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3 years ago

8

A protractor is used to measure an angle. One ray points to 0° and the other ray points to 125° and 75°. What is the measure of

the angle if we know it is an acute angle?

1 answer:

Amiraneli [1.4K]3 years ago

6 0

It would be 75° because we know it is an acute angle, and an acute angle is an angle less than 90°

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a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers starte

ankoles [38]

Answer:

<em>Worker B needs 9 days to finish the rest of the work</em>

Step-by-step explanation:

<u>Proportions</u>

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

$\frac{1}{12}+\frac{1}{16}=\frac{7}{48}$

After 3 days they have completed:

$3*\frac{7}{48}=\frac{7}{16}$

parts of the project, this means it still remains:

$1-\frac{7}{16}=\frac{9}{16}$

parts of the project and it is done by B alone. Since B does $\frac{1}{16}$ per day, he now takes

$\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9$

days to complete the project.

Worker B needs 9 days to finish the rest of the work

4 0

3 years ago

ΔEFG is located at E (0, 0), F (−7, 4), and G (0, 8). Which statement correctly classifies ΔEFG?

MariettaO [177]

Answer:

ΔEFG is an isosceles triangle.

Step-by-step explanation:

Given:

E (0, 0),

F (−7, 4),

G (0, 8)

ΔEFG

Solution:

Distance formula

Distance d = $\sqrt{(x_2-x_1)^2 +( y_2-y_1)^2$

Step 1: Finding the length of EF

By using distance formula,

$EF = \sqrt{(-7 - 0)^2 + (4-0)^2}$

$EF = \sqrt{(49) + (16)}$

$EF = \sqrt{(49) + (16)}\\EF = \sqrt{65}\\$

Step 2: Finding the length of FG

By using distance formula,

$FG = \sqrt{(0-(-7))^2+(8-4)^2}\\FG = \sqrt{(7)^2 +(4)^2}\\FG = \sqrt{49 +16}\\FG = \sqrt{65}$

Step 2: Finding the length of GE

$GE= \sqrt{(0-0)^2 + (0-8)^2}\\\\GE =\sqrt{(-8)^2}\\GE = \sqrt{64}\\GE = 8$

Thus we could see that the sides EF = FG

So it is a isosceles triangle.

6 0

2 years ago

Explain how to find the vertex of 2x^2+12x+16

Elina [12.6K]

The vertex form:

$y=a(x-h)^2+k\\\\(h,\ k)-vertex$

Use $(a+b)^2=a^2+2ab+b^2\qquad(*)$

$2x^2+12x+16=2(x^2+6x)+16=2(x^2+2(x)(3))+16\\\\=2(\underbrace{x^2+2(x)(3)+3^2}_{(*)}-3^2)+16=2((x+3)^2-9)+16\\\\=2(x+3)^2+(2)(-9)+16=2(x+3)^2-18+16\\\\=\boxed{2(x-(-3))^2-2}\to h=-3,\ k=-2$

<h3>Answer: (-3, -2).</h3>

Other method:

$f(x)=ax^2+bx+c\\\\vertex:(h,\ k)\\\\h=\dfrac{-b}{2a},\ k=f(h)$

We have

$f(x)=2x^2+12x+16\\\\a=2,\ b=12,\ c=16$

Substitute:

$h=\dfrac{-12}{(2)(2)}=\dfrac{-12}{4}=-3\\\\k=f(-3)=2(-3)^2+12(-3)+16=2(9)-36+16=18-36+16=-2$

<h3>Answer: (-3, -2).</h3>

5 0

3 years ago

A jar contains jelly beans, and there are 87 pink, 74 purple, 35 white, 70 black, 25 orange, and 47 green. if two jelly beans ar

balu736 [363]

$\frac{2}{338}$

7 0

3 years ago

Round to the nearest cent<br><br> $1.6845

vova2212 [387]

Answer:

$1.68

Step-by-step explanation:

Remember that cents are in the hundredths place. So think of it as rounding to the nearest hundredth place. 1.6845 ---> 1.68

5 0

2 years ago

Read 2 more answers