F^-1(4) when f(x) = 3x - 4/ 5

The solution is x = 7 and y= 3

Solution:

Given pairs of equation are:

x = 1 + 2y ------- eqn 1

2x + y = 17 ------- eqn 2

We have to use algebraic method

Algebraic method involves substitution and elimination method

Let us use the substitution method

From equation 1, we can see that x is equal to 1 + 2y. If we substitute this for y in equation 2, we have:

2(1 + 2y) + y = 17

Solve for brackets

2 + 4y + y = 17

Combine the like terms which has same variable

2 + 5y = 17

5y = 17 - 2

5y = 15

Divide both sides of equation by 5

y = 3

So the value of y is 3. This value of y can be substituted into either equation 1 or 2 to find the value of x

Substitute y = 3 in eqn 1

x = 1 + 2(3)

x = 1 + 6

x = 7

So the solution is x = 7 and y = 3

Answer:

The length of the rectangle is 76 feet and the width of the rectangle was 25 feet that is extended by x feet.

Step-by-step explanation:

The total area, in square feet, of a rectangular stage that has been widened by x feet, is represented by 1,900 + 76x.

Now, factorizing the expression for the area we get,

A = 1900 + 76x

⇒ A = 76(25 + x)

Therefore, from the above expression, we can assume that the length of the rectangle is 76 feet and the width of the rectangle was 25 feet that is extended by x feet. (Answer)

Answer:

c 2x+1

Step-by-step explanation:

Answer: 21.5

Step-by-step explanation:

Rounding 15.89: Find the number in the tenth place  8  and look one place to the right for the rounding digit  9 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 . = 15.9

Rounding 5.557: Find the number in the tenth place  5  and look one place to the right for the rounding digit  5 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .  = 5.6

Sum up 15.9+5.6 and get 21.5

Answer:

This is not a direct variation

Step-by-step explanation:

if 12 dollars for 6 bagels is true then each bagel is $2

if 9 dollars for 24 bagels then each bagel is $0.38

Answer:

b=4

Step-by-step explanation:

6b+2=2b+18 add and subtract like terms

-2b. -2b

4b+2=18

-2. -2

4b=16

----- ----- divide

4. 4

b= 4

Answer: b = +4

Step-by-step explanation: When we have this kind of a setup, we want to put our variables together on one side of the equation and our numbers together on the other side of the equation.

So first, let's put our variables together on the left side by subtracting 2b from both sides of the equation. That gives us 4b + 2 = 18.

Now we can move our numbers to the right by subtracting 2 from both sides and we get 4b = 16.

Divide both sides by 4 and b = +4.

A general term used to refer to buying and selling of homes is the house market.

Final answer:

The term 'real estate' is generally used to describe the buying and selling of homes, covering both new home construction, which impacts real GDP, and the resale of existing homes, which is a significant component of the housing market.

Explanation:

The general term commonly used to refer to the buying and selling of homes is real estate. This term encompasses the market for new homes, which are part of real gross domestic product (real GDP), as well as the resale of existing homes. While the buying and selling of existing homes is not counted in real GDP, it is a significant part of the housing market. Real estate can be influenced by factors such as supply and demand, economic conditions, and demographics. The American Association of Realtors suggests that when there is a six months' supply of houses, the market is considered to be in equilibrium, which can help determine whether housing prices are likely to rise or fall.

Rachel needs 1776 inches of board

Solution:

Given that, Rachel is making a planter box

Her box measures 345 inches long and 543 inches wide

Length = 345 inches

Width = 543 inches

To find: Inches of board she needs

So we need to find the perimeter of the board

The board is usually of rectangular shape

Perimeter of rectangle is given as:

Perimeter = 2(length + width)

Perimeter = 2(345 + 543)

Perimeter = 2(888)

Perimeter = 1776

Thus she needs 1776 inches of board

36 chairs are left

Solution:

Given that, 240 beach chairs are on sale

85% of the chairs are sold

To find: remaining chairs

Total number of chairs = 240

Number of chairs sold = 85 % of total chairs

Number of chairs sold = 85 % of 240

[tex]\rightarrow 85 \% \text{ of } 240\\\\\rightarrow \frac{85}{100} \times 240\\\\\rightarrow 204[/tex]

Thus 204 chairs are sold

Remaining chiars = total chairs - sold chairs

Remaining chairs = 240 - 204 = 36

Thus 36 chairs are left

36 chairs are left

the store sold 204 chairs

Answer:

Although our example says the correct answer is 2/3 x 1/2, remember, with multiplying ... If we divide both 525 and 700 by 175, we can see that 525/700 is equal to 3/4.

Step-by-step explanation:

Final answer:

To solve '4/6 times what equals 1/6', you need to find the reciprocal of 4/6 and multiply it by 1/6. The reciprocal of 4/6 is 6/4, and when you multiply this by 1/6, you get 1/4. Thus, 4/6 times 1/4 equals 1/6.

Explanation:

The question asks for the unknown value that when multiplied by 4/6 gives the result of 1/6. To find the unknown value, you would set up the equation:

[tex]\(\frac{4}{6} \times x = \frac{1}{6}\)[/tex]

To find the value of x, you can divide both sides of the equation by 4/6. In other words, you are looking for the reciprocal of 4/6 that, when multiplied by 1/6, gives 1. The reciprocal of 4/6 is 6/4. Thus, when you perform the division, you get:

[tex]\(x = \frac{1}{6} \times \frac{6}{4}\)[/tex]

To simplify, you multiply the numerators and the denominators:

[tex]\(x = \frac{1 \times 6}{6 \times 4}\)[/tex]

[tex]\(x = \frac{6}{24}\)[/tex]

Since 6 and 24 have a common factor of 6, you can simplify the fraction:

[tex]\(x = \frac{1}{4}\)[/tex]

Therefore, 4/6 times 1/4 equals 1/6.

Answer:

Step-by-step explanation:

the sum of a negative number and a positive number will always be negative.

counter example :

-1 + 3 = 2

-2 + 5 = 3

-1 + 7 = 6

this is only sometimes true....

-5 + 3 = -2........-3 + 5 = 2

-6 + 1 = -5......-1 + 6 = 5

The sum of a negative number and a positive number always will not be negative.

The given statement is the sum of a negative number and a positive number will always be negative.

We need to find a counter example to the statement.

The rule for adding integers with different signs is to retain the sign of the absolute value of the bigger number and subtract the absolute value of the bigger number from the smaller number.

Example:

-1+3=2 and -7+8=1

Therefore, the sum of a negative number and a positive number always will not be negative.

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Answer:

6. The equation needs to be correct for every pair (x, y) of values from the table. If we want to find the right equation, we simply plug a pair from the table and see if it fits. Let's take the first pair (1, -2) and plug it in the equation a):

-2 = 1+2 ---> obviously not correct

Now let's do the same for equation b):

-2 = 3+3 ---> again incorrect

Equation c):

-2 =1-11 --> incorrect

And equation d):

-2 = 2-4 ---> correct

It's important to know that we could've chosen any pair from the table to check the equation. However, sometimes one pair can fit into more than one equation. In that case, we have to plug in other pairs as well to see which equation is the right one.

7. Scale factor, simply put, shows how many times one value of the figure changed when mapping onto another.  

We are given the triangle ABC. Let's say the side of each of these little squares in 1 unit. That way, we conclude that the length AB is 4 units and BC is 3 units.

Now, let's look at the triangle A'B'C'. Length of the A'B' is 12 units and B'C' is 9 units.

Now to find the scale factor we simply have to find how many times are the sides of the mapped triangle greater then the triangle ABC:

AB/A'B' = BC/B'C' = 3

So, the scale factor is 3.

8. Note that the plumber charges two fees:

- base fee is a constant fee, for all appointments, regardless of the repair needed and hours spent.

- repair fee is a fee paid only if the repair is needed and is dependent on the number of hours spent repairing (more hours greater the fee)

So, in our equation

y = 25x + 30

y represents the total cost and x represents hours.

Now, we can see that this 25x part of equation represents repair fee, because it depends on x (for every hour spent, one pays another $25).

That means that 30 from our equation represents the base fee, the amount everyone will be charged regardless of the need for repair.

9. A relationship is linear if it's graph is a straight line, which means that its rate of change is constant. That means that the change in values of x of the two adjacent points, divided by the change of y is always the same number. That means that:

(x2 - x1)/(y2-y1) = (x3 - x2)/(y3 - y2) = (x4 - x3)/(y4 - y3) etc.

Let's test this.

Our first point is (0, 1) and next one is 1, 2). So, our first change of rate is:

(1-0)/(2-1) = 1/1 = 1

Let's find the rate of change for the next two adjacent pairs:

(x2, y2) = (1, 2)

(x3, y3) = (2, 4)

So, the rate of change is:

(2-1)/(4-2) = 1/2  

It's obvious that the rate of change isn't always the same, which means this relation isn't linear.

Answer:

12 times k equals 84

Hope this helps

-Amelia

Answer:

D

Step-by-step explanation:

$974.95 + $246.00 + $98.48 - $721.00 - $35.35 - $3.00 + $0.75 = $560.83

Eric Schneider's present balance is calculated by adding his previous balance and deposits, subtracting the checks written and service fees, and then adding any interest earned. The result is $560.83.

In order to find Eric Schneider's present bank balance, we need to add the money he deposited to his previous balance, subtract any checks he wrote and service charges, and add any interest earned. So, to break this down:

So, Eric Schneider's new balance is $560.83 (option d).

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Answer:

3

Step-by-step explanation:

y=3x+7

y=mx+b where m=slope and b=y-intercept

Answer: [tex]-31\ \°F[/tex]

Step-by-step explanation:

Degrees Celsius and Degrees Fahrenheit are defined as units of measurement of temperature.

In order to make the conversion from Degrees Celsius to Degrees Fahrenheit, you need to follow these steps:

Step 1: You must multiply the temperature in degrees Celsius by [tex]\frac{9}{5}[/tex] (or you can multiply it by 1.8).

Step 2: Then you must add 32 to the product obtained.

In this case, according to the information given in the exercise, you know that the reading at an Arctic research station showed that the temperature was [tex]-35\°C[/tex]

Therefore, applying the steps indicated before, you get that that temperature in degrees Fahrenheit is:

[tex]T_{(\°F)}=(-35)(\frac{9}{5})+32\\\\T_{(\°F)}=-31\ \°F[/tex]

Answer:

the price for a dozen is 12.00

Step-by-step explanation:

Answer: the price per dozen is 11.8

Step-by-step explanation:

-you have $2.95 for three muffins

-a dozen = 12

- if you add 2.95 +2.95 +2.95 +2.95 (because 3 muffins are worth $2.95 and it 3 times 4 is equal to 12 for the dozen) you get 11.8

The store bought 90 half gallons of milk.

To find the number of half gallons of milk the store bought, we can set up an equation using the given information.

Let x be the total number of half gallons of milk bought by the store.

The store bought each half gallon of milk for $2.80, so the total cost of x half gallons of milk is 2.80x dollars.

After the refrigerator malfunction, 12 half gallons of milk were ruined. So the remaining milk is x - 12 half gallons.

The remaining milk is sold for $4.00 per half gallon, so the total revenue from selling the remaining milk is 4(x - 12) dollars.

The profit made by the store is given as $60.00, so the equation becomes:

4(x - 12) - 2.80x = 60

Simplifying the equation: 4x - 48 - 2.80x = 60

Combining like terms: 1.20x - 48 = 60

Adding 48 to both sides: 1.20x = 108

Dividing both sides by 1.20: x = 90

Therefore, the store bought 90 half gallons of milk.

292 days

Solution:

Step 1: Given data:

Principal = $2500

Annual rate = 9.3%

Simple interest paid = $186

Step 2: To find the number of year for the loan paid.

Simple interest = [tex]\frac{Principal\times rate\times year}{100}[/tex]

[tex]186=\frac{2500\times9.3\times years}{100}[/tex]

Do cross multiplication.

⇒ 186 × 100 = 2500 × 9.3 × years

⇒ [tex]\frac{186\times100}{2500\times9.3}=years[/tex]

⇒ [tex]years=\frac{4}{5}[/tex]

Step 3: To find how long the loan was paid in days:

1 year = 365 days

Multiply years by 365

⇒ [tex]days=\frac{4}{5}\times365[/tex]

⇒ days = 292

Hence, the loan was paid in 292 days.

Answer:

4/6

Step-by-step explanation: numerator is the top number and denominator is the bottom number so in this case 4 is the numerator and 6 is the denominator.

The fraction with a numerator of 4 and a denominator of 6 is 4/6, which simplifies to 2/3.

To write a fraction with 4 as the numerator and 6 as the denominator, we simply place 4 above 6, resulting in the fraction 4/6. This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which in this case is 2. Therefore, the simplified fraction is 2/3.

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Answer:

Therefore, 3 feet less than the Legnth is

[tex]Length - 3[/tex]  OR

[tex]L - 3[/tex]

Step-by-step explanation:

What is 3 feet less than the Legnth  ?

Solution:

It is the Algebraic Expression in Statement form.

Algebraic Expression is given in the form numbers and variables with the operands such as,

' + ' Plus Sign

' - ' Minus Sign

' × ' Multiplication Sign

' ÷ ' Division Sign, etc.

Here let Length be the variable denoted as 'L'

So .3 feet less means Subtract 3,

'Than the Length' means from the Length,

Then the Expression will be

[tex]Length - 3[/tex]  OR

[tex]L - 3[/tex]

Therefore, 3 feet less than the Legnth is

[tex]Length - 3[/tex]  OR

[tex]L - 3[/tex]

Answer:

B. [tex](x,y)\rightarrow (x-4,y+3)[/tex]

Step-by-step explanation:

To get from point A to point A', you need to move 4 unite to the left and 3 units up.

To get from point B to point B', you need to move 4 unite to the left and 3 units up.

To get from point C to point C', you need to move 4 unite to the left and 3 units up.

To get from point D to point D', you need to move 4 unite to the left and 3 units up.

Hence, the translation rule is

[tex](x,y)\rightarrow (x-4,y+3)[/tex]

Answer:

The dimensions of the original sheet of paper are 8 inches by 6 inches.

The total area of the sheet of paper = 8 inches [tex]\times[/tex] 6 inches  = 48 [tex]inches^{2}[/tex]

Step-by-step explanation:

i) the two parts of the sheet of paper are 6 inches by 5 inches and 3 inches by   6 inches.

ii) therefore we see that the both parts have a 6 inch side.

iii) therefore we can say that the width of the sheet of paper is = 6 inches

iv) therefore we can also say that the length of the sheet of paper =  3  +  5 inches  = 8 inches.

v) therefore the dimensions of the original sheet of paper are 8 inches by 6 inches.

vi) therefore the total area of the sheet of paper = 8 inches [tex]\times[/tex] 6 inches

                                                                          = 48 [tex]inches^{2}[/tex]

11

Step-by-step explanation:

subtract 4 from 48 which gives you 44

then divide 4 by 44 to leave t alone

that would give you 11

t equals 11

[tex]g(x) = 2(x-2)^2-5 \text{ is equivalent to } 2x^2-8x+3[/tex]

Solution:

Given expression is:

[tex]f(x) = 2x^2-8x+3[/tex]

We have to find the equivalent expression

[tex]\mathrm{Write}\:2x^2-8x+3\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2[/tex]

[tex]f(x) = 2x^2-8x+3[/tex]

[tex]\mathrm{Factor\:out\:}2[/tex]

[tex]2\left(x^2-4x+\frac{3}{2}\right)[/tex]

[tex]\mathrm{Add\:and\:subtract}\:\left(-2\right)^2\:[/tex]

[tex]2\left(x^2-4x+\frac{3}{2}+\left(-2\right)^2-\left(-2\right)^2\right)[/tex]

Simplify the above equation

[tex]2(x^2-4x + \frac{3}{2} + 4 -4)\\\\2(x^2-4x +4 + \frac{3}{2} - 4)\\\\2(x^2-4x +4 -\frac{5}{2}) ------- eqn 1[/tex]

Using the algebraic identity,

[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]

Therefore,

[tex]x^2-4x+4=\left(x-2\right)^2[/tex]

Substitute the above in eqn 1

[tex]2((x-2)^2-\frac{5}{2})[/tex]

Simplify the above equation by multiplying 2 with terms inside the bracket

[tex]2(x-2)^2 -5[/tex]

Thus the equivalent expression is [tex]g(x) = 2(x-2)^2-5[/tex]

Answer: There were 22 cats and 3 dogs at the shelter on Tuesday.

Step-by-step explanation:

Let be "c" the number of cats at the shelter on Tuesday and  "d" the  number of dogs at the shelter on Tuesday.

Set up a System of equations:

[tex]\left \{ {{c+d=25} \atop {4.5c+8d=123}} \right.[/tex]

You can use the Elimination Method to solve the System of equations.

The steps are:

1. Multiply the first equation by -8.

2. Add the equations.

3. Solve for the variable "c".

Then:

[tex]\left \{ {{-8c-8d=-200} \atop {4.5c+8d=123}} \right.\\....................\\-3.5c=-23\\\\c=22[/tex]

4. Substitute the value of "c" into the first original equation.

5. Solve for the variable "d" in order to find its value.

Then, you get:

[tex]22+d=25\\\\d=25-22\\\\d=3[/tex]

Answer:

-3 or 4

Step-by-step explanation:

If I am wrong I am sorry :[

pls brainlest

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&if&a\geq0\\-a&if&a<0\end{array}\right\\\\x\geq0,\ \text{then}\ |x|=x\\\\x+|x|=x+x=2x\geq0[/tex]

Answer:

92 ft squared

Step-by-step explanation:

6*7=42

5*10=50

42+50=92 ft squared

Answer:

120

Step-by-step explanation:

hope this helps :) have a good day

Answer:

From Walter's steps we have that Step2: Reason 2 is incorrect.

The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )

Step-by-step explanation:

Given equation is three halves times x plus ten equals forty

It can be written as below

[tex]\frac{3}{2}x+10=40[/tex]

To solve the given equation :

Step1 Reason1 : [tex]\frac{3}{2}x+10=40[/tex]

Step2 Reason2: Subtracting 10 on both sides of the above equation we get

[tex]\frac{3}{2}x+10-10=40-10[/tex] which is Subtraction property of equality

Step3 Reason3: [tex]\frac{3}{2}x=30[/tex]

Step4 Reason4: Multiply the above equation into [tex]\frac{2}{3}[/tex] on both sides we get

[tex]\frac{3}{2}x\times \frac{2}{3}=30\times \frac{2}{3}[/tex]

which is the Multiplication Property of Equality

Step5 Reason5: Simplify the above equation we get

 [tex]x= \frac{60}{3}[/tex]

Therefore x=20

From Walter's steps we have that Step2: Reason 2 is incorrect.

The correct reason is Subtraction property of equality (we are using this property only not addition property of equality )

Answer:

b

Step-by-step explanation: