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3 years ago

What is x^2=7x number 9

Mathematics

1 answer:

ipn [44]3 years ago

8 0

Let's do this in steps, show your work!

#1. We need to move all terms to one side.

x^2 - 7x = 0

#2. Then factor out the common term x.

x(x - 7) = 0.

#3. Simplify to get..

x = 0, 7.

If you need help with any other question let me know.

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Simplify 2.67 + (−8.9).

OlgaM077 [116]

Answer:

-6.23 is the answer

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2 years ago

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A rectangular prism has a length of 18 feet, a height of 14 feet, and a width of 2 feet. What is its volume, in cubic feet?

Rama09 [41]

Answer:Right rectangular prism

Solve for volume

V=504ft³

l Length

w Width

h Height

Step-by-step explanation:

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3 years ago

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A flooring company needs to tile a section of a kitchen that is in the shape of a triangle.

Usimov [2.4K]

Answer: It is possible to determine the height of the triangle by using the formula of the area of a triangle and creating an equation to find the missing value (height). Also, the value of the height is 7ft

Explanation:

The area of a triangle is found by using both the height and the base of a triangle. Indeed, the general formula for this is A( area) = h (height) x b (base) ÷ 2. Now, this general formula can be used to find any of the values missing if two values are known. This means the height can be calculated using the area and the base. To do this, create a simple equation and solve it. The process is shown below:

1. Write the general equation

$A = \frac{h b}{2}$

2. Replace the letters with the values you have

$21 =\frac{6b}{2}$

3. Find the missing value by moving the values to the other side of the equal symbol (=) and changing its symbol

21 x 2 = 6b -For example 2 divided 6b but if it is changed to the other side it needs to multiply

42 = 6 b

42 / 6 = b

b = 7

This means the value of the height is 7 ft. If you want to double-check this, use the original formula:

A = 6 ft x 7 ft / 2

A= 42 $ft^{2}$ / 2

A= 21 $ft^{2}$

6 0

3 years ago

Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

3 years ago

Acar can travel 25 miles per gallon. Approximately how many gallons of fuel will the car need to travel 30

FrozenT [24]

Answer:

The gallons of fuel car need to travel 30 km is 0.75 approximately .

Step-by-step explanation:

Given:

The car can travel 25 miles per gallon. (1 mile = 1.6 km)

Now, we need to convert 25 miles into km .

25 miles = 25 × 1.6 km

= 40 km

So, the car can travel 40 km per gallon.

Then, we find out in 1 km how many gallons are used:

$40 km = 1 gallons$

$1\ km = \frac{1}{40}\ gallons$

$1\ km = 0.025\ gallons$

Now, we find out how much gallons of fuel will the car need to travel 30 km:

Gallons of fuel the car need to travel 30 km = $30\times 0.025$

= $0.75 gallons$ .

Therefore, the gallons of fuel car need to travel 30 km is 0.75 approximately.

6 0

3 years ago