Given: <1 and <2 are complementary. <1 and <3 are complementary

Prove: 22 = 23
Complete the proof.

Answer:

a) 6.2%
b) £13,687

Step-by-step explanation:

a)

To find the rate of interest, we first find the interest itself.
£7965.00 - £7500.00 = £465.00
Using this, we find the rate of interest in percentage as a fraction of the original loan.

(£7500.00 ÷ £465.0) × 100 = 6.2%

Thus, the rate of interest is 6.2%.

b)
Compound interest is found using the formula
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
Where

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

Thus, with an initial balance of £7500, an interest rate of 6.2% and a time period of 10 years, calculated per annum, we can plug the numbers into the formula, giving us

[tex]A = 7500(1 + \frac{6.2}{100})^{10}[/tex]
   [tex]=[/tex] £13,686.94
   ≈ £13,687 (to nearest £1)

Some things to note: number of time periods elapsed mean the amount of times it is compounded; if the question says compounded quarterly for 3 years, t = 12 as it is compounded 4 times a year for 3 years, giving is 12 time periods. This also applies to monthly, bi-weekly etc.

Answer:

  -425

Step-by-step explanation:

You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.

The sum is given by the formula ...

  Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio

The sum of 8 terms of the given series is ...

  S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425

The sum of 8 terms is -425.

The measure of angle 4 is 125° for the given triangle.

According to the question,

We have the following information:

A figure is given of triangle and its exterior angles.

m∠1 = 70°

Now, the two sides (with line on them) of the triangle are equal. So, it means that it is an isosceles triangle.

We know that sum of three angles of a triangle is 180°.

Let's take the two equal angles to be x°.

x+x+70 = 180

2x+70 = 180

2x = 180-70

2x = 110

x = 110/2

x = 55°

We know that angles made on a straight line is 180°.

∠4 and angle x will make a straight line.

∠4 = 180-55

∠4 = 125°

Hence, the correct option is A.

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The equation where y is the price of the ticket with the coupon, and x is the original price of the ticket.

y= 0.55 x.

Given:

A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the​ situation, where y is the price of the ticket with the​ coupon, and x is the original price of the ticket.

If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately  pays (y) is  the original price (x) minus a 45% of this price:

y= x -0.45 x

By association: y= (1-0.45) x

and then y= 0.55 x.

The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).

Hence we get the required equation.

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Answer: It will take 24 years to have 7 million.

Step-by-step explanation:

1.65% of 5.04 million is 83,160.

2018 is 6 years from 2012.

83,160 x 6 = 498,960.

498,960k + 5,040,000mil =5,538,960mil. still not quite 7 million.

498,960k x 4 = 1,995,840mil.

1,995,840mil + 5,040,000mil = 7,035,840mil.

It will take the city 24 years to have 7 million.

Answer:

False

Step-by-step explanation:

The correct answer is y = -25x + 450

Answer:327

Step-by-step explanation:

Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:

y = 78 * 4 + 15

Because of order or operations (PEMDAS), we do multiplication first.

y = 312 + 15

y = 327

Hope this helped!

Answer:

x= -2

Step-by-step explanation:

-2 = 3x + 8/2

-2+2=3x+4+2          (add 2 to both sides)

0=3x+6                          

-6=3x+6-6

3x=-6

x=-6/3

x= -2

Answer: 1 -1/20

Step-by-step explanation:

Based on the given conditions, formulate: 42 divided by 40

Cross out the common factor: 21/20

Convert to mixed fraction: 1- 1/20

Answer:

-7g - 9

Step-by-step explanation:

Subtract the numbers

-5g -2 -2g -7

-5g - 9 - 2g

Combine like terms

-5g - 9 - 2g

-7g - 9

Solution

-7g - 9

Answer:

-7g -9

Step-by-step explanation:

Just subtract and then combine like terms

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Step-by-step explanation:

Point Form:

[tex](\frac{2}{3} ,-\frac{5}{3}) , (-1, -5)[/tex]

Equation Form:

x= [tex](\frac{2}{3}[/tex], [tex]-\frac{5}{3} )\\[/tex] , y= [tex]-\frac{5}{3}[/tex]

x = -1 , y =-5

Hope this answer your question... sorry I couldnt help more, if it didnt.

Answer:

x = 154

Step-by-step explanation:

[tex]\frac{x}{11}[/tex] + 16 = 30 ( subtract 16 from both sides )

[tex]\frac{x}{11}[/tex] = 14 ( multiply both sides by 11 to clear the fraction )

x = 11 × 14 = 154

Answer:

x = 154

Step-by-step explanation:

Given equation,

→ (x/11) + 16 = 30

Now the value of x will be,

→ (x/11) + 16 = 30

→ x/11 = 30 - 16

→ x = 14 × 11

→ [ x = 154 ]

Hence, value of x is 154.

The original amount is $92.202.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.

Given:

Total amount = 83.82

rate of increase = 10%

So, the original amount

= 83.82 + 83.82 x 0.1

= 83.82 + 8.382

= $92.202

Hence, the original amount is $92.202.

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The rate, in inches per hour, at which the rain fell during that time on Friday is 3/8 inches per hour.

Time for which the rain fell = 2 hours

The total amount of rain that fell = 3/4 inch

So, in 2 hours, the amount of rain that fell = 3/4

In 1 hour, the amount of rain that fell = 3/8 inches

Hence, The rate, in inches per hour, at which the rain fell during that time on Friday = 3/8 inches per hour.

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Answer: The constant of variation, k , is 54

Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.

Answer: 2/3

Step-by-step explanation:

12 out of 18 prefer summer sports so as a fraction it would be 12/18 = 6/9 = 2/3

Answer:

33.3333%

Step-by-step explanation:

EXPLANATION

Based on the given conditions, formulate: (18-12) ÷ 18

Calculate the sum or difference:[tex]\frac{6}{18}[/tex]

Cross out the common factor:[tex]\frac{1}{3}[/tex]

Rewrite a fraction as a decimal: 0.333333

Multiply a number to both the numerator and the denominator: 0.333333x[tex]\frac{100}{100}[/tex]

Write as a single fraction:[tex]\frac{33.33333x100}{100}[/tex]

Calculate the product or quotient:[tex]\frac{33.333}{100}[/tex]

Rewrite a fraction with denominator equals 100 to a percentage: 33.3333%

Answer: 33.3333%

Answer:    A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of

20

∘

off a direct heading to Barbados. The captain maintains the 22-knot speed for 9 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained? (a) The captain should head through an angle of (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is hours (Do not round until the final answer. Then round to one decimal place as needed.)

The true statement about the function of area of by rectangle and width of rectangle are:

The correct answer option is options A and D

A rectangle is a quadrilateral having opposing sides parallel and four right angles.

At point (x, y) = (10, 100) the area is maximum.

This means that the area of the rectangle is maximum when width is 10m.

If the width of the rectangle is more than 10m, the area reduces or decreases.

Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.

The statement "To get the greatest area, the width should be 20" is false.

Complete question:

Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).

Wlhich of these statements are true?

A. Greater width relates to greater area as long as the width is less than 10.

B. Greater width relates to greater area as long as the width is more than 10.

C. To get the greatest area, the width should be 10

D. To get the greatest area, the width should be 20

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The equation of line passes through the point (-6, -3) will be;

⇒ y = 5/3x + 7

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (-6, -3).

And, The parallel line is,

⇒ 5x - 3y = 9

⇒ y = (5x - 9) / 3

Now,

Since, The equation of line passes through the point (- 6, -3).

So, We need to find the slope of the line.

Since, The slope of the parallel line is same.

Hence, Slope of the line is,

y = 5/3x - 3

m = dy/dx = 5/3

m = 5/3

Thus, The equation of line with slope 5/3 is,

⇒ y - (-3) = 5/3 (x - (-6))

⇒ y + 3 = 5/3 (x + 6)

⇒ y + 3 = 5/3x + 10

⇒ y = 5/3x + 10 - 3

⇒ y = 5/3x + 7

Therefore, The equation of line passes through the point (-6, -3) will be;

⇒ y = 5/3x + 7

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Answer:

b>19

Step-by-step explanation:

15<b−4

Rewrite so b is on the left side of the inequality.

b−4>15

Move all terms not containing b to the right side of the inequality.

Add 4 to both sides of the inequality.

b>15+4

Add 15 and 4.

b>19

b>19

The result can be shown in multiple forms.

Inequality Form:

b>19

Interval Notation:

(19,∞)

Answer: 18

Step-by-step explanation:

There are no parenthesis or exponents, so you use multiplication first.

6 x 2 = 12

That makes your equation 14 + 12 - 16 + 8

Now you only have adding and subtracting left, which you’ll do from left to right.

14 + 12 = 26

26 - 16 + 8

26 - 16 = 10

10 + 8 = 18

Hope this helps!

After solving the equation for x , we get the solution as  x = 1 [tex]+[/tex] √47 and x = 1 - √47 .

In the question ,

it is given that ,

the equation in words is written as "2 x squared plus 3 x minus 7 [tex]=[/tex] x squared plus 5 x plus 39 " .

So , the equation in number can be written as

2x² [tex]+[/tex] 3x - 7 = x² [tex]+[/tex] 5x + 39

Making Like terms together ,

we get ,

2x² - x² [tex]+[/tex] 3x - 5x - 7 - 39 [tex]=[/tex] 0

(2 - 1)x² [tex]+[/tex] (3 - 5)x - 46 [tex]=[/tex] 0

x² - 2x - 46 [tex]=[/tex] 0

Applying quadratic formula in the above quadratic Equation ,

we get ,

x = -b ± √(b² - 4ac)/2a

From the given quadratic equation , we get that a = 1 , b = -2 and c = -46 .

So ,

x = -(-2) ± √((-2)² - 4(1)(-46))/2(1)

= 2 ± √(4 [tex]+[/tex] 4(46))/2

= 2 ± √4(1 [tex]+[/tex] 46)/2

= 2 ± 2√47/2

= 2(1 ± √47)/2

= 1 ±√47

x = 1 + √47 and 1 - √47 .

Therefore , After solving the equation for x , we get the solution as  x = 1 + √47 and x = 1 - √47 .

The given question is incomplete , the complete question is

Solve for x in the equation , "2 x squared plus 3 x minus 7 = x squared plus 5 x plus 39 " .

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Answer:

you can do the favour of marking the answer brainlest pls

She will have run a total of 2.25 racers in 27 racers

From the question, we have the following parameters that can be used in our solution:

Total number of racers = 27 racers

Number of racers in a run = 12 racers

From the above parameter, we can calculate the total number of racers using the following equation

The total number of racers is calculated as

Total number of racers in the run = Total number of racers/Number of racers in a run

Substitute the known values in the above equation

So, we have the following equation

Total number of racers in the run = 27/12

Evaluate the quotient

Total number of racers in the run = 2.25

Hence, the total number of racers in the run is 2.25 racers

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Answer:

Step-by-step explanation:

Zeros of the given polynomial are -2, 2, -3/2, 3/2

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.

Given a polynomial 1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36)

1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0

(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0

4[tex]x^{4}[/tex] - 16[tex]x^{2}[/tex] - 9[tex]x^{2}[/tex] + 36= 0

4[tex]x^{4}[/tex]([tex]x^{2}[/tex] - 4) - 9([tex]x^{2}[/tex] - 4) = 0

(4[tex]x^{4}[/tex]-9)([tex]x^{2}[/tex] - 4) = 0

(x+2)(x-2)(2x+3)(2x-3) = 0

x = -2, 2, -3/2, 3/2

Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2

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Answer:

Part B: (0, -6)

Part C: x = -1

Part D: (-1, -8)

Explanation:

see the attached pdf