Evaluate Piecewise Functions. (Everything you need to know is in the photo. You can also use the word "undefined" next to the answer only if necessary).

1) given

2) base angles theorem

3) PN=QN

4) [tex]\angle 3=\angle 4[/tex]

5) MP=OQ

7) PQ, QP

8) MQ=PO

9) ASA

The domain of the function y = x² - 1 in interval notation is (-∞, + ∞).

The given is y = x² - 1.

The domain of the function is;

Thus, the domain of the function in interval notation is  (-∞, + ∞).

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Answer:

81 mph

Step-by-step explanation:

2x+2(x-12) = 300

Answer:

C' = (15, 7)

Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.

Step-by-step explanation:

If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.

Given vertices of triangle ABC:

To maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.

Given:

If ΔABC is dilated by a scale factor of 3, with the origin as the center of dilation, B' = (3, 12).  If the triangle is then translated 1 unit up, B' = (3, 13), which matches the given coordinate of point B'.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (3x, 3y + 1)

Therefore, the coordinates of point C' are:

⇒ C' = (3(5), 3(2) + 1) = (15, 7)

The statements that describe key features of function g if g(x) = f(x + 2) are;

a. y-intercept at (0,4)

b. domain of {x|-∞ < x < ∞}

c. horizontal asymptote of y = 0

We are given the function f(x) = 2^(x)

We want to find the features of the function g if;

g(x) = f(x + 2)

Let us first find f(x + 2);

g(x) = f(x + 2) = 2^(x + 2)

The y-intercept is when x = 0;

g(0) = 2^(0 + 2)

g(0) = 4

Some features in a function that limit the x values are: roots, fractions, etc.

g(x) = 2^(x + 2) does not have any restricting value of x.

This means the value of x ranges from negative infinity to positive infinity.

Hence, the domain is: (-∞, ∞)

Next, calculate the horizontal asymptote.

To do this, we plot the graph of g(x) --> see attachment

Then we trace a horizontal line from the horizontal part of the curve of g(x) till it gets to the y-axis.

From the attached graph of g(x), the line touches the y-axis at y = 0

So, the horizontal asymptote is: y = 0

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The missing options are;

a. y-intercept at (0,4)

b. domain of {x|-∞ < x < ∞}

c. horizontal asymptote of y = 0

d. horizontal asymptote of y=2

e. y-intercept at (0,1)​

Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

Explanation:

To solve for x first we have to put all terms that contain x together:

Substract x from both sides:

Now substract 5 from both sides:

And finally divide both sides by 3:

Answer:

x = 3

When 10kg is increased by 20%, the number becomes 24%

Percentage is a measure of frequency that is used to express a quantity as a number out of 100. The sign that is used to represent percentages is %. In order to convert a number to a percentage, multiply the number by 100.

The new increased number = (100% + percentage increase) x initial number

(100 + 20%) x 20%

120% x 20%

1.20 x 20% = 24%

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The ratio of 29: 1 is 29
The mathematical equation is 29/1

A ratio can simply be defined as an ordered pair of numbers, say x and y, written in the form x / y where  of the denominator is note equivalent to zero.

It is known to explain how many times a given number contains another number in a proportion.

It is seen as the comparison of two numbers , elements or quantities having the same units and moving further to explain how much of one of the element or quantity is present in the another one.

This is achieved based on their magnitude or sizes.

A proportion is a mathematical equation with which two ratios are set equivalent to each other.

A ratio is expressed mathematically as;

x/y

Given the ratio;

29: 1

The equation is = 29/1 = 29

Hence, the ratio is 29

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When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3

The expression is given as

6 + root 27over 4 - root 3

Mathematically, the expression can be represented as

6 + √27/4 - √3

Expand 27 as the product of 9 and 3

So, we have the following equation

6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3

Expand the products in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 + √9 * √3/4 - √3

Evaluate the square root of 9 in the above equation

So, we have

6 + √27/4 - √3 = 6 + 3/4√3 - √3

Evaluate the like terms in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 - 1/4√3

Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3

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Answer:

26

Step-by-step explanation:

​(f​+g)(​-5)=

​f(-5)+g(-5)=

​-5+1+(-5)^2-(-5)=

-4+25+5=

-4+30=

30-4=26

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

a 50% probability means 1/2 or 0.5.

that means

desired cases = 1/2 × totally possible cases

at start we have

3 red

3 white

5 blue

that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.

so, the starting probability to pull a white marble is

3/11.

now, we need to say

(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)

to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).

6 + 2x = 11 + x

6 + x = 11

x = 5

we need to add 5 white marble to give us a 50% probability to pull a white marble.

we have then

3 red

3 + 5 = 8 white

5 blue

that makes 5+8+3 = 16 totally possible cases and 8 desired cases.

so, the probability is

8/16 = 1/2

=> our calculation was correct

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A bag contains 3 red marbles, 3 white marbles, and 5 blue marbles. only white marbles will be added to the bag.

Let 'x' be the number of white marble added. Then the equation is given as,

0.50 = (x + 3) / (x + 3 + 3 + 5)

Simplify the equation, then we have

0.50 = (x + 3) / (x + 3 + 3 + 5)

0.50 = (x + 3) / (x + 11)

0.50x + 5.5 = x + 3

0.50x = 2.5

x = 5

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

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Answer:

Derivative of y=(x⁴-2x³+5x²-4)³

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

You have to use rise over run. For example, to go from (-1,0) to (-2,2), you have to go up 2 squares and go left 1. That gives you 2/-1, which is -2. Hope this helps!

Given that 2500 students entered the Teacher Education Program.

20% of the students are male. Thus,

Thus,

Thus, the ratio of the number of males to the number of females is evaluated as

Hence, the ratio of the number of females to the number of males is thus 4:1

Answer:

24

Step-by-step explanation:

Opposite sides on a rectangle are equal

So 2(3x+3)+2(4x)=104

Now expand, so 6x+6+8x=104

Simplify like terms, 14x+6=104

14x+6-6=104-6

14x=98

14x/14=98/14

x=7

Now just substitute the 7 in for the 3x+3 as thats what we are looking for.

3×7+3=24

The solution to the given addition problem is 150.6 ft^9.

Converting everything to the same unit is the simplest solution to this problem.

The conversions are:

1 cubic yard = (27 cubic feet)

1 cubic inch = (0.000578704 cubic feet)

The addition can be performed as,

(6 cu yd × 9 cu ft × 134 cu in) + (1 cu yd × 12 cu ft × 200 cu in)

=  [6(27 cu ft) × 9 cu ft × 134(0.000578704 cu ft)] + [1(27 cu ft) × 12 cu ft × 200(0.000578704 cu ft)]

= 150.6 ft^9

The result of the addition is 150.6 ft^9.

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Answer: [tex]\frac{1}{1024}[/tex]

Step-by-step explanation:

[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]

[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]

[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The value of x is 4 and 0

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc. Consider that James and Natalie came up with the notion to arrange matchsticks into numerical patterns when they were fiddling with them.

Given that : [tex](x-2)^{2} = 2[/tex]

[tex](x-2)^{2} = 2[/tex]

(x-2)=±2

x= 4

x=0

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Answer:

20

Step-by-step explanation:

Every 1 hour it cost $20

You can find this by using the equation y2-y1 divided by x2-x1

y2 is 40 y1 is 20

x2 is 2 and x1 is 1

40-20 divided by 2-1 equals 20

This year, one of her fields yielded 176.4 bushels of corn. $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.

Given that,

On her farm, Molly raises corn that she sells for pig food. This year, one of her fields yielded 176.4 bushels of corn.

We have to find how much will Molly make from this field if corn is now selling for $3.75 per bushel.

We have to multiply

=176.4×3.75

=661.5

Therefore, $661.5 will Molly make from this field if corn is now selling for $3.75 per bushel.

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Answer:

d

Step-by-step explanation:

Divide

6x2+5x+1

x+2

=6x−7+

15

x+2

We know that Emma has skydived 16 times, and also Emma has skydived twice as many times as Nico, so Nico has skydived:

So, Nico has skydived 8 times.

Finally, we know that Gus has skydived 4 more times than Nico, so:

Gus has skydived 32 times.

Answer: The Brown family ate 1.85 pies in all

Step-by-step explanation: If you think about it all you have to do is 0.75+0.5= 1.25 and then you do 1.25+ 0.6  and then get 1.85 so they ate 1.85 pies in all

Hope this helped!!!!

The number of percussionists on the sidelines is 40.

Given:

Total number of members in high school band = 180

Let's assume "x" is the number of percussionists that are on the sidelines.

According to the question, there are two percussionists to every seven marching instruments. Then,

Number of members = 7 + 2 = 9

You can write the following proportion knowing that there are 180 total members of the high school band:

[tex]\frac{x}{180} = \frac{2}{9}[/tex]

Solving the proportion to get the value of x,

[tex]x = \frac{2}{9} * 180[/tex]

x = 40

Therefore, there are 40 percussionists on the sidelines.

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Shiloh can run 04 laps per minute if in 25 minutes Shiloh can run in 10 laps around the track and it is Laps per minute is simply division.

The ratio that is connecting two given numbers is what is known as the exact proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names that can be given for the constant of proportionality.

To represent the equation in laps per min,

L/m = 10/25

= 2/5

= 0.4 laps per minute

The constant of proportionality in this situation

10/25 = 0.4

The equation to represent the relationship.

y = 0.4x

Identifying the same x and y variables is the first step in determining the proportionality constant. X will be the weight and Y will be the number of butter sticks in order to calculate the exact weight to stick ratio.

Then to determine the proportionality constant, we can use the constant equation k = y x.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

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Solution

The bullfdng dataset has its median close to the center of the boxplot.

- This implies that the dataset is symmetric.

- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.

- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed

Final Answer

OPTION A

Answer:

a. Exponential decay

b. f(x) = a (1 - r)^x

c. f(x) = 25(1 - 0.06)^x

d. 16 terms

Explanation:

a. Does this problem represent exponential growth or decay? How do you know?

Each day the number of terms that you know is less than the day before, so there is a decrease in the vocabulary terms memorized. It means that the problem represents exponential decay.

b. Which exponential formula below will you use for this problem? Why?

The formula for the exponential decay is:

Where a is the initial value and r is the rate of decay.

So, the formula that you will use is f(x) = a (1 - r)^x

c. Write the formula for this specific problem. Explain how you know where each number goes in the formula.

The initial value is 25 terms and the decay rate is 6%, so the specific equation is:

d. How many terms will you remember seven days later for the test? Show all your work and explain your computations.​

Now, we need to replace the value of x by 7, so:

Therefore, you will remember 16 terms seven days later.

The number of units that is needed to be manufactured and sold per month by the company to break even is 222 units

The first step is to write out the parameters given in the question

The sales price per unit is $50

The fixed cost per month is $4000

The variable cost per unit is $32

The formula for calculating the units needed to break even can be expressed as follows

Fixed Costs ÷ (Sales price per unit – Variable costs per unit)

4000/(50-32)

= 4000/18

= 222.2

Hence 222 units are needed to be manufactured per month

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Answer:

Because first multiple and divide and Again Multiple and ans