BC is the diameter of the semicircle. The area of rectangle ABCD is 20 and the length of line AB is 5.What is the area of the semicircle?

BC Is The Diameter Of The Semicircle. The Area Of Rectangle ABCD Is 20 And The Length Of Line AB Is 5.What

Answers

Answer 1

Answer:

2[tex]\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

BC is equal to 4 because 5*4=20.

The radius is 2. The equation for the area of a circle is [tex]\pi r^2[/tex].

Therefore, if we plug in 2 we will get [tex]4\pi[/tex].

But then we divide by 2 to get 2[tex]\pi[/tex] [tex]units^{2}[/tex] as our answer.

Hope this helped! :)


Related Questions

The daily recommended allowance of calcium for a sixth grader is 1,200 mg. One cup of
milk has 25% of the recommended daily allowance of calcium. How many milligrams of
calcium are in a cup of milk? If you get stuck, consider using the double number line.



what's the answer pls tell me

Answers

Answer:

300 milligrams are in aa cup of milk.

Step-by-step explanation:

.25 x 1200 = 300

Solve for Inequality 5-1/2 x >30

Answers

Answer:

X < - 50

Step-by-step explanation:

5 - 1/2 x > 30

Move 5 to the other side of the inequality

- 1/2 x > 25

Multiply both sides by 2, to get rid of the denominator on the left side

-x > 50

Now switch the inequality sign and multiply to get the minus on the other side

x < - 50

[tex]5-\dfrac{1}{2} x > 30[/tex]

Simplify:

[tex]-\dfrac{1}{2} x+5 > 30[/tex]

Subtract 5 from both sides:

[tex]-\dfrac{1}{2} x+5-5 > 30-5[/tex]

[tex]-\dfrac{1}{2} x > 25[/tex]

Multiply both sides by [tex]-\dfrac{2}{1}[/tex]:

[tex]-\dfrac{2}{1} \times(-\dfrac{1}{2} x) > -\dfrac{2}{1} \times(25)[/tex]

[tex]\fbox{x} < \fbox{-50}[/tex]

2/3-5/6 over 3/4. What’s the answer

Answers

The value of (2/3 - 5/6) / 3/4 is -2/9.

What is a fraction?

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

(2/3 - 5/6) / 3/4

2/3 - 5/6

= (4 - 5)/6

= -1/6

Now,

(-1/6 )/(3/4)

= -1/6 x 4/3

= -4/18

= -2/9

Thus,

The value is -2/9.

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3a²b and 3ab² are like terms true or false​

Answers

Step-by-step explanation:

false.

3a²b≠3ab².

If a is 3 and b is3 it is not equal

Use the drop-down boxes to show a function in the form y = mx + b for the line that contains the points (–6.4, –2.6) and (5.2, 9).

Answers

The equation in the slope-intercept form is y = x + 3.8

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

A line that contains the points (–6.4, –2.6) and (5.2, 9).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

So, the equation,

y + 2.6 = {(9 + 2.6)/(5.2 + 6.4)} (x + 6.4)

y + 2.6 = x + 6.4

y = x + 6.4 - 2.6

y = x + 3.8

Therefore, the equation y = x + 3.8 is in the slope-intercept form.

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a line has a slope of 7/10 and a y intercept of (0,-4) what is the equation of the line in standard form

Answers

Considering the definition of a line, the equation of the line in standard form is y - 7/10x= -4

What is Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

The standard form of a linear equation is Ax + By = C. In this type of equation, x and y are variables and A, B, and C are integers.

Equation in this case

In this case, you know:

A line has a slope of 7/10.A line has a y-intercept of (0,-4).

So, the line can be expressed as:

y=7/10x -4

Expresed in standard form:

y - 7/10x= -4

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how many full cases and additional items are needed to fulfill the order 56 items ordered 6 items per case

Answers

There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

56 items ordered for 6 items per case.

Now, After divide the quotient shows the number of full case and remainder shows the additional items.

Hence, We get;

 6 ) 56 ( 9

      54

   ---------

        2

Thus, There are 9 full cases and 2 additional items are needed to fulfill the order 56 items ordered 6 items per case.

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Consider whether it's wrong or right.​

Answers

The solution to the equations are

0 ∈ N is False               7/2 ∈ Q is True

√16 ∈ Q' is False          π ∈ Q' is True

3/2 ∈ I is False              -3 ∈  R is True

0 ∈ I is True                  -1 ∈ I⁺ is False

( 1 - 3 ) ∈ N is False       8/2 ∈ I is True

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the equation will be

a)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is not a natural number

So , the equation is False

b)

Let the number be A = √16

The value of A = 4

The number 4 is a natural number , whole number , rational number and an integer

4 is not an irrational number

So , the equation is False

c)

Let the number be A = 3/2

The number 3/2 is a rational number

3/2 is not an integer

So , the equation is False

d)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is an integer

So , the equation is True

e)

Let the number be A =  ( 1 - 3 )

The value of A = -2

The number -2 is a rational number and an integer

-2 is not a natural number

So , the equation is False

f)

Let the number be A = 7/2

The number 7/2 is a rational number

7/2 is a rational number

So , the equation is True

g)

Let the number be A = π

The number π  is an irrational number

π is an irrational number

So , the equation is True

h)

Let the number be A = -3

The number -3 is a real number

7/2 is a real number

So , the equation is True

i)

Let the number be A = -1

The number -1 is an integer and real number

-1 is a negative integer

So , the equation is False

j)

Let the number be A = 8/2

The value of A = 4

The number 4 is a natural , whole , integer and rational number

4 is an integer

So , the equation is True

Hence , the equations are solved

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Any help would be awesome

Answers

Answer: 72 square units

Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.

summarize how you can find the slope of a perpendicular line.

Answers

Finding the slope of a perpendicular line is fairly simple…

Let’s say we have the line given in slope-intercept form (y=mx+b), y=3x+1.

We know looking at this equation that the slope of the line is 3. To find a slope that is perpendicular you need to find it’s opposite reciprocal. In the case of 3, it’s opposite would be from + to -, so -3. The reciprocal would flip the number into a fraction -3 => -1/3. So the line perpendicular would have a slope of -1/3.


Steps:
1. Determine the slope of the line

2. Switch from a positive to a negative or a negative to a positive

3. Find the reciprocal (2/5 => 5/2, 1/4 => 4)

Since "slope" tells us the angle of the line being graphed, the word "slope" is commonly used in mathematics.

Planar geometry states that all lines have slopes. Any slope can be calculated by comparing it to another line, usually the x-axis. A line's slope, or angle, in relation to that x-axis value is how steep it is.

In mathematics, slope is the proportion of the change in the y value to the change in the x value.

Two perpendicular lines have a slope such that the reciprocal of the negative slope of one line equals the slope of the other. The slope of perpendicular lines is -1 as a result.

The relationship between the slopes of parallel lines can be demonstrated using the formula m1.m2 = -1, if the slopes of the two perpendicular lines are m1, m2.

Like a fraction, a slope works by favoring the rise, up-and-down movement, over-the-run, or side-to-side movement. If a line rose up one unit for every rightward unit traveled, the slope would be a positive one.

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i am Once again asking for help on this difficult question- i am timed pls help :

Answers

C: It shows the audience clearly seemed to enjoy it at first and it continues rising showing C is correct

Your company is considering a new project that will require $250,000 of new equipment at the start of the project. The equipment will have a depreciable life of eight years and will be depreciated to a book value of $10,000 using straight-line depreciation. The cost of capital is 12 percent, and the firm's tax rate is 21 percent. Estimate the present value of the tax benefits from depreciation.

Answers

The present value of the tax benefits from depreciation which is a non cash expenditure under capital budgeting decisions is $10432.80

What is Depreciation?

According to the prudence concept of accounting convention, Depreciation is a non cash expenditure that has been charged against the profit. Depreciation is value that amortized over useful life of tangible fixed asset. The absolute decline in the value of asset due to obsolesce, usage of asset, wear & tear of fixed asset is referred as depreciation.

As per accounting standard on property, plant & equipment depreciation can be computed by straight line method and written down value method.

While analyzing the capital budgeting decision from the equipment to be acquired the cash inflows and outflows during the currency of the project shall be accounted for.

The tax benefit from depreciation expenses will be consider as cash inflow. The same shall be calculated by the present value annuity factor for the as follows:

cost of capital = 12 %

Depreciation = $10000

Life of the project = 8 years

Tax rate = 21%

Present value annuity factor (PVAF) at 12% for 8 years will be:

0.893 0.797 0.712 0.636 0.567 0.507 0.452 0.404

Grand total of the (PVAF) at 12% = 4.968

Now multiply the PVAF with depreciation amount

Present Value of Depreciation = 4.968 × 10000 = $49,680

Tax benefit from depreciation = $49,680 × 21% = $10432.8

Thus the tax Tax benefit from depreciation is $10432.80

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Which expression could be used to determine the product of –4 and 3 and one-fourth?
(negative 4) (3) times (negative 4) (one-fourth)
(negative 4) (3) + (negative 4) (one-fourth)
(3) (negative 4) times (3) (one-fourth)

Answers

The expression which could be used to determine the product of -4 and 3 and one-fourth as required is; negative 4) (3) + (negative 4) (one-fourth).

Which expression can be used to determine the product of the given word phrase?

As evident in the task content; the expression which could be used to determine the product of; -4 and 3 and one-fourth is required to be determined.

Since the given expression is; -4 and 3 and one-fourth; we have that;

-4 × 3 ¼

However, since 3 ¼ can be written as; ( 3 + ¼ ), it follows that we have;

-4 × ( 3 + ¼ )

Ultimately, the resulting expression using the distributive property is;

( -4 ) ( 3 ) + ( -4 ) ( ¼ )

Therefore, the correct answer is; (negative 4) (3) + (negative 4) (one-fourth).

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PLEASE Help. The answers I got so far are A. 72. B. 301. C 90 and D 252. I am having the most trouble with B and D.

Answers

The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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Which of the following shows the prime factorization of using exponential notation?




Which of the following shows the prime factorization of using exponential notation?









Which of the following shows the prime factorization of using exponential notation?



Which of the following shows the prime factorization of using exponential notation?









Which of the following shows the prime factorization of using exponential notation?








how do i simplify 12 /16 to the lowest terms and find equivalent fraction that has a denominator of 32

Answers

The prime factorization of 72 using exponential notation is 2³ x 3².

What is Prime Factorization?

Prime factorization is a process of writing all numbers as a product of primes.

Given:

Prime factorization is representing a number in form of products of its primes.

Consider the given number 72

72 = 2 x 2 x 2 x 3 x 3

So, 72 can be written as 2 × 2 x 2 × 3 × 3.

                                     

Thus, exponential notation it can be written as 2³ x 3².

Also, Simplifying 12 /16 as

= 12/16

= 3/4

and, the equivalent fraction whose denominator is 32.

Then, 3/4 = x/32

4x = 96

x = 24

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MODELING REAL LIFE When the average price of an item increases from $p_1$ to $p_2$ over a period of $n$ years, the annual rate of inflation $r$ (in decimal form) is given by $r=\left(\frac{p_2}{p_1}\right)^{1/n}-1$
. Find the rate of inflation for each item in the table.

Per pound Per pound
2009 2019

Potatoes $0.620 $0.749

Oranges $0.910 $1.280

Ground beef $2.251 $3.775

Potatoes:
, or %

Oranges:
, or %

Ground beef:
, or %

Answers

The rate of inflation of potatoes is 0.019.

The rate of inflation of Oranges is 0.019.

The rate of inflation of Ground beef is 0.019.

What is Rate of Inflation?

Inflation is an increase in the level of prices of the goods and services that households buy. It is measured as the rate of change of those prices.

Given:

Here, the annual rate of inflation r (in decimal form) is given by

r = [tex](p_2/ p_1)^{1/n[/tex] - 1

Now, The average price of a  potatoes increased from $0.620 in 2009 to $0.749 in 2019.

Thus, The required rate of inflation,

r = [tex](0.749/ 0.620)^{1/10[/tex] - 1

r = 1.019 - 1

r = 0.019

Now, The average price of a Oranges increased from $0.910 in 2009 to $1.280 in 2019.

Thus, The required rate of inflation,

r = [tex](1.280/ 0.910)^{1/10[/tex] - 1

r = 1.034 - 1

r = 0.034

Now, The average price of a Ground beef increased from $2.251 in 2009 to $3.375 in 2019.

