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Step2247 [10]
2 years ago
11

Solve the quadratic for x, then enter the numerical value of your solution. (If there are two solutions, either one will work.)

2(x-5)^2+7=79

Mathematics
1 answer:
xz_007 [3.2K]2 years ago
6 0

Answer: X= -1 OR X= 11

Step-by-step explanation:

Step 1 : Equate ( x-5)² since it occurred twice, hence the reason 2 is added in front of (x-5)²

= (x-5)²

= (x-5)(x-5)

= (x²-5x-5x+25)

= (x²-10x+25)

Step 2: multiply the result by two since it occurs twice and also bring the equation

= 2 (x²-10x+25) +7 = 79

= 2x²- 20x+50+7 = 79

= 2x²- 20x+57 =79

Step 3: most quadratic equation are always equal to zero, let's make this one equal to Zero by subtracting 79 from both sides

= 2x²-20x+57-79 = 79-79

= 2x²-20x-22=0

Step 4: divide the equation by a common number to get the least coefficient of the three coefficients

Dividing the three by 2

(2x²-20x-22)/2 = x²- 10x- 11

Step 5: Factorise completely

Sub step 1 : the first term in the equation is X² which makes the first term coefficient 1; the second term in the equation is -10x which makes the second term coefficient -10, the constant has a coefficient of -11

Sub step 2: multiply the coefficient of the first term (1) and the constant (-11) which gives us (-11)

1*-11 = -11

Sub step 3: Get two numbers in such a way that the addition of the first number and the second number gives the second coefficient in the quadratic equation and the multiplication of the two numbers will give us the product of the first coefficient and the constant.

And the two numbers is +1 and -11, the sum of the two numbers will give us -10 and the product will give us -11.

Step 6: slot the two numbers (+1, -11) into the equation by making themr replace the second coefficient

x²-10x-11=0

= x²+x-11x-11 =0

Step 7: split the equation into two and Factorise further

= (x²+x)(-11x-11) =0

= x(x+1)-11(x+1) = 0

= x+1= 0 or x-11 =0

Step 8 split them into individual equation

= x+1= 0.

Subtract 1 from both sides

= X+1-1=0-1

= x= -1

Or X should be

= x-11=0

Add 11 to both sides

= X-11+11 = 0+11

= x= 11

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The ratio of two numbers is 4:9. When 5 is subtracted from each of them the new ratio becomes 3:8. Find the numbers.​
natta225 [31]

Answer:

FIRST NUMBER IS 20

AND

SECOND NUMBER IS 45

Step-by-step explanation:

LET THE RATIO BE X

FIRST NUMBER = 4X

SECOND NUMBER = 9X

A/Q,

=}4X - 5 / 9X - 5 = 3 / 8

CRISS CROSS,

=}8 ( 4X - 5 ) = 9X - 5 ( 3 )

=}32X - 40 = 27X - 15

=}32X - 27X = - 15 + 40

=}5X = 25

=}X = 25 / 5

=}X = 5

THEREFORE,

FIRST NUMBER

=} 4X

=} 5 × 4

=} 20

SECOND NUMBER

=} 9X

=} 5 × 9

=} 45

8 0
3 years ago
What is the equation of the line that passes through the point (-2,5) and has a<br> slope of -4?
adoni [48]

Answer:

\boxed {\boxed {\sf y= -4x -3}}

Step-by-step explanation:

We are asked to find the equation of a line given a point and the slope. We will use the point-slope formula.

y-y_1= m(x-x_1)

In this formula, m is the slope and (x₁, y₁) is the point the line passes through. The slope of this line is -4 and the line passes through (-2,5).

  • m= -4
  • x₁= -2
  • y₁ = 5

Substitute the values into the formula.

y-5 = -4 (x--2)

y-5 = -4 (x+2)

We are finding the equation of the line, so we should find the slope-intercept form or y=mx+b ( where m is the slope and b is the y-intercept).We must isolate the variable y on one side of the equation.

First, distribute the -4 on the right side of the equation. Multiply each term inside the parentheses by -4.

y-5=( -4 *x ) + (-4* 2 )

y-5 =(-4x)+ (-8)\\y-5= -4x -8

5 is being subtracted from y. The inverse operation of subtraction is addition, so we will add 5 to both sides of the equation.

y-5 =-4x -8 + 5

y= -4x -3

The equation of the line is y= -4x -3. The slope of the line is -4 and the y-intercept is -3.

6 0
3 years ago
Expand the expression 4(y+z)
Ilia_Sergeevich [38]

Answer: 4y+4z

Step-by-step explanation:

5 0
3 years ago
11x+4y=-46<br> 7x-4y=10 <br> Find x and y
UNO [17]

Answer:x=-2 y=-6

Step-by-step explanation:

11x+4y=-46..........(1)

7x-4y=10..............(11)

Add (1) and (11)

11x+7x+4y-4y=-46+10

18x=-36

Divide both sides by 18

18x/18=-36/18

x=-2

substitute x=-2 in (11)

7x-4y=10

7(-2)-4y=10

-14-4y=10

Collect like terms

4y=-14-10

4y=-24

Divide both sides by 4

4y/4=-24/4

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D. Is the correct answer
4 0
3 years ago
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