Write an expression for the volume of a rectangular prism with length 7.5 ft, width w ft, and height 4.2 ft. Enter the smaller number first. sad :'(

Question:

Let [tex]p=x^2-2[/tex] .

Which equation is equivalent to in terms of p ?

Answer:

[tex]p^2+18=9p[/tex] or [tex]p^2+18 - 9p = 0[/tex]

Step-by-step explanation:

Given

[tex]p=x^2-2[/tex] .

Required

Find the equation equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]

To get the equation equivalent to the given expression, we simply simplify [tex](x^2-2)^2+18=9x^2-18[/tex] and solve in terms of p

[tex](x^2-2)^2+18=9x^2-18[/tex]

Factorize expression on the right hand side

[tex](x^2-2)^2+18=9(x^2-2)[/tex]

Substitute [tex]x^2 - 2[/tex] for p

[tex](x^2-2)^2+18=9(x^2-2)[/tex] becomes

[tex]p^2+18=9p[/tex]

Hence, equation [tex]p^2+18=9p[/tex] is equivalent to [tex](x^2-2)^2+18=9x^2-18[/tex]

Solving further to get the value of p

[tex]p^2+18=9p[/tex]

Subtract 9p from both sides

[tex]p^2+18 - 9p = 9p - 9p[/tex]

[tex]p^2+18 - 9p = 0[/tex]

Rearrange

[tex]p^2 - 9p +18 = 0[/tex]

Factorize

[tex]p^2 - 6p - 3p +18 = 0[/tex]

[tex]p(p - 6) - 3(p -6) = 0[/tex]

[tex](p - 3)(p -6) = 0[/tex]

p - 3 = 0 or p - 6 = 0

p = 3 or p = 6

Answer:

p^2-18+9p=0

Step-by-step explanation:

Khan

Answer:

[tex]y=-\frac{6x}{5}[/tex]

Step-by-step explanation:

[tex]-2x + 7y = -5\\-2.0 - 4y = 6[/tex]

[tex]y=-\frac{6x}{5}[/tex]

Hey there!

Another word for the mean is the average. To find the mean in a set of numbers, you add up the numbers and then divide by the number of numbers!

39+82+74+96+64+52+74=481

Now, we see that we have seven numbers. So, we divide by seven!

481/7≈68.71 (rounded to nearest hundredth)

I hope that this helps!

Answer:

3 or 7

Step-by-step explanation:

[tex]-2x^2+20x-42=0\\-2(x^2-10x+21)=0\\-2(x-7)(x-3)=0\\x=7, 3[/tex]

Hope this helps!

Answer:

Find two points on the line and write them out: (x1,y1) (x2,y2)

Use this formula: y2-y1/x2-x1

The answer you get is the slope which is "m" in y=mx+b

Now in y=mx+b plug in one point's y into y and x into x. 

Find b

Answer:

Use points from the graph to create a table of data points. Then find a rule for the data in the table and write an equation that represents that rule. Lastly, check that the equation holds true for other data points in the table or graph.

Step-by-step explanation:

Answer: 84 ft

Step-by-step explanation:

Answer:

No, a trapezoid is not a rectangle.

This is because trapezoids by definition have only one pair of parallel sides while rectangles must have at least two sets of opposite parallel sides. Also, trapezoids do not have 90 degrees at every angle like rectangles do.

Answer:

5 + 3x = 41

x = 12 miles

Step-by-step explanation:

A taxi cab company charges a flat amount of $5.00 plus a rate of $3.00 per mile traveled.

Let x is the number of miles traveled.

If the total cost of the fare was $41.00 then

5 + 3x = 41     eq. 1

The above equation can be used to determine the number of miles traveled.

Solving the equation for x,

5 + 3x = 41

3x = 41 - 5

3x =  36

x = 36/3

x = 12 miles

Therefore, 12 is the total number of miles traveled if the fare was $41.00.

Answer:

[tex] \frac{9}{14} [/tex]

Step-by-step explanation:

times top numbers and bottom numbers

6 × 3 = 18

7 × 4 = 28

18/28

*simplify*

9/14

Answer B

Step-by-step explanation:

2x+1+14

Answer:

B.)

Step-by-step explanation:

B)2x+15

Answer:

The height of the triangle is 8 cm

Step-by-step explanation:

First we need to write down the question in a mathematical format and then solve.

let b be the base of the triangle and h be the height of the triangle

"The base of a right triangle is 13 less than 2 times the height" can be written as

b = 2h - 13 -----------------------------------------------------(1)

"The area of the triangle is 12 square cm" can be written as;

area of the triangle = 12 cm²

but area of a triangle = [tex]\frac{1}{2}[/tex] ×b × h

This implies that

[tex]\frac{1}{2}[/tex] ×b × h = 12 cm²

bh = 24 cm² --------------------------------------------------(2)

substitute equation (1) in equation (2)

(2h - 13)h = 24

2h² - 13h = 24

2h² - 13h - 24 = 0 ----------------------------------------------(3)

The above is now a quadratic equation, so we will solve by completing the square method.

Find two numbers such that its product will give -48 and its sum will give -13

The two numbers are -16 and 3

Replace -13h by  (-16h +  3h) in equation (3)

2h² - 13h - 24 = 0

2h² - 16h + 3h - 24 = 0

2h(h - 8) + 3(h-8) = 0

(h-8)(2h+3) = 0

either h-8 = 0

           h = 8

OR

2h + 3 = 0

2h = -3

h =-3/8

There is no such thing as negative length, therefore h= 8 is the answer

The height of the triangle is 8 cm

Step-by-step explanation:

x2 - 4x +4 -4 + y2 + 20y +100 -100 + 55=0

(x-2)2 + (y+10)2 =49

center:(2,-10)

r=7

Answer:

[tex](-2,\, 4)[/tex].

Step-by-step explanation:

To find the vertex of this parabola, start by rewriting it in the vertex form [tex]f(x) = a\, (x - h)^2 + k[/tex].

Start with the original expression:

[tex]f(x) = (x + 2)^2 + 4[/tex].

Note that in the vertex form, the sign in front of [tex]h[/tex] should be a minus. However, in [tex]f(x) = (x + 2)^2 + 4[/tex], the sign in front of [tex]2[/tex] is a plus. Since adding

[tex]f(x) = (x - (-2))^2 + 4[/tex].

Therefore:

Hence, [tex](-2,\, 4)[/tex] is the vertex of this parabola.

Answer:

5

Step-by-step explanation:

the probability of getting a 6 every time you roll the die once is just 1/6. multiply that by 30 and we get our answer, which is 5 times.

Answer:

Option (4). 25%

Step-by-step explanation:

The graph attached shows the exponential growth.

Let the graphed function is y = [tex](1+\frac{r}{100})^{t}[/tex]

Here 'r' = Rate of growth

t = Duration of time in years

y = enrollments after time 't' years

Graph shows at time 't' = 0 or initially number of enrollments = 20

After 8 years number of enrollments will be

120 = [tex]20(1+\frac{r}{100})^{8}[/tex]

[tex]\frac{120}{20}=(1+\frac{r}{100})^{8}[/tex]

6 = [tex](1+\frac{r}{100})^{8}[/tex]

log 6 = [tex]8\text{log}(1+\frac{r}{100})[/tex]

0.77815 = [tex]8\text{log}(1+\frac{r}{100})[/tex]

[tex]\text{log}(1+\frac{r}{100})[/tex] = 0.0972689

[tex](1+\frac{r}{100})=1.251[/tex]

[tex]\frac{r}{100}=0.251[/tex]

r = 25.1%

r ≈ 25%

Therefore, Option (4) will be the answer.

Answer:

25%

Step-by-step explanation:

did test and it was right

Answer:

x+ 4x-85 = 90

Step-by-step explanation:

The two angles are complementary so they add to 90 degrees

x+ 4x-85 = 90

Combine like terms

5x - 85 = 90

Add 85 to each side

5x = 175

Divide by 5

5x/5 =175/5

x =35

Answer:

x (4-85)  =  -81x

Step-by-step explanation:

Equation: x (4-85)

Answer: x (4-85)

1: Find the missing side

2: add the other numbers

Hope this helps.

Answer:

10 x 10n^2 -1

Step-by-step explanation:

any expression as long as they equal the same as your equation (100n^2-1)

Answer:

(10n + 1)(10n - 1)

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Answer: im pretty sure it is a domain

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

-7 = -7 + 0i

On a plane mark -7 on real axis and go 0 units on imaginary axis

Answer:

f(0)=1

Step-by-step explanation:

The question asks us to find f(0). We want to find what f(x), or y is, when x is equal to 0.

f(x)=3^x

Therefore, we can substitute 0 in for x.

f(0)=3^0

Evaluate the exponent, 3^0.

Any number raised to the power of zero is equal to 1.

f(0)=1

Answer:

1

Step-by-step explanation:

f(0) = 3^0

f(0) = 1

anything to the 0th power = 1

Answer:

She needs 301.8 in² of tissue paper.

Step-by-step explanation:

In order to calculate the amount of tissue paper she needs to make 21 hats, we need to find the area of each hat and multiply it by the total number of hats she wants to make.

Since the Vietnamese conical hats are hollow and don't have a base, we need to find the area of the it's lateral walls, this is given by the following expression:

lateral area = pi*r*l

r = d/2 = 16/2 = 8 in

We were given the height, but we need the slant height, therefore:

l = sqrt(r² + h²) = sqrt(8² + 9²) = sqrt(64 + 81) = sqrt(145)  = 12.041 in

Then the lateral area is:

lateral area = pi*8*12.0141 = 301.8 in²

She needs 301.8 in² of tissue paper.

Answer:

1.5707

Step-by-step explanation:

i solved it using the formula :

[tex]2\pi \times r \frac{45}{360} [/tex]

Answer:

14 cubic inches

Step-by-step explanation:

First, we have to find the radius from the circumference. We know that the circumference can be found using the equation c = 2pi(r). Set c equal to 7.1, and solve for r by dividing by 2pi.

Now, we have a radius of 1.13. Using this, we can plug the radius and the height into the equation used to find the volume of a cone: v = pi(r^2)(h/3)

This leads us to 14.04, or 14, when rounded to the nearest tenth of a cubic inch.

Answer:

d= -16

Step-by-step explanation:

-16 +4=-12

Answer:

d=−16  

Step-by-step explanation:

d+4−4=−12−4

d=−16

i dont understand your question

Answer: f(x) = 1^(x + 1)

Step-by-step explanation:

we have that h(x) = 1^x

and h(x) = f(g(x))

This mean that we are evaluating the function f(y) in the point y = g(x)

where g(x) = x - 1

then:

f(g(x) = f(x - 1) = h(x) = 1^x

then we should have that:

f(x) = 1^(x + 1)

then:

f(x - 1) = 1^(x - 1 + 1) = 1^x

Volume of a cube is Volume = S^3, where S is the length of one side.

Volume = 2 1/4^3 = 2 1/4 x 2 1/4 x 2 1/4 = 11 25/64 in^3

The answer is D.

Answer: 30 3/8

Step-by-step explanation:

Answer:

f (-4) = 3x(-4)^2 - 7x(-4) - 32 =  44

Step-by-step explanation:

you should replace every x with the number given which is here equals -4