Taylor was earning an income of $1,000 a week. Then his income was reduced by 10%. Two months later, his income increases by 10%. How much is Taylor earning, in dollars, after his income increases?

The transformed parallelogram P'Q'R'S' is smaller than the original parallelogram PQRS, due to a scale factor of less than 1 (0.75) being applied in this dilation.

The given transformation (x, y) → (0.75x, 0.75y), the scale factor is 0.75, indicating a reduction in size. This means that the transformed parallelogram P'Q'R'S' is smaller than the original PQRS. The scale factor of 0.75 signifies that both the x and y coordinates of every point in the original parallelogram are multiplied by 0.75, leading to a proportional reduction in dimensions. Therefore, option B) stating that Parallelogram P'Q'R'S' is smaller than parallelogram PQRS due to the scale factor being less than 1, accurately describes the transformation, illustrating the diminished size of the transformed figure in comparison to the original one.

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The correct answer is B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS because the dilation scale factor is 0.75, which is less than 1.

The question asks about the effect of a given dilation on a geometric figure, specifically a parallelogram named PQRS, which is transformed into parallelogram P'Q'R'S'.

This transformation is performed using the dilation rule (x, y) → (0.75x, 0.75y), which indicates that every point on the original parallelogram is multiplied by the scale factor of 0.75 when creating the new parallelogram.

Since the scale factor is less than 1, each coordinate is reduced to 75% of its original value, resulting in a figure that is proportionally smaller than the original.

Therefore, the correct statement about the relationship between the original parallelogram PQRS and the dilated parallelogram P'Q'R'S' is Option B: Parallelogram P'Q'R'S' is smaller than parallelogram PQRS, because the scale factor is less than 1.

Answer:

56.1 in^2

Step-by-step explanation:

When given sides "a" and "b" and the angle α between them, the applicable formula for the area of the triangle is ...

A = (1/2)ab·sin(α)

Substituting the given values, we find the area to be ...

A = (1/2)(14.2 in)(8 in)sin(99°) ≈ 56.1 in^2

Answer:

56.1

Step-by-step explanation:

Diagram

Let's look at the diagram for a moment.

The 8 in line has been extended.

The dashed line is the height associated with the 8 inch line

The dashed line and the 8 inch line's extension meets at right angles.

Discussion

Normally you would take the 8 inch line and the height and divide their product by 2. You don't have the height. So you have to somehow get an expression for it.

The 81o angle is the supplement of the 99o angle. If you take the sine of both of them the sines are equal.

h = sin(81) * 14.2 because

sin(81) = opposite / hypotenuse.

opposite = hypotenuse * sin(81)

opposite = height = hypotenuse* sin(81)

height = 14.2 * sin(81)

Now we can find the area

Area

Area = height * base

base = 8

height = 14.2 * sin(81)

Area = 1/2 * 8 * 14.2 * sin(81)

Area = 56.1

61/3 - 42/3 = 19/3 feet

Answer:

60%

Step-by-step explanation:

It went up 12 dollars, and you need to find how much 12 is of 20 as a percent. You do 12/20 times 5/5 and get 60/100, so 60% markup

Answer:

Step-by-step explanation:

The Answer Well -12$

20 - 32 = -12

Answer:

Area_lawn = 393.75 π ft^2

Step-by-step explanation:

Maximum radius : 30 feet

Minimum radius:  30 feet - 0.25*(30feet)  =  22.5 feet

(25 percent reduction)

To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.

Since the sprinklers have a circular area:

Area = π*radius^2

Max area  = π*(30 ft)^2 = 900π ft^2

Min area  = π*(22.5 ft)^2 = 506.25π ft^2

Maximum area of lawn that can be watered by the sprinkler:

Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2

Area_lawn = 393.75 π ft^2

Answer:

1,590.4 sq ft

Step-by-step explanation:

Answer: x=12

Explanation:

In a parallelogram, adjacent angles equals 180 (consecutive angles). Therefore, (132-x)+(6x-12)=180

Simplify:

-x+6x+132-12=180

5x+120=180

5x=60

x=12

It is located in the 2nd quadrant.

(x,y) - 1st quadrant

(-x,y) - 2nd quadrant

(-x,-y) - 3rd quadrant

(x,-y) - 4th quadrant

Answer:

Second quadrant

Step-by-step explanation:

That coordenates are located in the second quadrant of the cartesian plane

Best regards

Answer:

Picture 1 is the answer.

Step-by-step explanation:

The expression states that the absolute value of a number x , is equal to the number 7. Absolute Values have an 2 inputs for every output (except for 0), the negative and positive inputs both output the same positive number.

Example: abs(-5) = abs(5) = 5

The Absolute value of -5 and 5 both output 5. Therefore, there are two possible x values for the answer to be 7 and those values are -7 and 7. Since these are the only possible values they would be represented on a number line as closed dots.

The only picture with closed dots on both -7 and 7 is picture 1. So that is the answer.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: graph one

Step-by-step explanation:

The system has two solutions: [tex]\( (2, -2) \) and \( (-1, 4) \),[/tex] found by solving their simultaneous equations.

let's solve the system step by step:

Given the system of equations:

[tex]1. \( y = -2x + 2 \)\\2. \( y = x^2 - 3x \)[/tex]

We want to find the values of [tex]\( x \) and \( y \)[/tex] that satisfy both equations simultaneously.

First, we set the equations equal to each other since they both equal [tex]\( y \):[/tex]

[tex]\[ -2x + 2 = x^2 - 3x \][/tex]

Now, let's rearrange this equation to get a quadratic equation:

[tex]\[ x^2 - 3x + 2x - 2 = 0 \]\[ x^2 - x - 2 = 0 \][/tex]

Now, we can use the quadratic formula to solve for [tex]\( x \):[/tex]

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where [tex]\( a = 1 \), \( b = -1 \), and \( c = -2 \).[/tex]

[tex]\[ x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}} \]\[ x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2} \]\[ x = \frac{{1 \pm \sqrt{9}}}{2} \]\[ x = \frac{{1 \pm 3}}{2} \][/tex]

So, we have two potential values for [tex]\( x \): \( x = 2 \) and \( x = -1 \).[/tex]

Now, let's find the corresponding [tex]\( y \)[/tex] values for each [tex]\( x \)[/tex] value using either of the original equations:

For [tex]\( x = 2 \):[/tex]

[tex]\[ y = -2(2) + 2 = -4 + 2 = -2 \][/tex]

For [tex]\( x = -1 \):[/tex]

[tex]\[ y = -2(-1) + 2 = 2 + 2 = 4 \][/tex]

So, we have two solutions for the system:[tex]\( (2, -2) \) and \( (-1, 4) \).[/tex] Therefore, the system has 2 solutions.

Answer:

The state with the second lowest population has the lowest population density.

Step-by-step explanation:

The state with the second lowest population has the lowest population density.

State B has the second lowest population, and it has the lowest population distance considering it has a substantial amount of area compared to other states, yet 1, 333, 089 people, in comparison it therefore as the lowest population density.

The statement "The state with the second-lowest population has the lowest population density." is true.

The population density can be found by dividing the total population of an area by the area.

We must calculate the population densities of all the states to determine which state has the highest density.

This can be done as shown below:

State A:

Population density = Population/Area

= 1,055,173/2,677

= 394.162

State B:

Population density = Population/Area

= 1,333,089/36,418

= 36.605

State C:

Population density = Population/Area

= 3,596,677/5,543

= 648.87

State D:

Population density = Population/Area

= 6,745,408/10,555

= 639.072

We can see that the state with the second-lowest population has the lowest population density.

Therefore, we have found that the statement "The state with the second-lowest population has the lowest population density." is true. The correct answer is option B.

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Answer:

42 correct; if all were answered, that means 7 were wrong. 7/49 reduces to 1/7; one seventh were wrong.

Answer:

  6.3  (x, y) = (3, 1)

  6.4  (x, y) = (-4, 2)

Step-by-step explanation:

An augmented matrix in this context is an array of the coefficients in the equation. For example, the equation x -2y = 3 can be represented by the row of numbers 1 -2 3. When writing the matrix by hand, we usually just separate the elements in a row using blank space. Some calculators require a comma or other character between matrix elements. The entire array is enclosed in square brackets.

An augmented matrix may have a vertical line separating the square matrix of coefficients from the rightmost column of constants.

Many graphing calculators have functions available for entering and solving linear equations in this form.

__

6.3 The augmented matrix is ...

[tex]\left[\begin{array}{cc|c}2&3&9\\1&-4&-1\end{array}\right][/tex]

This array can be used to solve the system of equations using "row operations." The idea is that any row can be multiplied by any number, and any row can be added to any other row (multiplied by some number or not). So, the same techniques used to solve a system by elimination can be used here.

We can, for example, subtract twice the second row from the first. Then we have ...

[tex]\left[\begin{array}{cc|c}2-2(1)&3-2(-4)&9-2(-1)\\1&-4&-1\end{array}\right]\\\\\left[\begin{array}{cc|c}0&11&11\\1&-4&-1\end{array}\right] \quad\text{simplified}\\\\\left[\begin{array}{cc|c}0&1&1\\1&-4&-1\end{array}\right] \quad\text{first row divided by 11}\\\\\left[\begin{array}{cc|c}0&1&1\\1+4(0)&-4+4(1)&-1+4(1)\end{array}\right] \quad\text{4 times row 1 added to row 2}\\\\\left[\begin{array}{cc|c}0&1&1\\1&0&3\end{array}\right] \quad\text{simplified}[/tex]

When we turn this last matrix back into equations, we get ...

  0x +y = 1

  1x + 0y = 3

That is, the solution is (x, y) = (3, 1).

__

6.4 The augmented matrix is ...

[tex]\left[\begin{array}{cc|c}4&5&-6\\3&2&-8\end{array}\right][/tex]

Let's start the solution of this one by dividing the first row by 4.

[tex]\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3&2&-8\end{array}\right] \\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\3-3(1)&2-3(\frac{5}{4})&-8-3(-\frac{3}{2})\end{array}\right] \quad\text{row 2 minus 3 times row 1}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&-\frac{7}{4}&-\frac{7}{2}\end{array}\right] \quad\text{simplify}\\\\\left[\begin{array}{ccc}1&\frac{5}{4}&-\frac{3}{2}\\0&1&2\end{array}\right] \quad\text{multiply row 2 by -4/7}[/tex]

We can eliminate the y-term in the first row by subtracting 5/4 times the second row. This will put the matrix in the form that shows us the solution directly.

[tex]\left[\begin{array}{ccc}1-\frac{5}{4}(0)&\frac{5}{4}-\frac{5}{4}(1)&-\frac{3}{2}-\frac{5}{4}(2)\\0&1&2\end{array}\right] \quad\text{row 1 minus 5/4 times row 2}\\\\\left[\begin{array}{ccc}1&0&-4\\0&1&2\end{array}\right][/tex]

This tells us ...

  x = -4

  y = 2

So the solution is (x, y) = (-4, 2).

An augmented matrix organizes the coefficients of a system of linear equations. After setting up the matrix with the coefficients from the equations, methods like Gaussian elimination or Gauss-Jordan elimination can be used to solve the matrix and consequently, solve the system.

An augmented matrix is a compact way of keeping track of the coefficients in a system of linear equations. Here's how to form it and solve the system:

Gaussian elimination involves using elementary row operations to manipulate the matrix to a form where the solution is easier to find, often called reduced row echelon form. For the Gauss-Jordan method, the main idea is to get zeros below (and above when possible) a leading 1, and make sure that leading 1 is the only nonzero entry in its column.

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Answer:

The formula to calculate standard deviation from probability is \sqrt(n*p*(1-p)). n is the sample size, and 200 in this case (number of putts for practice). p is 80% or 0.8, the probability that he can make it. So the standard deviation is \sqrt(200*0.8*(1-0.8)=\sqrt(200*0.8*0.2)=\sqrt(16)=4.

Answer:

The area of the circle is [tex]530.93\ units^{2}[/tex]

Step-by-step explanation:

we know that

The area of a circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=26/2=13\ units[/tex] ----> the radius is half the diameter

assume

[tex]\pi=3.1416[/tex]

substitute

[tex]A=(3.1416)(13)^{2}=530.93\ units^{2}[/tex]

ANSWER: 15.5 units^2

well, 1/6 of 3/4 is simply their product, thus

[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3}{6}\cdot \cfrac{1}{4}\implies \cfrac{1}{2}\cdot \cfrac{1}{4}\implies \cfrac{1}{8}[/tex]

im pretty sure it’s D

The k value in the equation y = f(x) + k causes a vertical shift of the graph. If k is positive, the graph shifts up; if k is negative, it shifts down. Thus, the correct answer is B.

In the function transformation y = f(x) + k, the term k represents a vertical shift of the graph. Specifically:

Thus, the correct answer to the question is:

B. Shifts the graph up k units.

To summarize, the value k in the equation y = f(x) + k causes a vertical shift upwards if it's positive and downwards if it's negative.

Answer:

5.92

Step-by-step explanation:

-71/-12=5.92

Answer:

[tex]\frac{71}{12}[/tex]

Step-by-step explanation:

Reduce the expression, if possible, by cancelling the common factors.

Exact Form :

[tex]\frac{71}{12}[/tex]

Decimal Form :

  5.916

Mixed Number Form :

5[tex]\frac{11}{12}[/tex]

Hope this helps,

Davinia.

Answer:

  b.  6 cm

Step-by-step explanation:

Q is the midpoint of PR, so QR = PR/2 = (12 cm)/2 = 6 cm

QUESTION 1

The given logarithm is

[tex]\log_7\sqrt{a^3b^9}[/tex]

We rewrite to obtain;

[tex]\log_7(a^3b^9)^{\frac{1}{2}}[/tex]

Use the power rule of logarithm ; [tex]\log_a(m^n)=n\log_a(m)[/tex]

[tex]\frac{1}{2}\log_7(a^3b^9)[/tex]

Use the product rule; [tex]\log_a(mn)=\log_a(m)+\log_a(n)[/tex]

[tex]\frac{1}{2}[\log_7(a^3)+\log_7(b^9)][/tex]

Use the power rule of logarithms again;

[tex]\frac{1}{2}[3\log_7(a)+9\log_7(b)][/tex]

Or

[tex]\frac{3}{2}\log_7(a)+\frac{9}{2}\log_7(b)][/tex]

QUESTION 2

Given;

[tex]\log_6(\frac{x^5}{y^9})[/tex]

Apply the quotient rule of logarithm; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]

[tex]\log_6(\frac{x^5}{y^9})=\log_6(x^5)-\log_6(y^9)[/tex]

Apply the power rule to get;

[tex]\log_6(\frac{x^5}{y^9})=5\log_6(x)-9\log_6(y)[/tex]

QUESTION 3

Given;

[tex]\log_8(x^3y^7)[/tex]

Use the product rule to get;

[tex]=\log_8(x^3)+\log_8(y^7)[/tex]

Use the power rule now;

[tex]=3\log_8(x)+7\log_8(y)[/tex]

Answer:

16 feet

Step-by-step explanation:

Since the scale is 3 in : 4 ft, the model car is 16 ft.

To find the actual length of a model car given a scale of 3 inches : 4 feet with the model car being 12 inches long, set up a proportion to calculate the actual car length, which is 16 feet.

A scale of 3 inches : 4 feet means that for every 3 inches on the model car, the actual car is 4 feet long. Given that the model car is 12 inches long, you can set up a proportion:

Solving for x, you get the actual length of the car to be 16 feet.

Answer:

(2,0) is not a solution of the system. The point does not belong to any of the graphs.

Step-by-step explanation:

To easily solve this question, we can graph both equations in a graphing calculator, and verify the intersection point, which is equal to the solution of the system of equations.

Plotting the graphs

y = 3x + 2

g = |x-1| +1

We obtain the intersection point

(0,2)

Solution of the system of equations

Answer:

=55m

Ahh. Correct me if I'm wrong.

Answer:

So the answer is (3, 0) on a graph.

Step-by-step explanation:

What I use is a graphing calculator. It helps tremendously. It is called desmos.com. Hope this helps.

Answer:

The given function is

[tex]y=log(x-2)[/tex]

To graph any function, we just have to five arbitrary values to x-variable, and see the y-values that gives to formed coordinate pairs to graph them then.

In this case, the table that shows these values is gonna be

X       Y

2.5   -0.3

3        0

3.5    0.2

4       0.3

4.5 0.4

Notice that we started from [tex]x=2.5[/tex]. The reason is beacuse the given logarithmic function is not defined for values equal or lower than 2, when taht happens, the function becoms undetermined. This means the domain of the given function has to be restricted to [tex]D= (x>2)[/tex], otherwise the function won't be defined.

Next, we evalute the function for each case.

[tex]x=2.5[/tex]

[tex]y=log(x-2)=log(2.5-2)=log(0.5) \approx -0.3[/tex]

[tex]x=3\\y=log(x-2)=log(3-2)=log(1)=0[/tex]

[tex]x=3.5\\y=log(x-2)=log(3.5-2)=log(1.5) \approx 0.2[/tex]

[tex]x=4\\y=log(x-2)=log(4-2)=log(2) \approx 0.3[/tex]

[tex]x=4.5\\y=log(x-2)=log(4.5-2)=log(2.5) \approx 0.4[/tex]

When you have the table completed, you proceed to graph each coordinate.

In this case, the graph of the logarithmic function would be as the image attached. That's all the process to graph the function.

(In the graph, you can observe how fast the function drops when is near to x=2, that's the undetermination behaviour we talk about lines above).

Answer:

Dependant Variable

Step-by-step explanation:

Answer:

Step-by-step explanation:

The response variable is the dependent variable.

Answer:

Its the First choice.

Step-by-step explanation:

(3 m-2 n)^-3  / 6m n^-2

= (1/27) m^6 n^-3 / 6 m n^-2

= m^5 n ^-3 / 27*6  n^-2

= m^5 n^2 / 162 n^3

= m^4 / 162 n  (answer).

The correct answer is option (A) m5 /162n

Let us solve step by step

See the attached figure for solution

Answer:

[tex]a_n=-12-4(n-1)[/tex]

Step-by-step explanation:

The given sequence is

-12,-16,-20...

The first term of this sequence is [tex]a_1=-12[/tex].

The common difference is

[tex]d=-16--12[/tex]

[tex]d=-16+12=-4[/tex]

The nth term of this arithmetic sequence is;

[tex]a_n=a_1+d(n-1)[/tex]

We substitute the values for the first term and the common difference to obtain;

[tex]a_n=-12-4(n-1)[/tex]

Answer:

[tex]a_{n} = -12-4(n-1)[/tex]

Step-by-step explanation:

We have given a arithmetic sequence.

-12,-16,-20,...

We have to find formula for a given sequence.

The general formula for nth term of sequence is :

[tex]a_{n} = a_{1}+d(n-1)[/tex]

In given sequence,

[tex]a_{1} = -12[/tex]

d is the common difference between consecutive terms.

d = -16-(-12)  = -16+12

d = -4

Putting given values in formula, we have

[tex]a_{n} = -12-4(n-1)[/tex] which is the answer.

After calculating the perimeters, both the square and the rectangle have the same perimeter of 32 inches when the square has each side measuring 8 inches and the rectangle has dimensions of 6 inches by 10 inches.

To determine which shape has the greater perimeter, calculate the perimeter of both the square and the rectangle. The formula for the perimeter of a square is 4 × side length, and the formula for the perimeter of a rectangle is 2 × (length + width).

For the square with each side measuring 8 inches, its perimeter is 4 × 8 = 32 inches.

For the rectangle with a width of 6 inches and a length of 10 inches, its perimeter is 2 × (10 + 6) = 2 × 16 = 32 inches.

Therefore, both the square and the rectangle have the same perimeter of 32 inches.