Graph h(x) = (x - 2)(x - 4)

It is proved that a multiple of a pythagorean triple is also a pythagorean triple

When ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

\(|AC|^2 = |AB|^2 + |BC|^2\)

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

WE can see few pythagorean triple as

\({3}^{2} + {4}^{2} = {5}^{2} {(3 \times 2)}^{2} + {(4 \times 2)}^{2} = {(5 \times 2)}^{2} {6}^{2} + {8}^{2} = {10}^{2}\)

3-4-5 is a Pythagorean triple.

Now Multiplying each of these numbers by 2, we obtain 6-8-10,

This is a Pythagorean triple.

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Answer:

22

Step-by-step explanation:

222

The value of k in the given functions is; 24

We are given the functions;

g(x) = 4x  + k as a tangent to f(x) = -x² +8x +20

For f(x) = -x² +8x +20

=> f'(x)  = -2x + 8

Thus, slope of tangent at ( x , y) = -2x + 8  

For g(x) = 4x  + k

g'(x) = 4.

Thus, slope is 4

Therefore;

-2x  + 8 = 4

-2x = -4

x = 2

Putting 2 for x in f(x) gives;

f(2) = -2² + 8(2) + 20  

f(2) =  32

Thus, it is at (2 , 32)

Thus, (2 , 32) lies on g(x) = 4x + k

4(2) + k = 32

k = 32 - 8

k = 24

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At the circle's center, the arc's radius and angle are 9 cm and 4/3 radians, respectively.

Any section of a circle's circumference is considered an arc. Remember that the circumference of a circle is its perimeter or distance.

Given the length of the arc is 12cm and the area of the arc is 108 cm Square.

Since the length of the arc = θ × r

Area of the arc (A) =  (θ/360°) × πr2

Substituting values in the formulas

12  = θ × r

108 = θ × r²

comparing both equations

r = 9 cm

θ = 4/3 radian

Therefore, the radius and the angle subtended at the center of the circle by the arc are 9 cm and 4/3 radian respectively.

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A numerical measure computed from a sample, such as sample mean, is known as Sample statistic

What is Statistic?

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

A sample statistic is a metric that is calculated from a sample, such as sample mean. A population parameter is a numerical measure derived from a population, such as a mean.

Any value calculated from your sample data is referred to as a sample statistic (or simply a statistic). The sample average, median, sample standard deviation, and percentiles are a few examples. Because a statistic is based on data gathered through random sampling, which is a random experiment, it is a random variable.

Hence, A numerical measure computed from a sample, such as sample mean, is known as Sample statistic

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Answer:

n=20

Step-by-step explanation:

4n = 80

n=80/4

n=20

Answer:

will or will not

Step-by-step explanation:

The inequality that represents the number of games [g] Cynthia can bowl to remain within her budget is -

gx ≤ 20

The general equation of a straight line is -

[y] > [m]x + [c]

[y] < [m]x + [c]

[y] ≥ [m]x + [c]

[y] ≤ [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Strict inequalities are those inequalities which use either > or < to compare expressions. Example : 2x + 4 > 5

Slack inequalities are those inequalities which use either ≤ or ≥ to compare expressions. Example : 2x + 4 ≥ 5

We have Cynthia’s mom who gave her $20.00 to spend at her friend’s birthday party on Friday night.

Assume that a single game costs $x. Then, the inequality that represents the number of games [g] Cynthia can bowl to remain within her budget is-

gx ≤ 20

Therefore, the inequality that represents the number of games [g] Cynthia can bowl to remain within her budget is -

gx ≤ 20

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The power of a that makes it equal to b is x = 5/6

The square root of a number is a number when multiplied by itself gives another number.

The cube root of a number is a number when multiplied by itself three times gives another number.

The power of a number is the exponent of that number

Since two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. It follws that

4√a = 9∛b

⇒∛b = 4√a/9

⇒ b = ∛[4√a/9]

Since we require the  of x is a, to the x power equal to b if a = 2/3.

This implies that

aˣ = b

Substituting b into the equation, we have

aˣ =  ∛[4√a/9]

Since a = 2/3, we have

(2/3)ˣ =  ∛[4√(2/3)/9]

(2/3)ˣ =  ∛[4/9 × √(2/3)]

(2/3)ˣ =  ∛[2²/3² × √(2/3)]

(2/3)ˣ =  ∛[(2/3)² × √(2/3)]

(2/3)ˣ =  ∛[2/3)

\((\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{2 + \frac{1}{2}} } \\(\frac{2}{3} )^{x} = \sqrt[3]{(\frac{2}{3} )^{\frac{5}{2}} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{2} \times \frac{1}{3} } \\(\frac{2}{3} )^{x} = (\frac{2}{3} )^{\frac{5}{6}\)

Equating both powers, we see that x = 5/6

So, the power of a is x = 5/6

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Let v be a vector space and f ⊆ v be a finite set. To show that f ∪{u} is a linearly independent set, we need to prove that the only linear combination of its elements that equals the zero vector is the trivial one (i.e., all coefficients are zero).

Suppose that there exist scalars a1, a2, ..., an, b such that:

b*u + a1*v1 + a2*v2 + ... + an*vn = 0
where v1, v2, ..., vn are elements of f.

We want to show that all coefficients are zero.

Since u /∈span f, we know that u cannot be written as a linear combination of elements of f. Therefore, b ≠ 0.

We can rearrange the equation to get:
b*u = -(a1*v1 + a2*v2 + ... + an*vn)

Since f is linearly independent, we know that the only linear combination of its elements that equals the zero vector is the trivial one. Therefore, a1 = a2 = ... = an = 0.

Substituting this into the equation, we get
b*u = 0

Since b ≠ 0, we know that u = 0, which contradicts the fact that u is not in the span of f.

Therefore, our assumption that there exist nontrivial coefficients that satisfy the equation is false, and f ∪{u} is indeed a linearly independent set.

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Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning

Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.

By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.

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Answer:

Yes, they are equivalent.

Step-by-step explanation:

20 divided by 15 = 1.333333...

4 divided by 3 = 1.333333...

Answer:

18 months

Step-by-step explanation:

it grows 1 inch per month which means 18inchs =18months

IF YOU CHECK YOU WILL FIND THAT THIS IS A DIFFERENCE OF TWO SQUARES

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

ATTACHED IS THE SOLUTION

Answer:

726 minutes

Step-by-step explanation:

Answer:

its 726

Step-by-step explanation:

Answer:

1,008 pairs of earrings

Step-by-step explanation:

14 multiplied by 72 equals 1,008

Answer:

D.

Step-by-step explanation:

I don't know for a fact but I'm pretty sure its D. sorry if its wrong.

Hope this helped.

Answer:

I do not know what this is

Step-by-step explanation:

The prices for the train ticket from Bristol to London are given as follows:

The prices are obtained applying the proportions in the context of the problem.

Considering the 2019 price as x, the 2020 price is given as follows:

1.035x.

The difference was of 2.80, hence the 2019 price is given as follows:

1.035x - x = 2.8

x = 2.8/0.035

x = 80.

The 2020 price is given as follows:

80 + 2.8 = 82.8.

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Increasing marginal productivity infers that extra units of capital and labor contribute more to yield, driving productive asset allotment. ∝ and ß < 1 expect reducing returns, adjusting with reality.

To appear that the generation work has to expand the marginal productivity of capital (in case ∝ > 1) and labor (on the off chance that ß > 1), we ought to take fractional subsidiaries with regard to each input calculation. For capital (K), the fractional subsidiary of the generation work is:

\(\dfrac{dy}{dK }= \alpha AK^{(\alpha-1)}L^\beta\)

Since ∝ > 1, (∝ - 1) is positive, which implies that the fractional subordinate \(\dfrac{dy}{dK}\) is positive. This shows that an increment in capital input (K) leads to an increment in yield (y), appearing to expand the marginal efficiency of capital.

Additionally, for labor (L), the fractional subordinate of the generation work is:

\(\dfrac{dy}{dL} = \beta AK^{\alpha}L^{(\beta-1)}\)

Since \(\mathbf{\beta > 1, (\beta-1)}\) it is positive, which implies that the halfway subordinate \(\dfrac{dy}{dL}\) is positive. This demonstrates that an increment in labor input (L) leads to an increment in yield (y), appearing to increase the marginal productivity

The economic importance of increasing marginal productivity is that extra units of capital and labor contribute more to yield as their amounts increment.  This suggests that the more capital and labor a firm employments, the higher the rate of increment in yield. This relationship is vital for deciding the ideal assignment of assets and maximizing generation effectiveness.

In most generation capacities, it is accepted that ∝ and ß are less than 1. This presumption adjusts with experimental perceptions and financial hypotheses.

In case ∝ or ß were more prominent than 1, it would suggest that the marginal efficiency of the respective factor increments without bound as the calculated input increments.

In any case, there are decreasing returns to scale, which suggests that as calculated inputs increment, the Marginal efficiency tends to diminish. Therefore, accepting ∝ and ß are less than 1 permits for more reasonable modeling of generation forms and adjusts with the concept of diminishing marginal returns.

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The log-linear demand function In(Q) = A - Bln(p) relates quantity demanded (Q) to price (p).

a. Q as a function of p:

Q = e^A / p^B

dp/dQ = -B * e^A / p^(B+1)

b. p as a function of Q:

p = e^(A/B) / Q^(1/B)

To solve this problem, let's start with the given demand function: In(Q) = A - Bln(p), where Q represents the quantity demanded, p is the price of the product, A and B are constants.

a. Express Q as a function of p:

To find the relationship between Q and p, we need to exponentiate both sides of the equation to remove the natural logarithm. By taking the exponential function, we get:

e^(In(Q)) = e^(A - Bln(p))

Using the property e^(A - Bln(p)) = e^A / e^(Bln(p)) = e^A / p^B, the equation becomes:

Q = e^A / p^B

Now, let's differentiate both sides of this equation with respect to p:

dQ/dp = d/dp(e^A / p^B)

To differentiate e^A / p^B, we can use the quotient rule:

dQ/dp = [e^A * (-B) * p^(B-1) - e^A * p^B * 0] / (p^B)^2

Simplifying this expression, we have:

dQ/dp = -B * e^A / p^(B+1)

b. Express "p" as a function of Q:

To find the relationship between p and Q, we can rearrange the equation Q = e^A / p^B:

p^B = e^A / Q

Now, taking the B-th root of both sides:

p = (e^A / Q)^(1/B)

Simplifying further:

p = e^(A/B) / Q^(1/B)

So, we have expressed "p" as a function of Q.

In summary, for the log-linear demand function In(Q) = A - Bln(p):

a. Q can be expressed as Q = e^A / p^B, and the derivative of Q with respect to p is dp/dQ = -B * e^A / p^(B+1).

b. p can be expressed as p = e^(A/B) / Q^(1/B).

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Answer: what is it?????

Step-by-step explanation:

Thx for pts

the answer is:

there is no question

The expected value of buying one ticket in this charity raffle is $0.42. This means that, on average, a person can expect to win approximately $0.42 if they purchase a single ticket.

To calculate the expected value, we need to consider the probability of winning each prize multiplied by the value of the prize. Let's break it down:

- There is a 1/5000 chance of winning the $600 prize, so the expected value contribution from this prize is (1/5000) * $600 = $0.12.

- There are 3/5000 chances of winning the $300 prize, so the expected value contribution from these prizes is (3/5000) * $300 = $0.18.

- There are 5/5000 chances of winning the $40 prize, so the expected value contribution from these prizes is (5/5000) * $40 = $0.04.

- Finally, there are 20/5000 chances of winning the $5 prize, so the expected value contribution from these prizes is (20/5000) * $5 = $0.08.

Summing up all the expected value contributions, we get $0.12 + $0.18 + $0.04 + $0.08 = $0.42.

Therefore, if you buy one ticket in this raffle, the expected value of your winnings is $0.42.

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The yearly salary, considering the proportions, is given as follows:

R184,320.

The yearly salary is obtained applying the proportions in the context of the problem.

The monthly expenses are given as follows:

Hence the monthly fraction that is used for expenses is given as follows:

1/12 + 1/16 + 5/6 = (4 + 3 + 40)/48 = 47/48.

The remaining amount of R320 is 1/48 of your monthly salary, which is 1/12 of your yearly salary, which is given as follows:

48 x 12 x 320 = R184,320.

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The center of the circle (x + 9)² + (y − 6)² = 10² is at (-9, 6) and the radius of the circle is 10 units.

It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

The equation of the circle is given as

(x + 9)² + (y − 6)² = 10²

Then the center of the circle is at (-9, 6) and the radius of the circle is 10 units.

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Answer:

A. (-9, 6)

Step-by-step explanation:

i did it B)

This statement is - true.

Two angles that lie in the same plane and have a common vertex and a common side but have no common interior points are the meaning of adjacent angles.

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