Factor this polynomial expression.


x2 + 12x + 36


A. (x + 9)(x + 4)

B. (x - 6)(x - 6)

C. (x + 6)(x + 6)

D. (x - 9)(x - 4)

Step-by-step explanation:

if

c = 3 + 6 = 9

and

n = 4 + 5 = 9

then it could be true

Answer:

X = 18

Y = 9√3

Step-by-step explanation:

use sin equation for right angle triangle

The sine of the angle

= ( the length of the opposite side ÷ the length of the hypotenuse.)

according to this question,

sin 30 = 9 / X

1/2 = 9 / X

X = 18

use cosine to find y

The cosine of the angle

= (the length of the adjacent side ÷ the length of the hypotenuse.)

cos 30 = y/x

√3/2 = y/ 18

y = 9 ✓3

Answer:

224 ft

Step-by-step explanation:

The tree makes a 90° angle with the ground, so we have a right triangle.

For the 32° angle, the height of the tree is the opposite leg. The length of the shadow on the ground is the adjacent leg.

The trig ratio that relates the opposite leg to the adjacent leg is the tangent.

Let the length of the shadow of the tree on the ground be x.

tan A = opp/adj

tan 32° = 140 ft/x

x = 140 ft/tan 32°

x = 224 ft

Answer: 224 ft

Answer:34/45

Step-by-step explanation:

x+y,=3

x_y=-3

A.,(0,3)

B. (0,3)

C. (0,6)

D. (0 _3)

Given:

The temperature on a mountain peak was 7°F at 6:00 p.m.

By 8:00 p.m., the temperature had dropped to 0°F.

To find:

The temperature at 11:00 p.m. if the temperature continued to drop at about the same rate.

Solution:

Time between 6:00 p.m. to 8:00 p.m. is 2 hours.

Change in temperature in 2 hours is -7°F.

Change in temperature in 1 hours is [tex]-\dfrac{7}{2}^\circ[/tex]F.

Time between 8:00 p.m. to 11:00 p.m. is 3 hours.

Change in temperature in 3 hours is [tex]3\times \dfrac{-7}{2}^\circ[/tex]F, i.e., [tex]-\dfrac{21}{2}^\circ[/tex]F.

Now, the temperature at 11:00 p.m is:

[tex]0-\dfrac{21}{2}=-10.5[/tex]

Therefore, the temperature at 11:00 p.m. is -10.5°F.

Note: All options are incorrect.

Answer:

[2,10,18]

y = 4x + 2

0,2

1,6

2,10

3,14

4,18

Step-by-step explanation:

Answer:

x=0  y=2

x=2  y= 10

x=4  y= 18

Step-by-step explanation:

Is means equals

y = 4x+2

Let x = 0

y = 4(0)+2 = 2

Let x = 2

y = 4(2)+2 = 8+2 = 10

Let x =4

y = 4(4)+2 = 16+2 = 18

Answer:

.36

Step-by-step explanation:

To find the decay factor

y = a(1-b)^x

b = 1-rate of decrease

   = 1-64%

   = 1-.64

   = .36

Answer:

The correct answer is

D) e and l

Answer:

a)

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

The absolute value always gives a positive value , that is

| - a | = | a | = a , then

| - 16 | = | 16 | = 16

Answer:

x = 30

Infinite Solutions

No Solutions

Step-by-step explanation:

First, combine like terms

Then move all variable to one side and isolate them by undoing the action being done to them

Example 1:

6x + 4x - 6 = 24 + 9x

10x - 6 = 24 + 9x

-9x                 -9x

x - 6 = 24

  +6     +6

x = 30

Example 2:

25 - 4x = 15 - 3x + 10 -x

25 - 4x = 25 - 4x

Since they are the same on both sides, this equation has Infinite Solutions

Example 3:

4x + 8 = 2x + 7 + 2x -20

4x + 8 = 4x - 13

-4x        -4x

8 = -13

This statement is untrue, therefore this equation has No Solution

Answer:

-70

Step-by-step explanation:

keep adding -4 until you reach the 18th term for example

-2

-6

-10

-14

-18

-22

-26

-30

-34

-38

-42

-46

-50

-54

-58

-62

-66

-70

Answer:

Step-by-step explanation:

x+2y=-2

2y=-x-2

y=-x/2-2/2

y=-x/2-------(1)

y=1/2x-5-----(2)

(1)=(2)

-x/2=1/2x-5

-x=x-10

-2x=-10

x=5

substitute in 2

         y=(1/2)*5-5

           =5/2-5

          =-2.5

Answer:

42

Step-by-step explanation:

prime factorisation of 1764 = 2^2 × 3^2 × 7^2

hence,

√1764 = √(2^2 × 3^2 × 7^2) =2 x 3 x 7 = 42

Answer:

