The perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ has an equation of the form $y = mx + b$. Find $m+b$.

Answer:

Step-by-step explanation:

To find the length of a we use the cosine rule

That's

a² = b² + c² - 2bc cos A

We have

a² = AB ² + AC ² - 2(AB)(AC) cos A

From the question

AB = 6

AC = 5

A = 20°

Substituting the values into the above formula we have

a² = 6² + 5² - 2(6)(5) cos 20

a² = 36 + 25 - 60cos 20

a² = 61 - 56.38

a² = 4.62

Find square root of both sides

a = √4.62

We have the final answer as

Hope this helps you

Answer:

[tex] \boxed{\sf B. \ 2x^{2} + 11} [/tex]

Given:

f(x) = 3x² + 2

g(x) = x² - 9

To Find:

(f - g)(x)

Step-by-step explanation:

[tex]\sf (f -g)(x) = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} + 2) - (x^{2} - 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} + 2 - x^{2} + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} - x^{2} + 2 + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} - x^{2}) + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + 11 [/tex]

Answer:

k=0

Step-by-step explanation:

8(4k-4)=5k-32

32k-32=-5k-32

32k-32+32=-5k-32+32

32k=-5k

32k+5k=-5k+5k

37k=0

37k/37=0/37

k=0

Answer:

k=0

Step-by-step explanation:

To solve for k, we need to first distribute the 8 through the parenthesis.

32k-32=-5k-32

Lets add 5k to both sides.

37k-32=-32

add 32 to both sides

37k=0

divide 37 from both sides

k=0

Answer:

She had $2.00 left.

Step-by-step explanation:

PEMDAS

$75 - [(3 x $4) + (2 x $20) + $21 ]

$75 - [ $12 + $40 + $21]

$75 - [ $52 + $21]

$75 - $73

$2

Answer:

140°

Step-by-step explanation:

[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]

Answer:

Hey there!

Our equation can be: 2y+3=4y+2

Hope this helps :)

Answer:

2y+3=4y+2

I hope you got it..

Answer:

I would not separate the same edges when making a second net. Also,  I would make sure that the result cannot be rotated or flipped so that it is the same  as the first.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]3x+4\geq13\\\\3x\geq9\\\\x\geq3\\\\A=\big<3\,,\ \infty)[/tex]                         [tex]\frac12x+3\leq4\\\\\frac12x\leq1\\\\x\leq2\\\\B=(-\infty\,,\ 2\big>[/tex]

[tex]A\cup B\not=\varnothing\quad for\ all\ x\in(-\infty\,, 2\big>\cup\big<3\,,\ \infty)[/tex]

so:

     [tex]A\cup B=\varnothing\quad for\ x\in(\,2\,,\ 3\,)[/tex]

Answer:hi, the answer would be (a) or 2<x<3 hope this helps :)

Step-by-step explanation: i just took the test got em all correct

Answer:

m = 3

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (7, 3)

m = [tex]\frac{3+3}{7-5}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Answer:

S = x + 10

R = 2x + 10

Step-by-step explanation:

If R is Roberto's age, and S is his sister's age, then:

R = S + x

R − 10 = 2 (S − 10)

Solve with substitution.

S + x − 10 = 2 (S − 10)

S + x − 10 = 2S − 20

S = x + 10

R = 2x + 10

Answer:

5/14 = 0.36

7/10 = 0.7

5/6 = 0.83

11/15 = 0.73

19/21 = 0.9

(round to the tenth)

so the answer is;

5/14, 7/10, 11/15, 5/6, 19/21

Step-by-step explanation:

Hope it helps!

Answer:

Step-by-step explanation:

The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.

Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).

The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.

The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.

The interval of x-values where the function is increasing is therefore (-3, -1).

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Answer:well the answer is 2 hours 16 minutes.

Step-by-step explanation:

To find your plane's rate of speed, you calculate the distance ... amount of time in the air (2 hours and 16 minutes) to.

Answer:

Step-by-step explanation:

the degree of 8^8t

16777216t : the degree of the mnonmial is 1, because the degree of the variable is 1

Answer:

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Step-by-step explanation:

Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.

Therefore:

x + y = z                                  (1)

Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:

Cost of buying = Price it was sold for

The cost of the mango = 5z and the price it was sold for = 3x + 6y

3x + 6y = 5z                            (2)

Substituting z = x + y in equation 1

3x + 6y = 5(x + y)

3x + 6y = 5x + 5y

6y - 5y = 5x - 3x

y = 2x

x / y = 1/ 2 = 1 : 2

The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2

Work Shown:

A = P*(1+r/n)^(nt)

A = 500*(1+0.04/1)^(1*3)

A = 562.432

A = 562.43

Answer: $562.43

Step-by-step explanation:

The initial start up amount is 500  and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.

So 100%  + 4 % = 104% = 1.04  

The common difference is 1.04.

so  500 * 1.04^n= A where n is the number of years and A is the total amount.

A = 500 * [tex]1.04^{3}[/tex]  

A= 562.43

Answer:

Hey there!

