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3 years ago

What are the solutions to the equation?

Mathematics

2 answers:

kirill [66]3 years ago

8 0

<u>Answer:</u>

x = −10 and x = 4

<u>Step-by-step explanation:</u>

We are given the following quadratic equation and we are to solve it to find the two solution for the variable x:

$x^2+6x=40$

Rearranging the equation by putting the constant on the same side as the variables to get:

$x^{2} +6x-40=0$

Now factorizing it to get:

$x^{2} -4x+10x-40=0\\\\x(x-4)+10(x-4)=0\\\\(x+10)(x-4)=0\\\\x= -10, x= 4$

Therefore, the solution to the given quadratic equation $x^2+6x=40$ are x = −10 and x = 4.

olga2289 [7]3 years ago

6 0

Answer:

x = −10 and x = 4

Step-by-step explanation:

x2 + 6x = 40

Subtract 40 from each side

x^2 + 6x -40 =0

Factor, what 2 numbers multiply to -40 and add to 6

10 * -4 = -40 10+-4 = 6

(x+10) (x-4) = 0

Using the zero product property

x+10 =0 x-4=0

x=-10 x=4

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Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

For what value of x is (2x^2+8x)/(x+4)(x^2-9) undefined?

irakobra [83]

Answer:

The value at x =3 is undefined for the given expression

Step-by-step explanation:

Given expression is $\frac{2x^2+8x}{(x+4)(x^2-9)}$

To find for what value of x is undefined in the given expression :

$\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{2x(x+4)}{(x+4)(x^2-9)}$

$=\frac{2x}{x^2-9}$

$\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{2x}{x^2-9}$

If we put x=3 in the above expression we get

$\frac{2x}{x^2-9)}=\frac{2(3)}{3^2-9}$

$=\frac{6}{9-9}$

$=\frac{6}{0}$

Therefore $\frac{2x^2+8x}{(x+4)(x^2-9)}=\frac{6}{0}$

The value at x =3 is undefined for the given expression

7 0

3 years ago

Write an equation in slope-intercept form of the line shown.<br><br> An equation is

ycow [4]

Using the slope intercept formula, the equation for the line in slope intercept form is y = -x - 4

<h3>Slope intercept equation</h3>

The slope intercept equation can be describe as follows:

y = mx + b

where

m = slope
b = y-intercept

Therefore,

(-4, 0)(1, -5)

m = -5 - 0 / 1 + 4 = -5 / 5 = -1

Therefore, let's find b using (1, -5)

-5 = -1(1) + b

-5 = -1 + b

b = -5 + 1

b = -4

Therefore, the equation is y = -x - 4

learn more on slope intercept equation here: brainly.com/question/21010520

5 0

3 years ago

An electric motor pumps water into a pool at a rate of 500 liters per hour. After a tune up, it's rate increases by x liters per

Sidana [21]

Answer:

(500+x)*3=1800

Step-by-step explanation:

x will increase the rate so that the motor will pump 1800 liters in 3 hours, which makes x=100, and (500+100)*3=1800

4 0

3 years ago

Which is shown by the map

professor190 [17]

Answer:

Step-by-step explanation:

Well I am not fully sure but I would say A

3 0

3 years ago