A swimming pool measures 40 ft long by 20 ft wide. The pool is filled to a depth of 5 ft. Find the volume of the water in the pool.

Answer:

The third option (9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-[tex]\sqrt{49}[/tex])

Step-by-step explanation:

With FOIL, this can be expanded. (a+b)(a-b) is equal to a²+ab-ab-b² or a²-b².

In this case, all the answers have 4 terms, so we want the first option. This makes the equation 3²+(3×[tex]\sqrt{7}[/tex])-(3×[tex]\sqrt{7}[/tex])-([tex]\sqrt{7}[/tex])².

Solving these gives 9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-7. This is the same as  9+[tex]3\sqrt{7}[/tex]-[tex]3\sqrt{7}[/tex]-[tex]\sqrt{49}[/tex].

**This content involves multiplying with surds and expanding perfect squares, which you may wish to revise. I'm always happy to help!

The equivalent expression is (c) [tex]9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}[/tex]

The difference of squares equation is given as:

[tex](a + b)(a - b) = a^2 -b^2[/tex]

And the radical expression is given as:

[tex] (3+ \sqrt 7)(3- \sqrt7)[/tex]

By comparing the above expression to [tex](a + b)(a - b) = a^2 -b^2[/tex], we have:

[tex]a =3[/tex]

[tex]b = \sqrt 7[/tex]

Substitute these values in [tex](a + b)(a - b) = a^2 -b^2[/tex]

[tex] (3+ \sqrt 7)(3- \sqrt7) = 3^2 - (\sqrt 7)^2[/tex]

This gives

[tex] (3+ \sqrt 7)(3- \sqrt7) = 9 - \sqrt {49}[/tex]

By complete expansion, we have:

[tex] (3+ \sqrt 7)(3- \sqrt7) = 9 - 3\sqrt 7 + 3\sqrt 7 - \sqrt {49}[/tex]

Hence, the equivalent expression is (c)

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Answer:

2x^2-9x+15

It is prime/unfactorable

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total surface area of a cone is given by the expression,

SA = πrl + B

Here, r = Radius of the circular base

l = slant height

B = Surface area of the base

Surface area of the circular base = πr²

                                                       = π(5)²

                                                       = 25π cm²

Slant height 'AC' = [tex]\sqrt{AB^2+BC^2}[/tex]

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

                            = [tex]\sqrt{5^2+(12)^2}[/tex]

                            =  13 cm

Substitute the values in the expression of surface area,

SA = π(5)(13) + 25π

     = 65π + 25π

     = 90π cm²

Therefore, SA = 90π cm² will be the answer.

Answer:

C

Step-by-step explanation:

√9 = 3

3 • √5 • √2 = 3√10

Alternatively, √9 • √5 • √2 = √90 = 3√10

Answer:

C

Step-by-step explanation:

First, multiply all the square roots.

So, sqrt(9) x sqrt(5) x sqrt(2) = sqrt(9x5x2) =sqrt(90)

Think of two numbers that multiply to 90. One possible pair is 9x10.

So, sqrt(90) = sqrt(9x10)

Using the properties of surds,

Sqrt(9x10) = sqrt(9) x sqrt (10)

We know that sqrt(9) = 3

So, sqrt(90) = 3 x sqrt(10)

Hope this helps

Answer:

the too left graph us the abswer,

Because

f(x) = (x + 3)(x - 2) has positive cieff of the x^2 term, and also it has roots of -3 and 2

The graph of the function  f(x) = (x + 3)(x - 2) is first graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

To graph the function f(x) = (x + 3)(x - 2), we can start by finding its x-intercepts, y-intercept, and any vertical or horizontal asymptotes.

First, to find the x-intercepts, we set y = 0 and solve for x:

(x + 3)(x - 2) = 0

This equation is true when x = -3 or x = 2. Therefore, the x-intercepts of the graph are -3 and 2.

Next, to find the y-intercept, we set x = 0 and evaluate:

f(0) = (0 + 3)(0 - 2) = -6

Therefore, the y-intercept of the graph is -6.

The graph of f(x) = (x + 3)(x - 2) is a parabola that opens up because the sign of the two factors, (x + 3) and (x - 2), are both positive.

This means that the graph of f(x) will be a parabola that opens up with its vertex located at the point where the two factors are equal to each other

Hence, the graph of the function  f(x) = (x + 3)(x - 2) is first graph.

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p²-q²

p²-q²= (p+q)(p-q)

[by formula: (A+B)(A-B) = A²-B²]

Proof of the formula

Proof of the formula (A+B) • (A-B)

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2

Proof of the formula (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2

Answer:

A to C

rotated 180° around the orign

Aand D

rotated 270° clockwise, or 90° counterclockwise, also around the orign

Answer

80 m^2

Step-by-step explanation:

basically 10 x 8 plus the value

Answer:

8

Step-by-step explanation:

if one tree equals 700 bags, then you would divide the amount of bags that were used, 5600, by 700 to get answer. 5600 divided by 700 = 8

Answer:

Translate 2 unit(s) to the right and then reflect over the x-axis

Step-by-step explanation:

You have to move the coordinates of P, Q, and R to the right by 2 so just add 2 to the x coordinate in order to to the first part of the transformation.

After that flip it so that y coordinate of the points are negative to the position they were after translating to the right.

After translating two units to the right, reflect over the x-axis.

A transformation known as a translation involves shifting each point in a figure by the same amount and in the same direction. For instance, this transformation shifts the parallelogram 3 units upward and 5 units to the right. The formula is (x, y) →(x + 5, y + 3).

Given

Simply add 2 to the x coordinate to complete the first phase of the transformation since you must move the coordinates of P, Q, and R to the right by 2.

Then reverse it so that the points' y coordinates are opposite to where they were before being translated to the right.

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Answer:

the answers  is =-0

Step-by-step explanation:

is -0

Answer:

35

Step-by-step explanation:

These 3 vacancies aren’t distinct. That means if Amy, Bob, and Carla were chosen, it is the same as Bob, Carla, and Amy are chosen and so on.

Therefore, we will use “choose.”

Solving, I get 7!/((7-3)!3!) = 7!/(4!3!) = (7*6*5)/(3*2*1) = 35.

I hope this helps! :)

Answer:

There is no sufficient evidence

Step-by-step explanation:

The hypothesis :

H0 : μ = 436

H1 : μ < 436

Xbar = 433

s = 23

Sample size, n = 28

The test statistic :

(xbar - μ) ÷ (s/√(n))

(433 - 436) ÷ (23/√(28))

-3 ÷ 4.3465914

Test statistic = - 0.690

The Pvalue, calculated from test statistic value, df = n - 1 = 28 - 1 = 27

Pvalue = 0.248

Pvalue > α ; Hence, we fail to reject the null and conclude that there is no sufficient evidence to support the claim that the bags are underfilled

Answer:

Step-by-step explanation:

according to the Pythagoras theorem ,

SohCahToa

Soh - sine is opposite , hypotenuse

Cah -cos is adjacent , hypotenuse

Toa - tan is opposite, adjacent

from the diagram above , the tan is 8/15.

Hope this is helpful ,

have a nice day :-)

Answer:

4x+12+mx+3m

You use the FOIL method.

Answer:

(4+m)(x+3)

Step-by-step explanation:

x+3 is a common factor, so you can convert this to put the other 2 parts in a bracket. This results in (4+m)(x+3).

An example of how this works is if you made m=1 and x=2. This would make the original expression 4(2+3)+1(2+3), or 4×5+1×5, which is 5×5 or 25. (1+4)(2+3) also equals to 5×5.

**You may want to revise factorising algebraic equations. I'm always happy to help!

Answer:

To complete the square, we need to have the equation set up like this:

x^2 +4x =9

To do that, we'd need to move the 4x to the left side producing

4x + x^2 = 9

And that can be rewritten as

x^2 +4x =9

So the term that needs to be moved is -4x

https://www.1728.org/quadr2.htm

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

f(x) = y = 4 - 7x/4

7x/4 + y = 4

7x/4 = 4 - y

7x = 4(4-y)

x = 4(4-y)/7 = 16/7 - 4y/7

renaming to regular function convention (with x as input variable and y as function result) :

inverse function f(x) = y = -4x/7 + 16/7 = g(x)

so, yes, they are inverses of each other.

Answer:

13 quarters and 24 dimes

Step-by-step explanation:

13*.25=3.25

24*.1=2.4

3.25+2.4=5.65

Answer:

so to find the amount of meters in 24 hours we divided 180 by 24 which is 7.5 so the snail goes 7.5 meters in a hour  so multipy 7.5 by 100 to get 750

so the snail goes 750 cm in a hour

Answer:

4/7

Step-by-step explanation:

Pr = Expected outcome/Total outcome

Since Total movies = 15

Total outcome = 15

If there are 9 actions movies

Pr(selecting the first action movie) = 9/15

Since the total remaining movies will be 14 (no replacement)

If the second movie is taken, Pr(second action movie) = 8/14 = 4/7

Answer:what’s the question?

Step-by-step explanation:

Answer:

answer for this solution is 10 degrees

Step-by-step explanation:

sin x + cos x = 90

5x + 3x +10 = 90

x = 10

Answer:

The smallest integer is 11.

Step-by-step explanation:

Let the first integer be x.

Then the second will be (x + 1) and the third will be (x + 2).

The sum is 36. Hence:

[tex]x+(x+1)+(x+2)=36[/tex]

Solve for x:

[tex]3x+3=36[/tex]

So:

[tex]3x=33[/tex]

Hence:

[tex]x=11[/tex]

Our sequence is 11, 12, 13.

So, the smallest integer is 11.

Answer:

Ali serves 24 customers an hour

Alyssa severs 60 customer an hour

Alyssa severs more customers in one hour

Step-by-step explanation: