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4 years ago

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options.

Mathematics

1 answer:

Margarita [4]4 years ago

3 0

Answer:

m∠CEA = 90°

∠CEF is a straight angle.

∠AEF is a right angle

Step-by-step explanation:

Took the test

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Lee's summer job was to sell newspapers. He sold 24 in the morning. In the afternoon, he sold 2/7 of the remaining newspapers. T

EastWind [94]

Sorry, but I can only see the algebra way

in the morning, he sold 24 plus 2/7 of what he had left
what he had left was all-24

2/7 of left was sold
5/7of the ones left=1/2 of all
2/7 of left+24=1/2 of all
therefor
5/7 of the ones left=2/7 of the ones left+24
minus 2/7 of left fro mboth sides
3/7 of the ones left=24
divide both sides by 3
1/7 of the ones left=8
times 7 both sides
ones left=56

left+24=1/2 of all
56+24=1/2 of all
80=1/2 of all
times 2
160=all

he had 160 to start with

3 0

3 years ago

The radius of a right circular cylinder is increasing at a rate of 9 inches per minute and the height is decreasing at a rate of

pav-90 [236]

Answer:

$\frac{dA}{dt}=1840.97 in^{2}/min$

Step-by-step explanation:

The equation of the surface of the right circular cylinder is:

$A=2\pi rh+2\pi r^{2}=2\pi(rh+r^{2})$

Now, the rate change of this area will be:

Using the change rule

$\frac{dA}{dt}=\frac{\partial A}{\partial r}\frac{\partial r}{\partial t}+\frac{\partial A}{\partial h}\frac{\partial h}{\partial t}$

Where:

$\frac{\partial h}{\partial t}$ is the rate change of height (-16 in/min)
$\frac{\partial r}{\partial t}$ is the rate change of radius (9 in/min)

$\frac{dA}{dt}=\frac{\partial A}{\partial r}9+\frac{\partial A}{\partial h}(-16)$

$\frac{dA}{dt}=2\pi(h+2r)9-2\pi r16=2\pi((h+2r)9-16r)$

Now, r = 16 and h = 29

$\frac{dA}{dt}=2\pi((29+2*16)9-16*16)$

$\frac{dA}{dt}=1840.97 in^{2}/min$

I hope it helps you!

8 0

4 years ago

Amelia receives two dozens roses for her birthday. 18 of the roses are pink what percent of the roses are pink

ollegr [7]

18/24 = pink roses... 75% of the roses are pink.

4 0

3 years ago

a person invested $6700 for one year, part at 8%, part at 10%, and the remainder at 12%. the total annual income from these inve

lukranit [14]

Answer:

The amount invested at 8% rate is $1,200

The amount invested at 10% rate is $2,000

The amount invested at 12% rate is $3,500

Step-by-step explanation:

step 1

Let

x-----> the amount invested at 8% rate

y-----> the amount invested at 10% rate

z-----> the amount invested at 12% rate

$z=(x+y)+300$ ----> equation A

$x+y+z=6,700$ ----> equation B

substitute equation A in equation B

$x+y+(x+y+300)=6,700$

$2x+2y=6,400$

$x+y=3,200$ -----> equation C

we know that

The simple interest formula is equal to

$I=P(rt)$

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=1\ year\\ P=\$6,700\\ I=\$716$

substitute in the formula above

$716=x(0.08)+y(0.10)+z(0.12)$

substitute equation A

$716=x(0.08)+y(0.10)+(x+y+300)(0.12)$

$716=0.08x+0.10y+0.12x+0.12y+36$

$716=0.20x+0.22y+36$

$0.20x+0.22y=680$ -----> equation D

step 2

Solve the system of equations

x+y=3,200 -----> equation C

$0.20x+0.22y=680$ -----> equation D

Solve the system by graphing

The solution is the point (1,200,2,000)

see the attached figure

Find the value of z

$z=(x+y)+300$

$z=(1,200+2,000)+300=3.500$

therefore

The amount invested at 8% rate is $1,200

The amount invested at 10% rate is $2,000

The amount invested at 12% rate is $3,500

8 0

4 years ago

Arley’s Bakery makes fat-free cookies that cost $1.50 each. Arley expects 30% of the cookies to fall apart and break. Assume tha

Lesechka [4]

First we see the cost of making 200 cookies:
(200) * (1.50) = 300 $
Then, we see the amount of cookies that are not broken:
(200) * (0.30) = 60
200-60 = 140
Arley wants to 50% markup on cost and produces 200 cookies:
(300) * (1.50) = 450 $
Arley can sell the broken cookies for $ 1.40 each:
(1.40) * (60) = $ 84
For each unbroken cookie the price will be then:
(450-84) / (140) = 2.61 $
Answer:
Arley should charge $ 2.61 for each unbroken cookie

6 0

4 years ago