You would write that as 2(9-n), where n is the number.

Hope this helps :)

Answer:

0.88175960442

Step-by-step explanation:

The square root of 0.7775 is 0.88175960442

The value of standard deviation will be;

⇒ 0.8803

What is mean by square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The value of Variance = 0.7775

Now,

Since, The standard deviation is the square root of the variance.

Hence, We can formulate;

The value of standard deviation = √0.7775

                                                 = 0.8803

Thus, The value of standard deviation will be;

⇒ 0.8803

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Answer:

  d) m - 2 l = - 6; m - l = 5

Step-by-step explanation:

Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...

  m = 2l -6

Subtracting 2l from both sides gives the equation ...

  m -2l = -6 . . . . . matches choice D

Answer:

The answer is

Step-by-step explanation:

Circumference of a circle( C) = πd

where d is the diameter

π = 3.142

From the question

d = 1.8cm

Substitute d = 1.8 into the above formula

Circumference of the circle is

3.142 × 1.8

= 5.6556

We have the final answer as

Hope this helps you

Answer:

  swap the middle two steps to put them in order

Step-by-step explanation:

The steps in order would be ...

Answer:

Domain = x - values

Range = y - values

Step-by-step explanation:

main points I'll use as examples for the rest on graph are: (-3,4) (1,2) and (1,6)

Domain: simple numbers here are {-3,1} dont repeat the same x value twice!

Range: {2,4,6}

Make sure values are in numerical order.

Find the rest by these three points! (Which are on graph)

Hope this helps, have a good day :)

Answer:

try 2

Step-by-step explanation:

because it an X-value and it on the graph

Answer:

The answer is C.

Step-by-step explanation:

First, you want to isolate the variable you are look for, 'l'. First subtract [pi]L from both sides. Then subtract S from both sides.

-[pi]L+S=[pi]r(superscript)2 ->

-[pi]L=[pi]r(superscript)2-S

Now, since you have your variable 'l', you want to remove the [pi] away from your variable. To do this, multiply by negative 1 divided by pi, or -1/[pi].

L=S-r(superscript)2.

Therefore, the answer is C.

Answer:

C

Step-by-step explanation:

[tex]s = \pi .l \: + \pi. {r}^{2} [/tex]

Make the term including 'l' stand alone.

[tex]s - \pi. {r }^{2} = \pi.l[/tex]

Now make L stand alone by dividing through by pi.

[tex] \frac{s - \pi. {r}^{2} }{\pi} = l[/tex]

This is the same as

[tex] \frac{s}{\pi} - {r}^{2} = l[/tex]

Answer:

Glass A

Step-by-step explanation:

Volume = п r ² h

п = 3.14  aprox.

r = radius = diameter/2

h = tall

volume = 3.14 * (84/2)² * 175

volume = 3.14 * 42² * 175

volume = 3.14 * 1764 * 175

volume = 969318mm³

volume = 3.14 * (96/2)² * 125

volume = 3.14* 48² * 125

volume = 3.14 * 2304 * 125

volume = 904320mm³

Answer:

969318 > 904320

then:

Glass A holds more liquid

Answer:

31 Feets

Step-by-step explanation:

Given the expression for the height of a baseball:

Height(t) = -16t^2 +64t +3

Height in Feets ; time (t) in seconds

Height of baseball after 3.5 seconds :

Height(3.5) = -16(3.5)^2 + 64(3.5) + 3

Height = - 16(12.25) + 64(3.5) + 3

Height = - 196 + 224 + 3

Height = 31 Feets

Height after 3.5 seconds = 31 feets

Answer:

Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].

Step-by-step explanation:

The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.

Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].

Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].

By the power rule:

Therefore:

[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].

In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.

Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].

Answer:

58.28 m/s

Step-by-step explanation:

y = 62t - 1.86t²

Speed, S = dy/dt = 62 - 2(1.86)t

S = 62 - 3.72t

When t = 1

S = 62 - 3.72 = 58.28 m/s

Answer:

12,157,665,459,057,000,000

Step-by-step explanation:

It seems like it would have to involve exponents.  3 to the 40th power would be 12,157,665,459,057,000,000.  

1. The first step here is to arrange the data set's form least to greatest,

Sherelle:  26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85

Venita:  44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79

Now we can determine our 5 - number summary based on the numbers respective positions.

First Data Set,

(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85

Second Data Set,

(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79

2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.

3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -

Sherelle:  1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985

Venita:  1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979

( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.

( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,

Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,

Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5

( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.

Answer:

x = 5, y = 8, z = -3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent so to find x:

x + 7 = 3x - 3

-2x = -10

x = 5

To find y:

y + 2 = 2y - 6

-y = -8

y = 8

Therefore, z = x - y = 5 - 8 = -3.

There are 12 factors which are perfect squares is 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

Factors can be define splitting the value in multipliable values.

Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3

Perfect squares can be formed by above factors are
= 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

Thus, there are 12 factors which are perfect squares is 1,  4,  9,  16,  36,  64,  81, 144,  324, 576, 1296, 5184.

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