What is the slope of the line containing (–1, 8) and (3, –12)? A. 5 B. – C. –5 D.

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  [tex]x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}[/tex]

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

Answer: 0.5(43,560)/ 40(128)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Subtracting a negative is like adding

3 +7

10

Step-by-step explanation:

ANGLE ,x=60

B=C(isoscles)

A=B.As sides are equal.

Answer:

Solution given

-2u+(-1)=-13

open bracket

-2u-1=-13

add 1 on both side

-2u-1+1=-13+1

-2u=-12

divide both side by -2

-2u/-2=-12/-2

u=6

[tex]\huge\text{Hey there!}[/tex]

[tex]\textsf{-2u + (-1) = -13}\\\textsf{-2u - 1 = -13}\\\large\text{ADD 1 to BOTH SIDES}\\\textsf{-2u - 1 + 1 = -13 + 1}\\\large\text{CANCEL out: -1 + 1}\\\large\text{KEEP: -13 + 1}\\\rightarrow\textsf{-2u = -12}\\\large\text{DIVIDE -2 to BOTH SIDES}\\\mathsf{\dfrac{-2u}{-2}= \dfrac{-12}{-2}}\\\textsf{CANCEL out: }\mathsf{\dfrac{-2}{-2}}\\\textsf{KEEP: }\mathsf{\dfrac{-12}{-2}}\\\mathsf{u = \dfrac{-12}{-2}}\\\mathsf{u = \bf 6}\\\huge\boxed{\mathsf{Answer: u = 6}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

It doesn't say what to do with that 0.1 of a gallon. I would buy another gallon or dilute what I had so it came to exactly 9.1 gallons. In math, I suppose the answer is 9.

In reality it would be 10.

You have to choose.  What has been done with other questions like this.

Step-by-step explanation:

1 can covers 55 square feet.

h = 10

w1 = 10 feet

w2 = 10 feet

w3 = 15 feet

w4 = 15 feet

Total area = Area of wall 1 + wall 2 + wall 3 + wall 4

Total area = 10*10 + 10*10 + 10*15 + 10* 15

Total area = 100  + 100 + 150 + 150

Total area = 500  feet^2

1 gallon / 55 ft^2 = x / 500 ft^2          Cross multiply

55 * x = 500                                       Divide by 55

x = 500/55

x = 9.1 gallons.

In real life you would buy another gallon.

Answer:

21

Step-by-step explanation:

1.365÷65=21 dollars

Answers:

Length = 270 feet

Width = 45 feet

========================================================

Work Shown:

x = width

6x = length, since it is 6 times the width

P = perimeter of rectangle

P = 2*(Length + Width)

P = 2*(6x + x)

P = 2*(7x)

P = 14x

Plug in the given perimeter P = 630 and solve for x.

P = 14x

14x = P

14x = 630

x = 630/14

x = 45

The width is 45 feet.

The length must be 6x = 6*45 = 270 feet.

The required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

Given that,
A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 6 times its width. If 630 feet of pipe was used to do the job, what is the length and the width of the lawn is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
let the length be l and the width be w,
According to the question,
l = 6w
and
Perimeter of the lawn = 630
2 [l + w] = 630
2 [6w + w] = 630
14w = 630
w = 45
Now,
l = 45[6] = 270

Thus, the required length and width of the lawn is given as Length = 270 feet and Width = 45 feet.

learn more about perimeter here:

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Answer:

Cheena has 6 pieces of fabric.

Step-by-step explanation:

3/4 yard of fabric also means 6/8 yard of fabric.

(6/8) / (1/8) = 6

Or

6/8 yard = 6  1/8 yard pieces

Answer:

i hope it helped U

stay safe stay happy

Answer:

(-9,-6)

Explanation

Answer:

(9,-6)

Step-by-step explanation:

(x,y)→(y,-x)

Negate the x then switch

(x,y)→(y,−x)

(6,9)→(9,−(6))=(9,−6)

Answer:

0.4141 rounded to the nearest thousandth is 0.414.

Step-by-step explanation:

Since the number is 0.4141, and the number following the thousandths place is under 5, the thousandth place stays the same. If it were 5 or over, it would round up making it 0.415, but it's not so it is 0.414.

Explanation:

The like terms k and -5k combine to -4k

The like terms -5 and 1 combine to -4

So overall, that's how we end up with -4k-4

Answer:

Step-by-step explanation:

1). (k - 5k) + (-5 + 1) {Collect like terms}

2). -4k - 4 {Simplify}

Hi

Answer:

3bc

Step-by-step explanation:

3×b=3b

3b×c=3bc

Taking into account the original image that appears in the attached document and verifying the correct solution in each case:

1. The figures that are scaled copies of the original are:

2. I'm not agree with Tyler's affirmation.

SCALING FIGURES.

When you must scale figures, you must remind the scale must be applied in all dimensions of the figure, when a figure is in two dimensions, I mean, the figure has height and length, the scale must be applied to this two dimensions, and the figure must the same form of the original to be a scaled copy.

In the first exercise, the original A is a figure with two squares of height and two squares of length 2x2, by this reason, each scaled copy must be the same height as length (1x1, 3x3, 4x4, 5x5, 6x6 and others).

As you can see, the figure 2 has 4 units of height and 4 units of length 4x4, it's a scaled copy, the figure 4 has 1 unit of height and 1 units of length 1x1, it's a scaled copy, but the figure 1 has 3 units of height and 2 units of length 3x2, it's not a scaled copy, and the figure 3 hasn't the same form of the original A, by this, it's not a scaled copy.

In the second exercise, you can´t agree with Tyler because the figure B is the half of the figure A, but just in the height, remember this must be the same in the length to obtain a correct scaled copy, you can see in the exercise, the figure B has the same length as the figure A, by this reason, the affirmation of Tyler is wrong, for that to be true, the height and the length should be half in the figure B.

You can see other exercises with scales in the next links:

https://brainly.com/question/22384038?referrer=searchResults

https://brainly.com/question/21605248?referrer=searchResults

Answer:

288m^3

Step-by-step explanation:

the volume is base* height

to find the second side, use the Pythagorean theorem : [tex]\sqrt{10^2-8^2} = \sqrt{100-64}= \sqrt{36} = 6[/tex],

now find the area of the triangle: 6*8/2=24

now multiply it by the height and you get the volume: 24*12=288

Answer:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = 2x^2 + 3x - 8[/tex]

And we want to find:

[tex]\displaystyle f(b + 2)[/tex]

Substitute:

[tex]\displaystyle f(b+2) = 2(b+2)^2 + 3(b+2) - 8[/tex]

Expand and simplify:

[tex]\displaystyle \begin{aligned}f(b+2)&= 2(b^2+4b+4)+(3b+6)-8 \\ &= (2b^2+8b+8)+(3b+6)-8 \\ &= (2b^2) + (8b+3b)+ (8+6-8) \\ &= 2b^2 + 11b + 6 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle f(b+2) = 2b^2 + 11b +6[/tex]

Answer:

[tex] \frac{3(x + 4)(x + 1)}{(x + 2)(x - 2)} \\ x = 4 \\ then \frac{3(4 + 4)(4 + 1)}{(4 + 2)(4 - 2)} \\ = \frac{3 \times 8 \times 5}{6 \times 2} \\ = \frac{120}{12} = 10 \\ thank \: you[/tex]

Step-by-step explanation:

Hey there!

The given points are: (-3,-6) and (3,-6).

x 1 = -3 y1 = -6

x 2 = 3 y2 = -6

Use distance formula;

[tex]d = \sqrt{( {x2 - x1)}^{2} + ( {y2 - y1)}^{2} } [/tex]

Keep all the values;

[tex]d = \sqrt{( {3 - ( - 3))}^{2} + ( { - 6 - ( - 6))}^{2} } [/tex]

Simplify:

[tex]d = \sqrt{ {(6)}^{2} + {( - 6 + 6)}^{2} } [/tex]

[tex]d = \sqrt{ {(6)}^{2} } [/tex]

Therefore, the distance is 6 units.

Hope it helps!

Answer:

12

Step-by-step explanation:

To find the greatest common factor if 72 and 84 first we need to find factors of them separately

72 :  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

84 :  1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

there are 6 common factors that are 1, 2, 3, 4, 6, and 12

Therefore, the highest common factor of 72 and 84 is 12.

we can find highest common factor by other method called prime factorization for the you need to factorize them separately

prime factorization of

72 : 2 × 2 × 2 × 3 × 3

84: 2 × 2 × 3 × 7

now we have to find common prime factors

those are 2 × 2 × 3

now multiply them

= 12

The greatest common factor of 72 and 84 is 12

The HCF (Highest Common Factor) of two or more numbers is the highest number among all the common factors of the given numbers.

Given is to find the greatest common factor or HCF of 72 and 84.

We will first find the factors of each of the numbers given.

The factors of 72 are as follows : 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

The factors of 84 are as follows : 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.

Check the bolded numbers. It can be seen that it is both common and largest of the other common numbers. From the definition of HCF, we can write that the HCF of 72 and 84 would be 12. So, the greatest common factor or HCF is 12.

Therefore, the greatest common factor of 72 and 84 is 12.

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Hi! I'm happy to help!

For our equation, we need to find out what our two smaller equations are.

We can see that angle HGF is our largest angle, and it is composed of EGF, and HGE. We can insert our values into an equation to solve:

16x+4=110+3x+11

We can then combine like terms:

16x+4=121+3x

To solve for x, we need to put it by itself on one side of the equation. So, let's subtract 4 from both sides:

16x=117+3x

Now, let's subtract 3x from both sides:

13x=117

Now, let's divide both sides by 13 to solve for x:

x=9

Now, we know that x=9.

I hope this was helpful, keep learning! :D

Answer:

[tex]y=3x+6[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)

We're given that the slope of the line is 3. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=3x+b[/tex]

We're also given the point (0,6). Since the y-intercept occurs when x=0, the y-intercept is therefore 6. Plug this into [tex]y=3x+b[/tex] as b:

[tex]y=3x+6[/tex]

I hope this helps!