Find the area and perimeter
2x+7
9x

Answer:

9 students

Step-by-step explanation:

34 -25

The expression for h(x) is,

⇒  h (x) = √(x - 2) + 4

Now, Given that;

Initially the graph f (x) is shifted horizontally to the right.

When the graph shifts to right the function then becomes

f (x) → f (x-b)

Where b is the units by which it is shifted towards right .

So, in the figure we can see that it is shifted 2 units to the right .

So, f(x) → f(x-2)

Since f(x) is,

⇒ f (x) = √x

So, f (x-2) = √x - 2

Now, the new obtained graph is again shifted vertically upward

When the graphs shifts upward;

⇒ f(x) → f(x) + b

where b is the units by which it is shifted upward

So, our obtained f(x-2) when shifted upward by 4 units so using the above given transformation of upward shift

i.e. f(x) → f(x) + b

So, Our new graph h(x) = f(x-2) + 4

⇒  h (x) = √(x - 2) + 4

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Answer:

  (d)  24/49

Step-by-step explanation:

You want to know P(A|B) when P(AB) = 3/7 and P(B) = 7/8.

The general equation for conditional probability tells you ...

  P(A|B) = P(AB)/P(B)

  P(A|B) = (3/7)/(7/8) = (3/7)·(8/7)

  P(A|B) = 24/49

The value of R500 decrease to ratio 9:8 is x = 400.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.

Given that, decrease R450 in the ratio 9:8.

Let 9 = 450

Then 8 will have the value = x.

That is,

9 = 450

8 = x

Using cross multiplication we have:

9x = 450(8)

x = 50(8)

x = 400

Hence, the value of R500 decrease to ratio 9:8 is x = 400.

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Answer:

Step-by-step explanation:

\(\sqrt{2} cos x-1=0\\cos x=\frac{1}{\sqrt{2} } =cos (\frac{\pi }{4} ),cos (2\pi -\frac{\pi }{4} )\\cos x=cos(2n\pi +\frac{\pi }{4} ),cos(2n\pi +\frac{7\pi }{4} )\\x=2n\pi +\frac{\pi }{4} ,2n\pi +\frac{7\pi }{4} \\n=0\\x=\frac{\pi }{4} ,\frac{7\pi }{4}\)

9514 1404 393

Answer:

  a) yes

  b) no

  c) no

  d) yes

Step-by-step explanation:

To use the HL congruence theorem, the triangle must be a right triangle, and congruence must be shown for the hypotenuse and a leg of the triangle.

a) yes, the hypotenuse and leg are shown as the same lengths

b) no; not a right triangle. SAS congruence can be used.

c) no; only a leg is shown congruent; the hypotenuse is not.

d) yes, the legs are shown congruent, and the hypotenuse is congruent to itself.

The absolute value of the complex number is √2. The graph is plotted and attached.

A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.

The given complex number as;

2−i

The absolute value is found as;

\(\rm R = \sqrt{1^2 +(-1)^2 } \\\\ R = \sqrt 2\)

The graph for the complex number is attached.

Hence the absolute value of the complex number is √2.

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Answer:

x+5y = 32

Step-by-step explanation:

Equation of a line with slope m and passes through (x1,y1) is y-y1 = m(x-x1)

Equation is,

y-7 = (-1/5) (x-(-3))

y-7 = (-1/5)(x+3)

Multiply by 5,

5(y-7) = -(x+3)

5y-35 = -x-3

x+5y = -3+35

x+5y = 32

Answer:

x=6x okay that should help

After the law firm agrees to deposit $10,000 into the college graduate's savings account and pay off $25,000 in student loans, the college graduate's new net worth is C. $13,833.

Net worth refers to the difference between a person's assets and liabilities or credit obligations to others.

Assets are property owned, while liabilities are property funded on credit.  The difference between these two is the net worth, representing property funded by the owner.

Furniture $14,278

Savings Account Balance $14,337 ($4,337 + $10,000)

Car Value $14,950

Computer and Software $11,744

Total assets = $55,309

Car Loan $3,250

Credit Card Balances $5,129

Student Loans $33,097 ($58,097 - $25,000)

Total liabilities = $41,476

Net worth = $13,833 ($55,309 - $41,476)

Thus, this college graduate now has a net worth of $13,833.

