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dsp73
3 years ago
7

Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza. Mary received a gift card of $11

0 for a different pizza restaurant. The restaurant charges $20 per pizza.
Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.
Amount of money left on Keith's card in dollars = __________
Amount of money left on Mary's card in dollars=____________
Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.
Mathematics
1 answer:
stepan [7]3 years ago
5 0

Answer:

a)Amount of money left on Keith's card in dollars = $90 - $15x

= $(90 - 15)

b) Amount of money left on Mary's card in dollars= $110 - $20x

= $(110 - 20x)

c) Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.

$90 - 15x = $110 - 20x

Step-by-step explanation:

Let x be the number of pizzas purchased. For each card, write an expression for the amount of money left on the card after purchasing x pizzas.

For Keith

Keith received a gift card of $90 for a pizza restaurant. The restaurant charges $15 per pizza.

x numbers of pizza costs = $15x

Hence, the amount of money left on Keith's card after purchasing x pizzas =

$90 - $15x

For Mary,

Mary received a gift card of $110 for a different pizza restaurant. The restaurant charges $20 per pizza.

Hence, x number of pizzas cost =$20 × x

= $20x

Therefore, the amount of money left on Mary's card after she buys x pizzas =

$110 - $20x

Amount of money left on Keith's card in dollars = __________

Amount of money left on Mary's card in dollars=____________

Write an equation to show that the two cards have the same amount of money left on them [don't know how to do this part.

To find the equation that shows that the two cards have the same amount of money =

Equation 1 = Equation 2

$90 - 15x = $110 - 20x

Collect like terms

-15x + 20x = $110 - $90

5x = 20

x = 20/5

x = 4

Hence, anytime Keith and Mary buys 4 pizzas their gift card will have the same amount of money left on them.

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Pretty Pavers company is installing a driveway. Below is a diagram of the driveway they are
prohojiy [21]

Answer:

The most correct option is;

(B) 958.2 ft.²

Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

The dimension of the diameter of the small semicircle = 10·√3

Radius of the small semicircle = Diameter/2 = 10·√3/2 = 5·√3

Area of the small semicircle = (π·r²)/2 = (π×(5·√3)²)/2 = 117.81 ft.²

Similarly;

The dimension of the diameter of the large semicircle = 10·√3 + 2 × 6 × √3

∴ The dimension of the diameter of the large semicircle = 22·√3

Radius of the large semicircle = Diameter/2 = 22·√3/2 = 11·√3

Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

Area of rectangle = 11·√3 × 17·√3 = 561

Area, A of large semicircle cutting into the rectangle is found as follows;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2

Where:

\theta = 2\times tan^{-1}( \frac{The \, number \, of  \, vertical  \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle}{The \, number \, of  \, horizontal \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle} )

\therefore \theta = 2\times tan^{-1}( \frac{10\cdot \sqrt{3} }{5\cdot \sqrt{3}} ) = 2.214

Hence;

A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (2.214 - sin2.214) \times (11\cdot\sqrt{3} )^2 = 128.3 \, ft^2

Therefore; t

The area covered by the pavers = 561 - 128.3 + 570.2 - 117.81 = 885.19 ft²

Therefor, the most correct option is (B) 958.2 ft.².

4 0
3 years ago
Who can help me needed for tomorrow please
blagie [28]

a) 170.00 =8n -30

200= 8n

n = 200/8 = 25 items


b) since the expenses increased the profits would decrease

profit = 8(25)-40 = 200-40 = 160

170-160 = 10.00

 profit decreased by $10.00

6 0
3 years ago
Read 2 more answers
10
natka813 [3]

Answer:

x= -8 , y = 5

x= 25/4 , y = 1/4

Step-by-step explanation:

substitute first eqn into the second eqn:

(7 - 3y)^2 -y^2 = 39

49 - 42y + 9y^2 - y^2 = 39

8y^2 - 42y +10 =0

4y^2 - 21y + 5 = 0

(4y-1) (y-5) = 0

y= 1/4 , 5

when y=1/4

x = 7- 3/4

=25/4

when y= 5

x = 7- 15

= -8

5 0
3 years ago
Read 2 more answers
Given the point (-6, 1) & slope = 1/3, what is the equation of the line? *
bekas [8.4K]

Answer:

y=1/3 + 3

Step-by-step explanation:

y= 1/3x + b

(1) = 1/3(-6) + b

1 = -2 +b

3 = b

y=1/3 + b

4 0
3 years ago
What else would need to be congruent to show that ABC = PQR by sss
Katen [24]
Ab=pq
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and so on
7 0
3 years ago
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