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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

Alexandra [31]

37x + 45y = 7940
75x + 45y = 10,410

Since 45y is in both equations we can more easily transfer from first equation to 2nd equation.

In the first equation, subtract 37x from each side and you have 45y = 7940 - 37x. Replace the 45y in the second equation with (7940 - 37x).

Now you have 75x + (7940 - 37x) = 10,410

Simplify by combining 75x - 37x and you have 38x + 7940 = 10,410

Subtract 7940 from both sides and you have 38x = 2470.

Divide both sides by 38 and you have x = 65

To solve for y, take you first equation (or even the second one) and substitute c for 65.

(37 x 65) + 45y = 7940
2405 + 45y = 7940

Subtract 2405 from each side.

45y = 5535

Divide each side by 45 and you have y = 123

Regular tickets = $65
VIP tickets = $123

7 0

2 years ago

Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.

wlad13 [49]

Answer:

Each golf ball costs about $2.

Step-by-step explanation:

Given:

Donald bought a box of golf balls for $9.27. There were 18 golf balls in the box.

Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.

Now, to find the cost of each golf ball.

As given:

Rename the decimal dividend as a whole number that is compatible with the divisor to estimate the quotient.

As, the cost of golf ball box = $9.27.

So, 9.27 nearest to whole number is 9.

Thus to get the cost of each ball:

18 golf balls cost = $9.

So, 1 golf ball cost = $18\div 9=2.$

Therefore, each golf ball costs about $2.

3 0

3 years ago

How many x intercept appear on the graph of the polynomial function F(x)=x4-5x2

4vir4ik [10]

$f(x)=x^4-5x^2\\\\x^4-5x^2=0\\\\x^2(x^2-5)=0\\\\x^2[x^2-(\sqrt5)^2]=0\\\\x^2(x-\sqrt5)(x+\sqrt5)=0\iff x=0\ \vee\ x=\sqrt5\ \vee\ x=-\sqrt5$

Answer: 3 x-intercepts.

3 0

3 years ago

The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center

Katyanochek1 [597]

The length of one side of the octagon is given by:
$L = 72/8

L = 9$
Then, the apothem can be determined using the Pythagorean theorem in the following way:
$11.8 ^ 2 = (9/2) ^ 2 + a ^ 2
$
Clearing to have:
$a ^ 2 = 11.8 ^ 2 - (9/2) ^ 2$
$a = \sqrt{11.8 ^ 2 - (9/2) ^ 2}$
$a = 10.91$
Then, the area is given by:
$A = (8) * (1/2) * (L) * (a)
$
Where,
L: length of the octagon sides
a: apotema
Substituting values:
$A = (8) * (1/2) * (9) * (10.91)

A = 392.76 feet ^ 2$
Answer:
the approximate length of the apothem is:
a = 10.91 feet
The approximate area of the floor of the gazebo is:
A = 392.76 feet ^ 2

8 0

3 years ago

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He normal pulse rate of a 13-year-old is between 70 and 100 beats per minute. As part of a health program, the medical staff at

SVEN [57.7K]

From the box plot, it can be seen that for grade 7 students,
The least value is 72 and the highest value is 91. The lower and the upper quartiles are 78 and 88 respectively while the median is 84.

Thus, interquatile range of the resting pulse rate of grade 7 students is upper quatile - lower quartle = 88 - 78 = 10

Similarly, from the box plot, it can be seen that for grade 8 students,
The least value is 76 and the highest value is 97. The lower and the upper quartiles are 85 and 94 respectively while the median is 89.

Thus, interquatile range of the resting pulse rate of grade 8 students is upper quatile - lower quartle = 94 - 85 = 9

The difference of the medians of the resting pulse rate of grade 7 students and grade 8 students is 89 - 84 = 5

Therefore, the difference of the medians is about half of the interquartile range of either data set.

6 0

3 years ago

Read 2 more answers