6+
5-
4+
3-
2+
1+
y
++
-6 5-4-3-2-1₁-
-2+
-3+
4+
-5+
-6+
2 3 4 5 6
f(x)=(x-3)²-4
Consider the function shown. How can you restrict the
domain so that f(x) has an inverse? What is the
equation of the inverse function?
0x20;-¹(x)=3-√x+4
O x ≥ 0;¹(x) = 3+√x+4
x23;¹(x)=3-√√x+4
x23;¹(x)=3+√√x+4

Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

Answer:

Low rope course = $19

High rope course = $95

Step-by-step explanation:

Let H denote the price of the high rope course and L the price of the low rope adventure.

The following system can be modeled from the given information:

\(5L=H\\11L+18H=1,919\)

Replacing the first equation into the second gives us the price of the low rope course:

\(11L+18*(5L)=1,919\\L=\frac{1,919}{101}\\L=\$19\)

Now we can determine the price of the high rope course:

\(H=5*19\\H=\$95\)

The low rope course costs $19 and the high rope course costs $95.

Step-by-step explanation:

Greetings !

Given fraction

\(4 \frac{5}{6} \)

convert mixed fraction to improper fraction

\(a \frac{b}{c} = \frac{a.c + b}{c} \)

\(4 \frac{5}{6} = \frac{4.6 + 5}{6} = \frac{29}{6} \)

Hope it helps!

Answer:

0.5625

Step-by-step explanation:

You do the parenthasis first and get 18 and then you divide 18/32 and get 0.5625

PEMDAS if need help understanding the order

(Parenthesis, Exponent, Multiply, Divide, Add, Subtract)

(21-3)÷32 (do parenthesis first)

18÷32 (divide)

answer is about 0.5625

The first step is to assume values for x and input them into the equation to get corresponding values for y.

For x = 0, y = - 0/5 + 7 = 7

For x = 1, y = - 1/5 + 7 = 6.8

For x = 2, y = - 2/5 + 7 = 6.6

We would plot these values of x and y on the graph. The diagram of the graph is shown in the attcahed photo.

Answer:

22050 J

Step-by-step explanation:

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Since Nancy has $400 dollars ans spends $20 each week. The word "Has" and "Spends" indicates the positive and the negative. so if we write the function rule saying f(d) then we should use it to our equation saying.

Answer:

f(d)=400-20d

Hope this helps! :)

Answer:

14

Step-by-step explanation:

7x2

Answer:

Answer:

11+ 9 = 20

Step-by-step explanation:

=> 21-9=11

21 - 9 equals to 11 is actually a wrong answer

So in order to find the subtraction problem that will help us truly know whether the equation is wrong

=> 11+ 9 = 20

Based on the information, we can infer that the salary a worker earns depends on the hourly wage they earn. In this case we will have to multiply the value of each hour by the number of hours worked. Additionally, I would agree to have a higher minimum wage to benefit workers.

Based on the information in the graph, we can infer that workers will have wages of $5.2, $6.0, and $6.6. According to the above, the salary varies depending on the number of hours.

On the other hand, I believe that you would agree to a salary increase because this would benefit workers who would be better paid for each hour of work.

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To implement the second method, the administrator should first create two separate lists, one for each class.

Then, the administrator should use a computer with a random number generator to select a simple random sample of 30 students from the combined class lists. To do this, the administrator should assign a unique number to each student in each list and generate a random set of 30 numbers that correspond to the students in the list.

For example, using the random digits 47899, 92198, 80657, 73914, and 18360, the administrator can choose student 47899 from the first class and student 92198 from the second class.

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Answer:

it is A

Step-by-step explanation:

it's right lol

Given the data from the question, the first 12 cupcakes cost $2.00 each, and all cupcakes after that cost $1.00 each (Option A)

From the graph,

12 cupcakes = $24

Therefore,

1 cupcake = 24 / 12

1 cupcake = $2

Thus, for the first 12 cupcakes, each cost $2

From the graph, we can determine the price of each of the remaining cupcakes as illustrated below:

18 - 12 = 6 cupcakes

30 - 24 = $6

Thus,

6 cupcakes = $6

Therefore,

1 cupcake = 6 / 6

1 cupcake = $1

Thus, we can conclude that, the first 12 cupcakes cost $2.00 each, and all cupcakes after that cost $1.00 each (Option A)

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Answer:

yikes shes just some simple fractions

a. 12/6

b. 6/6

c. 3/6

d6/6

Answer:

parallelogram.

quadrilateral.

rectangle.

rhombus.

square.

Answer:

Which graph represents Y as a function of X ?​

step-by-step explanation:

a. The graph of y = 2x represents a transformation of the parent function, y = x, which makes the graph twice as steep.

b. The graph of y = 2x represents a transformation of the parent function, y = x, which makes the graph half as steep.

c. The graph of y = x represents a transformation of the parent function, y = 2x, which makes the graph half as steep.

d. The graph of y = x represents a transformation of the parent function, y = 2x, which makes the graph twice as steep.

Answer:

is y=x^2 a proportional relationship?

\({ \sf{yes. \: constant \: of \: proportionality = 1}}\)

is y=2+x a proportional relationship?

\({ \sf{no. \: unless \: y \: is \: proportinal \: to \: (2 + x)}}\)

is y=2/x a proportional relationship?

\({ \sf{yes. \: where \: proportianality \: constant \: is \: 2}}\)

is y=2x a proportional relationship?

\({ \sf{yeah. \: constant \: is \: 2}}\)

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

Answer

Explanation

The amount deposited into savings every week = 10% of (

The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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Answer:

x=500

Step-by-step explanation:

\( \frac{2}{3} = \frac{x}{750} \\ 3 \times x = 2 \times 750 \\ 3x = 1500\\ \frac{3x}{3} = \frac{1500}{3 } \\ x = 500 \)

Answer:

AB = 11

Step-by-step explanation:

Using the external secant property,

CB*CA = CD*CL (=CT^2  if T is tangent throught C)

substitute values,

7*(7+2x+3) = 9*(9+x+1)

Expand and simplify

70+14x = 90 + 9x

5x = 20

x = 4

=>

AB = 2x+3 = 2(4)+3 = 8+2 = 11

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

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The size of angle y in the quadrilateral is 130 degrees.

A quadrilateral is a polygon with 4 sides and angles. The quadrilateral above is a kite. The sum of angles in a quadrilateral is 360 degrees.

Therefore, let's find the angles in the quadrilaterals as follows:

y + y + 70 + 30 = 360(sum of angles in a quadrilateral)

2y + 100 = 360

2y = 360 - 100

2y = 260

divide both sides by 2

y = 260 / 2

y = 130 degrees

Therefore, the size of y is 130 degrees.

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The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

From the question, we have the following parameters that can be used in our computation:

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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The solution is given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Remember that the Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

According to this, the correct answer is: given below.

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Answer:

x could be 3 or 1

Step-by-step explanation:

x²+3=4x

x²-4x+3=0

(x-3)(x-1)

x could be 3 or 1

The values could be 1 or 3.

In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.

Translating the word problem into an algebraic expression, we have;

\(n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0\)

We would solve the quadratic equation by using the factorization method;

\(n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0\)

Therefore, the values could be 1 or 3.

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