the interest paid on a $8,000 loan is $600, a rate of 4%
how many years did it take to pay back the loan? round to 1 decimal.

Answer:

B

Step-by-step explanation:

A polynomial cannot have variables raised to negative exponents.

Answer: B

Answer:

20 km rate should 7.76

Step-by-step explanation:

Definitions

The variable rate is the rate for every km.

The fixed rate is what is charged for someone just getting on their bicycle.

Givens

Length of race = 6 km

variable rate = 0.22 / km

fixed rate = x

Total cost = 4.68

Formula

Total cost = fixed rate + variable rate * distance

Solution

4.68 = 6*0.22 + x

4.68 = 1.32 + x                       Subtract 1.32 from both sides.

4.68 - 1.32 = 1.32 - 1.32 + x   Combine

3,36 = x

The fixed rate is 3.36

Before getting the answer to the question asked, we should see if we get the same fixed rate for 24 km

Check

Total Cost = fixed rate + variable rate*distance

Total Cost = 8.64

fixed rate = x

variable rate = 0.22

distance = 24 km

8.64 = x + 0.22 * 24                Combine

8.64 = x + 5,28                        Subtract 5.28 from both sides

8.54 - 5,28 = x + 5.28 - 5,28  Combine

3.36 = x which agrees with our first calculation for the fixed rate.

Answer

y = 3.36 + 20*0.22

y = 3.36 + 4.4                           Combine

y = 7.76

Answer:

A. [tex]( 8 \times \frac{1}{2} )\frac{1}{3}[/tex]

Explanation:

Associate property of multiplication: a × (b × c) = (a × b) × c

Option A

Shows associate property of multiplication. Does not change final answer.

Option B

The grouping does not change inside the parenthesis.

Option C

This does show associate property but multiplying first 8 × 1/3 is complex.

Option D

Product of this changes the final answer. Not correct.

Answer:

7/30 of her music library

Step-by-step explanation:

We are looking for 7/10 of 1/3. In this case this "of" means we will multiply the two fractions. To multiply fractions, we multiply

top × top

and

bottom × bottom

1/3 × 7/10

is 1×7 on top, and

3×10 on the bottom.

= (1×7)/(3×10)

= 7/30

7/30 cannot be simplified, so that is the answer.

Answer:

You will have 25in as your answer

Answer is 25

To find this you need to find the dilation ratio of one figure side to the other

Take the like sides of 5 and 12-1/2 compared to sides 10 and x

5 10

_ ____

12-1/2. X

Your dilation (make bigger) ratio from 5 to 10 is 2

So you do the same ratio to 12-1/2

Which gives you the answer of 25

I hope this helps!

Answer:

A

Step-by-step explanation:

sin 30 = y/7

Sin is being used and there is only one option with sin in it, so that is the right one.

Option D is correct.

Figures are missing in the question.

The images below shows the missing figures of question.

For congruent figures, we need the same shape, same area, and inverse direction.

Congruent figures have congruency. That seems simple enough, but congruent figures need not be turned the same way or face the same direction to be congruent.

In the case of geometric figures, line segments with the same length are congruent and angle with the same measure are congruent.

In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.

In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas.

The figure in option D satisfies all these conditions. Hence, Option D is correct.

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Answer:

Least common multiple (LCM) of 20, 8, 4 is 40.

LCM(20, 8, 4) = 40

Answer:

x = 9

Step-by-step explanation:

since the terms are in AP then there is a common difference between consecutive terms, that is

a₂ - a₁ = a₃ - a₂ ( substitute values )

x - 7 = 11 - x ( add x to both sides )

2x - 7 = 11 ( add 7 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Answer:

9

Step-by-step explanation:

The nth term of an AP has the formular

a+ ( n - 1 ) d

a = first term

n = number of terms

d = common difference

common difference d = T2 - T1 0r T3 - T2

d = x - 7 or 11 - x

Therefore,

3rd term

a + (3 - 1)d

a + 2d

Hence,

7 +2d = 11

substitute the value of d above

7 + 2 (x -7) = 11

7 + 2x - 14 = 11

2x = 11 +14 -7

2x = 18

dividing bothsides by 2

x = 18/2

x = 9

Answer:

Two Ions will bond.

