Malin and Shawn begin with the same number, $t$. Malin subtracts $6$ from $t$ and then divides the result by $6$. Shawn adds $7$ to $t$ and then divides the result by $7$. If Malin's final answer is the same as Shawn's final answer, what was the number $t$

Answers

Answer 1

Answer:

t=84

Step-by-step explanation:

Malin's answer is $\frac{t-6}{6}$. Shawn's answer is $\frac{t+7}{7}$. We know these are equal, so we have the equation

$$\frac{t-6}{6} = \frac{t+7}{7}.$$

To eliminate denominators from the problem, we multiply both sides by $6\cdot 7$:

$$\frac{6\cdot 7\cdot (t-6)}{6} = \frac{6\cdot 7\cdot (t+7)}{7},$$

then simplify to get

$$7\cdot (t-6) = 6\cdot (t+7).$$

The parentheses are important here! For example, the parentheses on the left side of the equation tell us that it is $t-6$, not just $t$, which is multiplied by $7$.

Now we expand using the distributive property:

7t - 7\cdot 6 &= 6t + 6\cdot 7;\\

7t - 42 &= 6t + 42.

Adding $42$ to both sides gives

$$7t = 6t + 84,$$

then subtracting $6t$ from both sides gives $t=\boxed{84}$.

(We can check that starting from $t=84$, Malin and Shawn do indeed get the same final answer -- namely, $13$.)


Related Questions

The diagram below shows a Sudoku puzzle with a difference. Some of the lines between adjacent cells have a number on them; this is the product of the numbers in the cells.
The normal rules of Sudoku also apply: the numbers 1 to 9 must appear once each in each row, once in each column, and once in each square block.
Can you solve this puzzle?​

Answers

I don’t understand the puzzle but I’ll try my best :)

Will give thank,brainly and 5 stars!

Answers

The second and last one.

The second one multiplies the cost of each type of ticket by two, therefore saying that you wanted to buy two of each type of ticket.

The last one multiplies the cost of a single ticket of all three types and multiplies it by 2.

Answer:

The second and last one

Step-by-step explanation:

Hope this helps and have a good day!

Which inequality represents this statement?

A number is no more than 5.


n<5

n≥5

n>5

n≤5

Answers

Answer: the last one!! [tex]n\leq 5[/tex]

Step-by-step explanation:

When there is a line under it means no more than!

The manger of a water park keeps track of the amount of money collected, M, and the number of tickets,T, each day.

Answers

Answer: The variable t us the dependent variable because it affects the amount of money collected, m, each day.

please keep it simple.

Answers

Answer:

[tex]z^{2} +\frac{1}{2} +11z[/tex]

Step-by-step explanation:

→ Minus the z² terms

[tex]1\frac{1}{2} z^{2} -\frac{1}{2} z^{2}=1 z^{2}[/tex]

→ Minus the whole numbers

[tex]3\frac{1}{2} -3=\frac{1}{2}[/tex]

→ Add the z terms

11z

State the slope and y-intercept for the graph of
- 8x + y = -12.

Answers

Answer:

y must have a numerical coefficient of 1. This equation does. If it does not, then you must divide through by whatever is in front of the y.

To read the slope, you must have x and its coefficient on opposite sides of the equal sign.

So you get

y = 8x – 12 when you add 8x to both sides

Next, the y intercept is found when x = 0

y = 8x – 12

y = 8(0) – 12

y = – 12

The  y intercept is -12 or in point form (0, – 12)

Answer

slope = 8

y intercept = – 12

Step-by-step explanation:

How many different terms are in the expression? 28s + 3t+ 6b + 21f

Answers

Answer:

4

Step-by-step explanation:

In math, the word difference is the result of subtracting one number from another. It refers to the difference in quantity between two numbers. In math, we get the difference between two numbers by subtracting the subtrahend (the number being subtracted) from the minuend (the number being subtracted from).

What is 7 x 1/4 ? Draw a model of your choice to help you solve in decimal form

Answers

Answer:

1 and 3/4

Step-by-step explanation:

7×1/4 (the / symbolizes ÷)

(7×1) ÷4

7/4 ( divide by 4)

=1 and 3/4

1. You are planning an extended trip to Mexico. You have a new smartphone to keep in touch with your friends but are concerned about the roaming charges since you will be outside the home network service area. Your plan costs $40.00 per month plus $0.35 per minute for roaming charges. Write a linear model relating your monthly cost, C, and the roaming minutes, t.

A: C = $40 + $0.35t
B: C = $40 $0.35t
C: C = $0.35 + $40t
D: C = $0.35 $40t

Answers

a. $40 is the set price per month and $.035 is the changing rate per minute. If t represents the minutes you use the phone, then you have to multiple that amount by $.035

PLS HELP using only the marking in the diagram, what theorem can be used to show that the two triangles are congruent
a.) AAS
b.)ASA
c.)HL
d.)SSS

Answers

Angle Side Angle theorem (ASA)

We can see that angles BAC and EDF are equal

We can also see that lines AC and DF are equal

And we can see that angles ACB and DFE are equal

Solve the inequality-8≤3x-17<19

Answers

Answer: The answer is X∈[3,12).

Answer:

-8≤3x-17<19

-8+8 ≤ 3x - 17 + 8 < 19 + 8

0 ≤  3x - 9 < 27

0 ≤  3x - 9 + 9 < 27 + 9

0 ≤  3x <  36

0 ≤ 3x / 3 <  36/3

0 ≤ x < 12

So x can be 0 or less than 12. A number between 0 and 12

Identify the vertical asymptotes of f(x) = quantity x plus 6 over quantity x squared minus 9x plus 18. X = â’6 and x = â’3 x = â’6 and x = 3 x = 6 and x = â’3 x = 6 and x = 3.

Answers

The vertical asymptotes of the function are 3 and 6

Given the function

[tex]\frac{x+6}{x^2-9x+18}[/tex]

The vertical asymptotes of the function occur at the point where the denominator is zero.

Equate the denominator to zero.

x^2 - 9x + 18 = 0

Factorize the quadratic expression:

x^2 - 3x - 6x + 18 =0

x(x-3)-6(x-3) = 0

(x-3)(x-6) = 0

x - 3 = 0 and x - 6 = 0

x = 3 and 6

Hence the vertical asymptotes of the function are 3 and 6

Learn more on vertical asymptotes here: https://brainly.com/question/21678319

what is the greatest common factor of 32 and 56

Answers

its 8. hope this helps you.


What is the value of the digit in the millions place?
56,931,446
A. 9,000,000
B. 50,000,000
C. 6,000,000
D. 400,000

Answers

Answer:

C 6,000,000

Step-by-step explanation:

The angle measures of an isosceles triangle are shown. Find the value of w.

Answers

Answer:

[tex]w=7[/tex]

Step-by-step explanation:

Using the Angle Sum Theorem which states that all the interior angles in a triangle add up to 180 degrees you can use that to solve for w with the following:

[tex]62 +9w-1+8w=180[/tex]  First combine like terms

[tex](62-1)+(9w+8w)=180[/tex]

[tex]61+17w=180[/tex] Then subtract 61 from both sides.

[tex]17w=180-61[/tex]

[tex]17w=119[/tex] Now divide by 17

[tex]w=119/17[/tex]

[tex]w=7[/tex]


[tex] \huge \red{\boxed{ \colorbox{black}{ \color{gold}{question}}}}[/tex]


Need help~

[tex] \sqrt{3 + 3 + 3 + 3 + 3 + 3} [/tex]

Answers

Answer:

3√2

Step-by-step explanation:

First, combine all the numbers in the square root, and then square root the number provided:

√(3 + 3 + 3 + 3 + 3 + 3) = √18

When square rooting, first, find prime factors of the number, 18. If there are pairs, they will be combined into a whole number:

√18 = √(3 * 3 * 2) = 3√2

3√2 is your answer.

~

pleeeeeeeease help meeeee

Answers

Answer:

45

Step-by-step explanation:

First, we have to find the Nth term of this sequence. Since this is linear we can just find the difference to get the n. For example, we can do 3-2 which is one and we can also do 5-4 which is also 1 which confirms that the n is 1. So in other words, 1n However, we don't write the 1 in front of the n because the n itself represents 1n. Next, we have to take away 1 from the first term, which also gives us 1. This is the adjustment to the 1n. So our answer is n+1, which is the nth term for this linear sequence. So now we just substitute 44 into the equation. 44+1=45, which is the 44th term.

For a given series, s1=1, s2=8, s3=21 what is the 3rd term in the sequence?

Answers

Answer:

S=13, read pictures below

Step-by-step explanation:

If b = the number of boys, which algebraic expression represents the phrase
below?
the sum of the number of boys and 15 girls
A. b + 15
B. b. 15
C. b - 15
D.
b
15

Answers

Answer:

A. b + 15

Step-by-step explanation:

b = the number of boys, substitute below:

The sum of the number of boys and 15 girls → The sum of b and 15 → b + 15

Correct choice is A

help i have math homework and im real bad at it i got a B- last year so help

Answers

4y-12 is the answer
4y-12 is correct. whatever number is outside of the parentheses you just multiply that with the two numbers in the parentheses to distribute :)

19. The present age of brother and sister are in the ration 4:5 Before three years the ration of their age was 3:4. find their present age-​

Answers

Answer:

Sister = 15 years old

Brother = 12 years old

Step-by-step explanation:

Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X

Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have

B = 3X

S = 4X

B-3 = (3/4)(S-3)

Therefore, we have a system of equations

B = (4/5)S

B-3 = (3/4)(S-3)

Substitute (4/5)S for B into the second equation to only have one variable

(4/5)S - 3 = (3/4)(S-3)

(4/5)S - 3 = (3/4)S - 9/4

add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient

(1/20)S = 3/4

multiply both sides by 20 to isolate the S

S = 15

B = (4/5)S = 12



y=x−4
y=4x+2

Find x and y

Answers

Answer:

x = -2

y = -6

Step-by-step explanation:

x - 4 = 4x + 2

-4 = 3x + 2

-6 = 3x

x = -2

y = -2 - 4;  y = -6

Jeremy got a haircut and paid 15% as a tip. What percent of the cost did Jeremy pay the barber, including the tip?

Answers

The percentage of the cost that Jeremy will pay including the tip paid is 115% of the cost.

Assuming the cost was $100 and Jeremy gave a 15% tip. The total he would pay is:

= 100 + tip

= 100 + (100 x 15%)

= $115

In percentage this is:

= 115/100 x 100%

= 115%

In conclusion, Jeremy would pay 115% of the tip.

Find out more at https://brainly.com/question/22444616.

Can someone please help me with this and I’ll give you a lot of points

Answers

Answer:

C

Step-by-step explanation:

It’s A

Slope intercept form is Y = Mx + b

So the additional hour is being added on

X/2 = Y/3 = Z/4. prove that :2X-Y+5Z / 3Y-X =3. note :: (/) is for a fraction aka divide. help pls I've been stuck on it for a few days​

Answers

The given equation

x/2 = y/3 = z/4

can be broken into three separate equations which I'll call equations (A), (B) and (C)

x/2 = y/3 ..... equation (A)y/3 = z/4 .... equation (B)x/2 = z/4 .... equation (C)

We'll start off solving for z in equation (C)

x/2 = z/4

4x = 2z ... cross multiply

2z = 4x

z = 4x/2 ... divide both sides by 2

z = 2x

Now let's solve for y in equation (A)

x/2 = y/3

3x = 2y

2y = 3x

y = 3x/2

y = (3/2)x

y = 1.5x

The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.

We won't be using equation (B) at all.

---------------------

The key takeaway from the last section is that

z = 2xy = 1.5x

Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:

(2x-y+5z)/(3y-x)

(2x-y+5(2x))/(3y-x) ..... plug in z = 2x

(2x-y+10x)/(3y-x)

(12x-y)/(3y-x)

(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x

(12x-1.5x)/(4.5x-x)

(10.5x)/(3.5x)

(10.5)/(3.5)

3

We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.


Does anyone get this??

Answers

Answer:

the answer is 12m

Step-by-step explanation:

u know the side c and side B.

C=15m but u have to square it which is 225

B=9m but u have to square it which is 81. then subtract 82 from 225.which will give u 144 which is a perfect square route of 12

solve the equation 5x+x-7=4x-2-x

Answers

Answer:

[tex]x=\frac{5}{3}[/tex]

Step-by-step explanation:

Brainliest pls?

Find the product:
[tex] \frac{1}{8} \times \sqrt{8} [/tex]

Answers

Answer:

≈ 0.35

Step-by-step explanation:

First simplify [tex]\sqrt{8}[/tex] and [tex]\frac{1}{8}[/tex] :

[tex]\sqrt{8}[/tex] ≈ 2.83

[tex]\frac{1}{8}[/tex] = 0.125

Now multiply them as shown in the original equation:

0.125 x 2.83 = 0.35375 ≈ 0.35

Find the area of each figure

Answers

Answer:

flu

Step-by-step explanation:

ugh

if 10 apples cost $1 how much would it cost per Apple

Answers

Answer:

10 cents per apple

Step-by-step explanation:

1 divided by 10 which is 1. And move the decimal one place to the left, leaving you with .1 or 0.1 or 0.10

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