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Svetradugi [14.3K]
2 years ago
13

Courtney works at the local shoe store and receives $150 a week plus 3% of all sales over $1000. This week her sales were $3200.

Find her commission using composition of two functions; then find her total earnings for the week.
f (x) = g (x) =
Will you use f(g(x)) or g(f(x)) to solve for the commission?
Solve for the commission using the composition of two functions below:
The commission of sales will be:
Courtney’s total earnings for the week will be:
Mathematics
1 answer:
schepotkina [342]2 years ago
6 0

The equation you would use to find her earning for the week would be:

y=0.03(x-1000)+150

This would mean she made $66 from commissions and $216 total.

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What are the similarities and differences between comparing whole numbers and decimals
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Analyze the diagram to complete the statements. The m∠MXN is the m∠YZX. The m∠LZX is the m∠ZYX + m∠YXZ. The m∠MYL is 180° − m∠ZY
Xelga [282]

By using the picture that was provided below, you can see that

m<MXN is greater than m<YZX.  

Angles m<LZX is equal to m<ZYX + m<YZX and

m<MYL is equal to 180 degrees minus M<ZYX.


I hope this helps! Have a good day


8 0
2 years ago
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An ostrich can run 6 mph faster than a giraffe. An ostrich can run 7 miles in the same time that a giraffe can run 6 miles. Find
LUCKY_DIMON [66]

NOTE THIS IS AN EXAMPLE:

Let t = time, s = ostrich, and g = giraffe.

Here's what we know:

s = g + 5 (an ostrich is 5 mph faster than a giraffe)

st = 7 (in a certain amount of time, an ostrich runs 7 miles)

gt = 6 (in the same time, a giraffe runs 6 miles)

 

We have a value for s, so plug it into the first equation:

(g + 5)t = 7

gt = 6

 

Isolate g so that we can plug that variable value into the equation:

g = 6/t

so that gives us:

(6/t + 5)t = 7

Distribute:

6 + 5t = 7

Subtract 6:

5t = 1

Divide by 5:

t = 1/5 of an hour (or 12 minutes)

 

Now that we have a value for time, we can plug them into our equations:

1/5 g = 6

multiply by 5:

g = 30 mph

 

s = 30 + 5

s = 35 mph

 

Check by imputing into the second equation:

st = 7

35 * 1/5 = 7

7 = 7

5 0
2 years ago
An isosceles triangle ABC with the base BC is inscribed in a circle. Find the measure of angles of it, if measure of arc BC = 10
Usimov [2.4K]

Answer:

The measures of the angles of the triangle are 51° , 64.5° , 64.5°

OR

The measures of the angles of the triangle are 129° , 25.5° , 25.5°

Step-by-step explanation:

* Lets explain the meaning of the inscribed triangle in a circle

- If a triangle inscribed in a circle, then the vertices of the triangle lie

 on the circumference of the circle and each vertex is an inscribed

 angle in the circle subtended by the opposite arc

- Fact in the circle the measure of the inscribed angle is 1/2 the

 measure of its subtended arc

* Now lets solve the problem

- Δ ABC is an isosceles with the base BC

∴ AB = AC

∴ m∠B = m∠C

- Δ ABC is inscribed in a circle

∴ ∠A is inscribed angle subtended by arc BC (minor or major)

# The measure of the minor arc is less than 180° and the measure of

  the major arc is greater then 180° and the sum of the two arcs

  equals the measure of the circle which is 360°

∴ ∠B subtended by arc AC

∴ ∠C subtended by arc AB

∵ The measure of the arc BC = 102°

- There is two cases in this question

(1) If the angle A subtended by the minor arc BC

(2) If the angle A subtended by the major arc BC

- Lets solve case (1)

∵ ∠A is an inscribed angle subtended by the minor arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the arc BC is 102°

∴ m∠A = 1/2 × 102 = 51°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 51 + m∠B + m∠C = 180° ⇒ subtract 51 from both sides

∴ m∠B + m∠C = 129°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 129/2 = 64.5°

* The measures of the angles of the triangle are 51° , 64.5° , 64.5°

- Lets solve case (2)

∵ ∠A is an inscribed angle subtended by the major arc BC

∴ m∠A = 1/2 the measure of the arc BC

∵ The measure of the minor arc BC is 102°

∵ The measure of the circle is 360°

∴ The measure of the major arc = 360 - 102 = 258°

∴ m∠A = 1/2 × 258 = 129°

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠A + m∠B + m∠C = 180°

∴ 129 + m∠B + m∠C = 180° ⇒ subtract 129 from both sides

∴ m∠B + m∠C = 51°

∵ m∠B = m∠C ⇒ isosceles Δ

∴ m∠B = m∠C = 51/2 = 25.5°

* The measures of the angles of the triangle are 129° , 25.5° , 25.5°

4 0
2 years ago
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