Let g(x) be the transformation, vertical translation 5 units down, of f(x)= 3x+9. Write the rule for g(x).

To convert from radical form to exponential in fractional form, we can follow:

Firstly, notice that 9 is the same as 3 squared:

Now, we can apply the change:

Also, notice that we can factor out the 2 on the denominator to cancel with the two on the numerator:

So, the expression in the simples form and fractional exponent is:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define what happens when a function is shrunk vertically

When the factor is greater than 1, the condition that satisfies the function is to multiply by 1.4

When the graph is verticcally shrunk, this means that the function is multiplied by 1.4

Hence, the function becomes:

STEP 2: Define what happens when the graph is shifted left by 3 units.

If the function is shifted left by 3 units, this implies that we add 3 units to the x of the function.

This gives:

The general form of the equation: x2 + y2 − 41 = 0

The Correct option is (B).

Given,

A circle with center O (0,0) has point B (4,5) on its circumference

To find the what is the general form of the equation  for the given circle centered at O(0, 0).

Now, According to the question:

How do you find the equation of a circle with center (0,0)?

x2 + y2 = r2 , and this is the equation of a circle of radius r whose center is the origin O(0, 0). The equation of a circle of radius r and center the origin is x2 + y2 = r2 .

The general form of the equation:

x2 + y2 − 41 = 0

Hence, The general form of the equation: x2 + y2 − 41 = 0

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Formula of simple interest rate:

Where,

For Monica interest rate is:

For Paul interest rate is:

No, Paul interest rate higher then Monic.

The relation which represents a function is the mapping diagram.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).

In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.

Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.

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The length has a value of  9 meters

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

Length = 5 meters less twice it’s width

This means that

Length = 2Width - 5

The perimeter is given as

Perimeter = 38 meters

The perimeter is calculated as

Perimeter = 2 x (Length + Width)

So, we have

2 x (2Width - 5 + Width) = 38

Divide by 2

2Width - 5 + Width = 19

This gives

3Width= 21

Divide

Width - 7

Recall that Length = 2Width - 5

So, we have

Length =  2 * 7 - 5

Evaluate

Length =  9

Hence, the length is 9 meters

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Answer:

Step-by-step explanation:

B

Answer:

Well your answer is down below

Step-by-step explanation:

First as a Inequality −3(2x−5)<5(2−x)

Step 1: Simplify both sides of the inequality.

−6x+15<−5x+10

Step 2: Add 5x to both sides.

−6x+15+5x<−5x+10+5x

−x+15<10

Step 3: Subtract 15 from both sides.

−x+15−15<10−15

−x<−5

Step 4: Divide both sides by -1.

−x−1<−5−1 x>5

So your answer is x>5

hope this helps

~~Wdfads~~

Answer: 2/7

Step-by-step explanation:

Substract 7/7 AKA the whole, by 5/7 tp get 2/7

2/7 is the fraction of males.

The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.

Given,

The function is :

f(x) = mx + b

and, where m> 0

Described the graph of the function and also write the name of the function:

Now, According to the statement is :
f(x) = mx + b , m > 0

It is an increasing line.

So, The correct option is D. i.e., Linear Function, Diagonal line which slants upward from left to right.

What is a increasing line in a graph?

If a linear graph is increasing then its gradient is positive, since when x increases by 1, y changes by a positive number. If a linear graph is decreasing, the gradient is a negative number.

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Compound interest formula:

A = P (1+r/n)^nt

Where:

A = total amount

P = principal investment

r= interest rate in decimal form = 2/100 = 0.02

t= years

n= number of compounding periods in a year= 12

Replacing:

A = 30,000 (1+0.02/12)^4x12

A = 30,000 (1.001666667)^48

A= 32,496.45

Answer:  [-4, 0] which is choice A

=====================================================

Reason:

lowest point is when y = -4

highest point is when y = 0

The range is any value of y between these values, including the endpoints themselves. We say the range is [tex]-4 \le y \le 0[/tex] which condenses to the interval notation [-4, 0]

Use square brackets to include the endpoints.

If there were open holes at the highest and lowest points, then we would use curved parenthesis instead.

Answer:

Salton City could have an elevation less than -2 or greater than 2 (depends on what u meant.

Step-by-step explanation:

Usually when u talk abt elevation, when it is lower than sea level, you write it with a negative sign. If you meant that new Orleans is 2 feet below sea level, the Salton City elevation could be anything less than -2. If you meant 2 feet above sea level, the New Orleans elevation could be anything above 2.

HOPE THIS HELPS!
CAN U PLSSSSSS HELP ME WITH THIS PROBLEM????

5. How many ways are there to distribute 10 indistinguishable candies among 4 different

children? Children may end up with no candies.

SOLUTION:

The parent function is;

The transformation applied is;

Graphing this, we have;

The period is the time to complete a cycle .

From the graph, the period is;

The asymptotes are those lines for which sec x is undefined. those are lines where;

Answer:

Step-by-step explanation:

Given p(x) = x⁴ + 4x³ - 7x² - 22x + 24 with known factors (x +4) and (x -1), you want the function written as a product of linear factors, and a sketch of the graph.

