Writing a multi-step equation for a real-world situation
TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 118 MP3 and DVD players.
Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.
total profit (in dollars)

The equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively

Perimeter of rectangle = 2(L + W)

104 = 2{(1 + 2w) + w}

104 = 2(1 + 2w + w)

104 = 2(1 + 3w)

104 = 2 + 6w

104 - 2 = 6w

102 = 6w

w = 102 / 6

w = 17 cm

Recall,

Length of the rectangle, l = 1 + 2w

= 1 + 2(17)

= 1 + 34

= 35 cm

Therefore, the equation for L in terms of W is ( 1 + 2w) where length and width of the rectangle is 35 cm and 17 cm respectively

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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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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

Answer:

x = 22.5

∠ADE = 67.5

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° and the given is a right triangle so we can find the value of x easily:

90 + x + 3x = 180 add like terms

90 + 4x = 180 subtract 90 from both sides

4x = 90 divide both sides by 4

x = 22.5

To find the measure of angle ADE we use the same equation:

90 + 22.5 + ∠ADE = 180 add like terms

112.5 + ∠ADE = 180 subtract 112.5 from both sides

∠ADE = 67.5

Answer:

1 = 34°

2 = 52°

3 = 38°

4 = 94°

5 = 56°

6 = 38°

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:

3600

Step-by-step explanation:

N = 300 x 12 =3600

Answer:

4915

Step-by-step explanation:

y= 983 so multiply 983 by 5

5x983 = 4915

Answer: 4915

Step-by-step explanation: Pls brainliest.

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 rectangular equivalence to the parametric equations is;

(x - 2)²/9 + (y + 1)²/4 = 1

We want to find the rectangular equivalence to the parametric equations;

x(θ) = 3cosθ + 2

y(θ) = 2sinθ − 1

where 0 ≤ θ < 2π .

Making the trigonometric ratio the subject gives us;

cosθ = (x - 2)/3

sinθ = (y + 1)/2

Now, from trigonometric identities, we know that;

cos²θ + sin²θ = 1

Thus;

((x - 2)/3)² + ((y + 1)/2)² = 1²

(x - 2)²/9 + (y + 1)²/4 = 1

Thus, the rectangular equivalence to the parametric equations is;

(x - 2)²/9 + (y + 1)²/4 = 1

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Answer:

I can help you.

Step-by-step explanation:

so, you have to write in a)

2•5=10, 4÷2=2, 6+10=16, 16+2=18, 18-3=15. so answer is 15

And then, u have to write in b) 6+2=8, 8•5=40, 40+4=44, 44÷2=22, 22-3=19. so answer is 19.

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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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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Answer:

y=1x-1

Step-by-step explanation:

The journal entry will be:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

We know that:

1) The $10,000 will be posted to the debit side of the Equipment Account as the equipment is an asset and it is being bought in the company. So, purchasing an asset is being debited in the account.

2) The $10,000 will be posted to the credit side of the Cash Account as cash is also an asset which is being given. Since, the asset is going out from the company, it is being credited in the company's account.

The journal entry then will become as:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

Therefore, the journal entry will be:

Date            General           Debit      Credit

                                                $             $

Dec 31        Equipment        10000  

                  Cash                                 10000

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Your question was incomplete. Please refer the content below:

On December 31, the company purchases equipment for $10,000 and pays cash of $10,000. Complete the necessary journal entry by selecting the account names from the pull-down menus and entering dollar amounts in the debit and credit columns.

Check the picture below.

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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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?

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.

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:

Step-by-step explanation:

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

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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Answer:

d

Step-by-step explanation:

as x→-∞ , y→+∞

as x→∞ , y→-∞

Answer: 6x-5

5 less is just subtract 5 from whatever follows

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]

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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Answer:

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

then subtract with 4

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.