Thus, The required rate of inflation,

r = [tex](3.775/ 2.251)^{1/10[/tex] - 1

r = 1.0321 - 1

r = 0.0321

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Please help me I’ll mark you brainly

Answers

On solving the provided question, we can say that -  here in graph we have on solving equation  [tex]2x^2+ 9y^2 \\[/tex] = [tex]8 + 9 = 17[/tex]

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

[tex]2x^2+ 9y^2 \\[/tex]

[tex]8 + 9 = 17[/tex]

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15 minutes for 5 songs = minutes per song

Answers

Answer:

The average minutes per song would be 3.

Between 2020 and 2021, the population of a town decreased by 35%
In 2021, the population of the town was 94 900. What was the population of the town in 2020?​

Answers

Answer:

Step-by-step explanation:

if 2021 is 35% decrease of the original number then 2020 is 100% ,and 2021 = 65%.

so, we do the rule of three:

x = (94900 * 100)/ 65

x = 146000

and that is the population in 2020.

Answer:

Hey there! Based on the information provided, it seems that the population of the town decreased by 35% between 2020 and 2021. We can use this information to calculate that in 2021, the population of the town was 65% of its population in 2020. If the population of the town in 2021 was 94,900, then we can use this information to calculate that the population of the town in 2020 was 146,155. Does that make sense?

One root of the equation 4x² + 12x + k = 0, k = Z and x = R, is five times the other root.
Find the value of k.

Answers

We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2

What is quadratic equation?

An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.

How to determine the value of k in the question?

We are given, 4x²+ 12x +k =0, k =Z and x = R

the quadratic equation is 4x²+12x+k =0

we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a

when the quadratic equation is ax²+bx+ c= 0

Hence, roots of the equation given in question will be,

 x = - 12 ±√ (12² - 4×4×k) / 2×4

x = - 12 ± √(144-16k) / 8

as per the condition given in question, one root of this equation is 5 times the other root.

hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5

multiplying both sides by 8

- 12 - √(144-16k) = [-12 + √(144-16k)] ×5

- 12 - √(144-16k) = - 60 + 5√(144-16k)

- 12 + 60 = 6√(144-16k)

48 = 6√(144-16k)

8 = √(144-16k)

64 = 144 -16k

16k = 80

k = 5

the value of k =5

by putting the value of k =5

x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8

x = -1/2 and x = -5/2

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In the diagram below, QR is parallel to NO. If NQ = 12, QR 20, and NO = 35, find the length of QP. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.

Answers

Note that in the attached Geometric Figure (Diagram) which features QR as parallel to NO, if NQ = 12, QR 20, and NO = 35, then the length of QP is equal to 16.

What is the rationale for the above result?

[tex]\overline {QR}[/tex] is Parallel to [tex]\overline {NO}[/tex]; therefore

QR/NO = PQ/PN

⇒ 20/35 = PQ/PQ +12

This is because:

PN = PQ + NQ; which is also
PN = PQ +12

(PQ + 12) x 20 = 35PQ
20PQ + 240= 35PQ ; Collect like terms

240= 35 PQ - 20 PQ

240 = 15PQ; Divide both sides by 15

⇒ 240/15 = 15PQ/15
⇒ 16 = PQ

Therefore, QP = PQ which is equal to 16.

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Find the radius of the circle, if the big square is 30 square units more than the area of the small square.

Answers

Answer:

The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:

Area of small square = s^2

Area of big square = b^2

Since the area of the big square is 30 units more than the area of the small square, we can write the equation:

b^2 = s^2 + 30

To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:

s^2 = b^2 - 30

s = sqrt(b^2 - 30)

Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:

s = sqrt(d^2 - 30)

To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:

r = d/2 = sqrt(d^2 - 30)/2

So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:

The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2

What is area of circle?

The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately  3.142

Here, we have,

The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:

Area of small square = s^2

Area of big square = b^2

Since the area of the big square is 30 units more than the area of the small square, we can write the equation:

b^2 = s^2 + 30

To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:

s^2 = b^2 - 30

s = sqrt(b^2 - 30)

Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:

s = sqrt(d^2 - 30)

To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:

r = d/2 = sqrt(d^2 - 30)/2

So to find the radius of the circle, we just need to know the diameter of the circle.

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If a pair of shoes was discounted from an original price of P5000 to P2800 what is the percent decrease or discount

Answers

Answer:  44% decrease

Work Shown:

a = old price = 5000

b = new price = 2800

c = change in price

c = b-a

c = 2800-5000

c = -2200

The value of c is negative to indicate a price decrease.

d = percent change

d = (c/a)*100%

d = (-2200/5000)*100%

d = -44%

There is a 44% decrease or discount.

