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Oksi-84 [34.3K]

2 years ago

7

On Sunday, a local hamburger shop sold a combined total of 378 hamburgers and cheeseburgers. The number of cheeseburgers was sol

d 2 times the number of hamburgers. How many hamburgers were sold?

1 answer:

ipn [44]2 years ago

5 0

Answer:

The number of hamburgers sold was 126.

Step-by-step explanation:

Let h = number of hamburgers sold

let c = cheeseburgers sold

c+h = 378

c = 2h

Substitute c =2h into c+h =278

c+h =378

2h+h = 378

Combine like terms

3h = 378

Divide by 3

3h/3 =378/3

h =126

The number of hamburgers sold was 126.

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Step-by-step explanation:

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Which function has an average rate of change of -4 over the interval [-2,2]?

kolbaska11 [484]

Only p(x) has an average rate of change of -4 over [-2, 2].

Find the average rate of change of each given function over the interval [-2, 2]]:

The average rate of change of m(x) over [-2, 2]:

<h3>What is the average rate?</h3>

The average rate of change = $\frac{m(b)-m(a)}{b-a}$

Where, a = -2, m(a) = -12

b = 2, m(b) = 4

Plug the values into the equation

The average rate of change

$=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}$

The average rate of change = 4

The average rate of change of n(x) over [-2, 2]:

The average rate of change = $\frac{n(b)-n(a)}{b-a}$

Where, a = -2, n(a) = -6

b = 2, n(b) = 6

Plug the values into the equation

The average rate of change

$=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}$

The average rate of change = 3

The average rate of change of q(x) over [-2, 2]:

The average rate of change = $\frac{q(b)-q(a)}{b-a}$

Where, a = -2, q(a) = -4

b = 2, q(b) = -12

Plug the values into the

The average rate of change = $\frac{-4-12}{2-(-2)}$

= $\frac{-16}{4}$

The average rate of change = -2

The average rate of change of p(x) over [-2, 2]:

The average rate of change = $\frac{p(b)-p(a)}{b-a}$

Where, a = -2, p(a) = 12

b = 2, p(b) = -4

Plug the values into the equation

The average rate of change = $\frac{-4-12}{2-(-2)}$

$=\frac{-16}{4}$

The average rate of change = -4

The answer is D.

Only p(x) has an average rate of change of -4 over [-2, 2].

To learn more about the average rate of visit:

brainly.com/question/8728504

#SPJ1

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11 months ago

Brian made a tasty burger at the diameter of the burger was 5 cm what was the area of the burger

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2 years ago

Read 2 more answers

Solve the following equations.<br> log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

6 0

3 years ago