factor the polynomial completely y^3+6y^2-4y-24

π radians =180∘

1 radian = tex] \frac{180°}{ \pi} [/tex]π

3 radians = [tex] \frac{540°}{ \pi} [/tex]

Answer: Correct answer is (x, y) → ( x − 3, y − 4); (5, −1)

Step-by-step explanation: Starting from point 8,3 we go down 4 on the y-axis (y-4)and stopping at -1 then we go left on the x-axis (x-3) stopping at 5.

So the new coordinate for the vertex C should read 5,-1.

After the translation , the coordinates of vertex C are ( 5 , -1 )

There are several types of transformations:

Let us now tackle the problem!

This problem is about Translation.

The triangle is translated 4 units down and 3 units left.

The rule that represents the translation will be [tex]\left[\begin{array}{ccc}-3\\-4\end{array}\right][/tex]

Let's find the translation for every vertice of Triangle ABC:

A(-3 , 4) → A'(-3 + (-3) , 4 + (-4)) = A'(-6 , 0)

B(4 , -2) → B'(4 + (-3) , -2 + (-4)) = B'(1 , -6)

C(8 , 3) → C'(8 + (-3) , 3 + (-4)) = C'(5 , -1)

From the results above, we can illustrate the translation process as shown in the attached picture

After the translation , the coordinates of vertex C are ( 5 , -1 )

Grade: High School

Subject: Mathematics

Chapter: Function

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle

11 foot wall,

 the center of the wall would be 5 1/2 feet which is 5 feet 6 inches

the shelf is 2 feet 6 inches, so the center of that would be 1 foot 3 inches

5 ft 6 in - 1 ft 3 in = 4 ft 3 inches from corner

To determine Susan's share of the daycare earnings, the simple equation T + 2T = 225 was solved to give Terry's share as $75. Susan's share, being double Terry's, is therefore $150.

The total earnings of Susan and Terry together: 2x (Terry's share) + Terry's share = 225

Given that the total earnings are 225:

2x (Terry's share) + Terry's share = 225

3x (Terry's share) = 225

Terry's share = 225/3 = 75

Susan's share = 2 x 75 = 150

Therefore, Susan's share is 150.

Final answer:

The statement that -5 + x is negative, given the distance from 0 to x on a number line is less than 5, is true sometimes. This depends on the value of x, whether it is a small positive number or any negative number.

Explanation:

The question revolves around the concept of distance on a number line and the calculation of numerical expressions. To understand whether -5 + x is always, sometimes, or never negative given the condition that the distance from 0 to x on a number line is less than 5, let's analyze the scenarios.

First, the absolute value |x| < 5 indicates that x must be between -5 and 5 (not including -5 and 5). This means x can be any value closer to 0 than 5, whether positive or negative.

If x > 0 (but less than 5), then -5 + x would be negative because x cannot neutralize the -5 completely.

For example, if x=4, then -5 + 4 = -1.

If x < 0, then -5 + x is negative since you are adding two negative numbers.

For example, if x=-4, then -5 + (-4) = -9.

The statement -5 + x is negative is true sometimes based on the value of x. If x is a positive number close to 5, the expression may approach 0 but will stay negative. If x is negative, the expression is further negative.

Answer:

In the equation [tex]\(y = 5.5x\), \(5.5\)[/tex] is the constant of proportionality.

This equation represents a proportional relationship between [tex]\(x\)[/tex] and [tex]\(y\),[/tex] where [tex]\(y\)[/tex] is always [tex]\(5.5\)[/tex] times the value of [tex]\(x\).[/tex] Therefore, [tex]\(5.5\)[/tex] is the constant by which [tex]\(x\)[/tex] is multiplied to get [tex]\(y\).[/tex]

Explanation:

In the equation [tex]\(y = 5.5x\), \(5.5\)[/tex] represents the constant of proportionality. In a proportional relationship, one quantity is always a constant multiple of the other. Here,[tex]\(y\)[/tex] is always [tex]\(5.5\)[/tex] times the value of [tex]\(x\)[/tex]. This means that as [tex]\(x\)[/tex] increases or decreases, [tex]\(y\)[/tex] changes in direct proportion, always maintaining a ratio of [tex]\(5.5:1\)[/tex] between [tex]\(y\)[/tex] and [tex]\(x\)[/tex]. The constant of proportionality, [tex]\(5.5\)[/tex], determines the rate at which [tex]\(y\)[/tex] changes with respect to changes in [tex]\(x\)[/tex], serving as a scaling factor in the relationship between the two variables.

Answer:

5b  

Step-by-step explanation:

Given,

The base area of the prism = base area of the pyramid = b,

Also, the height of the prism = 30 ft,

While, the height of the pyramid = [tex]\frac{\text{height of prism}}{2}[/tex]

[tex]=\frac{30}{2}=15\text{ ft}[/tex]

Now, the volume of the pyramid = [tex]\frac{1}{3}[/tex] × base area × height

[tex]=\frac{1}{3}\times b\times 15[/tex]

[tex]=\frac{15b}{3}[/tex]

= 5b ft²

Hence, THIRD option is correct.

Answer:

(-6,-8)

Step-by-step explanation:

2x+4=x-2

2x-x=-2+-4

x=-6

y=-6-2

y=-8

perimeter = 2 times the length plus 2 times the width

 which can also be written as 2(4/3w+w) so the answer is D

part 2

 28 = 2(4/3w+w) when you do the calculation w = 6

length = 4/3 *6 = 8

 area = 6 * 8 =48 square inches

Final answer:

To find how far Ebony walked, multiply her walking rate (3 1/2 miles per hour) by the time walked (1 1/3 hours), resulting in a total distance of 4.665 miles.

Explanation:

The question asks, "Ebony walked at a rate of 3 1/2 miles per hour for 1 1/3 hours. How far did she walk?" To answer this, we need to multiply the rate at which Ebony walked by the time she spent walking. The rate is 3½ (or 3.5) miles per hour, and the time is 1⅓ (or 1.333) hours.

So, the calculation is as follows:

Distance = Rate × Time

Distance = 3.5 miles/hour × 1.333 hours

Distance = 4.665 miles

Therefore, Ebony walked a total of 4.665 miles.

The number that will be equal to 2 tens 15 ones is 35.

The place values on the left of the decimal point start as ones, tens, hundreds, and so on. The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so on. The tens mean multiplied by 10. The tenth means the tenth part of that digit which is that digit divided by 10

We are given multiple number names and asked to add them.

We will call d as ones digit, c as tens digit (it get multiplied by 10), b as hundreds digit etc.

We call e as digit at 10th place (division by 10), f as digit at hundredth place and so on.

To find this problem, it will be easier to split the sentences into multiple parts like this;

1. "2 tens" mean 2 x 10 =20

2. "15 ones" mean 15 x 1= 15

Then, if we add them up it will be;

20+15= 35

The answer to this problem would be 35

Therefore, the number that will be equal to 2 tens 15 ones is 35.

Learn more about place value here:

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An expression satisfying all the conditions specified is [tex]5x^2 + 5xy + 3xy + 7[/tex]

Here's an expression with four terms that meets all the requirements :

[tex]5x^2 + 5xy + 3xy + 7[/tex]
1. Term with an exponent: [tex]\( 5x^2 \)[/tex] (The exponent is 2)
2. Term with a coefficient of 5: [tex]\( 5xy \)[/tex]
3. Term with three factors: [tex]5xy[/tex] (The factors are 5, x, and y)
4. Constant term: 7
Like terms:[tex]\( 5xy \)\ and\ \( 3xy \)[/tex]
So the expression [tex]\( 5x^2 + 5xy + 3xy + 7 \)[/tex] includes all the specified requirements.

To convert a quadratic function in standard form to vertex form, follow these steps: identify the given equation, find the x-coordinate of the vertex, substitute the x-coordinate to find the y-coordinate, and write the function in vertex form.

To convert a quadratic function in standard form to vertex form, follow these steps:

For example, if the quadratic function is given as 2x² - 8x + 5 = 0, we first find the x-coordinate of the vertex using the formula x = -b/2a as x = -(-8)/(2*2) = 2. Substituting this x-coordinate into the equation, we find the y-coordinate of the vertex as y = 2*(2)² - 8*(2) + 5 = -3. Therefore, the quadratic function in vertex form is y = 2(x-2)² - 3.

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