A line passes through the point (8,-8) and has a slope of 3/4. Write an equation in slope-intercept form for this line.

The vertex is located at (h,k)

The two roots p and q can be defined as such

where r is the horizontal distance between the vertex and either root. We use the same r value for each equation because of symmetry. The diagram below shows what I mean.

Let's add up those two equations to get

p+q = 2h

The left hand sides p and q add to p+q. The right hand sides add to (h-r)+(h+r) = 2h. Note the r's cancel.

From here, we divide both sides by 2 and we end up with

h = (p+q)/2

In short, if we know the roots p and q, then we find the x coordinate of the vertex (h) to be the average of those roots. You add up the roots and then divide by 2.

After you figure out the value of h, finding the value of k will have us plug in this h value into the quadratic equation and simplifying.

------------------------

Example:

Let's say we have the quadratic y = x^2 - 8x + 12. This factors to (x-2)(x-6)

Solving (x-2)(x-6) = 0 shows that x-2 = 0 becomes x = 2 and x-6=0 becomes x = 6.

So the roots here are p = 2 and q = 6. The order of the roots doesn't matter.

Averaging these roots gives us

h = (p+q)/2

h = (2+6)/2

h = 8/2

h = 4

The x coordinate of the vertex is x = 4.

Plug this back into the original equation to find...

y = x^2 - 8x + 12

y = (4)^2 - 8(4) + 12

y = 16 - 32 + 12

y = -16 + 12

y = -4

Or you could say

y = x^2 - 8x + 12

y = (x-2)(x-6)

y = (4-2)*(4-6)

y = (2)*(-2)

y = -4

Either way, we find that k = -4 is the y coordinate of the vertex

The vertex for this example is located at (h,k) = (4, -4)

Refer to the diagram below.

Answer:

50$

Step-by-step explanation:

Answer:

Step-by-step explanation:

-8x - 8y = -20

8x + 8y = 24

0 ≠ 4

2y = -2x + 10

y = -x + 5

8y = -8x + 24

y = -x + 3

inconsistent

Answer:

x=52

Step-by-step explanation:

A triangle 3 interior angles add up to 180 so the third angle is 52. Since the two lines are parallel and have a transversal angle x and 52 are alternate interior angles so x=52

Answer:

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Step-by-step explanation:

They would both have to sell 14 candies.

Step-by-step explanation:

They both sell 14 candies

Answer:

= 4(1+sin2theta)²

Step-by-step explanation:

Given the equations

tantheta -cottheta =a... 1

costheta +sintheta =b .... 2

We are to find 4b^2(2-b^2)​

Squaring both sides of equation 2

(costheta +sintheta)^2 = b^2

cos^2theta + 2costheta sintheta + sin^2 theta = b^2

(cos^2theta+ sin^2 theta) + 2costheta sintheta = b^2

1 + 2costheta sintheta = b^2

1 + sin2theta = b^2

substitute

4b^2(2-b^2)​

= 4(1+sin2theta)(2-1+sin2theta)

4(1+sin2theta)(1+sin2theta)

= 4(1+sin2theta)²

Answer:

72.32

Step-by-step explanation:

i have spoken

Answer:

72.32 degrees

Step-by-step explanation:

the picture shows a supplementary angle, which equals 180 degrees.

first, solve for x.

since the entire figure equals 180 degrees, set the equation equal to 180. then add in the measurements, which are 7x, 8x, and 44.4.

180 = 7x + 8x + 44.4

combine like terms (7x and 8x).

180 = 7x + 8x + 44.4 ⇒ 180 = 15x + 44.4

subtract 44.4 from both sides. the positive 44.4 will cancel out, so all you have to do is subtract 44.4 from 180.

180 - 44.4 = 135.6

now, your equation is...

135.6 = 15x

divide both sides by 15.

(135.6)/15 = (15x)/15 ⇒ 9.04 = x, or x = 9.04

now plug 9.04 in for x in both 7x and 8x.

7x ⇒ 7(9.04) ⇒ 63.28

8x ⇒ 8(9.04) ⇒ 72.32

*the highlighted angle, 8x, is 72.32 degrees.

checking your work:

now, all your measurements are 63.28, 72.32, and 44.4

check your work by adding all the measurements together and setting that equal to 180.

63.28 + 72.32 + 44.4 = 180

180 = 180

since both sides are equal, all of the values are correct!

now that you know your work is correct, it is fully safe to say that the highlighted angle is 72.32 degrees.

Answer:

I believe the answer would be [tex]\sqrt{6}+\sqrt{2}[/tex] or 3.8637

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Omar could invite 19 friends.

Step-by-step explanation:

the equation for this word problem would be

5x+30=125

subract 30 from both sides

5x=95

divide both sides by 5

x=19

Answer:

(125-30) divided by 5. Your answer is 19.

Step-by-step explanation:

subtract 30 from 125 and your left with 95. Divide 95 by 5 and you get 19.

9514 1404 393

Answer:

  75

Step-by-step explanation:

Since there are twice as many chachalacas as flamingos, the ratio of flamingos to parrots to herons to chachalacas is 10:7:3:5. This is a total of 25 ratio units. Each ratio unit stands for 375/25 = 15 birds, so the number of chachalacas is 5·15 = 75.

There are 75 chachalacas at the sanctuary.

Answer:

x = 11

Step-by-step explanation:

sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal

perimeter is the sum of all sides, so set up equation:

95 = 4x - 2 + 4x - 2 + x

95 = 8x - 4 + x

95 = 9x - 4

99 = 9x

x = 11

Answer:

I dont know if you still need it but the area of the figure is 51.5 ft2.

The area of the given figure is equivalent to 39.5 square feet.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is to find the area of the given figure as shown in the image.

We can write the area of the given figure as -

A{total} = A{Rectangle} + A{Δ1} + A{Δ2}

A{total} = (8 x 4) + (1/2 x 3 x 3) + (1/2 x 3 x 2)

A{total} = 32 + 4.5 + 3

A{total} = 39.5 square feet

Therefore, the area of the given figure is equivalent to 39.5 square feet.

To solve more questions on areas, visit the link-

https://brainly.com/question/29213222

#SPJ2

Answer: (4,-2)

Step-by-step explanation: step1.- -1/2x=-x+2 (solving for x) x=4

Step 2- y=-1/2x4(substitute the value of X)

Step 3- y=-1/2x4 (solve the equation for y) =2

Step 4- (x,y)=(4,-2) simplify —>(x,y)=(4,-2)

Answer:

3x = 18

x=6

check: 3(6)=18. 18=18

x/3 = -4

X=-12

Check: 12/3=4. 4=4

11x=121

x=11

Check: 11(11)=121. 121=121

-8y=32

x=-4

Check: -8(-4)=32. 32=32

y/4=12

y=48

Check: 48/4=12. 12=12

6y=-48

y=-8

Check: 6(-8)=-48. -48=-48

y/7=-7

y=-1

Check: (-1)/7=-7. -7=-7

x/5=5

x=1

Check: (1)/5=5. 5=5

1) solve

3x=18

x=6

check

3(6)=18

2) solve

x/3=-4

x=-12

check

-12/3=-4

3) solve

11x=121

x=11

check

11(11)=121

4) solve

-8y=32

y=-4

check

-8(-4)=32

5) solve

y/4=12

y=48

check

48/4=12

6) solve

6y=-48

y=-8

check

6(-8)=-48

7) solve

y/7=-7

y=-49

check

-49/7=-7

8) solve

x/5=5

x=25

check

25/5=5

Answer:

[tex]t = \frac{1}{4}\sqrt d[/tex]

Time to reach 100ft is 2.5 seconds

Step-by-step explanation:

Given

[tex]d = 16t^2[/tex]

Solving (a): Determine the inverse function

[tex]d = 16t^2[/tex]

Swap the positions of d and t

[tex]t = 16d^2[/tex]

Make d the subject

[tex]\frac{t}{16} = d^2[/tex]

Take positive square root of both sides

[tex]\sqrt{\frac{t}{16}} = d[/tex]

[tex]d = \sqrt{\frac{t}{16}}[/tex]

[tex]d = \frac{1}{4}\sqrt t[/tex]

Swap the positions of d and t

[tex]t = \frac{1}{4}\sqrt d[/tex] --- The inverse function

Solving (b): Find t when d =100

Substitute 100 for d in [tex]t = \frac{1}{4}\sqrt d[/tex]

[tex]t = \frac{1}{4}\sqrt {100[/tex]

[tex]t = \frac{1}{4}* 10[/tex]

[tex]t = \frac{1* 10}{4}[/tex]

[tex]t = \frac{10}{4}[/tex]

[tex]t = 2.5[/tex]

Answer:

d i think can u give me a bainliest

Step-by-step explanation:

Answer: 0/12 would be 0; 12/0 would be undefined

Step-by-step explanation: 0/12 is 0 because properties of zero; 12/0 is undefined because of properties of zero.

Answer:

2/3*3/4 = 1/2

Step-by-step explanation:

9514 1404 393

Answer:

  120°

Step-by-step explanation:

There are several ways you can redraw this figure to help you find the value of x. One of them is to draw a line perpendicular to the parallel lines, intersecting the vertices of the given angles*. Then the interior angles of the triangle formed will be ...

  125° -90° = 35°

  115° -90° = 25°

The angle that is a vertical angle with x is the third angle of the triangle, so its measure is ...

  x = 180° -35° -25° = 120°

The value of x is 120°.

Answer:

not sure

Step-by-step explanation:

Answer:

Step-by-step explanation: o847434y3u3u44y4u5u5u5uu6

Answer:

18x - 9

Step-by-step explanation:

[tex](7x - 12) + (11x + 3)\\7x - 12 + 11x + 3\\18x - 9[/tex]

Hi there! Your answer to this question would be 90%..

Step By Step Explanation:

So we know that 100% is the average grade for an correct for an entire test.

But how can we find 90%?

Let think like this. 10=100%.

Well if 10 is 100% then 9 would be 90% since every 1 of 10 is 10%.

Final Result: 90%

Answer:

loss, 144 yds loss

Step-by-step explanation:

Answer:

g(-4) = 1

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

What g(-4) is saying is what the output of the function g(x) when x= -4. According to the graph, when x = -4, y = 1.

∴ g(-4) = 1

Answer:

Step-by-step explanation:

(2x + 7)(x + 1)

answer is A

Answer:

a. (5,5)

b. (-5,-5)

Step-by-step explanation:

reflection over x-axis flips the sign of y-coordinate

reflection over y-axis flips the sign of x-coordinate

Answer:

Decay, 60%

Step-by-step explanation:

Remember that the exponential function is written in the form [tex]y=ab^x[/tex]. In this problem, a=57 and b=0.4. A function is considered a growth function when [tex]b>1[/tex]. Since 0.4 not greater than 1, this is an exponential decay function.

Now, to find the rate of decrease we can use part of the form [tex]y=a(1-r)^x[/tex].

[tex]1-r[/tex] represents the percentage decrease, in this case, 0.4. If that entire term is 0.4, we need to solve for [tex]r[/tex].

[tex]1-r=0.4\\r=0.6[/tex]

So, the rate of percentage decrease is 60%.

I hope this helps!

Answer:

20

Step-by-step explanation:

you just divid the number of points earned (14), by the percent earned (70). This gives you the total becuase you would divid 14 by the total to get 70.