What is the volume of this aquarium

Answer:

m = -2 and n = 10

Step-by-step explanation:

If the polynomial mx^3 - 3x^2 + nx + 2 is divided by x + 3, the remainder is -1. Then;

x+ 3 = 0

x = -3

Substitute x =-3 into the polynomial and equate to -1

-1 = m(-3)³-3(-3)²+n(-3) + 2

-1 = -27m - 27 - 3n + 2

27m + 3n = -25 + 1

27m + 3n = -24 ... 1

Similarly, if it is divided by x - 2, the remainder is -4, then;

-4 =  m(2)³-3(2)²+n(2) + 2

-4 = 8m - 12- 2n + 2

8m -2n = -4 + 10

8m + 2n = 6 ... 2

Solve 1 and 2 simultaneously

27m + 3n = -24 ... 1 * 2

8m + 2n = 6 ... 2 * 3

______________________

54m + 6n = -48

24m + 6n = 12

54m - 24m = -48 - 12

30m = -60

m = -60/30

m = -2

Get n by substituting m = -2 into 1

From 1:  27m + 3n = -24

27(-2) + 3n = -24

-54 + 3n = -24

3n = -24 +54

3n = 30

n = 30/3

n = 10

Hence m = -2 and n = 10

This is an right angle ∆ and the side lengths containing a right angle are 9 and 11.

By Pythagoras theoram,

[tex] {p}^{2} + {b}^{2} = {h}^{2} [/tex]

where p is the perpendicular, b is the base and h is the hypotenuse.

Plugging the values,

[tex] {9}^{2} + {11}^{2} = {h}^{2} [/tex]

Then,

[tex]h = \sqrt{ {9}^{2} + {11}^{2} } [/tex]

[tex]h = 14.12(approx.)[/tex]

The x of the right angled ∆ = 14.12

Answer:

the top angle is 11 and the angle on the left is 9 so the X will be rounded to the nearest hundreth since it's the biggest angle so 11×9=109 so yea I THINK its 100 since it's rounding

Answer:

6

Step-by-step explanation:

add 18 on both sides

7w = 42

divide by 7 on both sides

w = 6

Answer:

Step-by-step explanation:

7w-18=24

7w= 24+18

w=42:7

w=6

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete as the radius of the sphere is missing.

The volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

Substitute 3.14 for [tex]\pi[/tex]

[tex]V = \frac{4}{3}* 3.14* r^3[/tex]

[tex]V = \frac{4* 3.14}{3}* r^3[/tex]

[tex]V = \frac{12.56}{3}* r^3[/tex]

[tex]V = 4.187* r^3[/tex]

At this point, assume that r = 3.

The expression becomes:

[tex]V = 4.187* 3^3[/tex]

[tex]V = 4.187* 27[/tex]

[tex]V = 113.05[/tex]

it's a I know this because I'm in the 8th

Step-by-step explanation:

it's a

Answer:

x = 3

Step-by-step explanation:

3x - X - 9 = 3(2 - x)  (Given)

2x - 9 = 3(2 - x) (combine like terms)

2x - 9 = 6 - 3x (distributive property of equality)

5x = 15 (addition property of equality)

x = 3 (division property of equality)

Ace

Answer:

52 kilometers per hour

:)

Answer:

33.33%

Step-by-step explanation:

Percent change equation is:

(x2 - x1) / x1 * 100%

where x1 is initial and x2 is final

_______________________________

1lbs = 30min

________________________________

Answer:

Step-by-step explanation:

.

Answer:

I answered the first two Q but i dont know the third one sorryy

Step-by-step explanation: i put the answers as pics

Answer:

It's simple the answer is 8%

Step-by-step explanation:

$. 36/ $4.50 × 100 = 8%

Answer:

8%

Step-by-step explanation:

Sales price x sales tax rate = sales tax

4.50 x sales tax rate = .36

sales tax rate = .36/4.50

sales tax rate = .08 or 8%

Answer:

It would take the apprentice 14 hours to make the fireplace on his own.

Step-by-step explanation:

Let x represent the hours it takes the bricklayer to make a fireplace on his own and x + 10 represent the hours it takes the bricklayer's apprentice to make a fireplace on his own.

7/(x + 10) + 2/x = 1

7/(x+10) represents the fraction of the fireplace the bricklayer's apprentice made (total amount of time the bricklayer's apprentice worked on the fireplace/time it takes the bricklayer's apprentice to make a fire place on his own) while 2/x represents the fraction of the fireplace the bricklayer made (total amount of time the bricklayer worked on the fireplace/time it takes the bricklayer to make a fire place on his own). The 1 on the right side of the equation represents the number of fireplaces they made in that time.

Multiply both sides of the equation by x(x + 10) to get rid of the denominators:

x(x + 10)[7/(x + 10) + 2/x] = x(x + 10)1

x(x + 10)[7/(x + 10)] + x(x + 10)(2/x) = x(x + 10)

7x + 2(x + 10) = x² + 10x

7x + 2x + 20 = x² + 10x

Gather all the terms to one side of the equation:

x² + 10x - 7x - 2x - 20 = 0

x² + x - 20 = 0

Factoring the simplified equation:

(x + 5)(x - 4) = 0

Solving for each factor:

When x + 5 = 0,

x = -5

When x - 4 = 0,

x = 4

Since a negative solution wouldn't make sense for this question, it would take the bricklayer 4 hours to complete the fireplace on his own.

Substituting x = 4 into x + 10 to find out how long it would take the apprentice to make the fireplace on his own:

x + 10 = 4 + 10 = 14

Therefore, it would take the apprentice 14 hours to make the fireplace on his own.

Answer:

y=68

x=12

Step-by-step explanation:

Variables= x and y

Lets make y the larger variable.

x+y=80

y=5x+8

substitution

x+5x+8=80

6x+8=80

x=12

plug 12 back in to find y

5(12)+8=68

y=68

x=12

Answer:

[tex]p = 4 \times 6 + 3 \times 5 - 19 = 20[/tex]

Step-by-step explanation:

Number of packs available with Alena initially = 4

Number of gums in each pack = 6

Total number of gums initially present with Alena can be found by multiplying the number of packs with the number of packs.

i.e. number of gums initially present with Alena = 4 [tex]\times[/tex] 6 = 24

Number of packs available with Hugh initially = 3

Number of gums in each pack = 5

Total number of gums initially present with Hugh can be found by multiplying the number of packs with the number of packs.

i.e. number of gums initially present with Hugh = 3 [tex]\times[/tex] 5 = 15

Total number of gums present initially = 24 + 15 = 39

Number of gums left with Alena and Hugh = 19

The number of gums chewed can be found by subtracting the number of gums left with them from the number of gums initially present with them.

i.e. Number of gums chewed, [tex]p[/tex] = 39 - 19 = 20

The equation that can be used is:

[tex]p = 4 \times 6 + 3 \times 5 - 19 = 20[/tex]

Answer:

x=28

Step-by-step explanation:

sum of all angles im a triangle = 180°

(2x+5) + (4x+10) + (x-31) = 180

7x=196

x=28

Answer:

x = 28°

Step-by-step explanation:

Sum of a triangle is equal to 180°. Firstly you need to form an equation. Add all the angles which equals to 180°.

2x + 5 + 4x + 10 + x - 31 = 180°

Now simply and find the value of x. Add all the x terms and whole numbers.

7x + 5 + 10 - 31 = 180°

7x + 15 - 31 = 180°

7x - 16 = 180°

7x = 180° + 16

7x = 196

x = 196 ÷ 7

x = 28°

So the angles are:

Angle A = 2x + 5

2 x 28 + 5 = 61°

Angle B = 4x + 10

4 x 28 + 10 = 122°

Angle C = x - 31

28 - 31 = -3°

Answer:

The answer is 245.7

Step-by-step explanation:

7 days in a week. 9 weeks. 9 x 7 = 63.

63 x 3.9 = 245.7

Answer:

B

Step-by-step explanation:

3x6 is 18 so therefore its B

Answer:

The cube of [tex](x+2)^3 \:is\:\mathbf{(x+2)(x^2-2x+4)}[/tex]

Step-by-step explanation:

We need to find cube of [tex](x+2)^3[/tex]

It can be found using formula: [tex](a+b)^3=(a+b)(a^2-ab+b^2)[/tex]

In the question given:

We have a = x and b = 2

Now finding cube using the above formula:

[tex](x+2)^3\\=(x+2)(x^2-(x)(2)+(2)^2)\\=(x+2)(x^2-2x+4)[/tex]

So, the cube of [tex](x+2)^3 \:is\:\mathbf{(x+2)(x^2-2x+4)}[/tex]

Answer: 54 in.

Step-by-step explanation:  So, the problem does something a little sneaky, and that is they ask for the TOTAL amount of wood needed for triangle DFG.  And to find that, we simply have to multiply side AC by 3 to get side DG.  We do this because triangle ABC is 3 times as small as triangle DFG.   Then, add your side DG that you just got, (21) to side FG and FD to get the total amount of wood needed, 54 in.

The length of wood needed for triangle DFG is 54 inches

Start by calculating the side length DG in triangle DFG

The side lengths of DFG are three times the corresponding side length of ABC

So, we have:

[tex]DG = 3 \times AC[/tex]

[tex]DG = 3 \times 7\ in[/tex]

[tex]DG = 21\ in[/tex]

The perimeter of triangle DFG is then calculated as:

[tex]P = DF + FG + DG[/tex]

This gives

[tex]P = 15 + 18 + 21[/tex]

[tex]P = 54[/tex]

Hence, the length of wood needed is 54 inches

Read more about perimeter at:

https://brainly.com/question/24571594

Answer:

Always

Step-by-step explanation:

We know that,

As every natural number n be represented in a rational form: n/1, any natural number can be represented in the form p/q, where q≠0. Hence, all natural numbers are rational numbers.

Answer:

Hydrogen = 13.4

Oxygen = 85.76

Carbon =  26.8

Step-by-step explanation:

H= 13.4

When you multiply by 1/10 all you have to do is move the decimal point to the LEFT.

So... 134←. = 13.4

_______________________________________________________

O= 85.76

134×[tex]\frac{16}{25}[/tex]=85.76

________________________________________________________

C= 26.8

134×[tex]\frac{1}{5}[/tex]=26.8

Answer:

5,4

Step-by-step explanation:

Answer: D. 53    [tex]a_{4}=53[/tex]

Step-by-step explanation:

[tex]a_{1}=4\\a_{2}=2(a_{1})+3\\a_{3}=2(a_{2})+3\\a_{4}=2(a_{3})+3[/tex]

[tex]a_{2}=2(a_{1})+3\\a_{2}=2(4)+3\\a_{2}=8+3\\a_{2}=11[/tex]

[tex]a_{3}=2(a_{2})+3\\a_{3}=2(11)+3\\a_{3}=22+3\\a_{3}=25[/tex]

[tex]a_{4}=2(a_{3})+3\\a_{4}=2(25)+3\\a_{4}=50+3\\a_{4}=53[/tex]

Answer:

Step-by-step explanation:

(5-2i) ( 5+2i) = (5^2) - ((2i)^2) = 25 - 4i^2

= 25 - 4(-1) = 25 +4 = 29 + 0i

The Solution is 29 + 0i.

The sum of a real number and an imaginary number is called a complex number. A complex number is usually represented by z and has the form a + ib. Here, both a and b are real numbers. The real part, denoted by Re(z), is represented by the value "a," and the imaginary part, represented by "b," is represented by Im(z). Also known as an imaginary number, ib.

Given Expression (5 – 2i)(5 + 2i)

we know a² - b² = (a - b)(a + b)

(5 – 2i)(5 + 2i) = 5² - (2i)²

= 25 - 4i²

and i² = -1

= 25 - 4(-1)

= 25 + 4 = 29

since the solution has 0i

so the equation is 29 + 0i

where a = 29 and b = 0

Hence, equation is 29 + 0i.

Learn more about complex numbers;

https://brainly.com/question/20566728

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