The ages of three teachers are consecutive even integers. Three times the age of the youngest teacher is 48 years more than the older teacher’s age. What is the age of the youngest teacher?A.14 B.18 C.22 D.26

Answer:

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

Step-by-step explanation:

The general form of the equation of the line (linear equation) is:

y = ax + b

The line passes through (-3, -1) and (6, -7), i.e:

(1) (x=-3, y=-1) is a point that verifies the equation of the line, and

(2) (x=6, y=-7) also verifies the equation.

So we can put up a system of 2 equations to obtain a and b:

y = ax + b

(1) -1 = a (-3) + b

(2) -7 = a (6) + b

______________

substracting (1) - (2) we can obtain a:

-1 - (-7) = a (-3-6) ⇒ 6 = -9 a  ⇒ a = -2/3

by replacing a in (1) we can obtain b:

-1 = -2/3 (-3) + b ⇒ -1 -2 = b ⇒ b = -3

so, the equation is:  y = ax + b ⇒ y = -2/3 x - 3

Verification: (2) giving x= 6, let's see if y=-7 is obtained:

y = -2/3 6 - 3 ⇒  y = -4 - 3 = 7 ⇒ RIGHT!

Answer:

nsnsuieieiwiwiweuejjeejeje

Answer:

no it is not a function

domain: -4, 0, 6

range: 12, 18, 40

Answer:

y = 69

Step-by-step explanation:

start with the distributive property:

5/9 * y and 5/9 * 3

and now you have: 5/9y + 15/9 = 40

and we have to isolate y so subtract 15/9 from both sides:

5/9y + 15/9 = 40

        - 15/9     -15/9

and now you have 5/9y = 345/9

and now divide both sides by 5/9 so: 5/9y divided by 5/9 = y

and 345/9 divided by 5/9 = 345/5 and lets simplify....

y= 69

hope this helps luv

Answer:

P = ( -2, -4.5 )

Step-by-step explanation:

-2 on the x axis;

-4.5 on the y-axis.

Answer:

x,y=(0,-7)

Step-by-step explanation:

Multiply eq2 by 3:

[tex]18x-3y=21\\18x+3y=-21[/tex]

Subtract:

[tex]-6y=42\\y=-7[/tex]

Substitute:

[tex]x=0[/tex]

Hope this helps :D

Answer:

C

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer: x = 16

Step-by-step explanation: The y values keep going up by multiplying 2. 2x2=4, 4x2=8, so 8x2=16.

To plot the points just put the point coordinated with the x values and y values.

Answer:

I got 4.875

Step-by-step explanation:

so it would be either $4.87 or rounded up would be $4.88

Step-by-step explanation:

The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1. The probabilities of all the outcomes add up to 1.

Answer:

K=5

Step-by-step explanation:

12k-15=35+2k

12k=50+2k

10k=50

k=5

Answer:

[tex]k = 5[/tex]

Step-by-step explanation:

[tex]12k - 15 = 35 + 2k[/tex]

Our goal is to isolate k

[tex]12k - 15 = 35 + 2k\\\;\;\;\;+15 \;\;\;\;\;\;\; +15[/tex]

[tex]12k = 50 + 2k\\-2k \;\;\;\;\;\;\;\; -2k[/tex]

[tex]10k = 50[/tex]

Now we have k isolated to one side. Our final step is to have k be just k, no coefficient. We can do this by dividing each side by the coefficient.

[tex]\large\frac{10k}{10} = \frac{50}{10} \\\\10k\;\div\;10 = k\\50\;\div\;10 = 5\\[/tex]

[tex]\large\boxed {k \;=\;5}[/tex]

~[tex]InLoveWithPugs[/tex]

[tex]Moderator\\Math\ Enthusiast[/tex]

Answer:

24 teaspoons of red paint would be needed.

Step-by-step explanation:

Given that the initial mixture contains 8 teaspoons of red paint and 12 teaspoons of blue paint, this mixture contains a total of 20 units of paint, of which 8 are red, that is, 8 out of 20. Therefore, the proportion of red paint is 40%, while the proportion of blue paint is 60% remaining.

Therefore, in the case of making the same mixture (with the same proportion) using 36 teaspoons of blue paint, the necessary amount of red paint is determined through the following calculation:

60 = 36

40 = X

((40 x 36) / 60) = X

1,440 = 60 = X

24 = X

Thus, 24 teaspoons of red paint would be needed.

Answer:

C. [tex] \overline{GI} < \overline{GH} < \overline{HI} [/tex]

Step-by-step explanation:

In a triangle, the longest side is opposite to the largest measure of angle. The medium side is opposite to the medium angle, while the shortest side is opposite to the smallest angle.

In ∆GHI,

✍️m<G = 95°, it is opposite to [tex] \overline{HI} [/tex]

<G is the largest angle, therefore, [tex] \overline{HI} [/tex] is the longest side.

✍️m<I = 180 - (95 + 38) = 47°.

<I is opposite to [tex] \overline{GH} [/tex]

<I is the medium angle, therefore, [tex] \overline{GH} [/tex] is the medium side.

✍️m<H = 38°, it is opposite to [tex] \overline{GI} [/tex]

<h is the smallest angle, therefore, [tex] \overline{GI} [/tex] is the shortest side.

✅This means:

[tex] \overline{GI} < \overline{GH} < \overline{HI} [/tex]

Answer:

6?

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

2 + 4 =6

just add 2 by 4 than ans 6

Answer:

6042915 balls.

Step-by-step explanation:

Volume of a ping pong ball is;

V = (4/3)πr³

diameter of ping pong ball is given 4cm = 0.04 m

Radius; r = 0.04/2 = 0.02 m

V = (4/3)π(0.02³)

V = 0.00003351032 m³

Room is 9.5 meters long, 7.5 meters wide, and 3 meters high.

Volume; V = 9 × 7.5 × 3 = 202.5 m³

Number of ping pong balls that will fit into the room = volume of room/volume of ping pong balls = 202.5/0.00003351032 = 6042914.540956151

Approximately 6042915 balls.

Answer:

0.35%

Step-by-step explanation:

Answer:

y=5x-3

Step-by-step explanation:

Slope intercept form is y=mx+b and you know the slope so you can get y=5x+b

Then you are given a point, (2, 7), so you can plug that into the equation to find the y-intercept

7=5(2)+b

Then you just solve for b

7=10+b

-10

-3=b

So the final equation is y=5x-3

The required equation of the line passing through the point (2, 7) and having a slope of 5 is y - 5x = -3

The standard equation of the line using the point-slope form is expressed as:

y-y0 = m(x-x0)

m is the slope of the line

(x0, y0) is the point on the line

Given the following parameters

m =  5

(x0, y0) = (2, 7)

Substitute the given expressions into the formula as shown:

y - 7 = 5(x-2)

y - 7 = 5x - 10

y - 5x = -10 + 7

y - 5x = -3

Hence the required equation of the line passing through the point (2, 7) and having a slope of 5 is y - 5x = -3

Learn more here: https://brainly.com/question/17003809

Answer:

3.83

Step-by-step explanation:

find 9% of 42.50

Answer:

m<B = 62°

Step-by-step explanation:

Given that ∆ABC is congruent to ∆TUV, it follows that their corresponding angles are equal to each other. Therefore:

m<B = m<U

m<B = (3y + 2)°

m<U = (4y - 18)°

Thus,

3y + 2 = 4y - 18

Collect like terms

18 + 2 = 4y - 3y

20 = y

y = 20

m<B = (3y + 2)°

Plug in the value of x

m<B = 3(20) + 2

m<B = 60 + 2

m<B = 62°

Answer: Is there more to the question if so please tell me and i'll answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 + b + h

Okay so we know that b is 6 and that h is 10 so we can change the question to this : 1/2 + 6 + 10. We know that 1/2 is also writen as 0.5 , now all you need to do is 0.5 + 6 + 10 = 16.5 . The question asks to round to the nearest 10th so you need to add a 0 after the 5 so you can round up or down.

16.50

Now you need to look at the 10th number which is 5 and to round it up you need to look at the number after that which would be 0, we know that anything that is 4 or below gets rounded down so your answer for this question is simply 16.5.

I hope that helped you and good luck!

Answer:

Step-by-step explanation:

Use the slope-intercept form

y=mx+b

to find the slope m and y-intercept b.

Slope: −13

y-intercept: (0,−9)

Answer:

Yes

Step-by-step explanation:

x=10 would not however since it is a vertical line and fails the vertical line test where an x value cannot be repeated more than once.

y=10 would be a horizontal line coming from the point (0,10)

Answer:

A=1,3,5,15

B=1,3,5,7,9,11,13,15

C=3,6,9,12,15

U=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15

Answer:

7

Step-by-step explanation:

6×4=24

52-24=28

28÷4=7

Answer:

42x+−17

Step-by-step explanation:

(7)(6x)+(7)(−4)+11

42x+ −28 + 11

(42x)+(−28+11)

42x+−17

Answer:

The acceleration is 2.9m/s^2

Step-by-step explanation:

Given

[tex]Initial\ Speed\ (u) = 6m/s[/tex]

[tex]Final\ Speed\ (v) = 35m/s[/tex]

[tex]Time\ (t) = 10s[/tex]

Required

Determine the acceleration

This question will be answered using Newton's first equation of motion.

[tex]v = u + at[/tex]

Substitute values for v, u and t

[tex]35 = 6 + 10 * a[/tex]

[tex]35 = 6 + 10 a[/tex]

Collect Like Terms

[tex]10a = 35-6[/tex]

[tex]10a = 29[/tex]

Solve for a

[tex]a = 29/10[/tex]

[tex]a = 2.9[/tex]

Hence, the acceleration is 2.9m/s^2

Answer:

2121.8

Step-by-step explanation:

2000(1+0.03/1)^2

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

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

I don't remember what I learned. So, this might be wrong because I googled the formula :)