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A parabola's maximum value is the y-coordinate of its vertex when it opens downward.

Therefore, a parabola's maximum value is the y-coordinate of its vertex when it opens downward.

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The rationalization the denominator of the given expression is [tex]\frac{5\sqrt{6}x^3 }{2\sqrt{y} }[/tex] .

We have given an expression [tex]\frac{5\sqrt{3}x^3 }{\sqrt{2y} }[/tex] .

The denominator of the expression is [tex]\sqrt{2y}[/tex] .

Multiply the fraction in the numerator and denominator by [tex]\sqrt{2y}[/tex] , we get

         [tex]\frac{5\sqrt{3}x^3\times\sqrt{2y} }{\sqrt{2y} \times\sqrt{2y} }=\frac{5\sqrt{6}x^3\sqrt{y} }{2y}[/tex]

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The value of x for the equation 3ˣ = 27 is 3.

A linear equation with one variable is one that has just one variable. It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

One method for expressing a linear equation is in the slope-intercept form (the equation of a line). Y = mx+b, where m is the slope and b is the y-intercept, is the formula for the slope-intercept form (the point where the line crosses the y-axis). Using y=mx+b to graph a line is often simple.

The equation is -

3ˣ = 27

It can be expressed as -

3ˣ = 3³

x= 3

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The value of x when r(x) = -4 is 20/3.

Given, the function is r(x) = ₋2/3x ₊ 4

substitute r(x) = ₋4 in the value of r(x)

r(₋4) = ₋2/3(₋4) ₊ 4

r(₋4) = 8/3 ₊ 4

r(₋4) = 8 ₊ 12/3

r(₋4) = 20/3

hence we get the value as 20/3

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Answer:

D

Step-by-step explanation:

hope this works for you :)

The data from the stemplot is $459,000, $277,000, $67,000, $123,000, $213,000, $482,000, $85,000, $181,000, $225,000, $92,000, $181,000, $287,000, $196,0900, $276,000.

A stemplot is a table that has similar features with to a histogram. A stemplot divides a number into a stem and a leaf. The stem is the first digit in a number and the leaf is the rest of the numbers. For example, the number 223, 2 would be the stem and 23 would be the leaf.  

Advantages of a stemplot is that it displays all of the data in the dataset. A stemplot is also easy to interpret.  Stemplots also give a concise representation of a dataset. A disadvantage of a stemplot is that is can only be used for a small dataset.

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The another endpoint of a line is (13, -3).

What is Straight line?

A line with no curve is called a straight line.

Given that;

One endpoint of a line = (-3, 7)

Midpoint of a line = (5, 2).

Now, Let the other endpoint of a line = (x, y)

Then, Other endpoint is solve by the definition of midpoint of two points as;

(x + (-3) / 2 , y + 7 / 2 ) = (5, 2)

(x - 3 / 2 , y + 7 / 2) = (5, 2)

By compare we get;

x - 3/ 2 = 5

x - 3 = 2 * 5

x - 3 = 10

x = 10 + 3

x = 13

And,  

y + 7 / 2 = 2

y + 7 = 2 * 2

y + 7 = 4

y = 4 - 7

y = -3

Hence, The another endpoint of a line is (13, -3).

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The number of pairs of parallel sides the rotated figure have is 2

Parallel sides or lengths are line segments or lines in the same plane that extend on both sides without intersecting

The shape is given as:

Shape = Rhombus

Rotation= 90 degrees counterclockwise rotation about the vertex G

The rotation transformation is a rigid transformation

This means that when a shape is rotated by 90 degrees counterclockwise about a vertex (in this case, the vertex G), the image of the rotation would have the same properties as the preimage

A rhombus has 2 pairs of parallel sides

This means that the number of pairs of parallel sides the rotated figure have will also be 2 (same as the original shape)

Hence, the number of pairs of parallel sides the rotated figure have is 2

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The inequality represented by the number line is x ≤ -6

A straight line of numbers is shown visually as a number line. . On a horizontal number line, the numbers grow as we walk to the right and decrease as we move to the left.

Given that,

The response must include both a less than and a negative sign.

At -6, the graph displays a closed circle.

which means that -6 is a solution to the inequality.

