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2 years ago

AFD=114 AFB=31 WHAT DOSE AFE=

1 answer:

7 0

The diagram looks really off, so I'm assuming ( ( and (( (( are equal.

First off, AFD is 114 degrees, and is split into three angles, two of them being equal to 31 (AFB and CFD = (( ) and the other one needed to be found.

114 = 2(31) + x
114 = 62 + x
52 = x

Therefore, (( is 52 degrees. Now since AFE has two (( and two (, use this expression to find AFE.

52(2) + 31(2)
104 + 62
166

Therefore, AFE is equal to 166 degrees.

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The cable company charges $30 to install new supplies at your house. Each month the cable bill is $75. Which equation models the

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Equation: $30+$75m
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1 year ago

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The population of Champaign, Illinois is given for three years in the table below:

Crazy boy [7]

Answer:

See below

Step-by-step explanation:

a) Using the first two lines to get the equation:

Since t = 0 represents a start point, the y-intercept is 163488

Slope is:

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And the equation:

P(t) = 490.4(t - 1970) + 163488

b) Prediction of the population in 2012 using the function:

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As we see the number we got is less than the one on the line 3 of the table. So the model underestimated the actual population.

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1 year ago

A high school wants to sell postage stamps with the school logo on them. The fundraising group have purchased 500 sheets of stam

erma4kov [3.2K]

Answer:

a) Cost

$C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050$

b) Sales income

$S(q)=20q\\\\S(500)=20\cdot 500 = 10,000$

c) Table of values

$\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]$

d) Attached

e) Breakeven point = 12.5 sheets

f) Profit at 550 sheets = $1,950

Step-by-step explanation:

a) We have a fixed cost for the image, at $50.

We also have a variable cost of $16 a sheet.

The purchased quantity is 500 sheets.

Then, the cost function is:

$C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050$

b) The price for each sheet is $20, so the income from sales are:

$S(q)=20q\\\\S(500)=20\cdot 500 = 10,000$

c) Table of values

$\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right]$

d) Attached

e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:

$S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5$

f) This profit can be calculated as the difference between the sales income and the cost:

$P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950$

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1 year ago

What are the zeros of the quadratic function f(x) = 2x2 + 16x – 9?

Tamiku [17]

$2x^{2} +16x - 9 = 0

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1 year ago

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Given: KL ║ NM , LM = 45, m∠M = 50° KN ⊥ NM , NL ⊥ LM Find: KN and KL

Mice21 [21]

Answer:

$KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08\\ \\KN=45\sin 50^{\circ}\approx 34.47$

Step-by-step explanation:

Given:

KL ║ NM ,

LM = 45

m∠M = 50°

KN ⊥ NM

NL ⊥ LM

Find: KN and KL

1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

LM = 45

m∠M = 50°

So,

$\tan \angle M=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{NL}{LM}=\dfrac{NL}{45}\\ \\NL=45\tan 50^{\circ}$

Also

$m\angle LNM=90^{\circ}-50^{\circ}=40^{\circ}$ (angles LNM and M are complementary).

2. Consider triangle NKL. This is a right triangle, because KN ⊥ NM . In this triangle,

$NL=45\tan 50^{\circ}$

$m\angle KLN=m\angle LNM=40^{\circ}$ (alternate interior angles)

$m\angle KNL=90^{\circ}-40^{\circ}=50^{\circ}$ (angles KNL and KLN are complementary).

So,

$\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08$

and

$\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47$

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1 year ago

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