An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77^{\circ} ∘ with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.

Answer:

f(x) = -x^2 + x + 12.

Step-by-step explanation:

f(x) = a(x - 4)(x + 3)    as the x-intercepts are  -3 and 4.

a is some costant.

At the y intercept x = 0 so we have:

y = 12 = a(0-4)(0+3)

12 = -12a

a = -1

So our eaution is f(x) = -(x - 4)(x + 3)

= -(X^2 - x - 12)

=  -x^2 + x + 12

Answer: The answer is 13, read on to find out

Step-by-step explanation: The traingles are simliar so the values are similar as well. Find a lowest common factor of the values.

The lowest common factor is 4 because all the numbers can be divided by the number 4.

20 divided by 4 is 5 which is already shown on the graph

48 divided by 4 is 12

All we have to do now is 52 divided by 4

Hope I helped you answer the question! Have a great day/afternoon!

Answer: 2d+3<=9

Step-by-step explanation:2 times a number is 2d plus 3 is +3 less than or equal to is <=

Answer:

y = 6 x + 1

y = 1 x + 1

'^' :)))))

Answer:

X' (-8,-2)

Step-by-step explanation:

You move -6 two spaces to the left making -8 and 3-5 = -2

Answer:

The number line "D" represents the solution to 5+8x<3(2x+4)

Answer:

Solve;

5 + 8x < 3(2x + 4)

Perform the distributive property:

5 + 8x < 6x + 12

-5              -5

8x < 6x + 7

-6x     -6x

2x < 7

/2   /2

x < 3.5, so your answer is D.

Solution 1

7(g - 19) ≥ -14

7g - 133 ≥ -14

7g  ≥ -14 + 133

7g ≥ 119

g ≥ 17

Solution 2

3(7g+17) > -19 + 14g

21g + 51 > -19 + 14g

21g - 14g > -19 -51

7g > -70

g > -10

Solution 3

6(-6g + 6) > -2(19g - 17)

-36g  +36 > -38g + 34

-36g + 38g > 34 - 36

2g > -2

g > -1

Answer:

R is reflexive and transitive but not symmetric.

Step-by-step explanation:

R = {(a, b); a ≤ b}

Clearly (a, a) ∈ R as a = a.

R is reflexive.

Now,

(2, 4) ∈ R (as 2 < 4)

But, (4, 2) ∉ R as 4 is greater than 2.

R is not symmetric.

Now, let (a, b), (b, c) ∈ R.

Then,

a ≤ b and b ≤ c

→ a ≤ c

→ (a, c) ∈ R

R is transitive.

Thus, R is reflexive and transitive but not symmetric.

Answer:

Step-by-step explanation:

Answer:

Male

Step-by-step explanation:

There are 28 males and 26 professors so you are more likely to choose a male rather than professor of any other gender!

Answer:

See below ↓↓↓

Step-by-step explanation:

a) 2 . 1 4 0             b) 2 9 . 9 9          c) 6 . 1 5 7

+ 1 . 7 2 5              +    1 . 4 2             - 1 . 0 0 9

   3 . 8 6 5                 3 1 . 4 1               5 . 1 4 8

Answer:

Step-by-step explanation:

Using the formula for the growth of investment:

           .....[1]

where,

A is the amount after t year

P is the Principal

r is the growth rate in decimal

As per the statement:

Scott invests $1000 at a bank that offers 6% compounded annually.

⇒P = $1000 and r = 6% = 0.06

substitute these in [1] we get;

⇒

Therefore, an equation to model the growth of the investment is,

There are multiple possible solutions for x, two examples are x = 0° and x = 360°.

We need to solve the equation:

sin(2x) = sin(x)

Then we need to find a value x such that the sine of 2x is equal to the sine of x.

Now, because of the periodicity of the sine equation, there are a lot of possible values of x.

One example, trivial, is x = 0, this is because 2*0 = 0, then we would have:

sin(2*0) = sin(0)

sin(0) = sin(0).

Another case is if we take x = 360° (remember that 360° is the period of the sine function), then we can have:

sin(2*360°) = sin(360°)

sin(720°) = sin(360°) = 0

Then x = 360° is another solution.

If you want to learn more about the sine function, you can read:

https://brainly.com/question/9565966

Answer:

282.74

Step-by-step explanation:

Answer:

[tex]\fbox{Surface area of cylinder = 282.6 sq. in.}[/tex]

Step-by-step explanation:

Given:

Shape of object = cylinder

height of cylinder= 4 inches

radius of cylinder= 5 inches

To find:

surface area of cylinder = ?

