2. Noah is solving the equation x² + 8x + 15 = 3. He begins by rewriting the
expression on the left in factored form and writes (x + 3)(x + 5) = 3. He
does not know what to do next.
Noah knows that the solutions are x = -2 and x = -6, but is not sure how
get to these values from his equation.
Solve the original equation by completing the square.

The value of s to the nearest whole number is 14. The correct option is the last option 14

From the question, we are to determine the value of s

Using the laws of cosines

a² = b² + c² -2bc Cos A

Then,

s² = 8² + 9² -2(8)(9) cos111°

s² = 64 + 81 - 144 cos111°

s² = 145 - (-51.605)

s² = 145 + 51.605

s² = √196.605

s = 14.0216

s ≅ 14

Hence, the value of s to the nearest whole number is 14. The correct option is the last option 14

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Based on the balance at the start of May and the purchases and payments made by Ruth, the balance at the beginning of April was b. $797.22.

First find the monthly rate:

= 10.91% / 12

= 0.909%

The beginning balance is x:

May balance = (Beginning balance x (1 + monthy rate) + Purchases - Payments

847.64 = x × 1.00909 + 88.34 - 45.17

1.00909x = 847.64 - 88.34 + 45.17

x = $797.22

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Answer:

B on edge

Step-by-step explanation:

Answer:

5[tex]\pi[/tex]/12 rad

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

75(π/180) = 5π/12 radians

arc length = central angle (2πr)

360

measure of the inscribed angle = 75º

measure of the central angle = 150º

arc length = 150 (2π1000)

360

arc length = (5/12)

Answer:

y = - 3x

Step-by-step explanation:

an equation involving direct proportion has the form

y = kx ← k is the constant of proportion

the only equation in this form is

y = - 3x ( with k = - 3  )

The amount I can predict a catfish with a length of 32 inches would weigh is 28in.

Let say the fraction is = yx + b

m = [tex]\frac{20-4}{23-20}[/tex]

= 6/3

=2

Note also that 4= 2 x 20 x b

Make b the subject of the formula and it will be=

B= -36

Therefore, the function will be:

Y= 2x - 36

If x = 32

Then  y = 2. 32 - 36

=28

Therefore, the amount I can predict a catfish with a length of 32 inches would weigh is 28in.

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The P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%, and P(pass | Test C) is 22.07%

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

Part A:

Total number of students = 154

Total number of students passed the test = 49

The probability:

P(pass | Test A) = 49/154 = 31.81%

Part B:

Total number of students = 154

Total number of students passed the test = 46

The probability:

P(pass | Test B) = 46/154 = 29.87%

Similarly, for the probability:

P(pass | Test C) = 34/154 = 22.07%

Thus, the P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%, and P(pass | Test C) is 22.07%

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Answer:

The y axis is the vertical line which goes up and down the x axis is the horizantal line which goes side to side or straight across

Step-by-step explanation:

Answer: 77 children tickets were sold that day

Step-by-step explanation:

5.20x+9.50y=1255.40

x+y=167

                                               5.20x+9.50(167-x)=1255.40

x+y=167                                   5.20x+1586.50-9.50x=1255.40

-x    -x                                       -4.30x+1586.50=1255.40

y=167-x                                              -1586.50   -1586.50

                                                    -4.30x=-331.1

                                                      -4.30  -4.30

                                                       x=77

Considering that the square root of 49 is 7, and 52 > 49, Alejandro was not correct, as the correct integer is of 48.

The integer that has square root n is given by:

S(n) = n².

Hence the closest is given by:

C(n) = n² - 1.

In this problem, we have n = 7, hence:

C(7) = 7² - 1 = 48.

Which means that Alejandro was not correct.

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

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

             What is the equation of the line that passes through the point  (2, 5) and has a slope of 5?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

First let's write the equation of the line in point-slope form:-

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Substitute 5 for y₁, 5 for m and 2 for x₁:-

[tex]\sf{y-5=5(x-2)}[/tex]

That's the equation of the line in Point-slope form.

Now let's convert it into slope-intercept:-

[tex]\sf{y-5=5x-10}[/tex]

Adding 5 to both sides results in our slope intercept equation, which looks like this:-

[tex]\dashrightarrow\bigstar\boxed{\boxed{\bold{\underline{y=5x-5}}}}\bigstar\dashleftarrow[/tex]

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

Answer:

n = 3

Step-by-step explanation:

Isosceles means that the left and right sides (non-parallel sides) are equal to each other and so the base angles are also equal to each other. Then you can make an equation with the 8n^2-11 set equal to the 2n^2+7.

see image.

To solve it you have to set everything equal to zero (get all terms on one side of the equation) FACTOR (you end up with the difference of two squares) and solve, using zero product property. See image.

Answer:

6a+11

Step-by-step explanation:

-24a-44/-4

=

6a+11

have a wonderful day :))

Answer:

-4(6a + 11)

-Step-by-step explanation:

−24a − 44 if −4 is factored out than...

-4 times ____ = -24a

-4x = -24  → divided both sides by -4    

-4x / -4 = -24 / -4  → x = 6

-4 times     6     = -24a

-4 times ____ = -44

-4x = -44  → divided both sides by -4    

-4x / -4 = -44 / -4  → x = 11

-4 times     11     = -44

combine: -4 x 6a - 4 x 11

The equivalent equation of the algebraic Equation (4x - 7)² + 16 = 40x - 70 is; p² + 16 - 10p = 0

We want to simplify the algebraic Equation;

(4x - 7)² + 16 = 40x - 70

Factorize right hand side to get;

(4x - 7)² + 16 = 10(4x - 7)

If p = 4x - 7, then we have;

p² + 16 = 10p

Using subtraction property of equality gives;

p² + 16 - 10p = 10p - 10p

p² + 16 - 10p = 0

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Answer:

%25 of $12 an hour = 3

Answer:

2q + 94

Step-by-step explanation:

2q + 2 + 92 ← collect like terms

= 2q + (2 + 92)

= 2q + 94

Answer:

Step-by-step explanation:

2q + 2 + 92

Reorder and group

2q + (2 + 92)

Caculate

2q + 94

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Answer:

254.34

Step-by-step explanation:

3.14 x 9^2

or

3.14(9 x 9)

hope this helps

have a good day

Answer: Therefore the  length of the pole in  10.1 foot (approx) .

Step-by-step explanation:

To proof

As given

The pole casts a 12-foot shadow when the sun is at a 40° angle of elevation.

x represented the length of pole .

As shown in the diagram

By using the trignometric identity

tan40° = 0.839099631 ( approx )

Put in the above

x = 12 × 0.839099631

x = 10.1 foot (approx)

Therefore the  length of the pole in  10.1 foot (approx) .

Answer the right answer is a

Answer:

Step-by-step explanation:

36-3=33

33 divided by 1.5 equals 22

answer is 22 miles

Answer:

Step-by-step explanation:

1.5x + 3 = 36

1.5x = 33

x = 22 miles

Answer: Ellipse

This cross section is not parallel to the circular base, so we get a stretched out circle of sorts. In other words, we get an ellipse.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

multiply numerator and denominator of [tex]\frac{1}{4}[/tex] by 3

[tex]\frac{1}{4}[/tex] = [tex]\frac{3(1)}{3(4)}[/tex] = [tex]\frac{3}{12}[/tex]

the 2 fractions now have a common denominator of 12 and can be added

[tex]\frac{1}{4}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex]

Answer:

12

Step-by-step explanation:

This a Venn Diagram.....the shaded overlapping area is common to both sets.... it must be a multiple of 3   AND a multiple of  4

12    would work....Right?

Answer:

B.  12.

Step-by-step explanation:

The numbers that will go into the shaded area are those who are divisible by 3 and 4.

12  = (3*4)is the only one in the list.

Answer:

E. 12.5

Step-by-step explanation:

[tex](12 \times 2) + 1 = 25 \\ \frac{25}{2} [/tex]

Answer:

B

Step-by-step explanation:

25/2  = 12.5

so, 12.5 /100

= 1/8

Therefore b is the correcrt answer

Answer:

(6, -5)

Step-by-step explanation:

Midpoint :

Equations formed :

    2. y + 1 / 2 = -2

Coordinates of B : (x, y)

Answer:

12+9r

Step-by-step explanation:

3(4+3r) = 3*4+3*3r = 12+9r

Answer:

The circumference is 6.3 in

The circumference of the circle is given by the equation C = 6.3 inches

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the circumference of the circle be represented as C

Now , the equation will be

Let the radius of the circle be r = 1 inch

Now , circumference of circle = 2πr

Substituting the values in the equation , we get

The circumference of the circle C = 2 ( 3.14159 ) x 1

On simplifying the equation , we get

The circumference of the circle C = 6.3 inches

Hence , the circumference of the circle is 6.3 inches

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