When you isolate the variable, the goal is to get the variable
A
to equal 1.

B
on both sides of the equal sign to show they are equal.

C
by itself on one side of the equal sign and a value on the other.

D
by itself on one side of the equal sign and zero on the other side.

Step-by-step explanation:

If [tex]mKg[/tex] of mass is placed on spring with spring constant [tex]k[/tex],

[tex]mg=kx[/tex]

where [tex]g[/tex] is universal gravitational constant

[tex]x[/tex] is the displacement in the spring.

In case 1:

[tex]25g=k(0.15)\\k=\frac{25g}{0.15}[/tex]

In case 2:

[tex]mg=k(0.23)[/tex]

Using  result from case 1,

[tex]mg=\frac{25g}{0.15}\times 0.23[/tex]

[tex]m=[/tex][tex]38.33Kg[/tex]

Answer:70

Step-by-step explanation:

You do the inverse operation which would be subtraction and multiplication. You add the 6 to the 8 and you get 14. Then you would multiply 14 by 5 to get 70. Hope this helps :D

Answer:

Step-by-step explanation:

Answer:

Area = 12 ft²

Step-by-step explanation:

Convert values to feet

12 inches = 1 foot

48 / 12 = 4 feet

36 / 12 = 3 feet

Area = l x w = 3 x 4 = 12 ft²

Answer: The answer is 1,728 in. squared

Step-by-step explanation:

All you do is multiply 48 by 36 because in order to get area,you multiply base and height.

Good evening ,

Answer:

15x⁷y⁵.

Step-by-step explanation:

5x³y²×3x⁴y³ = (5×3)(x³x⁴)(y²y³) = 15x⁷y⁵.

:)

Answer:

g(x) = |x+3| - 5

Step-by-step explanation:

Let y = f(x)

⇒y = |x+3|

When y is replaced by Y + k, the graph of y = f(x) shifts k units down

⇒ y replaced by Y + 5 translates the graph of y = f(x) 5 units down

∴ Y = g(x) is represented by Y + 5 = |x+3|

⇒ Y = |x+3| - 5

or g(x) = |x+3| - 5

Answer:

The velocity is the speed in a given direction hence the units are the same as that of speed, m/s. Thus the answer is 30 m/s.

Step-by-step explanation:

I do not understand the second option.

Answer:

The length of the first banner = 8 ft

The length of the second banner = 12  ft

The length of the third banner  = 16 ft

Step-by-step explanation:

The total length of the banner material = 36 ft

Now, let us assume the length of the first banner  = k ft

So, the length of the second banner  = First banner + 4 ft = ( k + 4) ft

The length of the third banner = Second banner  + 4 ft  = [( k + 4) + 4]  ft

Now, according to the question:

The length of ( First  + Second + Third) banner  = 36 ft

⇒ (k) + (k +4) + (k + 8)  = 36

or, 3 k = 36 - 12= 24

or, k = 24/3  = 8

⇒ k = 8 ft

So, the length of the first banner = k = 8 ft

The length of the second banner = k + 4 = 8 + 4 = 12  ft

The length of the third banner = k + 4 + 4  = 8 + 8 =  16 ft

Answer:

A

Step-by-step explanation:

Answer:

They need to make 5 pies for 15 people.

Step-by-step explanation:

15*3=45 slices of pie in total,

each pie is cut into 9 slices,

45/9=5 pies

Answer:

8/13.

There's 12 face cards & 26 black cards. In the 26 black cards, theres 6 face cards. Theres 32 cards overall that is either a black card or a face card. So in conclusion the answer is 8/13 because 52 (the total amt in the deck) divided by 32 = 8/13.

The probability of randomly selecting either a face card or a spade from a standard deck of 52 playing cards is approximately 0.4231.

The question involves calculating the probability of selecting either a face card or a spade from a standard deck of 52 playing cards. A standard deck consists of four suits (spades, hearts, diamonds, clubs), each with 13 cards, making a total of 52 cards. Among these, 12 are face cards (Jacks, Queens, Kings across all suits), and 13 are spades (including the spade face cards).

First, note that there are 3 face cards (Jack, Queen, King) in each suit, resulting in 12 face cards in total. However, 3 of these face cards are spades, and we must avoid double-counting them when adding the spade cards. Therefore, we have 12 face cards and 10 non-face card spades (since 3 spades are already counted among face cards), giving us a total of 22 unique cards that fulfill the conditions.

The probability of drawing either a spade or a face card from a deck of 52 cards is calculated by dividing the number of favorable outcomes (22) by the total number of outcomes (52), which is 22/52 or approximately 0.4231.

Answer: Matt's rate is 2 pages per hour.

Step-by-step explanation:

25 hours = 45 pages

1. First, let's divide 45 by 25 to find how much it takes for one page to be done: [tex]\frac{45}{25}[/tex] = 1.8

2. This answer means it takes 1.8 hours to do one page.

3. Now, we can choose to round 1.8, which is 2.

The last house on Oak Street has a house number 8 greater than the last house on Maple Street.

The correct answer is option C.

Let's denote the house numbers on Maple Street as M1, M2, M3, M4, and M5, where each house number is six more than the one to its left. Similarly, on Oak Street, denote the house numbers as O1, O2, O3, O4, and O5, where each house number is eight more than the one to its left.

For Maple Street:

M2 = M1 + 6

M3 = M2 + 6

M4 = M3 + 6

M5 = M4 + 6

For Oak Street:

O2 = O1 + 8

O3 = O2 + 8

O4 = O3 + 8

O5 = O4 + 8

Now, let's find the difference between the last house on Oak Street (O5) and the last house on Maple Street (M5):

The difference is (O4 + 8) - (M4 + 6) = (O3 + 8 + 8) - (M3 + 6 + 6) = (O2 + 8 + 8 + 8) - (M2 + 6 + 6 + 6) = (O1 + 8 + 8 + 8 + 8) - (M1 + 6 + 6 + 6 + 6).

Simplifying the expression, the constant terms cancel out, leaving:

The difference is O1 - M1 + (8 + 8 + 8 + 8) - (6 + 6 + 6 + 6) = O1 - M1 + 32 - 24 = O1 - M1 + 8.

So, the house number of the last house on Oak Street is 8 greater than the house number of the last house on Maple Street.

The question probable may be;

The picture below shows 5 houses on maple street anf the five houses on oak street.

Each house number on maple street is six more than the house number to its left. Each house number on oak street is eigth more than the house number to its left.

How much greater is the house number of the last house on oak street than the house number of the last house on maple street?

2

6

8

10

Answer:

1.5 miles per hour

Step-by-step explanation:

9 (1/6) = 1.5

Answer:

1.5 miles per hour

Step-by-step explanation:

In the attached file

Answer:

13x-12 the last one

Step-by-step explanation:

Answer:

13x-12

Step-by-step explanation:

4(3x-5)+x+8

12x-20 +x+8

13x-12

Answer:

413 minutes of long distance calls

Step-by-step explanation:

$80.00 - $18.00 = $62.00

$62.00/$0.15 = 413.33

The trampoline will attract a sales tax of $12 which will take its total price to $312.

The trampoline costs $300 without taxes being accounted for yet.

The tax is 4%. In dollar terms this is:

= Sales tax percentage x Cost of trampoline

= 4% x 300

= $12

The total price of the trampoline will therefore be:

= Cost of trampoline + sales tax

= 300 + 12

= $312

In conclusion, the sales tax would be $12 and the total price would be $312.

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Answer:

No Solution.

Step-by-step explanation:

-(6x-5)=-6x+13

-6x+5=-6x+13

-6x-(-6x)+5=13

-6x+6x+5=13

0+5=13

5=13

Answer:

Exact form : x=-1/3

Decimal form : x=-0.3 (line over the 3!!!)

Step-by-step explanation: Isolate the variable by divinding each side by factors that don't contain the variable.

Hope this helps you out! ☺

Answer:

Step-by-step explanation:

16

The value of x in the equation 3x + 7x + 9 = 35 is 2.6 after simplification and carrying out the necessary algebraic steps.

The subject of your question is Mathematics, specifically algebra. Now, let's solve the equation: 3x + 7x + 9 = 35.

To start, combine like terms on the left side of the equation. That gives us 10x + 9 = 35. Next, subtract 9 from both sides to isolate the term with x. This gives us 10x = 26. Finally, divide both sides by 10 to find the value of x. So, x = 2.6.

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Answer:

20 full people

Step-by-step explanation:

100-65=35

35/1.16= 30.1724

30.1724/1.5=20.1149

You can't feed a .1149 of a person so 20 people

Given the maximum budget and cost per pound, the largest turkey you can purchase is approximately 30.17 pounds. This will feed about 20 guests, considering each person consumes 1.5 pounds of turkey.

The subject of this question is mathematics, specifically, problem-solving involving budgets and limits. Given that the maximum budget for this dinner is $100 and the fixed costs total to $65, we're left with $35 for the turkey. Each pound of turkey is priced at $1.16.

By dividing the remaining amount of money (which is $35) by the cost per pound of turkey (which is $1.16), we compute the total pounds of turkey we can afford. That is, $35 / $1.16 = approximately 30.17 pounds.

Each guest requires 1.5 pounds of turkey, so we now calculate how many guests can be fed by this amount of turkey. We do this by dividing the total pounds of turkey (30.17 pounds) by the amount required per guest (1.5 pounds), which gives us 30.17 / 1.5 = approximately 20.11. Since you can't invite a fraction of a person, the largest size turkey you can afford can feed about 20 people.

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Answer: m = -120

Step-by-step explanation: In this equation, m is being multiplied by -0.06 so we will need to divide both sides of the equation in order to get m b itself.

On the left side of the equation, the -0.06's cancel and we are left with m. On the right side of the equation, we divide -7.2 by -0.06 and we get -120.

Now we have m = -120

Don't just do this problem in your head. It's extremely important to develop the habit of putting all your steps down on paper/or digitally too. It will really pay off for you down the line.

Image provided.

The weight of crate when it has 19 bricks is 165 pounds

Given that, A crate with 20 bricks weighs 167 pounds.  

When the same crate has 32 bricks, it weighs 191 pounds.  

Now, let the weight of each brick be "m" pounds and weight of the crate be 'n" pounds.

Then, when crate has 20 bricks

Total weight = weight of bricks + weight of crate

[tex]167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }[/tex]

[tex]167=20 \times m+n[/tex]

20m + n = 167 ----- eqn (1)

Now, when crate has 32 bricks

Total weight = weight of bricks + weight of crate

[tex]191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }[/tex]

[tex]191=32 \times m+n[/tex]

32m + n = 191 ----- eqn (2)

Now, subtract (1) from (2)

32m + n = 191

20m + n = 167

(-) ----------------

12m + 0 = 24

m = 2

Then, from eqn (1)  

20(2) + n = 167  

40 + n = 167  

n = 167 – 40 = 127

Now, when the box has 19 bricks

Total weight = 19 bricks x 2 pounds per brick + 127 pounds of crate

[tex]\text { Total weight }=19 \times 2+127=38+127=165[/tex]

Hence, the weight of crate when it has 19 bricks is 165 pounds.

Answer:

i dont know

Step-by-step explanation:

i dont know

For this case we have that by definition, the equation of a line in the standard form is given by:

[tex]ax + by = c[/tex]

According to the statement we have the following equation of the line:

[tex]y + 1 = \frac {2} {5} (x + 3)[/tex]

We manipulate algebraically to write in the standard form. To do this we follow the steps below:

We apply distributive property on the right side of the equation:[tex]y + 1 = \frac {2} {5} x + \frac {6} {5}[/tex]

We subtract [tex]\frac {6} {5}[/tex] on both sides of the equation:

[tex]y + 1- \frac {6} {5} = \frac {2} {5} x\\y- \frac {1} {5} = \frac {2} {5} x[/tex]

We multiply by 5 on both sides of the equation:

[tex]5y-1 = 2x[/tex]

We subtract 5y on both sides of the equation:

[tex]2x-5y = -1[/tex]

Finally, the equation in its standard form is:

[tex]2x-5y = -1[/tex]

Answer:

[tex]2x-5y = -1[/tex]

Answer:

b

Step-by-step explanation:

Answer:

The correct answer is C = It gives reliable results

Answer:

D. it excludes those who are indifferent

Step-by-step explanation:

Answer:

2462.4 square inches

Step-by-step explanation:

To find the length of the longer wall use the following ratio and solve for x.

x/36= 4.75/ 2.5

x= 68.4

Area of a rectangle = l(w)

68.4(36)= 2462.4 square inches

The area of the wall is the product of its dimension.

