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2 years ago

The 24 stundas the students, except 2 went bowling. What is the total cost each student who went bowling paid $5

Mathematics

1 answer:

mrs_skeptik [129]2 years ago

4 0

Answer:

$4.40

Step-by-step explanation:

you do 24=5x-2 so first you do 24-2 and u get 22 so then divide that by 5 since they each pay 5. then u end up with 4 dollars and 40 cents

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

2 years ago

Kyra was at soccer practice. she blocked 55% of the goals that were kicked at her during a team drill. ashley scored two of the

Minchanka [31]

Total kicks that were attempted = 40

Goals blocked by Kyra = 55%;

Goals which could not be blocked by Kyra = 100 - 55 = 45%

Goals made during team drill = 18

Let total kicks attempted be 'n';

Therefore;

(18/n) × 100 % = 45 %

18/n = 45/100;

n = 1800/45;

n = 40

To learn more about this; visit: brainly.com/question/18522423

#SPJ4

7 0

2 years ago

7.Sabrina wants to deposit $3,066 into savings accounts at three different banks: Bank of the US,

sweet-ann [11.9K]

The amount Sheila deposits in the Bank of US saving account is $511.

Sabrina has a total of $3,066 she wants to deposit. She has three banks that she wants to deposit her money in.

Let, a represent the amount she would deposit she would invest 7/4 bank.

The amount invested in Catch bank = 6 x a = 6a

The amount invested in Bank of US = 20% x ( 6a + a)

= 0.2 x 7a

= 1.4a

The total amount invested in the three banks can be represented with this equation:

1.4a + a + 6a = 3066

In order to determine the amount she would save in the Bank of US, the amount deposited in 7/4 bank has to be determined first.

8.4a = 3066

a = $365

The amount deposited in the Bank of US = 1.4a

= 1.4 x 365

= $511

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7 0

3 years ago

the difference of two number is 28 if the larger number is three time of the smaller find the number

Elza [17]

Set up an equation:

3x - x = 28

Simplify:

2x = 28

Divide both sides by 2

X = 14

3(14) = 42

The numbers are 42 and 14

5 0

3 years ago

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$