Determine whether 81 − 49n^4 is a difference of two squares. If so, factor it. If not, explain why.
(9 + 7n^2 )(9 − 7n^2 )
(9 − 7n^2)(9 − 7n^2)
(9 − 7n^4)(9 + 7n^4)
Not a difference of squares because −49n^4 is not a perfect square.

Answer:

60

Step-by-step explanation:

With 50 percent representing half, 30 is half of 60.

C. X > -1

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−2x + 5 < 7

Step 2: Subtract 5 from both sides.

−2x + 5 − 5 < 7 − 5

−2x<2

Step 3: Divide both sides by -2.

−2x/−2 < 2/−2

x > −1

Answer:

-$2.50

Step-by-step explanation:

Since it said that one stock fell $12.50,that means that the $12.50 is negative.Then you have to do -12.50 ÷ 5 which equals -2.50

Hope this helped!

The number of points gained overall by Julia playing the game is 30 point

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

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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The median would be 22:

Step-by-step explanation: The median is the number that is in the middle

Simply defined, the median is the number right in the middle of a set.

But before I get down to finding the median, I will order the numbers from least to greatest:

15, 17, 19, 20, 21, 22, 23

Now, the middle number is 20. So that's the median.

As for the range, it's the difference between the largest number and the smallest one:

Range = Greatest number - Smallest number

           = 23 - 15

           = 6

In summary, the median, the number in the middle, is 20, and the range, the difference between the largest number and the smallest one, is 6.

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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The equation of the tangent line at (1,1) is given as follows:

y - 1 = -0.25(x - 1).

The curve for this problem is given as follows:

x² - y² = 2x + y + xy - 4.

Applying implicit differentiation, we obtain the slope of the tangent line, as follows:

2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y

(dy/dx)(1 + x + 2y) = 2x - 2 - y

m = (2x - 2 - y)/(1 + x + 2y).

At x = 1 and y = 1, the slope is given as follows:

m = (2 - 2 - 1)/(1 + 1 + 2)

m = -0.25.

Hence the point-slope equation is given as follows:

y - 1 = -0.25(x - 1).

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Answer:

Forgot to turn the 7% into a 0.7... if you dont do that, then it will come out larger then it was supposed to be :)

Answer:

Sample response: Juanita did not change the 7% to the decimal 0.07. When she completes the problem as written, the interest will be greater than the money she borrowed.

Step-by-step explanation:

This is a sample response, be sure to change the wording up a bit.

The volume of the composite figure is 6,330.24 in^3

We know that the volume of half a sphere of radius R is:

V = (2/3)*pi*R^3

Here we know that pi = 3.14 and R = 12 inches, then the volume is:

V = (2/3)*3.14*(12 in)^3 = 3,617.28 in^3

And the volume of a cone of height H and radius R is:

v = (1/3)*pi*R^2*H

So here the volume is:

v = (1/3)*3.14*(12in)^2*18in = 2,712.96 in^3

Then the total volume is:

3,617.28 in^3 +  2,712.96 in^3 = 6,330.24 in^3

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Answer: The probability of choosing an ace or a club is 16.

Step-by-step explanation:

Answer:

£0

Step-by-step explanation:

To calculate the outstanding loan balance for each person after 10 years, we can use the following formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial loan amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time in years

For Olivia, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Olivia's outstanding balance would be £2829.71.

For Sadie, we can calculate her outstanding balance after 10 years as follows:

P = £2000

r = 6.5% per year = 0.065

n = 1 (compounded annually)

t = 10 years

A = £2000(1 + 0.065/1)^(1*10) = £3829.71

After paying back £1000, Sadie's outstanding balance would be £2829.71.

To find the difference between Sadie's outstanding balance and Olivia's outstanding balance, we can subtract Olivia's balance from Sadie's balance:

£2829.71 - £2829.71 = £0

Therefore, Sadie does not owe more money than Olivia after 10 years, as both of their outstanding balances are the same at that point in time.

This text describes a scenario where two individuals, Olivia and Sadie, take out a loan of £2000 each at the same time. The loans have a compound interest rate of 6.5% per year. Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods.

Two years after taking out the loan, Olivia pays back £1000, which reduces her outstanding loan balance to £2000 plus accumulated interest. Three years after taking out the loan, Sadie pays back £1000, which also reduces her outstanding loan balance to £2000 plus accumulated interest.

The question asks how much more money Sadie owes than Olivia 10 years after taking out the loan. To solve this problem, we need to calculate the outstanding loan balance for both Olivia and Sadie after 10 years, using the compound interest formula. We can then subtract Olivia's outstanding balance from Sadie's outstanding balance to find the difference.

It's worth noting that the question specifies that the answer should be given in pounds to the nearest 1p, which means we need to round our final answer to the nearest penny.

Answer:

The first one : x^2 - 8x + 15 sq ft

Step-by-step explanation:

To find the ares you need to multipy L and W : (x - 3) x ( x - 5)

(x - 3) x ( x - 5)

(x times x) - ( 3x + 5x) + ( 5 x 3)

=x^2 - 8x + 15

If this helps you, please give brainliest!

Answer:

(x-3)(x-5)=x^2-5x-3x+15=x^2-8x+15

Step-by-step explanation:

Because the patio is a rectangle, so it's area is I.w=(x-3)(x-5)

Unbiased estimators are statistical estimators that give an estimate of a population parameter that is equal to the true population parameter on average, regardless of the sample size.

The analysis suggests that the process Î 3 is more efficient than Î 1 and Î 2 when considered separately. However, when combined, the processes Î 1/2 and Î 2/2 are less efficient.

(a) To find out if Î 3=Î 1+Î 22 is unbiased, we must compute its anticipated value and contrast it with Î.

If Î 1 and Î 2 are unrelated and unbiased, E(Î 3) = E(Î 1 + Î 22) = E(Î 1) + E(Î 22) = Î + Î = 2Î

E(Î3) is biased as it does not equal Î.

(b) The formula for the variance of a linear combination of random variables can be used to assess if Î3 is more effective than Î1 and Î2.

Var(Î 3) is equal to Var(Î 1) plus 2Cov(Î 1, Î 2) plus Var(Î 2)/4.

Var(Î 1) = Var(Î 2) and Cov(Î 1, Î 2) = 0 result in:

Var(^θ3) = 5/4

Var(^θ1)

Var(Î 1) > 4/5Var(Î ), meaning that Î 3 is more effective than Î 1 and Î 2. If not, Î1 is more effective.

(c) If Var(Î1|Î2|Î3] Var(Î1|Î3]), then Î2 is more effective than Î1. Assume that Î1 and Î2 are equal and that Var(Î1) Var(Î2) independent. To calculate the variance of Î3, we can use the following formula for the variance of a linear combination of random variables:

As Î1 and Î2 are independent, Var(Î 3) = Var(Î 1) + 2Cov(Î1, Î2) + Var(Î2)/4 = Var(Î1) + 0 + Var(Î2)/4.

Var(Î 1) + Var(Î 2) = 4 and (Var(Î 1) + Var(Î 2)) = 2

As a result, Ï 3 is more effective than Î 1 and Î 2 taken separately, but not as effective as Î 2/2 and Î 1/2 taken together.

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Use trigonometry.

sin x = opposite ÷ hypotenuse

sin x = 7/9

Take the arcsin on both sides.

arcsin(sin x) = arcsin(7/9)

x = 51.057558731

Rounding to the nearest whole number means to round to the ones place.

Answer: x = 51 degrees

Answer:

It's A :)

Step-by-step explanation:

30/2 is 15

15 is a whole number so it applies to everything except for irrational numbers

Hope this helps :)

Additive inverse property of real numbers was used to transition from step 3 to step 4

The property of real numbers used to transition from Step 3 to Step 4 is the additive inverse property or the property of adding the opposite. The additive inverse property states that for any real number a, there exists an additive inverse -a, such that a + (-a) = 0. In other words, adding the opposite of a number results in the sum being zero.

In Step 3 of the given expression, we have "12 + (-12) + 6x." Notice that "-12" is the opposite of "12." To simplify this expression further, we can apply the additive inverse property by combining the positive and negative numbers.

Adding 12 and its additive inverse (-12) results in 0, according to the additive inverse property. So, in Step 4, we replace "12 + (-12)" with "0." By applying the additive inverse property, the expression simplifies to "0 + 6x," which can be further simplified to just "6x."

The use of the additive inverse property is crucial in algebraic simplifications as it allows us to eliminate terms that add up to zero. This property helps streamline calculations and reduce complex expressions to simpler forms.

Overall, the transition from Step 3 to Step 4 in the given expression utilizes the additive inverse property to eliminate the sum of opposite numbers and simplify the expression to its final form, which is "6x."

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Answer:

1. domain: {-11, -7, 3, 6} range: {-7, -4, 0, 5}

2. domain: {-27, -18, 3, 6, 9} range: {-3, -2, -1, 6, 9}

3. domain: {-8, 2, 5} range: {4, 7}

Answer:

30

Step-by-step explanation:

It is a 30 60 90 triangle if you ever heard of it. Look at it and it will make more sense.

The area of the rectangular figure with two semicircles on the opposite side is  36.56 sq cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

Given, A rectangle with two semicircles on two opposite sides.

The length of the rectangle is 6cm and the width of the rectangle is 4cm.

The two given semicircles have a diameter of 4cm seems obvious.

∴ The area of the total figure is an area of the rectangle added to the area of 2 semicircles which makes up to a circle with a radius 2 cm.

∴ (4×6) + π(2)² sq cm.

= 24 + 4π sq cm.

= 24 + 12.56 sq cm.

= 36.56 sq cm.

The area which is not taken up in the rectangle and two circle questions are

(area of the rectangle - 2 times the area of a circle).

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I suppose you mean

\(g(x) = \dfrac x{2\sqrt{36-x^2}} + 18\sin^{-1}\left(\dfrac x6\right)\)

Differentiate one term at a time.

Rewrite the first term as

\(\dfrac x{2\sqrt{36-x^2}} = \dfrac12 x(36-x^2)^{-1/2}\)

Then the product rule says

\(\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 x' (36-x^2)^{-1/2} + \dfrac12 x \left((36-x^2)^{-1/2}\right)'\)

Then with the power and chain rules,

\(\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12\left(-\dfrac12\right) x (36-x^2)^{-3/2}(36-x^2)' \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} - \dfrac14 x (36-x^2)^{-3/2} (-2x) \\\\ \left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-1/2} + \dfrac12 x^2 (36-x^2)^{-3/2}\)

Simplify this a bit by factoring out \(\frac12 (36-x^2)^{-3/2}\) :

\(\left(\dfrac12 x(36-x^2)^{-1/2}\right)' = \dfrac12 (36-x^2)^{-3/2} \left((36-x^2) + x^2\right) = 18 (36-x^2)^{-3/2}\)

For the second term, recall that

\(\left(\sin^{-1}(x)\right)' = \dfrac1{\sqrt{1-x^2}}\)

Then by the chain rule,

\(\left(18\sin^{-1}\left(\dfrac x6\right)\right)' = 18 \left(\sin^{-1}\left(\dfrac x6\right)\right)' \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac x6\right)'}{\sqrt{1 - \left(\frac x6\right)^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18\left(\frac16\right)}{\sqrt{1 - \frac{x^2}{36}}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{3}{\frac16\sqrt{36 - x^2}} \\\\ \left(18\sin^{-1}\left(\dfrac x6\right)\right)' = \dfrac{18}{\sqrt{36 - x^2}} = 18 (36-x^2)^{-1/2}\)

So we have

\(g'(x) = 18 (36-x^2)^{-3/2} + 18 (36-x^2)^{-1/2}\)

and we can simplify this by factoring out \(18(36-x^2)^{-3/2}\) to end up with

\(g'(x) = 18(36-x^2)^{-3/2} \left(1 + (36-x^2)\right) = \boxed{18 (36 - x^2)^{-3/2} (37-x^2)}\)

Answer:

2x/3 + 2= 16

=21

Step-by-step explanation:

Standard form:

2

3

x − 14 = 0  

Factorization:

2

3 (x − 21) = 0  

Solutions:

x = 42

2

= 21

Answer:

C) √221 units

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-7, 7)

Point (7, 2)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

2,4 3,5

Step-by-step explanation:

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer:

  2.06

Step-by-step explanation:

You want the value of the numerical expression √36÷5×12÷∛343.

This is a straightforward calculator problem. Your pocket calculator, or any of numerous calculator apps, online calculators, or spreadsheets can evaluate this expression for you.

The attachment shows the result is 2.06.

__

Additional comment

As expressed in this problem statement, the expression is ...

  \(\dfrac{\sqrt{36}\times12}{5\times\sqrt[3]{343}}=\dfrac{6\cdot12}{5\cdot7}=\dfrac{72}{35}\)

If you mean something else, you need to identify the quantities that need to be considered as a unit.

Answer:

x = 2

y = -2

z = 9

(2,-2,9)

Step-by-step explanation:

Answer: decreasing by 1.25

Step-by-step explanation:

4.5-3.25=1.25, 3.25-2=1.25, etc.

Answer:

deacreasing by 1.25

Step-by-step explanation:

Answer:

Difference in weight is 24 once

Step-by-step explanation:

got it right