The area of the actual wall is  2462.4 square inches

The scale is given as:

[tex]\mathbf{Scale = 4.75 : 2.5}[/tex]

The shorter side of the actual wall is 36 inches.

So, we have:

[tex]\mathbf{Long : 36= 4.75 : 2.5}[/tex]

Express as fractions:

[tex]\mathbf{\frac{Long }{36}= \frac{4.75 }{ 2.5}}[/tex]

Multiply both sides by 36

[tex]\mathbf{Long= 36 \times \frac{4.75 }{ 2.5}}[/tex]

[tex]\mathbf{Long= 68.4}[/tex]

So, we have:

[tex]\mathbf{Long= 68.4}[/tex]

[tex]\mathbf{Short= 36}[/tex]

The area is then calculated as:

[tex]\mathbf{Area = 68.4 \times 36}[/tex]

[tex]\mathbf{Area = 2462.4in^2}[/tex]

Hence, the area of the actual wall is  2462.4 square inches

Read more about areas at:

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Mitch paid $ 33600 altogether

Given that mitch took out a school laon for $ 24000

The interest rate on the loan was 8%

Number of years = 5

To find: total amount paid altogether

We can use simple interest to calculate the total amount

Total amount paid altogether = simple interest + principal amount

The simple interest is calculated as:

[tex]\text { simple interest }=\frac{\text { principal } \times \text {rate of interest } \times \text {number of years}}{100}[/tex]

Plugging in values, we get

[tex]\text { simple interest }=\frac{24000 \times 8 \times 5}{100}=240 \times 8 \times 5=9600[/tex]

Total amount paid altogether = simple interest + principal amount

Total amount paid altogether = 9600 + 24000 = 33600

Thus Mitch paid $ 33600 altogether

Answer:

Money spent on each student is $36.17

Step-by-step explanation:

$875.49 = 29 students & 4 teachers

33 people = $875.49

1 person = $26.53 (pass)

29 students = $279.56

1 student = $9.64 (lunch)

each student = $9.64 + $26.53

= $36.17

the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.

To find out how much money was spent on a pass and lunch for each student, we need to calculate the total amount spent on passes and lunch and then divide it by the total number of students.

Given:

- Total amount spent on passes for 29 students and 4 teachers: $875.49

- Total amount spent on lunch for just the students: $279.56

- Total number of students: 29

1. First, let's find the total amount spent on passes for just the students:

  Total amount spent on passes for students and teachers = $875.49

  Total amount spent on passes for 4 teachers = ?

  Total amount spent on passes for students = $875.49 - (amount spent on passes for teachers)

  Since each pass costs the same amount for students and teachers, we can divide the total amount spent on passes by the total number of passes (students + teachers) to find the cost per pass.

  Total number of passes (students + teachers) = 29 students + 4 teachers = 33 passes

  Cost per pass = Total amount spent on passes / Total number of passes

                = $875.49 / 33

                ≈ $26.56 (rounded to two decimal places)

2. Now, let's find out how much money was spent on lunch for each student:

  Total amount spent on lunch for students = $279.56

  Cost per student for lunch = Total amount spent on lunch for students / Total number of students

                              = $279.56 / 29

                              ≈ $9.63 (rounded to two decimal places)

So, the amount spent on a pass and lunch for each student is approximately $26.56 + $9.63 = $36.19.

Alright, so we have the difference = 4500-2800=1700. To find the percent increase, we do 1700/2800=around 0.61 = around 61% percent. Hope I helped! ☺☼

Answer:

Step-by-step explanation:

y ≤ x − 5

1<10-5

1<5

Pair: (10,1)

y ≤ −x − 4

-10<-1-5

-10<-6

Pair: (1,-10)

Answer:

Step-by-step explanation:

If we graph this system of inequalities, we could find the solution.

From the graph you can deduct that the only right answer is the last one (1,-10), because the area of solution is only for negative values of y.

Therefore, the right choice is the last one.

If you can't graph, you can try another method. If we replace the value in the system, it should satisfy it, that is, it should gives us a true result like 0<1 for example. Let's try

For x=1 and y=-10, we have

-10 ≤ 1 − 5

-10 ≤ −1 − 4

-10 ≤ -4

-10 ≤ -5

As you can see, the result is true, because -10 is less than -4 and -5, so that's the right answer.