Bentley leans a 22-foot ladder against a wall so that it forms an angle of 74 degrees with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary

Answer:

Step-by-step explanation:

(2,1) and (4,2) are on the line.

slope

[tex]=\frac{2-1}{4-2} =\frac{1}{2} \\[/tex]

eq. of line is

[tex]y-1=\frac{1}{2} (x-2)\\2y-2=x-2\\2y=x\\or \\x-2y=0\\[/tex]

in slope intercept form

[tex]y=\frac{1}{2} x[/tex]

Answer:

Step-by-step explanation:

Answer: 123 boxes

Step-by-step explanation:

Find how many nails she used.

692-200=492

she used 492 nails

we know that 4 nails are needed to set up a box

so we divide.

492/4=123

Sally set up 123 boxes

Answer:

option c

Step-by-step explanation:

a) NOT TRUE

A composite number is a positive integer that can be formed by multiplying two smaller positive integers.

3 and 7 are not composite numbers because each of them can only be divided by one and itself

b) NOT TRUE

2 is also a prime number so 3 and 7 are not the only numbers

c) TRUE

All the number listed are prime numbers hence why they are all at the bottom of the tree (only have 1 and itself as factors)

d) NOT TRUE

21 is not a prime number. The number 21 is divisible by 1, 3, 7, 21. For a number to be classified as a prime number, it should have exactly two factors. Since 21 has more than two factors, i.e. 1, 3, 7, 21, it is not a prime number.

Answer:

For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range

Step-by-step explanation:

The vertex is (1, 2), the domain is all real numbers, and the range is y ≥ 2.

The vertex is (1, 2), the domain is all real numbers, and the range is y ≤ 2.

The vertex is (–1, 2), the domain is all real numbers, and the range is y ≥ 2.

Answer:

see explanation

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 1)² + 2 ← is in vertex form

with vertex = (1, 2 )

The domain of a parabola exists for all real values of x

domain : x ∈ R

the range of the parabola are the values of y from the y- coordinate of the vertex, upwards.

range : y ≥ 2

The expression that is equivalent to 14xy – 28x – 36y + 48 is 2[7x(y-2)-6(3y-4)]

Factorization is a way of separating the equations into two separate factors.

Given the expression below;

14xy – 28x – 36y + 48

Group

(14xy – 28x) – (36y + 48)

14x(y - 2) - 12(3y-4)

Factor out the value of 2 from both terms

2[7x(y-2)-6(3y-4)]

Hence the expression that is equivalent to 14xy – 28x – 36y + 48 is 2[7x(y-2)-6(3y-4)]

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Answer:

2[7x(y – 2) – 6(3y – 4)]

Step-by-step explanation:

I got it right on the test.

Answer:

[tex]\boxed{\sf x = 11.7}[/tex]

[tex]\boxed{\sf b = 9.4}[/tex]

Sine Rule states:

[tex]\sf sin(x) = \dfrac{opposite}{hypotenuse}[/tex]

[tex]\hookrightarrow \sf sin(51) = \dfrac{x}{15}[/tex]

[tex]\hookrightarrow \sf x = 15sin(51)[/tex]

[tex]\hookrightarrow \sf x = 11.657 \ \ \approx \quad 11.7[/tex]

Additional, cosine rule:

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

[tex]\hookrightarrow \sf cos(51) = \dfrac{b}{15}[/tex]

[tex]\hookrightarrow \sf b = 15cos(51)[/tex]

[tex]\hookrightarrow \sf b = 9.4398 \quad \approx \ \ 9.4[/tex]

Step-by-step explanation:

= 5 • ( 4• x )

= 5 ( 4x )

= 20x

[tex]...[/tex]

Answer:

2

Step-by-step explanation:

Start by simplifying the expression:

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

Use distribution:

[tex]4x-4(3)+5x-x^2\\4x-12+5x-x^2[/tex]

Add like terms:

[tex]9x-12-x^2[/tex]

Now, substitute the given value of x into the expression:

[tex]9(2)-12-2^2\\18-12-4\\6-4\\2[/tex]

Answer:

2

Step-by-step explanation:

Given: 4(x − 3) + 5x − x²

Substitute 2 for the value of x in the expression and simplify:

➜ 4(2 − 3) + 5(2) − (2)²

➜ 4(−1) + 10 − 4

➜ -4 + 10 - 4

➜ 2

Therefore, the value of the expression when x equals 2 is 2.

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Answer:

a(y=-5x+2500) b(2,380) c(25months)

Step-by-step explanation:

someone point out if I'm wrong. I'm not so sure about "c".

(how I got b)

So 2 years=24 months

y=-5x+2500

So x would be 24.

