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hammer [34]
3 years ago
9

The equations 8x +4y = 32 and 16x +12y = 72 represent the cost for lunch and dinner for a family eating out on vacation. If x is

the number of adults and y is the number of children, how many adults are in the family?
Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

Answer:

There are 3 adults in the family.

Step-by-step explanation:

The equations 8x + 4y = 32 and 16x + 12y = 72 represent the cost of lunch and dinner for a family in which x is the number of adults and y is the number of children.

We have to find the number of adults or the value of x by solving these equations.

equations are 8x + 4y = 32 -------(1)

16x + 12y = 72 --------(2)

Now we will multiply equation 1 by 3 and subtract it by equation 2.

(16x + 12y) -3(8x + 4y) = 72 - 96

16x + 12y - 24x - 12y = -24

(16x - 24x) + (12y - 12y) = -24

-8x = - 24

8x = 24

x = 3

Therefore, there are 3 adults in the family.

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Which statement best describes a method that can be used to sketch the graph. y = |x - 2| a. Translate the graph of y = |x| two
ser-zykov [4K]

f(x) + n - translate the graph of f(x) n units up

f(x) - n - translate the graph of f(x) n units down

f(x + n) - translate the graph of f(x) n units left

f(x - n) - translate the graph of f(x) n units right

--------------------------------------------------------------------------

We have

y = |x - 2|

f(x) = |x| → f(x - 2) = |x - 2|

<h3>Answer: c. Translate the graph of y = |x| two units right.</h3>
6 0
3 years ago
The quotient of two numbers is 4 and their difference is 39. What is the smaller number of the two?
MatroZZZ [7]

Answer:

13

Step-by-step explanation:

x/y = 4

x=4y

x - y = 39

4y - y = 39

3y = 39

y= 13

3 0
3 years ago
The slope of the line below is -5. Which of the following is the point slope form of the line (2,-7)
tatyana61 [14]

Plugging in (2,-7) into

y=-5x+b, we get that b=3.

Therefore, the equation is y=-5x+3

7 0
4 years ago
What value of m makes the equation true? m + 2m - 6 = -12 + 2m.
denpristay [2]

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4 0
4 years ago
Read 2 more answers
Find the equation of the circle with a diameter whose end points are (-1,-2) and (-3,2)
Sergeeva-Olga [200]

Answer:

The equation of the circle with a diameter whose end points are (-1,-2) and (-3,2) is

x^{2} +y^{2}+4x-1=0

Step-by-step explanation:

<u>Explanation:</u>-

<u>Step 1:</u>-

The equation of the circle having center and radius is

(x-h)^2+(y-k)^2=r^2

here center is (h,k) and radius is r

Given diameter whose end points are (-1,-2) and (-3,2)

The diameter of the circle is passing through the center of the circle

so center of the circle = midpoint of two end points

      (\frac{-1 +(-3) }{2} ,\frac{-2+2 }{2}  )

    (-2,0)

therefore center (h,k) = (-2,0)

<u>Step 2:-</u>

we have to find the radius of the circle

the radius of the circle = the distance from center to the one end point

i.e., C P = r

Given one end point is P(-3,2) and center C(-2,0)

The distance formula of two points are

\sqrt{(x_{2}-x_{1} ) ^{2}+ (y_{2}-y_{1} ) ^{2}}

r=\sqrt{{(-3)-(-1) ) ^{2}+ (2-(-2)) ^{2}}

r=\sqrt{5}

<u>Step 3</u>:-

center (h,k) = (-2,0) and

radius r=\sqrt{5}

The standard form of circle equation

(x-h)^2+(y-k)^2=r^2

(x-(-2))^2+(y-0)^2=\sqrt{5} ^2

on simplification is

x^{2} +y^{2}+4 x-1=0

5 0
3 years ago
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