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3 years ago

In APQR, PQ- QR. If map

Mathematics

1 answer:

Hitman42 [59]3 years ago

7 0

Answer:

3x-120 = x - 30

2x -120 = -30

2x= 90

x= 45

3(45) -120 (plug x into angle p to check your answer)

135-120

15 degrees

45-30 (plug x into angle r to make sure it's the same thing as angle p)

15 degrees (they're equal so now figure out angle Q and answer the question)

180 - (15 +15)

180- 30

150 is the measure of angle Q

so, the triangle is an obtuse isosceles triangle

Step-by-step explanation:

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9) Tony the Tiger spent $95 on 5 sweaters that each cost the

Shalnov [3]

Answer:

5 sweaters cost = $95

1 sweater = $19

3 × 19 = 57

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3 years ago

Read 2 more answers

Find the inverse of the following function:

tigry1 [53]

First, we are going to find the inverse function of $f(x)$ by replacing $f(x)$ with $y$ , and then, interchanging $x$ and $y$ and solving for $x$ :
$y=-2 \sqrt{3x-1} -5$
$x=-2 \sqrt{3y-1} -5$
$-2 \sqrt{3y-1} =x+5$
$\sqrt{3y-1} = \frac{x+5}{-2}$
$3y-1=( \frac{x+5}{-2} )^{2}$
$3y=( \frac{x+5}{-2} )^{2} +1$
$y= \frac{( \frac{x+5}{-2})^{2}+1 }{3}$

Next we are going to evaluate our inverse function at $x= \frac{1}{3}$ :
$y= \frac{( \frac{ \frac{1}{3}+5 }{-2})^{2}+1 }{3}$
$y= \frac{( \frac{ \frac{16}{3} }{-2})^{2}+1 }{3}$
$y= \frac{(- \frac{8}{3})^{2}+1 }{3}$
$y= \frac{ \frac{64}{9}+1 }{3}$
$y= \frac{ \frac{73}{9} }{3}$
$y= \frac{73}{27}$

We can conclude that the inverse function of $f(x)=-2 \sqrt{3x-1} -5$ when $x= \frac{1}{3}$ is $\frac{73}{27}$

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3 years ago

Finn is swimming at a constant speed.

Reil [10]

Answer:

31.25 seconds

Step-by-step explanation:

Examine division

11.6 + 24.4 = 36 m < 50m

and 36 + 37.2 - 73.2m > 50m

50 - 36 = 14m

14 * 23.25/37.2 = 8.75 seconds

7.25 + 15.25 + 8.75 = 31.25 seconds

so it would take him 31.25 seconds to swim 50 meters.

6 0

2 years ago

Find the measures of the three angles, in radians, of the triangle with the given vertices: d(1,1,1), e(1,−5,2), and f(−2,2,7).

Oduvanchick [21]

Consider triangle DEF with vertices D(1,1,1), E(1,-5,2) and F(-2,2,7).

1. Find

$\overrightarrow{DE}=(1-1,-5-1,2-1)=(0,-6,1),\\ \\\overrightarrow{DF}=(-2-1,2-1,7-1)=(-3,1,6).$

Then

$\cos \angle D=\dfrac{0\cdot (-3)+(-6)\cdot 1+1\cdot 6}{\sqrt{0^2+(-6)^2+1^2}\cdot \sqrt{(-3)^2+1^2+6^2}}=\dfrac{0}{\sqrt{37} \cdot \sqrt{46} }=0.$

2. Find

$\overrightarrow{ED}=(1-1,1-(-5),1-2)=(0,6,-1),\\ \\\overrightarrow{EF}=(-2-1,2-(-5),7-2)=(-3,7,5).$

Then

$\cos \angle E=\dfrac{0\cdot (-2)+6\cdot 7+(-1)\cdot 5}{\sqrt{0^2+6^2+(-1)^2}\cdot \sqrt{(-3)^2+7^2+5^2}}=\dfrac{37}{\sqrt{37} \cdot \sqrt{83} }=\sqrt{\dfrac{37}{83}}.$

3. Find

$\overrightarrow{FE}=(1-(-2),-5-2,2-7)=(3,-7,-5),\\ \\\overrightarrow{FD}=(1-(-2),1-2,1-7)=(3,-1,-6).$

Then

$\cos \angle F=\dfrac{3\cdot 3+(-7)\cdot (-1)+(-5)\cdot (-6)}{\sqrt{3^2+(-7)^2+(-5)^2}\cdot \sqrt{3^2+(-1)^2+(-6)^2}}=\dfrac{46}{\sqrt{83} \cdot \sqrt{46} }=\sqrt{\dfrac{46}{83}}.$

$\angle E=\arccos0=\dfrac{\pi}{2},\\ \\
\angle D=\arccos\letf(\sqrt{\dfrac{37}{83}}\right)\approx 0.27\pi,\\ \\
\angle F=\arccos\letf(\sqrt{\dfrac{46}{83}}\right)\approx 0.23\pi.$

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3 years ago

A apple pie is 2 oz. for 9.99 what is the unit rate

lora16 [44]

1 oz is 5 dollars rounded.

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