Identify the angle relationship and find the measure of the indicated angle.

(Alternate Interior, Alternate Exterior, Corresponding, Same-side Interior)

Answer-  A) 59,600 ; B) 4.12% per year.

Explanation

84,200 minus 24,600 is 59,600. This means the originally cost put into the account was 59,600.

Next we have to divide the amount of interest earn into the number of years that the amount was accumulated. 24,600 divided by 10 is 2460. This means that each year 2,460 were earned in interest. 59,600 divided into 2,460 is 0.0412751678. This rounds to .0412 If we move our decimal to a percentage this leaves us with 4.12% This means that annual interest on the investment is 4.12%

Hope this helps! Good Luck!

Answer:

========================

Let the weekly salary is x.

Since both options end up with same amount, it can be shown as:

The matching choice is C.

The unit price of the pair of gloves is $6.59

The package contains 4 pairs of insulated gloves costs ​$26.36.

The unit price of the pairs of gloves can be found as follows:

Unit price is the price at which a single quantity of a product is being sold.

Therefore, the unit price is the price of a single pair of gloves.

Hence,

unit price of the pair of gloves = total price / number of pairs of gloves

where

Therefore,

unit price of the pair of gloves = 26.36 / 4

unit price of the pair of gloves = $6.59

Therefore, the unit price of the pair of gloves is $6.59

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The amount of money that Gary can withdraw each month is equal to $4026.18.

Given the following data:

APR is an acronym for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

This ultimately implies that, the annual percentage rate (APR) would be calculated by dividing the rate of interest by twelve (12).

Rate of interest, r = APR/12

Rate of interest, r = 0.05/12

Rate of interest, r = 0.0041667

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-nt}]/r]

Substituting the given parameters into the formula, we have;

Present value = [750,000 ÷ [(1 - (1 + 0.0041667)^{-30 × 12})/0.0041667]

Present value = [750,000 ÷ [(1 - (1.0041667)^{-360})/0.0041667]

Present value = [750,000 ÷ [(1 - 0.2238239)/0.0041667]

Present value = [750,000 ÷ [0.7761761/0.0041667]

Present value = 750,000 ÷ 186.280773754

Present value, PV = $4026.18.

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The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).

Given,

25 + 35.

We need to find its GCF and another sum.

It is the greatest factor common to both 25 and 35.

Example: 8 and 24

- 4 x 2 = 8

- 4 x 6 = 24

4 is the GCF.

Find the GCF of 25 and 35.

5 x 5 = 25

5 x 7 = 35

5 is the GCF of 25 and 35.

Now,

25 + 35 = 60

5 x ( 5 + 7 ) = 5 x 12 = 60

The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 )

Thus,

The sum of the numbers as a product of their GCF is 5 x ( 5 + 7 ).

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Answer:

[tex]{ \tt{ \frac{dy}{dx} = yx( x + 3)}} \\ \\ { \tt{ \frac{dy}{y} = \frac{x(x + 3) \: dx}{1} }} \\ \\ { \tt{ \int \frac{dy}{y} = \int( {x}^{2} + 3x) \: dx }} \\ \\ { \tt{ ln(y) = \frac{ {x}^{3} }{3} + \frac{ {3x}^{2} }{2} + c }} \\ \\ [/tex]

The equation of a line which is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1) will be [(4y + x) = 2].

As per the question statement, a line is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1).

We are required to determine the equation of the above mentioned line.

Now, we know that, the standard equation of a line goes as [y = (mx + c)] where, "m" is the slope of the line while "c" is the y-intercept.

Comparing [y = (4x - 11)] to the standard form, we can identify that (m = 4), i.e., slope of the given line is 4.

Since the products of the slopes of two perpendicular lines is (-1), and considering the slope of our required line to be "m₁", we can say that,

[tex]4*m_{1}=(-1)\\ or,m_{1}=\frac{-1}{4}[/tex]...[since our required line is perpendicular to [y = (4x - 11)]

                        and slope of [y = (4x - 11)] is 4]

That is, slope of our required line is [tex](\frac{-1}{4})[/tex].

Another concept we need to know about forming the equation of a line is that, the equation of a line can be written as  [tex][(y-y_{1})=m(x-x_{1})][/tex], if the line passes through the point (x₁, y₁).

Here, our concerned line passes through the point (-2, 1) and has a slope of [m =  [tex](\frac{-1}{4})[/tex]].

Therefore, equation of our concerned line can be written as

[tex](y-1)=(\frac{-1}{4})[x-(-2)]\\or,(y-1)=(\frac{-1}{4})(x+2)\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{4}*2)\\ or,(y-1)=(\frac{-x}{4})+(\frac{-1*2}{4})\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+1+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+(1-\frac{1}{2})\\or, y=(\frac{-x}{4})+\frac{1}{2}\\or,4y=(-x)+2\\or,4y+x=2[/tex]

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(-7/5) is the multiplicative inverse of the number - 5/7.

The answer to the question is (b/a), which is the multiplicative inverse of the fraction number that is (a/b).

So, according to the question:

The reciprocal of (-5/7) is (-7/5).

As a result, (-7/5) is the right response to a multiplicative inverse.

The reciprocal of the supplied integer can be used to establish a number's multiplicative inverse. The denominator must not be 0 in order for a multiplicative inverse to exist. And the result of the multiplication should be 1.

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Answer:

12, 12, and 12

Step-by-step explanation:

12 is an even integer, and 12 + 12 + 12 = 36, so it would be logical for 12 to be the unknown integer.

Answer:

u= 55/17

Step-by-step explanation:

Answer:

Step-by-step explanation:

u/11=5/17 so cross multiplication, 17u=5*11, 17u=55, so u =55/17

The difference between the distances flown by these birds is 150 Km.

According to the statement

We have to find that the rate of each birds speed in kilometers per hour.

So, For this purpose, we know that the

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the given information:

We have the graph given within the question to understand it please see the image below.

We have to search out the difference within the distances flown by these two birds after 3 hours of flight.

According to the question -

The slope of the road is -

m = 400/5 = 80

The y - intercept of the road is 0.

Therefore  c = 0.

Therefore, the equation of the road are -

y = 80x

The distance covered by Bird 1 is

D[1] = initial distance + 80 x 3 = 250 + 240 = 490 Km.

And

The distance covered by Bird 2 is

D[2] = initial distance + 80 x 3 = 400 + 80 x 3 = 400 + 240 = 640 Km.

Then

difference between the distances flown by these birds is D[2] - D[1] = 640 - 490 = 150 Km.

Therefore, The difference between the distances flown by these birds is 150 Km.

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The initial amount and rate of change given a table for a linear function are $65 and $86, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 476) and (10, 736)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (736 - 476)/(10 - 6)

Evaluate

Rate = 65

This means that the rate of change is $65

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 65

So, we have

y = 65(x - x1) + y1

Using one of the points, we have

y = 65(x - 6) + 476

Set x = 0

So, we have

y = 65(0 - 6) + 476

Evaluate

y = 86

Hence, the initial amount and rate of change given a table for a linear function are $65 and $86, respectively

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What is the 10% of number in which the 14% is 160

Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it. A% is a number that has neither dimensions nor a defined unit of measurement.

being that,

14% × x = 160

14/100 × x = 160

x = 160 × 100/14

x = 1142.86

The current value is 1142.86.

10% of the total number must be located.

to say,

10% x 1142.86 = 10 / 100 x 1142.86

= 114.286

Consequently, 114.286 is the value of the 10% of the number.

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Answer:

sec 30° + cos 30°

Important trigonometric values

Calculation:

sec 30° + cos 30°

⇒ 2/√3 + √3/2

⇒ (4 + 3)/2 √3

⇒ 7√3/6

∴ 7√3/6

Answer:

x = 10

Step-by-step explanation:

Answer:

Hope this helps

Step-by-step explanation:

350*.06=21

annually 21*7=147

quarterly 21(4*7)=588

monthly 21(12*7)=1764

Based on the definition of complementary angles, the measure of the other angle, to 1 decimal place, is: 31.4°.

If the sum of two angles equals 90 degrees, they are called complementary angles.

Given:

One angle = 58.6ﾟ

The second angle = 90 - 58.6

The second angle = 31.4°.

Therefore, based on the definition of complementary angles, the measure of the other angle, to 1 decimal place, is: 31.4°.

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a and b are vertically opposite angle ...

☘☘☘...

In linear equation , The company which has the best buy is company C, they sell 1 lion for $2.77 (highest selling price among the three companies.

What in mathematics is a linear equation?

Company A = 16 lions for $45.60

Price per lion = $45.60 / 16

= $2.85

Company B = 18 lions for $50.76

Price per lion = $50.76 / 18 eagles

= $2.82

Company C = $34.44 for 12 lion

Price per lion = $34.44 / 12 lion

= $2.87

The company which has the best buy is company C, they sell 1 lion for $2.87 (highest selling price among the three companies)

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Answer

5.6967 rounded up will be 5.697.

Step-by-step explanation:

Answer:

vhdvbhahshsh

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Hello,

[tex]\boxed{-4} - 3 = - 7[/tex]

Answer:

-7/18

Step-by-step explanation:

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.

( -1/2 × 9/9) + (1/9 × 2/2) = ?

Complete the multiplication and the equation becomes:

-9/18 + 2/18 = ?

Then:

-9+2/18 = -7/18

Therefore:

-1/2 + 1/9 = -7/18

Given the perimeter, the length and width of the rectangular planter bed are 35ft and 11ft respectively.

The perimeter of rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

Let 'x' represent the width of the rectangle.

Plug the given values into the above above equation.

P = 2( l + w )

92 = 2( ( 3x + 2 ) + x )

Solve the equation for x.

92 = 2( ( 3x + 2 ) + x )

92 = 6x + 4 + 2x

92 = 8x + 4

8x = 92 - 4

8x = 88

x = 88/8

x = 11

Hence;

Width of the rectangular planter bed = x = 11ft

Length of the rectangular planter bed = 3x+2 = 3(11) + 2 = 33 + 2 = 35ft

Given the perimeter, the length and width of the rectangular planter bed are 35ft and 11ft respectively.

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The correct option is option C.

T(x) = 2.9(1.05)⁴ˣ ⁺ ⁵

Given the number of cities in a region is represented by the function:

C(x) = 2.9(1.05)ˣ

The approximate number of people per city is represented by the function P(x) = (1.05)³ˣ⁺⁵

we are asked to determine T(x), the approximate population in the region = ?

combine C(x) and P(x)

therefore, T(x) = C(x)P(x)

T(x) = 2.9(1.05)ˣ(1.05)³ˣ⁺⁵

During multiplication, when bases are same then powers are added.

T(x) = 2.9(1.05)³ˣ⁺ˣ⁺⁵

T(x) = 2.9(1.05)⁴ˣ⁺⁵

Hence we get the approximate function of T(x) as T(x) = 2.9(1.05)⁴ˣ⁺⁵

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The 12th term in the sequence is -26.

Given,

B (n) = -4 – 2(n – 1)

We have to find the 12th term in the sequence:

To find the nth term in an arithmetic sequence:

An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d. The common difference, or d, is the difference between any two consecutive terms in an arithmetic series; it can be calculated by deducting any pair of terms starting with a and an+1.

Here,

First term, a = -4

Common difference, d = -2

nth term = 12

Now, let’s find 12th term

B(n) = -4 -2(n – 1)

B(12) = -4 – 2(12 – 1)

B(12) = -4 -2(11)

B(12) = -4 -22

B(12) = -26

That is, the 12th term in the sequence is -26.

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The amount of money left with them is $12,800.

The first step is to determine the amount left after 1/4 of the budget is spent on food stalls.

Budget left : (1 - 1/4) x amount of budget

(1 - 1/4) x 32,000

3/4 x 32,000 = 24,000

The second step is to determine how much of the budget is left after spending on games and activities :

(1 - 3/10) x 24,000

7/10 x 24,000 = 16,800

The third step is to determine how much is left after spending the remainder on gift distribution

(1 - 5/21) x 16,800

16/21 x 16,800 = $12,800

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