write an equation of the line in point slope form that passes through (-16, 8) and (4,-2)
a.) y-8=-1/2(x+16)
b.) y-8=1/2(x-16)
c.) y+8=2(x+16)
d.) y+8=-(x-16)

The rate of change of y (miles traveled) with respect to x (time in hours) is 59, the coefficient of x. The appropriate choice is ...

... C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 shows that Megan's rate of change in distance traveled is 59 miles for every hour driven at cruise control, after the first 13 miles. So, the correct answer is C. For every hour, she will drive 59 miles.

The equation y = 59x + 13 represents Megan's total distance traveled after driving the first 13 miles without cruise control. The variable y stands for the total number of miles driven, and x represents the number of hours driven at a constant speed using cruise control. To identify the rate of change in the distance traveled, we look at the coefficient of x in the equation, which is 59. This coefficient indicates how many miles are added to the initial 13 miles for every hour of driving at cruise control. Therefore, for every hour, Megan will drive 59 miles after the initial 13 miles are accounted for. It is important to note that the initial 13 miles are a fixed distance and do not change with time. Thus, the correct statement describing the rate of change in the distance traveled is C. For every hour, she will drive 59 miles after the first 13 miles.

y- coordinate 0f A' = 2

note that the coordinates of A(1, 2 ) and the centre of dilatation (4, 2) both have the same y- coordinate 2

This means they are both on the horizontal line y = 2

and so the y- coordinate of A' will also be 2

X= amount of rides

Y=total price (33.50)

Equation: 0.75(18) + X = 33.50

                     13.50+ X=33.50

                    -13.50      -13.50

                                X=20.00

Admission=20.00

Answer:

Part a) [tex]x=18\ tickets[/tex], [tex]y=\$33.50[/tex]

Part b) [tex]y=0.75x+20[/tex]

Step-by-step explanation:

Let

x------>  the number of ride tickets.

k-----> constant that represent the cost for festival admission

y----> the total cost

we know that

[tex]y=0.75x+k[/tex]

we have that

[tex]x=18\ tickets[/tex]

[tex]y=\$33.50[/tex]

substitute the values

[tex]33.50=0.75(18)+k[/tex]

solve for k

[tex]k=33.50-0.75(18)[/tex]

[tex]k=\$20[/tex]

The linear equation to calculate the cost for anyone who only pays for festival admission and rides is equal to

[tex]y=0.75x+20[/tex]

A graph shows zeros near -1.449 and +3.449. These suggest that one factor is the quadratic (x -1)² -6. That makes the other quadratic factor be (x -0.5)² +0.75. So, the complete factorization in integers is

... f(x) = (x² -2x -5)(x² -x +1)

The two real roots are near ...

... d. -1.4, 3.4

If the second coordinate of the ordered pair represents the dollar amount in Jeremy's savings account, then adding 10 to it means that $10 has been added to Jeremy's account.

4.  Supplementary angles together make a straight line (two right angles).  So BOE is supplementary to BOC

Answer: ∠BOE

5. Distance and midpoint between (4,-2), (6,8)

[tex]d = \sqrt{ (6-4)^2 + (8 - -2)^2} = \sqrt{2^2+10^2}=\sqrt{104}=2 \sqrt{26}[/tex]

midpoint

[tex]\left(\dfrac{4 + 6}{2}, \dfrac{-2 + 8}{2} \right) = (5, 3)[/tex]

Answer: distance 2√26, midpoint  (5, 3)

6.That's a rectangle oriented parallel to the axes, width parallel to the x axis of 7 - -3 = 10 and length along y of  1 - - 4 = 5, so an area of 10(5)=50

Answer: 50

The number of rows will be a divisor of 550 such that the quotient is 3 more.

... 550 = 1×550 = 2×275 ≈ 5×110 = 10×55 = 11×50 = 22×25

Factors 22 and 25 differ by 3.

The number of rows of seats is 22.

_____

The number of seats in a row is 25.

The theater has 22 rows of seats. To find this, we solve the equation x(x - 3) = 550, where x is the number of seats per row, leading to x = 25 seats per row and 22 rows after subtracting 3.

To find out how many rows of seats are in the theater with a seating capacity of 550, where the number of rows is 3 less than the number of seats in each row, we can set up an equation to solve for the number of rows. Let the number of seats per row be represented by x, and the number of rows will then be x - 3. Since the total number of seats in the theater is the product of the number of rows and the number of seats per row, we have the equation x(x - 3) = 550.

Now, we will factor this quadratic equation to find the value of x.:

x² - 3x - 550 = 0

Factoring this, we find that it breaks down into (x - 25)(x + 22) = 0. We can then find the value of x by setting each factor equal to zero:

We ignore the negative solution since we cannot have a negative number of seats. Hence, there are 25 seats in each row. To find the number of rows, we subtract 3 from the number of seats per row: 25 - 3 = 22 rows.

Therefore, the theater has 22 rows of seats.

First, let's count:

there are 26 possible outcomes for E1 (black card)

there are 4x9 = 36 possible outcomes for E2, to pick a numbered card (any color)

there are 2x9 =18 possible outcomes for E1 (black) AND E2 (numbered, spade + clower)

the probability of E1 AND E2 is the ratio of the count of possible outcomes for E1 + E2 and the count of all possible outcomes (52 choices to pick a card from the deck):

P(E1 and E2) = 18/52 (34.6%)

And as asked:

P(E1) = 26/52 = 1/2 (50%)

P(E2) = 36/52 = 9/13 (69.2%)

[tex]n (S) = 5\\ n (E_1) = 2 x 13 = 26\\P (E_1) \frac{n (E_1)}{n (S)} = \frac {26}{52} = \frac{1}{2} \\\\ n (E_2) 4 x 9 = 36\\P (E_2)\frac{n (E_2)}{n (S)}=\frac{36}{52}= \frac{9}{13}[/tex]

EDMENTUM / PLATO ANSWER!!!!!!!!

CAN JUST WRITE:

[tex]P (E_1) \frac{n (E_1)}{n (S)} = \frac {26}{52} = \frac{1}{2}[/tex] =  (50%)

[tex]P (E_2)\frac{n (E_2)}{n (S)}=\frac{36}{52}= \frac{9}{13}[/tex] =  (69.2%) :)))))

Answer:

x=-11/12

Step-by-step explanation:

Given an equation for x

x -2/3(3x - 4) + 3x = 5/6

We are asked to find the value of x.

We use equation rules to solve

To get rid of denominator in fraction, let us multiply the whole equation by 6.

6x-4(3x-4) +18x = 5

Simplify:

-6x+18x+16 =5

12x = 5-16 = -11

x = -11/12

Answer:

- 11/6

Step-by-step explanation:

Let x equal the number of books in the box.

x* 1/6 = 8

Multiply each side by 6

x=48 books

The correct answer is B) 48 books.

To determine how many books a completely full box would hold, we need to consider the information given:

The box contains 8 books and it is 1/6 full. To find out how many books would be in the box if it were completely full, we need to set up a proportion:

[tex]\(\frac{8}{\frac{1}{6}} = \frac{8 imes 6}{1} = 48\)[/tex]

This means the box can hold 48 books when full.

So, the correct answer is:

B) 48 books

You are asking for the proportion of numbers 1–6 that are greater than 2. The ones greater than 2 are 3, 4, 5, 6. There are 4 of them, out of the 6 possible numbers. Since the cube is fair, all numbers have equal probability. This means the probability of an outcome greater than 2 is

... 4/6 = 2/3

The appropriat choice is ...

... C.) 2/3

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

let y = f(x), then rearrange making x the subject

y = [tex]\frac{3x}{x-2}[/tex] ( multiply both sides by (x - 2 ))

y(x - 2 ) = 3x (distribute )

xy - 2y = 3x ( subtract 3x and add 2y to both sides )

xy - 3x = 2y (factor out x on left side )

x(y - 3 ) = 2y ( divide both sides by (y - 3) )

x = [tex]\frac{2y}{y-3}[/tex]

change y to x for inverse function

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

Final answer:

The percent of decrease for the magazine's subscription is 20%.

Explanation:

To find the percent of decrease for the magazine's subscription, we need to calculate the difference between the original price and the new price, and then divide it by the original price.

The decrease in price is $66 - $52.80 = $13.20.

The percent of decrease is ($13.20 / $66) * 100% = 20%.

Biconditionals are statements that work both ways.

Some examples:

If it rains, I go out, and if I go out, it must be raining.

This can be stated concisely in mathematical terms as

I go out IF AND ONLY IF it rains.

So looking at the given statements, only the last two work both ways, namely:

If the sun rises in the east, then it is morning, and if it is morning, the sun rises in the east.

Victoria will play outside if and only if the weather is nice.

Answer:

Step-by-step explanation:

The sum of the interior angles in a triangle is 180°. To find the value of x, you must subtract 47 and 71 from 180.

180-47-71=x

x=62

The answer is A. 62°

Answer:

7 ft.

Step-by-step explanation:

1 ft./12 in. = x/84

Cross multiply:

1 × 84 = 84

x · 12 = 12x

12x = 84

12x/12 = 84/12

12x/12 = x

84/12 = 7

Ans. x = 7

Hope this helps! :)

There are 7 feet in 84 inches.

Given that we need to determine that how many feet in 84 inches.

To convert inches to feet, you need to divide the number of inches by the number of inches in a foot.

There are 12 inches in a foot.

Given that you have 84 inches, you can divide this value by 12 to find the equivalent in feet:

84 inches ÷ 12 inches/foot = 7 feet

So, 84 inches is equal to 7 feet.

Hence there are 7 feet in 84 inches.

Learn more about unit conversion click

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b = - 252 and c = - 1126

the equation of a parabola in vertex form is

y a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

y = - 14(x + 9)² + 8 ← equation in vertex form

expand and compare coefficients

y = - 14(x² + 18x + 81 ) + 8 = - 14x² - 252x - 1134 + 8

compare to y = - 14x² + bx + c

b = - 252 and c = - 1126

The percentage increased by 42.86%.

To calculate the percentage increase:

First: work out the difference (increase) between the two numbers you are comparing.

Increase = New Number - Original Number

Then: divide the increase by the original number and multiply the answer by 100.

% increase = Increase ÷ Original Number × 100.

If your answer is a negative number then this is a percentage decrease.

For the first one,

x = 10.

For the second one,

x = 12

x = [tex]\frac{60}{9}[/tex] and x = [tex]\frac{45}{8}[/tex]

Since in both cases the figures are similar then the ratios of corresponding sides are equal

[tex]\frac{x}{15}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )

9x = 60 ( divide both sides by 9 )

x = [tex]\frac{60}{9}[/tex]

and [tex]\frac{x}{5}[/tex] = [tex]\frac{9}{8}[/tex]

8x = 45 ( divide both sides by 8 )

x = [tex]\frac{45}{8}[/tex]

∠KLM = 36°

the angle bisector divides ∠NLK into 2 equal angles

∠NLK = ∠NLM + ∠KLM

since ∠NLK = 72° then ∠NLM = ∠KLM = 36°

Answer:

Jimmy run in t minute =  [tex]\frac{m*t}{60}[/tex] miles.

Step-by-step explanation:

Given  : Jimmy ran with the speed of m miles per hour.

To find : How far did he run in t minutes.

Solution : We have given

Speed  = m miles per hour .

Speed =  [tex]\frac{Distance}{time}[/tex].

We can say in 1 hour Jimmy ran =m  miles.

1 hour = 60 minute .

Jimmy ran in 60 minute = m miles .

Jimmy run in 1 minute = [tex]\frac{m}{60}[/tex] miles.

Jimmy run in t minute =  [tex]\frac{m}{60}* t[/tex] miles.

Jimmy run in t minute =  [tex]\frac{m*t}{60}[/tex] miles.

Therefore, Jimmy run in t minute =  [tex]\frac{m*t}{60}[/tex] miles.

The distance covered by Jimmy after t minutes is

[tex]m \: \times ( \frac{t}{60} )[/tex]

Recall :

Distance = Speed × Time

Speed = m miles per hour

Time = t minutes

Converting t to hours :

Recall :

1 hour = 60 minutes

t minutes = t/60 hours

Multiplying Jimmy's speed by the number of minutes run

Distance covered :

[tex]m \: \times ( \frac{t}{60} )[/tex]

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(1)

given [tex]\frac{j}{6}[/tex] = [tex]\frac{9}{10}[/tex] ( cross- multiply )

10j = 54 ( divide both sides by 10 )

j = [tex]\frac{54}{10}[/tex] = [tex]\frac{27}{5}[/tex] ← in simplest form

(9)

let h be the hours worked daily , then

3h = 20 [tex]\frac{2}{3}[/tex] = [tex]\frac{62}{3}[/tex] ( divide both sides by 3 )

h = [tex]\frac{62}{3}[/tex] ÷ 3

  = [tex]\frac{62}{3}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{62}{9}[/tex] = 6 [tex]\frac{8}{9}[/tex]

She worked  6 [tex]\frac{8}{9}[/tex] hours each day

Solution: We are given data points and associated residuals:

Data Point           Residual          Absolute value(Residual)

(20,6)                     -2.00                      2.00

(15,5)                       6.75                       6.75

(5,3)                        -1.25                       1.25

(10,10)                     4.50                       4.50

From the above absolute value(Residual) column, we clearly see the data point (15,5) has the residual with greatest absolute value of 6.75.

Therefore, the data point and its associated residual is:

(15,5)  and 6.75    

Answer:

Data Point: (10,10); Residual = 4.50

67!/2 = k = 18 235 555 459 094 342 644 124 929 548 302 732 213 583 817 657 024 762 296 850 814 250 133 981 218 471 936 000 000 000 000 000

about 1.82×10⁹⁴

Answer:

k=64

Step-by-step explanation:

To find out the greatest integer such that 2^{k}is a factor if 67!

We divide the quotients by 2 and then finally add all the quotients.

67/2 = 33.5 --------> 33

33/2 = 16.5 ---------> 16

16/2 = 8 --------> 8

8/2= 4 ---------> 4

4/2  = 2--------> 2

2/2 = 1 ----------> 1

k= 33+16+8+4+2+1

   = 64

Hence, 64 is the greatest integer such that 2^{k} is a factor of 67!.

            50*2= 100

               So 50 is one half of One hundred and if we use 100 divided by 2 to get 50 then we need to do 80 / 2 which will give us 40.

1 | 1 - 2 - 5 6

    1 - 1 - 6 0

quotient = x² - x - 6 = (x - 3 )( x + 2 )

The number, 19/7, is B. a rational number

Rational numbers are numbers that can be written as a fraction.

In this case, 19/7 is already a fraction

~Rise Above the Ordinary

Try this option:

rule: if to make a dividing by negative number (<0), the inequatlity sign must be changed to opposite.

According the rule described above, the correct answer is

'When dividing by -5, he did not change the ≤ to ≥'.

When dividing by - 5 he did not change ≤ to ≥

His calculations are correct down to the line - 5x ≤ 9

When dividing or multiplying by a negative quantity the inequality symbol must be reversed, thus

- 5x ≤ 9 ( divide both sides by - 5 )

x ≥ 9 ← inequality symbol reversed

GT = 13 and TA = 3

Triangles GRT and GEA are similar and so the ratios of corresponding sides are equal

[tex]\frac{16}{16-x}[/tex] = [tex]\frac{8}{5}[/tex] ( cross- multiply )

8(16 - x) = 80

128 - 8x = 80

- 8x = - 48 ⇒ x = 3 = TA

16 - x = 16 - 3 = GT

Answer: GT = 13 and TA = 3

Triangles GRT and GEA are similar and so the ratios of corresponding sides are equal

=  ( cross- multiply )

8(16 - x) = 80

128 - 8x = 80

- 8x = - 48 ⇒ x = 3 = TA

16 - x = 16 - 3 = GT

TA = 6 and GT = 10 ( arithmetic !!)

Step-by-step explanation:

I had a test and this was one of the questions and the answer it said was (3x1/3) x 42 so you dont have to figure it out. hope this helps anyone who needs it. :)