2 right triangles have identical angle measures but different side lengths. The first triangle has side lengths of 6, 10, 8 and the second triangle has side lengths of 3, 5, 4.
Which transformation maps the large triangle onto the small triangle?

dilation
reflection
rotation
translation

Answer:

9

Step-by-step explanation:

First, all the sides of a rhombus are congruent (equal).

So, we just set the side values equal to each other.

This gives us:

6x-5 = 4x+13

-4x      -4x

2x-5 = 13

   +5   +5

2x = 18

Then, divide both sides by 2

x = 9

Hope this helps!

The distance between the given points (4, 9) and (7, 13) is 5 units. The distance between the given points (1, 7) and (5, 10) is also 5 units.

The distance between the given points is given by the formula of distance between two points which is given below:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where d is the distance between the given points. (x₁, y₁) and (x₂, y₂) are the given points.

Using the above formula, we have:

(4, 9) and (7, 13)

Here, x₁ = 4, y₁ = 9, x₂ = 7, and y₂ = 13

We have to find the distance between the given points.

Therefore, we have to use the distance formula as given below.

d = √((7 - 4)² + (13 - 9)²)

d = √(3² + 4²)

d = √(9 + 16)

d = √25

d = 5

Therefore, the distance between the points (4, 9) and (7, 13) is 5.

Using the above formula, we have:

(1, 7) and (5, 10)

Here, x₁ = 1, y₁ = 7, x₂ = 5, and y₂ = 10

We have to find the distance between the given points.

Therefore, we have to use the distance formula as given below.

d = √((5 - 1)² + (10 - 7)²)

d = √(4² + 3²)

d = √(16 + 9)

d = √25

d = 5

Therefore, the distance between the points (1, 7) and (5, 10) is 5.

We can also use this formula to calculate the distance between two points in a three-dimensional space. We would just need to add an extra term to the formula to account for the third dimension.

The distance between the given points (4, 9) and (7, 13) is 5 units.The distance between the given points (1, 7) and (5, 10) is also 5 units.

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Answer:

N/A

Step-by-step explanation:

the question is not in depth could you add a photo

Answer:

The expression (8-i)/(2+i) in standard form is, 3 - 2i

Step-by-step explanation:

The expression is,

(8-i)/(2+i)

writing in standard form,

\((8-i)/(2+i)\\\)

Multiplying and dividing by 2+i,

\(((8-i)/(2+i))(2-i)/(2-i)\\(8-i)(2-i)/((2+i)(2-i))\\(16-8i-2i-1)/(4-2i+2i+1)\\(15-10i)/5\\5(3-2i)/5\\=3-2i\)

Hence we get, in standard form, 3 - 2i

The expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

To write the expression (8-i)/(2+i) in standard form a+bi, we need to eliminate the imaginary denominator. We can do this by multiplying the numerator and denominator by the conjugate of the denominator.

The conjugate of 2+i is 2-i. So, we multiply the numerator and denominator by 2-i:

(8-i)/(2+i) * (2-i)/(2-i)

Using the distributive property, we can expand the numerator and denominator:

(8(2) + 8(-i) - i(2) - i(-i)) / (2(2) + 2(i) + i(2) + i(i))

Simplifying further:

(16 - 8i - 2i + i^2) / (4 + 2i + 2i + i^2)

Since i^2 is equal to -1, we can substitute -1 for i^2:

(16 - 8i - 2i + (-1)) / (4 + 2i + 2i + (-1))

Combining like terms:

(15 - 10i) / (3 + 4i)

Therefore, the expression (8-i)/(2+i) in standard form a+bi is (15 - 10i) / (3 + 4i).

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Among the given sets of vectors, the sets that can be bases for ℝ³ are (a) (2, 0, 0), (4, 4, 0), (6, 6, 6) and (b) (3, 1, -3), (6, 3, 3), (9, 2, 4). The correct options are (a) and (b).

In order for a set of vectors to form a basis for ℝ³, they must satisfy two conditions: (1) The vectors must span ℝ³, meaning that any vector in ℝ³ can be expressed as a linear combination of the given vectors, and (2) the vectors must be linearly independent, meaning that no vector in the set can be expressed as a linear combination of the other vectors.

(a) (2, 0, 0), (4, 4, 0), (6, 6, 6): These vectors span ℝ³ since any vector in ℝ³ can be expressed as a combination of the form a(2, 0, 0) + b(4, 4, 0) + c(6, 6, 6). They are also linearly independent, as no vector in the set can be expressed as a linear combination of the others. Therefore, this set forms a basis for ℝ³.

(b) (3, 1, -3), (6, 3, 3), (9, 2, 4): These vectors also span ℝ³ and are linearly independent, satisfying the conditions for a basis in ℝ³.

(c) (4, -3, 5), (8, 4, 3), (0, -10, 7): These vectors do not span ℝ³ since they lie in a two-dimensional subspace. Therefore, they cannot form a basis for ℝ³.

(d) (4, 5, 6), (4, 15, -3), (0, 10, -9): These vectors do not span ℝ³ either since they also lie in a two-dimensional subspace. Hence, they cannot form a basis for ℝ³.

In conclusion, the correct options for sets of vectors that form bases for ℝ³ are (a) and (b)

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Answer:

A

Step-by-step explanation:

divide all sides by four and you get first answer.

A possible equation to represent the situation described is  x (total of markers)= 90 + (15 x 3) and the diagram is attached below.

An equation can be defined as a mathematical expression that shows equality of two mathematical expressions. Due to this, equations include the symbol =.

A possible equation to represent this situation is:

x = 90 + (15 x 3)

In this equation:

X = Number of total markers

90 = Number of markers left after the first markers were given to the teachers

15 = Number of markers given to the teachers

3 = Number of teachers

In this way, we know that the total of markers is equivalent to ninety markers plus forty-five markers as fifteen markerts were given to three different teachers.

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(a) Prime factorization of each number as a product of powers: 12^9:

12 can be factored as 2^2 * 3^1. Therefore, (2^2 * 3^1)^9 = 2^(29) * 3^(19) = 2^18 * 3^9.

36^15:36 can be factored as 2^2 * 3^2. Therefore, (2^2 * 3^2)^15 = 2^(215)* 3^(215) = 2^30 * 3^30. 169^3: 169 is a prime number, so its prime factorization is simply 13^2. Therefore, 169^3 = (13^2)^3 = 13^(2*3) = 13^6 (b) Prime factorization of each number as a product of powers: 16^13: 16 can be factored as 2^4. Therefore, 16^13 = (2^4)^13 = 2^(4*13) = 2^52.

14^7: 14 can be factored as 2^1 * 7^1. Therefore, (2^1 * 7^1)^7 = 2^(17) * 7^(17) = 2^7 * 7^7. 81^14: 81 can be factored as 3^4. Therefore, 81^14 = (3^4)^14 = 3^(4*14) = 3^56. Note: In each case, the prime factorization is obtained by breaking down the given number into its prime factors and expressing it as a product of those factors raised to their respective powers.

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The area under the graph of f(x) = x^2 + 3x + 1 over the interval [0, 4] using four approximation rectangles and right endpoints is R_4 = 64, and using left endpoints is L_4 = 36.

We have,

We can estimate the area under the graph of f(x) = x^2 + 3x + 1 over the interval [0, 4] using four approximation rectangles and right endpoints as follows:

The width of each rectangle is Δx = (4-0)/4 = 1.

Using the right endpoints, the heights of the rectangles are:

f(1) = 1^2 + 3(1) + 1 = 5

f(2) = 2^2 + 3(2) + 1 = 11

f(3) = 3^2 + 3(3) + 1 = 19

f(4) = 4^2 + 3(4) + 1 = 29

The area of each rectangle is then:

A_1 = f(1)Δx = 5(1) = 5

A_2 = f(2)Δx = 11(1) = 11

A_3 = f(3)Δx = 19(1) = 19

A_4 = f(4)Δx = 29(1) = 29

The total area estimate using the right endpoints.

R_4 = A_1 + A_2 + A_3 + A_4 = 5 + 11 + 19 + 29 = 64

Now, let's repeat the approximation using left endpoints:

The heights of the rectangles are:

f(0) = 0^2 + 3(0) + 1 = 1

f(1) = 1^2 + 3(1) + 1 = 5

f(2) = 2^2 + 3(2) + 1 = 11

f(3) = 3^2 + 3(3) + 1 = 19

The area of each rectangle is then:

A_1 = f(0)Δx = 1(1) = 1

A_2 = f(1)Δx = 5(1) = 5

A_3 = f(2)Δx = 11(1) = 11

A_4 = f(3)Δx = 19(1) = 19

The total area estimate using left endpoints is:

L_4 = A_1 + A_2 + A_3 + A_4 = 1 + 5 + 11 + 19 = 36

Therefore,

The estimate of the area under the graph of f(x) = x^2 + 3x + 1 over the interval [0, 4] using four approximation rectangles and right endpoints is R_4 = 64, and using left endpoints is L_4 = 36.