A graphing calculator can help with both parts of this. It can show you the remaining zeros are -3 and 2, so the remaining linear factors are (x +3) and (x -2). At the same time, it produces a graph of the function. This is shown in the first attachment.

Synthetic division is a convenient way to find the remaining factors of the polynomial. Dividing by (x+4) gives ...

  p(x) = (x +4)(x^3 -7x +6) . . . . . . shown in the second attachment

And dividing the cubic by (x -1) gives ...

  p(x) = (x +4)(x -1)(x^2 +x -6) . . . . . . shown in the second attachment

The quadratic will have linear terms with constants that sum to 1 and have a product of -6. These constants are 3 and -2.

The rewrite of p(x) is ...

  p(x) = (x +4)(x +3)(x -1)(x -2)

The 4th degree polynomial has a positive leading coefficient, so is above the x-axis at both the left and right ends of the graph. The graph crosses the x-axis at x = -4, -3, 1, and 2.

We note these roots are symmetrical about x=-1, so there will be a maximum at that point. That maximum is p(-1) = (-1 +4)(-1 +3)(-1 -1)(-1 -2) = 3·2·(-2)(-3) = 36. The minimum values will be found approximately halfway between -4 and -3, and again between -1 and -2. Those minima will be approximately p(-3.5) = (-.5)(.5)(-4.5)(-5.5) ≈ -6.2

The y-intercept is +24, the constant in the polynomial.

With the zero crossings, line of symmetry, local maximum, approximate local minima, and the y-intercept, we can make a passable sketch of the graph.

A graph is seen in the first attachment.

Answer:

wow your so goood

Step-by-step explanation:

The hyperbola has a center of (2, -3)

The equation of the hyperbola is given as

(y + 3)²/9 − (x − 2)²/2 = 1

A hyperbola is generally represented as

(y - k)²/a² − (x − h)²/b² = 1

Where the coordinates of the center of the hyperbola is

Center = (h, k)

Next, we compare (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1

From the comparison, we have

(h, k) = (2, -3)

This means that the center is (2, -3)

Hence, the coordinates of the center is (2, -3)

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The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.

Given,

A random  sample of n = 40  

The mean time μ = 21.4

and, standard deviation is σ =  3.6 min

The z score (z) is given by the equation:

z = (x - μ) / σ / [tex]\sqrt{n}[/tex]

Substituting , the values we get

z = (20 - 21.4) / 3.6 /[tex]\sqrt{40}[/tex]

z = -2.45

Using the z table:

P(x < 20) = P(z < -2.45)= 0.00714

Hence, The probability that a random sample of n=40 oil changes results in a sample mean time of less than 20 minutes is 0.00714.  

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Note that if the area of any figure is multiplied by a factor of a.

The perimeter will be multiplied by √a

From the problem, the are of the square is multiplied by 1/9, so we need to get the square root of that factor to get the factor for the perimeter.

Therefore, the answer is C. multiplied by 1/3

The image of the point after the dilation is (-2, -1)

Dilation is the process of altering the side length of a shape or a function

From the question, the given parameters are:

Point =  (-8, -4)

The scale factor of dilation is given as

Scale factor = 1/4

Mathematically, this transformation can be represented as

(x, y) = k(x, y)

Where k = 1/4 i.e. the scale factor

So, we have

(x, y) = (kx, ky)

This gives

(x, y) = (1/4x, 1/4y)

When represented as an equation, we have

Image = 1/4 * Point

Substitute the equation Point =  (-8, -4) in the equation Image = 1/4 * Point

So, we have the following equation

Image = 1/4 * (-8, -4)

Evaluate the product

Image = (-2, -1)

Hence, the image is (-2, -1)

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Answer:

The number “2” that is a outside the brackets multiplies both of the numbers inside the brackets.

Step-by-step explanation:

3+2(2x-4)

3+4x-8

4x-5

5. The two triangles are similar. The value of x = 12.

6. The information cannot be used to show that the triangles are similar triangles.

Two triangles are similar to each other if they have the same shape but different sizes, in order words, they must have the same corresponding angle measures but different corresponding side lengths that are proportional to each other.

5. In the first figure, we see that there are two pairs of corresponding congruent angles (a pair of right angles and a pair of vertical angles in both triangles), but different corresponding side lengths.

Therefore, based on the AA similarity theorem that says two triangles are similar of they have two pairs of congruent sides, we can prove that both triangles are similar to each other.

Therefore:

x/9 = 20/15

15x = (9)(20)

15x = 180

15x/15 = 180/15

x = 12

6. The second image shows that the two triangles share a common side, which means they have a pair of corresponding sides that are congruent. Therefore, the information given cannot be used to prove they are similar triangles.

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Based on the vertices of the triangle, the area of the triangle can be found to be 8 cm²

First, find the lengths of JK, KL, and JL. When given vertices, you can find the length of a line by the formula:

= √ ( (x₂ - x₁)² + (y₂ - y₁)²)

The length of JK is therefore 2.83 units

The length of KL is therefore 5.66 units

The length of JL is therefore 6.32 units.

Given these units, the area of the triangle can be found by the formula:

= √ s(s - a) ( s - b) ( s - c)

Where:

s = semi perimeter

a, b, and c are the sides of the triangle which are JK, KL, and JL.

The semi-perimeter can be found by the formula:

= ( a + c + c) / 2

= 15.47 / 2

= 7.74

The area of the triangle is therefore:

= √ s(s - a) ( s - b) ( s - c)

= √ 7.74 (7.74  - 2.83) ( 7.74 - 5.66) ( 7.74 - 6.32)

= 8 cm²

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Considering the given figure, the conjecture with the rephrased statement of proof to show the diagonals of a parallelogram bisect each other is: In parallelogram EFGH show EK is congruent to KG and F.K is congruent to KH

The diagonals refer to the lines running between the two opposite ends of the parallelogram

Bisecting means sharing into two equal parts

congruent means a copy that is equal in dimension hence can be used in place of the other image  

The diagonals of a parallelogram bisect each other means that the diagonals cut each other to form two equal parts such that each part is congruent to each other.

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The scatterplot of the data is attached accordingly. The Linear Regression equation for Y is ŷ = 0.82X + 2.31. Note that there is a positive correlation. This is because the y variable tends to increase as the x variable increases.

Linear regression is a statistical method for modeling the connection between a scalar output and one or more explanatory factors. When there is only one independent factor, simple linear regression is employed; when there are more than one, multiple linear regression is utilized.

Note that the regression equation is usually given as:
ŷ = bX + a; where

y = dependent variable

b  = Slope/coefficient

X  = Independent Variable
a = Constant/ Intercept.

Notice that the regression line splits evenly between the data points exhibiting a linear relationship that is positively correlated.

From the graphing calculation, we have:

The sum of X = 21

The sum of Y = 33.39

Mean X = 3

Mean Y = 4.77

Sum of squares (SSₓ) = 28

Sum of products (SP) = 22.96

Recall that the regression equation is given as:
ŷ = bX + a;

Where;

b = SP/SSₓ and
a = [tex]M_{y}[/tex] -[tex]bM_{x}[/tex]

Hence,

b = 22.96/28

= 0.82

a = [tex]M_{y}[/tex] - bMₓ = 4.77 - (0.82*3) = 2.31

hence,

ŷ =  0.82X + 2.31.

Lets find Y if x = 10

y = 0.82 (10) + 2.31 [plugging in the value]

= 8.2 +2.31

= 10.51

Let's find X where Y = 10

10 =  0.82X + 2.31. [Plugging in the value]

collect like terms over the equation sign

10-2.31 = 0.82X
⇒ 7.69 = 0.82X [Divide both sides by 0.82
7.69/0.82 = X

X = 9.37804878049
X [tex]\approx[/tex] 9.38

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The value of x that makes the equation 2x+5 = 1.99x + 22 is 1700

The equation is

2x+5 = 1.99x+22

First we have to rearrange the given term and combine the like terms, then we have to find the value of x

Move 1.99x to left hand side of the equation and move 5 to the right hand side of the equation

2x+5 = 1.99x+22

2x-1.99x = 22-5

We have to do the subtraction in like  terms

(2-1.99)x = 22-5

0.01x = 17

Move the number 0.01 to the right hand side of the equation

x = 17/0.01

Division

x = 1700

Hence, the value of x that makes the equation 2x+5 = 1.99x + 22 is 1700.

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At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method draws a relation between given data. Following the regular trend, information can be calculated. It is also called the 'Mango Method'.

At this rate, Tommy will earn $211.2 working for 12 hours.

The Unitary Method is only valid for regular increases or decreases. Information about unity is drawn from given data, which is multiplied as required. It is widely used in the calculation of prices, amounts, etc.

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Answer:

see explanation

Step-by-step explanation:

since the dilatation is centred at the origin , then multiply each of the original coordinates by the scale factor of 2

Q (2, 2 ) → Q' (2(2), 2(2) ) → Q' (4, 4 )

P (0, 0 ) → P' (2(0), 2(0) ) → P' (0, 0 )

R (- 2, - 4 ) → R' (2(- 2), 2(- 4) ) → R' (- 4, - 8 )

S (4, - 2 ) → S' (2(4), 2(- 2) ) → S' (8, - 4 )

The inequality of the two triangle are 32° < x < 68° and the range of the value x is defined as  x ≥ 4.

Inequality:

Inequality means the relationship between two values that are not equal is defined by inequalities which means they are not equal.

Given,

Here we have the two triangles with some angle values.

Now, we need to find the inequality of these triangle.

To find the inequality of the triangle first we have to write down the values provided, they are,

77, 11x - 33, 68°, 32°

Through this we have identified that, the value of x is lies in between 68° and 32°.

So, it ca be written as,

32° < x < 68°

The next this is to use the triangle inequality theorem, that is,

"The sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c."

Therefore, based on the given equation we have written it as,

11x - 33 ≥  77

Subtract 33 on both sides then we get,

11x ≥ 44

Therefore, x ≥ 4.

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