Given triangle ABC with m

The function g(x) is a piecewise function For x 4, 1 g(x) = |x + 1| and for

x 1, 3 g(x) = 2.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

From the graph, we can conclude that g(x) is a piecewise function.

When x is - 4, 1 g(x) = |x + 1|.

And when x is 1, 3 g(x) = 2, A constant function.

Now, g(-2) = | - 2 + 1| = 1.

g(1) = | 1 + 1| = 2.

g(4) = 2.

The value of x when g(x) = 3 is - 4.

The value of x when g(x) = 1 is (0, - 2) as both satisfy g(x).

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The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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-28 is the standard form of the equation.

Ax+By=C is the formula for a linear equation. You must place the x and y on the same side of the equal sign and the constant on the other side in order to convert an equation in slope-intercept form (y=mx+b) to standard form. Terms can be moved using inverse procedures.

The standard form of a linear equation is

Ax+By=C A x + B y = C .

y=-3/4x+7 in standard form

Multiply both sides by 4  .

4y=4(3.4x+7) 4 y = 4 ( 3 4 x + 7 ).

3x - 4y = -28

-28 is the standard form of the equation.

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Answer:8a<8b

Step-by-step explanation:

8a<8b

The answer to this Question based on probability is discussed below

What is probability of a event?

It is just defined as number of favourable outcomes divided by the total number of outcomes.

Solution:

First of all we need total number of events here as we know probability of sample space is 1 only. hence lets assume there are P elements in sample space and Solving more than number of expected puzzles in 5 minutes is 1 favourable case.

Hence probability will be 1/P where P is no of elements of sample space.

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To solve the given equation, t² - t = 12, by factoring, we will use (t + 3)(t - 4) = 0. The correct option is the first option

From the question, we are to determine how to solve the given equation by factoring

From the given information,

The given equation is

t² - t = 12

First, we will solve the equation by factoring

t² - t = 12

Transfer the constant to the other side

t² - t - 12 = 0

Factorize the expression

t² -4t + 3t - 12 = 0

t(t - 4) +3(t - 4) = 0

(t + 3)(t - 4) = 0

Then,

t + 3 = 0 OR t - 4 = 0

t = -3 OR t = 4

Hence, to solve the equation we will use (t + 3)(t - 4) = 0

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Kara erred when she answered the equation 2x + 6 = -8. Instead, she should have solved the equation 2x + 6 = 8 because it relates to the second situation (where -2x + 6 + 10 is smaller than 0).

Kara made a mistake when solving the equation |- 2x + 6 + 10| = 2. The correct steps to solve this equation are as follows:

First, we need to find the value of -2x + 6 + 10. To do this, we need to remove the absolute value bars by considering two cases:

a. If -2x + 6 + 10 is greater than or equal to 0, then the absolute value is equal to -2x + 6 + 10.

b. If -2x + 6 + 10 is less than 0, then the absolute value is equal to the negative of -2x + 6 + 10.

In the first case, we have -2x + 6 + 10 = 2. Solving this equation gives us x = -1.

In the second case, we have -(-2x + 6 + 10) = 2. Solving this equation gives us x = 7.

Therefore, the solution to the equation |- 2x + 6 + 10| = 2 is x = {7, -1}.

She made a mistake when she solved the equation 2x + 6 = -8. She should have solved the equation 2x + 6 = 8 instead, because this is the equation that corresponds to the second case (where -2x + 6 + 10 is less than 0).

As a result, Kara got the wrong value for x and included the incorrect solution {7, -1} in her final answer.

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The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.

For k=- 5, y=f(x) + k represents a vertical shift down.

For h=4, the horizontal shift left is y=f(x+h).

Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

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Answer:

Step-by-step explanation:

f −1 (x)= 3x−2

​

f, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 3, end fraction.

Answer:

the answer to your question is 11

Step-by-step explanation:

1620÷180= 9

9+2=11

Answer:

Right and Left: Negative Infinity

Even Function

Negative Leading Coefficient

Step-by-step explanation:

First of all, both ends of the graph go down to negative infinity. As a result of this, we can determine that the sign of the leading coefficient was also negative. The graph is even because it shifts directions thrice and both ends of the graph go in the same direction.

Answer:

1. (A.)

2.(D.)

3.(D.)

4.(A.)

5.(A.)

6. (B.) & (D.)

7. (A.), (D.)

Step-by-step explanation:

Trust

Answer: 27.5, B

Step-by-step explanation:

      its a right angled trianalgle,

    ==> (30)^2= ((12)^2)+(x^2)

   ==> x^2= 900-144

==> x^2 = 765

==> x=(756)^(0.5)

==> x=27.49

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Answer:

His profit would be (-20)*3 or -60 $

Step-by-step explanation:

First month profit = -20 $

if the next three months will be the same, then:

(-20)*3

-60 $

The required scale factor  for the given line segment is 2.

In math, a line segment  is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.

Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.

We have,

QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2

Then the scale factor is of the dilation is 2 (magnification)

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Answer:  here is your answer

Step-by-step explanation:

(9.3 × 10^6) + (1.8 × 10^4) is 93.18E+5.

(9.3 × 106) + (1.8 × 10^4)

(9.3 × 106) + (0.018 × 10^6)

(9.3 + 0.018)× 10^6

(9.318)× 10^6

scientific notation

(93.18E+5)

Answer:

as u can see the pattern is going up by 7.

Step-by-step explanation:

Answer:

Yup I think so to

Step-by-step explanation:

Answer:

Yes, it is an elimination problem.

x = -1.69230769

Step-by-step explanation:

You can eliminate 20y by adding both equations together.

Then, you will get 13x = -22.

Divide by 13 on both sides to get x= -1.69230769

Answer:

∠ GFC = 70°

Step-by-step explanation:

∠ BFE and ∠ CBF are alternate angles and are congruent, that is

∠ BFE = 37°

∠ BFE , ∠ BFC and ∠ GFC lie on a straight line and sum to 180° , then

37° + 73° + ∠ GFC = 180°

110° + ∠ GFC = 180° ( subtract 110° from both sides )

∠ GFC = 70°

Therefore, the distance between the points (-3, -6) and (5,0) is 10 units. This is option A.

A mathematical procedure called the distance formula is used to calculate the separation between two locations on a plane. The Pythagorean theorem, which asserts that the square of a distance between two locations is equal to the sum of the squares of a difference in their coordinates, is where the formula is derived from.

To utilise the distance formula, you must first have the coordinates of the two places. These coordinates are usually expressed as (x1, y1) and (x2, y2), where x1 and y1 stand for the coordinates of the first point and x2 and y2 stand for the coordinates of the second point, respectively.

d = √((x2 - x1)^2 + (y2 - y1)^2)

How to solve?

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((5 - (-3))^2 + (0 - (-6))^2)

 = sqrt((8)^2 + (6)^2)

 = sqrt(64 + 36)

 = sqrt(100)

 = 10

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The dotted line represents that the region is strictly less than the equation of the line.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The dotted line shown in the graph and the yellow region described by the equation of a line is the region that is strictly less than the given line.

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Answer:

The rate of change is also called the slope.  The slope is -2

Step-by-step explanation:

Find 2 points on the line.  I am going to use the points (0,5) and (4, -3).  the rate is the change in y over the change in x.  From the two points, my values are -3 and 5.  The x values are 4 and 0.

To find the change, I subtract the y values and the x values.

[tex]\frac{-3-5}{4-0}[/tex] = [tex]\frac{-8}{4}[/tex] = -2

Answer: -2

Step-by-step explanation: The rate of change is also known as the slope!

To find the slope, you need to find the rise/run.

Let's pick two points ( 0,5) ( 4, -3)

You see that the y goes down by 8 and the x goes right by 4, so the rate of change is -8/4 = -2

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That is a change in the hypotenuse's length of -2.6 inches per second.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7

h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)

= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second

2.6 inches are lost from the hypotenuse every second.

Check the response by observing what transpires in one second.

30 to 35 on the short leg

greater leg descends from 40 to 37

From 50 to 47.4 is the hypotenuse

In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.

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Answer: 0.235

Step-by-step explanation:

To round up you need a number = 5 or > 5

So to round to 2 sig fig, the number will have to be 0.235

Answer:

0.62

Step-by-step explanation:

1.86 divided by 3 is 0.62

The Rate of Tax for his state is 2.3%.

What is tax rate?

The ratio at which a business or individual is taxed in a tax system is known as the tax rate. Statutory, average, marginal, and effective tax rates are some of the ways that are used to present them. The terms inclusive and exclusive can be used to present these rates when applied to a tax base.

Annual Salary of Marcus Hatfield is = $43500

His Exemption from the tax is = $2000

He pays tax on the remaining amount i.e.

$43500 - $2000 = $41500.

His contribution toward the tax is $ 954.50,

Let the Rate of tax is x, thus

[tex](\frac{X}{100} *41500) = 954.50\\ x = \frac{95450}{41500} \\x = 2.3[/tex]

Thus, the rate of tax is 2.3% of his salary.

Hence, the Rate of Tax for his state is 2.3%.

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To view the representation of graph of check the attached image.

Given that ;

Stewart's overdue assignment = 36

Per day he complete 4 overdue assignments.

To find : In how many days he complete all the overdue assignments

To complete 36 overdue assignments = 36/4

                                                                = 9 days

Therefore, In 9 days he complete all the overdue assignments

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By using slope of a curve, it can be calculated that

This information cannot be estimated by a single linear model

What is slope of a curve?

Slope of a curve at a point is the tangent of the angle that the tangent to the curve at the point makes with the positive direction of x axis.

The sale of the board game is as follows-

After 12 months, they sold 4 thousand games; after 18 months, they sold 7 thousand games; and after 36 months, they sold 15 thousand games.

The curve passes through (12, 4000), (18, 7000) and (36, 15000)

Slope of curve passing through  (12, 4000) and (18, 7000) = [tex]\frac{7000 -4000}{18 -12}[/tex] = 500

Slope of curve passing through  (18, 7000) and (36, `15000) = [tex]\frac{15000-7000 }{36 -18}[/tex] = [tex]\frac{4000}{9}[/tex]

As the slope is not the same, this information cannot be estimated by a single linear model

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Answer from left to right: 48, 80, 4.5, 160

Step-by-step explanation: