RSM Question NEED HELP!!! A cyclist rides into the country at an average speed of 10 miles per hour. When his bicycle gets a flat tire, he walks it back at an average speed of 3 miles per hour. If he returns home 6 and a half hours after he starts, how far into the country does he go?

Answer:

part A:

M = 4(2x + 6)

   = 8x + 24

part B:

option 1) i think the x value is equal for both M and N since they have the value 8.

option 2)  If you meant to solve M and N with an EQUATION then here's your answer:

8x+24 = 8x+10

24≠10   (you subtract 8x when taken to the other side)

So, the answer would be NO SOLUTION

Final answer:

To apply the distributive property to expression M, multiply each term inside the parentheses by 4, resulting in M = 8x + 24. Comparing this to expression N, which is N = 8x + 10, one can see that M and N are not equivalent because their constant terms differ.

Explanation:

Part A: Equivalent Expression for M

To find an equivalent expression for M, we use the distributive property which states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Therefore:

M = 4(2x + 6)

Apply the distributive property to get:

M = (4 × 2x) + (4 × 6)

M = 8x + 24

Part B: Are M and N Equivalent?

To determine if M and N are equivalent expressions, we must compare the expressions that we have for M and N:

M = 8x + 24

N = 8x + 10

Since the coefficients of x are the same but the constant terms are different, the two expressions are not equivalent for any value of x.

Answer:

The two numbers are 15 and 6.

Step-by-step explanation:

Given:

The difference between two numbers is 9.

The first number plus twice the other number is 27.

Now, to find the two numbers.

Let the first number be [tex]x.[/tex]

And the other number be [tex]y.[/tex]

So, the difference between two numbers is 9.

[tex]x-y=9[/tex]

[tex]x=9+y[/tex]    ............(1)

As, given the first number plus twice the other number is 27.

According to question:

[tex]x+2y=27[/tex]

Substituting the value of [tex]x[/tex] from equation (1):

[tex](9+y)+2y=27\\9+y+2y=27\\9+3y=27[/tex]

Subtracting both sides by 9 we get:

[tex]3y=18[/tex]

Dividing both sides by 3 we get:

[tex]y=6.[/tex]

The other number = 6.

Now, substituting the value of [tex]y[/tex] in equation (1):

[tex]x=9+y\\x=9+6\\x=15.[/tex]

The first number = 15.

Therefore, the two numbers are 15 and 6.

The value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x) for x=2

Step-by-step explanation:

We have to write the given problem mathematically to solve it

So,

[tex]4(5x-8) = 2(4-x)+4[/tex]

First of all, distributive property will be applied

[tex]20x-32 = 8-2x+4\\20x-32 = 12-2x[/tex]

We have to isolate the variable on one side of the equation

Adding 2x on both sides of equation

[tex]20x-32+2x = 12-2x+2x\\22x-32 = 12[/tex]

Addition property of equality with 32

[tex]22x-32+32 = 12+32\\22x = 44[/tex]

Division Property of Equality (22)

[tex]\frac{22x}{22} = \frac{44}{22}\\x = 2[/tex]

Hence,

The value of the expression 4(5x–8) is 4 more than the value of the expression 2(4–x) for x=2

Keywords: Linear equation, variables

Learn more about linear equations at:

#LearnwithBrainly

i suppose that 3.5% means every 100g of water there is 3.5g if salt...so...

3.5g ->100g

1g ->100/3.5

100g->(100/3.5)*100

=10000/3.5

2857.1428g

=2.857kg

Answer:

3.5 grams

Step-by-step explanation:

100g x 3.5% = 3.5 grams

Answer:

y = 25

Step-by-step explanation:

Given that the quantities are proportional then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition y = 10 when x = 6

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex]

y = [tex]\frac{5}{3}[/tex] x ← equation of proportion

When x = 15, then

y = [tex]\frac{5}{3}[/tex] × 15 = 5 × 5 = 25

Answer:

x=-8, y=-2. (-8, -2).

Step-by-step explanation:

y-x=6

y+x=-10

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

2y=-4

y=-4/2=-2

-2-x=6

x=-2-6=-8

Answer:

x=-8, y=-2. (-8, -2).

Step-by-step explanation:

Answer:

Step-by-step explanation: 2:16 because Proportion is a mathematical concept, which states the equality of two ratios or fractions. meaning it's kind of  like equivalent fractions and if you times 1/8 times 2 you get 2/16 and all you do is turn it into a ratio  

Answer:

The correct option is c) n=5.

Therefore the solution to

[tex]3n+4=24-n[/tex]

is

[tex]n=5[/tex]

Step-by-step explanation:

Given:

[tex]3n+4=24-n[/tex]

To Find;

n = ?

Solution:

[tex]3n+4=24-n[/tex]      ........Given

Add + n to both the side

[tex]3n+4+ n=24-n+n\\4n+4=24[/tex]

Now Subtract 4 on both the side

[tex]4n+4-4=24-4\\4n=20[/tex]

Dividing by 4 on both side

[tex]\dfrac{4n}{4}=\dfrac{20}{4}\\\\n=5[/tex]

Therefore the solution to

[tex]3n+4=24-n[/tex]

is

[tex]n=5[/tex]

Answer:

0.800

Step-by-step explanation:

its almost 0.800

Answer:

.800

If the second digit after the decimal is 50 or is over 50 you change the first digit after the decimal point to the next digit up, and make the rest of the digits after the decimal point zero. If it is lower than 50 then you do the same but keep the same first number after the decimal point.

The chances of it being less than 5 is 4/6

So if he spins it 150 times the chances of it landing on 5 or less than it will be: 4/6 * 150 = 100 (c)

Answer:

i think its c 100

Step-by-step explanation:

sorry if it makes no sense

The sequence is a function

Step-by-step explanation:

The sequence is given as;

[tex]A_n=A_n-1 +25[/tex]

where n is the number of months since his initial deposits, and A₀=50

The sequence is a function because its domain is a set of natural numbers.

For example,

A₁=A₀+25 =75

A₂=A₁+25=100

A₃=A₂+25=125

A₄=A₃+25=150

Learn More

Sequence:https://brainly.com/question/14005212

Keywords : saving, college, depositing, amount, money, modeled, sequence

#LearnwithBrainly

Answer:

Yes, because for each input value, , there is only one possible output value.

Step-by-step explanation:

i just did it on IM

Step-by-step explanation:

[tex](+)(+)=(-)(-)=(+)\\(+)(-)=(-)(+)=(-)\\\\-(-x-3)=-1(-x-3)\qquad\text{use the distributive property}\\\\=(-1)(-x)+(-1)(-3)=x+3[/tex]

Answer:

The four consecutive even integers are 4, 6, 8 and 10.

Step-by-step explanation:

Let the four consecutive even integers be [tex]x, x+2, x+4, x+6[/tex]

It is provided that the sum of these consecutive even integers is 28.

Solve for x as follows:

[tex]x+ x+2+ x+4+ x+6=28\\4x+12=28\\4x=16\\x=4[/tex]

The four consecutive even integers are:

[tex]x=4\\x+2=4+2=6\\x+4 = 4 +4 =8\\x+6=4+6=10[/tex]

Thus, the four consecutive even integers are 4, 6, 8 and 10.

No they are not.

8÷2=4

2÷8=0.25

Step-by-step explanation:

The price has gone up by 30% each year so each year it is 130% compared to last year. that means a price rate of 1.3^n, with n as number of years gone by. In this case n=3 so 1.3^3=2.197. $120,000.00×2.197=$263,640.00, which is D

Answer: [tex]3a\sqrt[3]{b^{7}}[/tex]

Step-by-step explanation:

We have the following expression:

[tex]\sqrt[3]{27 a^{3} b^{7}}[/tex]

This can be rearranged as:

[tex]\sqrt[3]{27} \sqrt[3]{a^{3}} \sqrt[3]{b^{7}}[/tex]

Since [tex]\sqrt[3]{27}=3[/tex] and [tex]\sqrt[3]{a^{3}}=a[/tex] we have:

[tex]3a\sqrt[3]{b^{7}}[/tex] This is the simplest form

Answer:

3ab^2 (^3sqrt{ b}) or A on Edg. 2020

Step-by-step explanation:

Answer:

$242.19

Step-by-step explanation:

6 1/4 as a percent: 25/400

25*3,875= 96,875

96,875^400=242.1875, rounded is equal to $242.19

For radius x, Choice 'A' π/4 is the correct answer.

For radius 10x, Choice 'B' π/4 is the correct answer.

For radius 100x, Choice 'B' π/4 is the correct answer.

Step-by-step explanation:

The Area of the circle = πr^2, where "r" is the length of the radius.

The Area of square = a^2, where "a" is the length of an edge of a square.

CASE 1 :

Substitute radius r = x and edge length a = 2x,

Area of circle = π*x*x = πx^2

Area of square = 2x*2x = 4x^2

The ratio of the area of the circle to the area of square = πx^2 / 4x^2 = π/4

Choice 'A' π/4 is the correct answer.

CASE 2 :

Substitute radius r = 10x and edge length a = 20x,

Area of circle = π*10x*10x = 100πx^2

Area of square = 20x*20x = 400x^2

Ratio of the area of the circle to the area of square = 100πx^2 / 400x^2

                                                                                         = π/4

Choice 'B' π/4 is the correct answer.

CASE 3 :

Substitute radius r = 100x and edge length a = 200x,

Area of circle = π*100x*100x = 10000πx^2

Area of square = 200x*200x = 40000x^2

Ratio of area of the circle to the area of square = 10000πx^2 / 40000x^2

                                                                                  = π/4

Choice 'B' π/4 is the correct answer.

Answer:

  factor

Step-by-step explanation:

We assume this is a vocabulary question and you want the word that has the definition you have supplied.

Such an expression is called a factor.

Answer:

Explanation:

The given information can be summarized in this way:

Following Newton's second law, net force equal mass times acceleration:

To predict the motion, you apply Newton's second law in each direction (vertical and horizontal)

        Net vertical force = 8N - 8N = 0. This means there is not motion in the vertical direction.

         Net horizontal force = 6N - 4N = 2N. This means there is a net force of 2N to the right, which lets you predict that the bone starts to accelerate to the right; this is, the bone begins to move toward the right.      

Answer:

A. It begins to move toward the right.

Step-by-step explanation:

Answer: x = 42

Step-by-step explanation:

Step  1  :

           x

Simplify   —

           3

Equation at the end of step  1  :

 x    

 — -  14  = 0  

 3    

Step  2  :

Rewriting the whole as an Equivalent Fraction :

2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         14     14 • 3

   14 =  ——  =  ——————

         1        3    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x - (14 • 3)     x - 42

————————————  =  ——————

     3             3    

Equation at the end of step  2  :

 x - 42

 ——————  = 0  

   3    

Step  3  :

When a fraction equals zero :

3.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 x-42

 ———— • 3 = 0 • 3

  3  

Now, on the left hand side, the  3  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  x-42  = 0

Solving a Single Variable Equation :

3.2      Solve  :    x-42 = 0  

Add  42  to both sides of the equation :  

                     x = 42

Your answer: x = 42

Answer:

42

Step-by-step explanation:

x / 3 = 14.

The question required you to solve for x.

First, multiply both the LHS and the RHS by 3. The aim is to make x independent.

x/3 * 3 = 14 * 3

Therefore:

x = 42

hmmm first off, let's convert the decimal to a fraction, and then the mixed fraction to an improper fraction and proceed from there.

[tex]\bf 6.\underline{2}\implies \cfrac{62}{1\underline{0}}\implies \cfrac{31}{5}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ 6.2\div (2x+1)=2\frac{1}{3}\div 4\implies \cfrac{31}{5}\div (2x+1) = \cfrac{7}{3}\div 4[/tex]

[tex]\bf \cfrac{31}{5}\div \cfrac{(2x+1)}{1} = \cfrac{7}{3}\div \cfrac{4}{1}\implies \cfrac{31}{5}\cdot \cfrac{1}{(2x+1)} = \cfrac{7}{3}\cdot \cfrac{1}{4}\implies \cfrac{31}{5(2x+1)}=\cfrac{7}{12} \\\\\\ \cfrac{31}{10x+5}=\cfrac{7}{12}\implies \stackrel{\textit{cross multipling}}{372 = 7(10x+5)}\implies 372=70x+35\implies 337=70x \\\\\\ \cfrac{337}{70}=x\implies 4\frac{57}{70}=x\implies 4.81\approx x[/tex]

Answer:

$7 per cupcake

Step-by-step explanation:

A unit rate is the cost of one item. So we would do $168 divided by twenty-four. That would be equivalent to seven.

Answer:

Let's use these two sets given to explain what is the domain.

Each value from the left set is x, and from the right is f(x).

If we plug any x from the left set in the function, we'll get f(x)  that corresponds to it and that's exactly what the arrows are showing.

Domain of the function is, basically, a set of all values x can have.

In this case, it's easy to see, those are all members of the left set (-6, 1, 5, 8), but sometimes this set can have lots and lots of members, even infinity.

Answer:

n = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

3(n+1) = 4

distributive property means multiply every term in the parentheses by the number on the left and add the new terms.

(3*n) + (3*1) = 4

3n + 3 = 4

     -3    -3         subtract 3 from both sides.

3n = 1

/3     /3                divide by 3 on both sides.

n = [tex]\frac{1}{3}[/tex]

The given statement, "Deposits of gold can be found in the deep ocean" is true.

Explanation:

According to the report of National Ocean service, oceans have nearly 20 million pounds of gold that are suspended in normal sea water to the tune of parts per trillion. Deep down the ocean floor, larger amount of gold are encased in rocks that could be mined. But mining in the deepest part of the ocean is not much cost efficient and would not bring any profits. Moreover, since gold will not get decomposed by salt water, it stays undisturbed on the ocean floor.

Answer:

ture!!!!!

Step-by-step explanation:

To answer the question, we evaluated two absolute value expressions individually by converting mixed numbers to improper fractions, performing the operations, and taking absolute values. The sum of these evaluations is 14.

The question involves evaluating two absolute value expressions and adding the results. We will work through each expression step by step.

First Expression

|6 3/8 - 2|

To solve this, convert the mixed number to an improper fraction, subtract 2, and then find the absolute value.

Convert 6 3/8 to an improper fraction: (6 × 8) + 3 = 51/8.

Subtract 2 (written as 16/8) from 51/8: 51/8 - 16/8 = 35/8.

The absolute value of 35/8 is 35/8, as it is already positive.

Second Expression

|-8 5/8 + (-1)|

Similar approach: convert to an improper fraction, add -1, and find the absolute value.

Convert -8 5/8 to an improper fraction: (-8 × 8) - 5 = -69/8.

Add -1 (written as -8/8) to -69/8: -69/8 - 8/8 = -77/8.

The absolute value of -77/8 is 77/8, as we discard the negative sign in absolute value operations.

Add the results of both expressions: 35/8 + 77/8 = 112/8 = 14.

Answer:

12

Step-by-step explanation:

8(4)-20

32-20

12

Answer:

Below.

Step-by-step explanation:

You could multiply the first equation by 3 and the second one by -2 so that the 2 y terms would be -6y and 6y:

12x - 6y =  21

-6x + 6y = -30

Adding these will eliminate the y variable.