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1. Kristen spent $131 on shirts at Target last week. She bought some fancy shirts for

Masja [62]

Answer:

Kristen bought 2 fancy shirts and 5 plain t-shirts.

Step-by-step explanation:

Given that,

Kristen spent $131 on 7 shirts.

Cost of one fancy shirt = $28

Cost of one plain t-shirt = $15

Let,

x be the number of fancy shirts

y be the number of plain t-shirts

x+y = 7 Eqn 1

28x+15y=131 Eqn 2

Multiplying Eqn 1 by 15

15(x+y=7)

15x+15y=105 Eqn 3

Subtracting Eqn 3 from Eqn 2

(28x+15y)-(15x+15y)=131-105

28x+15y-15x+15y=26

13x=26

Dividing both sides by 13

$\frac{13x}{13}=\frac{26}{13}\\x=2$

Putting x=2 in Eqn 1

2+y=7

y=7-2

y=5

Hence,

Kristen bought 2 fancy shirts and 5 plain t-shirts.

3 0

3 years ago

Given the following three points, find by the hand the quadratic function they represent (0,6, (2,16, (3,33)

Lisa [10]

Answer:

$f(x) = 4x^2 - 3x + 6$

Step-by-step explanation:

Quadratic function is given as $f(x) = ax^2 + bx + c$

Let's find a, b and c:

Substituting (0, 6):

$6 = a(0)^2 + b(0) + c$

$6 = 0 + 0 + c$

$c = 6$

Now that we know the value of c, let's derive 2 system of equations we would use to solve for a and b simultaneously as follows.

Substituting (2, 16), and c = 6

$f(x) = ax^2 + bx + c$

$16 = a(2)^2 + b(2) + 6$

$16 = 4a + 2b + 6$

$16 - 6 = 4a + 2b + 6 - 6$

$10 = 4a + 2b$

$10 = 2(2a + b)$

$\frac{10}{2} = \frac{2(2a + b)}{2}$

$5 = 2a + b$

$2a + b = 5$ => (Equation 1)

Substituting (3, 33), and c = 6

$f(x) = ax^2 + bx + x$

$33 = a(3)^2 + b(3) + 6$

$33 = 9a + 3b + 6$

$33 - 6 = 9a + 3b + 6 - 6$

$27 = 9a + 3b$

$27 = 3(3a + b)$

$\frac{27}{3} = \frac{3(3a + b)}{3}$

$9 = 3a + b$

$3a + b = 9$ => (Equation 2)

Subtract equation 1 from equation 2 to solve simultaneously for a and b.

$3a + b = 9$

$2a + b = 5$

$a = 4$

Replace a with 4 in equation 2.

$2a + b = 5$

$2(4) + b = 5$

$8 + b = 5$

$8 + b - 8 = 5 - 8$

$b = -3$

The quadratic function that represents the given 3 points would be as follows:

$f(x) = ax^2 + bx + c$

$f(x) = (4)x^2 + (-3)x + 6$

$f(x) = 4x^2 - 3x + 6$

6 0

3 years ago

What is the length of AC¯¯¯¯¯ ?

insens350 [35]

Answer:

AC = 6

Step-by-step explanation:

y is the dimension of the horizontal segment (see the attached image).

The hypotenuses are the same dimension, so:

(x+4)^2=(x/2)^2+y^2

(3x-8)^2=(x/2)^2+y^2

So,

(x+4)^2 = (3x-8)^2

x+4 = 3x-8

x-3x = -8-4

-2x = -12

x = 6

And x is the dimension of the segment AC.

7 0

3 years ago

Read 2 more answers

The actual Mount Rushmore carving was made from a scale model with a scale of 1 inch = 1 foot. On the model, Teddy Roosevelt's m

IRISSAK [1]

Answer:

Step-by-step explanation:

The carving was made from a scale model with a scale of 1 inch = 1 foot. This means that one foot on the actual carving is represented by one inch on the model. So the model is smaller than the actual carving.

On the model, Teddy Roosevelt's mustache was 1 foot by 8 inches long.

We would convert the 1 foot on the model to inches because the model is represented in inches

12 inches = 1 foot

This means that on the model, Teddy Roosevelt's mustache was 12 inches by 8 inches long. Therefore,

Teddy Roosevelt's mustache was 12 feets by 8 feets long on the monument or carving

8 0

3 years ago

Andi purchased 1/3 pound of cashews for $2.85.What is the cost of 1 pound of cashews.

Minchanka [31]

1/3 lb. = $2.85
1/3 lb = $2.85
1/3 lb. = $2.85

1 lb of cashews costs $ 8.55

6 0

3 years ago