-5(24)+2500

-120+2500

2,380

Answer:

201.062in²

Step-by-step explanation:

area for formula of a circle

[tex] {r}^{2} \pi[/tex]

we can now plug in the radius to solve

[tex] {8}^{2} \pi \\ 64\pi \\ 201.062[/tex]

that is the answer

- kan Academy Advance

Answer:

[tex]\tan U = 1[/tex]

Step-by-step explanation:

[tex]\text{Apply Pythagorean theorem,}\\\\~~~~~~\text{Hypotenuse}^2 = \text{Base}^2 + \text{Perpendicular}^2\\\\\implies UT^2 = UV^2 +VT^2\\\\\implies UV^2 = UT^2 -VT^2\\\\\implies UV^2 = \left(7\sqrt 2 \right)^2 - 7^2\\\\\implies UV^2 = 49(2)-49\\\\\implies UV^2 = 49\\\\\implies UV = \sqrt{49} \\\\ \implies UV = 7[/tex]

[tex]\text{Now,}\\\\~~~~~~~~\tan \theta = \dfrac{\text{Perpendicular}}{\text{Base}}\\\\\\\implies \tan U = \dfrac{7}{7}\\\\\\\implies \tan U = 1[/tex]

Answer:

Step-by-step explanation:

Each grandchild will receive 655/13 = 50 with 5 coins left over. She can keep the 5 coins and start again.

Answer

Answer:

50 coins for each grandchild

5 left over.

Step-by-step explanation:

13x50=650

655-650=5

Step-by-step explanation:

oksosjaoqkqeand

[tex]66 \sqrt[3x9 \frac{ \sqrt[xx. \sqrt[36 \sqrt[3136(2 > kaki \: kwl{]{?} ]{?} ]{?} }{?} ]{?} [/tex]

Answer:

20 inches

Step-by-step explanation:

there is only 12 inches in a foot

They want you to solve the iterative process to a point where the value of x is greater than or equal to 6 decimal places.

An iterative process is a mathematical approach that employs an initial value to build a series of improving estimated solutions for a problem, where the nth-term estimation is generated from the prior ones.

You're required to put the value of x₁ = -1 into the equation:

[tex]\mathbf{x_{n+1}= \dfrac{(x_n)^3-1}{4}}[/tex]

So;

[tex]\mathbf{x_{2}= \dfrac{(-1)^3-1}{4}}[/tex]

[tex]\mathbf{x_{2}=-0.5}[/tex]

[tex]\mathbf{x_{3}= \dfrac{(-0.5)^3-1}{4}}[/tex]

[tex]\mathbf{x_{3}=-0.28125}[/tex]

[tex]\mathbf{x_{4}=\dfrac{(-0.28125)^3-1}{4}}[/tex]

[tex]\mathbf{x_{4}=-0.2555618286}[/tex]

x₄ ≅ -0.255562  ( to 6 decimal places)

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Using the line of best fit, it is found that the projected time for a man who is 166 cm tall is of 7.966 minutes.

It gives the project time in minutes to run the 3000 meters for a men of a height of x centimeters, according to the following function:

y = -0.081x + 21.412.

Hence, for a men of 166 centimeters, x = 166 and the projected time in minutes is given as follows.

y = -0.081(166) + 21.412 = 7.966.

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Answer:

[tex]3*(2x+3)*(x+1)[/tex]

Step-by-step explanation:

pull like terms from the problem to re-arrange it into a product

[tex]\left(2x+3\right)\left(3x+3\right)\\3x + 3 = 3 \cdot (x + 1)\\3 \cdot (2x + 3) \cdot (x + 1)\\[/tex]

Answer:

38% is your answer boss. hope that helps :)

The percentage of people who supported the home team is 38 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The total number of people attending the baseball game = 3500 people

The number of people supporting the home team = 1300 people

The number of people supporting the visiting team is = 2170

Now , the equation will be

The percentage of people supporting the home team is = number of people supporting the home team / total number of people attending the baseball game

Now , the equation will be

The percentage of people supporting the home team is A = ( 1300 / 3500 ) x 100

The percentage of people supporting the home team is A = 0.38 x 100

The percentage of people supporting the home team is A = 38 %

Therefore , the value of A is 38 %

Hence , The percentage of people who supported the home team is 38 %

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Answer:

2

Step-by-step explanation:

because (x,y)=(1,2)

Therefore, domine(d)=(x)=1

And, range(r)=(y)=2

So the ans is 2

To increase sales, an online clothing store began giving a 50% off coupon to random customers Six customers each made purchases from the website the binomial random variable and  mean and standard deviation of X  is mathematically given as

[tex]X ~ Bin(n = 6, p = 0.2)[/tex]

x= 0.9798

Generally, the equation for is mathematically given as

P(coupon) = 1/5

P(coupon)= 0.2

the binomial distribution

[tex]X ~ Bin(n = 6, p = 0.2)[/tex]

Therefore, The mean and standard deviation of X

[tex]пВ = np \\np= 6* 0.2 = 1.2\\[/tex]

[tex]x=\sqrt{ np(1 - p)} \\ x=\sqrt{ 6 * 0.2 + (1 -0.2)} \\[/tex]

x= 0.9798

In conclusion, mean and standard deviation of X

x= 0.9798

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Using proportions, it is found that the scale factor of the transformation is of 1/3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, during the transformation, each coordinate was divided by 3, hence, applying the proportion, the scale factor of the transformation is of 1/3.

