/3

x = 3/4 × 3/1

x = 9/4

x = 2 1/4 cups of yellow paint

Hence, 1 cups of red paint requires 2 1/4 cups of yellow paint

If there were 4 cups of red paint added to the mixture, how many cups of yellow paint would need to be added to keep a constant rate of proportionality?

1 cups of red paint = 2 1/4 cups of yellow paint

4 cups of red paint = x cups of yellow paint

Cross Multiply

x cups of yellow paint = 4 × 2 1/4 cups of yellow paint

= 4 × 9/4 cups of yellow paint

= 9 cups of yellow paint

Therefore, 4 cups of red paint requires 9 cups of yellow paint

Answer:

yes its linear

Step-by-step explanation:

Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

10 oz.

Step-by-step explanation:

There are 16 oz in 1 lb. So for the 10 lb. cake there is a total of 160 oz to start. If the cake is cut in half and then in 8 pieces. There will be a total of 16 pieces.

10 lb/whole cake

= 160 oz/2 halves

= 160 oz/16 slices

= 10 oz/slice

Each slice of icecream cake is 10 oz.

Answer: The measure of angle 1 is equaled to 20

Step-by-step explanation:

4x= 80 (You divide 80 by 4, which is 20), so the measure of angle 1 is 20.

Answer:

x=50°

Angle at A=108°

Step-by-step explanation:

If the triangle ABC is isosceles,then <ABC=<ACB=65°

We can now use angle properties to find <BAC

<BAC+65+65=180°

<BAC=180°-130=50°

Since line AB and CD are parallel,line AC is a transversal line which means <BAC=<ACD=x=50°

Therefore x=50°

For the parallelogram,

opposite interior angles are equal so <BAD=<BCD and <ABC=<ADC

3x+3x+2x+2x=360°

10x=360°

x=360°/10=36°

The angle at a=3x=3×36°=108°