Point F is between points T and K.
The points are collinear.

The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

What is Range of set?

The range is the set of possible output values, which are shown on the y-axis.

The function is given as;

y = -1/2 x + 3

Now, The values of x are given as;

x = 0, 2, 4, 6

Hence, The value of y are find as;

When x = 0

y = -1/2 * 0 + 3 = 3

When x = 2

y = -1/2 * 2 + 3

y = 2

When x = 4

y = -1/2 * 4 + 3

y = 1

When x = 6

y = -1/2 * 6 + 3

y = 0

Hence, All values of y are {3, 2, 1, 0}

So, The Domain of set is {0, 2, 4, 6}

The Range of the set is {3, 2, 1, 0}

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The domain of the function is (0,∞) , {x|x>0}

and the range of the function is (−∞,∞),  {y|y ∈ R}

given the function is y = 3 log x

Set the argument in  log x greater than 0 to find where the expression is defined.

x > 0

The domain is all values of x that make the expression defined.

Interval Notation:

(0,∞)

Set-Builder Notation:

{x|x>0}

The range is the set of all valid y values. Use the graph to find the range.

Interval Notation:

(−∞,∞)

Set-Builder Notation:

{y|y∈R}

Determine the domain and range.

Domain: (0,∞) , {x|x>0}

Range :  (−∞,∞),  {y|y ∈ R}

Hence we get the required domain and range of the given function.

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Answer:

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

We have the following linear equation to represent given situation:

Solve it for x to get the average number of miles:

In linear equation, He ride 3 miles each day.

Variable: x = Constant distance distance traveled each day.

Equation : 10+4x= 22

What is a formula for linear equations?

Total distance needs to travel = 22 miles

Distance already traveled = 10 miles

He will ride bicycle for 4  more days.

Let x = Constant distance distance traveled each day.

Total distance = 10+4x

10+4x = 22

4x = 22 - 10

4x = 12

  x = 3

Hence, he rode 3 miles each day.

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He will use 18 teaspoons of baking powder for the oatmeal recipe

A recipe requires 2 cups of flour and 2.5 cups of oats

For each cup he must add 1.5 teaspoons of baking powder

He uses 15 cups of oats

Each recipe uses 2 cups of flour, the teaspoons of baking powder used in one recipe is

1.5 × 2 = 3

2.5 cups of oats is used for one recipe, he uses 15 cups of oats, this means that the number of recipes is 6 (15/2.5)

Since the number of recipes is 6 and 3 teaspoon of baking powder is used for one recipe, then the number of teaspoons used is

= 6 × 3

= 18

Hence he used 18 teaspoons of baking powder

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Answer:

[tex]\left[\begin{array}{ccc}-48&-60\\44&30\end{array}\right][/tex]

Step-by-step explanation:

0.5 X + 3A = B implies

X = 2(B-3A)

3A simply means multiplying each cell by 3

[tex]3A = \left[\begin{array}{ccc}12&24\\-33&-3\end{array}\right][/tex]

B-3A is a corresponding cell by cell subtraction

[tex]B-3A = \left[\begin{array}{ccc}-24&-30\\22&15\end{array}\right][/tex]

Finally multiply that by 2, result is at the top.

Using the rules of exponents, the expression (5 x^−5 y^3)^−2 is equivalent to x^10 / (25 y^6) or "x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity".

Given: (5 x^−5 y^3)^−2

1. Distribute the power of two using the Power of a Power Rule. "When a power is raised to another power, multiply the exponents."

5^−2 x^(−5)(−2) y^(3)(−2) =  5^−2 x^10 y^-6

2. Use Negative Rule of Exponent. "A number with a negative exponent should be put to the denominator, and vice versa."

5^−2 x^10 y^-6 = (x^10) / (5^2 y^6)

3. Simplify the constant term.

(x^10) / (5^2 y^6) = x^10 / 25 y^6

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Answer:

y = 105

x = 31

Step-by-step explanation:

We have y and 75 as consecutive interior angles.
(Consecutive interior angles are are found between the two parallel lines and on the same side of the transversal)

Sum of two consecutive interior angles = 180°

so we have y + 75 = 180
y = 180-75 = 105

So y = 105

y and (3x+12) are opposite angles and are equal
So 3x+12 = y
3x + 12 = 105
3x = 105-12 = 93
x = 93/3 = 31

So x = 31

The domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

We are given the two functions as:

f (x) = x - 4

g (x) = x² - 16

Now, first, we need to subtract f (x) from g (x).

So, we get that:

g (x) - f (x) = x² - 16 - (x - 4)

g (x) - f (x) = x² - 16 - x + 4

g (x) - f (x) = x² - x - 12

Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.

Therefore, we get that the domain for g (x) - f (x) = x² - x - 12 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.

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Finding LCM for the problem, you should cut the cornbread into 6 parts, Sue will get 3 parts and Dena will get 2 parts.

LCM is referred to as the least common multiple for a set of numbers that can be divided by the same whole number as a result.

At first, we have to find LCM of 2 and 3, which is the denominator of 1/2 and 1/3, and its 6 and we will cut it into 6 pieces.

So, Sue will get 3 pieces from the cornbread ( 3/6 = 1/2 ) and Dena will get 2 pieces from the cornbread ( 2/6 = 1/3 ).

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The simplified form is [tex]4 ^{\frac{2+t}{3} }[/tex].

Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.

The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.

Converting mixed numbers to an improper fraction,

[tex]16^{1/3} . 4^{t/3} \\4^{2/3} .4^{t/3} \\4^{\frac{2+t}{3} }[/tex]

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The inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g: TRUE

So,

Given inverse function: f₁(x)=b^(x-h)

First, find out the inverse of this function.

Switch the variables x & y as follows;

Solve for y as shown below and take logarithm both sides:

So,

From the first equation we get the inverse of as f₁ follows:

Therefore, the statement "the inverse of f₁(x)=b^(x-h) is not equal to a vertical stretch or compression of g" is TRUE.

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Answer:

365 * 88 (^7) =  B=10

The growth factor for the annual rate of change of +12.5 % is 1.125.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = + 12.5 % = + 12.5 / 100 = + 0.125

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (+ 0.125)

B = 1.125

Now, the value of B is greater than 1 therefore, the corresponding growth factor is 1.125.

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The function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

We are given the function:

y = 4 (3) x

Multiply 4 and 3, we get that:

y = 12 x

Now, subtract y from both the sides, we get that:

12 x - y = 0

We can see that the degree of each variable is 1 .

So, it will be a linear function.

Therefore, we get that, the function y = 4 (3) x which can also be written as 12 x - y = 0 is a linear function.

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Answer:

The fourth option

Step-by-step explanation:

Formula to find the area of a circle is [tex]\pi r^{2}[/tex]

[tex]\pi 7^2[/tex]

[tex]49\pi[/tex]

Based on Cameron's current music service fees, the number of songs that would make the new service a less expensive option is 101 songs

The expression for the new service assuming the number of songs is x is:

= 15 + 0.80x

The expression for Cameron's current service is:
= 0.95x

Equating them gives:

0.95x = 15 + 0.8x

0.95x - 0.8x = 15

0.15x = 15

x = 100 songs

The cost will be the same at 100 songs so the new service would be cheaper at 101 songs.

First part of question:

Cameron pays $0.95 per song with his current music service.

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Answer:

Mitchell owes his mom =$18. sum of money his mom reduced =$12.

Step-by-step explanation:

SO IT 6 DOLLARS

Answer: $6

Explanation: $18-$12=$6

Hope this helps!!! have a nice day!

True response is that the function represented by the graph is Increasing on (-∞, 0) and decreasing on (0, ∞)

A function is said to be increasing in its domains if the value of its range is increasing in that domain.

Similarly, if the function is decreasing in its domain then it's range must be decreasing with the domain.

When the value of x(domain) is increasing on the left side. The value of y(range) is increasing constantly. But when the value of x increases further after 0, then the value of y is decreasing constantly.

So we can say, the following function represented on the graph is increasing in the interval of ( -∞,0) and decreasing in (0,∞).

As per the situation described in the graph the option third which say increasing on (×,0) and decreasing on (0,×).

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Answer:

The top 2 and the bottom right!

Hope this helps!

In linear equation, 1875  does Hoppy weight .

What are instances of linear equations?

A = 42b = 56c

a : b : c  = 42 : 100 : 75

total Mr Flopsy weights = 2500

then  Hoppy weight =  75 = 2400/100 * 75

                                  = 1875

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Answer:

196 degrees, reflex.

Step-by-step explanation:

The angles fit around a point, therefore, they add up to 360 degrees.
Let [tex]x[/tex] be the size of the third angle.

[tex]x + 113 + 51 = 360 \\x + 164 = 360 \text{ / Subtract 164 on both sides} \\x + 164 - 164 = 360 - 164} \\x = 196[/tex]

The angle is larger than 180 degrees and smaller than 360 degrees, therefore, its a reflex angle.

Answer:

196 degrees, reflex.

Step-by-step explanation:

Step-by-step explanation:

Technically none of these are the right answer. The decrease in his account would be -27.

But out of the given choices, I'll go with option C because he has $8 left in his savings

If PQRS is a square & TR= 17, then

PR= 34

QS= 34

QT= 17

PQ= [tex]17\sqrt{2}[/tex]

A square in geometry is a two-dimensional plane figure having four equal sides and four equal but 90 degree angles. The characteristics of a rectangle and a square are somewhat comparable, however only the opposite sides of a rectangle are equal. So, only if all four of a rectangle's sides are the same length can it be said to be a square.

A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is another name for a rectangle with two sides that are opposite and the same length.

The following is a list of a square's most significant characteristics:

We know that,

Diagnose of a square are equal in magnitude and bisect each other.

So, In the given figure,

diagonals PR and QS are bisected at T.

RT = PT = 17

Hence,

PR=2RT=2*17=34

PR= 34

QS=34

[tex]QT=\frac{1}{2}QS = \frac{1}{2}*34 = 17[/tex]

QT=17

PQ = side of square

Let PQ= QR= a

In ΔPQR

[tex]PQ^{2} + QR^{2} = PR^{2}[/tex]

[tex]PQ^{2}+ PQ^{2} = 34^{2}[/tex]

[tex]2PQ^{2} = 34*34[/tex]

[tex]PQ = \sqrt{17*34} = 17\sqrt{2}[/tex]

PQ = [tex]17\sqrt{2}[/tex]

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Answer:

y = - x + 8

Step-by-step explanation:

y = - x + 8

The value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

The expression is given as

R = x^2/y

Where

y = 3.8 x 10^5

x = 5.9 x 10^4

Substitute y = 3.8 x 10^5 and x = 5.9 x 10^4 in the equation R = x^2/y

So, we have

R = (5.9 x 10^4)^2/3.8 x 10^5

Evaluate the exponent

So, we have

R = 34.81 x 10^8/3.8 x 10^5

Evaluate the quotient

So, we have

R = 9.16052631579 x 10^3

Approximate the above expression

So, we have

R = 9.2 x 10^3

Hence, the value of the expression R = x^2/y when y = 3.8 x 10^5 and x = 5.9 x 10^4 is 9.2 x 10^3

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 [tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.

Given: [tex]\frac{ln(e^2)}{2}[/tex]

Now,

=> [tex]\frac{ln(e^2)}{2}[/tex] = [tex]\frac{2 (ln(e))}{2}[/tex]

=>  [tex]\frac{ln(e^2)}{2}[/tex] = ln (e)

=>  [tex]\frac{ln(e^2)}{2}[/tex] = 1

Hence,  [tex]\frac{ln(e^2)}{2}[/tex] = 1, by properties of logarithm.

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The value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

[ -2/3 x (-2/3) ] x ( -9/4)

Evaluate the expression in the bracket

So, we have

[ -2/3 x (-2/3) ] x ( -9/4) = [4/9] x ( -9/4)

Evaluate the product

[ -2/3 x (-2/3) ] x ( -9/4) = -1

Hence, the value of the expression [ -2/3 x (-2/3) ] x ( -9/4) is -1

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