The Computer Club has a budget of $90 for a pizza party. The club can get large pizzas for $10 and cases of soda for $3.50. The club would like to buy at least 5 large pizzas and at least 3 cases of soda.
a. Write a system of linear equations that describes the given information. Use x for the number of large pizzas and y for the number of cases of soda the club will buy.
b. Graph the system you wrote in part (a).
c. Can the club buy 6 pizzas and 4 cases of soda? Explain.
d. Find the maximum number of cases of soda the club can buy if the club decides to buy 7 pizzas.

If a function f(x) has an inverse f ⁻¹(x), then by definition

[tex]f\left(f^{-1}(x)\right) = x[/tex]

Differentiating both sides with respect to x yields

[tex]f'\left(f^{-1}(x)\right) \times \left(f^{-1}\right)'(x) = 1 \implies \left(f^{-1}\right)'(x) = \dfrac1{f'\left(f^{-1}(x)\right)}[/tex]

Now, if f(a) = b and b = f ⁻¹(a), then

[tex]\left(f^{-1}\right)'(a) = \dfrac1{f'\left(f^{-1}(a)\right)} = \dfrac1{f'(b)}[/tex]

Answer: 4.3%

Step-by-step explanation:

18^2 = 324

7 * 2 = 14

14/324 = 7/362 = 4.3%

Answer:

2,740,754.11467 or 2,740,754

Step-by-step explanation:

800,000(1.08)^16

y=a(b)^x

a is the starting point

b is growth

x is years

you get the growth by adding 8 to 100 then dividing by 100.

Answer:

Step-by-step explanation:

Remainder of cups of flour is:

25 cups of flour used to bake 150 cupcakes.

Each cupcake has:

Answer:

Step-by-step explanation:

Combine like terms:

21r - 6

Answer:

between 2 and 12.

Step-by-step explanation:

Hope this helps :)

Answer:

-7

Step-by-step explanation:

first multiply 3 and 4 because PEMDAS

so it now looks like

12 - 9 - x = 10

now minus 12 and 9

3 - x = 10

move x to the other side by adding x to both sides

3 = 10 + x

and move 10 to the other side by subtracting  10 to both sides

3 - 10 = x

x = -7

now check

3*4 - 9 - (-7) = 10 ?

12 - 9 + 7 = 10 ?

3 + 7 = 10 ?

10 = 10

Step-by-step explanation:

[tex]3\cdot \:4+\left(-9\right)-x=10[/tex]

[tex]\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a[/tex]

[tex]3\cdot \:4-9-x=10[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:3\cdot \:4=12[/tex]

[tex]12-9-x=10[/tex]

[tex]\mathrm{Subtract\:the\:numbers:}\:12-9=3[/tex]

[tex]-x+3=10[/tex]

[tex]\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}[/tex]

[tex]-x+3-3=10-3[/tex]

[tex]Simplify[/tex]

[tex]-x=7[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{7}{-1}[/tex]

[tex]Simplify[/tex]

[tex]x=-7[/tex]

Answer: 2(x+6)

Step-by-step explanation:

add the numbers

10x - 8x + 2 + 10

10x - 8x + 12

combine like terms

10x - 8x + 12

2x + 12

common factors

10x - 8x + 2 + 10

the answer is

2(x+6)

Answer:

-20 represents 20m below sea level.

-90 represents a movement of 90m to the South.

Check the picture below, with that template in mind

[tex]y = \stackrel{A}{2}|\stackrel{B}{1}x+\stackrel{C}{4}|\stackrel{D}{-3}\qquad \begin{cases} A=2~~,~~B=1\\ \qquad \textit{shrinks by a factor of 2}\\ B=1~~,~~C=4\\ \qquad \textit{horizontal leftwards shift by }\frac{4}{1}=4\\ D=-3\\ \qquad \textit{vertical downwards shift by 3} \end{cases}[/tex]

Answer:

398,000

Step-by-step explanation:

400,000-2,000=398,000

In word form the answer is three hundred ninety-eight thousand

I hope that has helped :)

Elapsed Time :

1. 24min - 9min = 15 Minutes

2. 56min - 48min = 8 Minutes

3. 36min -5min = 31 Minutes

4. 55min - 3min = 52 Minutes

5. 45min - 11min = 34 Minutes

PS. Mark as brainliest if this helped! :) Trying to get to Virtuoso.

Answer:

Step-by-step explanation:

(y2-y1)/(x2-x1)

-3-(-3)/(2-1)=0

Answer:

The answer is 4

Step-by-step explanation:

Edge 2020

Answer:

it is 4

Step-by-step explanation:

Answer:

8,588 people

Step-by-step explanation:

We can represent this exponential decay as [tex]P=10000(0.97)^n[/tex] where [tex]n[/tex] is the number of years later:

[tex]P=10000(0.97)^n\\\\P=10000(0.97)^5\\\\P=10000(0.8587340257)\\\\P=8587.340257\\\\P\approx8588[/tex]

Therefore, the population 5 years later will be 8,588 people

Step-by-step explanation:

Ok so after the first year we expect the population to reach 97% of it's initial population.

So 97% of 10 000 can be written as:

97/100 ×10 000=0.97×10 000=9 700

After the second year we expect the population to drop to 97% of the first year's population

So, it can be said that:

0.97×9700= 9409

Similarly after year 3,

0.97× 9409= 9126.73

Year 4,

0.97× 9126.72= 8852.9281

Year 5,

0.97× 8852.9281=8587 rounded to the nearest number

The new population would be 8587

Using the z-distribution, as we have the standard deviation for the population, to test the hypothesis, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

At the null hypothesis, it is tested if the mean time is of 28 minutes, that is:

[tex]H_0: \mu = 28[/tex]

At the alternative hypothesis, it is tested if the mean time is greater than 28 minutes, that is:

[tex]H_1: \mu > 28[/tex].

The test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are given by:

[tex]\overline{x} = 32, \mu = 28, \sigma = 5, n = 10[/tex]

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{32 - 28}{\frac{5}{\sqrt{10}}}[/tex]

[tex]z = 2.53[/tex]

Considering that we have a right-tailed test, as we are testing if the mean is greater than a value, with a standard significance level of 0.05, the critical value is of [tex]z^\ast = 1.645[/tex].

Since the test statistic is greater than the critical value, it is found that this is evidence that workers in the large city take longer than 28 minutes to get home from work.

To learn more about the z-distribution, you can check https://brainly.com/question/26454209

Answer:

The first choice.

Step-by-step explanation:

hope this helps!

Answer:

A is the answer took test on e2020

Step-by-step explanation:

Answer:

65 yd

Step-by-step explanation:

The diagonal of a rectangle can be found using

Pythagoras' Theorem  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse of a right triangle)

Given:

⇒ 25² + 60² = c²

⇒ c² = 4225

⇒ c = √4225

⇒ c = 65

Therefore, the length of the diagonal is 65 yd

Answer: he needs to fill it 20 times

Step-by-step explanation:

Answer:

50 km/h

Step-by-step explanation:

so you traveled total of 350 (km) in 7 (hours) right?, just take 350, divide it by 7, which will give you km/h. (or 50 km/h) and then when you add a direction it like "west" it's no longer a speed it's a velocity.

Displacement given (in metres) = (350 × 1000)m.

Displacement = 350000 metres.

Time = (7× 3600) seconds

Time = 25200 seconds.

Velocity = Displacement / Time

Velocity = 350000 / 25200

Velocity = 13.89m/s

Approximately, Velocity = 14m/s.

Answer:

B

Step-by-step explanation:

the cube (this is the ³ at the end of the numerator) of

the difference of 5 times the square of y and 7 :

(5y² - 7)

all divided by the square (that is the ² at the end of the denominator) of

2 times y :

(2y)

A would be

((5y)² - 7)³/(2y)²

C would be

(((5y)²)³ - 7)/(2y²)

D would be

(5y² - 7)³/(2y²)

Answer:

3.3

Step-by-step explanation: it said too the nearest so i think 3.3 cause its already 3.6

Answer: 121

Step-by-step explanation:

Answer:

I think absolute value

Step-by-step explanation:

One divided by anything is that same number

EX.

1/100=100

But if the number is negative it would still be that number just in negative form.

Ex.

1/(-3)= -3

Can I get Brainlest if you found this answer helpful

[NRAA]

One- (number)+th

eg- one tenth

one eighth

[xArtsy]

Answer:

96 inches

Step-by-step explanation:

Given the following question:

12 inches = 1 foot

To find the answer we simply need to multiply 12 by 8, since every 12 inches are equal to 1 foot and we need to find how many inches are in 8 feet.

[tex]12in=1ft[/tex]
[tex]8\times12=96[/tex]
[tex]=96in[/tex]

8 feet is equal to "96 inches."

Hope this helps.

-1248 -1248 -. 936

- 3432

Answer:6 rows per minute

Step-by-step explanation:

Add them and dividde by the number of numbers, which is 3.

112 + 109 + 115 = 336

336/3 = 112.

The average is 112.

Answer:

m = 3/4x + 4

I am not sure if this is what you are working on, hopefully this helps.

Answer:

1.[tex]\frac{24}{7}[/tex]
2.[tex]\frac{21}{6}[/tex]

Step-by-step explanation:

Given the following questions:

[tex]3\frac{3}{7} \\3\frac{5}{6}[/tex]

To convert mixed numbers into improper fractions we need to multiply the denominators by the whole numbers, and then add that answer to the numerator while of course keeping the denominator the same.

Question one:

[tex]3\frac{3}{7} \\3\frac{3}{7} =7\times3=21+3=24=\frac{24}{7} \\=\frac{24}{7}[/tex]

Question two:

[tex]3\frac{5}{6} \\3\frac{5}{6}=6\times3=18+3=21=\frac{21}{6} \\=\frac{21}{6}[/tex]

Your answers are "24/7, and 21/6."

Hope this helps.