find the value of the trigonometric ratio rounded to 4 decimal places

The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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After doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.

So, the amount Irene spends on gas:

Then, the amount of 6.5 gallons of gas:

Therefore, after doing some mathematical operations, we can conclude that Irene spends $24.05 on 6.5 gallons of gas.

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The perimeter and area of a rectangle are (5,6) and (6,5).

The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.

A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.

The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.

The perimeter of the rectangle:

P=2l+2w=22

divide 2 into both sides

l+w=11 -------------> (1)

w=11-l

Area of the rectangle:

l*w=30

l(11-l)=30

11l-l^2-30=0

l^2-11l+30=0

By factor method,

(l-5)(l-6)=0

l=5,6.

Substitute this value in w,

l=5 implies w=6

l=6 implies w=5

There we have two solutions.

The length and breadth of the rectangle is

(5,6) and (6,5).

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Answer:

6/6 or 1

Step-by-step explanation:

bow tie method

Answer:

muscular area of body are most flexible

Answer:

Step-by-step explanation: h(t)=-16t2+85

Let h(t)=0 to find when the object will hit the ground

0=-16t2+85

Solve for t=?

We need to get t term on its own

Take 85 from both sides

0-85=-16t2+85-85

-85=-16t2

To get t term on its own

Divide both sides by -16

-85/-16=-16t2/-16

5.3=t2

We have to solve for t squared that means we must take the square root of both sides

the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds

Answer:

4x²=2(x-4)

2x²=x-4

2x²-x+4=0​

x=1+√31​/ 4, 1-√31​/4

Step-by-step explanation:

1. Cancel log on both sides

2. Divide both sides by 2

3. Move all terms to one side

4. Use the quadratic formula

Answer:

Hello there

Step-by-step explanation:

Hope you figure it out the answer

You posted a lot of questions. I'll do the first three to get you started.

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Problem 1

Explanation:

Draw a vertical line to enclose the un-shaded region. Think of it like adding fencing to enclose a paddock or backyard.

What results are two rectangles. The larger rectangle has area = length*width = 8*10 = 80 square inches.

The smaller unshaded rectangle inside has area of 5*5 = 25 square inches.

The difference of those areas is:  80-25 = 55

You have the correct answer. Nice work.

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Problem 2

Explanation:

Follow the same set of steps as done in the previous problem. Draw a vertical line to form a larger rectangle.

The larger rectangle has area of 18*31.5 = 567 square feet.

The smaller unshaded rectangle has area of 9*9 = 81 square feet.

Subtract those results to get the shaded region only: 567-81 = 486

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Problem 3

Explanation:

This time we don't have to add any extra lines to enclose the figure.

A = larger area = 6*2.4 = 14.4

B = smaller unshaded area = 2*4.4 = 8.8

C = A-B = 14.4-8.8 = 5.6 square cm

You have the correct answer. Nice work.

Answer:

1)  55 in²

2)  486 ft²

3)  5.6 cm²

Step-by-step explanation:

To calculate the area of each given figure, subtract the area of the cut-out rectangle (marked in blue on the attached diagram) from the area of the larger rectangle.

\(\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}\)

\(\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&=8 \cdot 10- 5\cdot 5\\&=80-25\\&=55\; \sf in^2\end{aligned}\)

\(\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 31.5\cdot 18- 9\cdot 9\\&=567-81\\&=486\; \sf ft^2\end{aligned}\)

\(\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 6\cdot 2.4- 4.4\cdot2 \\&=14.4-8.8\\&=5.6\; \sf cm^2\end{aligned}\)

Answer:

18.09

Step-by-step explanation:2.4x2.4, then x3.14  

Answer:

answers below

Step-by-step explanation:

If you are trying to find the area the answers are:

Earth= 289.52918

Saturn=6,532.5021

The formula for area for a sphere is:

4 x pie x r2

If you are trying to find the volume the answers are:

Earth=57.90584

Saturn=46,647.01596

The formula for volume for a sphere is:

4/3 x pie x r3

Also the radius (r) is half of the diameter, so you divide the diameter by 2.

