What is the slope of a line that goes through (2, -2) and (5, 6)
8/3
4/3
3/4
3/8

Answer:

[tex]\boxed{\sf x = -4 \pm 2\sqrt{6} }[/tex]

Explanation:

3x² + 24x - 24 = 0

factor the coefficient

3(x² + 8x) -24 = 0

Halve the second term and square it

3(x + 4)² -24 -3(4)² = 0

simplify the answer

3(x + 4)² -72 = 0

add 72 on both sides

3(x + 4)² = 72

divide both sides by 3

(x + 4)² = 24

square root both sides

x + 4 = ±√24

subtract both sides by 4

x = -4 ± 2√6

Answer:

[tex]x=-4\pm2\sqrt{6}[/tex]

Step-by-step explanation:

Completing the square for quadratic in the form  [tex]ax^2+bx+c=0[/tex]

Given equation:

[tex]3x^2+24x-24=0[/tex]

Factor out 3:

[tex]\implies 3(x^2+8x-8)=0[/tex]

Divide both sides by 3:

[tex]\implies x^2+8x-8=0[/tex]

Add 8 to both sides:

[tex]\implies x^2+8x=8[/tex]

[tex]\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:[/tex]

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2[/tex]

[tex]\implies x^2+8x+16=8+16[/tex]

[tex]\implies x^2+8x+16=24[/tex]

Factor the left side:

[tex]\implies (x+4)^2=24[/tex]

Square root both sides:

[tex]\implies x+4=\pm2\sqrt{6}[/tex]

Subtract 4 from both sides:

[tex]\implies x=-4\pm2\sqrt{6}[/tex]

Answer:

Here is the ans...hope it helps

The probability that a person selected at random is Ages 16-18 and has prepared a meal for their family

From the table of values, we have:

Age 16 - 18 that has performed meal =  8

Total = 30

The probability is then calculated using:

P(16 - 18) = n(16 - 18)/Total

This gives

P(16 - 18) = 8/30

Simplify

P(16 - 18) = 4/15

Hence, the probability is 4/15

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x = -2/3 or -4

see the attachment for solution

hope it helps...!!!

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

the following expression can be solved as follows ~

[tex] \frac{x}{3} + 1 = \frac{x}{8} + \frac{1}{11} \\ [/tex]

Taking LCM on both the sides ,

[tex] \frac{x + 3}{3} = \frac{11x + 8}{88} \\ [/tex]

On cross multiplying ,

[tex]( x + 3)88 = (11x + 8)3 \\ \\ \implies \: 88x + 264 = 33x + 24[/tex]

let's now gather the like terms at either sides of the equation and solve ~

[tex]88x - 33x = 24 - 264 \\ \\ \implies \: 55x = - 240 \\ \\ \implies \: x = \cancel\frac{ - 240}{55} \\ [/tex]

on further simplifying ,

[tex]\implies x = \frac{ - 48 }{ 11} \\ [/tex]

hope helpful ~

Answer:

Question 1: ∠V = 40° and MD = 17.62 and VD = 27.41 (work below)

Question 2: b. 60

Question 3: b. sinC

Step-by-step explanation:

Answer:

p - 14.5 = 53

Step-by-step explanation:

The original price is p.

The discounted price is $14.50 less than p, or $14.50 subtracted from p. The discounted price is p - 14.5.

The discounted price is $53

Equation:

p - 14.5 = 53

Answer:

35.9 degrees

Step-by-step explanation:

the arctan of 0.724 is 35.9 degrees

Answer:

$30

Step-by-step explanation:

since 7 = 28

and 1 = 4

divide 1 in half to find the half hour amount

1/2 hr = 2

28 + 2 = 30

your answer is $30

hope this helps:)

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/3 and passes through (-3 , 2)

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{(-3)}) \\\\\\ y-2=\cfrac{1}{3}(x+3)\implies y-2=\cfrac{1}{3}x+1\implies y=\cfrac{1}{3}x+3[/tex]

The letter A represents where the amount of $158.29 should be written.

The letter D represents where the amount of $250 should be written.

This refers to the automated machine that is used to handle cash transactions and also for making calculations.

Hence, we can see that from the complete information, Ivan has a cash register where he records the amount he spends on groceries which is $158.29, and also the transaction of sending $250 to his savings account.

However, in the cash register, Ivan uses the letter A to show where the amount of $158.29 should be written and the letter D represents where the amount of $250 should be written.

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Answer:

A and D

Edge 2022

Answer:

Below in bold.

Step-by-step explanation:

The mean is 55 therefore, by definition:

On average the students are 55 inches tall.

The median is the middle ( or the average of 2 middle) value when the data is arranged in order.

So as the media is 46 inches about half are more than 46 ins tall.

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

To find the total number of different sundaes possible, we need to multiply the number of choices for each category: ice cream flavors, toppings, and sizes.

