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The theorem that verifies that the two right angled triangles are similar is HA.

Two triangles are said to be similar if the ratio of their corresponding sides and the corresponding angles are equal.

Analysis:

From the diagrams KL = OQ ( hypotenuse)

∠L is equal to ∠Q which are acute.

so the two triangles are similar in hypotenuse and acute angle which is the HA theorem.

In conclusion, the HA theorem verifies that the two triangles are similar.

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Answer:  Choice A

f(x) = (x + 2)^2 - 11

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

Work Shown:

y = x^2 + 4x - 7

y+7 = x^2 + 4x

y+7+4 = x^2 + 4x + 4

y+11 = x^2 + 4x + 4

y+11 = (x + 2)^2

y = (x + 2)^2 - 11

f(x) = (x + 2)^2 - 11

In the third step, I added 4 to both sides to complete the square for the x^2+4x portion. Notice that (x+2)^2 = x^2+4x+4. So I added 4 to fill in the missing piece needed to complete the square.

Put another way the '4' added to both sides is because we first divided the x coefficient 4 in half to get 4/2 = 2. Then you square it to get 2^2 = 4.

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

Alternative Method (optional)

y = x^2 + 4x - 7 is in the form of y = ax^2+bx+c

where: a = 1, b = 4, c = -7

Plug those a,b values into the formula below

h = -b/(2a)

h = -4/(2(1))

h = -2

This is the x coordinate of the vertex.

Use it to find the y coordinate of the vertex.

y = x^2 + 4x - 7

y = (-2)^2 + 4(-2) - 7

y = -11

The vertex is located at (h,k) = (-2,-11)

We have the template y = a(x-h)^2 + k update to y = (x + 2)^2 - 11 after plugging in a = 1, h = -2, and k = -11.

Answer:

[tex]11x - 4[/tex]

[tex]11x {}^{1 - 1} [/tex]

[tex]11x {}^{0} [/tex]

[tex]11 \times 1[/tex]

[tex]x = 11[/tex]

Answer

720π cm²

Step-by-step explanation:

Surface area of cylinder

A=2πr(s+r)

for r=12cm, s=18cm

A= 2π×12(12+18)

=24π×30

=720π

The correct answer is: [A]: " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). Also called "Ordinate".

Here, The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .

Thus, the correct answer is: [A]: " Look at the graph of the relationship.  Find the y-value of the point that corresponds to x = 1 . That value is the unit rate."

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If these coordinates are translated two units down, we will subtract 2 units from the y axis to have A(2, -1), B(0, -3) and C(2, -3)

Translation is a transformation technique of changing the position of an object on the xy-plane.

Given the following coordinate of a triangle expressed as:

A(2, 1)

B(0, -1)

C(2, -1)

If these coordinates are translated two units down, we will subtract 2 units from the y axis to have:

A(2, -1)

B(0, -3)

C(2, -3)

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The correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Given that:-

The equation of the line will be calculated as:-

The intercept of the line will be;-

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{500-250}{20-10}=25[/tex]

The equation of the line is given as:-

y - y₁ = m( x - x₁ )

Putting the coordinates:-

y - 250 = 25 ( x - 10 )

y - 250 = 25x - 250

y = 25x

Therefore the correct answer is option 3 which is the equation for the line of best fit of this data is y = 25x.

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If the linear equation with one variable is x / 4 + 2 = –2. Then the value of x will be negative 16.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The equation is given below.

x / 4 + 2 = –2

Solving for x, we have

x / 4 + 2 = –2

     x / 4 = – 2 – 2

     x / 4 = – 4

          x = – 4 × 4

          x = – 16

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We will see that g(x) is a reflection across the y-axis of f(x), then:

   [tex]g(x) = f(-x) = 3^{-x\\[/tex]

By looking at the graph, we can see that g(x) is a reflection across the y-axis of f(x).

So we can write:

g(x) = f(-x)

Here we know that:

[tex]f(x) = 3^x[/tex]

Then, replacing f(x) on the formula for g(x), we get:

[tex]g(x) = f(-x) = 3^{-x\\[/tex]

That is the function g(x) shown in the figure.

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Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

Answer:

Answer:

=5^(-4)*5^(-3)

=5^(-7)

=1/5^(7)

Step-by-step explanation:

i took the denominator and multiplied it to the numerator

when powers of the same base are multiplying we add the exponents, so I added the -3 to -4 and got -7 which gives me 5^(-7) which is 1/5^(7)

The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. The correct options are A, B, and, C.

The incenter of a triangle is the point at which the triangle's three internal angle bisectors connect. In other words, it is the point at which the internal angle bisectors of the triangle intersect.

The properties that are true about the incenter of a triangle are:

A. The incenter is equidistant from each side of the triangle.

B. The incenter of a triangle is always inside it.

C. The incenter is where all of the bisectors of the angles of the triangle meet.

Hence, the correct options are A, B, and, C.