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Using exponential function concepts, it is found that the common ratio would be given by 0.989.

A decaying exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

In this problem, the amount decays 1.1% a year, hence:

The common ratio would be given by 0.989.

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Answer: C

Step-by-step explanation:

Trust

The total surface area of the trapezoidal prism is S = 3,296 inches²

Given data ,

Let the total surface area of the trapezoidal prism is S

Now , the measures of the sides of the prism are

Side a = 10 inches

Side b = 32 inches

Side c = 10 inches

Side d = 20 inches

Length l = 40 inches

Height h = 8 inches

Lateral area of prism L = l ( a + b + c + d )

L = 40 ( 10 + 32 + 10 + 20 )

L = 2,880 inches²

Surface area S = h ( b + d ) + L

On simplifying the equation , we get

S = 2,880 inches² + 8 ( 52 )

S = 3,296 inches²

Hence , the surface area of prism is S = 3,296 inches²

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This is the formula

V=whl

V= 62x3.5x10=2,170 cm3

Hope this helps!

The additive and multiplicative inverse of v{x} are -1 and 1 respectively.

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a constant function -

v{x} = 1

We can write the additive inverse of v{x} as -

a⁻¹ (v{x}) = - v{x} = - 1

a⁻¹ (v{x}) = - 1                           ..... { 1 }

and

We can write the multiplicative inverse of v{x} as -

m⁻¹ (v{x}) = 1/v{x} = 1/1 = 1

m⁻¹ (v{x}) = 1                                ...... { 2 }

Therefore, the additive and multiplicative inverse of v{x} are -1 and 1 respectively.

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Answer: did u mean to put ukmt

Step-by-step explanation:

Answer:

5/6 or 0.8333333333 (83%)

Step-by-step explanation:

So she landed 15 out of 18 so we are going to divide 15 by 18 (15/18) which gets us 5/6 or 0.8333333333 or 83%

Hopes this help ^-^

The solution is the factor 4y - 6x:. 2(2y - 3x) = 2(2y - 3x). 8 = 2• 4 =. 2(2y - 3x)

8. 2• 4

cancel the common factor: 2

= 2y - 3x. the answer is 2y - 3x

4 4

Answer:

I think you mispelled something there... if the system of equation involves 2x-3, the answer is x = 6/5 and y = -27/5

Step-by-step explanation:

- 7x+3 = -2x-3

1. move -3 to the other side (so add it on both sides)

2. move 7x to the other side (in order to combine like terms)

3. Solve for x (Divide 5 by both systems)

4. Plug x into one of the equations to find y

Answer: yes, the value of x is 4 and angle HEB is 36 degrees

Step-by-step explanation:

1a. Find the value of angle CEB

Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees

2a.set up an equation

After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2

3a. Solve the equation

13x+9x+2=90

22x+2=90 | combine like terms

22x=88 | subtract 2 from both sides

x=4 | divide by 22 on both sides

1b. Set up equation

Knowing x=4 and that angle HEB is 9x the equation is 9(4)

2b. Solve the equation

9(4)

36

\( {16x}^{2} - 4x - 4x + 1 \\ = 4x(4x - 1) - 1(4x - 1) \\ = (4x - 1)(4x -1 )\)

The percentage of people who took less than 30 seconds to complete

the task 84.4%.

The diagram shows us how many people finished the task in what time.

40 people finished in 5-10 seconds.

40 people finished in 10-15 seconds.

30 people finished in 15-20 seconds.

30 people finished in 20-25 seconds.

25 people finished in 25-30 seconds.

25 people finished in 30-35 seconds.

25 people finished in 35-40 seconds.

25 people finished in 40-45 seconds.

15 people finished in 45-50 seconds.

That is what the diagram is telling us, and what "frequency" means in this case.

Therefore,

In total, 255 people participated.

only the last 2 groups took longer than 40 seconds.

Therefore,

The estimate of how many took less than 40 seconds is

255 - 25 - 15 = 215 people.

215 people are how many % of 255 :

100% = 255

1%  = 100%/100

     = 255/100

     = 2.55

215 is a many % as how often 1% fits into these 215 :

215 / 2.55 = 84.31372549%

                 ≈ 84.4%

Complete Question:

Times taken to complete a task. Here is a histogram showing the times taken to complete a task.

40- Estimate the percentage of 35 people who took less than 40 seconds to complete the task.

Give your answer to 1 decimal place.

Frequency Density : 1 5 0 5

Time (Density) :

10 15 20 25 30 35 40 45 50

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The area of the circle is 12.56 square yards.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The circumference of a circle is given by the formula:

Circumference = π x diameter

If the diameter of the circle is 4 yards, then the radius is half of the diameter, or:

radius = diameter / 2 = 4 / 2 = 2 yards

Using the formula for circumference, we can find:

Circumference = π x diameter = 3.14 x 4 = 12.56 yards

Therefore, the circumference of the circle is 12.56 yards.

To find the area of the circle, we can use the formula:

Area = π x radius²

Plugging in the value for radius, we get:

Area = 3.14 x 2² = 3.14 x 4 = 12.56 square yards

Therefore, the area of the circle is 12.56 square yards.

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Answer:

To find the inverse, interchange the variables and solve for  y .

Step-by-step explanation:

f − 1 ( x ) = x /4 + 3

Answer:

Consider the following graph

(a) Find the interval(s) on which fis increasing. (Enter your answer using interval notation.)  = (1,3)U(4,6).

(b) Find the interval(s) on which fis decreasing. (Enter your answer using interval notation.) = (0,1)U(3,4).

(c) Find the open interval(s) on which fis concave upward. (Enter your answer using interval notation.) = (0,2).

(d) Find the interval(s) on which fis concave downward. (Enter your answer using interval notation.) = (2,4)U(4,6).

(e) Find the coordinates of the point(s) of inflection. (x,y)

=  (2, 3), (4, 1)

The graph of the derivative f' of a function fis shown.

(a) on what intervals is f increasing? (Enter your answer using interval notation.) = (0,1)U(3,5)

(b) On what intervals is f decreasing? (Enter your answer using interval notation.) = (1,3)U(5,6)

(c) At what values of x does f have a local maximum or local minimum? (Enter your answers as a comma-separated list.) = 1,3,5

Answer:

Yes!

Step-by-step explanation:

Answer:

Step-by-step explanation:

D . 5

Answer:

D. 5

also its me kw

Answer:

a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

Step-by-step explanation:

Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:

An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x  (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y  (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

P(x, y, z) =

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

The explanation to the answers is now given as follows:

(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]

p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)

q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)

r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)

C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z

P(x, y, z) = profit function

x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively

Therefore, we have:

TR = Total revenue = px + qy + rz …………………………….. (1)

Substituting the relevant values into equation (1), we have:

TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z

TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2

Also,

P(x, y, z) = TR – C ……………………………………… (2)

Substituting the relevant values into equation (2), we have:

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)

P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z

P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26

P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)

Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.

(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]

As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:

In America

From equation (3), we have:

Px = 24 – 0.4x = 0

Therefore, we have:

24 – 0.4x = 0

24 = 0.4x

x = 24 / 0.4

x = 60

In Europe

From equation (3), we have:

Py = 12 – 0.2y = 0

Therefore, we have:

12 – 0.2y = 0

12 = 0.2y

y = 12 / 0.2

y = 60

In Asia

From equation (3), we have:

Pz = 16 - 0.2z = 0

Therefore, we have:

16 - 0.2z = 0

16 = 0.2z

z = 16 / 0.2

z = 80

Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.

To find the first five terms of the Fourier series of the function f(x) = x^2 on the interval [-T, T], we need to compute the coefficients of the cosine and sine terms in the series.

The general form of the Fourier series for a function f(x) on the interval [-T, T] is given by:

f(x) = a0/2 + Σ[ancos(nπx/T) + bnsin(nπx/T)]

To determine the coefficients, we can calculate them using the formulas:

an = (2/T) * ∫[f(x)*cos(nπx/T)] dx

bn = (2/T) * ∫[f(x)*sin(nπx/T)] dx

For the function f(x) = x^2, we can substitute it into the above formulas and compute the integrals to obtain the coefficients.

However, without specifying the value of T, it is not possible to calculate the exact values of the coefficients. The interval [-T, T] needs to be defined, as it determines the period of the function.

Once the value of T is provided, we can evaluate the integrals and compute the coefficients, which will allow us to determine the first five terms of the Fourier series for f(x) = x^2 on the given interval.

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Answer:

Step-by-step explanation

taco: góc FBC + góc FBA = 90° mà góc FBA + góc FAB = 90

⇒góc FAC = góc FBC mà góc FBC = góc EDC ⇒ góc FAC = góc EDF

xét Δ ABF và Δ DCE có

góc FAC = góc EDF

góc F = góc E = 90°

⇒ tam giác ABF đồng dạng với tam giác DCE

⇒ AB/DC = BF/EC ⇒ AB.EC = DC.BF mà AB = DC ⇒ EC=BF=4