Solve similar triangles (advanced) khan academy. solve for x

1. The scenario represents a payout annuity.

2. Marcy can withdraw $1,833.60 per quarter until after 3 years when the inheritance will be exhausted.

A periodic withdrawal is the opposite of a periodic payment.

In a periodic withdrawal, the investor withdraws a constant amount from the investment that earns interest until it is exhausted.

A periodic withdrawal is the same as a payout annuity, which involves periodic receipts from the invested capital.

Using an online finance calculator, we can compute the quarterly withdrawals as follows:

N (# of periods) = 12 quarters (3 x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $20,000

FV (Future Value) = $0

Results:

Withdrawals = $-1,833.60

Sum of all periodic payments = $-22,003.20

Total Interest $2,003.20

Thus, in this payout annuity, Marcy can withdraw $1,833.60 quarterly for 3 years.

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Answer:

A. y = 8x

Step-by-step explanation:

y = 8x

From first term

32 = 8(4)

32=32

Correct

The slope of the line perpendicular to the line given by equation  2x+2y=-12 is found as 1.

The slope can be calculated using the following formula:

m = Δy/Δx

Where, m is the slope.

The equation of the line is; 2x+2y=-12

Write the equation in slope-intercept form.

2x + 2y = -12

Divide by 2.

x + y = -6

y = -x - 6

Slope m₁ = -1 and y-intercept = -6.

As, both line are perpendicular.

Thus,

m₁ x m₂ = -1

m₂ = -1/m₁

Put the value.

m₂ = -1/(-1)

m₂ = 1

The slope of the perpendicular line is found as 1.

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14) y = 6x + 1

( 2, y)

if x = 2 as stated in the coordinate, then y = 6(2) + 1 = 12 + 1 = 13

y =13

The ordered

Although part of your question is missing, you might be referring to this full question: Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices:

f(x) = 50^x

f(x) = 100^x

f(x) = 2(25)^x

f(x) = 4(25)^x

The equivalent function too expression is f(x)= 2(25)ˣ. Thus option c is correct.

The expression of function f(x) given, f(x)=2(5)²ˣ.

Functions are said to be equal if they have same domain or codomain such that f(x) = g(x). Thus, the two functions are equal functions.  

∴ The function after solving expression is,

f(x)= 2×(5²)ˣ

f(x)= 2×(25)ˣ

Hence, the correct equivalent function is f(x)= 2(25)ˣ.

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GIVEN

Two triangles ABC and ACD where two corresponding sides of the two triangles are equal.

SOLUTION

The two triangles have equal sides such that:

By this, the length of the remaining sides BC and DC are related such that the side opposite the greater angle has the greater length.

Since [tex]BC>DC[/tex]Substitute known values into the inequality:

Solving the inequality:

Recall that the side DC has to be greater than 0. Therefore:

Combining both solutions:

Answer:

The answer is 17/52. Explanation: The number of diamond cards is 13, and the number of '6' cards is 4 Picking one diamond out of 13 is 13C1

Step-by-step explanation:

The equation of the line in point slope form that passes through (1,5) and slope = -3 , is  y = -3x+6 .

The equation of line in point slope form passing through the points (x₁,y₁) and slope =m is given by the formula

(y-y₁)=m(x-x₁)

In the question ,

it is given that

the line passes through the point (1,5) and has a slope m = -3.

so the values become x₁=1 and y₁=5 and m = -3

Substituting the values in the formula for equation of line , we get

(y-5)=(-3)(x-1)

y-5= -3x + 1

y = -3x + 1 + 5

y = -3x+6

Therefore , the equation of the line in point slope form that passes through (1,5) and slope = -3 , is  y = -3x+6 .

The given question is incomplete , the complete question is

Write the equation of the line in point-slope form that passes through the point (1,5) with slope = -3.

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Answer:

$26

Step-by-step explanation:

65 x 60% = 39

65 - 39 = 26

By using trigonometric formulas and integration rules, we conclude that the integral is approximately equal to - 7.764 units.

In this problem we must determine the solution to a definite integral of trigonometric equations, which requires the use of trigonometric formula and integration rules to be found. The integral can be simplified by using the following formulas:

sin⁴ x = (1 / 8) · (3 - 4 · cos 2x + cos 4x)

sin² x = (1 /2) · (1 - cos 2x)

Then, the integral is simplified into this form:

[tex]I = \pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{4} x \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} \sin^{2} x \,dx[/tex]

[tex]I = \frac{\pi}{8} \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (3 - 4\cdot \cos 2x + \cos 4x) \,dx + 4\pi \int \limits_{\frac {\pi}{6}}^{\frac{3\pi}{4}} (1 - \cos 2x) \,dx[/tex]

[tex]I = \frac{3\pi}{8}\cdot x - \frac{\pi}{4} \cdot \sin 2x + \frac {\pi}{32}\cdot \sin 4x - 4\pi \cdot x - 2\pi\cdot \sin 2x[/tex], for x ∈ [π / 6, 3π / 4]

And the definite integral is:

I = 2.159 + 1.466 - 0.085 - 23.028 + 11.724

I = - 7.764

The definite integral of f(x) = sin⁴ x + 4 · sin² x for x ∈ [π / 6, 3π / 4] is approximately equal to - 7.764.

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The equation of the line in slope intercept form is y = -7x/2 - 5.

For the given question,

The graph of the straight line is given.

Select two points which lies on the line.

(x₁, y₁) = (0, -5)

(x₂, y₂) = (-2, 2)

Find the slope using the formula.

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 + 5)/(-2 - 0)

m = -7/2

The equation of the line in slope intercept form is given as;

y - y₁ = m(x - x₁)

Put the values.

y + 5 = (-7/2)(x - 0)

y = -7x/2 - 5

Thus the equation of the line in slope intercept form is y = -7x/2 - 5.

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Answer:  [tex]-4 < m \le -3[/tex]

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

Reason:

If m = -4, then f(x) = m becomes f(x) = -4. This yields the single solution x = -4

How do we get this solution? Start at -4 on the y axis. Move horizontally until reaching the curve. You should arrive at (-4,-4) which is the lowest point of this curve. Then move upward until reaching the x axis to arrive at x = -4

All of this says that the input x = -4 leads to the output y = f(x) = -4

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

We've gone over m = -4 leading to one solution, so that's out of the question since we want two solutions.

But if m = -3 for instance, then notice how tracing a horizontal line to the curve arrives at two locations instead of one. We arrive at x = -2 and x = -5 as the solutions to f(x) = -3

All of these solutions mentioned are negative which fits the criteria we're after. If m is in the interval from -4 to -3, excluding -4 but including -3, then we'll have f(x) = m with two negative solutions for x.

Answer:

if x=0than 3×0×(6×0)_< 9

Answer:

Output= -31

Step-by-step explanation:

f(x)= -3x²+8x-3

Therefore, f(-2)= -3(-2)²+8(-2)-3

                        = -3×4 -16 -3

                         = -12-16-3

                          = -31

Answer

he trapeziunm is an isosceles trapezoid since there are pairs of congruent base angles ADC and BCD

Lines AB and DC are the bases'

To proof that

WDraw perpendicular line segments from A to P and from B to Q which are perpendicular to line DC

∠APD =∠BQC (Right angle)

That is ∠D ≅ ∠C

Now the perpendiculars AP and BQ are congruent

By AAS Property, triangles APD and BQC are congruent and this implies that the hypotenuses AD and BC are congruent.

Therefore the legs AD and BC are congruent.

The percent markup is 124.30%.

The wholesale cost of one candle is $5.35

The selling price of the candle is $12

The profit she earns = 12 - 5.35

                                  = $6.65

Here we have to find the percent markup.

The formula for the percent markup =( profit/ wholesale cost )× 100

Markup percent = 6.65 / 5.35 × 100

                          = 1.24299 × 100

                          = 124. 30%

Therefore the markup percentage is 124.30%.

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The conditions for which it is possible to construct triangles are:

So, the condition for which it is possible to construct a triangle:

(A) 60°, 80°, and 80°:

(B) 4cm, 5cm, and 6cm:

(C) 4 cm, 5 cm, and 15 cm:

(D) 4cm, 5 cm, and 50°:

(E) 30°, 60°, and 3 cm:

Therefore, the conditions for which it is possible to construct triangles are:

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Answer:

30 1/2

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

We can see that the same input is mapped into two different outputs, so this is not a function.

A relation maps elements called inputs into another elements called outputs.

Such that a relation is a function if each input is mapped into only one output.

The notation used is (input, output).

So, here we can see the points:

(4, 12) and (4, 15).

The input 4 is being mapped into two different outputs, thus, this is not a function.

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The prime factorization given as 2².3².5 is for the number D. 180.

It should be noted that prime numbers are numbers that can only be divided by itself and one. This include 2, 3, 5, 7, etc

A composite number is one that can be generated by multiplying two smaller positive numbers. It is a positive integer with at least one divisor other than 1 and itself. Prime factorization is defined as the process of determining a number's prime factors so that the original number is evenly divisible by these factors.

In this case, it should be noted that we are given the expression as 2². 3². 5. It simply means that we have to multiply them to get the original number.

This will be:

= 2² × 3² × 5

= 4 × 9 × 5

= 180

Therefore, the number is 180.

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Answer:

8

Step-by-step explanation:

[tex] \frac{72h}{9h} = 8[/tex]

The h is common in the numerator and the denominator, so it cancels out. We are left with 72/9 = 8.

The value of the given expression in simplest form is  34/63.

Mixed fraction

It is a form of a fraction which is defined as the ones having a fraction and a whole number.

Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.

To convert 2(1/7) into improper fraction , we will multiply 7 and 2 and then add 1 to it to get the numerator part and 7 will be the denominator of the fraction that is 15/7.

Given expression:

4(6/7) ÷ 9

We have to find the value of the given expression in simplest form.

We can write the mixed fraction 4(6/7) as 34/7

(34/7)  ÷ 9

(34/7)*(1/9) = (34*1)/(7*9) = 34/63

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As per the given condition for the system of equation, the two numbers are equal to 4 and 3.

As given in the question,

To begin with the solution, let the two unknown numbers be x and y. Now, translating the two mathematical statements into system of equations,

When three times the first of two numbers decreased by the second number equals 9.

3 x - y = 9 ____(1)

Twice the first number increased by the second number equals 11,

2 x + y = 11   ____(2)

By solving resultant system of equations we get,

3 x - y = 9

2 x + y = 11

5x        = 20                    (by adding the two equations)

=> x = 4

Substituting the value of x in second equation,

y = 11 - 2x

 = 11 - 2(4)

  = 11 - 8 = 3

Therefore, as per given condition for the system of equation, the two numbers are equal to 4 and 3.

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Answer:

Quadrant IV .

Step-by-step explanation:

I hope it will be helpful for you.

Answer: answer to A: Clockwise rotations clockwise, while counterclockwise rotations rotate in the opposite direction  

Answer to B: i have no idea but i hope the first one helps

Step-by-step explanation:

The correct options are (A) and (B).

Because

Answer:

(−12,2)

Step-by-step explanation:

1:

Dividing the function by 2 divides all the y-values by 2 as well. So to get the new point, we will take the y-value

(4) and divide it by 2 to get 2

.

Therefore, the new point is

(−12,2)

2:

Subtracting 2 from the input of the function makes all of the x-values increase by 2 (in order to compensate for the subtraction). We will need to add 2 to the x-value

(−12) to get −10

.

Therefore, the new point is

(-10,4)

3:

Making the input of the function negative will multiply every x-value by

−

1

. To get the new point, we will take the x-value

(−12) and multiply it by −1 to get 12.

Therefore, the new point is

(12,4)

4:

Multiplying the input of the function by 4 makes all of the x-values be divided by 4 (in order to compensate for the multiplication). We will need to divide the x-value

(−12) by 4 to get −3

.

Therefore, the new point is

(−3,4)

5:

Multiplying the whole function by

4

increases all y-values by a factor of

4

, so the new y-value will be

4

times the original value

(4), or 16.

Therefore, the new point is

(−12,16)

6:

Multiplying the whole function by

−1

also multiplies every y-value by

−1

, so the new y-value will be

−1

times the original value

(4), or −4.

Therefore, the new point is

(−12,−4)

Answer:

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