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The probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their outcomes. It is the measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

To find the probability that a randomly selected adult has an IQ between 93 and 117, we need to standardize the distribution using the z-score formula, and then find the area under the normal distribution curve between those two z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the IQ score we are interested in, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

For the lower bound of 93, the z-score is:

z = (93 - 105) / 20 = -0.6

For the upper bound of 117, the z-score is:

z = (117 - 105) / 20 = 0.6

Now, we need to find the area under the normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this probability. Using a calculator, we can use the normalcdf function:

normalcdf(-0.6, 0.6, 0, 1)

This gives us a probability of 0.6827.

Therefore, the probability that a randomly selected adult has an IQ between 93 and 117 is approximately 0.6827 or 68.27%.

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Answer:

a very weak relationship between cost and volume

Step-by-step explanation:

The R factor is used to access the strength of the relationship between a dependent and independent variable. The R factor ranges between - 1 and 1. With negative values depicting a negative linear relationship and positive values meaning a positive relationship. The closer the R factor is to - 1 or + 1, the greater the strength, a value of 0 means, no correlation exists.

Hence, a R factor of 0.15 depicts a positive but very weak relationship between cost and volume as the R value is close to 0.

The correct answer is D. The graph of k(x) is the graph of f(x) vertically compressed by a factor of 8.

To see this, let's compare the equations of the two functions:

f(x) = x²

k(x) = (1/8)x²

The function k(x) is obtained by multiplying the function f(x) by (1/8).

This multiplication affects the vertical scale of the graph.

The factor of 1/8 causes the graph of k(x) to be compressed vertically compared to the graph of f(x). This means that the values of k(x) will be smaller than the corresponding values of f(x) for the same x-values.

Therefore, the graph of k(x) is the graph of f(x) vertically compressed by a factor of 8.

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Answer:

6 feet

Step-by-step explanation:

we'll say the length of blue is B, the length of red is R and the length of green is G. we know B = 24

R multiplied by 4 = B

so R is 6

we also know G = R

so G, or the green rope is 6 feet long

Answer:

6

Step-by-step explanation:

The red rope is 24/4 which is 6 because the blue rope is 4 times as long.

The green rope is also 6 because the red and green rope are the same length.

Answer:

B

Step-by-step explanation:

Answer:

A. 14(2/5.1/7)

Step-by-step explanation:

Answer:

3572 m^3

Step-by-step explanation:

volume of prism = Ah

where A = area of the base, and

h = height of the prism

The base is a regular hexagon. We are given the side length, 8.1 m, and the apothem, 7 m.

A = nsa/2,

where n = number of sides,

s = length of one side

a = apothem

volume = Ah

volume = nsa/2 * h

volume = 6(8.1 m)(7 m)/2 * 21 m

volume = 3572.1 m^3

Answer: 3572 m^3

Answer:

8 More athletes play soccer than tennis

Step-by-step explanation:

Answer:

The first one

Step-by-step explanation:

Answer:

\(f(2\pi) = 32\pi^3 - 2\)

Step-by-step explanation:

Main steps:

Step 1: Use integration to find a general equation for f

Step 2: Find the value of the constant of integration

Step 3: Find the value of f for the given input

Step 1: Use integration to find a general equation for f

If \(f'(x) = g(x)\), then \(f(x) = \int g(x) ~dx\)

\(f(x) = \int [12x^2 - sin(x)] ~dx\)

Integration of a difference is the difference of the integrals

\(f(x) = \int 12x^2 ~dx - \int sin(x) ~dx\)

Scalar rule

\(f(x) = 12\int x^2 ~dx - \int sin(x) ~dx\)

Apply the Power rule & integral relationship between sine and cosine:

\(f(x) = 12*(\frac{1}{3}x^3+C_1) - (-cos(x) + C_2)\)

Simplifying

\(f(x) = 12*\frac{1}{3}x^3+12*C_1 +cos(x) + -C_2\)

\(f(x) = 4x^3+cos(x) +(12C_1 -C_2)\)

Ultimately, all of the constant of integration terms at the end can combine into one single unknown constant of integration:

\(f(x) = 4x^3 + cos(x) + C\)

Step 2: Find the value of the constant of integration

Now, according to the problem, \(f(0) = -2\), so we can substitute those x,y values into the equation and solve for the value of the constant of integration:

\(-2 = 4(0)^3 + cos(0) + C\)

\(-2 = 0 + 1 + C\)

\(-2 = 1 + C\)

\(-3 = C\)

Knowing the constant of integration, we now know the full equation for the function f:

\(f(x) = 4x^3 + cos(x) -3\)

Step 3: Find the value of f for the given input

So, to find \(f(2\pi)\), use 2 pi as the input, and simplify:

\(f(2\pi) = 4(2\pi)^3 + cos(2\pi) -3\)

\(f(2\pi) = 4*8\pi^3 + 1 -3\)

\(f(2\pi) = 32\pi^3 - 2\)

Answer:

\(f(2 \pi)=32\pi^3-2\)

Step-by-step explanation:

\(\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))\)

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given:

If g(x) is the first derivative of f(x), we can find f(x) by integrating g(x) and using f(0) = -2 to find the constant of integration.

\(\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}\)     \(\boxed{\begin{minipage}{4 cm}\underline{Integrating $\sin x$}\\\\$\displaystyle \int \sin x\:\text{d}x=-\cos x+\text{C}$\end{minipage}}\)

\(\begin{aligned} \displaystyle f(x)&=\int f'(x)\; \text{d}x\\\\&=\int g(x)\;\text{d}x\\\\&=\int (12x^2-\sin x)\;\text{d}x\\\\&=\int 12x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\int x^2\; \text{d}x-\int \sin x \; \text{d}x\\\\&=12\cdot \dfrac{x^{(2+1)}}{2+1}-(-\cos x)+\text{C}\\\\&=4x^{3}+\cos x+\text{C}\end{aligned}\)

To find the constant of integration, substitute f(0) = -2 and solve for C:

\(\begin{aligned}f(0)=4(0)^3+\cos (0) + \text{C}&=-2\\0+1+\text{C}&=-2\\\text{C}&=-3\end{aligned}\)

Therefore, the equation of function f(x) is:

\(\boxed{f(x)=4x^3+ \cos x - 3}\)

To find the value of f(2π), substitute x = 2π into function f(x):

\(\begin{aligned}f(2 \pi)&=4(2 \pi)^3+ \cos (2 \pi) - 3\\&=4\cdot 2^3 \cdot \pi^3+1 - 3\\&=32\pi^3-2\\\end{aligned}\)

Therefore, the value of f(2π) is 32π³ - 2.

Answer:

P’(-1, 1), I’ (1, 2), G’(1,0)

Step-by-step explanation:

By using the coordinates of the labeled point, the point-slope equation of the line include the following: D. y + 5 = -3(x - 3)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

0 5 2 -2

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 5)/(0 - 3)

Slope (m) = -9/3

Slope (m) = -3

At data point (3, -5) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 3(x - 3)  

y + 5 = -3(x - 3)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Given that,

The vertices of a rectangle are (–1, 1), (3, 1), (–1, –4), and (3, –4).

To find,

The perimeter of the rectangle.

Solution,

Let the points are :

A(–1, 1), B(3, 1), C(3, –4) and D(–1, –4)

Let's find AB and BC using distance formula :

\(AB=\sqrt{(3-(-1))^2+(1-1)^2} \\\\=4\ \text{units}\)

\(BC=\sqrt{(3-3)^2+(-4-1)^2} \\\\=5\ \text{units}\)

The perimeter of a rectangle = 2(sum of two adjacent sides)

= 2(AB+BC)

= 2(4+5)

= 18 units

So, the perimeter of the rectangle is 18 units.

The volume of the box is 99 unit cubes.

A cube is a three-dimensional object that has six faces, twelve edges and eight vertices. The length, width and height of a cube usually has equal dimensions. The volume of the box is a function of the dimension of the cubes in it and the number of layers.

Volume of a box = number of layers x amount of units

9 x 11 - 99 unit cubes

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Answer:

y = 3x + 4

Step-by-step explanation:

✔️First, find the slope using any two given pairs form the table, say (2, 10) and (5, 19):

Slope (m) = ∆y/∆x = (19 - 10) / (5 - 2) = 9/3

m = 3

✔️Find y-intercept (b) by substituting (x, y) = (2, 10) and m = 3 into y = mx + b

10 = 3(2) + b

10 = 6 + b

10 - 6 = b

4 = b

b = 4

✔️Write the equation by substituing m = 3 and b = 4 into y = mx + b

y = 3x + 4

The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.

Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.

To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.

Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.

Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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Answer:

a = 77.91 units²

Step-by-step explanation:

a = (∅/360) * πr²

a = (62/360) * π(12²)

a = (62/360) * 3.14159(144)

a = 77.91 units²