8.326 rounded to the nearest tenth

Answers

The answer to the question is 8.3

Answer:

8.3

Step-by-step explanation:

The number after three is below 5 so it stays as 8.3

-3/5(1+5n) =102
Solve for n

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two cards are drawn at random from a well shuffled pack of cards. What is the probability that
i)both are spades or both are diamonds?
ii)both are queens or both are red coloured?
iii)both are diamonds or neither is a king?

Answers

Answer:

Step-by-step explanation:

1 in a tenth of a million. I did the math with all the cards and how many are kinds diamonds or red or queens yk.

How many total lines of symmetry may be found in the image?
O 16
8
12
4

Answers

12 it’s 12 because if you do the mathematics in the equation the answer comes out to be 12

There are total 12 lines of symmetry may be found in the image.

We have to given that;

A image is shown in figure for find the lines of symmetry .

Since, We know that;

Exactly dividing a form in half, a line of symmetry exists. This indicates that the form would fold perfectly in half if you did so along the line.

Hence, By definition of line of symmetry we get;

There are total 12 lines of symmetry may be found in the image.

Thus, The correct answer is,

⇒ 12 line of symmetry

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onsider the transformation.
Which statement about the transformation is true?
O It is isometric because the side lengths remained the
same,
• It is isometric because all
angle measures remained
the same.
It is not isometric because the side
lengths did not
remain the same.
O It is not Isometric because the
not remain the same.
angle measures did
Mark this and return
Save and Exit

Answers

The transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

What is isometric transformation?

An isometric transformation is one that keeps the angles and distances between the original and changed shapes the same. There are numerous techniques that can be used to alter any image in a plane.

The two figures are isometric only if they are congruent. In the given figure the angles remain the same however the lengths of the side are transformed as the figure is dilated.

Hence, the transformation is not isometric because the side lengths did not remain the same and hence option C is the correct answer.

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A store is having a sale on chocolate chips and walnuts. For 4 pounds of chocolate chips and 8 pounds of walnuts, the total cost is $33. For 2 pounds of chocolate chips and 3 pounds of walnuts, the total cost is $13.
Find the cost for each pound of chocolate chips and each pound of walnuts.

Answers

Answer:

chocolate chip 7

walnuts 3.5

Step-by-step explanation:

assume x=chocolate chips

 y=walnuts.

equation

4x + 8y=33

(2x+3y=13)×2

new eq

4x + 8y=33

4x + 6y=26

------------------

 2y=7

  y=7/2

4x+ 8y = 33

4x + 8(7/2)= 333

4x= 33-28

x=7.00

Mr. Smith has saved $1,800 each year for 20 years. A year after the saving period ended, Mr. Smith withdrew $7,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $5,000 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 6% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?

Answers

At the end of the eighth year, the amount Mr. Smith withdrew was $41,757.68.

How the ending withdrawal is determined?

The amount that Mr. Smith withdrew at the end of the eighth year is a product of a series of computations, involving future value determination.

In this situation, we have used an online finance calculator to determine the future value of the investment at each leg.

First Leg:

N (# of periods) = 20 years

I/Y (Interest per year) = 6%

PV (Present Value) = $0

PMT (Periodic Deposits) = $1,800

Results:

FV = $66,214.06

Sum of all periodic payments = $36,000 ($1,800 x 20)

Total Interest = $30,214.06

Second Leg:

N (# of periods) = 5 years

I/Y (Interest per year) = 6%

PV (Present Value) = $,

PMT (Periodic Withdrawal) = $-7500

Results:

FV = $46,331.15

Sum of all periodic payments = $-37,500 ($7,500 x 5)

Total Interest $17,617.09

Third Leg:

N (# of periods) = 2 years

I/Y (Interest per year) = 6%

PV (Present Value) = $46,331.15

PMT (Periodic Withdrawal) = $-5000

Results:

FV (Final Withdrawal) = $41,757.68

Sum of all periodic payments = $-10,000 ($5,000 x 2)

Total Interest = $5,426.53

Thus, the amount of $41,757.68 was withdrawn by Mr. Smith at the end.

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