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

\( - \frac{29}{18} \)

\( \frac{8}{9} - \frac{5}{2} \)

Find the difference between 8/9 and 5/-2

\( \frac{8}{9} - \frac{5}{2} \)

\( \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} \)

\( \frac{16}{18} - \frac{45}{18} \)

\( \frac{16 - 45}{18} \)

\( \frac{ - 29}{18} \)

\( - \frac{29}{18} \)

The end behavior for f(x)=x^5 is as x approaches infinity, f(x) approaches infinity and as x approaches negative infinity, f(x) approaches negative infinity

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

f(x) = x^5

Calculate f(oo) and f(-oo) i.e the function at infinity and negative infiniyt

So , we have

f(x) = (oo)^5 = +oo

f(x) = (-oo)^5 = -oo

This means that x increases with f(x)

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Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

\(x > \ln(x)\) for all \(x\), so

\(\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}\)

Similarly, \(\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}\)

We can of course see the limits are identical by replacing \(x\mapsto e^x\), so that

\(\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)\)

You can also rewrite the limands to accommodate the application of l'Hôpital's rule. For instance,

\(\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)\)

Using the rule, the limit here is

\(\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0\)

so the overall limit is

\(\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty\)

Answer:

THE ANSWER IS B

Step-by-step explanation:

B mine please im so single

Answer:

m² would be the best unit if you want to measure a room.

Step-by-step explanation:

The unit cm² is too small and would be less exact.

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer:

4ft, 7 inches

Step-by-step explanation:

4 ft (48 inches), 7 inches

Step-by-step explanation:

208

= 128 + 64 + 16

= 1 * 2⁷ + 1 * 2⁶ + 1 * 2⁴

= 11010000. (base 2)

Answer:

r=3

Step-by-step explanation:

Answer:

The probability of obtaining a Merit Scholarship = 0.23

Step-by-step explanation:

From the given information:

The probability of obtaining a merit scholarship P(A) = 0.18

The probability of obtaining both P(A ∩ M) = 0.11

The probability of getting at least one P(A ∪ M)  = 0.3

The objective is to determine the probability of obtaining a Merit Scholarship.

So, as given:

if M represents Merit Scholarship and A represent Athletic Scholarship,

the probability of obtaining a Merit Scholarship is as follows;

P(M) = P(A ∪ M) + P(A ∩ M) - P(A)

P(M) = 0.3 + 0.11 - 0.18 = 0.23

P(M) = 0.23

Answer:

500 tiles

Step-by-step explanation:

First find the area of the hall=10ft×(10ft×5)=500ft²

Number of tiles required=500ft²÷1ft²=500

Answer: The graph of g is the graph of f translated 5 units right, and g(x) = f(x - 5).

Step-by-step explanation:

The graph f(x) = 2x = 6 translated (1,4,5 or 6) units (left, right, up, or down) are g(x) = 2(x + 1) + 6, g(x) = 2(x - 4),  2x + 11, g(x) = 2x.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Given, a function f(x) = 2x + 6.

g(x) is translated 1 units left.

g(x) = 2(x + 1) + 6.

g(x) is translated 4 units right.

g(x) = 2(x - 4).

g(x) is translated 5 units up.

g(x) = 2x + 6 + 5 = 2x + 11.

g(x) is translated 6 units down.

g(x) = 2x.

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Answer:

(13, -67.4°)

Step-by-step explanation:

In the general case, for a point (x, y), the same point written in polar coordinates is (r, θ), such that:

r = √(x^2 + y^2)

θ = Atg(y/x)

Then if we have the point with coordinates (-5, 12)

The polar coordinates will be:

r = √((-5)^2 + 12^2) = 13

θ = Atg(12/-5) = -67.4°

Then the polar coordinates are:

(13, -67.4°)

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

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Calculating interest on the principal borrowed as well as any prior interest. $6,000 for six years at a daily compounded rate is None of these. No option is correct. The amount is $991.15.

Annual interest compounding adjective finance. If you borrow $100,000 at 5% interest compounded annually, you would owe $5,250 after the first year on a principal of $105,000. This method involves calculating and adding interest to an investment or loan once a year rather than for a longer period.

The formula to determine how much an investment will grow to overtime when it is placed in an account for years during which it generates dollar-compound interest is:

A = P(1 +r/m) m t

The values for each of these variables are provided as follows, presuming that a year has 365 days: m =365 t=6r  8.5% = 0.085The investment's worth is then computed after six years, as illustrated below.

A =991.15

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