which of the following pairs of functions are inverses of each other​

Answer:

1st Q- B

2nd Q- A

Step-by-step explanation:

1st Q:

n²<220<(n+1)²

n²<220<(n²+2n+1)

we can plug in the values in the answers and see which one satisfies the inequality:

when n=13 --> 13²<220<(13²+2*13+1) => 169<220<196 (this one does not work)

when n=14 --> 14²<220<(14²+2*14+1) => 196<220<225 (this one works)

when n=15 --> 15²<220<(15²+2*15+1) => 225<220<256 (this one does not work)

when n=16 --> 16²<220<(16²+2*16+1) => 256<220<289 (this one does not work)

so the answer is B

2nd Q:

A

(see the attachment below for explanation)

The total number of lines of symmetry for this figure is 4.

Option D is the correct answer.

The symmetry line, or horizontal axis, that divides a shape into two identical halves is called a horizontal symmetry line. This means that the axis here intersects the shape and is cut into two equal parts. English alphabets such as B, C, H, and E are examples of horizontal symmetry.

Symmetry represents resistance to the possibility of change. The stubborn core of shapes, phrases, laws, or formulas remains unchanged under certain transformations.

Explanation;

two lines of symmetry along mid point horozontally and vertically from centre.

two lines along each arm of X

total line of symmetry is = 2+2 = 4

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Answer:2 is the correct answer

Answer: i cant see it

Step-by-step explanation:

Answer: It's the second one

Step-by-step explanation:

Answer:

12, 18, 24. that finishes the table

Answer:

the answer to the question is option B

Answer:

The answer is B.

Step-by-step explanation:

B

Rebecca needs 6 \( \frac{1}{4} \) more yards of fabric to make the quilt.

Firstly calculating the fabric available to Rebecca = 2 \( \frac{1}{2} \) + 4 \( \frac{1}{4} \)

Fabric available to Rebecca = 5/2 + 17/4

Taking LCM we get 4

Fabric available to Rebecca = 10 + 17/4

Fabric available to Rebecca = 27/4

Let the required fabric be x. So,

17/4 + x = 21/2

x = 21/2 - 17/4

Performing subtraction

Taking LCM we get 4

x = 42 - 17/4

x = 25/4

Converting it back into mixed fraction -

x = 6 \( \frac{1}{4} \)

Thus, the required fabric is 6 \( \frac{1}{4} \) yards.

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The complete question is -

Rebecca needs 10 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabric that is 4 1/4 yards. How many more yards of fabric does Rebecca need to make a quilt.

Using compound interest, it is found that the maximum amount of money he can borrow is of $8,700.

------------------------

The compound interest formula is given by:

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

Maximum monthly payments of $200 per month per five years, thus:

\(A(t) = 5 \times 200 \times 12 = 12000\)

\(A(t) = P(1 + \frac{r}{n})^{nt}\)

\(12000 = P(1 + \frac{0.065}{12})^{60}\)

\(1.38282P = 12000\)

\(P = \frac{12000}{1.38282}\)

\(P = 8678\)

To the nearest 100, $8,700.

The maximum amount of money he can borrow is of $8,700.

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Answer:

Mary spent more than 24dollars at the mall

Step-by-step explanation:

\(x - 8 > 16 \\ x - 8 + 8 > 16 + 8 \\ x = 24\)

A matrix is the sum of two non-singular matrices is not generally true.

I'm sorry, but I'm unable to prove that a matrix is the sum of two non-singular matrices. The statement itself is not true.

A non-singular matrix, also known as an invertible matrix or non-singular square matrix, is a matrix that has an inverse. In other words, a non-singular matrix is one that can be multiplied by another matrix to give the identity matrix.

If we consider the sum of two non-singular matrices, it does not necessarily result in a non-singular matrix. The sum of two non-singular matrices can be a non-invertible matrix or a singular matrix.

For example, let's consider two non-singular matrices:

A = [1 0] B = [0 1]

[0 1] [1 0]

The sum of A and B would be:

A + B = [1+0 0+1] = [1 1]

[0+1 1+0] [1 1]

The resulting matrix A + B is a singular matrix since its determinant is 0. Therefore, it is not the sum of two non-singular matrices.

Hence, the claim that a matrix is the sum of two non-singular matrices is not generally true.

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It will take approximately 4.91 hours for Enrique's body to metabolize half of the 86 mg of caffeine.

To determine this, we can use the concept of exponential decay. The amount of caffeine in Enrique's body decreases by 14.1% per hour, which means that each hour the amount of caffeine remaining is 86% of the previous amount.

To find the time it takes for half of the caffeine to be metabolized, we need to solve the equation:

86 mg * (0.861)^t = 43 mg

Where t represents the time in hours.

