The function f(x)= (x+8)^2 -1 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function.

Answer:

\(5x= 15\)

Step-by-step explanation:

Given

\(3x - 5 = -2x +10\)

Required

Write the variables and constants on different sides

\(3x - 5 = -2x +10\)

Add 2x to both sides

\(2x + 3x - 5 =2x -2x +10\)

\(5x - 5 =10\)

Add 5 to both sides

\(5x - 5 + 5 = 10 + 5\)

\(5x= 10 + 5\)

\(5x= 15\)

Hence, the equation is

\(5x= 15\)

Solving further [divide both sides by 5]

\(x = 3\)

I think it is -5=x

Step-by-step explanation:

The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

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The value of h'(2) is 25

The chain rule is a fundamental rule in calculus that provides a method to differentiate composite functions.

A composite function is a function that is formed by taking the output of one function and using it as the input of another function.

For instance, if we have two functions f(x) and g(x), then the composite function h(x) can be defined as h(x) = f(g(x)), where g(x) is the input to f(x).

here we have

h(x) = √6 + 5f(x)

Derivative of h(x) with respect to x

h'(x) = d/dx (√6 + 5f(x))

h'(x) = d/dx (√6) + d/dx (5f(x))

h'(x) = 0 + 5f'(x)

h'(x) = 5f'(x)

Now substitute x = 2 and f'(2) = 5, to find h'(2)

h'(2) = 5f'(2)

h'(2) = 5(5)

h'(2) = 25

Therefore,

The value of h'(2) is 25

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Complete Question:

If h(x) = √6 + 5f(x), where f(2)= 6 and f'(2) = 5, find h'(2).

The correct value of k is k=18.

If x−1 is a factor of f(x), it means that f(1)=0. We can substitute x=1 into the expression for f(x) and solve for k.

f(1)=−9(1)⁴+7(1)³+k(1)²−13(1)+6

f(1)=−9+7+k−13+6

f(1)=k−9

Since we know that f(1)=0, we have:

0=k-9

k=9

Therefore, the correct value of k that makes x−1 a factor of f(x) is k=9. The other options (1, 0, 18) are incorrect.

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314.29 miles can be driven using 20 gallons of gas.

Given, it takes 21 gallons of gas to drive 330 miles,

We have to find the miles that can be driven using 20 gallons of gas.

So, 21 gallons of gas = 330 miles

1 gallon of gas = 330/21

20 gallons of gas = (330×20)/21

20 gallons of gas = 314.285 miles

20 gallons of gas = 314.29 miles

Hence, 314.29 miles can be driven using 20 gallons of gas.

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Answer:

Gram.

Step-by-step explanation:

the correct answer is 36°

The measure of segment ST is 12

The point where two lines meet or intersect is known as an angle.

If Point S is between points R and T and P is the midpoint, then the following are true;

Given the following segments

RT = 20

PS = 4

Substitute into the given expression

2(4) + ST = 20

8 + ST = 20

ST = 20 - 8

ST = 12

Hence the measure of segment ST is 12.

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Answer:

B

Step-by-step explanation:

I'm sorry if I'm wrong

Answer:

5

Step-by-step explanation:

meant b haha

Answer: x=7/2, x=-3

Step-by-step explanation:

First lets do look at it without the absolute value marks

4x-1=13

4x=14

x=7/2

Now lets do the same but assume 13 is negative,

4x-1=-13

4x=-12

x=-3

Note: When dealing with the coordination change when the figure is in the state of reflection through x-axis, only switch the signs of the y values.

T(-1,-10) → T'(-1,10)

U(-1,-1) → U'(-1,1)

V(8,-2) → V'(8,2)

W(8,-10) → W'(8,10)

The best answer from the choices provided is option a. $149.12.

To calculate the cost of the extended warranty, we need to find 32% of the price of the speakers, which is $466.

32% of $466 can be calculated by multiplying $466 by 0.32:

$466 * 0.32 = $149.12

Therefore, the cost of the extended warranty is $149.12.

The best answer from the choices provided is option a. $149.12.We are given that the price of the floor speakers is $466. To find 32% of this price, we can multiply $466 by the decimal equivalent of 32%, which is 0.32.

Mathematically, we can express this as:

32% * $466 = 0.32 * $466

Calculating the right-hand side of the equation:

0.32 * $466 = $149.12

Therefore, the cost of the extended warranty is $149.12.

Out of the given choices, the best answer is option a. $149.12, as it matches the calculated result.

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Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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The length of a side of the hexagon or square is - 16 units

The length of a side of the hexagon or square = x

The perimeter of the square = 4 × lengths of its side

                                               = 4x

The perimeter of the hexagon = 6 × lengths of its side

                                                   = 6x

According to the question,

                            4x + 32 = 6x

                       ⇒ 6x - 4x = 32

                       ⇒  2x = 32

                       ⇒  x = 16

So, the length of a side of the hexagon or square is - 16 units.

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｡･:*:･ﾟ★,｡･:*:･ﾟ☆50｡･:*:･ﾟ★,｡･:*:･ﾟ☆

༶•┈┈⛧┈♛To find volume, you use the formula, bxwxh (base x width x hight), which gave me 50! (I also took the test ´◡` )♛┈⛧┈┈•༶

The volume of the sculpture in cubic meters should be considered as the 150 m3.

Since

The area of the base of the sculpture is 15 square meters and it has a height of 10 meters.

So here the volume be like

= 15 (10)

= 150 m3

hence, The volume of the sculpture in cubic meters should be considered as the 150 m3.

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Answer:it’s 10x + 12

Step-by-step explanation:

your welcome

The sum of ten times a number and 12 can be written as 10x + 12.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The expression "ten times a number" can be represented as 10x, where x is the number.

So, "the sum of ten times a number and 12" can be written as:

10x + 12

This expression represents a mathematical operation where 10 times the number is added to 12.

Thus,

The sum of ten times a number and 12 can be written as 10x + 12.

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Answer:

The equation of the line that passes through the point (-5,2) and is parallel  to the line 4x-5y is 5y-4x = 30

Step-by-step explanation:

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

Yes

Step-by-step explanation:

They have the same length. The length is 1.

I hope this helps!

Answer:

11

Step-by-step explanation:

The number 11 is called the base, while the number 12 is called the exponent .

Answer:

11

Step-by-step explanation:

An exponential has the base at the bottom, or the lower portion. Think of "basement" to help remember this. The exponent is the number up top, so 12 is the exponent.

The figure shows three types of unconformities: an angular unconformity (A - A) with tilted and eroded layers, a non-conformity (B- B) between uplifted and underlying rocks, and a paraconformity (C - C ) with a smooth transition between sedimentary layers indicating a potential time gap.

Based on the information provided, the figure shows three different unconformities

(A - A) represents an angular unconformity:

This occurs when horizontally layered rocks (A) are tilted or folded, eroded, and then overlain by younger, undeformed rocks (A). The angular discordance between the older and younger layers indicates a significant period of deformation and erosion.

(B- B) represents a non-conformity:

A non-conformity occurs when igneous or metamorphic rocks (B) are uplifted and eroded, exposing the underlying, usually sedimentary, rocks (B). The boundary between the two types of rocks represents a significant time gap and a change in the geological history of the area.

(C - C) represents a paraconformity:

A paraconformity is a type of unconformity where there is a relatively smooth transition between parallel layers of sedimentary rocks (C - C). Unlike angular unconformities and non-conformities, paraconformities do not show significant tilting, folding, or erosion. The time gap between the two layers may still exist, but it is often difficult to distinguish due to the lack of obvious discontinuities.

In summary, an angular unconformity (A - A) shows significant tilting and erosion, a non-conformity (B - B) indicates an uplift and erosion of older rocks, and a paraconformity (C - C) represents a relatively smooth transition between parallel sedimentary layers with a potential time gap.

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--The given question is incomplete, the complete question is given below " List and explain three different unconformities shown on this

figure. Explain your answer (15 points) "--

Answer:

49m^2 +( 77+77)m +121

49m^2 + 77m +77m +121

7m (7m +11) +11 (7m +11)

(7m+11) (7m+11)

hope it was helpful

Answer:

\((7m + 11 {)}^{2} \)

Step-by-step explanation:

\(49 {m}^{2} + 154m + 121\)

➡️ \( {7}^{2} {m}^{2} + 2 \times 7m \times 11 + {11}^{2} \)

➡️ \((7 m{)}^{2} + 2 \times 7m \times 11 + {11}^{2} \)

➡️ \( = (7m + 11 {)}^{2} \) ✅

The value of the missing lengths are;

x = 4

y = 3. 5

It is important to note that trigonometric identities are described as equalities that shows the certainty of all the values that are found the in the trigonometric functions in an equation.

There are distinct identities, such as;

From the information given, we have that;

sin θ = opposite/ hypotenuse

Now, substitute the values

sin 30 = 2/x

Find the sine value

0.5x = 2

x = 4

Using the Pythagorean theorem, we have;

4² - 2² = y²

y² = 16 - 4

y² = 12

Find the square root

y = 3. 5

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Answer:

(1,1)

Step-by-step explanation:

The line is on the point

The sum would end us as: 2.33333333

Answer:

Step-by-step explanation:

step 1: 4+ -1 2/3

Step 2: 4-1 2/3

Step 3 12/3- 5/3 common denominator required during addition or subtraction

Step 4: 7/3 or 2 1/3 simplify

Answer:

Step-by-step explanation:

4 Numbers Given, 1,8,6,4

Numbers start counting from 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ..... and so on

Here we can see that 1 is the first  Number.

Thus 1 is the Smallest Integer( Number ) in the given series.

In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9  .

We first simplify each expression inside the parentheses :

that means :

⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;

⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³)  ;

⇒ (x + 1/x² - 9) = (-9 + x + 1/x²)  ;

Now we substitute these expressions into original equation/expression :

we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)

Simplifying further ,

we get ;

⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x²  ;

On Combining the like terms, we get ;

⇒ 4x - 4/x² - 5/x³ + 9

Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.

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The given question is incomplete , the complete question is

Adding and subtracting rational expressions, Simplify the rational expression  (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9)  .