Is this statement true or false? a^(-3)+a^(-3)=a^(-6)​

a. Verify the function f(x) = x² - 4x + 7 satisfies the three hypotheses of Rolle's Theorem on the interval [0,4]. b. Find all values of c in the interval (0,4) such that f'(c) = 0 using Rolle's Theorem.

a. To verify the hypotheses of Rolle's Theorem, we need to check that f(x) is continuous on [0,4], f(x) is differentiable on (0,4), and f(0) = f(4).

f(x) is a polynomial function and is continuous everywhere.

f'(x) = 2x - 4 is a polynomial function and is differentiable everywhere.

f(0) = (0)² - 4(0) + 7 = 7 and f(4) = (4)² - 4(4) + 7 = 7. Therefore, f(0) = f(4).

Thus, all three hypotheses of Rolle's Theorem are satisfied.

b. f(0) = (0)² - 4(0) + 7 = 7 and f(4) = (4)² - 4(4) + 7 = 7.

c. By Rolle's Theorem, there exists at least one value c in (0,4) such that f'(c) = 0. We have:

f'(x) = 2x - 4 = 0

2x = 4

x = 2

Therefore, the only value of c in (0,4) such that f'(c) = 0 is c = 2.

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The shorter length of the leg of the right triangle is 10 units.

Given that a right triangle has legs (x+1) and (2x-2) has an area of 80, we need to find the length of the shorter leg,

Since we know that the area of a right triangle is the product of both legs divided by 2,

So,

[(x+1) × (2x-2)] / 2 = 80

[2x² - 2x + 2x - 2] / 2 = 80

Simplifying the equation,

x² - 1 = 80

x² = 81

x = 9

Now, put the value of x in the given measures of the legs,

x + 1 = 9 + 1 = 10

2(9) - 2 = 16 - 2 = 14

Hence the shorter length of the leg of the right triangle is 10 units.

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Answer:

Step-by-step explanation:

In a tent, there are nine boys.

There were five tents.

5 tents containing 9 boys can equal 45 boys.

(5 x 9 = 45)

In a cabin, there are seven boys.

There were four cabins.

4 cabins containing 7 boys can equal 28 boys.

(4 x 7 = 28)

Now, to find all the boys, add the numbers together.

28 boys with 45 boys will equal 73 boys.

Please check my answer for no one, not even me is right.

Good luck :)

The disjunction of pvq is represented by: x < -3 or x > 3.

The given statement is as follows:p:

x < -3q: x > 3

The statement pv q represents a "disjunction" of these two propositions.

It is used to find out if any of the propositions are true. The disjunction is true if one or both of the propositions are true. The disjunction can be represented by using the "or" operator (i.e., ∨).

The given disjunction is as follows:

p v q: x < -3 or x > 3

By combining the two propositions, it can be concluded that the value of x lies either to the left of -3 or to the right of 3 on the number line. The value of x is not restricted to any specific set of real numbers, as it could be any real number, which lies to the left of -3 or to the right of 3 on the number line.

Thus, the correct option is x < -3 or x > 3.

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Answer:

No

Step-by-step explanation:

To prove 2 triangles an congruent we need three pieces of information

SSS or SAS or ASA or RHS

S - Side

A - Angle

R - Right angle

H - Hypotenuse

We have an angle side and another side

So these two triangles can be proved congruent by SAS

Hope this helped and have a good day

Complete question :

The play director 190 hours preparing for a plane that time include attending 35 rehearsals that took varying amount of time in spending 93 3/4 hours on the other responsibilities related to the play. What question does the equation 3/5 x + 93 3/4 equal 190 help answer? A. How much longer did the director spend on rehearsals and on other responsibilities? B. What was the average length of each rehearsal? C. How long was each rehearsal?

Answer: C. How long was each rehearsal?

Step-by-step explanation:

Total time spent preparing for play = 790 hours

Of the 190 hours :

Number of rehearsals = 35

Others = 93 3/4 hours

What question does the equation 35 x + 93 3/4 equal 190

35x + 93 3/4 = 190

(Number of rehearsals) * x + others = total time

x = time spent on each rehearsal

35x = 190 - 93 3/4

35x = 96.25

x = 96.25 / 35

x = 2.75 hours

Each rehearsal took 2.75 hours

Answer:

4

Step-by-step explanation:

5x + 2 = 2x + 14

or, 5x - 2x = 14 - 2

or, 3x = 12

or, x = 12/3

.

. . x = 4

To understand the question, let us draw the graphs of each one

The red graph represents A

The blue graph represents B

The green graph represents C

The purple graph represents D

Let us find the narrowest

The blue graph is the narrowest because it is closed to the y-axis more than the other graphs

The correct answer is B

Answer:

x = 7, x = 2

Step-by-step explanation:

Given

x² = 9x - 14 ( subtract 9x - 14 from both sides )

x² - 9x + 14 = 0 ← in standard form

(x - 7)(x - 2) = 0 ← in factored form

Equate each factor to zero and splve for x

x - 7 = 0 ⇒ x = 7

x - 2 = 0 ⇒ x = 2

The following is an example of a quadratic inequality: x^2 + 2x - 8 > 0.

This is an example of a quadratic inequality because it is an inequality involving a quadratic function (x^2 + 2x - 8) which is of the form ax^2 + bx + c where a, b, and c are constants.

Quadratic inequalities can be solved by factoring the quadratic expression, using the Quadratic Formula, or graphing the inequality. In order to solve a quadratic inequality, it is important to understand the types of solutions that can be expected.

Solutions may include one solution, two solutions, or no solutions. Additionally, when graphing a quadratic inequality, the graph may be a line or a region. To determine which type of graph to use, the type of inequality must be identified (greater than or less than). If the inequality is a greater than or less than inequality, then the graph will be a region. If the inequality is an equal to inequality, then the graph will be a line.

Solving and graphing quadratic inequalities is an important skill in algebra as it allows us to visualize and solve complex problems.

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Answer:

Given statement is false.

Step-by-step explanation:

Given that,

All irrational numbers have some repeating pattern which can  be used to compare them to rational numbers.

We know that,

Rational number :

A rational number is defined such a number which can be written as a ratio.

It means we can write a rational number as a fraction.

For example : 2, 3/2 and 4/2... etc.

In the fraction, both number are4 whole number.

So, we can say that, a number which can be define as a fraction it is called rational number.

Irrational number :

An irrational number is defined such a number which can not be written as a ratio.

For example : √5, √10 and √15...etc

So, we can say that, a number which can not be define as a fraction it is called irrational number.

We need to find all irrational numbers have some repeating pattern which can  be used to compare them to rational numbers

According to rational number and irrational number

This statement is false.

Suppose, √2 is irrational but not repeating.

So, we can't write √2 as rational number.

Hence, Given statement is false.

Answer:

0.89

Step-by-step explanation:

31.95 is about 32

36.05 is about 36

32/36 is 0.888...

rounded is 0.89

Answer:

.89

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-9u+9u is 0 so all you are left with is -3

Answer:

-3

Step-by-step explanation:

-9u + 9u - 3

-9u and 9u cancel out, so it simplifies to -3

Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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The third binomial formula is given by ( a + b )( a - b) = a² - b².

Binomial theorem in the standard form is given by :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Binomial formula starts from n = 2

First binomial formula of the binomial theorem is given by :

( a ± b )² = a ² ± 2ab + b²

Second binomial formula is given by:

( a ± b )³ = a³ ± 3a²b + 3ab² ± b³

Third binomial formula is given by :

( a + b) ( a - b) = a² - b²

Therefore, the third binomial formula is equal to ( a + b )( a - b) = a² - b².

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Researchers must be cautious when designing web-based surveys because they are particularly sensitive to undercoverage, nonresponse and voluntary response bias. So, option B is correct.

Web-based surveys have become increasingly popular in recent years due to their convenience and cost-effectiveness. However, researchers must be cautious when designing web-based surveys because they are particularly sensitive to various types of biases that can affect the validity and reliability of the survey results.

One of the biases that can affect web-based surveys is undercoverage, which occurs when some members of the target population are not able to access or complete the survey due to lack of internet access, technical difficulties, or other reasons. This can lead to a biased sample that does not accurately represent the entire population of interest.

Another bias that can affect web-based surveys is nonresponse, which occurs when some individuals who are invited to participate in the survey choose not to do so. This can lead to a biased sample if those who choose not to participate have different characteristics or opinions from those who do participate.

Finally, web-based surveys are also susceptible to voluntary response bias, which occurs when individuals choose to participate in the survey because they have strong feelings or opinions on the topic, while others choose not to participate. This can lead to a biased sample that overrepresents certain groups or opinions.

Therefore, Option B is the correct answer.

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Complete question is:

Researchers must be cautious when designing web-based surveys because they are particularly sensitive to:

a. undercoverage.

b. All of the answer choices are correct.

c. nonresponse.

d. voluntary response bias.

Step-by-step explanation:

count the number of boxes

Answer:

k(-7) = = -89

Step-by-step explanation:

k(t) = 10t -19

Let t = -7

k(-7) = 10*-7 -19

      = -70-19

      = -89

Answer:

-89

Step-by-step explanation:

K(t) = K(-7)

10 is being multiplied by t. t = -7

so:

10(-7) = -70

-70 - 19 = -89

Hope this helps!

The complex number -2-5 can be expressed in polar form as approximately 5.39∠(196.3°).

To convert the complex number -2-5 into polar form, we need to find the magnitude (r) and the angle (θ) of the complex number.

The magnitude (r) can be calculated using the formula r = \(\sqrt{a^{2}+b^{2} }\), where a and b are the real and imaginary parts of the complex number, respectively. In this case, a = -2 and b = -5. Evaluating the formula, we get r = \(\sqrt{((-2)^{2}+(-5)^{2} }\) = \(\sqrt{4+25}\) = √29 ≈ 5.39.

The angle (θ) can be determined using the inverse tangent function: θ = \(atan\frac{b}{a}\). Plugging in the values, we have θ = \(atan\frac{-5}{-2}\) ≈ 1.11 radians. To express the angle in degrees, we convert radians to degrees by multiplying by 180/π. Therefore, θ ≈ 1.11 × (180/π) ≈ 196.3°.

Hence, the complex number -2-5 can be written in polar form as approximately 5.39∠(196.3°).

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Answer:

y = 2x-3

Explanation:

By definition, two lines are parallel if they have the same slope.

Given the equation for a line:

Comparing the given line with the slope-intercept form of a line:

Thus, we want to find the equation of the line with the following properties:

• Slope: m = 2

• Point: (x1,y1)=(2,1)

In order to do this, we employ the use of the point-slope form of the equation of the line:

We then simplify:

The equation of the parallel line is y=2x-3.

Answer:

Step-by-step explanation:

θ=85+1=86

or

θ=85-1=84

84°<θ<86°

sin 84<sinθ<sin86

0.994522<sin θ<0.997564

Answer:

Step-by-step explanation:
\(168yd^{2}\)

Answer:

168 yd²

Step-by-step explanation:

4 × 7 yd × 12 yd / 2 = 168 yd²

Answer:

1. 3, 12, 48, 192, 768               Ratio: x4

2. 8, 16, 32, 64, 128                Ratio: x2

3. 120, 60, 30, 15, 7.5             Ratio: ÷2

4. 5, 10, 20, 40, 80, 160          Ratio: x2

5.  1.3?, 4, 12, 36, 108, 324      Ratio: x3

Hope this helps!

I'm not sure about the first one on question 5 though.

The phrase describes a transformation of the graph of function to create the graph of function h is vertically stretched.

The answer is option D. vertically compressed.

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Answer: 12x-60

Step-by-step explanation:

-12 x 5/6 = 10

-12 x 5 = -60

10x-60+2x

12x-60

Answer:

D) y = -5x + 5

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 1/5x + 5. Its slope is 1/5. A line parallel/perpendicular to this one will have a slope of -5.

Plug this value (#) into your standard point-slope equation of y = mx + b.

y = -5x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -5). Plug in the x and y values into the x and y of the standard equation.

-5 = -5(2) + b

To find b, multiply the slope and the input of x (2)

-5 = -10 + b

Now, add 10 to both sides to isolate b.

5 = b

Plug this into your standard equation.

y = -5x + 5

This equation is parallel/perpendicular to your given equation (y = 1/5x + 5) and contains point (2, -5)

Hope this helps!

x = -15

Step-by-step explanation:

\(x = \frac{2}{3} x - 5\)

Collect like terms and simplify

\(x - \frac{2}{3} x = - 5 \\ \frac{1}{3} x = - 5\)

Cross multiply

\(x = - 5 \times 3 \\ \\ x = - 15\)

74-126+329/2

-52+329/2

277/2

138.5