Factor the expression

4b^2+28b+49

The formula for a cone is given as:

V = π r^2 h / 3                    ---> 1

Where,

V = volume of the cone

r = radius of the circle base of the cone

h = is the perpendicular length from the center of the base of the cone to the tip at the top

It was given that:

h = d

but d = 2 r, therefore:

h = 2 r

Substituting this to equation 1:

V = π r^2 (2 r) / 3             

V = 2 π r^3 / 3

Since r = x, the answer from the choices is:

2πx3

The expression representing the volume of the cone is (2/3)πx^3, where x represents the cone's radius.

Step 1: Identify Key Information

We are given that the height (h) of the cone is equal to the diameter (d) of the base. The diameter is twice the radius (r).

Step 2: Apply Formula and Substitute

        Volume (V) = (1/3) * π * r^2 * h

        V = (1/3) * π * r^2 * (2r)

Step 3: Simplify the Expression

Answer:

Additive inverse is the negative of the number, i.e. what you add to the number to get zero.

So the additive inverse of number b is - b

Additive inverse of 4 is - 4.

Then, you can verify the subtraction is the same that add the additive inverse.

For example subtracting 4 from 10 (10 - 4) is the same that adding -4:

10 - 4 = 10 + (-4).

Then given any expression if you have to subtract other expressión you just add the addive inverse of the second expression.

For example: given A(x) = x^2 + 3x + 5 and B(x) = 2x + 4

Find A(x) - B(x) = A(x) + [-B(x)]

=> x^2 + 3x + 5 + (-2x -4) = x^2 + 3x - 2x + 5 - 4 = x^2 + x + 1

Step-by-step explanation:

hope this helped!

After performing the addition operation on both expressions, the resulting simplified expression is 7x^3+2x-4

Given Data

To add both Expression let us open brackets

= (4x3 − 3x − 7) + (3x3 + 5x + 3)

=  4x3 − 3x − 7 + 3x3 + 5x + 3

Collect like terms we have

= 4x^3+3x^3-3x+5x-7+3

= 7x^3+2x-4

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To solve this problem, let us first assign the variables. Let us say that:

l = length of rectangle

w= width of rectangle

The given problem gives us the relation that:

l = 6 w – 2                            ---> 1

We know that the formula for area of rectangle is given as:

A = l w                                   ---> 2

Substituting equation 1 into 2:

A = (6 w – 2) w

A = 6 w^2 – 2 w

The area must not be greater 840 cm^2, therefore:

840 cm^2 = 6 w^2 – 2 w

w^2 – (1/3) w = 140

By completing the square:

w^2 – (1/3) w + (1/36) = 140 + (1/36)

(w – 1/6)^2 = 5041/36

w – 1/6 = ± 11.83

w = -11.66, 12

Therefore the maximum value that the width can take is 12 cm. Therefore the possibilities of width such that the area does not exceed 840 cm^2 is from 1 to 12 cm.

Answer:

1 cm to 12 cm

Solution of equqation 15 - 3 7/8 is 11 1/8.

To solve 15 - 3 7/8, you need to follow these steps:

First, convert 3 7/8 to an improper fraction:

Next, convert 15 to a fraction with a common denominator of 8:

Now you subtract the improper fraction from the whole number fraction:

Convert the result back to a mixed number:

So, 15 minus 3 and 7/8 is 11 1/8.

The number of the boys in the school is 272.

Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times or 3 is added 2 times.

Given, the ratio of boys to the total number of students in this class is typical of the whole school.

That means,

16 : 28 = x : 476

where x is the number of boys in the school.

Simplifying,

16/28 = x/476

Using cross multiplication,

x = 16 x 476/ 28

x = 272

Therefore, the number of the boys in the school is 272.

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To find the length of the diagonal of a square garden, you can use the Pythagorean theorem. In this case, the length of the diagonal is approximately 14.14 meters.

To find the length of the diagonal of a square garden, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the two shorter sides of the right triangle are the sides of the square garden. Let's call each side x. The hypotenuse (the diagonal) will be the side we are trying to find.

Using the Pythagorean theorem, we have: x^2 + x^2 = diagonal^2. Since the area of the square garden is 200 m², we can set up the equation: x^2 + x^2 = 200. Combining like terms, we get: 2x^2 = 200. Dividing both sides by 2, we have x^2 = 100. Taking the square root of both sides, we find that x = 10.

Therefore, each side of the square garden is 10 meters. And using the Pythagorean theorem one more time, we can find the length of the diagonal: diagonal^2 = 10^2 + 10^2. Simplifying, we get diagonal^2 = 200. Taking the square root of both sides, we find that the length of the diagonal is approximately 14.14 meters.

A) #3 y = x+3, if you subtract x from y there is a difference of 3 in all of them.

B) #5 y = -x^2, the y value is the negative value of x raised to the 2nd power

C)#6 y = x^2+3, if you raise the value of x to the 2nd power and then add 3 you get the y value

D)#2 y=3x-1, if you multiply the value of x by 3 then subtract 1 you get the y value

I think the answer is B= 62

some people use 22/7, some use 3.14

 it is used in formulas for circles

Answer:

its 3

Step-by-step explanation:

The required value of the unknown number x would be 3.

An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have been given that " 7 times a number is decreased by 8, the answer is the same as when 3 times the number is increased by 4".

Let the unknown number be x.

7x - 8 = 3x + 4

To solve the equation;

7x - 8 = 3x + 4

Collect the like terms;

7x - 3x = 8 + 4

4x = 12

Divide by 4 on both sides;

x = 12/4

x = 3

Therefore, the required value of the unknown number x would be 3.

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3 decimal places would be where the 9 is, since the next number is 8 , the 9 would become a 0 and the number before it (5) would become a 6

 so it would be 977.260

opposite angles need to equal 180

 so angle 2 = 180-111 = 69 degrees

A = (1,3)

C = (-4,-4)

-4-1 =-5, -5@ = 25

-4-3 = -7, -7^2 = 49

25+49 = 74

 sqrt(74) = 8.602

 round answer as needed.

Answer: Initial value: 2, rate of change: 1

Step-by-step explanation:

From the graph we can see the line is intersecting y axis at (0,2).

Therefore, y intercept of the graph = 2

Therefore, the initial value of the graph = 2

Also there as two point from which line is passing (0,2) and (1,3)

The rate of change of the line is given by :-

[tex]R=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{1-0}=1[/tex]

Hence, for the given graph, the Initial value is 2 and the rate of change is 1 .

Answer:

A) 5x^5 + 4x^4 + x^3

Step-by-step explanation:

Answer:

The equation of the line is

Y= 4X + 11

Step-by-step explanation:

The equation of the line is equall to

(Y- Y1)/(X-X1) = slope

X1 = -3

Y1= -1

Equation is

(Y-(-1))/(X-(-3))=4

(Y+1)/(X+3) = 4

Y+ 1 = 4X + 12

Y= 4X + 11