triple u, then raise the result to the 5th power

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer:

9a-2=7

Step-by-step explanation:

4a+ 5a-2=5+3-1

To simplify each side, combine like terms.

4a+5a = 9a

5+3-1 = 7

The equation becomes:

9a-2=7

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Step-by-step explanation:

π ∫₀¹ x² dx

This integral is obtained using disk method.  Each disk has a volume of V = πr²t, so the radius is r = x.

The region is 0 ≤ y ≤ x, 0 ≤ x ≤ 1.

Revolved around the x-axis, the resulting shape is a cone.

If the shape were a paraboloid, the integral would have been:

π ∫₀¹ (x²)² dx

π ∫₀¹ x⁴ dx

Answer: The solution to the system of equations by substitution is (x, y) = (-1, 1).

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

INnbdueif v ur[gtwogre gregabgbf

Answer:

\(slope = \dfrac{-680}{9}\)

Step-by-step explanation:

We are given coordinates of two points:

Let the points be A and  B respectively:

\(A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})\)

To find the slope of line AB.

Formula for slope of a line passing through two points with coordinates \((x_1, y_1)\) and \((x_2,y_2)\) is given as:

\(m = \dfrac{y_2- y_1}{x_2- x_1}\)

Here, we have:

\(x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\\)

Putting the values in formula:

\(m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}\)

So, the slope of line AB passing through the given coordinates is:

\(m = \dfrac{-680}{9}\)

Answer:

eight squared or 64

Answer:

8 to the 2nd power.

Step-by-step explanation:

First add all the power. This will get you 8*11/8*9. Next, divide this by subtracting which will get you 8*2! Have a nice day!!!

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer:

Jemma: 22x + 5

Debra: 20x

Step-by-step explanation:

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

i beleive 9 times

Step-by-step explanation:

50÷5.50=9.09

answer

212 - 147 = () times 3.75

147 × 4.25 =

add them together and that's the total amount

Answer:

slope: 1/2

y: intercept: (0;6)

so B

The equation of the line is y = x/2 + 6 which passes through the points (-6, 3) and (2, 7) option (B) is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that:

The line that passes through the points (-6, 3) and (2, 7)

The equation of the line:

y - 7 = (7 - 3)/(2 + 6)[x - 2]

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

y = (1/2)x - 1 + 7

y = x/2 + 6

Thus, the equation of the line is y = x/2 + 6 which passes through the points (-6, 3) and (2, 7) option (B) is correct.

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Answer:

  yes

Step-by-step explanation:

The domain is the set of x-values: {1, 2, 3, 4}. None of these are repeated, so this relation is a function.

Answer:

Sara has $144 at the beginning of the month.

Step-by-step explanation:

At the beginning of the month, x = 0 because no days have passed since the beginning of the month. When x = 0, g(0) = -4.5(0) + 144 = 144, therefore, we know that Sara has $144 on her card at the beginning of the month.

After rounding off the number we get ; 9,300

When a number is rounded to the closest thousand, it is changed to an approximated value that is simpler to recall and utilize. The closest value to the supplied integer is this value, which is a multiple of 1000. For instance, 342984 becomes 343000 if it is rounded to the closest thousand.

So as in this question the number given is 9340

Since we have to round it off to thousands

and the number next to 9 is 3

Thus we can say that after rounding off the number will be

9,300.

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The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

Option D is the correct answer.

We have,

We can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

Slope.

m = (y2 - y1) / (x2 - x1)

= (-6.4 - 8) / (-2.2 - 5)

= (-14.4) / (-7.2)

= 2

Next, we can use one of the two given points and the slope to write the equation of the line in the point-slope form:

y - 8 = 2(x - 5)

Expanding the right side and simplifying.

y - 8 = 2x - 10

y = 2x - 2

Therefore,

The equation of the line that passes through points (5, 8) and
(-2.2, -6.4) is y = 2x - 2.

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The piece wise function is \(\left \{ {{x} \ x < -1 \atop {1 \ -1 \leq x < 1}} \atop {x+ 1 \ x \geq 1}} \right.\) and the domain in the interval notation is {x| x ∈ R}.

A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs.

A function with many definitions in various x-intervals is said to be piecewise. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.

The piecewise function has the following intervals from left to right.

For an open dot on -1 we have x < -1.

For the close dot on -1 and open dot on 1 we have -1 ≤ x < 1.

For a close dot on 2 we have x ≥ 2.

The equation of the line on the interval is as follows:

The slope of the line is 1 and it intersects the y axis at 0, thus the function of the line is x.

The slope for the line in between is 0 and it intersect at 1, thus the function of the line is 1.

The slope of the line to the right is 1 and it intersects the y-axis when extended at 1. Thus, the function of the line is x + 1.

Putting the intervals and function together, the piece wise function is:

\(\left \{ {{x} \ x < -1 \atop {1 \ -1 \leq x < 1}} \atop {x+ 1 \ x \geq 1}} \right.\)

Domain are all the input values that the function takes, or the x-coordinates of the graph.

The domain of the piecewise function in the interval notation is:

Domain: {x| -∞ < x < ∞} or {x| x ∈ R}

Hence, the piece wise function is \(\left \{ {{x} \ x < -1 \atop {1 \ -1 \leq x < 1}} \atop {x+ 1 \ x \geq 1}} \right.\) and the domain in the interval notation is {x| x ∈ R}.

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To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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Answer:

For samples of size n=200, the standard error is of 0.033.

For samples of size n=300, the standard error is of 0.027.

For samples of size n=400, the standard error is of 0.024.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

The percentage of married couples who own a single family home is 33% for a given population.

This means that \(p = 0.33\)

Samples of 200:

\(s = \sqrt{\frac{0.33*0.67}{200}} = 0.033\)

For samples of size n=200, the standard error is of 0.033.

Samples of 300:

\(s = \sqrt{\frac{0.33*0.67}{300}} = 0.027\)

For samples of size n=300, the standard error is of 0.027.

Samples of 400:

\(s = \sqrt{\frac{0.33*0.67}{400}} = 0.024\)

For samples of size n=400, the standard error is of 0.024.

Answer:

Step-by-step explanation:

The solution of the equation 4x - 3  = 5 is not extraneous .

Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation.

Therefore, let's solve the equation to know whether it is extraneous solution.

Hence,

4x - 3  = 5

add 3 to both sides of the equation

4x - 3 + 3 = 5 + 3

4x = 8

divide both sides of the equation by 4

4x / 4 = 8 / 4

x = 2

Therefore, it is not extraneous solution.

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