What number would you add to both sides of x² + 7x = 4 to complete the square?
Answers:
A. 2²
B. 7²
C. 7²/2
D. [⁷/2]²​

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

Answer:

0.2

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Answer:

[tex]11x - 4[/tex]

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

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

[tex]11 \times 1[/tex]

[tex]x = 11[/tex]

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 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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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]

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:

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

Hope this helped and brainliest please

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]

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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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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Answer:

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

Step-by-step explanation:

Answer:

if a scale factor is less than 1 then your figure gets smaller

Step-by-step explanation:

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:

10

Step-by-step explanation:

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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Answer:

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

Step-by-step explanation:

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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 surface area of the given shape is 285.01 ft²

From the question, we are to calculate the surface area of the given shape.

The given shape in the diagram is a cone.

The surface area of a cone is given by the formula,

[tex]S = \pi r(r+l)[/tex]

Where S is the surface area

r is the radius

and [tex]l[/tex] is the slant height

First, we will calculate the slant height of the cone

[tex]l^{2}=9^{2} +5.6^{2}[/tex] (Pythagorean theorem)

[tex]l^{2}=81+31.36[/tex]

[tex]l^{2}=112.36[/tex]

[tex]l}=\sqrt{112.36}[/tex]

[tex]l=10.6 \ ft[/tex]

∴ The slant height is 10.6 ft

Now, for the surface area

[tex]S = \pi \times 5.6(5.6+10.6)[/tex]
[tex]S = \pi \times 5.6(16.2)[/tex]

[tex]S = 90.72\pi \ ft^{2}[/tex]

[tex]S = 285.0053 \ ft^{2}[/tex]

S ≅ 285.01 ft²

Hence, the surface area of the given shape is 285.01 ft²

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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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Answer:

Graph D

Step-by-step explanation:

Move the constant to the opposite side of the equation and group terms that include the same variable.

g(x) + 1 = x^2 + 2x

Finish the square. Remember to keep the equation balanced by using the same constants on both sides.

g(x) + 1 + 1 = x^2 + 2x + 1

g(x) + 2 = x^2 + 2x + 1

Rewrite as perfect squares

g(x) + 2 = (x + 1)^2

Equation in vertex form:
g(x) = (x + 1)^2 - 2

The vertex:

(-1, -2)

* This a minimum *

Answer:

1 - 135

2 - 45

3 - 45

4 - 135

5 - 135

6 - 45

7 - 45

8 - 135

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:

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

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 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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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 )

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

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

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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