Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y-2x. What error did Marcus make?

Answer:

17. Equation : [tex]y=-x-1[/tex]

18: Equation: [tex]y=\frac{1}{2}x+8[/tex]

19: Equation: [tex]y=3x-6[/tex]

20: Equation: [tex]y=\frac{1}{3}x-2[/tex]

Step-by-step explanation:

Using the Slope-Intercept Form for the following questions:

Equation of line: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept.

17. A(3, -4), [tex]y=-x+8[/tex]

First substitute the slope from the original line [tex]y=-x+8[/tex] (i.e. -1 in this case) into the equation of line.

[tex]y=(-1)x+b[/tex]        .....(1)

Now, substitute the given point A(3,-4) in the equation (1), we have;

[tex]-4=(-1)\cdot (3)+b[/tex]

[tex]-4=-3+b[/tex]

[tex]-4+3=b[/tex]

∴[tex]b=-1[/tex]

Substitute the value of b=-1 in the Slope-Intercept form i.e, [tex]y=-x+(-1)[/tex]

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

Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=-x-1[/tex].

18. A(-6, 5) , [tex]y=\frac{1}{2}x -7[/tex]

First substitute the slope from the original line [tex]y=\frac{1}{2}x -7[/tex] (i.e.  [tex]\frac{1}{2}[/tex] in this case) into the equation of line.

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

Now, substitute the given point A(-6, 5) in the equation (1), we have;

[tex]5=\frac{1}{2} \cdot (-6)+b[/tex]

[tex]5=-3+b[/tex]

[tex]5+3=b[/tex]

∴[tex]b=8[/tex]

Substitute the value of b=8 in the Slope-Intercept form i.e, [tex]y=\frac{1}{2}x+8[/tex]

[tex]y=\frac{1}{2}x+8[/tex]

Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=\frac{1}{2}x+8[/tex].

19. A(2,0), [tex]y=3x-5[/tex]

First substitute the slope from the original line [tex]y=3x-5[/tex] (i.e. 3 in this case) into the equation of line.

[tex]y=3x+b[/tex]       .....(1)

Now, substitute the given point A(2, 0) in the equation (1), we have;

[tex]0=3\cdot (2)+b[/tex]

[tex]0=6+b[/tex]

∴[tex]b=-6[/tex]

Substitute the value of b=-6 in the Slope-Intercept form i.e, [tex]y=3x+(-6)[/tex]

[tex]y=3x-6[/tex]

Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=3x-6[/tex]

20. A(3, -1), [tex]y=\frac{1}{3}x+10[/tex]

First substitute the slope from the original line [tex]y=\frac{1}{3}x +10[/tex] (i.e.  [tex]\frac{1}{3}[/tex] in this case) into the equation of line.

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

Now, substitute the given point A(3, -1) in the equation (1), we have;

[tex]-1=\frac{1}{3} \cdot (3)+b[/tex]

[tex]-1=1+b[/tex]

[tex]-1-1=b[/tex]

∴[tex]b=-2[/tex]

Substitute the value of b=-2 in the Slope-Intercept form i.e, [tex]y=\frac{1}{3}x+(-2)[/tex]

[tex]y=\frac{1}{3}x-2[/tex]

Therefore, the equation of the line passing through the given point that is parallel to the given line is, [tex]y=\frac{1}{3}x-2[/tex].

Hey there!

First, we'll solve for x = 0.

The first step is to replace x with 0 anytime it appears in the equation.

f(0) = 7(0) + 2

Multiply 7 by 0 next because multiplication comes before addition in PEMDAS.

f(0) = 0 + 2

Then, add 2 to 0 since it is the last step.

f(0) = 2   The value of f(x) when x = 0 is 2.

Now we can solve for x = 1.

The first step is to replace x with 1 anytime it appears in the equation.

f(1) = 7(1) + 2

Multiply 7 by 1 next because multiplication comes before addition in PEMDAS.

f(1) = 7 + 2

Then, add 2 to 7 because it is the last step.

f(1) = 9   The value of f(x) when x = 1 is 9.

Hope this helps!

One answer is 2 cars and 20 buses

The toll collector collected $188 in a 2-hour period. There are three possible solutions: 44 cars and 12 buses, 35 cars and 18 buses, or 26 cars and 24 buses.

Let's assume the number of cars passing through the toll booth is 'x' and the number of buses is 'y'.

We can form the following equations based on the given information:

4x + 9y = 188  (total amount collected)

2x + 2y = 2  (total number of hours)

Now we can solve these equations simultaneously to find the values of 'x' and 'y'.

Using substitution or elimination method, we can find that 'x = 44' and 'y = 12', or 'x = 35' and 'y = 18', or 'x = 26' and 'y = 24'.

Therefore, there are three possible solutions:

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Final answer:

To calculate deductions and taxes for Pat Brown, the Social Security tax is $130.20, Medicare is $30.45, and the FIT at 15% is $315.00, resulting in a net pay of $1,624.35.

Explanation:

To calculate the deductions and taxes for employee Pat Brown, we must consider the tax rates presented. Pat has a gross pay of $2,100.

For Social Security tax, which is 6.2%, we calculate: $2,100 x 0.062 = $130.20

For Medicare tax, at 1.45%, we calculate: $2,100 x 0.0145 = $30.45

Assuming a federal income tax (FIT) rate of 15%, the FIT amount deducted would be: $2,100 x 0.15 = $315.00

Therefore, the net pay for Pat Brown is calculated by subtracting all the deductions from the gross pay: $2,100 - $130.20 - $30.45 - $315.00 = $1,624.35

To find out how much more Nan earns per hour compared to Isabel, divide the amount earned by the number of hours worked for each person and calculate the difference.

To find out how much more Nan earns per hour compared to Isabel, we need to calculate their hourly rates.

Isabel earned $145.80 for 20 hours, so her hourly rate is $145.80 / 20 = $7.29 per hour.

Nan earned $112.50 for 15 hours, so her hourly rate is $112.50 / 15 = $7.50 per hour.

Therefore, Nan earns $7.50 - $7.29 = $0.21 more per hour compared to Isabel.

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I suppose you want to solve the equation for m. To do so, multiply both sides by 8m to get

[tex] 3m = -1 [/tex]

Now divide both sides by 3 to get

[tex] m = -\dfrac{1}{3}[/tex]

m = - [tex]\frac{1}{3}[/tex]

multiply both sides by 8m to eliminate fractions

3m = - 1 ( divide both sides by 3 )

m = - [tex]\frac{1}{3}[/tex]

A=Lw

P=2L+2w

216=Lw

W=216/L...substitute to Perimeter equation

60=2L+2(216/L)

60L=2L^2 + 432

2L^2-60L+432=0

2(L^2 - 30L + 216)=0

2(L-18)(L-12)=0

L=12, W=18 or L=18, W=12

Make the fractions equivalent.

1/3 ×2 = 2/6

Answer: 2/6

Answer:

19.625 cm² is your answer

Step-by-step explanation:

Area of the circle can be solved using the equation: Area = [tex]\pi r^2\\[/tex]

Solve for r (radius). To find radius, use Radius = [tex]\frac{diameter}{2}[/tex]

Solve for radius

[tex]\frac{5}{2} = 2.5\\[/tex]

Plug in 2.5 for radius. Remember that Area = [tex]\pi r^2\\[/tex]

Area = [tex]\pi 2.5^2\\[/tex]

Simplify

Area = [tex]\pi 6.25\\[/tex]

Area = [tex]\((3.14)(6.25)\\[/tex]

Multiply

Area = [tex]\ 19.625\\[/tex]

19.625 cm² is your answer

~Rise Above the Ordinary, Senpai

To get d . you would do the opposite to move it to the other side..so you would multiply.. v×d=t

Answer:

8f + 4g

Step-by-step explanation:

Distribute the 2 to all terms within the parenthesis

2(4f) = 8f

2(2g) = 4g

8f + 4g is your expression

~Senpai

Answer:

oh b this is a hard question

Step-by-step explanation:

i will answer it gimme a few mins to learn this things

Answer:

Options B and D are correct.

Step-by-step explanation:

The given equation is :

[tex]y= -16x^{2}+48x+64[/tex]

We can see that it is a quadratic equation.

Hence it is non linear.

The rate is dependent on x, so it does not have a constant rate of change  also.

We can check this :

At x= 0, y = 64

At x=1, y = [tex]-16+48+64=96[/tex]

Hence, the function does not have a constant rate of change.

So, the answer is :

Answer:

Second Picture 3rd Picture 1st Picture

Step-by-step explanation:

You're welcome!

The y-intercept of the given exponential graph is 2

The given graph is an exponential function with a general form y = ab^x

This means that we need to find the equivalent value of f(x) when x = 0. From the table, we can see that the required equivalent y-intercept at when x = 0 is 2

Hence the y-intercept of the given graph is 2

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Answer:  The correct option is

(C) 9x.

Step-by-step explanation:  We are given to simplify the following expression :

[tex]E=(7x)-(-2x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following rule in simplifying the given expression :

[tex]a-(-b)=a+b.[/tex]

From expression (i), we get

[tex]E\\\\=(7x)-(-2x)\\\\=7x+2x\\\\=(7+2)x\\\\=9x.[/tex]

Thus, the required simplified form is 9x.

Option (C) is CORRECT.

By applying the distributive property of equality, the expression, (7x)- (-2x), is simplified as: C) 9x.

To simplify (7x) - (-2x), follow these steps:

Step 1: Distribute the negative sign in front of (-2x) by using "-" to multiply -2x to open up the parentheses:

(7x) + (2x) [distributive property of equality]

Step 2: Combine like terms {7x and 2x) by adding the coefficients of the x terms:

7x + 2x = 9x

The simplified expression is 9x.

So, the correct answer is therefore:

C) 9x

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split ∠ P into a ∠45° and a ∠60° with altitude PO. ΔPOK is isosceles and ΔPOS is 30-60-90. PO=6=KO Pk=6√2

Answer:

6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Look at the pic below

Let me know if you have any questions

Also, if it's wrong will do my best to fix it

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i think the answer is the first one

Answer:

The first one

Step-by-step explanation:

The dimensions of the rectangle that has a perimeter of 42 cm are:

length = 12 cm

width = 9 cm

Recall:

The perimeter of a rectangle is given as:

Given the following:

Therefore:

[tex]2((x + 4) + (2x -7)) = 42[/tex]

[tex]2(x + 4 + 2x -7) = 42[/tex]

[tex]2(3x -3) = 42\\\\6x - 6 = 42\\\\[/tex]

[tex]6x - 6 + 6 = 42 + 6\\\\6x = 48\\[/tex]

[tex]x = 8[/tex]

Find the dimensions of the rectangle by plugging in the value of x

[tex]length = (x+4) = 8 + 4 = 12 $ cm\\\\width = (2x - 7) = 2(8) - 7 = 9 $ cm[/tex]

Therefore, the dimensions of the rectangle that has a perimeter of 42 cm are:

length = 12 cm

width = 9 cm

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Answer:

The required inequality is: [tex]8x+6y\geq 700[/tex]

The required graph is shown in figure 1.

Yes, he make enough money.

Step-by-step explanation:

Consider the provided information.

Part (A)

Carlos estimates that he will need to earn at least $700 to take his girlfriend to the prom.

Let the number of hours worked in Deli is x and the number of hours worked for babysitting is y.

Deli $8 per hour and babysitting $6 per hour. Carlos need to earn at least 700.

For at least use the inequity ≥

The required inequality is: [tex]8x+6y\geq 700[/tex]

Part (B)

Rewrite the inequity as an equation to find the the x and y intercept.

[tex]8x+6y=700[/tex]

Substitute x=0 in the above

[tex]8(0)+6y=700[/tex]

[tex]y=\frac{700}{6}[/tex]

[tex]y= 116.67[/tex]

Substitute y=0 in the above

[tex]8x+6(0)=700[/tex]

[tex]x =\frac{700}{8}[/tex]

[tex]x= 87.5[/tex]

Use the point (0,116.67) and (87.5,0) to draw the graph.

Since the sign of inequality is greater than equal to, so shade the graph above the line. Use solid line as the sign of inequality is ≥.

Thus, the required graph is shown in figure 1.

Part (C)

We need to find he make enough money if he works 50 hours at each job.

Substitute x=50 and y=50 in the inequality.

[tex]8(50)+6(50)\geq 700[/tex]

[tex]400+300\geq 700[/tex]

[tex]700\geq 700[/tex]

Which is true.

Hence, he make enough money.

Hello there!

The answer should be the first option A.

16-(-11)

16+11

Answer⇒=27

10-17

10+-17

Answer⇒=-7

-15-(-12)

-15+12

Answer⇒=-3

-25-2

-25+-2

Answer⇒=-27

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

Option a, 16-(-11), is the expression that has a value of 27.

To find the expression that has a value of 27, we can evaluate each option:

Let's evaluate each expression to determine which one equals 27:

a. 16−(−11)

Applying the rule that subtracting a negative number is the same as adding its positive counterpart:

16+11=27

Therefore, a equals 27.

b. 10−17

Subtracting 17 from 10:

10−17=−7

This does not equal 27.

c. −15−(−12)

Similar to the first expression, subtracting a negative is the same as adding its positive counterpart:

−15+12=−3

This does not equal 27.

d.−25−2                                                                                                                                                                                                              Subtracting 2 from -25:

−25−2=−27

This does not equal 27.

Hence, after evaluating each expression, the correct choice that equals 27 is option a: 16−(−11)

Therefore, option a, 16-(-11), is the expression that has a value of 27.

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which expression has a value of 27.a.16-(-11)  b.10-17  c.-15-(-12)  d.-25-2

The place value of 6 in 80.416 is in the thousandths place and is worth 0.006. The place value of 5 in 1.540 is in the tenths place and is worth 0.5.

Hope this helped!

Nate

Answer: length = 19 inches and width = 8 inches

Step-by-step explanation: To solve this problem, our first task is to set up variables.

Since the length of the rectangle is 5 inches less than 3 times its width, we can set up variables to represent this.

Variables

X ⇒ width

3x - 5 ⇒ length

To help set up our equation, I will draw a picture of the rectangle labeling the widths X and the lengths 3x - 5.

Going back to the original problem, the second sentence states that the perimeter of he rectangle is 54 inches. Remember that the perimeter is the distance around the rectangle.

Based on the picture I provided, our equation will read as followed.

X + X + (3x -5) + (3x - 5) = 54

8x - 10 = 54   ← simplify on the left side of the equation

     +10  +10   ← add 10 on both sides

8x = 64

÷8    ÷8

 X = 8

Therefore, the width of our rectangle is 8 inches and the length of our rectangle is (3 x 8) - 5 or 19.

Answer:

Step-by-step explanation:

x= base

one side= x-6

other side= 4+x

x+x-6+4+x = 43

3x=43+2

x=15 length of base

The length of base is 15 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the base of triangle be x

Length of one side = x- 6

and, length of other side = x+ 4

Now, perimeter of triangle= 43 cm.

x+ x -6 +x +4= 43

3x -2 = 43

3x= 45

x=15

So, x= 15 cm

x-6 = 15- 6 = 9cm

x+ 4 = 15+ 4= 19cm

Hence, the length of base is 15 cm.

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The slope-intercept form of an equation is given by y=mx+b. Substituting the given slope (m=7/4) and the y-intercept (b=-5) in this formula, we get the equation of the line as y = (7/4)x - 5.

The topic under discussion is mathematics, more specifically the slope-intercept form of the equation of a line.

The slope-intercept form is given by y=mx+b, where 'm' represents the slope and 'b' is the y-intercept.

Given the slope of 7/4 and y-intercept of -5, we can substitute these values into our equation:

Therefore, the slope-intercept form of this line is y = (7/4)x - 5.

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Answer:

125 ÷ 3 = ____

Jamie + 2 brothers = _____

Then divide __ by the number if toy cars. ( 125 )

A positive slope is represented by an upward tilt, Line A has the steepest slope, and none of the lines have an undefined slope.

In this case, line A represents a positive slope because it is a straight line that has an upward tilt or is increasing as we move from left to right. Line B represents a negative slope because it is a straight line that has a downward tilt or is decreasing as we move from left to right. Line C represents zero slope because it is a horizontal line without any tilt or change in y-values as we move along the x-axis.

To determine which line has the steepest slope, we need to look at the lines' tilt more closely. Line A has a steep positive slope as it increases quickly, while Line B has a less steep negative slope as it decreases slowly. Line C has a slope of zero, so it does not have any steepness. Therefore, Line A has the steepest slope.

None of the lines have an undefined slope. An undefined slope occurs when a line is vertical. Since none of the lines are vertical, they all have defined slopes.