One of Teddy's jobs at home is to pump gas for his family's sedan and truck. When he fills up the sedan with 12 gallons of gas, he notices that it costs him $50.28. How much does one gallon of gas cost? This is also called the unit rate. Explain how you found your answer.​

Answer:

2/14

Step-by-step explanation:

when you scale the numerator and denominator down by 4, you just divide both of them by 4. So since 8 divided by 4 is 2 and 56 divided by 4 is 14, the answer is 2/14

Answer:

yo can someone answere this i need it to

Step-by-step explanation:

Answer:

This thermometer shows a temperature of -6 degrees Celsius. If the temperature rises a few degrees and gets very close to 0 degrees without reaching it,

Step-by-step explanation:

hope this helps have a great day :)

Answer: 3 and 8

Step-by-step explanation:

5 and 6 only apply to line M, 2 and 4 only apply to line M, while 3 and 8 apply to both.

Answer:D) 10 3/8

Step-by-step explanation:

Have a wonderful rest of ur day!!

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{PROPERTIES of MATH (of addition)}}\\\\\large\bullet\boxed{\mathsf{\ Commutative \ property: \boxed{\bf x + y = y + x}}}\\\bullet\boxed{\mathsf{\ Identity\ property: \boxed{\bf x + y = x}}}\\\bullet\boxed{\ \mathsf{Associative\ property: \boxed{\bf (x + y) + z = z + (x + y)}}}\\\bullet\boxed{\ \mathsf{Distributive\ property: \boxed{\bf x(y + z) = x\times y + x\times z}}}[/tex]

[tex]\large\boxed{\mathsf{(10 + 1) + 9 = 10 + (1 + 9)}}\\\\\\\large\boxed{\mathsf{(10 + 1) + 9}}\\\large\boxed{\mathsf{= 10 + 1 + 9}}\\\large\boxed{\mathsf{= 11 + 9}}\\\large\boxed{= \mathsf{20}}\\\\\large\boxed{\mathsf{10 + (1 + 9)}}\\\large\boxed{\mathsf{= 10 + 1 + 9}}\\\large\boxed{\mathsf{= 11 + 9}}\\\large\boxed{= \mathsf{20}}\\\\\\\\\huge\boxed{\mathsf{20 = 20}}\huge\checkmark[/tex]

[tex]\huge\boxed{\mathsf{Based\ on\ the\ information\ we \ have\ above\ your}}\\\huge\boxed{\mathsf{answer \ is: \underline{\underline{\bf Associative \ Property}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

(rounded) 9 miles OR 9 1/10 miles

Answer:

a = 3

b = 2

Step-by-step explanation:

Solve 4a - b = 10 for b:

Substitute 4a - 10 for b in 2a + 3b = 12

Substitute 3 for a in b = 4a - 10

Therefore, a = 3 and b = 2.

Hence, the value of x ix 5/21.

[tex]\sf \leadsto \dfrac{7x - 3}{2} = \dfrac{-2}{3}[/tex]

[tex]\sf \leadsto 3(7x - 3) = -2(2)[/tex]

[tex]\sf \leadsto 21x - 9 = -4[/tex]

[tex]\sf \leadsto 21x = -4 + 9[/tex]

[tex]\sf \leadsto 21x = 5[/tex]

[tex]\sf \leadsto x = \dfrac{5}{21}[/tex]

Answer:

5/42

Step-by-step explanation:

7x - 3/2 = -2/3          (Take -3/2 to the other side so it becomes +3/2)

7x = -2/3 +3/2          (Add the two fractions)

7x = 5/6                    (7 is taken to the other side so 5/6 ÷ 7)

x = 5/42

Answer:

x = 5/2cm

Step-by-step explanation:

Because this is a square and each side is equal to each other in length, we can say:

7x + 3 = 5x + 8

We can start rearranging this equation to collect like terms:

7x = 5x + 8 - 3

7x = 5x + 5

7x - 5x = 5

2x = 5

x = 5/2

We can test this out by substituting our new found value for x into the original equation:

7 * (5/2) + 3 = 5 * (5/2) + 8

(35/2) + 3 = (25/2) + 8

I'm going to change the integers (3 and 8) to fractions so the arithmetic is easier, as they'll all have the same denominator.

(35/2) + (6/2) = (25/2) + (16/2)

(41/2) = (41/2)

So as you can see above, with x = 5/2, both sides are equal.

You don't need to put the fractions in brackets; I just do that to make it look a little less messy.

Also, I've only included the units (cm) in the answer. I don't like using units when doing calculations, but your teacher may ask you to perform the calculations using the units throughout.

Answer:

here you go

Step-by-step explanation:

Algebra questions and answers. Write an equation of the line that passes through (4,5) and is parallel to the line defined by 4x+y=-2. Write the answer in slope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.

Sorry that this is long, but hopefully this has the answers and explanations you are looking for. Have a nice day!

1a: P' (0, 1) Q' (9, 7)

First, we will look at point P. It is at (-7, -2). If we move it up three and right 7, we will do (-7 +7, -2 +3) which gives us (0, 1). We do the same for Q, (2, 4) -> (2+7, 4 +3) = (9, 7)

2a: This transformation represents the point being moved down 5 units and to the right 2 units. X is left/right and it's being moved positive two, hence right 2. Y is up/down, and it's being moved negative 5, hence down 5.

2b: (4, -3) (not 100% sure on this one)

The wording slightly confused me, but if it's talking about having point A be apart of 2a, here is what we do:

(2, 2) -> (2 + 2, 2 - 5) -> (4, -3)

3a: (x - 26, y + 17)

So (in the y) -13 becomes 4, so it moves 17 units up. For the x, -2 becomes -28, so it is moved 26 units down. This becomes x - 26 and y + 17, which is written correctly above.

3b: A. AP and A'P' have different locations

For a translation shape, size, and direction doesn't change, just where it's at (location).

Answer: 0.05

Step-by-step explanation:

1) Re-arrange the formula given to find the rate (r)

I = Prt

becomes r = I / Pt

Now we add in the values we know

P = 3000, t = 3 years, I = 450

r = 450 / ( 3000 × 3 )

r = 0.05 or 5% / year

Answer:

B. 432 feet

Step-by-step explanation:

36 yards * 3 = 108 feet

108 feet * 12 = 1296 inches

Step-by-step explanation:

30x³y³z²+12x²y²z³-18x⁵y⁶z

6x²y²z(5xyz+2z²-3x³y⁴).

hope this helps you.

Answer:

y = 6x + 3

Step-by-step explanation:

y2 - y1 / x2 - x1

9 - 3 / 1 - 0

6/1

= 6

y = 6x + b

3 = 6(0) + b

3 = 0 + b

3 = b

Answer:

y = 6x+3

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}\\\\= \frac{9-3}{1-0}\\\\= \frac{6}{1}\\\\= 6[/tex]

Hence, the slope is 6.

Substituting the slope value to the equation 'y=mx+c',

y = 6x +c

Substituting (0,3):

3 = 0 + c

c = 3

Hence,

y = 6x + 3

Feel free to mark this as brainliest! :D

Answer:

3

Step-by-step explanation:

there are only x y and z used in the expression no matter how many times they multiply.

Answer:

Step-by-step explanation:

The table shows that Mrs. Garcia types 70 words in the first minute and 70 additional words in each additional minute.

That is, in x minues, Mrs. Garcia types 70x words:

  y = 70x . . . . words Mrs Garcia can type in x minutes

__

When x=49, the number of words Mrs. Garcia is expected to type is ...

  y = 70×49 = 3,430

She will type 3,430 words in 49 minutes.

Answer:

see below

Step-by-step explanation:

x < -3  for the first equation

x > 4 for the second equation

your answer is 740 {:

Step-by-step explanation:

let x be the original price

then we write our equation

x-60%x=200 (x=100%x)

100%x-60%x=200

40%x=200

(40/100)x=200

x=(200*100)/40

x=20000/40=500

so the original price was $500

Answer:

d=30°

e=117°

f=66°

Answer:

E: 117

D: 30

F: 33

Step-by-step explanation:

360-117-117-30-30=66

66 divide by 2 = 33

The number of days passed to have an accumulated heartbeat of 504,000 is the ratio of the total heartbeat and the number of beat per minute ; Hence, the number of days is 5 days

Number of heartbeats per day = 70 × (24 × 60) = 100,800 beats

Number of days = (504,000) ÷ (100,800) = 5days

Therefore, the Number of days elapsed is 5 days.

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Answer:

24 hours

Step-by-step explanation:

If 12 workers take 10 hours to build a wall, assuming they build at the same rate, it would take one worker 120 hours to build a wall.

By this logic, it would take 120/5 or 24 hours for 5 workers to build a wall

The number of hours 5 men take with the same rate of 12 workers taking 10 hours will be 24 hours.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

The number of hours 1 person take to build the wall = 12 x 10 = 120 hour

Number of men = 5

The number of 5 men will take as 120/5 = 24 hour

Hence "The number of hours 5 men take with the same rate of 12 workers taking 10 hours will be 24 hours".

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Answer:

y = -6x^2 + 15x -5

Step-by-step explanation:

equation step 1 for parabola

y2-y1 /x2-x1

= 1 - 4 / 0 - - 1

= -3 / 1

y = -3

We try again different points  

y2-y1 / x2-x1

= 7 - 1 / 2 - 0

= 6 / 2

y = 3

we can see that one side is descending and 1 side is ascending

The start of the parabola is 0,1 as x = 0 and crosses the line.

we try again

y2-y1 /x2-x1

7-1 / 2-0

= 6 / 2

y = 3

You should know that a parabola is determined by 3 points, so unless your points happen to be collinear, they will determine a parabola. A straight forward, if not always the easiest way would be to take the general equation

y = ax^2 + bx + c

plug in each point, eg.y = y1   and x = x1   eg) y = y2 and x = y2   eg) y = y3 x=x3

Top equation re-used last see at end.

4 = a(-1)^2  + b(-1 ) + c  = a+b+c=4

1  = a(0)^2 +b(0) + c = c =1

7 = a(2)^2 + b(2) + c = 4a+2b=7

a= -1-0 = -1   b = -1-0 = -1  and 4-1 = 3

-a +-b = 3

2nd set of equations

4a-0a = 4a

2b-0b = 2b

7-1 = 6

4a +2b=6  and previous

-a +-b = 3  here we can multiply by -2 to get 2b equality to 1st equation

2a + 2b = -6

4a + 2b = 6

2a = -12

2a = -12 / 2

a = -6

plug a

4(-6) + 2b = 6

-24 + 2b = 6

2b = 6 +24

2b = 30

b = 15

then put a + b+ c into top equation

(-6) + (15) + c = 4

9 + 0  = 4

9 -9 = 4 -9   cancel

c = -5

Then put into first equation as c and complete equation

To find that;

y = -6x^2 + 15x -5   =   is our equation of the parabola.

This is how to solve your two linear equations in three unknowns.

The equation of parabola passing through (-1, 4), (0, 1), and (2, 7) is y = 2x² - x + 1.

To find equation of parabola that passes through the given points, we use the general-form of quadratic equation: y = ax² + bx + c.

Since we have three points, we substitute the coordinates of each point into the equation to create a system of equations. Solve for a, b, and c:

Substitute (-1, 4), We get,

4 = a(-1)² + b(-1) + c,

4 = a - b + c,

Next, Substitute (0, 1):

1 = a(0)² + b(0) + c

1 = c

Next, Substitute (2, 7):

7 = a(2)² + b(2) + c

7 = 4a + 2b + c

Now, we have a system of equations:

a - b + c = 4          ...equation(1)

c = 1                      ...equation(2)

4a + 2b + c = 7     ...equation(3)

From equation(2), we know that c = 1. Substituting this into equation(1) and 3, we get,

a - b + 1 = 4

4a + 2b + 1 = 7

Solve equation(1) for a - b:

We get, a - b = 3,

Solve equation(3) for 4a + 2b:

4a + 2b = 6

Now we have a system-of-equations as :

a - b = 3

4a + 2b = 6

Solving the system for "a" and "b", We get,

a = 2; b = -1

Now we can write the equation of the parabola:

y = ax² + bx + c  ⇒  y = 2x² - x + 1,

Therefore, the required equation of parabola is y = 2x² - x + 1.

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I hope this step by step explanation helps.

A plane travels 800 meters along the runway before taking off, then the distance travelled from the starting point will be equal to 1793.24 meters.

Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.

In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.

As per the given data in the question,

Distance travelled by plane = 800 meters

Use the equation,

a² = b² + c² -2bc cos A

d² = 800² + 1000² - (2 × 800 × 1000 × cos 170°)

d² = 1640000 - 1600000(cos 170°)

d² = 3215692.405

d = 1793.24

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