100 POINTS WILL MARK BRAINLIEST x^2 − 8x + 13 = 0 Which of the following is the first correct step to write the above equation in the form (x − p)^2 = q, where p and q are integers? Subtract 5 from both sides of the equation Add 3 to both sides of the equation Add 5 to both sides of the equation Subtract 3 from both sides of the equation

Answer:

Okkk I will answer

Answer:

what question do you have?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Before we begin this, there are a few things that need to be said and a few formulas you need to know. First is that we need to use the work form of a parabola, which is

[tex]y=a(x-h)^2+k[/tex]

All of the parabolas listed in blue highlight open either up or down, and this work form represents those 2 options. The only thing we need to know is that if there is a negative sign in front of the a, the parabola opens upside down like a mountain instead of up like a cup.

Another thing we need to know is how to find the focus of the parabola. The formula to find the focus for an "up" parabola is (h, k + p) and the formula to find the focus for an upside down parabola is (h, k - p). Then of course is the issue on how to find the p. p is found from the a in the above work form parabola, where

[tex]p=\frac{1}{4|a|}[/tex] .

In order to accomplish what we need to accomplish, we need to put each of those parabolas into work form (as previously stated) by completing the square. I'm hoping that since you are in pre-calculus you have already learned how to complete the square on a polynomial in order to factor it.  Starting with the first one, we will complete the square. I'll go through each step one at a time, but will provide no explanation as to how I got there (again, assuming you know how to complete the square).

[tex]y=-x^2+4x+8[/tex] and, completing the square one step at a time:

[tex]-x^2+4x=-8[/tex] and

[tex]-(x^2-4x+4)=-8-4[/tex] and

[tex]-(x-2)^2=-12[/tex] and

[tex]-(x-2)^2+12=y[/tex]

From this we can see that the h and k values for the vertex are h = 2 and k = 12. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct focus formula (h, k - p), we get that the focus is

[tex](2, 12-\frac{1}{4})[/tex] which simplifies to (2, 11.75) which is choice 2 in your options.

Now for the second one (yes, this takes forever...)

[tex]y=2x^2+16x+18[/tex] and completing the square one step at a time:

[tex]2x^2+16x=-18[/tex] and

[tex]2(x^2+8x+16)=-18+32[/tex] and

[tex]2(x+4)^2=14[/tex] and

[tex]2(x+4)^2-14=y[/tex]

From this we can see that the vertex is h = -4 and k = -14. Now to find p from a.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex] .

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-4, -14+\frac{1}{8})[/tex] which simplifies down to (-4, -13.875) which is choice 3 in your options.

Now for the third one...

[tex]y=-2x^2+5x+14[/tex] and completing the square step by step:

[tex]-2x^2+5x=-14[/tex] and

[tex]-2(x^2-\frac{5}{2}x+\frac{25}{16})=-14-\frac{50}{16}[/tex] and

[tex]-2(x-\frac{5}{4})^2=-\frac{137}{8}[/tex] and

[tex]-2(x-\frac{5}{4})^2+\frac{137}{8}=y[/tex]

From that we can see the vertex values h and k. h = 1.25 and k = 17.125. Now to find p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upside down parabola (h, k - p),

[tex](1.25, 17.125-\frac{1}{8})[/tex] which simplifies down to (1.25, 17) which is choice 4 in your options.

Now for the fourth one...

[tex]y=-x^2+17x+7[/tex] and completing the square step by step:

[tex]-x^2+17x=-7[/tex] and

[tex]-(x^2-17x)=-7[/tex] and

[tex]-(x^2-17x+72.25)=-7-72.25[/tex] and

[tex]-(x-8.5)^2=-79.25[/tex] and

[tex]-(x-8.5)^2+79.25=y[/tex]

From that we see that the vertex is h = 8.5 and k = 79.25. Now to find p.

[tex]|a|=1[/tex], ∴

[tex]p=\frac{1}{4(1)}=\frac{1}{4}[/tex]

Using the correct formula for an upside down parabola (h, k - p),

[tex](8.5, 79.25-\frac{1}{4})[/tex] which simplifies down to (8.5, 79) and I don't see a choice from your available options there.

On to the fifth one...

