Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)

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

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°

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = 2x + 10 is in this form

To express in functional notation replace y by f(x), thus

f(x) = 2x + 10

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:

Hello!

To find the equation of the line with a y-intercept of (0, -3) and a x-intercept of (-4.5, 0), we need to use the slope formula.

The slope formula is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

With that, we substitute the given ordered pairs into the formula, and solve.

[tex]\frac{0 - (-3)}{-4.5 - 0} = \frac{3}{-4.5} =\frac{3}{-\frac{9}{2} } = -\frac{2}{3}[/tex]

The slope of this line is -2/3 or -0.667 repeated (doesn't specify).

Therefore, the equation of the line is y = -2/3x - 3. (I also included the graph!) :-)

Answer:

C. (12, 0)

Step-by-step explanation:

Try the choices:

A. 10 > -3 -7·10 . . . true

B. 10 > 0 -7·7 . . . . true

C. 10 > 12 -7·0 . . . false . . . this is your answer

D. 10 > 2 -7·10 . . . true

The option that is not a solution of the inequality 10 > x - 7y is C. (12, 0), as substituting these values into the inequality gives 10 > 12, which is false.

To find out which option is not a solution of the inequality 10 > x
- 7y, we need to substitute the values of x and y from each given pair into the inequality and check if it holds true.

The only option that does not satisfy the inequality is C. (12, 0), because 10 is not greater than 12.

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!.

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.

Answer:

adults = 40

children = 68

Step-by-step explanation:

Let the children=c

Let the adults = a

Equations

a + c = 108                 (1)

3.75a + 1.5c = 252    (2)

Multiply (1) by 1.5

1.5a + 1.5c = 162        (3)

Subtract (3) from (2)

3.75a + 1.5c = 252

1.5   a + 1.5c = 162    Subtract

2.25a             = 90   Divide by 2.25

a = 90/2.25

a = 40

Find the number of children

a + c = 108

40 + c = 108

c = 108 - 40

c = 68

Check

LHS

3.75 * 40 + 1.50 * 68

150 + 102

252 Which checks with the right hand side.

            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.

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%.

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

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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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

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

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

∠KLM = 36°

the angle bisector divides ∠NLK into 2 equal angles

∠NLK = ∠NLM + ∠KLM

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

Answer:

Marked-down price: $19.99

Step-by-step explanation:

The markdown amount is ...

$29.99×33 1/3% = $10.00 . . . . . 9.99667 rounded up

The marked-down price is the original price less the markdown:

$29.99 - 10.00 = $19.99

_____

You will recognize that 33 1/3% = 1/3, so that the calculation is ...

[tex]\text{markdown}\,=\dfrac{\$29.99}{3}=\$9.99\overline{6}\approx\$10.00[/tex]

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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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]

your answer would be 9h

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.

[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]

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]

(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

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

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:

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

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%) :)))))

1 | 1 - 2 - 5 6

    1 - 1 - 6 0

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