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The graph for Suav's trip is attached along with the values derived from the information provided.

The key to understanding the graph is that every time spent while he was on the way to the back and back are all added cumulatively.

So when he stops at the store which is 8 blocks away from home, the time spent is recorded as 4 + 2 at location 8 blocks.

It is also to be noted that the time spent is plotted on the x-axis and the blocks away from home on the y-axis.

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#Part A

Volume of rectanglular prism

Volume of one cube

Total cubes

#2

Volume=

No of cubes ×volume of 1 cube

Answer:

A)  84 cubes

B)  Volume = 4 x 3 x 7 = 84 small cubes

    [tex]\sf Volume=3 \frac{1}{9}\:\:ft^3[/tex]

Step-by-step explanation:

As the lengths of each side of the small cube are ¹/₃ ft each, to find the number cubes in the rectangular prism, first find how many thirds are in each dimension of the prism:

[tex]\sf Length=1 \frac{1}{3}\:ft=\dfrac{4}{3}\:ft=4\:thirds[/tex]

[tex]\sf Width=1 \:ft=\dfrac{3}{3}\:ft=3\:thirds[/tex]

[tex]\sf height=2 \frac{1}{3}\:ft=\dfrac{7}{3}\:ft=7\:thirds[/tex]

Now simply multiply the number of thirds:

Number of cubes in prism = 4 x 3 x 7 = 84

As we have already found the dimensions of the prism in terms of the number of cubes, the volume of the prism in terms of the small cube is:

⇒ Volume = 4 x 3 x 7 = 84 small cubes

To find the volume of the prism in ft³, calculate the actual volume of the small cube:

[tex]\textsf{Volume of small cube}=\sf \dfrac{1}{3} \times \dfrac{1}{3} \times \dfrac{1}{3}=\dfrac{1}{27}\:ft^3[/tex]

Now multiply the volume in terms of number of cubes by the actual volume of a cube:

[tex]\begin{aligned}\textsf{Volume} &= \sf \textsf{Volume in cubes} \times \textsf{Volume of cube in ft}^3\\\\& = \sf 84 \times \dfrac{1}{27}\:ft^3\\\\& =\sf \dfrac{84}{27}\:ft^3\\\\& =\sf 3\frac{1}{9}\:ft^3\end{aligned}[/tex]

Answer:

5.7 and 4.2

Step-by-step explanation:

Outside diagonal = √a² + a² = √4² + 4² = 4√2

= 5.7

Inside diagonal = √b² + b² = √3² + 3² = 3√2

= 4.2

Answer:

rawrrrrrrrrrrrrrrrrr

Step-by-step explanation:

Why is P(A) •P(B/A) = P(B) • P(A/B)

P/B + P = A

P/B/P

- A

The regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

Using a technology such as a graphing calculator, we simply input the data values in the graphing calculator and then wait for the result.

The x coordinates must be entered into the x values and the y coordinates must be entered into the y values

Using a graphing technology, the regression equation of the data values is y = 0.3x^2 - 2.8x +4.2

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The products of the polynomials are:

To do this, we multiply each pair of polynomial as follows:

Pair 1: (xy + 9y + 2) and (xy – 3)

(xy + 9y + 2) * (xy - 3)

Expand

(xy + 9y + 2) * (xy - 3) = x²y² - 3xy + 9xy² - 27y + 2xy - 6

Evaluate the like terms

(xy + 9y + 2) * (xy - 3) = x²y² - xy + 9xy² - 27y - 6

Pair 2: (2xy + x + y) and (3xy² - y)

(2xy + x + y) * (3xy² - y)

Expand

(2xy + x + y) * (3xy² - y) = 6x²y³ - 2xy² + 3x²y² -xy + 3xy³- y²

Pair 3: (x – y) and (x + 3y)

(x - y) * (x + 3y)

Expand

(x - y) * (x + 3y) = x² + 3xy - yx + 3y²

Evaluate the like terms

(x - y) * (x + 3y) = x² + 2xy + 3y²

Pair 4: (xy + 3x + 2) and (xy – 9)

(xy + 3x + 2) * (xy – 9)

Expand

(xy + 3x + 2) * (xy – 9)  = x²y² - 9xy + 3x²y - 27x + 2xy - 18

Evaluate the like terms

(xy + 3x + 2) * (xy – 9)  = x²y² - 7xy + 3x²y - 27x  - 18

Pair 5: (x² + 3xy - 2) and (xy + 3)

(x² + 3xy - 2) * (xy + 3)

Expand

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 9xy - 2xy - 6

Evaluate the like terms

(x² + 3xy - 2) * (xy + 3)  = x³y + 3x² + 3x²y² + 7xy - 6

Pair 6: (x + 3y) and (x – 3y)

(x + 3y) * (x – 3y)

Apply the difference of two squares

(x + 3y) * (x – 3y) = x² - 9y²

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