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Answer:

Step-by-step explanation:

x^2 + 44^2 = 55^2

x^2 + 1936 = 3025

3025-1936 = 1089

sqrt(1089) = 33

x = 33

Answer:

X=33

Step-by-step explanation:

this is a right traingle so you can use pythagorean theorem

A^2 +B^2 =C^2

A^2 +44^2= 55^2

A^2 + 1936= 3025 subtract 1936 from both sides

A^2= 1089 now square root both sides

A=33

Work Shown:

[tex]_{n} C _{r} = \frac{n!}{r!(n-r)!}\\\\_{25} C _{3} = \frac{25!}{3!*(25-3)!}\\\\_{25} C _{3} = \frac{25!}{3!*22!}\\\\_{25} C _{3} = \frac{25*24*23*22!}{3!*22!}\\\\ _{25} C _{3} = \frac{25*24*23}{3!}\\\\ _{25} C _{3} = \frac{25*24*23}{3*2*1}\\\\ _{25} C _{3} = \frac{13800}{6}\\\\ _{25} C _{3} = 2300\\\\[/tex]

Answer:

0.2

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Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

Answer:

I believe I found your question, I hope this helps.

Step-by-step explanation:

Answer:

Yes because 2(3) + 3 equals 9

Step-by-step explanation:

He correctly substituted x=3 into the equation and y=9. When working out both sides, he saw that both sides were equal to each other, so (3,9) is a solution!

Answer:

Step-by-step explanation:

we are given a right triangle and the measure of its two legs .

x represents the length of the hypotenuse.

……………………………………………………………………

Then (by applying the Pythagorean theorem) we obtain :

[tex]x=\sqrt{24^{2}+7^{2}}[/tex]

  [tex]=\sqrt{576+47}[/tex]

  [tex]=\sqrt{625}[/tex]

  [tex]=25[/tex]

Answer:

10

Step-by-step explanation:

Answer:

square root function; y = -√(x + 2) - 1

Step-by-step explanation:

the graph shown is a square root function

the parent of a square root function is y = √x

you transform this equation using y = a√(x - h) + k

it is reflected across the x axis so you put the negative before the a

since there is no dilation the a is blank

y = -√(x - h) + k

the h is the horizontal shift

it went 2 to the left so that is -2

that makes it y = -√(x - -2) + k

which is also y = -√(x + 2) + k

the k is the vertical shift

it went 1 down

that makes it y = -√(x + 2) - 1

that is your equation

Proving that Triangle CDA is congruent to triangle CDB below:

Congruent triangles can be defined as triangles that have the same size and shape.

A congruent triangle, corresponding angles are equal also the corresponding sides are equal.

In conclusion, the proof that Triangle CDA is congruent to triangle CDB is given above

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The length of PC  is 6

Sure hope this helps you :D

Answer:

D

Step-by-step explanation:

the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.

note that BP = 16 - PC , then

[tex]\frac{BP}{PC}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )

[tex]\frac{16-PC}{PC}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex] ( cross- multiply )

4 PC = 5(16 - PC) ← distribute parenthesis

4 PC = 80 - 5 PC ( add 5 PC to both sides )

9 PC = 80 ( divide both sides by 9 )

PC = 8.888... ≈ 9 ( to the nearest whole number )

After 15 seconds rocket reaches to maximum height is 225 units.

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, the given equation of height

            h(t) = -t² + 30t

             y = -t² + 30t

Now, on differentiating both side with respect to t, we get

        dy/dt = -2t + 30

put dy/dt = 0, we get

       0 = -2t + 30

        2t = 30

        t = 15

Now, at t = 15 sec. rocket reach at its maximum height.

maximum height at t = 15 sec is

     h(15) = -(15)² + 30(15)

     h(15) = -225 + 450

    h(15) = 225

Thus, after 15 seconds rocket reaches to maximum height is 225 units.

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The sequence of Transformation that could take figure 1 to figure 2 is; Translate by direct Line segment AD.

In the given graph, we can notice that figure 1 is exactly the same as figure two just that they are at different coordinates.

Now, to map figure 1 to figure two, what needs to be done is called translation. This is because In translation transformation, all the points in the object are moved in a straight line in the same direction.

Thus, the correct answer will be to translate by directed line segment AD.

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Answer:

3x^2-5x+8 is the answers for the question

Step-by-step explanation:

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The time taken for the person to get to school based on the equation will be 7 minutes.

From the information given, the equation is given as:

g(x) = x⁴ - 3x² + 4x - 5

Then, we'll put 2 as x. This will be:

= 2⁴ + 3(2)² + 4(2) - 5

= 16 - 12 + 8 - 5

= 7

Therefore, the time taken for the person to get to school based on the equation will be 7 minutes.

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Answer:

84.

Step-by-step explanation:

mean = total of the values  / number of numbers

If the total of the numbers = T:

14 = T / 8

T = 8*14 = 84.

Answer:

909

Step-by-step explanation:

sqrt(30² + 3²) = x

hence the number in the box should be 909

Answer:

909

Step-by-step explanation:

Using pythagoras theorem :

a² + b² = x²

30² + 3² = x²

900+9 = x²

909 = x²

x = √909

Hence the number in the box should be 909

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