Solution:

we know that,

[tex]surface \: area \: of \: cylinder =2\pi{rh} + 2\pi {r}^{2}\\Substituting \:the \:constant\: (π =3.14)\\and \:given\: data,\\2\pi{rh} + 2\pi {r}^{2} \: =\\ 2×3.14×5×4+2×3.14× {5}^{2} \\2\pi{rh} + 2\pi {r}^{2} = 125.6 + 157 \\ 2\pi{rh} + 2\pi {r}^{2} = 282.6\\ \fbox{Surface area of cylinder = 282.6 sq. in.}[/tex][/tex]

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Answer:

the answer for question 15 is going to be D. since wen u draw the line on a graph there is only one point that connects to the points we are given in the question so it's (-8,4)

Answer:

The slope is -1/2

Step-by-step explanation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{k-2k}{3k-k}\\ \\m=\frac{-k}{2k}\\ \\m=-\frac{1}{2}[/tex]

Using the t-distribution, as we have the standard deviation for the sample, we could claim that the mean weight in pounds is in the interval (79.1, 85.7).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 100 - 1 = 99 df, is t = 2.6259.

The other parameters have values given by:

[tex]\overline{x} = 82.4, s = 12.6, n = 100[/tex].

We could claim that the mean is any value in the 99% confidence interval, which has bounds given by:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 82.4 - 2.6259\frac{12.6}{\sqrt{100}} = 79.1[/tex]

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 82.4 + 2.6259\frac{12.6}{\sqrt{100}} = 85.7[/tex]

More can be learned about the t-distribution at https://brainly.com/question/16162795

Answer:

Anything between 4 and 14

Step-by-step explanation:

When two lengths of a triangle are added together, they must be greater than the third side. Therefore the unknown length cannot be equal to or less than 4 nor equal to or greater than 14.

Answer:

11, 15, 20

Step-by-step explanation:

[tex]there \: would \: be \: 11 \: between \: 4 \: and \: 9 \\ 4 + 11 = 15 \\ 11 + 9 = 20 \\ 20 + 15 = 35 \\ \: please \: rate \: brainliest[/tex]

The numbers in the grid are:

4     11     9

  15     20

     35

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

4 + x = a _____(1)

9 + x = b ______(2)

And a + b = 35

From (1) and (2),

4 + x = a

9 + x = b

13 + 2x = a + b   ( Adding )

Now,

13 + 2x = a + b

13 + 2x = 35

2x = 22

x = 11

Thus,

4     11     9

  15     20

     35

Learn more about expressions here:

https://brainly.com/question/3118662

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Answer: 1.8 cubic cm

Step-by-step explanation:

Answer:

1.91 ft

Step-by-step explanation:

Formula

where :

Solving for r

Answer:

x=-5/2

Step-by-step explanation:

Hi there!

We are given the following equation:

[tex]6^{x+3} = \sqrt{6}[/tex]

We want to find the value of x

This is an exponential equation. In order to find the value of x, we need to make sure that both sides of the equation are at the same bases before we solve the equation

On the left side, we have 6 (the base) raised to the power of x+3

On the right, we have √6

Here's a trick to make this problem easier: the square root of a number is equal to that number, raised to the power of 1/2. In other words, √a is equal to [tex]a^\frac{1}{2}[/tex]

Therefore, √6 is equal to [tex]6^\frac{1}{2}[/tex]

Rewriting the equation then:

[tex]6^{x+3}=6^\frac{1}{2}[/tex]

Both sides have the same base (6)

Now we can solve the equation for x. Simply take what the exponents are, and then set them equal to each other.

This means:

x + 3 = 1/2

Subtract 3 from both sides

x+3=1/2

  -3   -3
___________

x = -5/2

Hope this helps!

Answer:

that would be C.) 1 and 1/8

Step-by-step explanation:

becuase the denominator never changes and you would make it a mixed number versus leaving it as 9/8

Answer: c

Step-by-step explanation:

Add the numerators

7+2=9

8 out of the 9 will make a whole number

9-8=1

The last 1 in the numerators will make 1/8

1 and 1/8

Answer:

41/20

Step-by-step explanation:

or 2 1/20

Answer:

17190 years.

Step-by-step explanation:

The half-life of carbon-14 is

5730 years.

Therefore, after1 half-life there is 50%=12 of the original amount left.2half-lives there is 25%=14of the original amount left.3 half-lives there is 12.5%=18 of the original amount left.

1−78=18

So, your answer would be the time it takes for carbon-14 to elapse 3 half-lives.

5730⋅3=17190

Answer:

5 days

Step-by-step explanation:

26+35+41+ 18 = 120

120/24 = 5

Answer:

x²-x-20

Step-by-step explanation:

Using Vieta's formula

x²-(sum of roots)x+(product of roots)=0

x²-(5+-4)x+(5×-4)=0

x²-x-20=0

Answer:

h = 16.5

Step-by-step explanation:

Remark

The formula below really is the Pytharagan formula disguised.

h^2 = hypotenuse (side)^2 - (1/2 side)^2

Givens

side = 19 cm

Solution

h^2 = 19^2 - (1/2*19)^2      Substitute given into formula

h^2 = 361 - (9.5)^2            square 9.5

h^2 = 361 - 90.25             Subtract

h^2 = 270.75                    Take the square root of both sides

√h^2 = √270.75

Answer: h = 16.5

Answer:

1.25a-4.4

Step-by-step explanation:

you take :1.5a+0.25a-0.5a=1.25

then:4.7+0.3=4.4

1.25a-4.4

but am not sure sorry

Answer:

Step-by-step explanation:

Collect like terms and simplify