Dividing both sides of the equation by 86 mg, we get:

0.861^t = 0.5

Taking the logarithm of both sides, we can solve for t:

t x log(0.861) = log(0.5)

t = log(0.5) / log(0.861)

Using a calculator, we find that t is approximately 4.91 hours.

Therefore, it will take approximately 4.91 hours for Enrique's body to metabolize half of the 86 mg of caffeine.

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Step-by-step explanation:

You want to set one of the equations equal to either x or y. For this, I put x+y=-2 equal to y which would be y=-x-2. Then you plug this in to the other equation for y. This would give you 5x+2(-x-2)=2. When you factor the two into the parenthesis, combine like terms, and keep the x values on ones side and the other numbers on the other side, you get 3x=6

Answer:

I think the sum of the measures of the interior angles of an octagon =(8−2)180° . The sum of the measures of the interior angles of an octagon is 1080° .

I hope this help!:)

Answer:

\(135^{\circ}\)

Step-by-step explanation:

The sum of the interior angles of a polygon with \(n\) sides is equal to \((n-2)180\). Since an octagon has 8 sides, the sum of its interior angles is equal to:

\((8-2)180=6\cdot 180=1,080^{\circ}\)

By definition, a regular polygon is a polygon with equal sides and angles. An octagon has 8 sides and 8 angles. Therefore, a each interior angle of a regular octagon must be equal to:

\(\frac{1,080}{8}=\boxed{135^{\circ}}\)

The net present value (NPV) of the project, with an initial investment of $200,000 and an expected cash flow of $220,000 at the end of the year, discounted at a rate of 25 percent, is $-24,000.

Net Present Value (NPV) is a financial metric used to assess the profitability of an investment by comparing the present value of cash inflows and outflows. To calculate NPV, the future cash flows are discounted back to their present value using a specified discount rate.

In this case, the initial investment is $200,000, and the expected end-of-year cash flow is $220,000. The discount rate is 25 percent. To calculate the NPV, we need to discount the future cash flow back to the present value.

To find the present value, we divide the future cash flow by (1 + discount rate)^n, where n is the number of years. In this case, n is 1 year.

Present value = Cash flow / (1 + discount rate)^n

Present value = $220,000 / (1 + 0.25)^1

Present value = $220,000 / 1.25

Present value = $176,000

The NPV is then calculated by subtracting the initial investment from the present value of the cash flow:

NPV = Present value - Initial investment

NPV = $176,000 - $200,000

NPV = -$24,000

Therefore, at a discount rate of 25 percent, the NPV of the project is -$24,000, indicating a negative net present value. This suggests that the project may not be financially viable, as the present value of the expected cash flow does not sufficiently compensate for the initial investment.

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Answer:the existence of an association does not empty a causation

Step-by-step explanation:

a direct casual link cannot be inferred the association merely suggests a hypothesis such as a commom cause but does not offer proof

Answer: x(x) + x(2) + 1(x) + 1(2)

The simplified product is x² + 3x + 2

Hope this helps!

Answer:

Step-by-step explanation:

The equation for the line with a slope of 5/6 and passing through the point (22,12) is y=5/6x - 16.

The equation for the line with a slope of 5/6 and passing through the point (22,12) can be expressed as y=5/6x + b. To calculate the value of b, we can plug in the given point's coordinates, (22,12), into the equation. This will result in the equation 12=5/6(22)+b. Solving for b, we get b=-16. Therefore, the equation for the line is y=5/6x-16.

In summary, we can express the equation for the line with a slope of 5/6 and passing through the point (22,12) as y=5/6x - 16. To calculate the value of b, we plugged the point's coordinates, (22,12), into the equation, resulting in the equation 12=5/6(22)+b. Solving for b, we got b=-16. Thus, the equation for the line is y=5/6x - 16.

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Answer:

9

Step-by-step explanation:

The correct conversion is 68°F = 20°C.

Conversion is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

We are given that;

To convert 68°F

Now,

To solve the formula for C, we need to isolate C on one side of the equation. We can do this by subtracting 32 from both sides and then dividing by 1.8. The steps are:

F = 1.8C + 32

F - 32 = 1.8C

(F - 32) / 1.8 = C

Therefore, the correct formula for C is:

C = (F - 32) / 1.8

To convert 68°F to degrees Celsius, we can plug in F = 68 into the formula and simplify. The steps are:

C = (68 - 32) / 1.8

C = 36 / 1.8

C = 20

Therefore, after conversion the answer will be 68°F = 20°C.

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\((15+2\sqrt{6}) ^{2} = 15^{2} +2(15)(2\sqrt{6}) + (2\sqrt{6})^{2} = 225 + 60\sqrt{6} +24 = \bf 249 + 60\sqrt{6}\)

Answer:

494

Step-by-step explanation:

There's 60 seconds in 1 minute

multiply 8 * 60 and add 14

494

Answer:

494 seconds

Step-by-step explanation:

1 minute = 60 seconds

Convert 8 minutes into seconds:

Variable x = number of seconds in 8 minutes

1 min/60 seconds = 8 mins/x

Cross multiply:

1 × x = 60 × 8

1x = 480

x = 480 seconds

Add the 14 seconds to 480 seconds:

14 + 480 = 494

Answer:

  8.8 pounds

Step-by-step explanation:

There are 7 days in a week, so the daily loss was ...

  (28 kg)/(7 days) = 4 kg/day

In pounds, that is about ...

  (4 kg/day)(2.2 lb/kg) = 8.8 lb/day

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

Let the number = x

3/4 of x = 48

3/4x = 48

Divide both sides by 3/4

X = 48/ 3/4

X = 64

The number is 64

=πr^2h

=π(5)^2*11

=25*11π

=275π yd^3

For the given rectangular right prism the volume of the composite figure is 444 cubic inches.

What is rectangle?

A rectangle is a four-sided flat shape with straight sides where all interior angles are right angles (90°). It is a type of quadrilateral and can be defined as a parallelogram with four right angles.

To find the volume of the composite figure, we need to find the volume of the rectangular prism and the two square pyramids and then adjust for the addition and subtraction.

The volume of the rectangular prism is:

\(V_{rectangular\ prism\) = length x width x height

\(V_{rectangular\ prism\) = 12 x 6 x 6

\(V_{rectangular\ prism\) = 432 cubic inches

The volume of the first square pyramid that is cut from the prism is:

\(V_{cut\ pyramid\) = 1/3 x base area x height

\(V_{cut\ pyramid\) = 1/3 x \(6^2\) x 3

\(V_{cut\ pyramid\) = 36 cubic inches

Now, we need to subtract the volume of the cut pyramid from the volume of the rectangular prism:

\(V_{adjusted} = V_{rectangular\ prism} - V_{cut\ pyramid\)

\(V_{adjusted\) = 432 - 36

\(V_{adjusted\) = 396 cubic inches

The volume of the second square pyramid that is added to the opposite base is:

\(V_{added\ pyramid\) = 1/3 x base area x height

\(V_{added\ pyramid\) = 1/3 x \(6^2\) x 4

\(V_{added\ pyramid\) = 48 cubic inches

Finally, we need to add the volume of the added pyramid to the adjusted volume of the rectangular prism:

\(V_{composite\ figure} = V_{adjusted} + V_{added\ pyramid\)

\(V_{composite figure} = 396 + 48\)

\(V_{composite figure} = 444\ cubic\ inches\)

Therefore, the volume of the composite figure is 444 cubic inches.

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The approximated value of the definite integral is 0.396444

To approximate the definite integral ∫₀^(0.4) e^(-x^2) dx with an error less than 10^(-4), we can use the Taylor series expansion of the function e^(-x^2):

e^(-x^2) = 1 - x^2 + (x^4)/2 - (x^6)/6 + ...

Integrating this series term by term, we have:

∫₀^(0.4) e^(-x^2) dx ≈ ∫₀^(0.4) (1 - x^2 + (x^4)/2 - (x^6)/6) dx

Integrating each term separately, we get:

∫₀^(0.4) dx - ∫₀^(0.4) x^2 dx + ∫₀^(0.4) (x^4)/2 dx - ∫₀^(0.4) (x^6)/6 dx

Simplifying, we have:

(0.4 - 0) - (0.4^3)/3 + (0.4^5)/(2 * 5) - (0.4^7)/(6 * 7)

Calculating the values, we have:

0.4 - (0.4^3)/3 + (0.4^5)/10 - (0.4^7)/252

Now, we need to determine the number of decimal places to which we need to truncate the series expansion to achieve the desired accuracy of 10^(-4). Let's assume we need to truncate the series after the term (x^6)/6.

Using the remainder estimate for alternating series, the error in approximating the integral with the series expansion is bounded by the next term in the series:

Error ≤ (0.4^7)/(6 * 7)

To make sure the error is less than 10^(-4), we can set up the following inequality:

(0.4^7)/(6 * 7) < 10^(-4)

Simplifying this inequality, we get:

(0.4^7)/(6 * 7) < 0.0001

Solving for the term (0.4^7)/(6 * 7), we find:

(0.4^7)/(6 * 7) ≈ 0.000105

0.4 - (0.4^3)/3 + (0.4^5)/10 - (0.4^7)/252 ≈ 0.4 - 0.064/3 + 0.016/10 - 0.000105

Simplifying this expression, we get:

≈ 0.396444

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Answer:

\(\displaystyle d \approx 5.66\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Plane

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

B(-2, 1)

C(2, -3)

Step 2: Find distance d

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