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3 years ago

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The graph below shows the cost C for bowling g games at Strike King. Another bowling center, Thunder Alley, charges $2.25 per ga

me.
At what point do the graphs of Strike King (shown) and the graphs of Thunder Alley (not shown) intersect? Explain why this is always the case for proportional relationships.

1 answer:

Lunna [17]3 years ago

6 0

Answer:

They intersect when the Strike king is at (9,15.75) and Thunder Alley is at (7, 15.75). But only the X axes intersect. The X and Y axes intersect at (0,0) that's where they start and that is where they meet. Its a proportional relationship because their ratios are equivalent. It represents the constant of proportionality.

Step-by-step explanation:

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Need help with these 2 problems will give brainliest answer and worth 30 points!!

Elena L [17]

Question 1.
Step 1. Add the total cost of purchasing the luxury items:
$TotalCost=35.95+34.65+15.30+6.99+42.96=135.85$
You will spend $135.85 purchasing the luxury items.

Step 2. Add the total cost of purchasing the name brand items:
$TotalCost=19.95+15.98+9.40+4.99+29.75=80.07$
You will spend $80.07 purchasing the name brand items.

Step 3. Subtract the total cost of purchasing the name brand items from the total cost of purchasing the luxury items:
$135.85-80.07=55.78$

Answer to the original question:
We can conclude that you will spend $55.78 more by purchasing the luxury items.

Question 2:

Part 1. To find the how many months will take to pay the card debt, we are going to use the credit card equation: $N=- \frac{1}{30}* \frac{ln(1+ \frac{b}{p}*(1+ \frac{r}{365})^{30})) }{ln(1+ \frac{r}{365}) }$
where
$N$ is the months to pay the card
$b$ is the balance
$p$ is the monthly payment
$r$ is the interest rate in decimal form

We know from our problem that the balance of the credit card is $1,367.90 and the monthly payment is $400.00, so $b=1367.90$ and $p=400$ . To find convert the interest rate to decimal form, we are going to divide the rate by 100%
$r= \frac{9.5}{100}=0.095$ .
Now that we have all we need, lets replace the values in our credit card equation:
$N=- \frac{1}{30}* \frac{ln(1+ \frac{b}{p}*(1+ \frac{r}{365})^{30})) }{ln(1+ \frac{r}{365}) }$
$N=- \frac{1}{30}* \frac{ln(1+ \frac{1367.90}{400}*(1+ \frac{0.095}{365})^{30})) }{ln(1+ \frac{0.095}{365}) }$
$N=3.4799$

It will take you 3.5 months according to our calculation, but since you pay $400 each month on the due date, we can conclude that it will take you 4 months to pay off the card.

Part 2. To calculate the total amount paid including the interest, we just need to multiply the monthly payment by the number of payments.
We know from our problem that the monthly payment is $400. We also know from our previous calculations that the number of payments is 4, so lets multiply both quantities:
$400*4=1600$

We can conclude that the total amount paid including interest is $1,600

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3 years ago

Kenneth has 2,000$ to invest

Katarina [22]

The calculations for 2, 4, 8 year can be derived as follows,

For simple interest:

S.I = $\frac{P*T*R}{100}$

P= principle

T= Time

R= Rate

For 2 year;

S.I = $\frac{2000*2*5.6}{100}$ = $224

Amount = $2224

For 4 year;

S.I = $\frac{2000*4*5.6}{100}$ = $448

Amount = $2448

For 8 year;

S.I = $\frac{2000*8*5.6}{100}$ = $896

Amount = $2896

7 0

3 years ago

To fit between two windows, the width of a bookshelf must be no greater than feet. Mrs. Aguilar purchases a bookshelf that is 77

kozerog [31]

Given:
width of bookshelf no greater than 6 1/2 feet
purchased bookshelf that is 77 inches wide

We need to find the equivalent value in feet of the purchased bookshelf.

1 foot is equal to 12 inches

77 inches * 1 foot/12 inches = 77 ft/12 = 6 5/6 ft

Or we can convert the feet into inches:

6 1/2 feet convert to improper fraction.

((6*2)+1)/2 = 13/2 feet

13/2 ft * 12 inches/1ft = (13 * 12)/2 = 156/2 = 78 inches

Compare the maximum width of 78 inches to the actual width of 77 inches.

The purchased bookshelf can fit between two windows.

6 0

3 years ago

If triangle ABC defined by the coordinates A(1,1), B(9,1), C(1,9) is dilated by a scale factor of 1/2

alukav5142 [94]

Answer:

The transformed points of the triangle ABC are $A' (x,y) = \left( \frac{1}{2}, \frac{1}{2}\right)$ , $B'(x,y) = \left(\frac{9}{2}, \frac{1}{2} \right)$ , $C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)$

Step-by-step explanation:

The new points after applying the scale factor are, respectively:

$A' (x,y) = \frac{1}{2}\cdot (1,1)$

$A' (x,y) = \left( \frac{1}{2}, \frac{1}{2}\right)$

$B' (x,y) = \frac{1}{2}\cdot (9,1)$

$B'(x,y) = \left(\frac{9}{2}, \frac{1}{2} \right)$

$C'(x,y) = \frac{1}{2}\cdot (1,9)$

$C'(x,y) = \left(\frac{1}{2}, \frac{9}{2}\right)$

7 0

3 years ago

If a square has a perimeter of 40 yards, what is the length of one side of the square?

zhannawk [14.2K]

10 yards because a square has 4 sides and all four sides are equal and so 40 divided by 4 equals 10

3 0

3 years ago

Read 2 more answers