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alukav5142 [94]
3 years ago
7

Angles θ and φ are complementary, and θ = find the measure of φ.

Mathematics
1 answer:
IRINA_888 [86]3 years ago
4 0
The angles are complementary if and only if the sum of their measures is equal to 90 degrees. If one of the angles measures θ then, the measurement of the other one should be expressed through the equation,
                                            φ = 90 - θ
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What is the sum of a geometric series Sn=a+ar+ar2+ar3+…+arn-2+arn-1?
algol13

Answer:

Sn= \frac{a(1-r^n)}{1-r}

Step-by-step explanation:

A geometric sequence is a sequence such that any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r. The common ratio (r) is obtained by dividing any term by the preceding term.

from the given expression

the given data are

first term a1= a

second term a2= ar

third term a3= ar^2

the common ratio  is expressed as r=\frac{a2}{a1}= \frac{ar}{a} = r

Sum of Terms in a Geometric Progression

Finding the sum of terms in a geometric progression is easily obtained by applying the formulas:

Sn= \frac{a1(1-r^n)}{1-r}

nth partial sum of a geometric sequence substituting the values of a1=a and the common ratio= r we have

Sn= \frac{a(1-r^n)}{1-r}

4 0
3 years ago
A store owner estimates that by charging x dollars each for a certain lamp, he can sell 25 - x lamps each week. What price will
erma4kov [3.2K]

Answer:

\frac{25}{2} or 12.5

Step-by-step explanation:

So if 25 - x items are sold, and they each cost x, we can write an equation for the revenue to be

y = (25 - x)x

The vertex of this equation will represent the maximum revenue.  So we need to write this equation in vertex form so we can find the vertex.

Vertex from is

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

where (h,k) represent the vertex.

the vertex form of this equation would be

y= -(x-\frac{25}{2} )^{2} +\frac{625}{4}

And the vertex would be

(\frac{25}{2} ,\frac{625}{4})

This means the maximum revenue will occur when x = 25/2

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Answer:

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Step-by-step explanation:

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3 years ago
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Parallelogram PARL is similar to parallelogram WXYZ. If AP= 15, PL=25, and WZ= 75, Find the value of c.
julia-pushkina [17]

The value of c in the parallelogram is 45

<h3>How to determine the value of c?</h3>

From the question, we have the following parameters:

  • Parallelogram PARL is similar to parallelogram WXYZ.
  • AP = 15, PL = 25, and WZ= 75

To calculate the value of c, we make use of the following equivalent ratio.

AP : PL = XW : WZ

Substitute the known values in the above equation

15 : 25 = c : 75

Express the above equivalent ratio as fractions

15/25 = c/75

Multiply both sides of the equation by 75

75 * 15/25 = c/75 * 75

Evaluate the product

75 * 15/25 = c

Evaluate the product

1125/25 = c

Evaluate the quotient

45 = c

Rewrite the equation as

c = 45

Hence, the value of c in the parallelogram is 45

Read more about similar parallelograms at

brainly.com/question/10713530

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2 years ago
Twelve buses bring a total of 420 people to The Alhambra in Gramada,
yawa3891 [41]

Answer:

35 people

Step-by-step explanation:

This means we have to do 420/12, or 70/2. This is 35, so there are 35 people on each bus.

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4 years ago
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