Use a graphing calculator to solve the system of linear equations. 2.1x+4.2y=14.7 −5.7x−1.9y=−11.4

Remark

I'm going to interpret this equation as

D = ut + kt²  The only difference is the 2.

Solution

Subtract kt² from both sides.

D - kt² = ut   Now divide by u on both sides.

[tex]\dfrac{D - kt^2}{t} = \dfrac{ut}{t}[/tex]

The t's cancel out. on the right.  You are left with u on the right.

[tex]\dfrac{D - kt^2}{t} =\text{u}[/tex]

Given function: c(x) = 0.5x+70.

Where c is the cost (in dollars) and x is the number of miles you drive the truck.

If we compare given function by slope-intercept form y=mx+b, we get

Slope m = 0.5 in fractions could be written as 1/2.

And y-intercept b =70.

So, in order to graph it, we need to plot y-intercept at 70 first and then plot some more points using rise/run = 1/2.

The red line is the graph for the given function.

We can see that starting value of cost is $70 for 0 number of miles.

x values represents domain and C(x) represents range.

We can take x values greater than or equal to 0 and C values greater than equal to 70.

Therefore, Domain: x≥0 and Range : C(x) ≥ 70.

Answer:

Cost equation = 5x + 25000

Step-by-step explanation:

Given: The producing the product is 25,000 plus $5.00 per piece.

x is the number of pieces.

Production cost = fixed cost + cost per piece * number of piece.

Given: Fixed cost = $25000 and cost per piece - $5.00

Now plug in these values in the production cost equation.

So, to produce x number of items, the cost = 25000 + 5x

Which can be written as

Cost equation = 5x + 25000

Answer:

17 hours and 3 hours.

Step-by-step explanation:

Let us assume that Annie travels x hours and Brian y hours.

Then given that x = 5y+2

Together they travelled = total hours of both = x+y

Substitute x = 5y+2 in the total distance.

We have an equation in a single variable y as

= 5y+y+2 = 20

Simplify to get

6y+2 = 20

subtract 2

6y = 18

Divide by 6

y =3

x =5y+2

= 5(3) +2=17 hours

Annie traveled 17 hours and Brian 5 hours.

Answer:

Yes

Step-by-step explanation:

30% of 900 is 270

the cost to lease the machine is 200

therefore 270-200=70

leaving you with 70 dollars profit

Answer:

Yes

Step-by-step explanation:

I'm selling $900 per month of slushies, with a margin of profit of 30% that is:

[tex]P=\$900*(0.30)=\$270[/tex]

The machine has a cost of $200 per month, so the total profit is given by:

[tex]Tp=\$270-\$200=\$70[/tex]

Each month I have a profit of $70.

12 out of 36 is the same as 12/36

Both 12 and 36 are divisible by 12.

12/36 = (1 * 12)/(3 * 12) = 1/3 * 12/12 = 1/3 * 1 = 1/3

Answer: 1/3

0.75(x+20)=2+0.5(x-2)

Distribute on both sides

0.75x+15= 2+0.5x-1

Add common factors

0.75x+15=1+0.5x

Subtract 0.5x on both sides

0.25x+15=1

Subtract 15 on both sides

0.25x=-14

Divide by 0.25 on both sides

x = -56

The value of x that will make both equations to be equivalent to each other is = -56

From the equation:

0.75(x + 20) = 2 + 0.5(x - 2)

Open brackets

0.75x + 15 = 2 + 0.5x - 1

Collect like terms

0.75x - 0.5x = 2 - 1 - 15

0.25x = - 14

Divide both sides by 0.25

[tex]\mathsf{\dfrac{0.25x}{0.25} =\dfrac{ - 14}{0.25}}[/tex]

x = -56

Therefore, we can conclude that the value of x that will make both equations to be equivalent to each other is -56

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A- Stable electron configurations are likely to contain - filled energy sub-levels.

B- How many unpaired electrons are in a sulfur atom (atomic number 16)? Answer is 2

Answer:

Conexus:

Step-by-step explanation:

B, C, D, C, C, A.

the answer would be 6 buckets

Get the variable alone by doing the same thing to both sides. You will divide 5 by both sides which gets you to 5n/5 = -20/5. You can then cancel out the 5n/5 to get just n. Then find the greatest common factor of the numerator and denominator of -20/5, and then cancel out the GCF.

