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3 years ago

9

There are 53 students on the school basketball team. the number of 8th graders is 15 fewer than 3 times the number of 7th grader

s. how many 7th graders are there?

1 answer:

White raven [17]3 years ago

5 0

Answer:

17 7th graders

Step-by-step explanation:

grd 8 is x, grd 7 is y

x+y=53

x=3y-15

use substitution: (3y-15)+y=53

4y-15=53

4y=68

y=17

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Can someone help me with this

SashulF [63]

Answer:

$\angle NRQ =85 \degree$

Given:

$\angle RPQ = 45 \degree \\ \angle PQR = (6x + 4)\degree \\ \angle NRQ = (15x - 5)\degree$

Step-by-step explanation:

Property used: <em>An exterior angle of a triangle is equal to the sum of the opposite int</em><em>e</em><em>rior angles.</em>

<em> $= > \angle RPQ + \angle PQR = \angle NRQ \\ \\ = > 45 \degree + (6x + 4)\degree = (15x - 5)\degree \\ \\ = > 45\degree + 6x\degree + 4\degree = 15x\degree - 5\degree \\ \\ = > 49\degree + 5 \degree= 15x\degree - 6x\degree \\ \\ = > 54\degree = 9x\degree \\ \\ = > 9x\degree = 54\degree \\ \\ = > x\degree = (\frac{54}{9} )\degree \\ \\ = > x\degree = 6\degree \\ \\ Putting \: value \: of \: x \: in \: \angle NRQ \\ \\ = > \angle NRQ = (15x - 5)\degree \\ \\ = > \angle NRQ = (15 \times 6 - 5) \degree \\ \\ = > \angle NRQ =85 \degree$ </em>

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2 years ago

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Wittaler [7]

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Step-by-step explanation:

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2 years ago

The function f(x) = x5 + (x + 3)2 is used to create this table. A 2-column table with 4 rows. The first column is labeled x with

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Step-by-step explanation:

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3 years ago

Read 2 more answers

It takes four painters working at the same rate 1.25 work-days to finish a job. If only three painters are available, how many w

laila [671]

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.9375 days

Step-by-step explanation:

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3 years ago

Find f(g(x)). State the domain of the composite function.<br> f(x) = 3x-2/x+1<br> g(x) = x+5/2x-3

AnnyKZ [126]

Answer:

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

$g(x)=\dfrac{x+5}{2x-3}\Longrightarrow 2x-3\neq 0\iff \boxed{x\neq\dfrac{3}{2}}$

- Domain of f(g(x)): We'll find its expression:

$f(x) = \dfrac{3x-2}{x+1}\\\\f(g(x)) = \dfrac{3g(x)-2}{g(x)+1}\\\\f(g(x)) = \dfrac{3\cdot\dfrac{x+5}{2x-3}-2}{\dfrac{x+5}{2x-3}+1}=\dfrac{~~~\dfrac{3(x+5)-2(2x-3)}{2x-3}~~~}{\dfrac{(x+5)+(2x-3)}{2x-3}}\\\\f(g(x)) =\dfrac{3(x+5)-2(2x-3)}{(x+5)+(2x-3)}=\dfrac{3x+15-4x+6}{x+5+2x-3}\\\\\boxed{f(g(x)) =\dfrac{21-x}{3x+2}}$

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

$f(g(x)) =\dfrac{21-x}{3x+2}\Longrightarrow 3x+2\neq0\iff \boxed{x\neq-\dfrac{2}{3}}$

Lastly, we may write the domanin of f(g(x)):

$D(f(g(x)) = \left]-\infty,-\dfrac{2}{3}\right[\cup\left]-\dfrac{2}{3},\dfrac{3}{2}\right[\cup\left]\dfrac{3}{2},\infty\right[$

or, just writing in a shorter way:

$\boxed{D(f(g(x)) = \mathbb{R}-\left\{-\dfrac{2}{3},\dfrac{3}{2}\right\}}$

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2 years ago