[tex]y=2x^2+11x+5[/tex] and again step by step:

[tex]2x^2+11x=-5[/tex] and

[tex]2(x^2+\frac{11}{2}x+\frac{121}{16})=-5+\frac{242}{16}[/tex] and

[tex]2(x+\frac{11}{4})^2=\frac{81}{8}[/tex] and

[tex]2(x+\frac{11}{4})^2-\frac{81}{8}=y[/tex]

from which we see that h = -2.75 and k = -10.125. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the correct focus formula for an upwards opening parabola (h, k + p),

[tex](-2.75, -10.125+\frac{1}{8})[/tex] which simplifies down to (-2.75, -10) which is choice 1 from your options.

Now for the last one (almost there!):

[tex]y=-2x^2+6x+5[/tex] and

[tex]-2x^2+6x=-5[/tex] and

[tex]-2(x^2-3x+2.25)=-5-4.5[/tex] and

[tex]-2(x-1.5)^2=-9.5[/tex] and

[tex]-2(x-1.5)^2+9.5=y[/tex]

from which we see that h = 1.5 and k = 9.5. Now for p.

[tex]|a|=2[/tex], ∴

[tex]p=\frac{1}{4(2)}=\frac{1}{8}[/tex]

Using the formula for the focus of an upside down parabola (h, k - p),

[tex](1.5, 9.5-\frac{1}{8})[/tex] which simplifies down to (1.5, 9.375) which is another one I do not see in your choices.

Good luck with your conic sections!!!

Answer:

[tex]131.95[/tex] [tex]cm[/tex]

Step-by-step explanation:

[tex]C=2 \pi r[/tex]

[tex]C=2 \pi \times 21[/tex]

[tex]C=42\pi[/tex]

[tex]C \approx 131.946891451[/tex]

Answer: (15th street, 14th Avenue)

Step-by-step explanation:

Given the following :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location = 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari = (18th , 12th )

Gym distance = 2/3 of distance between ping and Ari

Gym distance = 2/3 × (18), 2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

Answer:

d) 15th Street and 14th Avenue

Answer:

The sum of all of the terms would be 255

Step-by-step explanation:You would continue to multiply all of the answers by 2 until you hit 128. Then you would add all of them together 128+64+32+16+8+4+2+1=255

Answer:

Step-by-step explanation:

Both B and C would be using e

Option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations or systems of equations:

3x-2y = 7 Equation 1

3x+4y= 17 Equation 2

As we know, in the elimination method:

We try to eliminate the variables at a time by making a similar coefficient of the x or y.

In option (B) Subtract the left side of equation 2 from the left side of equation 1.

It is not allowed to perform because first, we have to make the coefficient of y similar.

Thus, option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ5

Answer:

See explaination:

Graphs are on the right, equations are on the left, and they are color coded.

Step-by-step explanation:

Answer:

V =13/150 yd^3

Step-by-step explanation:

The volume of a rectangular prism is given by

V = l*w*h

V = 1/2*( 13/15)* 1/5

V =13/150 yd^3

Answer:

13\150 yd³

Step-by-step explanation:

V=height×weight×legth

1\2×13\15×1\5=13\150 yd³

Answer: there would be 106,am not sure

Step-by-step explanation:

Answer:

(x + 2) (3x + 1)

Step-by-step explanation:

3x² + 7x + 2

3x² + 6x + x + 2

3x(x + 2) + 1(x + 2)

(x + 2) (3x + 1)

Answer:

x= -7/5 y=8/5

Step-by-step explanation:

1. choose a variable to eliminate (i chose 6)

2. multiply the first equation by 2 and the second equation by 3

3. now you have

-6x+6y=18

6x-21y=-42

and the x's can now cancel out when you add the equations together

4. after adding the equations, you get

-15y=-24

5. solve for y (y= 8/5)

6. now plug in 8/5 for the y in one of the original equations to solve for x. (i chose the first one)

7. -3x+3(8/5)=9

-3x+24/5=9

-3x=21/5

x= -7/5

Answer: 2908.92435 inches.

Step-by-step explanation for shape 1: A = 2(wl + hl + hw) = 2 · (30 · 13 + 13 · 13 + 13 · 30) = 1,898 inches.

Step-by-step explanation for shape 2:

Using the formulas:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving for A:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·30+13·30+9·30+1

2·﹣94+2·(9·13)2+2·(9·9)2﹣134+2·(13·9)2﹣94≈1010.92435

Step-by-step explanation for total volume: 2908.92435 inches.

