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1. A student and a teacher work together to make toy cars. The student made 2/7 of the total toy cars, 21 less than the teacher. How many toy cars are there?​

Answers

Answer 1

The total number of cars both the student and the teacher made is 49

let

total cars = x

cars made by student = s

cars made by teacher = t

Total = student + teacher

x = s + t

s = 2/7x

So,

x = 2/7x + t

x - 2/7x = t

t = (7x - 2x) / 7

t = 5/7x

Similarly,

s = t - 21

s = 5/7x - 21

equate both s equation

2/7x = 5/7x - 21

2/7x - 5/7x = -21

(2x - 5x) / 7 = -21

- 3/7x = -21

x = -21 ÷ -3/7

= -21 × - 7/3

= (-21 × -7) / 3

= 147/3

x = 49

Therefore, the total number of cars both the student and the teacher made is 49

Learn more about fractions:

https://brainly.com/question/11562149


Related Questions

Add the following: (i) 2a+b+c, a - b -c, 3a + b​

Answers

Add like terms the answer will be 6a+b+c

A car travels 286 km in three hours with a constant speed. How far can It travel in four hours with the same speed?

Answers

Answer:

381.(3) [km.]

Step-by-step explanation:

if according to the condition distance=286 [km] per 3 hours, then it is possible to make up the equation:

[tex]\frac{286}{3}=\frac{d}{4};[/tex]

and to calculate required distance 'd':

[tex]d=\frac{286*4}{3}=381.(3)[km].[/tex]

WILL GIVE BRAINLIEST

Answers

Answer:

  A) 1: linear; 2: exponential (see equations in part B)

  B) the value of 2 will be almost 15% greater

Step-by-step explanation:

Part A:

As is often the case with multi-part questions, later parts of the question answer earlier parts. The equations shown in Part B are linear for Option 1 and exponential for Option 2.

The table values for Option 1 have a common difference of (1200 -1100) = 100.

The table values for Option 2 have a common ratio of (1210/1100) = 1.10.

Linear functions produce sequential values with a common difference (the slope of the function). Option 1 is linear.

Exponential functions produce sequential values with a common ratio (the growth factor). Option 2 is exponential.

__

Part B:

The investment values after 7 years will be ...

  Option 1: f(7) = 100(7) +1000 = 1700

  Option 2: g(7) = 1000(1.1^7) ≈ 1948.72

The value of Option 2 will be about $248.72 higher, or 14.6% higher than the value of Option 1. Whether that is significant or not is in the eye of the beholder. Many people might consider that to be significantly better performance. (It would take another 2 1/2 years for Option 1 to have that value.)

stions 5-7 the Grade 6 pupils graduated? In a school of 680 Grade 6 pupils, 646 graduated. What percent of the Grade 6 pupils graduated ? ​

Answers

Answer:

95% of Grade 6 pupils graduated

Answer:

95% of Grade 6 Pupils Graduated

Step-by-step explanation:

Express the Statement Mathematically:

646/680

Add Percentage

646/680 * 100%

By Division

0.95 * 100%

Then, Multiply

95%

Simplify to find the answer

Answers

[tex]\frac{-8(7-\sqrt{2)} }{47}[/tex]

A recipe that serves 8 people requires 4 1/2 cups of flour. How many servings are in one recipe? Suppose you need to make enough to serve 24 people. How many batches of the recipe would you need to make?

Answers

Answer:

check online for more information

Answer:

Check online for more informations.

Who are the two children that clung to the Ghost of Christmas Present? What do they symbolize?

Answers

Answer:

Ignorance and Want

Step-by-step explanation:

Igorance and Want symbolizes the poor in the 19th century. PS: I hope this helps

Answer:

The boy is ignorance and the girl is want, in my opinion (you may have a different take on this) they symbolize the poor. Throughout the novella, we have seen the good side of the poor through the Cratchints who work hard day in day out, and now Dickens is wanting to show how malnourished the poor really is. It can also show how Dickens is saying that if the government doesn't act and help out the poor as well as everyone else, this is what the future for the poor will look like, malnourished and uneducated. It is showing us the consequences of being basically abandoned from society in general, abandoned by the education system, and again, I think that Dickens here is trying to show the consequences of the abandonment of the poor and how the government and the rich should change their ways to stop that from happening by being kind and charitable ect.

A. -78
B. 49
C. 53
D. 14

Answers

Answer: 49

Step-by-step explanation:

help please anybody hmm​

Answers

Answer:

94.6-18.8=75.8

75.8 is the answer

Step-by-step explanation:

Hope this helps

May i get braineist pls?

Factor
x ^ 3 + 2x ^ 2 – 5x - 10 = 0

Answers

Answer:

Step-by-step explanation:

When you have four terms and 3rd degree equation (the highest power is 3) you will want to try to "factor by grouping"

Group together two terms, watch out for the negative signs!

x^3 + 2x^2-5x-10=0

(x^3 + 2x^2) - (5x+10)=0

Find a common factor in each group and factor it out. You're hoping that what is left in the parenthesis is the same in both cases.

x^2(x+2)-5(x+2)=0

Now you can factor out that (x+2) because it is both terms.

x^2(x + 2) - 5(x + 2)=0

~~~~ ~~~~

Pull these out.

What will be left is the x^2 and the - 5 (dont lose that - in front of the 5)

(x + 2)(x^2 - 5) = 0

If all you have to do is factor, then you're done. It is factored. But if you have to "solve" also, then put x+2=0 and x^2-5=0 and solve.

x = -2 and x = +- sqrt5

describe this graph of a Ferris wheel

Answers

Answer:

A wheel completes a rotation when it moves 360 degrees. The descriptions of the graph are: The Ferris wheel will rotate 4 times.

Step-by-step explanation:

but what graph

The Ferris wheel makes 4 rotations.

The maximum points on the graph represent when the Ferris wheel is at the top, and the minimum points on the graph represent when the Ferris wheel is at the bottom

Jane wrote all natural numbers from 5 to 12. including 5 and 12.

how many numbers did Jane write?

Answers

8 numbers including 5 & 12 :)

HELPPPPPPPPP!!! THIS IS DUE SOON!!!!!!!

Answers

I think it is 2/3X - 44
Hope this helps

Hello there, you are asking us to distribute [tex]\frac{2}{3}(x-66)[/tex], which can also be phrased as [tex](x\cdot\frac{2}{3})-(66\cdot\frac{2}{3})[/tex], complete what's in the parenthesis, and we get [tex]\frac{2}{3} x-44[/tex] as our answer,

Definition- Distribute Property - The distributive property is one of the most frequently used properties in math. In general, this term refers to the distributive property of multiplication which states that the Definition: The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.

Which number is greater than 555,621,000? A. 5.0 x 10 B. 6.2 x 10 C. 5.55621 x 10 D. 9.99 x 10

Answers

Answer:

None of these

Step-by-step explanation:

None of these are correct because you would need to multiply 5 x 10 to a certain power. 5.55621 x 10 to the 8th power would do it.

Answer: I believe D is correct

Step-by-step explanation:

benny uses 2/5 grams (G) of toothpaste each time he brushes his teeth. If benny buys 30-g tube, how many times will be able to brush his teeth?

Answers

Answer:

75

Step-by-step explanation:

First divide 2/5 to get 0.4. Then divide 30 by 0.4 to get the answer. A simple way to think about it is how many 0.4 grams are in 30 gram tube.

How can you find approximations of square roots?​

Answers

Answer:

you can do a trial and improvement

Step-by-step explanation:

what is n? solve for n+5=2n-6

Answers

Answer:

n = 11

Step-by-step explanation:

n+5=2n-6

you add 6 on both sides and you get

n+11=2n

you then subtract n on both sides and get

11=n

Step-by-step explanation:

n+5 = 2n - 6 -> Original equation

5 = n - 6 -> Take n away from both sides

11 = n -> Add 6 to both sides

n = 11 -> Final answer

*Remember, we are trying to get n by using inverse operations.

Pls help! Will mark Branliest!! 50 points for whoever answers!!!!!!

Answers

Answer: See below

Step-by-step explanation:

Isolate x for x-2y+2z=9

3x=9+2y

[tex]x=\frac{9+2y}{3}[/tex]....(1)

Substitute (1) into the 2nd equation

[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]

[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]

7y=-3

y=-3/7

Substitute y=-3/7

[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]

[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]

Isolate z by substituting it

[tex]3z+\frac{53}{7}=16[/tex]

[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]

[tex]z=\frac{59}{21}[/tex]

For x =9+2y/3 substitute z=59/21 and y=-3/7

[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]

[tex]x=\frac{19}{7}[/tex]

[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]

Answer:

(1, - 1, 3 )

Step-by-step explanation:

x - 2y + 2z = 9 → (1)

- x + 3y = - 4 → (2)

2x - 5y + 3z = 16 → (3)

Add (1) and (2) term by term to eliminate x

y + 2z = 5 → (4)

Multiply (2) by 2

- 2x + 6y = - 8 → (5)

Add (3) and (5) term by term to eliminate x

y + 3z = 8 → (6)

Subtract (6) from (4) term by term to eliminate y

- z = - 3 ( multiply both sides by - 1 )

z = 3

Substitute z = 3 into (4)

y + 2(3) = 5

y + 6 = 5 ( subtract 6 from both sides )

y = - 1

Substitute y = - 1, z = 3 into (1) and solve for x

x - 2(- 1) + 2(3) = 9

x + 2 + 6 = 9

x + 8 = 9 ( subtract 8 from both sides )

x = 1

solution is (1, - 1, 3 )

The digit in the hundreds place is 4 less then 5.

Answers

Yes?? i dont understand the question that much

Step-by-step explanation:

Given: △ABC, m∠A=60°,
m∠C=45°, AB=9
Find: Perimeter of △ABC,
Area of △ABC

Answers

Answer:

Perimeter of ΔABC: [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] units

Area of ΔABC: [tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] units

Skills required: HS Geo, Special Triangles

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

This states that if the side opposite the 30 degree angle is [tex]x[/tex], the side opposite the 60 degree angle is [tex]x*\sqrt3[/tex], and the side opposite the 90 degree angle is [tex]2x[/tex].

AB is 9 units, and it is opposite the 90 degree angle. This means that [tex]2x=9, x = \frac{9}{2}[/tex] ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is [tex]\frac{9}{2}[/tex] units. Segment BD (the height) is [tex]\frac{9}{2} * \sqrt3[/tex].

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

This states that if the side opposite the 45 degree angle is [tex]x[/tex], the other side opposite a 45 degree angle is also [tex]x[/tex], but the hypotenuse (side opposite the right (90 degree) angle) is [tex]\sqrt{2}*x[/tex].

BD is [tex]\frac{9}{2} * \sqrt3[/tex], which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is [tex]\frac{9}{2} * \sqrt6[/tex].

4) Area is [tex]\frac{1}{2}*b*h[/tex], the base (b) is AC (which is [tex]\frac{9}{2}+\frac{9}{2}*\sqrt3[/tex]), the height is BD ([tex]\frac{9}{2}*\sqrt3[/tex]). When multiple you will get [tex]\frac{81}{4}*\sqrt3 + \frac{243}{4}[/tex], then this multiplied by 1/2 is

[tex]\frac{81}{8}*\sqrt3 + \frac{243}{8}[/tex] <--> this is the area!

5) Perimeter is just the sum of all side: 9 + [tex]\frac{9}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] = [tex]\frac{27}{2}[/tex] + [tex]\frac{9}{2} * \sqrt6[/tex] unit

How many twelfths make one whole






How many twelfths make one whole

Answers

Answer:

12

Step-by-step explanation:

1/12x1/x

1x=12x1

x=12

Answer:

12 twelfths make a whole.

Step-by-step explanation:

when the numerator and the denominator of a fraction are the same, they always equal one. 12/12 would simply to one, just like 3/3 or 200/200.

I hope this helps

10 divided by 3 long division

Answers

Okay so the first thing we need to do is clarify the terms so that you know what each part of the division is:

The first number, 10, is called the dividend.The second number, 3 is called the divisor.

What we'll do here is break down each step of the long division process for 10 divided by 3 and explain each of them so you understand exactly what is going on.

10 divided by 3 step-by-step guideStep 1

The first step is to set up our division problem with the divisor on the left side and the dividend on the right side, like we have it below:

  __

3| 10

Step 2

We can work out that the divisor (3) goes into the first digit of the dividend (1), 0 time(s). Now we know that, we can put 0 at the top:

   _0_

3 | 10

Step 3

If we multiply the divisor by the result in the previous step (3 x 0 = 0), we can now add that answer below the dividend:

 _0_

3 | 10

    0

Step 4

Next, we will subtract the result from the previous step from the second digit of the dividend (1 - 0 = 1) and write that answer below:

 ___

3 | 10

- 0

__

1

Step 5

Move the second digit of the dividend (0) down like so:

 __0_

3 | 10

 - 0

-----------

10

Step 6

The divisor (3) goes into the bottom number (10), 3 time(s), so we can put 3 on top:

 __03_

3 | 10

- 0

___

10

Step 7

If we multiply the divisor by the result in the previous step (3 x 3 = 9), we can now add that answer below the dividend:

 _03_

3 | 10

- 0

__

10

 9

Step 8

Next, we will subtract the result from the previous step from the third digit of the dividend (10 - 9 = 1) and write that answer below:

  __03_

3 | 10

- 0

__

10

-9

_

1

So, what is the answer to 10 divided by 3?

Your answer is the top number, and any remainder will be the bottom number. So, for 10 divided by 3, the final solution is:

3 - Remainder 1Extra calculations for you:Using a calculator, if you typed in 10 divided by 3, you'd get 3.3333.You could also express 10/3 as a mixed fraction: 3 1/3If you look at the mixed fraction 3 1/3, you'll see that the numerator is the same as the remainder (1), the denominator is our original divisor (3), and the whole number is our final answer (3).

Find 3 other points for this equation for both x and y ( bots don’t answer pls )

Answers

Answers:

Row one:  x = -10 and y = -4Row two:  x = 0 and y = 6Row three: x = 2 and y = 8

There are infinitely many other possible answers.

===================================================

Explanation:

The [tex]\frac{3}{3}[/tex] simplifies to 1. Dividing any nonzero number over itself always leads to 1.

So the equation [tex]y = \frac{3}{3}x+6[/tex] simplifies to [tex]y = x+6[/tex]

To determine y, we add 6 to x.

Pick 3 random values you want for x.

Let's say we picked x = 0

y = x+6

y = 0+6

y = 6

So x = 0 leads to y = 6

-----------

If you tried something like x = 2, then,

y = x+6

y = 2+6

y = 8

So (2,8) is another point on the line

-----------

Lastly, let's try a negative number. Let's go for x = -10

y = x+6

y = -10+6

y = -4

The input x = -10 gives the output y = -4

There isn't any restriction on x, so you can use any number you want. Therefore, there are infinitely many possible answers.

David is deciding between two parking garages. Garage A charges an initial fee of $7 to park plus $3 per hour. Garage B charges an initial fee of $4 to park plus $4 per hour. Let A represent the amount Garage A would charge if David parks for t hours, and let B represent the amount Garage B would charge if David parks for hours . Write an equation for each situation , in terms of t, and determine which garage would be cheaper if David needs to park for 2 hours .

Answers

Answer:

Step-by-step explanation:

Garage A = 7+3t

Garage B = 4+4t

Garage A = 7+6

Garage B = 4+8

B = Cheaper

Answer:

A = 3t + 7, B = 4t + 4, B is cheaper

Step-by-step explanation:

A = 3(2) + 7 = 6 + 7 = 13

B = 4(2) + 4 = 8 + 4 = 12

If one of the roots of the equation x² – 4x + k = 0 exceeds the other by 2, then find the roots and determine the value of k.

Answers

Step-by-step explanation:

the solutions for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = k

x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)

x1 = 2 + sqrt(4 - k)

x2 = 2 - sqrt (4 - k)

x1 = 2 + x2

2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)

2×sqrt(4 - k) = 2

sqrt(4 - k) = 1

4 - k = 1

k = 4 - 1 = 3

x1 = 3

x2 = 1

Answer:

The roots are 1 and 3.

k = 3.

Step- by-step explanation:

We use the facts that if α and β are the roots of ax^2 + bx + c = o then α+ β = -b/a and  α β = c/a.

The roots are written as  α and α+2, then:

α + α + 2 = -(-4)

2α + 2 = 4

α + 1 = 2

α = 1

also

α (α + 2) = k

Substituting for α:

1(1 + 2) = k

k = 3.

The roots are 1 and 1 + 2 = 3.

Why were people concerned with the East India Tea's Company monopoly over the

tea industry?

Answers

Answer:

You accedently put Mathematics I think you meant Social Studies haha

Step-by-step explanation:

activist judges believe that federal judges should

Answers

Answer:

beyond the words of a constitution or statute to consider the broader societal implications of their decisions.

Step-by-step explanation:

1/4 of 90. …………………????

Answers

Answer:

22.5

Step-by-step explanation:

What starts with a p has a t in the middle and has an R at the end that has 12 letters that is for ur body


Note: its not any subject for school and its not anything for school so ignore the mathematics subject thing.

Answers

Answer:

Pronator??

Step-by-step explanation:

Solve for m.

35m>−30


m>−50

m<−50

m>−18

m<−18

Answers

[tex]35m>-30\\\\\implies \dfrac{35m}{35}>-\dfrac{30}{35}\\\\\implies m>-\dfrac{6}{7}[/tex]

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