The darkened arrow on all values greater than -6 denotes that x -6 is the proper inequality.

The inequality represented by the number line is x ≤ -6

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Answer:

x = 4

Step-by-step explanation:

[tex]\frac{x}{7}[/tex] = [tex]\frac{28}{49}[/tex] ( cross- multiply )

49x = 7 × 28 = 196 ( divide both sides by 49 )

x = 4

Answer:

2x + 15y + 2,960

Step-by-step explanation:

Single Rides are $2 each, represented by x

All day passes are $15 each represented by y

Combined they equal the total revenue; 2,960.

Answer:

74 degrees

Step-by-step explanation:

180-32=148

148÷2=7

Answer in decimal form = -26.25

Answer as an improper fraction = -105/4

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

Work Shown:

1/2 = 0.5

Replace every copy of x with 0.5 in the f(x) function.

f(x) = x-8

f(0.5) = 0.5-8

f(0.5) = -7.5

Repeat the same idea for the g(x) function

g(x) = x+3

g(0.5) = 0.5+3

g(0.5) = 3.5

Then multiply the results

f(0.5)*g(0.5) = (-7.5)*(3.5) = -26.25

Then optionally convert to an improper fraction following the steps shown below.

-26.25 = -(26.25)

-26.25 = -(26+0.25)

-26.25 = -(26+1/4)

-26.25 = -(26*(4/4)+1/4)

-26.25 = -(104/4+1/4)

-26.25 = -105/4

In M = rp+c, the equation illustrated shows that the value for p is p = (M - c)/r.

It should be noted that in Mathematics, an equation is used to illustrate or show the relationship that can be found with the variables that are expressed.

In this case, it should be noted that the given equation is illustrated as:

M = rp + c

Subtract c from both sides

M - c = rp + c - c

M - c = rp

Divide through by r

(M - c) / r = rp/r

p = (M - c)/r

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The transformation here is; the original function was moved '1' unit downwards.

Transformations simply takes the basic function and transforms it to another function.

The rules of transformation are;

From the question, the original function is;

f(x) = x + 4

Now, we are told that it undergoes a transformation to;

f(x + 4) - 1

From the transformation rules above, we can say that the transformation here is; the original function was moved '1' unit downwards.

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Inverse of the give function F(x) = ( x + 4 )³ - 1 is F⁻¹(x) = [√( x + 1 ) ] - 4.

Given is a function of x, F(x) = ( x + 4 )³ - 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = ( x + 4 )³ - 1 becomes y = ( x + 4 )³ - 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = ( x + 4 )³ - 1, we get

x = ( y + 4 )³ - 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = ( y + 4 )³ - 1

=> x + 1 = ( y + 4 )³

=>  (y + 4 )³ = x + 1

=> y + 4 = √( x + 1 )

=> y = √( x + 1 ) - 4

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = √( x + 1 ) - 4 becomes F⁻¹(x) = √( x + 1 ) - 4

Therefore, we get the inverse of the give function F(x) = ( x + 4 )³ - 1 as F⁻¹(x) = [√( x + 1 ) ] - 4.

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The recursive equation here is; a_n = 3n - 1

Formula for the nth term of an arithmetic sequence is;

an = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

We are given that;

First term; a = 2

Second term; a2 = 5

Common difference; d = 3

Thus, recursive equation here is;

a_n = 2 + 3(n - 1)

a_n = 2 + 3n - 3

a_n = 3n - 1

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Answer:

1225

Step-by-step explanation: i did the tesr b

Answer:

4 is 4 2/3

Step-by-step explanation:

3 can only go in 14 4 times with 2 leftover

After solving the equation, x = 3/2 is the value of x in [tex]3^{2x}[/tex] = 27

⇒ [tex]3^{2x}[/tex] = 27

⇒ [tex]3^{2x}[/tex]  = [tex](3)^3[/tex]

⇒ 2x = 3

⇒ x = 3/2

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Step-by-step explanation:

supplementary angles mean that they are together 180°.

so,

a + (a - 51) = 180

2a - 51 = 180

2a = 231

a = 115.5°

its supplement is 180 - 115.5 = 64.5°

The measure of the angle's supplement is 64.5 degrees.

Let's denote the measure of the angle as "a" degrees. The supplement of an angle is the angle that, when added to the given angle, results in a total of 180 degrees (because the sum of angles in a straight line is 180 degrees).

According to the problem, the measure of the angle's supplement is 51 degrees less than the measure of the angle. Mathematically, we can express this as:

Supplement angle = Angle - 51

Since the sum of the angle and its supplement is 180 degrees, we can write the equation:

Angle + Supplement angle = 180

Substitute the expression for the supplement angle:

a + (a - 51) = 180

Combine like terms:

2a - 51 = 180

Now, solve for "a":

2a = 180 + 51

2a = 231

a = 231 / 2

a = 115.5

So, the measure of the angle "a" is 115.5 degrees.

Now, to find the supplement angle:

Supplement angle = a - 51 = 115.5 - 51 = 64.5

Therefore, the measure of the angle's supplement is 64.5 degrees.

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Answer:

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] = [tex]\frac{b}{2}[/tex] ( cross- multiply )

8b = 6 ( divide both sides by 8 )

b = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]

Answer:

b=3/4

Step-by-step explanation:

3/8=b/2

First you will need to cross multiply because apparently that's how we do things. To cross multiply, you would just have to take the bottom of the fraction from the LHS (left hand side) and times it with the top part of the fraction in RHS (right hand side). You do the same thing to the other side (take the top part of LHS and multiply it with the bottom of RHS). Make sure to keep the = sign in the middle.

8 x b = 3 x 2 (8 x b= 8b)

8b=6

Then, you would have to make the b on the LHS alone so you would have to divide the RHS by 8. (To move from one side to another, you would have to change it to the opposite of the sign like if it's -9, then to the other side it would be +9 and if it's x8 then the other side would be /8 and vice versa).

b=6/8

You will have to simplify unless the question asks you not to but I'll do it anyways. 2 goes into 6 and 8 as a common factor and so the answer should look like this:

b=3/4

If you have any further questions please ask me!

We will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression

log 33,000- log 99+ log 30.

So,

Then,

[tex]\left\{\begin{array}{l}\log \cdot 33 \\000-\log \cdot 99+\log \cdot 30\end{array}\right.\\\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex]

Therefore, we will get [tex]\left\{\begin{array}{l}\log \cdot 33 \\-\log \cdot 99+\log \cdot 30\end{array}\right.[/tex] after simplifying the given expression log 33,000- log 99+ log 30.

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Answer:

  -4 ≤ y ≤ 2

Step-by-step explanation:

You want the range of the graph shown.

The range of a relation is the set of output values of the relation, the vertical extent of its graph.

The graph shown extends continuously from an absolute minimum of y=-4 to an absolute maximum of y=2.

The range is -4 ≤ y ≤ 2.

Answer:

7, 5

Step-by-step explanation:

Change the denominator to make the end result 0. Anything with a 0 denominator results in it being undefined.

The expression (10-t)/(t-7) is undefined when t=7.

The expression 10/(3t-15) is undefined when t=5.

To find the values of t for which the expressions are undefined, we need to look for any values of t that make the denominators equal to zero.

we know that dividing by zero is undefined.

For the expression (10-t)/(t-7),  the denominator is t-7.

So, this expression is undefined when t-7=0

To find the value of t that makes t−7=0, solve the equation:

t-7=0

t=7

So, the expression (10-t)/(t-7) is undefined when t=7.

For the expression 10/(3t-15), the denominator is t-7.

So, this expression is undefined when 3t-15=0

To find the value of t that makes 3t-15=0, solve the equation:

3t-15=0

Add 15 on both sides:

3t=15

Divide both sides by 3:

t=5

So, the expression 10/(3t-15) is undefined when t=5.

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The total length of the strips will be 6L. Then the total length of the ribbon should have been 6L + 6/8.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Shayla cuts six ribbon pieces to create hair bows. She completes it, only to discover that each strip is 1/8 inch too short.

Let L be the length of the strips of ribbon. Then the total length of the strips will be

⇒ 6L

The total length of the ribbon should have been

⇒ 6(L + 1/8)

⇒ 6L + 6/8

The total length of the ribbon should have been 6L + 6/8.

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