The answer is n = -4

The solution to the equation 5n = -20 is n = -4.

To solve the equation 5n = -20, you can follow these steps:

Step 1: Divide both sides of the equation by 5 to isolate the variable n.

(5n) / 5 = (-20) / 5

Simplifying the equation gives you:

n = -4

So the solution to the equation 5n = -20 is n = -4.

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The correct answer is a. 3x + 6

In order to find a compound function, you must use the first letter in the function (in this case f) and plug the second letter (g) in where you see x's.

f(x) = x + 2

f(g(x)) = (g(x)) + 2

f(g(x)) = (3x + 4) + 2

f(g(x)) = 3x + 6

Final answer:

To find the composition (g ° f)(x), substitute f(x) into g(x) and simplify. The correct answer is 3x + 10.

Explanation:

To find (g ° f)(x), also known as the composition of the functions g and f, you would substitute f(x) into g(x). This means we are looking for g(f(x)):

First, we have f(x) = x + 2.

Then, g(x) = 3x + 4.

To compose g with f, we replace every instance of x in g(x) with f(x). So, g(f(x)) becomes 3(x + 2) + 4.

We simplify this to get 3x + 6 + 4.

And finally, combining like terms gives us 3x + 10.

Therefore, the correct option is (g ° f)(x) = 3x + 10, which is choice b.

Answer:

$5000*0.816 = $4082

Step-by-step explanation:

It's a strange question, but based on the statement and the question it sounds like it's a poisson distribution:

* For 3 days she was able to get 2 good shots (typical of that time of the year)

* Good shots happen randomly

* Each day is independent of another

Let's call 'p' the probability that she makes a good shot per day

Let's call 'n' the number of days Karen is taking shots.

So, if in 3 days he got 2 good shots and that is typical at that time of the year, then the expected value for the number of good shots (X) is:

[tex]E(x)=\frac{2}{3}[/tex]

For a Poisson distribution [tex]E (x)=\lambda\\\lambda= np[/tex]

So:

[tex]\lambda =\frac{2}{3}[/tex]

For a Poisson distribution the standard deviation is:

[tex]\sigma = \sqrt{\lambda}\\\sigma = \sqrt{\frac{2}{3}}[/tex]

[tex]\sigma = 0.816[/tex] this is the standard deviation for the number of buentas taken.

So the standard deviation for income is the price of each shot per sigma

$5000*0.816 = $4082, which is the desired response.

THE QUESTION:After it is purchased, the value of a new car decreases $4000 each year. After 3 years, the car is worth $18,000. What was the original value of the car?

THE WORK: $4000x$3 = $12000_$18000-$12000 = $6000

MY ANSWER: based on my work, the answer is $24000

Final answer:

To find the original value of a car that depreciates by $4,000 each year, we add the total depreciation over 3 years ($12,000) to the car's value after 3 years ($18,000), resulting in an original price of $30,000.

Explanation:

The student is asking about the calculation of the original price of a car given its depreciation rate and its value after a certain period. Since the new car decreases by $4000 each year and after 3 years the value of the car is $18,000, we can calculate the original value by reversing the depreciation.

Depreciation calculation:

Answer:

The amount of money saved will be $0.25

Step-by-step explanation:

Sand sells [tex]8\frac{1}{2}[/tex] cents per pound.

So, the cost of 100 pounds will be:  [tex]8\frac{1}{2}*100=\frac{17}{2}*100 = 850[/tex] cents.

We know that,  1 dollar = 100 cents.

So, 850 cents [tex]=\frac{850}{100} dollar = \$8.50[/tex]

Thus, the amount of money saved by buying 100 pounds at $8.25 will be:  [tex](\$8.50-\$8.25)= \$0.25[/tex]

The amount saved by buying 100 pounds at $8.25 is the change in price per pound and the discounted price, which is 0.25 cents

Price per pound = 8.50 cent

Calculating the cost per pound of of Sand at $100 for $8.25 :

100 = 8.25

1 = p

Cross multiply :

100p = 8.25

p = 8.25 / 100

p = $0.0825 = 0.0825 × 100 = 8.25 cent

The amount saved = 8.50 - 8.25 = 0.25 cent

Therefore, the amount saved by buying 100 pounds at $8.25 is 0.25 cent.

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1) Given

Because it was given to you

2) Opposite sides in 1 ray

3) supplementary

Because Supplementary angles add up to 180 degrees

5) Opposite angles are congruent

6) Transitive property

Because you proved earlier that m<4=m<1

7) Supplementary

Because Supplementary angles add up to 180 degrees

Forgive me if the computer program doesn't accept the wording that I provided and marks the answer as wrong

N/3 - 5 = 13

(N-15/3) =13 taking lcm

N-15 = 13×3

N-15 = 39

Therefore, N = 39+15 = 54

N/3-5=13

n/3-5=13 // -13

n/3-13-5=0

N=54

Clue 1 : My number has two digits,and both digits are even.

Clue 2: the sum of my numbers digits is 10.

Clue 3. My number has 4 as a factor.

Clue 4 the difference between the two digits of my number is 6 .

If we see first option: A. 28.

a) Both digits 2 and 8 are even.

b) Sum of 2 and 8 is 10.

c) 28 has a factor 4.

d) Difference between 8 and 2 is 6.

Therefore, correct option is A. 28.

Answer:i would say A)28

Step-by-step explanation:

$720 becuase 120 divded by 1/6 is 720 and your mathbook couldve helped to

Answer:

[tex]\frac{1}{6}s = 120[/tex]

Step-by-step explanation:

Given : Israel added $120 to his savings. This added amount represents 1/6 of his total savings.

To Find : If s represents the total savings, which equation could be used to determine the value of s?

Solution :

Israel added $120 to his savings.

This added amount represents 1/6 of his total savings.

Let s be the total savings

So, ATQ

[tex]\frac{1}{6}s = 120[/tex]

So, The equation could be used to determine the value of s is [tex]\frac{1}{6}s = 120[/tex]

Answer:

33 is your answer

Step-by-step explanation:

Plug in -4 for m in the expression

(-4)^2 - 3(-4) + 5

Simplify. Remember to follow PEMDAS. First, solve the number connected to the power sign.

(-4)^2 = (-4)(-4) = 16

Next, solve -3(-4). Multiply

-3(-4) = 12

Finally, combine like terms.

16 + 12 + 5 = 33

33 is answer

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~Senpai

[tex]\dfrac{-20t^5u^2v^3}{48t^7u^4v}=\dfrac{-20}{48}\cdot\dfrac{t^5u^2v^2v}{t^5t^2u^2u^2v}=-\dfrac{5}{12}\cdot\dfrac{v^2}{t^2u^2}=-\dfrac{5v^2}{12t^2u^2}[/tex]

[tex]Used:\\\\a^n\cdot a^m=a^{n+m}[/tex]

Joelle should multiply 792 by 22 to get a perfect square

To figure out the smallest integer that Joelle could have multiplied by 792 to get a perfect square, we need to factorize 792 and ensure all prime factors appear in even powers.

First, we find the prime factorization of 792:

[tex]792 =2^3 \times 3^2 \times 11[/tex]

For a number to be a perfect square, all the exponents in its prime factorization must be even. The exponents of 2 and 11 are not even in this factorization, so we must multiply 792 by the smallest factors that will make these exponents even. So, we need an additional factor of 2 (to make [tex]2^4[/tex]) and an additional factor of 11 (to make [tex]11^2[/tex]). Therefore, we multiply as follows:

[tex]2 \times 11 = 22[/tex]

So, the smallest integer Joelle could have multiplied 792 by to get a perfect square is 22.

Using the Polynomial Division: Divide 5[tex]x^{4}[/tex]−2[tex]x^{3} -7x^{2} -39 by x^{2}[/tex] +2x−4 using long polynomial division.

Answer to the Polynomial Division: [tex]5x^{2} -12x+37+\frac{-122x+109}{x^{2}+2x-4}[/tex]

The question deals with the division of two polynomial expressions in mathematics. The process involves division of highest degree terms in the polynomials and subtraction of the result from the numerator polynomial, similar to the technique of long division.

The question involves the division of two polynomial expressions, which is a topic in Mathematics, specifically Algebra. The division of polynomials is performed similarly to the long division we use for numbers. In this case, the polynomial (5x^4-2x^3-7x^2-39) is divided by the polynomial (x^2+2x-4).

To perform the division, we divide the highest degree terms in the polynomials. So, we divide 5x^4 (from the numerator polynomial) by x^2 (from the denominator polynomial) to get 5x^2. Multiply this by the entire denominator polynomial and subtract the result from the numerator polynomial. The process is continued until we cannot continue dividing any further.

The result is your answer, which might be another polynomial or a number. Similar to long division with numbers, there might be a remainder after the division.

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Answer:

The  speed of air in still air =570 mph and

speed of wind = 40 mph

Step-by-step explanation:

Given that plane travelled 2135 miles in 3.5 hours with the wind.

Let the velocity of plane be x and that of wind be y.

Then with the wind speed =x+y and

against the wind the speed = x-y

Use distance = time x speed

Since travelled 2135 miles in 3.5 hours we have

2135 = 3.5 (x+y) ... i

Similarly with x-y speed it travelled 1855 miles in 3.5 hours

i.e. 1855 =   3.5(x-y) ... ii

Solving these two we can get x and y

i-ii gives

3.5y+3.5y = 2135-1855 = 280

i.e. 7y =280

Or y = 40 mph

Substitute in i

3.5(x+40) = 2135

x+40 = 610

x = 570 mph

Hence the  speed of air in still air= x =570 mph and

speed of wind = 40 mph

To find the speed of the plane in still air and the speed of the wind, set up a system of equations using the given information and solve them simultaneously.

To find the speed of the plane in still air and the speed of the wind, we can set up a system of equations using the given information. Let's call the speed of the plane in still air 'p' and the speed of the wind 'w'.

Given that the plane traveled 2135 miles with the wind in 3.5 hours, we can represent this as p + w = 2135/3.5.

Similarly, given that the plane traveled 1855 miles against the wind in 3.5 hours, we can represent this as p - w = 1855/3.5.

Solving these two equations simultaneously will give us the values of 'p' and 'w'.

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Hey There,

Your answer is:

486 R 1

2 goes into 17 8 times 17-16 = 1 bring down the 3, 2 goes into 13 6 times, 13-12 = 1

483 r 1

Answer-

The absolute value of the difference of the two numbers was found to be 7.

Solution-

The given two numbers are, 2 and -5.

Between these two number,

larger number = 2

smaller number = -5

(∵ As 2 is right of -5 on the number line)

[tex]\left |larger\ number-smaller\ number \right|[/tex]

[tex]=\left |2-(-5)\right |[/tex]

[tex]=\left |2+5 \right|= 7[/tex]

[tex]\left | smaller\ number -larger\ number \right|[/tex]

[tex]=\left |(-5)-2 \right|[/tex]

[tex]=\left |-5-2 \right|=\left |-7 \right|=7[/tex]

Therefore, it can be proved the order doesn't matter if we take the difference in absolute value.

Answer:

15 inches

Step-by-step explanation:

Area of a rectangle = width × length

We know the area and length so we can put them into the equasion.

375 in.^2 = width × 25 in.

We know that something times 25 is equal to 375. Therefore, we have to divide 375 by 25, which equals 15.

So, 375 in.^2 = 15 in. × 25 in.

The width of the rectangle is 15 inches.

To find the width of a rectangle, given its length and area, we can use the formula for the area of a rectangle:

Area = Length × Width

We are given that the length of the rectangle is 25 inches and the area is 375 square inches.

Let's substitute these values into the formula:

375 in² = 25 in × Width

To find the width, we need to isolate it on one side of the equation. We can divide both sides of the equation by 25 inches:

375 in² / 25 in = Width

Simplifying the expression:

15 in = Width

Therefore, the width of the rectangle is 15 inches.

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