Answer:

y = - x² + 1

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (0, 1 ) , then

y = a(x - 0)² + 1 = ax² + 1

to find a substitute any other point that lies on the graph into the equation

using (1, 0 ) , then

0 = a(1)² + 1 ( subtract 1 from both sides )

- 1 = a

y = - x² + 1 ← equation of graph

Answer:

- x² + 1

Step-by-step explanation:

the vertex of the graph is (0 , 1)

Then the equation of the graph has this form :

(x - 0)² + 1  or  - (x - 0)² + 1

Since the parabola is opening down

Then

the equation of the graph is :

- (x - 0)² + 1 = - x² + 1

Answer:

3/4.

Step-by-step explanation:

That would be (2 + 25) / 36

= 27/36

= 3/4.

The amount in dollars that is in the account after 50 years expressed in power is; 2⁹

We are told that the money doubles in value after every 10 years.

When the account was opened it had 2⁴ dollars in it and after 50 years it has doubled 5 times. The doubling increased by a factor of 2⁵ and is now has a balance of 2⁴ × 2⁵.

Using the rule of exponents, we have;

2⁴ × 2⁵ = 2⁹

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Answer:

65 degrees

Step-by-step explanation:

Relative to angle A, you are given the measure of the opposite side and the hypotenuse of the right triangle. When it comes to right triangles, we know through our trig identities that the sin of an angle is equivalent to the length of the opposite side over the hypotenuse. Therefore, we can use trig to solve this problem:

[tex]sinA=\frac{a}{c}[/tex]

If we sub in the values of a and c which are given to us, we get the following:

[tex]sinA=\frac{10}{11}[/tex]

To solve for A, we can take arcsin(10/11) because arcsin is inverse:

[tex]A=arcsin(\frac{10}{11} )[/tex]

Using a calculator, we get that A is approximately 65 degrees

Answer:

3.5kg

Step-by-step explanation:

Let original weight  of grapes in box be X and weight of grapes in basket be Y.

From the first sentence
X = 2Y  (weight in box = 2 times weight in basket)   --- (1)

If you add 2kg of grapes to basket, the weight of grapes in basket = Y + 2

From the second statement

Y + 2 = X + 0.5

Subtracting Y from the LHS gives 2 = X - Y + 0.5

Subtracting 0.5 from both sides gives 2-0.5 = X - Y or X - Y = 1.5  --- (2)

Substituting for X from the first equation in (2) we get
2Y - Y = 1.5 or Y = 1.5kg

But this is the original weight of the grapes in the basket. Since we have added 2 kg of grapes to the original weight, we get the weight of grapes in basket now as 1.5 + 2.0 = 3.5kg

If the Company pays. Rs 40 per her​. The total cost is Rs 16,000.

First step is to calculate the time taken to produce

Time= (10000/200) × 8

Time= 400 hours

Second step is to calculate the total cost

Total cost= 400 × Rs 40

Total cost= Rs 16,000

Therefore the total cost is Rs 16,000.

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Answer:

8, 12, 16, 20, 24, 28, 32, 36

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

a₁ is the first term and d the common difference

given a₁ = 4 and a₁₀= 40 , then

4 + 9d = 40 ( subtract 4 from both sides )

9d = 36 ( divide both sides by 9 )

d = 4

add d to each term to obtain the next term

4 + 4 = 8

8 + 4 = 12

12 + 4 = 16

16 + 4 = 20

20 + 4 = 24

24 + 4 = 28

28 + 4 = 32

32 + 4 = 36

the 8 terms between 4 and 40 are

8, 12, 16, 20, 24, 28, 32, 36

Answer:

The relation y=2x+8 is a function because the two different output values of the function have the one unique input value.

Step-by-step explanation:

The given relation is y=2x+8.

It is required to determine the relation is a function.

This solution can be obtained by using the concept of function. First write the given relation y=2x+8 and determine whether the given relation is a function.

Step 1 of 1

The given relation is y=2x+8.

This relation shows that the two different output values of the function have one unique input value and this relation is a linear function.

Hence, the relation is a function.

Answer:

1. 24a + 40

2. 24 - 8d or -8d + 24

3. 18x - 63y

Step-by-step explanation:

1.

multiply the 8 by 3a then by 5

8(3a + 5)

24a + 40

2. multiply the 4 by the 6 and -2d

4(6 - 2d)

24 - 8d or -8d + 24

3. multiply the 9 by the 2x and -7y

9(2x-7y)

18x - 63y

The value of x=55

The total angle of each diamond is 360 degrees. The opposite angles of the diamond are congruent.

Congruency: In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

The two adjacent angles are 2x + 20 degrees and 50 degrees.

Opposite angles measure 2x + 20 and 50 degrees.

The sum of the angles of each rectangle is 360

2x + 20 + 50 + 2x + 20 + 50 = 360

Add the line terms and subtract

4x + 140 = 360

Subtracting140 on both sides:

4x = 2

Divide both sides by 4

x = 55

55 is the correct answer.

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Answer: 11.44

Step-by-step explanation:

A = a + b / 2h = 8.49 + 16.97 / 2 * 0.9 = 11.44214

Which rounds up to: 11.44

I’m sorry, but i don’t know what it means by give answer in simpflied radical.

The next 4 terms are 375, 75, 15 and 3

The sequence is given as:

234375, 46875, 9375, 1875...

Notice that the current term of the sequence is 1/5 of the previous term.

So, the next four terms are:

Next 1 = 1/5 * 1875 = 375

Next 2 = 1/5 * 375 = 75

Next 3 = 1/5 * 75 = 15

Next 4 = 1/5 * 15 = 3

Hence, the next 4 terms are 375, 75, 15 and 3

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We cannot express the function [tex]x^{2} -sin(x+y)=1[/tex] in y=f(x) form it has an implicit function.

Given function [tex]x^{2} -sin(x+y)=1[/tex] and dy/dx=2x sec(x+y)-1

A relation is said to be an implicit solution of a differential equation involving x,y and derivatives of y with respect to x if defined explicit solution. In other words  the function which cannot be written as y=f(x).

Function is a relationship between two or more variables which have one value for each value of x.

We have to first differentiate the function with respect to x.

[tex]x^{2} -sin(x+y)=1[/tex]

2x-cos(x+y)(1+dy/dx)=0

2x-cos(x+y)+cos(x+y)dy/dx=0

cos(x+y) dy/dx=cos(x+y)-2x

dy/dx={cos(x+y)-2x}/cos(x+y)

dy/dx=cos(x+y)/cos(x+y)-2x/cos(x+y)

dy/dx=1-2x cos(x+y)

The given solution is incorrect.

when we solve the function to collect the variable y in one side we cannot be able to do that.

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Answer:

x = 175 units

Step-by-step explanation:

x is to (49 + 576)   as   49  is to x

x/ 625  =  49/x          cross multiply

x^2 = 30625

x=175

Answer:

x = 175 units

Step-by-step explanation:

x is to (49 + 576)   as   49  is to x

x/ 625  =  49/x          cross multiply

x^2 = 30625

x=175

HOPE THIS HELPS LOVE -3-

The hull speed of a boat when given by the function v = 1.34√l, makes the expression represent the speed of Santa Monica, v = a√b, with a = 1.34, and b = ln - 10, where lₙ is the length of the Nina Pinta. The restriction on lₙ is that lₙ > 10.

In the question, we are asked to express the speed of the boat of Santa Monica in terms of the length, lₙ of the Nina Pinta.

We are informed that the function is represented as v = a√b, for the speed of Santa Monica.

We are given that the hull speed of a boat of length l is given as v = 1.34√l.

Comparing, the speed of Santa Monica v = a√b, to the general formula v = 1.34√l, we get:

a = 1.34, and

b = the length of the boat of Santa Monica.

The length of the boat of Santa Monica is 10 ft. shorter than of Nina Pinta.

Thus, b = lₙ - 10, where lₙ is the length of the boat of Nina Pinta.

Since b has to be positive, as the function involves square root over b, lₙ - 10 > 0, or, lₙ > 10, is the restriction on the length of the boat of Nina Pinta.

Thus, the hull speed of a boat when given by the function v = 1.34√l, makes the expression represent the speed of Santa Monica, v = a√b, with a = 1.34, and b = ln - 10, where lₙ is the length of the Nina Pinta. The restriction on lₙ is that lₙ > 10.

Refer to the attachment for the complete question since the question provided is incomplete.

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Answer: check pic

Step-by-step explanation:

EDGE 2022

Triangle RST was reflected over the x-axis and translated 2 units to the left to form triangle ABC. The figures are congruent.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Reflection, translation and rotation are rigid transformation which preserve the shape and size of a figure, forming congruent figures.

Triangle RST was reflected over the x-axis and translated 2 units to the left to form triangle ABC. The figures are congruent.

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Answer:

Option A

Step-by-step explanation: