Simplify the expression 3(x + 2)(x2 − x − 8). (6 points)

Answer: Length = 35

Width = 21

Step-by-step explanation:

From the question, we are informed that the area of a rectangle is 735 in squared and that the ratio of the length to the width is 5 : 3.

To find the length and the width of the rectangle goes thus. We should note that the area of a rectangle is the length multiplied by the width.

Therefore, 5x × 3x = 735

15x² = 735

x² = 735/15

x² = 49

x = ✓49

x = 7

Recall that length = 5x = 5 × 7 = 35

Width = 3x = 3 × 7 = 21

Answer:

               [tex]\bold{x=-4\pm\sqrt{46}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\\\\\\x^2+8x-30=0\\\\\underbrace{x^2+2\cdot x\cdot 4+4^2}-4^2-30=0\\\\{}\qquad(x+4)^2\,-\,16-30=0\\\\{}\qquad\ \ (x+4)^2=46\\\\ {}\qquad\ \ x+4=\pm\sqrt{46}\\\\ {}\qquad\ \ x=-4\pm\sqrt{46}[/tex]

The solution to the quadratic equation by completing the square will be

x = -4 ± √46. The correct option is A.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given equation will be solved as below:-

x² + 8x − 30 = 0

Completing the square for the above equation.

( x + 4 )² - 16 - 30 = 0

( x + 4 )² = 46

x + 4 = ±√46

x = ±√46 - 4

Therefore, the solution to the quadratic equation by completing the square will be x = -4 ± √46. The correct option is A.

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Answer:

the 4th one pentagonal prism

Answer:

pentagonal prism

Step-by-step explanation:

it doesn't resemble a pyramid, so it could only be a prism, and it isn't a rectangular one, cause it has two pentagons, on top and bottom

Answer:

y= 3x+2

I hope this helped  :)

Answer:

true , because natural number is starte on no.1 to infinity but whole no. is started on 0 to infinity so it is true .

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.

Answer:

15 = 2x - 3y

Step-by-step explanation:

We have the two points P1(3,-3) and P2(9,1).

First, calculate the slope between those points:

slope [tex]= \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{9 - 3} = \frac{4}{6} = \frac{2}{3}[/tex]

Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):

(3,-3)

---> (2, -3 - (2/3)) = (2,-3 2/3)

---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)

---> (0, (-4 1/3) - 2/3) = (0,-5)

This tells us, that our line intersects the y-axis at (0,-5).

The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.

In our case: f(x) = y = (2/3)x -5.

To get it into the correct form, we simply subtract y from both sides and get:

0 = (2/3)x - y - 5

To get only integers just multiply everything with 3 and add 15 and get:

15 = 2x - 3y, which fulfils the form asked for in the problem.

Answer:

I think when u substitute the order pair for x and y Into the equation the y is gonna be les than the x + 10

Step-by-step explanation:

K so am confused abt ur question but here

example (2,5)

y < x + 10

substitute 2 for x and 5 for y

5 < 2 + 10

5 < 12

y is less than x + 10

Answer:

a=[tex]\sqrt{44}[/tex]

Step-by-step explanation:

A^2+B^2=C^2

Substitute the values for what you know so:

a^2+10^2=12^2

Simplify:

a^2+100=144

-100         -100

------------------------

A^2=44

A=[tex]\sqrt{44}[/tex]

Answer:

degree 8

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent of the variable in the polynomial.

6x³[tex]y^{5}[/tex] ← has degree 3 + 5 = 8

8[tex]y^{6}[/tex] ← has degree 6

Thus the polynomial is of degree 8

Answer:

multiply by three

Step-by-step explanation:

Step-by-step explanation:

1 x 3 = 3 x 3 = 9 x 3 = 27

=> Pattern rule = [tex]3^{n-1}[/tex]

=> The next three numbers = 81 , 243 , 729

Answer:

The answer are

[tex]34 = - 2x \\ 35 = - \frac{1}{4} n \\ 36 = - \frac{13}{3} a \\ 37 = - \frac{1}{24} b[/tex]

Answer:

Answer:

(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.

(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.

(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.

(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.

Step-by-step explanation:

The volume of the cylinder ([tex]V[/tex]), measured in cubic centimeters, is defined by the following formula:

[tex]V = \pi\cdot r^{2}\cdot h[/tex] (1)

Where:

[tex]r[/tex] - Radius, measured  in centimeters.

[tex]h[/tex] - Height, measured in centimeters.

From statement, we understand that volume of the cylinder is directly proportional to its height. That is:

[tex]V \propto h[/tex]

[tex]V = k\cdot h[/tex] (2)

Where [tex]k[/tex] is the proportionality constant, measured in square centimeters.

In addition, we eliminate this constant by constructing the following relationship:

[tex]\frac{V_{2}}{V_{1}} = \frac{h_{2}}{h_{1}}[/tex]

[tex]V_{2} = \frac{h_{2}}{h_{1}} \cdot V_{1}[/tex] (3)

Based on (3) and knowing that [tex]V_{1} = 48\pi[/tex], we calculate the volumes for each height ratio:

(i) For [tex]2\cdot h[/tex], the volume is [tex]96\pi[/tex] cubic centimeters.

(ii) For [tex]5\cdot h[/tex], the volume is [tex]240\pi[/tex] cubic centimeters.

(iii) For [tex]\frac{h}{2}[/tex], the volume is [tex]24\pi[/tex] cubic centimeters.

(iv) For [tex]\frac{h}{5}[/tex], the volume is [tex]9.6\pi[/tex] cubic centimeters.

Answer:

By measuring the length of the sides and angles

Answer: If they are congruent, you'll see that they are exactly the same as one another. If there's measurements, they'll have the same numbers. If they are similar, they might be the same shape or just have similar measurements

Step-by-step explanation:

Answer:

No. (see below)

Step-by-step explanation:

If you match up the ratios like this:

18 : 9

4 : 3

Matching the two numbers (one on top of another, since they correspond to each other), you can see that these are not equivalent.

Here's why:

The top ratio is 18 to 9, which can be represented by 18 total people to 9 girls in the amount of total people.

We know that the number of boys will also be 9 because 9 is half of 18.

Let's look at the second ratio:

This can be represented by 4 total people to 3 girls in the amount of total people.

4 - 3 = 1

So there would be only 1 boy. Meaning that they're not equal because 1 is not half of 4. It would only be 1/4.

1/4 ≠ 1/2

If we make them similar denominators, you can really see it:

1/4 ≠ 2/4

Answer:

3 1/2 slices each

Step-by-step explanation:

98/28=3.5

Answer:

Every student will get 3 to 4 slices of pizza

Step-by-step explanation:

This is because you need to divided 98 with he 28 student, which you will get 3.5. That is the correct answer, but the question asked equally, so each student will get 3 to 4 slices of pizza.

Hope this helped

Answer:

40

Step-by-step explanation:

80+60+40=180

There is 20 more of each type of apple

Answer:

25% of 48 = 12

Step-by-step explanation:

12 ÷ 25% = 12 ÷ 0.25 = 48

Answer: Divide each term by 25 % and simplify.

N = 48

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

12

Answer:

√200 or 14.1

Step-by-step explanation:

Pythagoras' Theorem: a²+b²=c²

Rearrange to get b² (one of the smaller sides): c²-a²=b²

225-25=200

√200 = 14.1

Answer:

14.1 I hope this helps! Brainliest please!

Step-by-step explanation:

So we use the Pythagorean theorem which is a squared + b squared = c squared. C is the hypotenuse. So we do:

15 squared - 5 sqaured = b squared

225 - 25 = b squared

200 = b squared

14.1 = b

Answer:

135

Step-by-step explanation:

supplementary angles: either of two angles whose sum is 180°.

180 - 45 = 135

Answer:

10a+6b=T------------2

Step-by-step explanation:

Given data

Let the number of adults be a

and the number of children be b

we are told that the total tickets is 100

hence

x+y=100-------------1

The cost of adult ticket = $10

The cost of children ticket = $6

since the total cost is T

Hence

10a+6b=T------------2

Answer:

abc + bca + cab

abc(1+1+1)

3×18

54

Answer:

54

Step-by-step explanation:

a + b + c = 18

abc + bca + cab = ???

18 / 3 = 6

a = ? = 6

b = ? = 6

c = ? = 6

(6 + 6 + 6) + (6 + 6 + 6) + (6 + 6 + 6)

(18) + (18) + (18)

abc + bca + cab = 54

Answer:

B) 2w + 3c = 9.45 AND 4w + 5c = 14.75

Step-by-step explanation:

Let us represent:

Number of water bottles = w

Number of bag of chips = c

Hence:

Samaia buys two water bottles and three bags of chips for $9.45.

2w + 3c = 9.45......Equation 1

Abdullah goes to the same store and buys four water bottles, as Samaia, and five bags of chips, same as ones Samaia bought, for $14.75.

4w + 5c = 14.75......Equation 2

Which choice below accurately represents a system of equations, w for water bottles and c for chips, for this scenario?

Option B) 2w + 3c = 9.45 AND 4w + 5c = 14.75 is the correct option.

Answer:

x=7

Step-by-step explanation:

f(x) =g(x)

12-2=x+3

10=x+3

10-3=x

x=7

Answer:

I think that the answer is either B or C

Step-by-step explanation:

I concluded to this answer simply by looking at where the lines were placed.

Remember that if a line is not touching, but next to another line, they are parallel to each other? Well, that doesn't change here. since, {m angle 1} and {m angle 2} added together equal 180, I would believe that the answer is C, but I may be wrong.

Well, I hope that helps :)

Step-by-step explanation:

Answer. in the attachment

Answer:

184 D

Step-by-step explanation:

A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.

Option D is the correct answer.

It is typically unknown and can only be estimated using sample data.

The goal of statistical inference is to use the information in a sample to make inferences or d

A population parameter is a numerical value that describes a characteristic of a population, such as the mean or standard deviation.

We have,

The estimate obtained from a larger sample size is likely to be closer to the actual parameter value of a population.

This is because a larger sample size reduces the effects of sampling variability and random errors, resulting in a more accurate estimate of the population parameter.

Thus,

A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.

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Answer:

y=-3/5x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-3/5(x-(-5))

y+4=-3/5(x+5)

y=-3/5x-15/5-4

y=-3/5x-3-4

y=-3/5x-7

Answer:

17 - 6j / 5

Step-by-step explanation: