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Natali5045456 [20]
3 years ago
15

Solve x^2-8x-9=0 algebrically

Mathematics
1 answer:
Svetach [21]3 years ago
3 0

Answer:

x=9   x=-1

Step-by-step explanation:

x^2-8x-9=0

Factor

What 2 numbers multiply to -9 and add to -8

(x-9) (x+1) =0

Using the zero product property

x-9 =0   x+1 =0

x=9   x=-1

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Find the distance from point A(−9,−3) to the line y = x−6. Round your answer to the nearest tenth.
Vladimir79 [104]

The distance from point A(−9,−3) to the line y = x−6 is 8.5 units

<u>What is slope ?</u>

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

step 1

Find the slope of the perpendicular line to the given line

y=x-6 ---> given line

The slope is m=1

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

m1*m2 = -1

we have

m1=1

substitute

(1)*m2 = -1

so

m2 = -1

step 2

Find the equation of the perpendicular line to the given line

The equation in point slope form is

y-y1=m(x-x1)

we have

m=-1

(x1,y1)=(−9,−3)

substitute

y+3=-1(x+9)--> equation in point slope form

y+3= -x-9

y= -x-12---> equation in slope intercept form

step 3

Find the intersection point between the given line and the perpendicular line to the given line

we have the system of equations

y = x−6.

y= -x-12

Solve the system by graphing

The intersection point is (-3,-9)

see the attached figure

step 4

we know that

The distance between the point A and the point (-3,-9) is the same that the distance between point A and the line y=x-6

the formula to calculate the distance between two points is equal to

d=√[(y2-y1)² + (x2-x1)²]

substitute the values

d=√[(-9+3)² + (-3+9)²]

d= √72 units

simplify

d= 6√2 = 8.5 units

To learn more about the slope from the given link

brainly.com/question/16949303

#SPJ1

8 0
9 months ago
Does anyone know the answer to this?
Alex

Answer:

10.5.

Step-by-step explanation:

By similar  triangles:

IJ / 21 = 8 /(8+8) = 1/2

IJ / 21 = 1/2

IJ = 1/2 * 21

= 10.5.

6 0
2 years ago
What is the area of a rectangular holding pond with length 8/15 mile and width 1/6 mile?
SSSSS [86.1K]

as you already know, the area of a rectangle is just length*width, so is just the product of those two.


\bf \cfrac{8}{15}\times \cfrac{1}{6}\implies \cfrac{8}{6}\times \cfrac{1}{15}\implies \cfrac{4}{3}\times \cfrac{1}{15}\implies \cfrac{4}{45}

4 0
2 years ago
Read 2 more answers
Could -2 be used to rewrite 32
Ostrovityanka [42]

Answer:Look at this list of whole number powers of -2:

(-2)0 = 1

(-2)1 = -2

(-2)2 = 4

(-2)3 = -8

(-2)4 = 16

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find 3 different ratios that are equivalent 7:3 explain why these ratios are equivalent
kkurt [141]

Answer:

7:3, 14:6, 28:12

multiples.. hope that helps.

6 0
3 years ago
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