Answer: 6825 in^3

Step-by-step explanation:

First divided the whole shape into two shapes.

The first shape will be a rectangular prism and the second shape will be a triangular prism.

The rectangular prism will have a length of 13, a width of 30 and the height of 13.

Now find the volume of the rectangular prism by multiplying the length by the width then by the height.

V= 13 * 30 * 13

V = 5070

This means the volume of the rectangular prism is 5070 cubic inches.

Now will will need to find the volume of the triangular prism.

The triangular prism has a triangle at the base, with a base of 9 and a height of 13. If you multiply the the area of the base by the whole height of the triangular prism which is 30 then you will get the volume.

Find the area of the base.

The area  is base time height times 1/2.

A = 9 * 13 * 1/2

A =  58.5  

Now multiply the area by 30.

58.5 * 30 = 1775

Finally, add both volumes to find the full volume of the figure.

5070 + 1775 = 6825

Answer:

D' = (-2, 1)

Step-by-step explanation:

Translating the point D one unit up and five units left moves it to (-2, 5)

Reflecting it across y=3 moves it from (-2, 5), to (-2, 1)

Answer:

D = (-2, 1)

This answer is 100% right hope it helps

Answer:

k(-7) = = -89

Step-by-step explanation:

k(t) = 10t -19

Let t = -7

k(-7) = 10*-7 -19

      = -70-19

      = -89

Answer:

-89

Step-by-step explanation:

K(t) = K(-7)

10 is being multiplied by t. t = -7

so:

10(-7) = -70

-70 - 19 = -89

Hope this helps!

Answer:

[tex]2a^2 + 3x - 2a[/tex]

Step-by-step explanation:

[tex] (6a^2 + 3x) - (4a^2 + 2a) = [/tex]

The first set of parentheses is unnecessary and can be removed.

[tex] = 6a^2 + 3x - (4a^2 + 2a) [/tex]

To remove the second set of parentheses, you must distribute the negative sign to its left as if it were a -1 multiplying the quantity inside the parentheses.

[tex] = 6a^2 + 3x - 1(4a^2 + 2a) [/tex]

[tex] = 6a^2 + 3x - 4a^2 - 2a [/tex]

Now combine like terms. Like terms are terms with the same variable part.

[tex] = 2a^2 + 3x - 2a [/tex]

Answer:

1) 4

2) 1

3) -7

4) 13

Step-by-step explanation:

Instructions:

a) Subtract or add the slope from each side

( it doesn't matter which one you pick )

b) Subtract or add the # next to the slope from each side

( it doesn't matter which one you pick )

c) Divide Each number by the slope

d You have you answer

____________________________________________

1) 9x - 35 = - 7x + 29

+7x + 7x

_____________________

16x - 35 = 29

+ 35 +35

_____________________

16x = 64

_____________________

16 16

x = 4

2). - 2x - 2 = 9x - 13

+2x +2x

_____________________

- 2 = 11x - 13

+ 13 + 13

_____________________

11 = 11x

_____________________

11 11

1 = x

3). 3x + 29 = - 5x - 27

+5x + 5x

_____________________

8x + 29 = - 27

-29 -29

_____________________

8x = -56

_____________________

8 8

x = -7

4). x - 11 = 3x - 37

- x - x

______________________

-11 = 2x - 37

+37 +37

______________________

26 = 2x

_______________________

2 2

13 = x

Hope this helps! (:

Answer:

570 miles

Step-by-step explanation:

If Damian rides 38 each week and we want to know how much it was for 15 weeks, then we just multiply the two to get 570 miles in a 15 week period.

Answer:570

Step-by-step explanation:

38 times 15= 570

Answer:

y= 1/3x

Step-by-step explanation:

points on the graph

(0,0), (3,1)

function as per above two points:

y= 1/3x

Answer:

Reflection about y=2

Step-by-step explanation:

Triangle A should be reflected about y=2 to map it onto Triangle B.

Answer:

reflection across y=2

Step-by-step explanation:

Answer:

    The correct answer is: (Line segment E F)

Answer:

x = 1/2

Step-by-step explanation:

9x=4.5

Divide each side by 9

9x/9 = 4.5/9

x = 45/90

x = 1/2

Answer:

x = 1/2 or x = 0.5

Step-by-step explanation:

9x = 4.5/9

= 45/90

= 1/2 or 0.5

Hope this helps, and please mark me brainliest if it does!

Answer:

The answer is 7.

Step-by-step explanation:

If you want to find what FE is, you have subtract GF from GE (GE - GF = FE).

Since GE = 13 and GF = 6, you have to subtract 6 from 13 which equals 7.

(13 - 6 = 7)

Answer:

[tex]=\left(x-4\right)^2[/tex]

Step-by-step explanation:

[tex]x^2-8x+16\\\mathrm{Rewrite\:}x^2-8x+16\mathrm{\:as\:}x^2-2x\cdot \:4+4^2\\x^2-8x+16\\\mathrm{Rewrite\:}16\mathrm{\:as\:}4^2\\=x^2-8x+4^2\\\mathrm{Rewrite\:}8x\mathrm{\:as\:}2x\cdot \:4\\=x^2-2x\cdot \:4+4^2\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\a=x,\:b=4\\=\left(x-4\right)^2[/tex]

Answer:

0

Step-by-step explanation:

Since it is asking you to factor out the quadratic, you need to make it equal zero first. -4 times -4 is both 16 and -8. So that means (x-4)^2

Answer:

D

Step-by-step explanation:

a = 2 ;  b = -6 ;  c = 5

[-b±√b²-4ac]/2a=[-(-6)±√6²-4*2*5]/2*2

=[6±√√36-40]/4

=[6±√-4]/4

=[6±√i²*2²]/4

=[6±2i]/4

=2[3±i]/4

=3±i/2

= 3+i/2  or 3-i/2

Answer:

Step-by-step explanation:

The area for a trapezoid is

[tex]A=\frac{1}{2}h(b_{1}+b_{2})[/tex]

h is the length of ST, one of the bases is the length of MK, and the other base is the length of AS.  First we'll find h:

The coordinates for S are (0, -2) and T are (1, 2). Using the distance formula:

[tex]d=\sqrt{(1-0)^2+(2-(-2))^2[/tex] and

[tex]d=\sqrt{17}[/tex].  So h = √17

Now for the length of MK. The coordinates for M are (-7, 4) and for K (5, 1). Using the distance formula again:

[tex]d=\sqrt{(-7-5)^2+(4-1)^2}[/tex] and

[tex]d=\sqrt{(-12)^2+(3)^2}[/tex] so

[tex]d=\sqrt{153}[/tex] which simplifies to

[tex]d=3\sqrt{17}[/tex]. So MK = 3√17.

Now for the length of AS. The coordinates for A: (-4, -1) and for S: (0, -2). Using the distance formula one more time:

[tex]d=\sqrt{(-4-0)^2+(-1-(-2))^2}[/tex] and

[tex]d=\sqrt{(-4)^2+(1)^2}[/tex] and

[tex]d=\sqrt{17}[/tex]. So AS = √17.

Now we can fill in our area formula:

[tex]A=\frac{1}{2}(\sqrt{17})(3\sqrt{17}+\sqrt{17})[/tex]

Simplifying a bit:

[tex]A=\frac{1}{2}(\sqrt{17})(4\sqrt{17})[/tex] and simplifying a bit more:

[tex]A=\frac{4*17}{2}[/tex] and

A = 34

Answer:

The total number of students in the college is 3,000.

Step-by-step explanation:

[tex]\frac{48}{100}=\frac{1,440}{x}[/tex]               Set up a proportion.

[tex]48x=144,000[/tex]         Cross-multiply.

[tex]x=3,000[/tex]                 Divide both sides by 48.

Answer:

The height of the ladder is 15 meters.

Step-by-step explanation:

To find the height of the ladder, we just need to use the cosine relation of the 60 degrees angle.

The adjacent side to the angle is the height of the ladder, and the hypotenuse of the triangle created is the length of the ladder. So, we have that:

cos(60) = height / length

0.5 = height / 30

height = 30 * 0.5 = 15 meters

The height of the ladder is 15 meters.

Answer:

-x - 12y

Step-by-step explanation:

(x-8y)-(2x-4y)=

x-8y-2x-4y=

x-2x-8y-4y=

-x - 12y

Answer: -x - 4y

Step-by-step explanation:

(x-8y)-(2x-4y)

x-8y-2x+4y

-x-4y