Chris is calculating his deductions for his tax return. He is filing singly. He can claim $1,813 from property taxes, $1,513 from medical expenses, and $761 from state income tax. The standard deduction for a single filer is $5,700. How does the standard deduction compare to Chris’s deductions? a. Chris’s deductions are $1,437 better than the standard deduction. b. Chris’s deductions are $4,087 better than the standard deduction. c. The standard deduction is $1,613 better than Chris’s deductions. d. The standard deduction is $664 better than Chris’s deductions.

To graph the given linear equations, convert them to slope-intercept form and plot their y-intercepts and slopes on a graph to draw the lines representing each equation.

To graph the equations:

x − 3y = − 12

2x − y = 1

You can use the following steps:

By following these steps, you will produce a graph with two lines, which could intersect at a point that represents the solution to the system of equations.

To graph the system of equations x - 3y = -12 and 2x - y = 1, convert each to slope-intercept form, plot the y-intercepts, use the slopes to determine another point for each line, and draw the lines through these points.

To graph the system of equations given by x – 3y = –12 and 2x – y = 1, you need to follow these steps:

With consistent practice, graphing systems of equations can become a more straightforward process.

Answer:

answer is b

Step-by-step explanation:

There are 9 thirds in 3 hours, since each hour is made up of 3 thirds.

To find out how many thirds are in 3 hours, we consider that 1 hour is equal to 3 thirds (since 1 divided by 1/3 equals 3). Therefore, if 1 hour equals 3 thirds, then 3 hours would contain 3 times as many thirds. We calculate this as follows:

1 hour = 3 thirds
3 hours = 3 hours × 3 thirds/hour = 9 thirds

Thus, there are 9 thirds in 3 hours.

The equation of the line in point-slope form is y = -2x + 7.

To find the equation of the line passing through the point (2, 3) with a slope of -2, we can use the point-slope form of a linear equation:

[tex]\[y - y_1 = m(x - x_1)\][/tex]

where m is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line.

Given that the point [tex]\((x_1, y_1)\)[/tex] is (2, 3) and the slope m is -2, we substitute these values into the point-slope form:

y - 3 = -2(x - 2)

Now, we can simplify the equation:

y - 3 = -2x + 4

Next, we can move the constant term to the other side:

y = -2x + 4 + 3

y = -2x + 7

So, the equation of the line in point-slope form is y = -2x + 7.

Answer:

Position of ball from top of tower after 1 second is 4.9 m

Position of ball: [tex]y=-4.9t^2+122.5[/tex]

Step-by-step explanation:

An object falls from rest on a high tower and takes 5.0 s to hit the ground.

Let position of object from top of tower be y

Using formula, v =u - gt

[tex]v=0-9.8\times 5[/tex]

[tex]v=49\ m/s[/tex]

Speed of object when hit the ground.

Height of tower, H₀

[tex]H_0=\dfrac{49^2-0}{2\times 9.8}=122.5\ m[/tex]

Velocity of ball after 1 s

[tex]v=0-9.8\times 1[/tex]

[tex]v=-9.8\ m/s[/tex]

Using formula, [tex]s=\dfrac{v^2-u^2}{2g}[/tex]

[tex]y=\dfrac{9.8^2-0^2}{2\times 9.8}[/tex]

[tex]y=4.9\ m[/tex] From top of tower

Now find position of ball from top of tower.

[tex]y=-\dfrac{1}{2}\times 9.8\times t^2+122.5[/tex]

[tex]y=-4.9t^2+122.5[/tex]

Please find the attachment for graph.

Answer:

3.9

Step-by-step explanation:

APEX

Answer:

Option A is correct.

AA similarity postulate justifies that [tex]\triangle HEF \sim \triangle HGE[/tex]

Step-by-step explanation:

The sum of the measures of a angles in a triangle add up to 180 degree.

In the triangle HGE:

[tex]\angle EHG+\angle EGH+\angle GEH = 180^{\circ}[/tex]

Substitute the given values;

[tex]90^{\circ}+37^{\circ}+\angle GEH = 180^{\circ}[/tex]

[tex]127^{\circ}+\angle GEH = 180^{\circ}[/tex]

Simplify:

[tex]\angle GEH = 180 -127 = 53^{\circ}[/tex]

In triangle HEF and triangle HGE

[tex]\angle FHE = \angle GHE = 90^{\circ}[/tex]   [Angle]

[tex]\angle EFH = \angle GEH = 53^{\circ}[/tex]  [Angle]

AA (Angle-Angle) similarity postulates states that two triangle are similar if they have two corresponding angles that are congruent or equal.

by AA similarity postulates;

[tex]\triangle HEF \sim \triangle HGE[/tex]

The answer would be 198.

Answer:

Option A is correct.

the profit for January was $2,300

Step-by-step explanation:

As per the statement:

In January, wally's widget world had sales of $12,500 and expenses of $10,200

⇒wally's widget world had sales(S.P) = $12,00 and expenses = $10,200.

By using formula:

[tex]\text{Profit} = \text{Sales} - \text{Expenses}[/tex]

Substitute the given value we have;

[tex]\text{Profit} = 12500-10200 =\$ 2300[/tex]

Therefore,  the profit for January was $2,300

Answer:

Graph A is the correct choice.

Step-by-step explanation:

Let x be the number of weeks.

We have been given that a  semiconductor manufacturing company employs 1,000 people. The average weekly salary of each employee is $750.

Let us find the weekly salary for 1000 employees by multiplying 1000 by $750.

[tex]\text{The weekly salary for 1,000 employees}=1,000\times \$750[/tex]

[tex]\text{The weekly salary for 1,000 employees}=\$750,000[/tex]

Let us find amount of salaries after 52 weeks as 1 year equals 52 weeks.

[tex]\text{The amount of salaries after 52 weeks for 1,000 employees}=52*\$750,000[/tex]

[tex]\text{The amount of salaries after 52 weeks for 1,000 employees}=\$39000000[/tex]  

Since at week 0, the salaries for 1000 employees will be also 0, so point (0,0) will be on the line of our graph.

Now let see which of our given graphs has point (0,0) and (52,39000000).

We can see that graph A has y-value 39 million on x equals 52, therefore, Graph A is the correct choice.

The correct unit cost per car is $1.83.

To find the unit cost per car, we need to divide the total cost by the number of cars built. Since each student builds three mouse trap cars and spends an average of $5.50, the total cost for one student is $5.50.

Let's denote the unit cost per car as [tex]\( C \)[/tex]. The equation representing the total cost for one student is:

[tex]\[ 3C = \$5.50 \][/tex]

Now, we solve for [tex]\( C \)[/tex] to find the unit cost per car:

[tex]\[ C = \frac{$5.50}{3} \][/tex]

[tex]\[ C = $1.8333... \][/tex]

Rounding to two decimal places, the unit cost per car is approximately $1.83.

Statement D may apply to the problem Heather is seeking to answer if her graph connects at an unlimited number of locations.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.

Since constants cannot intersect lines or parabolas in infinitely many points, and lines cannot intersect parabolas in more than two points,

Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, Statement  D could describe the equation Heather is attempting to solve.

By graphing the expressions on the two sides, Heather is resolving an equation. Statement D may apply to the problem Heather is seeking to answer if her graph connects at an unlimited number of locations.

Hence statement D is corect.

To learn more, about equations, refer;

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The set {0,1} is closed under both addition and multiplication, but not under subtraction. Closed means that any operation between any two elements in the set produces another element in the set.

The set {0,1} is closed under both addition and multiplication. This means that if you perform either of these operations on any two numbers from the set, the result is a number that is also within the set.

For example if you add 0 and 1 (0+1), or multiply them (0*1), the result (1 and 0 respectively) is still within the set {0,1}. However, the set is not closed under subtraction, because 0-1 gives -1, which is not in the set.

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The sinusoidal function described in the question is a cosine function that has been shifted vertically by 5 units. This can be written in the form f(x) = cos(x - π) + 5.

In the given question, we are told that a sinusoidal function intersects its midline at (0,5) and has a maximum point at (π,6). Since the function reaches its maximum at π, it implies that this is a cosine function which shifted 5 units up on the y axis.

The general form for a cosine function is f(x) = A cos(Bx - C) + D, where: A is the amplitude of the wave, B determines the period of the wave, C is the phase shift, and D is the vertical shift. Given that we reach a maximum at (π,6), the amplitude is 1 (since it rises 1 unit above the midline). The vertical shift is 5, as the function crosses at (0,5).

Considering these factors and that the function hits a maximum (as opposed to a minimum) at x = π, we can say that the cosine's phase shift is π. Thus, the function does not need to be horizontally shifted. Therefore, the function is f(x) = cos(x - π) + 5.

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Answer:

50 days

Step-by-step explanation:

It's simple, we just have to express this as an equation.

x we will take it as the number of days we do not know.

so..

(0.2 M * x) = 10 M

we divide on both sides by 0.2 M.

x *  0.2 M / 0.2M  = 10 M / 0.2 M

we simplify

x = 10M / 0.2 M

finally we only solve and the result of x will be the days it took.

x = 50

50 days

-3(m-2n)=5m             (distribute the negative 3)

-3m+6n=5m                 (add 3m to both sides)

6n= 8m                           (now divide by 8 to solve for m)

6n/8=m                           you can simplify

3/4n=m