Enter an equation in standard form to model the linear situation. A bathtub that holds 42 gallons of water contains 12 gallons of water. You begin filling it, and after 5 minutes, the tub is full.

Question:

Point T, the midpoint of segment RS, can be found using the formulas x = (1/2) (6 – 2) + 2 and y = (1/2) (4 – 6) + 6. What are the coordinates of point T?

Answer:

[tex]T(4,5)[/tex]

Step-by-step explanation:

Given

[tex]x = \frac{1}{2}(6 - 2) + 2[/tex]

[tex]y = \frac{1}{2}(4 - 6) + 6[/tex]

Required

Determine the coordinates of T

The coordinates of T can be represented as [tex]T(x,y)[/tex]

To do this, we simply solve for x and y

[tex]x = \frac{1}{2}(6 - 2) + 2[/tex]

Solve 6 - 2

[tex]x = \frac{1}{2}*4 + 2[/tex]

Solve 1/2 * 4

[tex]x = 2 + 2[/tex]

[tex]x = 4[/tex]

[tex]y = \frac{1}{2}(4 - 6) + 6[/tex]

Solve 4 - 6

[tex]y = \frac{1}{2}*-2 + 6[/tex]

Solve 1/2 * -2

[tex]y = -1 + 6[/tex]

[tex]y = 5[/tex]

Hence, the coordinates of T(x,y) is:

[tex]T(x,y) = T(4,5)[/tex]

Answer:

C

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

(a)  There 8 possible outcomes.

HHH TTT HHT HTH THH TTH THT HTT

(b) Prob(No Heads)

= Prob(TTT)

= 1/8.

(c) Possible outcomes of at least 2 tails are:

TTT, TTH THT HTT = 4

So Probability of this  is 4/8 = 1/2.

Answer:

x= -1

Step-by-step explanation:

First, distribute the -3 through the parentheses

4x-8= -3(2x+6)

= 4x-8= -6x-18

Second, move the variable to the left-hand side and change its sign

4x+6x= -18+8

10x= -10

Divide both sides by 10

x=-1

Answer:

x=-7

Step-by-step explanation:

first u wanna multiply (2x+6) which equals 12 the what u wanna do is move the constant to the right which is 4x-8=-36. Then calculate 4x=-36+8. then after that then u should end up with 4x=-28 then u divide it then u end up with ×=-7

Answer:

Are you 1 grade or what......

Answer:

6x^2 + 10x

Step-by-step explanation:

2x(3x + 5) = 2x * 3x + 2x * 5

= 6x^2 + 10x

Answer:

a) 15

b) 97/2

Step-by-step explanation:

a) f(g(6))

  g(6) = 6

   2(6)+3

    12 + 3

      15

b) gf(x) = 10

    2x+3

    2x+3 = 100

    2x = 97

     x = 97/2

Step-by-step explanation:

Area of a triangle= 1/2breadth × height

Answer:

Step-by-step explanation:

7x+4=10x-11

4=3x-11

15=3x

x=5

Answer:

5

Step-by-step explanation:

within the brackets do the parentheses (14-12)=2

according to PEMDAS, multiply first 2x3 to get 6

then add 3

you end up with 9 in the brackets so now all that’s left is 45/9 which is 5

Answer:

P(Pair of dice greater than 7) = 5/12

Step-by-step explanation:

When rolling a pair of dice, there are 36 combinations for the rolls.

(1,1), (1,2), (1,3), .... (2,1), (2,2), .... (6,1), ... (6,6)

Of those, there are 15 where the total is greater than 7.

15/36 = 5/12

#1 #2 Sum > 7

1 1 2 FALSE

1 2 3 FALSE

1 3 4 FALSE

1 4 5 FALSE

1 5 6 FALSE

1 6 7 FALSE

2 1 3 FALSE

2 2 4 FALSE

2 3 5 FALSE

2 4 6 FALSE

2 5 7 FALSE

2 6 8 TRUE

3 1 4 FALSE

3 2 5 FALSE

3 3 6 FALSE

3 4 7 FALSE

3 5 8 TRUE

3 6 9 TRUE

4 1 5 FALSE

4 2 6 FALSE

4 3 7 FALSE

4 4 8 TRUE

4 5 9 TRUE

4 6 10 TRUE

5 1 6 FALSE

5 2 7 FALSE

5 3 8 TRUE

5 4 9 TRUE

5 5 10 TRUE

5 6 11 TRUE

6 1 7 FALSE

6 2 8 TRUE

6 3 9 TRUE

6 4 10 TRUE

6 5 11 TRUE

6 6 12 TRUE

Answer:

5/12

Step-by-step explanation:

I can’t really explain it. I did the same problew though.

Answer:

hey look up it up it's  better

Step-by-step explanation:

the percentage is 75%

because 90 divided by 120 is 0.75.

Answer: Vertex is (-7/2, -81/4)

Axis of synmentary is x= -7/2

Directrix is y= -41/2

Step-by-step explanation:

Its on google

Answer:

Step-by-step explanation:

Step one:

given data

we are told that the  number of people under the survey is 3000

and also that 2100 people would like to buy again, these 2100 people represent the number of people who are satisfied with the type of car.

Step two:

Therefore the percentage of this number related to the total people under the survey is given below

=2100/3000*100

=21//30*100

=7/10*100

=7*10

=70%

Hence 70% of the people surveyed are satisfied with the type of car

Answer:

y=0x+1

Step-by-step explanation:

Hope this helps!(^-^)

Answer: either -4,1 (+) 6 or 2,1 (-) 6

Step-by-step explanation:

Answer:

Please, see the explanation.

Step-by-step explanation:

DETERMINING THE EQUATION FOR THE FIRST TABLE

Given the first table

x                     y

-5                   10

-1                    2

0                    0

11                   -22

From the given equation, we can verify and determine that

[tex]y=-2x[/tex] is the required equation that satisfies the table values of the first table.

substituting the table values of all the ordered pairs to check

FOR (-5, 10)

y =-2x

10 = -2(-5)

10 = 10

L.H.S = R.H.S

FOR (-1, 2)

y =-2x

2 = -2(-1)

10 = 2

L.H.S = R.H.S

FOR (0, 0)

y =-2x

0 = -2(0)

0 = 0

L.H.S = R.H.S

FOR (11, -22)

y =-2x

-22 = -2(11)

-22 = -22

L.H.S = R.H.S

As all the ordered pairs of the first table satisfy the equation.

Hence, [tex]y=-2x[/tex] is the equation for the first table.

DETERMINING THE EQUATION FOR THE SECOND TABLE

Given the first table

x                     y

-8                   -11

-2                    -5

1                      -2

7                      4

From the given equation, we can verify and determine that

[tex]y=x-3[/tex] is the required equation that satisfies the table values of the second table.

substituting the table values of all the ordered pairs to check

FOR (-8, -11)

y =x-3

-11 = -8-3

-11 = -11

L.H.S = R.H.S

FOR (-2, -5)

y =x-3

-5= -2-3

-11 = -5

L.H.S = R.H.S

FOR (1, -2)

y = x-3

-2= 1-3

-2 = -2

L.H.S = R.H.S

FOR (7, 4)

y = x-3

4 = 7-3

4 = 4

L.H.S = R.H.S

As all the ordered pairs of the second table satisfy the equation.

Hence, [tex]y = x-3[/tex] is the equation for the second table.

Therefore, the equations are:

[tex]y=-2x[/tex]

[tex]y = x-3[/tex]

Now, let us solve to determine the solution

[tex]\begin{bmatrix}y=-2x\\ y=x-3\end{bmatrix}[/tex]

Arrange equation variables for elimination

[tex]\begin{bmatrix}y+2x=0\\ y-x=-3\end{bmatrix}[/tex]

[tex]y-x=-3[/tex]

[tex]-[/tex]

[tex]\underline{y+2x=0}[/tex]

[tex]-3x=-3[/tex]

[tex]\begin{bmatrix}y+2x=0\\ -3x=-3\end{bmatrix}[/tex]

solving

[tex]-3x=-3[/tex]

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

[tex]x=1[/tex]

For [tex]y+2x=0[/tex],  plugin [tex]x = 1[/tex]

[tex]y+2\cdot \:1=0[/tex]

[tex]y+2=0[/tex]

[tex]y=-2[/tex]

Therefore, the solution to the system of equations are:

[tex]y=-2,\:x=1[/tex]

Answer:no hbu cutie?

Step-by-step explanation:

I do lol- can u help me

3.4–2.8d+2.8d-1.3=?

Answer:

8

one fourth

2

4

Step-by-step explanation:

hope with helped ^^

Answer:

9, 30, and 15.

Step-by-step explanation:

Let the three numbers be a, b, and c.

The sum of them is 54. So:

[tex]a+b+c=54[/tex]

The third number is 6 more than the first. In other words, c=a+6.

The second number is twice the third. In other words, b=2c.

Let’s write the second number in terms of a. Since b=2c, this means that b=2(a+6).

Let’s substitute them into our equation. So:

[tex]a+2(a+6)+(a+6)=54[/tex]

Solve for a. Distribute:

[tex]a+2a+12+a+6=54[/tex]

Combine like terms:

[tex]4a+18=54[/tex]

Subtract 18 from both sides:

[tex]4a=36[/tex]

Hence, the value of a is:

[tex]a=9[/tex]

So, the first number is 9.

The third number is 6 more than the first, so the third number is 15.

The second number is twice the third. So, the second number is 30.

Therefore, our numbers are:

9, 30, and 15.

Given:

[tex]\sin (x)=-\dfrac{1}{2}[/tex]

[tex]\cos (y)=-\dfrac{1}{3}[/tex]

x is an angle in quadrant III, and y is an angle in quadrant II.

To find:

The value of sin(x+y).

Solution:

We know that, only sin and cosec are positive in II quadrant. Only tan and cot are positive in III quadrant.

x is an angle in quadrant III,

[tex]\cos x=-\sqrt{1-\sin^2 x}[/tex]

[tex]\cos x=-\sqrt{1-(-\dfrac{1}{2})^2}[/tex]

[tex]\cos x=-\sqrt{1-\dfrac{1}{4}}[/tex]

[tex]\cos x=-\sqrt{\dfrac{4-1}{4}}[/tex]

[tex]\cos x=-\dfrac{\sqrt{3}}{2}[/tex]

y is an angle in quadrant II.

[tex]\sin y=\sqrt{1-\cos^2x}[/tex]

[tex]\sin y=\sqrt{1-(-\dfrac{1}{3})^2}[/tex]

[tex]\sin y=\sqrt{1-\dfrac{1}{9}}[/tex]

[tex]\sin y=\sqrt{\dfrac{9-1}{9}}[/tex]

[tex]\sin y=\sqrt{\dfrac{8}{9}}[/tex]

[tex]\sin y=\dfrac{2\sqrt{2}}{3}[/tex]

Now,

[tex]\sin(x+y)=\sin x\cos y+\cos x\sin y[/tex]

[tex]\sin(x+y)=(-\dfrac{1}{2})\times (-\dfrac{1}{3})+(-\dfrac{\sqrt{3}}{2})\times (\dfrac{2\sqrt{2}}{3})[/tex]

[tex]\sin(x+y)=\dfrac{1}{6}-\dfrac{2\sqrt{6}}{6}[/tex]

[tex]\sin(x+y)=\dfrac{1-2\sqrt{6}}{6}[/tex]

Therefore, the correct option is B.

Answer:

Choice B

Step-by-step explanation:

Answer:

x = 60

Step-by-step explanation:

Given: L ∥ M and the line going through them is transversal

The sum of the interior angles on the same side of a transversal is equal to 180 degrees; therefore, (2x + 5) degrees + (x - 5) degrees = 180 degrees.

2x + 5 + x - 5 = 180

2x + x + 5 - 5 = 180

3x + 0 = 180

3x = 180

x = 180/3

x = 60

Double Check:

2(60) + 5 + (60) - 5 = 180 degrees

120 + 5 + 55 =

125 + 55 =

180 degrees

180 degrees = 180 degrees

the answer is x=-4 hope it helps

Answer:

x = 6

Step-by-step explanation:

[tex] {x}^{3} - {x}^{2} + x - 1 + \frac{2}{x + 1} [/tex]

lmk if u want an explanation for this I can try type it out

Answer:

[tex]x^3-x^2+x-1+\frac{2}{x+1}[/tex]

Step-by-step explanation:

See the picture attached.

Notice how I set up [tex]x^4+1[/tex] as [tex]x^4+0x^3+0x^2+0x+1[/tex], as it makes it easier to solve.

Also, notice that the 2 as the remainder doesn't have anything else to divide to, so that means there will be an extra term [tex]\frac{2}{x+1}[/tex] in the end of the answer.

The central angle of the circle is given by the equation A = 120°

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. It is an angle whose vertex is the center of a circle with the two radii lines as its arms, that intersect at two different points on the circle.

The central angle of a circle formula is as follows.

Central Angle = ( s x 360° ) / 2πr

where s is the length of the arc

r is the radius of the circle

Central Angle = 2 x Angle in other segment

Given data ,

Let the center of the circle be O

Let the arc be represented as AB

Let the angle be represented as ∠AOB

Now , ∠AOB is a central angle with an intercepted minor arc from A to B.

Substituting the values in the equation , we get

m∠AB = 120º

The measure of the central angle ∠AOB = measure of m∠AB

So ,

The measure of the central angle ∠AOB = 120°

Hence , the central angle is 120°

To learn more about central angle click :

https://brainly.com/question/11877137

#SPJ2

Answer:

5. Slope: 2

y-intercept:(0,-6)

y=2x-6

6. Slope:1

y-intercept:(0,-1)

y=x-1

Answer:

1) 1[tex]\frac{1}{8}[/tex]

2) 2[tex]\frac{5}{7}[/tex]

3) 1[tex]\frac{8}{9}[/tex]

Step-by-step explanation:

Step-by-step explanation:

4 7/8 + __ = 6

__ = 6 - 4 7/8

__ = 1 1/8

3 2/7 + __ = 6

__ = 6 - 3 2/7

__ = 2 5/7

3 1/9 + __ = 5

__ = 5 - 3 1/9

__ = 1 8/9

Topic: Fractions

If you like to venture further, feel free to check out my insta (learntionary). It would be best if you could give it a follow. I'll be constantly posting math tips and notes! Thanks!

Answer: The Answer is 64

Step-by-step explanation: there  isnt  much really to it

Answer:

The answer is 64

Step-by-step explanation:

If you need me to explain my answer let me know.

Answer:

m=24

Step-by-step explanation:

First, we can combine like terms:

m/(5-2)=8

m/3=8

Now, we need to get m by itself. To do this, multiply by 3:

m/3*3=8*3

m=24

50

50 ÷ 5 = 10, 10-2 =8

kdjrjrjdjjfhrhy to truth thhrjrhejd

Answer:

Part B is Both batches have 2 more quarts of pineapple juice than sparkling water. The ratio of quarts of pineapple juice to quarts of fruity drink for the first batch is 3 to 5 or 3:5 or 3/5. The ratio for the second batch is 5 to 8 or 5:8 or 5/8. The second batch has a greater ratio of quarts of pineapple juice to quarts of fruity drink.

Answer:

22

Step-by-step explanation:

if a=15

then, 2(a-5)+2= 2(15-5)+2 = 2(10)+2= 20+2=22