Which expression represents the number rewritten in a + bi form?

[tex](f-g)(x)=3x+10-(4x-2)=3x+10-4x+2=-x+12[/tex]

A piecewise function is a function that is defined by several different formulas depending on the input (x). In this case, the function f(x) is a horizontal line for 0 ≤ x ≤ 20. The equation for this function would be y = constant, for 0 ≤ x ≤ 20, where the constant value is defined by the height of the horizontal line on the graph.

To write the equation of the piecewise function that is represented by a graph, you need to identify the different segments of the function and write a mathematical expression that describes each segment. In your case, the function f(x) is a horizontal line and is only defined between x = 0 and x = 20 (both inclusive). So, if we let y = f(x) be the horizontal line, then for the domain 0 ≤ x ≤ 20, the piecewise function can be written as:

Note that the 'constant' value of y is defined by the height of the horizontal line on the graph. This specification assumes that there are no other pieces to the function outside the range of x = 0 to x = 20.

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Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

============================================

We have the points (-4, -3) and (12, 1).

Substitute:

[tex]m=d\frac{1-(-3)}{12-(-4)}=\dfrac{4}{16}=\dfrac{1}{4}[/tex]

Put the volume of a slope and the coordinates of the point (12, 1) to the equation of a line:

[tex]y-1=\dfrac{1}{4}(x-12)[/tex]

The standard formula of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y-1=\dfrac{1}{4}(x-12)[/tex]           multiply both sides by 4

[tex]4y-4=x-12[/tex]             add 4 to both sides

[tex]4y=x-8[/tex]             subtract x from both sides

[tex]-x+4y=-8[/tex]         change the signs

[tex]x-4y=8[/tex]

Answer:

no

Step-by-step explanation:

There is no consistent scale factor.

Answer:

No

Step-by-step explanation:

For triangles to be similar there must be a proportion between their measurements.

That is, for example if from one triangle to another one side doubled, all other sides must also double.

The triangle side on the left sides measure 1.5, 1 and 2.

In the right triangle the sides measure 0.5, 1 and 1.5

There is no proportion factor that serves to convert all the measures of the first triangle to those of the second triangle.

So the triangles are not similar.

Answer:

The approximate solution is: x = -2.29; y = 0.46

Step-by-step explanation:

8x - 10y = -23

9x + 10y =-16

Since you have -10y in one equation and 10y in the other equation, add the equations to eliminate y and solve for x.

17x = -39

x = -39/17

Now substitute -39/17 for x in the first equation, and solve for y.

8(-39/17) - 10y = -23

-312/17 - 10y = -391/17

-10y = -79/17

y = 79/170

The exact solution is x = -39/17; y = 79/170

The approximate solution is: x = -2.29; y = 0.46

Answer:

You can use photo math it does all the math for you and explains why.

Hope this helps!

Step-by-step explanation:

Final answer:

For creating rectangular shaped fractions, Adobe Photoshop or Illustrator can be utilized for graphic designs, while EquatIO is fitting for educational materials involving math. Microsoft Word is another option that includes a built-in equation editor for such purposes.

Explanation:

If you are looking for an app that allows you to create graphics featuring rectangular shaped fractions, there are a few different tools that may be useful depending on your specific needs. For instance, graphic design apps like Adobe Photoshop or Illustrator have the capability to create almost any shape including rectangles, allowing you to design custom graphics that include fractions in any way you desire. If your goal is specifically to create educational materials, a math-oriented tool like EquatIO might be more suitable. This particular app is designed to help create mathematical equations, graphs, and shapes which can then be inserted into documents, making it very useful for educational purposes.

Additionally, if you're just looking to type fractions in a rectangular format for reports or presentations, you might consider using a word processor with good equation support, such as Microsoft Word, which includes a built-in equation editor that allows for the creation of rectangle shaped fractions and other mathematical notations. Always be sure that you have the appropriate licenses and access to these pieces of software before using them for any purpose.

Answer:

[tex]9x^3-2x-3[/tex]

Step-by-step explanation:

The question is

[tex](6x^3-8x-5)+(3x^3+6x+2)\\[/tex]

collect like terms

[tex](6x^3-8x-5)+(3x^3+6x+2)\\\\\\6x^3+3x^3-8x+6x-5+2\\\\\\9x^3-2x-3[/tex]

Answer:

$17.85

Step-by-step explanation:

Let the dollar amount per shirt be represented by s.

Let the dollar amount per pants be represented by p.

You have the following system:

3s+2p=104.81

2s+1p=61.33

If I multiply the bottom equation by -2, I can set the system up for elimination since the equations are already and the same form and I will have 2p and -2p in the same column there.  2p+(-2p)=0

Multiplying equation 2 by -2:

3s+2p=104.81

-4s-2p=-122.66

-----------------------Add the equations:

-1s      =-17.85

Multiply both sides by -1:

s=17.85

So one shirt cost $17.85

Answer:

35

Step-by-step explanation:

To calculate the mean(average) of a data set, add all of the numbers together and then divide by the amount of points you have.

Mean = (16+32+41+54+32)/5 because there are 5 numbers you are adding.

To find the mean of a set of data you must add the data together then divide the sum by the number of data in the set.

Step 1: Adding together the data

16 + 32 + 41 + 54 + 32 = 175

Step 2: Count how many number there are in the data set

There are 5 numbers in this data set

Step 3: Divide the sum of the data by the number of data in the set

175 ÷ 5 = 35

The mean of this data set is 35

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Choice D

Step-by-step explanation:

You are given for graphs.

A. This graph is translated graph of the graph of inverse proportion function

[tex]y=\dfrac{k}{x}.[/tex]

B. This graph is the graph of linear function

[tex]y=kx+b.[/tex]

C. This graph is the graph of quadratic function

[tex]y=(x-a)^2.[/tex]

D. This graph is the graph of logarithmic function

[tex]y=\log_ax.[/tex]

Answer:

A.

Step-by-step explanation:

The slope would be -2/3 and the y-intercept is -6

For this case we must indicate the graph of the following equation:

[tex]-6x-9y = 54[/tex]

Adding 6x to both sides we have:

[tex]-9y = 54 + 6x[/tex]

Dividing between -9 on both sides:

[tex]y = \frac {54} {-9} + \frac{6x} {-9}\\y = -6 - \frac {2} {3} x[/tex]

For an equation of the form[tex]y = mx + b[/tex], the slope is given by "m" and the point of intersection with the y axis is "b".

In this case we have that[tex]b = -6[/tex] and[tex]m = -\frac {2} {3}[/tex]. The slope is negative. So, the corresponding graph is option A

Answer:

Option A

Answer:

x = 20

Step-by-step explanation:

The converse of the same side exterior angles theorem states that when two same side exterior angles are supplementary, the two lines they are on are parallel.

So that means that 5x + 9 and 3x + 11 are supplementary.

Therefore, 5x + 9 + 3x + 11 = 180.

Add like terms: 8x + 20 = 180

Subtract: 8x = 160

Divide: x = 20

Answer:

*To be honest, we have a bunch of ways to find x, but I'm only going to use one.

So in order for A║B, we need the outer angle of these two lines but on the opposite sides to be equal, which means:

   5x + 9 = 180 - (3x + 11)

⇔ 5x + 3x = 180 - 9 - 11

⇔ 8x         = 160

⇔ x            = 160/8 = 20

So x is equal to 20.

Answer:

k=6

Step-by-step explanation:

As stated, x=2/3, so you need to eval in the whole expression given

[tex]k*x^{2} -x-2=0[/tex]

which becomes the following>

[tex]k*(\frac{2}{3}) ^{2}-\frac{2}{3} -2=0\\[/tex]

Solving for K gives>

[tex]k=(2+\frac{2}{3})*\frac{9}{4}\\k=(\frac{9}{2} +\frac{3}{2})[/tex]

[tex]k=\frac{12}{2}[/tex]

Answer:

x can be 0, -1/3, 8 or -2

Step-by-step explanation:

the equation is already expressed in factor form:

-2x(3x+1)(x-8)(x+2)=0​

Simply equate each of the factors to zero

i.e

-2x = 0 ----------> x = 0

3x+1 = 0 ----------> x = -1/3

x-8 = 0 ----------> x = 8

x+2 = 0 ----------> x = -2

Answer:

A. f(x)=155-6x

B. Plug in x=8 and solve.

Step-by-step explanation:

-we can develop an equation for this by first realizing that each week, the sales decrease by 6. thus, we know the amount of sales decreases by 6 every week so we know the formula is: the initial sales amount-6x (x being whatever week).

-we can find the initial amount by noting i=initial sales amount and using the Info from the first week.

149=i-6(1)

155=I

thus, the formula: f(x)=155-6x

- we can plug in 8=x to predict the sales amount on the eighth week:

155-6(8)

155-48

sales on eighth week=107

Answer:

[1, 1]

Step-by-step explanation:

When you plug in these coordinates, you will see that 4 + 2 = 6.

I am joyous to assist you anytime.

Answer:

B

Step-by-step explanation:

drawing from a sample space without replacement is a dependent event. subsequent draws depends on the result of previous draws

Check the picture below.

Answer:

10d cents.

Step-by-step explanation:

This is an everyday mathematics question, in which the value of the currency has to be known. It is a fact that:

1 dime = 10 cents and 1 cent = 1/10 dimes

These relationships can be used to determine the value of the dimes in terms of cents and the value of the cents in terms of dimes respectively. In the question, it is given that there are d dimes. Therefore, using the first formula, it can be inferred that:

d dimes = 10*d cents.

So, the value of d dimes in cents is 10d cents!!!

B. 46 feet because 132/12=11 and 12+12+11+11=46

Answer:

(10 2/3, 5)

Step-by-step explanation:

1/2 x + 1/3y = 7

1/4x + 2/3y = 6

I do not like fractions so I will multiply the first equation by 6 and the second equation by 12 to eliminate the fractions.

6(1/2 x + 1/3y) = 7*6

Distribute

3x+2y = 42

Now the second

12(1/4x + 2/3y) = 6*12

3x+8y = 72

My system of equation is

3x+2y = 42

3x+8y = 72

Subtracting the second from the first

3x+2y = 42

-3x-8y = -72

-------------------

  -6y = -30

Divide by -6

-6y/-6 = -30/-6

y =5

Substituting into 3x+2y = 42

3x+2(5) = 42

3x+10 =42

Subtracting 10 from each side

3x+10-10 =42-10

3x= 32

Dividing by 3

3x/3 = 32/3

x = 32/3 or 10 2/3

Answer:

10 2/3, 5)

Step-by-step explanation:

1/2 x + 1/3y = 7

1/4x + 2/3y = 6

I do not like fractions so I will multiply the first equation by 6 and the second equation by 12 to eliminate the fractions.

6(1/2 x + 1/3y) = 7*6

Distribute

3x+2y = 42

Now the second

12(1/4x + 2/3y) = 6*12

3x+8y = 72

My system of equation is

3x+2y = 42

3x+8y = 72

Subtracting the second from the first

3x+2y = 42

-3x-8y = -72

-------------------

 -6y = -30

Divide by -6

-6y/-6 = -30/-6

y =5

Substituting into 3x+2y = 42

3x+2(5) = 42

3x+10 =42

Subtracting 10 from each side

3x+10-10 =42-10

3x= 32

Dividing by 3

3x/3 = 32/3

x = 32/3 or 10 2/3

Step-by-step explanation:

Any line passing through (-3,7) and (6,4) is,

y-y1=(y2-y1) (x-x1)

(x2-x1)

y-7 = (4-7) (x+3)

(6+3)

y-7 = (-3/9)(x+3)

y-7= (-1/3)(x+3)

3y-21=-x-3

x+3y-21+3=0

x+3y-18=0

Which h is the required line.

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Just as a hint. On this editor, you have to use brackets a lot. We cannot be certain what you mean. I'm going to interpret the question one way, but there are others.

√(5x - 7) = √(3x + 5)

Square both sides.

(√(5x - 7) )^2 = (√(3x + 5) )^2

5x - 7 = 3x  + 5            

Add 7 to both sides.

5x - 7 + 7 = 3x + 5 + 7

Combine

5x = 3x + 12

Subtract 3x from both sides.

5x - 3x = 3x -3x + 12

Combine

2x = 12

Divide by 2

2x/2 = 12/2

x = 6

This confirms that x = 6 is indeed a solution. No other solutions are found, and so x = 6 is the unique solution to the problem.

The solution to the equation (square root 5x-7)= (square root 3x+5) requires squaring both sides to eliminate the square roots and then solving the resulting quadratic equation. We begin by squaring each side:

( square root 5x-7)2 = ( square root 3x+5)2

5x - 7 = 3x + 5

We move all terms to one side to obtain a standard quadratic equation form:

5x - 3x = 5 + 7

2x = 12

x = 6

However, because we squared both sides, we must check the solution in the original equation to ensure it does not produce extraneous solutions. Substituting x = 6 into the original equation, we get:

(square root 5(6)-7) = (square root 3(6)+5)

( square root 30-7) = ( square root 18+5)

square root 23 = square root 23

This confirms that x = 6 is indeed a solution. No other solutions are found, and so x = 6 is the unique solution to the problem.

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}x+b,\ \text{wher}\ b\in\mathbb{R}.}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\==========================\\\\\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\==========================\\\\\text{We have the equation of the line:}\ y=2x+17\to m_1=2.\\\\\text{Therefore}\ m_2=-\dfrac{1}{2}.\\\\\text{The equation of a line:}\ y=-\dfrac{1}{2}x+b,\ \text{wher}\ b\in\mathbb{R}.[/tex]

=====================================

How I got that answer:

A sequence is geometric if you are able to divide any term over its prior one and get the same result each time. Note with something like choice A we have...

term2/term1 = 13/6 = 2.17 (approx) and term3/term2 = 19/13 = 1.46

the results 2.17 and 1.46 are not the same, so we can rule out choice A

---------

Choice B however, we have...

term2/term1 = 3/(-3) = -1

term3/term2 = -3/3 = -1

term4/term3 = 3/(-3) = -1

each time we get -1, so this is the common ratio. We can multiply each term by the common ratio -1 to get the next term, for instance,

term2 = (common ratio)*(term1) = -1*(-3) = 3

term3 = (common ratio)*(term2) = -1*3 = -3

and so on. This proves that sequence B is geometric. Sequences C and D are not geometric for similar reasoning to choice A.

Answer:

(16x^2-1) can be factored over integers so, Option C is correct.

Step-by-step explanation:

Given: 256x^4y^2-y^2

Factorizing the given expression:

Taking y^2 common

=y^2(256x^4-1)

Using formula: a^2-b^2 = (a-b)(a+b)

=y^2((16x^2)^2-(1)^2)

y^2(16x^2+1)(16x^2-1)

y^2(16x^2+1)((4x)^2-(1)^2)

y^2(16x^2+1)(4x-1)(4x+1)

Since (16x^2-1) can be factored over integers so, Option C is correct.

Answer:

Step-by-step explanation:

The unknown [tex]x[/tex] and the numbers are mixed in the given equation. However, in the desired equation, the left-hand side contains only the unknown while the right-hand side contains only numbers.

Start with the given equation. That's statement 1.

The question chooses to move the number [tex]-2[/tex] from the right-hand side of the equation to the left-hand side in statement 2. This change can be done by adding [tex]2[/tex] (the opposite of [tex]-2[/tex]) to both sides of the equation.  

In statement 3, The question moves the term with the unknown [tex]4x[/tex] from the left-hand side of the equation to the right-hand side. This change can be done by adding [tex]-4x[/tex] (the opposite of [tex]4x[/tex]) to both sides of the equation.

The coefficient of the unknown [tex]x[/tex] in statement 3 is [tex]2[/tex]. In statement 4, the question turns this coefficient into [tex]1[/tex]. This change can be done by dividing both sides by the coefficient of [tex]x[/tex]. Keep in mind that multiplying both sides with the reciprocal of that coefficient, [tex]1/2[/tex], will achieve the same effect.

By the symmetric property of equality, [tex]a = b[/tex] if and only if [tex]b = a[/tex]. In other words, if [tex]3/2 = x[/tex] is true, [tex]x = 3/2[/tex] must also be true. That leads to statement 5.

Answer:

(3,3)

(-5,19)

Step-by-step explanation:

y= x^2 - 6

y=-2x + 9

Set the two equations equal to each other y=y

x^2 - 6  =-2x + 9

Add 2x to each side

x^2 +2x- 6  =-2x+2x + 9

x^2 +2x- 6  = 9

Subtract 9 from each side

x^2 +2x- 6-9  =9- 9

x^2 +2x- 15 =0

Factor the left hand side

What 2 numbers multiply to -15 and add to 2

-3 *5 = -15

-3+5 = 2

(x-3) (x+5) =0

Using the zero product property

x-3 =0        x+5 =0

x=3             x=-5

Now we find y for each x

x=3

y=-2(3) + 9 = -6+9 =3

(3,3)

x=-5

y=-2(-5) + 9 = 10+9 =19

(-5,19)

Without additional context or a diagram, it is not possible to determine the measure of angle XYZ from the information provided.

You have asked for the measure of angle XYZ but did not provide a specific diagram or context for angle XYZ. To determine the measure of an angle, one would typically need additional information such as the measures of other angles, the type of geometric figure involved, or an algebraic expression representing the angle.

Based on the information given, which does not directly provide an angle measure for XYZ, it is not possible to accurately determine the measure of angle XYZ. The listed measures (30.1°, 48.7°, 31.1°, 23.6°, 53.1°, etc.) represent other angles or calculations from different problems and cannot be used to infer the measure of angle XYZ without additional context.