Put the equation below into vertex form.

y=(x+9)(x+25)

Length of the diagonal of rectangular prism is equals to 13units.

" Rectangular prism is a three dimensional figure which has six faces in rectangular shape."

Formula used

Total surface area of the rectangular prism = 2(l b + b h +l h)

Sum of all the  edges of the prism = 4 (l +b + h)

length of the diagonal  of the prism = √l² + b² + h²

l = length of the prism

b = width of the prism

h = height of the prism

According to the question,

Given,

Total surface area of the rectangular prism = 56 units

⇒2(l b + b h +l h) = 56

Sum of all the edges of the prism = 60 units

⇒4(l + b + h) = 60

Divide both the side by 4 we get,

 (l + b + h) = 60 / 4

⇒(l + b + h) = 15                               ____(1)

Squaring both the side of (1)  we get,

  (l + b + h)² = (15)²

⇒l² + b² + h² + 2 (l b + b h +l h) = 225

Substitute the value of total surface area  to get length of the diagonal,

 l² + b² + h² + 56 = 225

⇒l² + b² + h²  = 225 - 56

⇒l² + b² + h²  = 169

⇒√l² + b² + h²  = √169

⇒√l² + b² + h²  =  13

Hence, length of the diagonal of rectangular prism is equals to 13units.

Learn more about rectangular prism here

https://brainly.com/question/21308574

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q = 12.5

hope it helps..!!!

Answer:

12.5

Step-by-step explanation:

u dont need it lol

Answer:

3. 1067

4. 11875

5. 1638

6. 19317

7. 3432

8. 42022642

9. 318384

Answer:

A. (-5, -28)

Step-by-step explanation:

The coordinates of the vertex of the function [tex]\rm f(x) = x^2+10x-3[/tex]  is

(-5, -28).

It is given that the function  [tex]\rm f(x) = x^2+10x-3[/tex]

It is required to find the coordinates of the vertex.

It is defined as the graph of a quadratic function that has something bowl-shaped.

We have a function:

[tex]\rm f(x) = x^2+10x-3[/tex]

This function represents a parabola.

We know the standard form of parabola in quadratic style:

[tex]\rm f(x)=ax^2+bx+c[/tex]

By comparing the given function to the standard form of parabola, we get

a = 1, b = 10, and c = -3

The vertex of the parabola is given by:

[tex]\rm x = -\frac{b}{2a}[/tex]

Putting the values in the above equation, we get:

[tex]\rm x = -\frac{10}{2\times1} \Rightarrow -5[/tex]

x = -5 put this value in the given parabola function, we get:

[tex]\rm f(-5) = (-5)^2+10(-5)-3\\\rm f(-5) = 25-50-3\\\rm f(-5) = -28[/tex]

or y = -28

The coordintes = (x, y) : (-5 , -28) which is shown in the graph.

Thus, the coordinates of the vertex of the function [tex]\rm f(x) = x^2+10x-3[/tex]  is (-5, -28).

Know more about the parabola here:

brainly.com/question/8708520

Answer:

√13

Step-by-step explanation:

Let,

( x1, y1 ) = ( 1, 1 )

Here,

x1 = y1 = 1

( x2, y2 ) = ( 3, 4 )

Here,

x2 = 3

y2 = 4

Formula : -

( Distance )² = ( x2 - x1 )² + ( y2 - y1 )²

( Distance )² = ( 3 - 1 )² + ( 4 - 1 )²

                    = 2² + 3²

                    = 4 + 9

( Distance )² = 13

Distance = √13

Answer:

3.61

Step-by-step explanation:

length=[tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} )}[/tex]

          =[tex]\sqrt{(3_{}-1_{} )^{2}+(4_{}-1_{} )^{2} )}[/tex]

          = 3.61

Answer:

BDC  and ADB

Step-by-step explanation:

Answer:

ITs a plus b then c ding

Step-by-step explanation:

Answer:

[tex]\frac{4}{5}[/tex] (4/5)

just fill out 4 in the blank

Step-by-step explanation:

1. Equal the denominator for 1/4

End result=[tex]\frac{11}{20}[/tex]

So all the other ones have to be made according to this

20/4=5

1x5=5

[tex]\frac{1}{4}[/tex] will now be [tex]\frac{5}{20}[/tex]

2. Figure out what ?/5 will be

If this number is getting subtracted by [tex]\frac{5}{20}[/tex] then, we have to add [tex]\frac{11}{20}[/tex] by [tex]\frac{5}{20}[/tex] to get our answer.

[tex]\frac{11}{20} +\frac{5}{20} =\frac{16}{20}[/tex]

this means that when [tex]\frac{16}{20}[/tex] gets subtracted by [tex]\frac{5}{20}[/tex] it will equal [tex]\frac{11}{20}[/tex]

3. Simplify 16/20 to it's lowest terms

5x4=20

20/5=4

so, each part ([tex]\frac{1}{5}[/tex]) worth's 4

20-4=16

So that means, that the simplest for for this is [tex]\frac{4}{5}[/tex]

just fill out 4 in the blank

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:D

Answer:

4

Step-by-step explanation:

Let the blank = x

Thus,

[tex]\frac{x}{5}-\frac{1}{4}=\frac{11}{20}[/tex]

[tex]\mathrm{Add\:}\frac{1}{4}\mathrm{\:to\:both\:sides}[/tex]

[tex]\frac{x}{5}-\frac{1}{4}+\frac{1}{4}=\frac{11}{20}+\frac{1}{4}[/tex]

[tex]\mathrm{simplify}[/tex]

[tex]\frac{x}{5}=\frac{4}{5}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}5[/tex]

[tex]\frac{5x}{5}=\frac{4\cdot \:5}{5}[/tex]

[tex]\mathrm{simplify}[/tex]

x = 4

Hence, the blank = 4

Equation = [tex]\frac{4}{5}-\frac{1}{5}=\frac{11}{20}[/tex]

[RevyBreeze]

Answer:

(x - 6)(x + 2)

Step-by-step explanation:

assuming you require the trinomial to be factorised.

x² - 4x - 12

consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (- 4)

the factors are - 6 and + 2 , since

- 6 × 2 = - 12 and - 6 + 2 = - 4 , then

x² - 4x - 12 = (x - 6)(x + 2)

Answer:

hee-hee!

Step-by-step explanation:

Marcy charges $3 to walk a small dog and $5 for a big dog.

She walks 15 small dogs and 6 big dogs.

We can use an expression that would show the problem:

3s + 5b

(s = small dogs & b = big dogs)

s = 15 | b = 6

3(15) + 5(6)

45 + 30 = 75

Marcy earns $75 of profit.

the answer is

35.6540944227

Answer:

1) [tex]\sqrt{2}[/tex]

2) 11

3) 5

4) 8

5) I feel like there is something wrong with this question

6) [tex]\sqrt{3}[/tex]

7) 10

8) 4

9) 18

10) 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

#1

In this rule, it is saying that is two of the sides are the same and two of the angles are 45 degrees, then you can find the measurement of the hypotenuse or one of the legs of the triangle

Here, the hypotenuse is equal to what the length of one of the legs are and multiplied by [tex]\sqrt{2}[/tex]

Since the length of one of the legs are 4, multiply that by [tex]\sqrt{2}[/tex] and you will get:

4[tex]\sqrt{2}[/tex]

#2

Same concept, but reverse

The hypotenuse is 11[tex]\sqrt{2}[/tex] and to go back to one of the leg lengths, instead of multiplying, you want to divide.

So:

[tex]\frac{11\sqrt{2} }{\sqrt{2} }[/tex]

Which is equal to:

11

You can also do this by knowing that the legs are the same length and knowing that b=11, and a=b, a is also equal to 11

#3

Same as the previous question

[tex]\frac{5\sqrt{2} }{\sqrt{2} }[/tex]

b = 5

#4

a and b are equal to x, and in this case, x is 8.

So going back to the picture, you can see that you need to multiply this x by [tex]\sqrt{2}[/tex] to get 8[tex]\sqrt{2}[/tex]

#5

You'd have to ask your teacher for this one because it is impossible to have a leg that is longer than the hypotenuse

#6-10

Apply the same rules for these set of questions:

Notice that there is a different system for these though, I will let you figure them out.

Step-by-step explanation:

11 ÷ 20 = 0.55

0.55 × 100 = 55

so 55%

Answer:

[tex]x=20[/tex]

Step-by-step explanation:

Solve the following equation for x:

[tex]1500=1/3(15)^{2} x[/tex]

Answer:

1

by looking only 1 is missing

Answer:

x = -8

Step-by-step explanation:

9+8x-4-5x=-19

5+8x-5x=-19

5+3x=-19

-5 =-19

3x = -24

3/3 = -24/3

x= -8

Answer:

102 or the 12th number considering 38 is the 4th

Answer:

b no. is the correct answer

The mean of the uniform distribution of X is the average of the distribution

The mean and standard deviation of X are 18 and 9.24, respectively

The uniform distribution of X is given as:

X∼U(3,34)

This means that:

a = 3 and b = 34

The mean is calculated as:

[tex]\bar x = \frac{a + b}{2}[/tex]

So, we have:

[tex]\bar x = \frac{2 + 34}{2}[/tex]

[tex]\bar x = \frac{36}{2}[/tex]

Evaluate

[tex]\bar x = 18[/tex]

This is calculated as:

[tex]\sigma = \sqrt{\frac{(b - a)^2}{12}}[/tex]

Substitute known values

[tex]\sigma = \sqrt{\frac{(34 - 2)^2}{12}}[/tex]

Evaluate the exponent

[tex]\sigma = \sqrt{\frac{1024}{12}}[/tex]

Divide

[tex]\sigma = \sqrt{85.33}[/tex]

Evaluate the root

[tex]\sigma = 9.24[/tex]

Hence, the mean and standard deviation of X are 18 and 9.24, respectively

Read more about mean and standard deviation at:

https://brainly.com/question/15858152

what is standard deviation round3d to one decimal place

Answer:

A.

While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.

Answer:

47

Step-by-step explanation:

3 x 4 = 12

7 x 5 = 35

35 + 12 = 47

[tex]\\ \rm\rightarrowtail 5x^2-2x-7=0[/tex]

[tex]\\ \rm\rightarrowtail 5x^2-7x+5x-7=0[/tex]

[tex]\\ \rm\rightarrowtail x(5x-7)+1(5x-7)=0[/tex]

[tex]\\ \rm\rightarrowtail (x-1)(5x-7)=0[/tex]

[tex]\\ \rm\rightarrowtail x=1,7/5[/tex]

Answer:

Yes.

Step-by-step explanation:

18 gal = 288 cups.

(1 gal = 16 cups)

If 240 students purchase 1 cup each, there will be 48 cups left over.

So,yes, there will be enough punch for everyone.

Please mark as brainliest!

Thanks!

Answer:

$22.26

Step-by-step explanation:

To solve, all we need to do is 28(1-.25) to get 21, then we set up the equation 21(1+.03) and we get our total for the price.

we subtract in the first place, because it is a discount, and we add in the second one because it is a sales tax.

please rate and mark as brainlest.

Answer:

Step-by-step explanation:

Formula

Area = B * h

Givens

Base = 2.5

height = 5.25

Solution

You choose the value for the base and height from the fact that the height touches the base (which has been extended) at right angles.

Area =  2.5 * 5.25

Area = 13.125

Answer: Area = 13.125 or 13 1/8

Answer:

25

Step-by-step explanation:

what is 35 divided by 1.4?

25.

25 x 1.4 (140%) = 35

you are looking for more than 100% of an unknown number so you can use this method to find the answer

hope that helped :)

Answer:

4(x² - x - 2)

Step-by-step explanation:

The highest common factor is 4 so factor it out.

Answer:

Step-by-step explanation:4x2−4x−84x2-4x-8Factor 44 out of 4x2−4x−84x2-4x-8.

Factor 44 out of 4x24x2.4(x2)−4x−84(x2)-4x-8Factor 44 out of −4x-4x.4(x2)+4(−x)−84(x2)+4(-x)-8Factor 44 out of −8-8.4(x2)+4(−x)+4(−2)4(x2)+4(-x)+4(-2)Factor 44 out of 4(x2)+4(−x)4(x2)+4(-x).4(x2−x)+4(−2)4(x2-x)+4(-2)Factor 44 out of 4(x2−x)+4(−2)4(x2-x)+4(-2).4(x2−x−2)

Factor x2−x−2x2-x-2 using the AC method

Consider the form x2+bx+cx2+bx+c. Find a pair of integers whose product is cc and whose sum is bb. In this case, whose product is −2-2and whose sum is −1-1.−2,1

Write the factored form using these integers.4((x−2)(x+1))4((x-2)(x+1))Remove unnecessary parentheses.4(x−2)(x+1)

Answer:

[tex]a_{n}[/tex] = 5n - 2

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 18 and a₁₀ = 48 , then

a₁ + 3d = 18 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

6d = 30 ( divide both sides by 6 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3

Then

[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2

10y⁵ + 30y³ - 15y =

5y * 2y⁴ + 5y * 6y² + 5y * (-3) =

5y (2y⁴ + 6y² - 3)