Jimmy’s age is one year less than the sum of the ages of his siblings Serena and Tyler. Which equation represents Jimmy’s age? Jimmy’s age is one year less than the sum of the ages of his siblings Serena and Tyler. Which equation represents Jimmy’s age?

y = 2x + 7

the equation of a line in ' slope-intercept form ' is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the ' gradient formula '

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (1, 9)

m = [tex]\frac{9-7}{1-0}[/tex] = 2

given the point (0, 7 ) then c = 7

y = 2x + 7  ← in slope-intercept form

easy 214.7 because if it was rounded it would be 214.700 an this is way bigger than 214.275

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:

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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[tex]f(x)=2x\to y=2x\\\\\text{change x and y}\\\\x=2y\\\\\text{solve for y}\\\\2y=x\qquad|:2\\\\y=\dfrac{x}{2}\\\\Answer:\ f^{-1}(x)=\dfrac{x}{2}[/tex]

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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The percent increase in Anil's hourly wage from $4 to $4.50, find the difference ($0.50), divide it by the original wage ($4), and multiply by 100, resulting in a 12.5% increase.

The student is asking how to calculate the percent increase in Anil's hourly wage from one week to the next. He was earning $4 per hour and then began to earn $4.50 per hour. The percentage increase is found by dividing the change in the quantity (the increase in pay) by the original quantity (the original pay) and then multiplying by 100 to get a percent.

To calculate the percentage increase:

Find the difference in pay: $4.50 - $4 = $0.50.

Divide this difference by the original pay: $0.50 / $4 = 0.125.

Multiply by 100 to get the percentage: 0.125 × 100 = 12.5%.

Therefore, the percent increase in Anil's hourly rate is 12.5%.

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

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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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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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Make the fractions equivalent.

1/3 ×2 = 2/6

Answer: 2/6

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

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]

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.

Answer: 11 sqrt3

Well, since this is an equilateral triangle, you know that all of the sides have the same length: 22 inches. If you want to find the altitude (height), you would have to use the Pythagorean theorem: a^2 + b^2 = c^2

This means that the sum of the two legs squared is equal to the hypotenuse of the triangle squared.

We already know that the hypotenuse is 22 inches, so we can plug that in as c.

We also know that to make the triangle a right triangle, we will need to halve the bottom side, getting 11 inches, which we can plug in as b.

Lastly, we need to know a, so that is our variable to solve (the height). Here is the equation:

a^2 + (11^2) = (22^2)

This is equal to:

a^2 + 121 = 484

Now subtract 121 from both sides to get a^2 on its own:

a^2 = 363

Lastly, take the square root of both sides to solve for a:

a = 11 sqrt3

The altitude of an equilateral triangle with a side length of 22 inches is 11√3 inches.

The altitude of an equilateral triangle can be found using the formula  altitude = (side length * √3) / 2.

In this case, the side length of the street sign is 22 inches. Plugging this value into the formula, we get:

altitude = (22 * √3) / 2.

Simplifying, we have:

altitude = 11√3 inches.

Therefore, the exact altitude length is 11√3 inches.

The equivalent number to the given equation is 54.861, calculated by using the order of operations and understanding of place value.

To solve this problem, you need to understand the concept of place value and order of operations in mathematics. Given the equation 5*10 + 4*1 + 8*1/10 + 6*1/100 + 1*1/1,000, we can begin solving using the order of operations, which is often remembered as PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Here, we multiply before adding. The solution would look like this:

Adding these results together, you get 50 + 4 + 0.8 + 0.06 + 0.001 = 54.861

So the equivalent number is 54.861, which corresponds to answer choice A.

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

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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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.

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

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

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!

i think the answer is the first one

Answer:

The first one

Step-by-step explanation: