State the parent function and transformation. WILL GIVE BRAINLIEST

Polynomial: 6x^3 + 12x^2 - 18x

Form 1: 6(x^3 + 2x^2 - 3x)

Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.

Form 2: 6x(x^2 + 2x - 3)

Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.

In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.

To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:

Polynomial: 6x^3 + 12x^2 - 18x

To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.

Form 1: 6(x^3 + 2x^2 - 3x)

In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.

Form 2: 6x(x^2 + 2x - 3)

In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.

We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.

In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.

In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.

By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.

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The area of the quarter with a diameter of 2 ⁴/₅ inches will be 6.15 square inches.

Let r be the sector's radius and be the angle subtended by the sector at its center. The region of the circle's sector will then be written as,

A = (θ/360°) πr²

A quarter has a diameter of 2 ⁴/₅ inches.

Transform the mixed fraction number into a decimal number.

2 ⁴/₅ = 2 + 0.80 = 2.8

In the quarter sector, the central angle is 90°.

A = (90°/360°) x 3.14 x (2.8)²

A = 6.15 square inches

The area of the quarter with a diameter of 2 ⁴/₅ inches will be 6.15 square inches.

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The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

What is one to one function?

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then function f is one to one.

The function, f(x), is a one to one function when one unique element from its domain will return each element of its range. This means that for every value of x, there will be a unique value of y or f(x).

f ( x₁ ) = f ( x₂ ) if and only if x₁ = x₂

Given data ,

Let the function be f ( x )

where f ( x ) = y

So , the equation will be

y =  2 ( x + 5 )² - 6

Now , on simplifying the equation , we get

y = 2 ( x² + 10x + 25 ) - 6

y = 2x² + 20x + 50 - 6

y = 2x² + 20x + 44

Therefore , the function is f ( x ) = y = 2x² + 20x + 44

Now , replace y with x , we get

f ( y ) = x = 2y² + 20 y + 44

And f ( x₁ ) = f ( x₂ )

So , the function is one to one function

Hence , The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

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Answer:

\(20\)

Step-by-step-Explanation:

Remember, the Pythagorean Theorem.

\(a^{2} + b^{2} = c^{2}\)

\(21^{2} + b^{2}=29^{2}\)

\(29^{2} -21^{2} =400\)

sq rt of \(400=20\)

John's second month's interest, given his starting principal and the interest rate, is $13.48

First, find the monthly interest rate as the savings account is compounded monthly:

= 10% / 12 months per year

= 10/12 %

The amount after the first month would be:

= 1, 604 x ( 1 + 10/12%)

= $1, 617.37

The second month's interest to John is therefore:

= 1, 617. 37 x 10/12%

= $13.48

In conclusion, in the second month of his savings investment, John would make an interest of $13.48.

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Answer:

thanos

Step-by-step explanation:

bc ya

The cities Alex could have drove between whose distance is about 2000 miles when rounded to the nearest thousand are : Chicago to San Francisco and Atlanta to Los Angeles

From the table attached which shows the distance in miles between two cities in the United States :

Only the distances between these two cities would give a value of 2000 miles when rounded to the nearest thousand mile

The other distances in the table will round to 1000 miles when rounded to the nearest thousand mile.

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Answer:

The answer you gave can only be solved if you know what the Variable is.

Step-by-step explanation:

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true. To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself.

Answer:

A

Step-by-step explanation:

(40.50 + 56.95) + 25.75 ; 25.75 + (40.50 + 56.95) correctly represent the situation using the commutative property.

Answer:

x ≈ 0.17

Step-by-step explanation:

There is a common ratio r between consecutive terms in a geometric sequence, that is

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{a_{3} }{a_{2} }\) , substitute values

\(\frac{2x+1}{x}\) = \(\frac{4x+10}{2x+1}\) ( cross- multiply )

x(4x + 10) = (2x + 1)² ← expand using FOIL

4x² + 10x = 4x² + 4x + 1 ( subtract 4x² + 4x from both sides )

6x = 1 ( divide both sides by 6 )

x = \(\frac{1}{6}\) ≈ 0.17 ( to the nearest hundredth )

Answer:

V = 6 cm^3

Step-by-step explanation:

To find the volume you multiply the dimensions of the three sides of the box, length times width times height

The length is 1 cm the width is 2 cm and the height is 3 cm

The units for volume will be cm^3 since we are multiplying cm* cm*cm

V = l*w*h

V = 1*2*3

V = 6 cm^3

Answer:

6 cm³

Step-by-step explanation:

The volume of a box or rectangular prism is l×w×h.

length × width × height

The dimensions of the box are 1cm × 2cm × 3cm

1 × 2 × 3

Multiply the numbers.

= 6

The volume of the box is 6 cm³.

The probability of getting a number greater than zero is 9/10.

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, 'x' be a random variable that takes values from 0 to 9 with an equal probability of 1/10.

We know, The total probability is 1.

Therefore, The probability of getting a number greater than zero is,

(1 - the probability of getting zero).

= 1 - 1/10.

= 9/10.

Some more concepts related to probability is a conditional probability which states,

The likelihood that one event will follow another given the occurrence of another event.

Q. let x be a random variable that takes values from 0 to 9 with equal probability 1/10, Find the probability of getting a number greater than zero.

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Answer:

Step-by-step explanation

The bottle had 20 ounces that before and 8 ounces after

8+x=20

20-x=8

20-8=x

20-8=12

Answer:

scale factor = 6

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, shape B to shape A

base of shape A = 1 , base of shape B = 6 , then

scale factor = \(\frac{6}{1}\) = 6

After finding the ratio of their corresponding sides of triangles the scale factor we get is 6.

The difference in scale between an original item's scale and a new object that is its representation but is larger or smaller is known as a scale factor.

From figure

For small triangle:

base = 1 units

For large triangle:

base = 6 units

Now the scale factor = ratio of adjacent sides

Scale factor = (Base of large triangle)/(Base of small triangle)

Scale factor = 6/1

Scale factor = 6

Hence,

The scale factor is 6.

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Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

Answer: $6.16

Step-by-step explanation:

Starting Amount: $30

30-6.97=23.03

23.03-11.37=11.66

11.66-5.50=6.16

Take into account that the area of a rectangular shape, is given by the following formula:

A = l·w

w: width = ?

l: length = 1 4/5 in

A: area = 33/20 in²

In order to determine the width of the photo, solve the previous formula for w:

w = A/l

convert 1 4/5 to a normal fraction:

1 4/5 = (5 + 4)/5 = 9/5

replace the values of A and l into the expression for w:

w = (33/20)/(9/5)

w = 165/180

simplify the previos fraction:

w = 165/180 = 33/36 = 11/12

Hence, the width of the photograp is 11/12 in

Answer:

Step-by-step explanation:

b·b·b= b³

The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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Zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

A polynomial graph can be defined as a type of graph that can be used to represent only positive (non-negative) integer exponents of a variable in an equation.

This ultimately implies that, a polynomial graph touches the x-axis at zeros, solutions, roots, x-intercepts, and factors with even multiplicities.

In conclusion, we can logically deduce that zeros, solutions, roots, x-intercepts, and factors are subjects that reference the same area on a polynomial graph.

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Explanation:

Draw a rectangle and one diagonal. Two identical triangles form. Focus on one of those triangles.

We have a right triangle with leg a = 27 and leg b = unknown. These represent the dimensions of the rectangular TV screen.

The hypotenuse is the diagonal which is c = 45.

Let's use the pythagorean theorem to find b.

\(a^2 + b^2 = c^2\\\\27^2 + b^2 = 45^2\\\\729 + b^2 = 2025\\\\b^2 = 2025 - 729\\\\b^2 = 1296\\\\b = \sqrt{1296}\\\\b = 36\\\\\)

This screen is 27 inches by 36 inches.

area = length*width = 36*27 = 972 square inches

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(y = \stackrel{\stackrel{m}{\downarrow }}{-2}x+8\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-2\implies \cfrac{-2}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-2}\implies \cfrac{1}{2}}}\)

so, we're really looking for the equation of a line whose slope is 1/2 and that it passes through (6 , -2)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{6}) \implies y +2= \cfrac{1}{2} (x -6) \\\\\\ y+2=\cfrac{1}{2}x-3\implies \LARGE \begin{array}{llll} y=\cfrac{1}{2}x-5 \end{array}\)

Answer:

-64.1 belong to Rational numbers.

Hope it helps!

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Step-by-step explanation:

since perimeter is adding all around she took the all the values and added them as above. as you can see 3√2 and 4√2 has the same square root so she added 3+4 which gave us 7√2 and then added the 2√5 but since they don't have the same square root we can't add them like we did in the other so we'll just put 7√2+2√5

Answer:

-50

Step-by-step explanation:

divide both sides by -6.2. This gets rid of the -6.2 on the right.

divide 310 by -6.2

f = -50