42

Step-by-step explanation:

1764 = 2 * 882

        = 2 * 2 * 441

        = 2 * 2 *  3 * 147

        = 2 * 2 * 3 * 3 * 49

        = 2 * 2 * 3 * 3 * 7 * 7

[tex]\sqrt{1764} = \sqrt{2*2*3*3*7*7} = 2*3*7 = 42[/tex]

Answer:

A.1800 B.360

Step-by-step explanation:

a- 12-2×180=1800

b- 30x12=360

Answer:

B

Step-by-step explanation:

z^2 - 6z - 27 = 0

(z - 9)(z+3) = 0

z - 9 = 0 z + 3 = 0

z = -3, 9

Make note of the coefficients in the first and fourth equations. They've been conveniently picked so that subtracting one equation from the other eliminates every variable but t. We have

(3r + 2s + t + 2u + 3v) - (3r + 2s + 3t + 2u + 3v) = 7 - 17

-2t = -10

t = 5

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Whenever she began to drive farther east, at 70 km per hour, Prachi was 5 km east of her home.

Let f(n) at the beginning of her nth hour drive be Prachi's distance to her home.

f is a sequence of arithmetic.

Write a series explicit form.

[tex]\to f(n) = 70n + 5[/tex]

Answer:

Arithmetic Sequence, f(n)=5+70(n-1)

Step-by-step explanation:

checked on khan

Answer:

AC = 7.3 in

Step-by-step explanation:

tan(51°) = 9/AC

1.24 = 9/AC

AC = 9/1.24

AC = 7.26

Answer:

2x^2 -1

Step-by-step explanation:

f(x)=2x^2+3

g(x)=x-4

g(f(x))

Replace x in g(x) with the function f(x)

g(f(x)) = 2x^2+3 -4

Combine like terms

         =2x^2 -1

Answer:

These are the intervals of the people who are at least adults and are mature enough to take the survey seriously and answer correctly

Step-by-step explanation:

Answer:

D, the horizontal line is a function

Step-by-step explanation:

To pass the vertical line test, a vertical line cannot go through the function more than once

A is a vertical line so it will fail the vertical line test

B will fail the vertical line test at many points.  One example is at

x =0 where you can see it will intersect at two points

C will fail the vertical line test at many points.  One example is at

x =0 where you can see it will intersect at two points

D is a horizontal line.  This will pass the vertical line test

Answer:

F. 1/2

Step-by-step explanation:

If the ratio of team assistants to players are 1/6 and there are 36 players that means that there are 6 team assistants. If we do the ratio of coaches to assistant that would be 3/6 or F. 1/2

Answer:

The probability is 0.044

Step-by-step explanation:

Step-by-step explanation:

Let p be the probability that the new principal’s performance is approved.

This is obtainable from the survey and it is 8/10 = 0.8

Let q be the probability that the new principal’s performance is disproved.

That will be;

1 - q = 1- 0.8 = 0.2

To calculate the probability that 14 parents names are chosen at random and they all

approve of the principal’s performance, we use the Bernoulli approximation of the binomial theorem.

That will be;

14C14 * p^14 * q^0

= 1 * 0.8^14 * 0.2^0

= 0.043980465111 which is approximately 0.044

Answer:

The correct solution is "(0.092, 0.148)".

Step-by-step explanation:

Given:

Sample size,

n = 500

True proportion,

[tex]\hat {p} = \frac{60}{500}[/tex]

  [tex]=0.12[/tex]

The standard error will be:

[tex]SE=\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

     [tex]=\sqrt{\frac{0.12(1-0.12)}{500} }[/tex]

     [tex]=\frac{0.12(0.88)}{500}[/tex]

The confidence interval is "1.96".

hence,

The required confidence interval will be:

= [tex](\hat p - 1.96 SE, \hat p + 1.96 SE)[/tex]

By substituting the values, we get

= [tex](0.12-1.96\sqrt{\frac{0.12(0.88)}{500} }, 0.12+1.96\sqrt{\frac{0.12(0.88)}{500} } )[/tex]

= [tex](0.092, 0.148)[/tex]

Answer:

Step-by-step explanation:

Let the initial velocity of the ball is u.

At the maximum height the speed is zero.

Let the time is t.

Use first equation of motion.

v = u - gt

0 = u - g t

t = u/g

Let the maximum height is H.

Use third equation of motion

[tex]v^2 = u^2 - 2 gh\\\\0 = u^2 - 2 gH\\\\H = \frac{u^2}{2 g}[/tex]

Answer:

−0.73333333333333

Step-by-step explanation:

This is the decimal form of -11/15

Answer:

Step-by-step explanation:

[tex]\dfrac{45}{56}*100= 0.8035 * 100 = 80.35[/tex] = 80%