ben positions his ladder against a wall so that the top of the ladder is 15 feet above the ground. about how long is his ladder?
A. 16.2 feet
B. 18.6 feet
C. 10.5 feet
D. 21 feet

Answer:

[tex]x = y = 3\sqrt{ 2[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find x and y

The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.

For this kind of parameter, the opposite = the adjacent

i.e. x = y

Apply Pythagoras theorem

[tex]x^2 + y^2= 6^2[/tex]

Substitute x for y

[tex]y^2 + y^2= 6^2[/tex]

[tex]2y^2= 36[/tex]

Divide by 2

[tex]y^2 = 18[/tex]

Take square root

[tex]y = \sqrt{18[/tex]

[tex]y = \sqrt{9 * 2[/tex]

Split

[tex]y = \sqrt{9} *\sqrt{ 2[/tex]

[tex]y = 3*\sqrt{ 2[/tex]

[tex]y = 3\sqrt{ 2[/tex]

[tex]x = y = 3\sqrt{ 2[/tex]

Answer:

40%

Step-by-step explanation:

6/15 = 0.4

0.4x100 = 40%

Answer:

274.05 (I assume they round it to A. 274.1)

Step-by-step explanation:

The figure seems to be comprised of 7 triangles, each of base 8.7 and height 9.

total area would be

7 * (8.7 * 9 / 2) = 7 * 39.15 = 274.05

Answer:

No solution

Step-by-step explanation:

Given

[tex]x - y = 11[/tex]

[tex]x - y = 5[/tex]

Required

Solve by graph

See attachment for graph.

From the attachment, lines [tex]x - y = 11[/tex] and [tex]x - y = 5[/tex] do not intersect. This implies that, no solution exist

Answer:

5^7

Step-by-step explanation:

3 per week + blank=8              Step-by-step explanation: brainly plz

Answer:

C. 4x-4

Step-by-step explanation:

If you divide by 4 on the left side you get...

16x/4 - 16/4

4x - 4

We are dividing by 4 because it was factored out of the expression.

Answer: 17.9

Step-by-step explanation:

Answer:

a. False the series [tex]\sum\limits_{i=1}^\infty (-1)^n[/tex]is bounded but does not converge

b. False, xₙ = n + (-1)ⁿ⁻¹(n - 1) does not diverge to infinity but it is not bounded for n ≥ 1

c. False some bounded sequences are divergent

An example of divergent sequences, aₙ, and bₙ, such that aₙ + bₙ converges is [tex]a_n = \sum\limits_{n} \dfrac{1}{n} , \, b_n = \sum\limits_{n} \dfrac{-1}{n}[/tex]

[tex]\sum\limits_{n} \dfrac{1}{n} + \sum\limits_{n} \dfrac{-1}{n}[/tex] is convergent

Step-by-step explanation:

Answer:

B: 9

Step-by-step explanation:

First plug in the numbers to the equation

[tex]\frac{1}{4} (c^{3} + d^{2})[/tex]

[tex]\frac{1}{4} (-4^{3} + 10^{2})[/tex]

Then use PEMDAS to solve

[tex]\frac{1}{4} (-4^{3} + 10^{2})[/tex]

[tex]\frac{1}{4} (-64 + 100)[/tex]

[tex]\frac{1}{4} (36)[/tex]

9

Answer:

8x(4) = 64

8x = 16

h = 2 inches

Answer:

5

Step-by-step explanation:

Answer:Surface Area = 6×542 = 17496 feet2

Step-by-step explanation:

Answer:

125 cubic inches

Step-by-step explanation:

Hey There!

We can easily find the volume of a cube by cubing the side length

[tex]5^3\\5*5=25\\25*5=125[/tex]

so we can conclude that the volume of the block of cheese is 125 cubic inches

Answer:

About 5 to 5.5 hours

Step-by-step explanation:

Get out of my swamp!

Answer:

b) Find P(X>0.6)

Explanation:

In order to find the product to the unknown variable you have to first solve the equation that has the parenthesis, The reason you should first find the parenthesis is because of  The Order Of Operations, You have to first do parenthesis to find the unknown variable.

Answer:

divide 9,255 divide 1/3 and you will get your answer hope this helps :)))

Step-by-step explanation:

In the town of Summit, 3,085 people have jobs. If there are 9,255 people in the town and 1/3 of them are employed.

To find the number of people in the town of Summit who have jobs, we can multiply the total population by the fraction representing the employed individuals.

Total population = 9,255 people

Fraction employed = 1/3

Number of people employed = Total population * Fraction employed

Number of people employed = 9,255 * (1/3)

To simplify the fraction (1/3), we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.

Dividing 1 and 3 by 1, we get:

1/1 = 1

3/1 = 3

So, the simplified fraction is 1/3.

Continuing the calculation:

Number of people employed = 9,255 * (1/3)

Number of people employed = 9,255 / 3

Number of people employed = 3,085

Therefore, in the town of Summit, 3,085 people have jobs.

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Answer:

triangular pyramid

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

Answer:

1,000

Step-by-step explanation:

pls give brainliest

Answer:

The p-value is approximately 0.9015  

Step-by-step explanation:

The statistic parameters are;

The population mean, μ₀ = $85,000

The population standard deviation, σ = $8,700

The size of the sample, n = 50

The sample mean annual profit, [tex]\bar x[/tex] = $82,441

The null hypothesis, H₀: μ = 81,000

The alternative hypothesis, Hₐ: μ > 81,000

Given that n > 30, a z-test is used

The test statistic ≈ 1.29

Therefore, we have;

[tex]z=\dfrac{\bar{x}-\mu_0 }{\dfrac{\sigma }{\sqrt{n}}} = 1.29[/tex]

From the z-score, the p value for a test statistic of 1.29 = 0.90147 which is 0.9015 after rounding up to 4 decimal places

The expression expressed as a difference is (a - 2) - (-7).

We have,

We can express a + 5 as a difference by subtracting a suitable term from it.

One way to do this is to subtract 2 and add 2, like this:

a + 5 = a + 5 - 2 + 2   (adding and subtracting 2)

     = (a - 2) + 7     (rearranging)

Now,

We can express a + 5 as the difference between a - 2 and -7, like this:

a + 5 = (a - 2) - (-7)

Thus,

The expression expressed as a difference is (a - 2) - (-7).

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Answer:

(-3b) (10a -3b)

Step-by-step explanation:

(5a–3b)^2–25a^2

Replace (5a–3b) with x

x^2 - (5a) ^2

We have the difference of squares

( x-5a) (x+5a)

Now replace x with (5a -3b)

(5a -3b -5a) ( 5a -3b +5a)

Combine like terms

(-3b) (10a -3b)

Answer:

(5a-3b)²-25a²

= 25a²+9b²-2×5a×3b-25a { (a-b)²= a²+b²-2ab}

=9b²-30ab

=3b(3b-10a)

= -3b(10a-3b)

Ans

Hope, it helped!

Answer:

Polynomials are closed under addition and subtraction, which is fancy mathspeak that means that whenever we add or subtract two polynomials, we always get another polynomial. In that way, they behave a lot like the numbers you're probably already familiar with. Adding and subtracting:

And it works the same with polynomials!

Answer: Equation for the line of best fit is given by f(x)=-4.28402x+0.0875

Step-by-step explanation: like what you just put in your picture

Long Course Season Recorded Best time

2005 2:33.42

2006 2:24.81

2007 2:10.93

2008 2:03.45

2009 1:58.67

2010 1:59.17

2011 1:55.06

2012 1:55.82

2013 1:54.81

2014 2:00.03

-Since we can see from the scatter plot that it has negative correlation.

Equation for the line of best fit is given by f(x)=-4.28402x+0.0875

- This is what I can give you I see some people do this work before and when I see it I just take note and I think it was the answer...

- Hope this help :)

Answer:

Step-by-step explanation:

You have to use the power rule for this. The way I teach my Algebra 1 students to do this is take everything inside the parenthesis and put it into its own set of parenthesis, and then raise each one to the outside power. One thing at a time makes it not so overwhelming. Like this:

[tex](4)^2(x^5)^2(y^3)^2[/tex]

Now follow the power rule. Multiply the power of each element in the parenthesis by the 2 outside.

[tex](4^1)^2=4^2=16[/tex], then [tex](x^5)^2=x^{10[/tex], and finally, [tex](y^3)^2=y^6[/tex].

Now put it all together to get:

[tex]16x^{10}y^6[/tex]

Step-by-step explanation:

180-123 = 57 G = 57

6x -1 + 5x +14 +57 = 180

11x = 110

x = 10

H = 6(10) - 1 = 59

Answer:

59°

Step-by-step explanation:

Use the equation:

( 6x - 1 )° + ( 5x + 14 )° = 123°

Combine like terms

6x + 5x = 11x         -1 + 14 = 13

New simplified equation:

11x + 13 = 123

Subtract 13 from both sides of the equation

11x + 13 = 123

       -13    -13

We are subtracting because the opposite of addition is subtraction and we are using PEMDAS backwards to isolate the variable 'x' on one side of the equation.

Equation now:

11x = 110

Divide both sides of the equation by 11

[tex]\frac{11x}{11}[/tex] = [tex]\frac{110}{11}[/tex]

Solve

x = 10

Solve for the measure of angle H

Plug in the variable

6(10) - 1

60 - 1 = 59

measure of angle H is 59°