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allsm [11]
2 years ago
9

Isabella is deciding between two parking garages. Garage A charges an initial fee of

Mathematics
1 answer:
bearhunter [10]2 years ago
7 0

Answer:

i. A = 4 + 3t .......... 1

  B = 12 + 2t .......... 2

ii. The hours required would be 8 hours.

Step-by-step explanation:

The charges at each of the garages can be expressed as;

i. For garage A,

A = 4 + 3t .......... 1

ii. For garage B,

B = 12 + 2t .......... 2

where A is the amount charged at garage A, B is the amount charged at garage B, and t is the number of hours.

To determine the number of hours  parked that would make the cost of each garage the same.

Let:

equation 1 = equation 2

4 + 3t = 12 + 2t

collect like terms

3t - 2t = 12 - 4

t = 8

The hours that would make the cost of each garage the same is 8 hours.

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A recipe requires ¾ cup of nuts for 1 batch of muffins. Write the number of batches of muffins that can be made using 7 ½ cups o
Ivahew [28]

Answer:

10 batches

Step-by-step explanation:

3/4 cups = 1 muffins

15/2 cups = x muffins

For x muffins,

3/4 × X = 15/2 × 1

3x × 2 = 15×4

6x = 60

Divide both sides by 6

6x/6 = 60/6

X = 10

Hence 10 batches of muffins will be made from 15/2 cups of nuts.

8 0
2 years ago
9. Find the point of intersection of the lines: y = 4x + 1 and y = - 2x + 4 A. (2,9) B.(1/2,3) C. (1,2) D. (1/4,2)
Colt1911 [192]

Step-by-step explanation:

y = 4x + 1 and y = -2x + 4

4x + 1 = -2x + 4, 6x = 3, x = 0.5

When x = 0.5, y = 4(0.5) + 1 = 3.

The point of intersection is (0.5, 3). (B)

3 0
2 years ago
Read 2 more answers
Find the area of the figure.
ipn [44]

Answer:

89m

Step-by-step explanation:

First, find the area of the rectangle (ignoring the missing triangle inside). The area of the rectangle is its base times its height, which is 8*13=104.

Next, find the area of the triangle. The area of the triangle is its base times height, divided by two.

The width of one side of the rectangle is 13, and the width of the side of the rectangle is 8 (4 + 4). Therefore, subtract 8 from 13 and the missing section in the side of the rectangle is 5. 5 is equal to the base of the triangle.

The height of the triangle is given, which is 6. As stated before, the area of a triangle is its base times height divided by two, which is 5*6/2 in this case. The area of the triangle is equal to 15.

Now, subtract the area of the triangle from the area of the rectangle. 104-15=89.

3 0
3 years ago
The sequence is recursive. find the value of the next term in the sequence. 8, 10, 12, 14, . . .
Mars2501 [29]
It's an arithmetic progression with first term = 8 and common difference d =2:
so the next term is 14 + 2 = 16
8 0
3 years ago
A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shif
omeli [17]

We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is \frac{7\pi}{12}. The graph of the function does not show a phase shift. We are asked to write the equation of our function.

We know that general form a cosine function is y=A\cos(b(x-c))-d, where,

A = Amplitude,

\frac{2\pi}{b} = Period,

c = Horizontal shift,

d = Vertical shift.    

The equation of parent cosine function is y=\cos(x). Since function is reflected about x-axis, so our function will be y=-\cos(x).

Let us find the value of b.

\frac{2\pi}{b}=\frac{7\pi}{12}

7\pi\cdot b=24\pi

\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}

b=\frac{24}{7}

Upon substituting our given values in general cosine function, we will get:

f(x)=-11\cos(\frac{24}{7}x)-9

Therefore, our required function would be f(x)=-11\cos(\frac{24}{7}x)-9.

7 0
2 years ago
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