Number of ice cream flavors = 20

Number of toppings = 5

Number of sizes = 3

Total number of sundaes = Number of ice cream flavors × Number of toppings × Number of sizes

Total number of sundaes = 20 × 5 × 3

Total number of sundaes = 300

There are 300 different sundaes possible with the given choices of 20 ice cream flavors, 5 toppings, and 3 sizes at the make-your-own sundae bar.

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Answer: the zeros are the xintercepts which are shown on the graph

Step-by-step explanation:

Answer:

26.7

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

12 x 100 = 1200

1200 / 48 = 25

The pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.

Finding out how much something changes over time is what the average rate of change is all about.

We have Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero.

As we know that the average rate of change can be calculated using:

= (Last quantity - starting quantity)/Time interval

The average rate of change, on the other hand, does not account for intermediate values, therefore you can't draw any conclusions about them.

In the given problem:

The average rate of change in depth = (Last quantity - starting quantity)/2

0= (Last quantity - starting quantity)

Final depth = Initial depth

Thus, the pool must have been the same depth at the start of the interval as it was at the end of the interval, option second is correct.

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

The given sequence is in Arithmetic progression, and we have to find its nth term ~

So, let's get it solved ~

First term of the sequence is :

Common difference is :

Now, if we have to write the 2nd Term with respect to first one, we can write :

similarly ~

Therefore, I similar pattern ~

[tex] \qquad \sf  \dashrightarrow \: nth \: term = a + (n - 1)d[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2 + (n - 1)2[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2(1 + (n - 1))[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2(1 + n - 1)[/tex]

[tex] \qquad \sf  \dashrightarrow \: nth \: term = 2 n [/tex]

Feel free to ask your doubts, if you have any ~

Answer:

Step-by-step explanation:

from the number sequence above, each term except the first is generated by adding 2 to the term immediately preceding it.

the nth term of the sequence is usually designated Tn, and it's usually a function of n

from the number sequence

T1= 2

T2 = 2+2= 4

T3= 4+2= 6

T4= 6+2= 8

therefore, Tn= 2+2×(n-1)

= 2+2n-2

=2-2+2n= 2n

Answer:

   46. (3) 29

   47. (1) y = -4x + 3

   48. (3) 3

   49. (3) -1/2

   50. (4) 25x - 75

Step-by-step explanation:

Question 46

Question 47

Question 48

Question 49

Question 50

Answer:

Company "A"

Step-by-step explanation:

its the highest line on the graph from the 300 point.

Answer:

0.525 is the number.

X = Y/P%

X = 0.84/160%

p = 160%/100 = 1.6

X = 0.84/1.6

X = 0.525

Answer:

the person earned one summer = $3,600

We have to show the amount in fraction that Paula spent during the following semester,

they spent for tuition = $2,500 =  × 100

=0.6944 × 100

=  69.44%  

they spent for rent = $650 =   × 100

= 0.1806 × 100

= 18.06%

they spent for food = $430 =   × 100

=0.1194 × 100

= 11.94%

they Spent in tuition, rent and food = 2,500 + 650 + 430 = $3580

Now they spent in miscellaneous expenses = 3600 - 3580 = $20.00   × 100

= 0.056 × 100

= 0.56%

Answer:

(x-3)(x+2)

Step-by-step explanation:

¹ you open brackets.

² you put the "x" in both brackets

³ you then check for factors, that will give you a "6" when you multiply them and give you the "x" when you add or subtract them.

The rate of change is $27 per month if the change in y values is 54 and change in x values is 2.

It is defined as the change in values of a dependent variable with respect to the independent variables.

From the data given in the table, we can find the rate of change per month:

To find the rate of change:

= change in y/ change in x

= (138-84)/(4-2)

= 54/2

= 27 per month

Thus, the rate of change is $27 per month if the change in y values is 54 and change in x values is 2.

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Step-by-step explanation:

here's the answer.......

Answer:

Step-by-step explanation:

Formula

speed = distance / time

Givens

speed = ?

distance = 162 miles.

Time = 3 hours.

Solution

speed = 162 / 3

speed = 54 miles per hour.

Answer:

Right Angle.

Step-by-step explanation:

A right angle (90°; /2 radians) exists between a tangent to a circle and the radius across the point of contact. To put it another way, the tangent and radius are perpendicular to one another.

Answer:

I would day right angle. It sounds like the best answer

Step-by-step explanation:

now, we don't have a compounding period above, so we're assuming the amount is compounding annually.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\pounds 8112\\ P=\textit{original amount deposited}\\ r=rate\to 30\%\to \frac{30}{100}\dotfill &0.30\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases}[/tex]

[tex]8112=P\left(1+\frac{0.30}{1}\right)^{1\cdot 2}\implies 8112=P(1.3)^2\implies \cfrac{8112}{1.3^2}=P\implies 4800=P[/tex]