A 9 ft ladder leans against the side of a house. The bottom of the ladder is 5 ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.

Answer: 1

\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)

Step-by-step explanation:

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

1

Step-by-step explanation:

Because the shape divided has to create another shape and for 1 it's an oval at the beginning and then after the lines of symmetry go through its seen as 8 triangles.

Answer:

\(6\frac{4}{7}\)

Step-by-step explanation:

Hello,

I am going to start with to change to a improper fraction:

1. I will convert 6 and 9/10 into a improper fraction:

\(69/10\)

2. Now that I have converted the mixed fraction into a improper I can multiply the numerator and the denominator.

\(69 * 20 / 21 * 10 = 1380/210\)

3. Now I can simplify this value and convert it into a mixed fraction

\(46/7\)

After further simplifying I can convert this into an mixed number

\(6\frac{4}{7}\)

The component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.

The component form of the velocity vector of an airplane traveling at 300 mph in the direction of S 45° E can be represented as ⟨300cos(45°), -300sin(45°)⟩. This breaks down the velocity vector into its horizontal (x) and vertical (y) components.

To determine the component form of the velocity vector, we need to consider the given direction and magnitude. The direction S 45° E can be broken down into two components: south (negative y-axis direction) and east (positive x-axis direction).

The magnitude of the velocity is given as 300 mph. The horizontal component of the velocity can be found by multiplying the magnitude by the cosine of the angle (45°) since cosine represents the adjacent side divided by the hypotenuse. Thus, the horizontal component is 300 * cos(45°) = 300 * √2 / 2 = 150√2.

Similarly, the vertical component of the velocity can be found by multiplying the magnitude by the sine of the angle (45°) since sine represents the opposite side divided by the hypotenuse. Therefore, the vertical component is 300 * sin(45°) = 300 * √2 / 2 = 150√2.

Combining these components, the component form of the velocity vector becomes ⟨150√2, -150√2⟩. This represents the velocity vector's magnitude and direction in terms of its x and y components.

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Answer:

y= 3 when x= 0

y=3

Step-by-step explanation:

in the problem, there's a patten in the difference of X and Y,

at first, Y is 3 more than X (2 and 5)

then y is 4 more, 5 more, and 6 more.

y goes up by 1 each time

so if Y is 5 when X is 2, then when X is 1 Y is 4

when X is 0 Y is 3

Answer:

2?

Step-by-step explanation:

y is adding by 3 every time...

Maybe that helps?

Answer:

Add 12x to both sides of the equation

Step-by-step explanation:

Since you are solving for in terms of y, you need to isolate the y variable. To do so, your first step is to add 12x to both sides because you need to get rid of 12x on the left side. However, you also need to add 12x to the right side or else the expression would change.

Answer:

Add 12x to both sides of the equation.

Step-by-step explanation:

9y - 12 x = 36

We want to isolate y

First add 12x to each side

9y -12x+12x = 12x+36

9y = 12x+36

Then divide by 9

9y/9 = 12x/9 +36/9

y = 4/3x +4

Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

Answer:

Step-by-step explanation:

x^2 + 4x - 5 = 0

-4/2 + (sqrt(16 - 4(1)(-5)))/2

-2 + (sqrt(16+20)/2

-2 + (sqrt(36)/2

-2 + 6/2

-2 + 3

-2 + 3 = 1

-2 - 3 = -5

Answer: The probability is 3 out of 20

Step-by-step explanation:

Given data are: Payment of $150 at the end of each of the next 3 years,Payment of $250 at the end of Year 4,Payment of $400 at the end of Year 5,Payment of $500 at the end of Year 6,Rate of interest = 8% annually

Hence, the Present Value of the investment is $382.20

Present value and future value of investment Formula used: PV = Pmt/(1+r)^n,

FV = Pmt((1+r)^n-1)/r

Let's find the Present Value of the Investment: Given, n = 3 years

Pmt = $150

Rate = 8% annually

PV = 150/(1+8%)³

PV = $382.20

Let's find the Future Value of the Investment: Given, n1 = 3 years

Pmt1 = $150

Rate = 8% annually

n2 = 1 year

Pmt2 = $250

n3 = 1 year

Pmt3 = $400

n4 = 1 year

Pmt4 = $500

FV = (150((1+8%)³-1)/8%)+((250+400+500)(1+8%)³)

FV = $1579.51

Hence, the Future Value of the investment is $1579.51.

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Answer:

I'm sorry i cant see the photo its very wierd

Step-by-step explanation:

Answer: A

Step-by-step explanation:

I don't have anything to explain sorry :(

I hope this helps though!

Answer

A

I changed it so no one would be confused.

Answer:

-22

Step-by-step explanation:

5(4+6)-72

5(10)-72

50-72

-22

Answer:

5(4+6)-72
5x10-72
50-72
-22

Step-by-step explanation:

If you use PEMDAS, the P is for parenthesis.
So first, you do the (4+6) and then multiply it by 5, when you get that answer, do the final step. Subtract 72.

Hope this helped!! <3

On solving we got that. he shorter pieces will therefore be 3 feet long and the longer pieces will therefore be 8 feet long.

Since equations are essentially questions, efforts to systematically find answers to those questions have been the driving force behind the development of mathematics. From straightforward algebraic equations that just require addition or multiplication to differential equations, exponential equations that use exponential expressions, and integral equations, there are many different types of equations that range in complexity.

The lengths of the shorter and longer pieces of a board should be determined.

the case

Let's say that the shorter parts are x in length.

as stated

Jared has an 11-foot wooden board with him.

In order for the longer piece to be 4 feet less than 4 times as long as the shorter piece, he wants to cut it into two pieces.

The length of the longer pieces is then equal to 4x - 4.

The equation then becomes

\(x + 4x - 4 = 11\\ 5x = 11 + 4\\ 5x = 15\\ x = 3 ft\)

The shorter pieces will therefore be 3 feet long.

The longer pieces' length -

\(4x - 4\\ = 4 X 3 - 4\\ = 12 - 4\\ = 8 ft\)

The longer pieces will therefore be 8 feet long.

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The solution set for the equation √2cos(2t) - 1 = 0, where 0 ≤ t < 2π, is given by option (b) {π/8, 7π/8}.To find the solution set for the equation √2cos(2t) - 1 = 0, we need to isolate the cosine term and solve for t. First, add 1 to both sides of the equation to obtain √2cos(2t) = 1.

Next, divide both sides by √2 to get cos(2t) = 1/√2. The next step is to find the values of t for which the cosine of 2t equals 1/√2. This occurs when 2t is equal to π/4 or 7π/4, as these are the angles where the cosine function takes the value of 1/√2.

Dividing these angles by 2, we find that t equals π/8 and 7π/8, which gives us the solution set {π/8, 7π/8}. Therefore, option (b) {π/8, 7π/8} is the correct solution set for the given equation in the specified interval.

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Answer:

V=1 4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4

Step-by-step explanation:

Answer:

Picture please

Step-by-step explanation:

Ill check on your other question,, and always make sure there is an image attached when asking something that includes and needs an image/picture/screenshot!

Answer:

\(n = \frac{l-a}{d}+1\)

Step-by-step explanation:

\(l= a+(n-1)d\\\)

\(l -a =(n+1)d\)

Divide both sides of the equation by d

\(\frac{l-a}{d} = \frac{(n-1)}{d}\\ \\\frac{l-a}{d} = n-1\\\\\frac{l-a}{d}+1 = n\)

Answer:

1st question: y=1/3x-1

2nd question: y=-2/3x+9

Step-by-step explanation:

Y=mx+b form is what you are using

when a line in parallel to a line they have the same slop wich is m

when a line in perpendicular they have the opposite reciprocal

Examples: 2/5 opposite reciprocal would be -5/2

Answer:

There would be 876 legs.

Step-by-step explanation:

To do it you could first find how many legs there are on one farm. SO you would take the 6 cats in one barrel. Then times it by the 6 kittens each of them have. That's the number of cats. Then times than number by 4 to get the total number of legs in one barrel. Then you add in the two legs of the farmer. Then times that total number by 6 to get all the legs on all six farms.

Answer:

B

Step-by-step explanation:B

Answer:

6) 12/3

7) 12 + n

8) 10 - w

9. a number t to the power of 2

10. 2 times a number x

11. 2 times 5

12. 4 more than a number n

Answer:

Step-by-step explanation:

Answer:

I dont know the exact numberbut i have clues below

Step-by-step explanation:

Gradient = -1

Rise = 5

Run = -5

We kindly invite to check the image attached below to see the representation of the exponential function. This function shows exponential growth.

In this occasion we must plot the graph of exponential functions of the form:

y = a · bˣ     (1)

Where:

First, we need to follow this procedure to create the graph of the curve on Cartesian plane:

Therefore, we build the exponential curve with the help of a graphing tool (i.e. Desmos), whose result is shown in the image attached below.

From (1) we must understand that exponential functions report growth for b > 1 and decay for 0 < b < 1. Thus, the exponential function y = 3ˣ shows exponential growth according to graphical and analytical findings.

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a) The derivative of the f(x) = 3x+4 / 6x²-x-12 is f'(x) = (18x² - 30x - 12) / (6x² - x - 12)².

b) The derivative of the function f(x) = ( 6x²-x-2 / 3x-2 ) ^3/2 is f'(x) = (18x² - 13x - 10) / (3x - 2)^2 * (6x² - x - 2)^(1/2)

a. To find the derivative of f(x) = 3x+4 / 6x²-x-12, we can use the quotient rule, which states that if f(x) = g(x) / h(x), then f'(x) = [h(x)g'(x) - g(x)h'(x)] / [h(x)]². Applying this formula to our function, we get:

f'(x) = [(6x² - x - 12)(3) - (3x + 4)(12x - 1)] / (6x² - x - 12)²

Simplifying the expression gives:

f'(x) = (18x² - 30x - 12) / (6x² - x - 12)²

b. To find the derivative of f(x) = (6x²-x-2 / 3x-2) ^3/2, we can use the chain rule, which states that if f(x) = g(h(x)), then f'(x) = g'(h(x))h'(x). Applying this rule to our function, we get:

f'(x) = (3/2)(6x² - x - 2)^(1/2)(12x - 1) / (3x - 2)^2

Simplifying the expression gives:

f'(x) = (18x² - 13x - 10) / (3x - 2)^2 * (6x² - x - 2)^(1/2)

In both cases, we can simplify the derivative further by factoring the numerator or by applying algebraic techniques such as long division or polynomial division.

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Answer:

C

Step-by-step explanation:

You know it is an acute angle, meaning that it has to be below 90 degrees.

~theLocoCoco

Answer:

Answer would be C

Step-by-step explanation:

The simple interest I on a principal P of $5,000 with a rate R of 2.5% and a time T of 3 years is $375.

To calculate the simple interest, we can use the formula: I = P * R * T.

Given that I varies jointly as R and T, it means that the interest is directly proportional to both the rate and time. The principal P is the constant of variation, which means it remains constant throughout.

In this case, the principal P is $5,000. The rate R is 2.5% (or 0.025 as a decimal) and the time T is 3 years.

Plugging these values into the formula, we get: I = 5,000 * 0.025 * 3 = $375.

Therefore, the simple interest on a principal of $5,000 with a rate of 2.5% and a time of 3 years is $375.

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