Parts of similar triangles

Find x

Answer:

-2

Step-by-step explanation:

The exponential function system that intersects as x = 1, is  [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].

The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The d Here are two different exponential functions of the required form that intersect at x = 1 -

[tex]y = 3(1)^x[/tex]

[tex]y = \frac{6}{8} \times (4)^x[/tex]

In the first equation, a = 3, and b = 2.

Plugging in x = 1, we get -

[tex]y = 3(1)^1[/tex]

y = 3 × 1

y = 3

So the point of intersection of this equation with the x-axis is (1, 3).

In the second equation, a = 6/8 , and b = 4.

Plugging in x = 1, we get -

[tex]y = \frac{6}{8} \times (4)^1[/tex]

y = 3/4 × 4

y = 3

So the point of intersection of this equation with the x-axis is also (1, 3).

So, both of these equations intersect at x = 1 and are of the form [tex]y = a \times b^x[/tex].

Therefore, the equations are [tex]y = 3(1)^x[/tex] and [tex]y = \frac{6}{8} \times (4)^x[/tex].

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Complete reference question:

144q-15 can be expressed as a product of two factors: 3 and (48q-5). The greatest common factor between 144q and 15 is 3:144q = 3 x 48q15 = 3 x 5, so we can factor out the common factor.

The number or algebraic expression that divides another number or expression completely or with no remainder is factor of that expression ,1 is a factor of every number. It is also the smallest factor of a number. or we can say a factor of a number is defined as an exact divisor of the given number. example, the factors of 20 are 1, 2, 4, 5, 10, and 20.

Given that an equation 144q-15

express 144q-15 as a product of two factors,

we can use factorization by grouping:

144q-15 = 12*12q - 3*5 = 3(412q - 5)

Therefore, 144q-15 can be expressed as the product of two factors:

3(48q-5)

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Answer:

512 ft and 1,232 ft

Step-by-step explanation:

area is length x width

the pool's area can be calculated doing 32ft x 16ft

the area of the pool is 512 ft

the deck's area can be calculated doing 28ft x 44ft

the area of the deck is 1,232 ft

you're welcome<3

Therefore  the probability of drawing a ball with a number less than 20 is 0.38 or 38%.

Probability is a measure of an event's likelihood or chance of occurring. It is usually expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is unavoidable.

The probability of drawing a ball with a number less than 20 is calculated by dividing the total number of balls by the number of balls less than 20.

There are 19 balls numbered 1 through 19. As a result, the likelihood of drawing a ball with a number less than 20 is:

P(less than 20) = total number of balls / total number of balls = 19 / 50 = 0.38

So the chance of drawing a ball with a value less than 20 is 0.38, or 38%.

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Answer:

50% chance

ur welcome-ssq

The total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

The interest you receive is referred to as compound interest. Using simple math, you can see how this works: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year.

A = P*(1 + r/n)[tex]^(^n^*^t^)[/tex]

A is the total amount

P is the principal (initial amount borrowed), which is $1,000 in this case

r is the annual interest rate expressed as a decimal, which is 0.08 (8%)

n is the number of times the interest is compounded per year, which is usually 12 (monthly compounding) or 1 (annual compounding)

t is the time in years, which is 4 in this case

Assuming that the interest is compounded annually (n=1), we can plug in the values and simplify:

A = 1000*(1 + 0.08/1)¹⁴

= 1000(1.08)⁴

= 1000*1.3605

= $1,360.50

the total amount of money you will pay back when borrowing $1,000 for 4 years at an annual interest rate of 8% with annual compounding is $1,360.50.

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Answer: 1.2 pounds of raisins

Step-by-step explanation:

If six pounds of raisins are distributed equally into five bags, then each bag will have an equal amount of raisins. To find out how many pounds of raisins are in each bag, we can divide the total amount of raisins by the number of bags:

6 pounds ÷ 5 bags = 1.2 pounds per bag

Therefore, each bag will have 1.2 pounds of raisins.

To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

Answer:

X=-1 or 9

Step-by-step explanation:

using the quadratic formula:

[tex]X=\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

X=-1

X=9

Answer:

(x - 5)^2 = 15 and (x + 13)^2 = 3

Step-by-step explanation:

Sure, I can help you with that.

Let's start with the first equation:

0 = x^2 - 10x + 10

To rewrite this equation in the form (x - p)^2 = q, we need to complete the square.

First, let's factor out the coefficient of x^2:

0 = 1(x^2 - 10x + 10)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (10/2)^2 = 25:

0 = 1(x^2 - 10x + 25 - 25 + 10)

Now we can rearrange the terms inside the parentheses and simplify:

0 = 1((x - 5)^2 - 15)

Finally, we can rewrite the equation in the desired form by adding 15 to both sides:

15 = (x - 5)^2

So the first equation in the form (x - p)^2 = q is:

(x - 5)^2 = 15

Now let's move on to the second equation:

x^2 + 26x + 167.5 = 0

Again, we need to complete the square to rewrite this equation in the form (x - p)^2 = q.

First, let's factor out the coefficient of x^2:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 167.5)

Next, we want to add and subtract a value that will allow us to complete the square inside the parentheses. In this case, we will add and subtract (26/2)^2 = 169:

x^2 + 26x + 167.5 = 1(x^2 + 26x + 169 - 169 + 167.5)

Now we can rearrange the terms inside the parentheses and simplify:

x^2 + 26x + 167.5 = 1((x + 13)^2 - 1.5)

Finally, we can rewrite the equation in the desired form by adding 1.5 to both sides:

1.5 = (x + 13)^2 - 1.5

So the second equation in the form (x - p)^2 = q is:

(x + 13)^2 = 3

The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Answer:

0=-ax^2+bx+c

Step-by-step explanation:

All corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]

We can use the distance formula to find the length of the sides of both quadrilaterals, and then find the ratio of corresponding side lengths to determine the scale factor of the dilation.

Let's start with the original quadrilateral ABCD. The length of AB is:

[tex]$\sqrt{(9 - (-3))^2 + (3 - 0)^2} = \sqrt{12^2 + 3^2} = \sqrt{153}$[/tex]

Similarly, the lengths of BC, CD, and DA are:

[tex]BC: $\sqrt{(9 - 9)^2 + (9 - 3)^2} = 6$[/tex]

[tex]CD: $\sqrt{(-3 - 9)^2 + (3 - 9)^2} = \sqrt{144 + 36} = \sqrt{180} = 6\sqrt{5}$[/tex]

[tex]DA: $\sqrt{(-3 - (-3))^2 + (3 - 0)^2} = 3$[/tex]

Now, let's find the corresponding side lengths of the dilated quadrilateral A'B'C'D'. The length of A'B' is:

[tex]$\sqrt{(3 - (-1))^2 + (1 - 0)^2} = \sqrt{16 + 1} = \sqrt{17}$[/tex]

Similarly, the lengths of B'C', C'D', and D'A' are:

[tex]B'C': $\sqrt{(3 - 3)^2 + (3 - 1)^2} = 2$[/tex]

[tex]C'D': $\sqrt{(-1 - 3)^2 + (1 - 3)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5}$[/tex]

[tex]D'A': $\sqrt{(-1 - (-3))^2 + (1 - 0)^2} = \sqrt{4 + 1} = \sqrt{5}$[/tex]

Now we can find the ratio of corresponding side lengths:

[tex]$\frac{\text{length of A'B'}}{\text{length of AB}} = \frac{\sqrt{17}}{\sqrt{153}} = \frac{\sqrt{17} \cdot \sqrt{153}}{153} \approx 0.821$[/tex]

[tex]$\frac{\text{length of B'C'}}{\text{length of BC}} = \frac{2}{6} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of C'D'}}{\text{length of CD}} = \frac{2\sqrt{5}}{6\sqrt{5}} = \frac{1}{3}$[/tex]

[tex]$\frac{\text{length of D'A'}}{\text{length of DA}} = \frac{\sqrt{5}}{3}$[/tex]

Since all corresponding side lengths have a ratio of [tex]\frac{1}{3}$[/tex] or less, we can conclude that the scale factor of the dilation is less than or equal to [tex]\frac{1}{3}$[/tex]. To find the exact scale factor, we can choose any two corresponding side lengths and take their ratio.

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Step-by-step explanation:

FV = PV ( 1 + i)^n     FV = future value ....what you are looking for

                                  PV = present value = $ 6000

                                    i = decimal periodic interest = .07/12

                                        n = periods = 5 yr * 12 monts/yr = 60 periods

FV = $ 6000 ( 1 + .07/12)^60 = $  8505.75

Answer:

Step-by-step explanation:

your mom

Answer:

The quotient of 13 and 0.4 can be found by dividing 13 by 0.4.

13 ÷ 0.4 = (13/1) ÷ (2/5) = (13/1) × (5/2) = 65/2 = 32.5

So the answer is D. 32.5.

Step-by-step explanation:

The quotient of 13 and 0.4 is 32.5. The method involves directly dividing 13 by 0.4, either manually or using a calculator.

The student is asking for the quotient of 13 and 0.4. Quotient means the result of a division operation. In this case, we divide 13 by 0.4. Here's how:

So, the quotient of 13 and 0.4 is 32.5. Therefore, the answer is (D) 32.5.

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Answer:

trust yourself cuh

Step-by-step explanation:

Winston's economic profit based on the forgone salary of $60,000, and the revenue of $150,000 is $78,000. The correct option is therefore;

$78,000

An economic profit is a profit that accounts for both the explicit and implicit costs of a business. The economic profit is obtained from the difference between the total revenue and the costs including the opportunity costs.

The annual salary of Winston as an accountant = $60,000

The amount Winston's financial asset generates = $4,000 per year

The cost of running the business = $8,000

The amount Winston earns as revenue = $150,000

Therefore;

Winston's opportunity cost which is the forgone alternative, is the amount he earns as an accountant = $60,000

The interest of $4,000, earned from the financial asset = The cost of using the financial asset for the business

The cost of running the business = $8,000

The total cost = Opportunity cost + Cost of making use of the financial asset + The business running cost

The total cost = $60,000 + $4,000 + $8,000 = $72,000

The economic profit = The total revenue - The total cost

Therefore;

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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Answer:4? Think

Step-by-step explanation:

The image of the original figure after the translation and reflection is congruent to the original figure.

A particular type of transformation on the coordinate plane called translation keeps the size of the point or geometrical shape constant while only changing the position. Along the x-axis and y-axis in the coordinate system, the point or the figure can be moved in any direction, including up, down, right, left, and multiple directions.

1. By taking away 4 from the x-coordinate and adding 8 to the y-coordinate, we can translate a point 4 units left and 8 units up.

2. Point A after translation is situated at (-2, 9).

3. We negate the x-coordinate and leave the y-coordinate unaltered to indicate a point over the y-axis.

4. Point B is obtained by reflecting point A over the y-axis (2, 9).

5. Indeed, the resulting representation is consistent with the original figure since the rigid transformations of translation and reflection maintain angles and distances. As a result, the original figure's picture after translation and reflection corresponds to the original figure.

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Answer:

7.2

Step-by-step explanation:

The 1 looks at the number to the right of it. If the number to the right is 5 or more, the 1 moves up to a 2. Hope this  helps!

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Based on the given conditions, the lock solution is 205.

To solve the lock, to calculate the total score based on the given conditions:

Crocus: + 20

Daffodil: + 25

Snowflake: - 50

Tulip: + 30

Bird-Red: + 25, else + 10

Calculating the scores for each input:

TULIP: +30

CROCUS: +20

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

TULIP: +30

DAFFODIL: +25

CROCUS: +20

Total score = 30 + 20 + 25 + 30 + 25 + 30 + 25 + 20 = 205

Therefore, the solution for the lock is 205.

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Image transcribed:

SPRING NOW LOADING.

<IF CROCUS, THEN +20>

<IF DAFFODIL, THEN +25>

<IF SNOWFLAKE, THEN -50>

<IF TULIP, THEN +30>

<IF BIRD-RED, THEN +25, ELSE + 10>

TULIP

CROCUS

DAFFODIL

TULIP

DAFFODIL

TULIP

DAFFODIL

CROCUS

Solve Lock

The calclulated value of c to make a perfect square trinomial from 6x^2 + 60x + c is 150

To make a quadratic trinomial a perfect square trinomial, we need to add a constant term that is equal to half of the coefficient of the x-term, squared.

In other words, we need to find a value of c such that:

6x^2 + 60x + c = Perfect square trinomial

Divide through by 6

So, we have

x^2 + 10x + c/6 = Perfect square trinomial

Take the coefficient of x

k = 10

Divide by 2

So, we have

k/2 = 5

Square both sides

(k/2)^2 = 25

This means that

c/6 = 25

So, we have

c = 150

Therefore, to make the trinomial 6x^2 + 60x + c a perfect square trinomial, we need to choose c = 150.

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