3 years ago

Determine the measure of the interior angle at vertex F

Mathematics

1 answer:

algol [13]3 years ago

7 0

The answer is a, i hope this helps

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3 years ago

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irinina [24]

Answer:

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Step-by-step explanation:

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2 years ago

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:

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

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3 years ago

Write each fraction as a unit fraction 12/84 13/143 23/138

alexandr1967 [171]

A unit fraction is a fraction whose numerator is 1.

$\frac{12}{84}=\frac{12 \div 12}{84 \div 12}=\frac{1}{7} \\ \\
\frac{13}{143}=\frac{13 \div 13}{143 \div 13}=\frac{1}{11} \\ \\
\frac{23}{138}=\frac{23 \div 23}{138 \div 23}=\frac{1}{6}$

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3 years ago

4 1/3 · 3/5 express your answer in simplest form. A. 2 3/5 B. 2 C. 4 1/5 D. 1 1/15

a_sh-v [17]

Oh the answer is a I looked it up this time

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3 years ago

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