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raketka [301]
3 years ago
6

The difference of the square of a number and 4 is equal to 3 times that number. Find the negative solution.

Mathematics
1 answer:
leonid [27]3 years ago
7 0

The negative solution is x = –1.

Solution:

Let the number be x.

Square of a number = x²

3 times a number = 3x

Difference of square of a number and 4 = 3 times that number

\Rightarrow x^2-4=3x

Subtract 3x from both sides of the equation, we get

\Rightarrow x^2-3x-4=0

–3x can be written as x – 4x.

\Rightarrow x^2+x-4x-4=0

\Rightarrow( x^2+x)+(-4x-4)=0

1st bracket have common term x and bracket have –4 common term.

\Rightarrow x( x+1)-4(x+1)=0

Take common term x + 1 outside.

(x+1)(x-4)=0

<em>By zero factor principle, if AB = 0 then A = 0 or B = 0.</em>

x + 1 = 0,   x – 4 = 0

x = –1,   x = 4

The negative solution is x = –1.

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A line with a slope of 2 passes through the point (9, 10). What is its equation in slope-intercept
defon

Answer:

y=2x-8

Step-by-step explanation:

Hi there!

We want are given a line with a slope of 2, that passes through the point (9, 10)

We want to find the equation of this line in slope-intercept form

Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept

As we are already given the slope, we can immediately plug it in as m in the formula.

y=2x+b

Now we need to find b, which is the value of the y intercept

As the equation passes through the point (9, 10), it is a solution to the equation, meaning that if we plug it into the equation of the line, it will create a true statement.

So we can use its values of x and y to help us solve for b.
Substitute 9 as x and 10 as y in the equation.

10=2(9) + b

multiply

10=18+b

Subtract 18 from both sides to isolate b on one side

-8=b
Substitute -8 as b into the equation

y=2x-8
Hope this helps!

If you would like additional problems to practice, here are two of them, both with explanations (n.b., the solution to the first link included uses a different method from the one in this answer.)
brainly.com/question/18112053
brainly.com/question/25508767

7 0
2 years ago
Multiply the following expressions<br> 81x5y6 × (-1x2y)​
Gnom [1K]
Answer: -4860y^2

Solution:
81 x (5y x 6) x (-2y)
-81 x 5y x 6 x 2y
= -4860y^2
5 0
2 years ago
Oil is leaking from a tanker at the rate of R(t) = 2000e^(-0.2t) gallons per hour where t is measured in hours. How much oil lea
Kipish [7]
The calculation of the integral will give us the answer.

Amount = Int (2000e^(-0,2t))dt

With t = 0 to t = 10

A = 2000.In(e^(-0,2t))dt


Making U = -0,2t

U = -0,2t

dU/dt = d(-0,2t)/dt

dU/dt = -0,2

dU = -0,2dt

dt = dU/-0,2
_______________


Then,

A = 2000.Int (e^U).dU/-0,2

A = -10.000.Int(e^U)dU

A = -10.000.e^U

A = -10.000.e^(-0,2t) | (0,10)

A = -10.000.(e^(-2)) - [ -10.000.e^(0)]

A = -10.000.e^(-2) + 10.000

A ~ 8,646 Gallons


6 0
3 years ago
Which angle measures are correct ? Check all that apply .
Aneli [31]
Correct
m<2 = 125
m<8 = 55
m<14 = 100
m<16 = 80
8 0
3 years ago
2(2x) + 10 = 3x + 13<br><br> Please help
zlopas [31]

Answer:

x = 3

Step-by-step explanation:

:))

5 0
2 years ago
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