Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
A furniture store has a sale offering ​10% off of all furniture. If Amanda spent ​$360.99 on furniture before​ tax, what was the price of the furniture she purchased before the discount and before​ tax?

The equation is____. The cost of the furniture before the discount and tax is ​$____
​(Type an equation using x as the​ variable.)

Answer:

Step-by-step explanation:

1.

Only the graph on the left is a function, due to the one on the right failing the vertical line test.

2.

This is asking for a positive x-value of the two functions, we can find that by setting them equal to a common value and then equal to each other.

Lets set them both equal to x.

First equation:

[tex]y=x^2\\\sqrt{y}=x[/tex]

Second equation:

[tex]y^2=x[/tex]

Now we set them equal to each other:

[tex]y^2=\sqrt{y}[/tex]

Then solve for y by squaring both sides:

[tex]y^4=y[/tex]

Now we solve by factoring:

[tex]y^4=y\\y^4-y=0\\y(y^3-1)=0\\y^3-1=0\\y^3=1\\y=\sqrt[3]{1}\\ y=1[/tex]

The method that will not give the correct number of inches is that the total length of the plant in a week is 19/4 inches.

Length of the small plant = 2 1/2 = 5/2 inches

Rate of growth = 3/4 inches

Increase in length in 3 weeks will be:

= 3 × 3/4 = 4

Total length = 5/2 + 9/4

= 19/4 inches.

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Answer:

[tex]g(x) = (x-4)^2\; and \;h(x)= x^2-4 \;are\;\bold{not}\;equivalent[/tex]

Step-by-step explanation:

For two functions g(x) and h(x)  to be equivalent, they must have the same domain and range.

Domain is the set of all values of x(inputs)  that result in a real and defined value for the function

Range is the set of all values of the function that it can take given the values of x in the domain

[tex]g(x)=(x-4)^2=16-8x+x^2\\[/tex]

Can be rewritten as
[tex]g(x) = x^2 -8x + 16[/tex]  The domain of g is unrestricted, g can be any value so the

Domain of g: [tex]-\infty < x < \infty[/tex]
Range of g: Since [tex](x-4)^2[/tex] is always positive including 0, the range of g(x) is g(x) ≥ 0

[tex]h(x) = x^2 - 4[/tex]

Domain of h : [tex]-\infty < x < \infty[/tex] since x can be any value and we will still get a real number as function output

However x² is always zero or a positive number so we have the restriction
x² ≥ 0

Subtract 4 on both sides

x²-4 >= -4

But the above is nothing but the outputs of h(x)

So h(x) >= -4 and can be written as -4 ≤ x ≤ ∞

So we can see that, while the domains of the two functions are the same, their ranges are different

Hence the two functions g(x) and h(x) are not equivalent

Tip
If you have difficulty determining domain and range, take a specific value of x for both functions and check if the function output values are the same. It may not always be easy choosing an appropriate x value depending on the function

For x = 0

g(0) = (0-4)² = (-4)² = 16

h(0) = 0^2 -4 = 0-4 = -4

So we get different output values for the same input value for both functions and therefore they are not equivalent

You can this latter explanation to the above explanation

Hope that helps and is understandable :)

Answer:

Given equations:

To multiply 1 and 2;

[tex]{ \tt{a \times b = (x + y)(x - y)}} \\ = { \tt{(x.x) + (x. - y) + (y.x) + (y. - y)}} \\ = { \tt{ {x}^{2} - xy + xy - {y}^{2} }} \\ = { \tt{ {x}^{2} - {y}^{2} }}[/tex]

Answer:

∠ C = 50°

Step-by-step explanation:

• each lower base angle is supplementary to the upper base angle on the same side.

then

∠ C + ∠ D = 180°

∠ C + 130° = 180° ( subtract 130° from both sides )

∠ C = 50°

Lindsay has the greater balance after one year and also had the greater balance in investment account after 12 years

What does monthly compounding mean?

The monthly compounding means that the interest is computed every month , 12 months a year rather than once a  year.

Monthly compounding?

FV=PV*(1+r)^N

FV=future worth

PV=initial investment=$80

r=monthly interest rate=1%/12=0.000833333333333333

N=number of months in one year=12

FV(1 year)=$80*(1+0.000833333333333333)^12

FV(1 year)=$80.80

FV(year 12)=$80*(1+0.000833333333333333)^(12*12)

FV(year 12)=$90.20

Weekly compounding:

weekly interest rate=2%/52=0.000384615384615385

FV(1 year)=$60*(1+0.000384615384615385)^52

FV(1 year)=$61.21

FV( year 12)=$60*(1+0.000384615384615385)^(52*12)

FV(year 12)=$76.27

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Concluding part of the question:

a. Whose balance is greater after one year?

b. Whose balance is greater after twelve years?

Answer:

1 = 34°

2 = 52°

3 = 38°

4 = 94°

5 = 56°

6 = 38°

Answer:

4-2*3=-2 At first we have to do multiple of2 and 3

then subtract with 4

The 5 friends ordered  16  items of $4 , 5 items of $6 , 3 items of $7 .

Let p and q be two variables and

a₁p+ b₁q=c₁              

a₂p+ b₂q =c₂        

Where a₁, a₂, b₁, b₂, c₁, c₂ are  constants   then  we can solve these simultaneous equations by substitution take value of p from equation (1) and then put it in (2) to get an equation for q only and then solve for q. Put value of q in equation (1) to get value of p.

Let the 5 friends ordered  x number of $4 items , y number of $6 and z number of $7 items

They ordered total a total of 24 items.

Then, x+ y + z = 24      ....(1)

Given that $4  was twice the $6 and $7 items combined

Then, x =2( y+ z )

Put this expression of x in (1),we get

2(y+ z)+ y + z =24

3y + 3z =24

y + z =8   ....(2)

Also given that they split the bill at the end, they each owed $23

Therefore total bill will be 5 times $23 = 5*23 = $ 115

Total money spent on bill = $ 4x+6y+7z

Thus, 4x+6y+7z = 115

Again put  x =2(y+ z) here and get

8(y+ z) +6y+ 7z =115

8y +8z + 6y +7z = 115

14y +15z = 115   ....(3)

Therefore, (2) and (3) is the system of equations we have to solve.

From (2) we get y =8 -z

Put this value of y into (3) and get

14(8-z)+15z =115

112 - 14z +15z =115

z= 115-112 = 3

Then, y = 8-z = 8-3 = 5

x = 2(y+ z)= 2(3+5) =16

Therefore x= 16 , y = 5, z=3  from system of equations generate by (2) and (3)

The 5 friends ordered 16 items of $4 and 5 items of $6 and 3 items of $7.

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The mean weight of the male graders will be 151 pounds.

It should be noted that from the information, the sample of 12 male eleventh graders are: 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165.

We will add the values together and this will be 1812. Also, there are 12 students.

Therefore, the mean will be:

= Total weight / Number of students

= 1812 / 12

= 151 pounds.

Therefore, the mean weight will be 151 pounds.

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Here are weights (in pounds) of sample of 12 male eleventh graders. 152, 175, 148, 175, 155, 175, 163, 166, 174, 164, 165. Calculate the mean weight.

Check the picture below.

Answer: x = -20

▬▬▬▬▬▬▬

[tex]7-7(x)-7=147-7\\-7(x)=140\\= \frac{-7x}{-7}=\frac{140}{-7}\\=-20\\= x = -20[/tex]

▬▬▬▬▬▬▬

Answer Explained:

Using phrases such as subtracted, times, a number, we make an equation using the integers in the equation, and make a variable for the unknown number, x. We then subtracted 7 from both sides, and for the division, substituted 7 as absolute number, |-7|.

Therefore,

7 - 7 × -20 = 147

Main answer:R57 894 is  79.3 dollors.

Concept and definitions should be there:

The formula for calculating exchange rates is: Starting Amount (Original Currency) / Ending Amount (New Currency) = Exchange Rate. For example, if you exchange 100 U.S. Dollars for 80 Euros, the exchange rate would be 1.25.

Given data

Convert R57 894 to dollars if the exchange rate is R7,30 = 1 dollar.

Soving part

The formula for exchanging rates

R (57894/730)

now dividing the starting amount and ending amount we get exchange rate.

Final Answer : 79.3 dollers.

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The probability that a randomly selected person from the survey plays pokemon go who belongs to the Age group 26 - 35 is 0.33.

We have the table for the survey,

                                                   Age 18 - 25         Age 26 - 35        Total

Plays Pokemon Go                            17                         39                  56  

Does not play Pokemon Go              37                         25                  62  

Total                                                    54                         64                  118

From the table,

We have,

The number of people in the age group 18 - 25 who play pokemon go is 17.

The number of people in the age group 18 - 25 who play don't pokemon go is 37.

The number of people in the age group 26 - 35 who play pokemon go is 39.

The number of people in the age group 26 - 35 who don't play pokemon go is 25.

The total number of people participated in the survey are 17 + 39 + 37 + 25 = 118

The total number of people in the Age group 18 - 25 is 54.

The total number of people in the Age group 26 - 35 is 64.

The total number of people that play pokemon go is 56.

The total number of people who do not play pokemon go is 62.

Now,

The probability of choosing a random person from the survey from the age group 26 - 35 who plays pokemon go will be:

= ( no. of people of age group 26 - 35 that play pokemon go) / total no. of people in the survey.

= 39/ 118

= 0.33

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Using inequalities, we can say that Yes, there are more than 1 possible ways to get the answer of inequalities.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Given,

the wavelength is greater than 4/100 nanometer and

less than 4 x 10^-1 nanometer

Let wavelength  = λ

4/100 ≤ λ ≤ 4/10

0.04 ≤ λ ≤ 0.4

or

1/50  ≤ λ ≤ 2/5

So, from the above three equations, we can conclude that there can be more possible ways to have more than 1 correct answer.

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The required solution is 5,14,15,12,14,10,6,16 respectively.

It is required to find round to the nearest tenth.

A number that is easily multiplied, divided, etc., and especially a number that ends in zero.

Given:

The tenth number is the first digit after decimal point. If the second digit is greater than or equal to 5 add 1 to calculate rounding to nearest tenth.

Rounding to the nearest tenth means adjusting the given number to an approximate value without changing the whole part of the number.

5.0 the nearest tenth is 5.

14.0 the nearest tenth is 14.

15.0 the nearest tenth is 15.

12.0 the nearest tenth is 12.

14.0 the nearest tenth is 14.

10.0 the nearest tenth is 10.

6.0 the nearest tenth is  6.

16.0  the nearest tenth is  16.

Therefore, the required solution is 5,14,15,12,14,10,6,16 respectively.

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Answer:

Step-by-step explanation:

um first add 7+11 u get 18 and so yeah

Answer:

can u help me with my homework

Answer:

Farmers are the backbone of our society. They are the ones who provide us all the food that we eat. As a result, the entire population of the country depends upon farmers. Be it the smallest or the largest country. Because of them only we are able to live on the planet. Thus Farmers are the most important people in the world. Though farmers have so much importance still they do not have proper living.

Answer:

Ok, so all you have to do, is substitute the numbers in for x.

Step-by-step explanation:

For example substitute -3 in for x and solve. I hope this helps some!

Answer:

(A)  -24 × 1/4 ft

(B)  -6 ft

A negative times a positive is a negative

Step-by-step explanation:

 Sea level is 0, therefore the elevation of city (A) is -96 , and the elevation of city (C) is -24 . The elevation of city (D) is  1/4 of city (C).

Expression = - 24 × 1/4

Part (B)

-24 × 1/4 = -6

Explanation A negative times a positive gives a negative product.

Answer:

3600

Step-by-step explanation:

N = 300 x 12 =3600

Answer: 26

Step-by-step explanation: 208/8=26

The function is decreasing at [3, 13], increasing at [0, 3] U [ 13, 18 ], maximum value is 2.6, the minimum value is 0.6, the domain is [0, 18] and the range is [0.6, 3].

We have been given the graph of the function.

We need to find the increasing and decreasing intervals by analyzing the graph.

So, we get that:

The function is decreasing at the interval:

[3, 13]

The function is increasing at the intervals:

[0, 3] and [13, 18]

= [0, 3] U [ 13, 18 ]

The maximum value is:

= 2.6

The minimum value is:

= 0.6

The domain of the function is:

D = [0, 18]

The range of the function is:

R = [0.6, 3]

Therefore, we get that, the function is decreasing at [3, 13], increasing at [0, 3] U [ 13, 18 ], maximum value is 2.6, the minimum value is 0.6, the domain is [0, 18] and the range is [0.6, 3].

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Answer:

y=1x-1

Step-by-step explanation:

Using an exponential function, it is found that 0.6% of the original carbon 14 in the charcoal was present.

The exponential function for the amount of the substance after t years is given by:

[tex]A(t) = A(0)e^{-kt}[/tex]

k is the exponential decay rate, given by:

k = ln(2)/5600 = 0.00012377628.

Hence:

[tex]A(t) = A(0)e^{-0.00012377628t}[/tex]

The amount after 41,000 years is given as follows:

[tex]A(41000) = A(0)e^{-0.00012377628 \times 41000}[/tex]

A(41000) = 0.006A(0).

Hence:

0.6% of the original carbon 14 in the charcoal was present.

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Hence , 10 liters of a 10% acid solution and 50 liters of a 40% acid solution must be used.

Let the amount of 10 % acid solution be " x " and the amount  40 % acid solution be " y " .

The total volume of the resulting solution is 60 L which can be given by

      x + y = 60       .....(1)

The total acid in the resulting solution is 35 % acid solution which is given by     0.10 x + 0.40 y = 0.35(60)            .....(2)

Multiplying by 100 in equation (2) , we get

        10 x + 40 y = 2100          .....(3)

Putting x = 60 - y in equation (3) , we get

   10 ( 60 - y ) + 40 y = 2100

        600 - 10y + 40y = 2100

                 30y = 1500

                    y = 50

Putting y = 50 equation (1) , we get

      x = 60 - 50 = 10

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Answer: ≈12 inches

Step-by-step explanation:

Lengh a circumference L=2πR

Divide both parts of the equation by 2π:

[tex]\displaystyle\\R=\frac{L}{2\pi } \\\\R=\frac{75}{(2)(3.14)} \\\\R=\frac{75}{6.28} \\\\R\approx12\ inches[/tex]

1. y = 5x + 15.

2. y = total cost

x = number of calendar

m = cost per calendar = slope = 5

b = initial value/y-intercept = 15

3. $1,015.

4. The equation in slope-intercept form is: y = 5x + 15

5. Slope (m) = 5

6. y-intercept (b) = 15; x-intercept = -3.

7. See attachment below for the graph.

Using the information given, we can create an equation in slope-intercept form y = mx + b, where m would be the slope and b would be the y-intercept of the linear equation.

Let,

1. To create an equation that models the situation, substitute m = 5 and b = 15 into y = mx + b:

y = 5x + 15.

2. The variables and numbers in the equation are:

y = total cost

x = number of calendar

m = cost per calendar = slope = 5

b = initial value/y-intercept = 15

3. Substitute x = 200 into y = 5x + 15

y = 5(200) + 15

y = 1,015

Total cost = $1,015.

4. The equation in slope-intercept form is: y = 5x + 15

5. The slope (m) = 5

6. The y-intercept (b) = 15

To find the x-intercept, substitute y = 0 into y = 5x + 15

0 = 5x + 15

-5x = 15

x = 15/-5

x = -3

The x-intercept = -3.

7. See attachment below for the graph.

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If the number of coins in Lauren's collection is 5 times the number in Michael's collection and  the total number of coins in both collection is 366, then the number of coins in Michael's collection is 61

The number of coins in Michael's collection = x

The number of coins in Lauren's collection is 5 times the number in Michael's collection

Then the number of coins in Lauren's collection = 5x

The total number of coins in both collection = 366

Combine the values and the equation will be

x+5x=366

Add like terms

6x= 366

x=[tex]\frac{366}{6}[/tex]
x=61

Hence, if the number of coins in Lauren's collection is 5 times the number in Michael's collection and  the total number of coins in both collection is 366, then the number of coins in Michael's collection is 61

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