Plz help! Simplify the expression.

Answer:

the answer is -9/35

Step-by-step explanation:

imjustgonnaeritedmrandomletterssinceotsajdit has to be 20 characters long but yea thee answer is -9/35

Answer:

Step-by-step explanation:

-1.68 is your answer

Answer:

Top left is 90, bottom right is 65.

Step-by-step explanation:

Answer:

43.44 for the first one

16 cats from the second one

496 for the third one

Step-by-step explanation:

Answer:

a. 43.44

b. 16

c. 496

Step-by-step explanation:

a. (14.48) x 3= 43.44

b. 25% of 64= 16

c. 31 x 16= 496

The square root of x is equal to x^1/2.

x to the 1/2 power.

When multiplying 2 numbers with same bases and different exponents, you add the exponents.

x^2 times x^1/2 = x^(2 + 1/2) = x^(5/2)

The answer is A and B, because a square root is basically raising it to the power of 1/2, and when you raise an exponent to another exponent you multiply, and 1/2 times 5 is 5/2.

Answer: No solution

Step-by-step explanation:

Expand the left side:

6x - 8 = 8x - 4 - 2x

Combine like terms and get

-8 = -4

No solution

Answer:

C

Step-by-step explanation:

Because I'm smart.

The equation 2sin(x)tan(x) + 3 = 0 has been proved to equal 2cos²(x) - 3cos(x) - 2 = 0

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

2sinxtanx+3=0

Rewrite as

2sin(x)tan(x) + 3 = 0

Express tan(x) as tan(x) = sin(x)/cos(x)

So, we have

2sin²(x)/cos(x) + 3 = 0

Multiply through by cos(x)

2sin²(x) + 3cos(x) = 0

Express sin²(x) as 1 - cos²(x)

So, we have

2(1 - cos²(x)) + 3cos(x) = 0

Expand

2 - 2cos²(x) + 3cos(x) = 0

Multiply through by -1

-2 + 2cos²(x) - 3cos(x) = 0

Rearrange the terms

2cos²(x) - 3cos(x) - 2 = 0

Hence, the equation has been proved

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Answer:

angle BAC = angle DAC it is correct answer of this question ....

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Answer:

The walkway should be 2ft wide.

Step-by-step explanation:

Let x be the width of the walkway surrounding the pool.

The area including the pool is 560ft².

Let's solve for the value of x.

The length plus twice the width of the pool is multiplied by the width plus twice the width of the pool. This makes up the whole area.

A = lw

560 = (24 + 2x)(16 + 2x)

560 = 384 + 48x + 32x + 4x²

4x² + 80x + 384 - 560 = 0

4x² + 80x - 176 = 0

Divide the whole equation by 4

x² + 20x - 44 = 0

(x + 22)(x -2) = 0

x = -22; x = 2

Since we are dealing with dimensions, take the one with the positive value.

x = 2ft

Let's check

560ft² = (24ft + 2x)(16ft + 2x)

560ft² = (24ft + 2(2ft)) (16ft + 2(2ft))

560ft² = (24ft + 4ft)(16ft + 4ft)

560ft² = (28ft)(20ft)

560ft² = 560ft² ✔

Answer:

-20x

Step-by-step explanation:

Let the number be x.

The product of -4 and this number is -4x.

5 times this is 5(-4x), which simplfiies to -20x.

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Answer:

Ans. Given, A1 = $2000 profit = A1 + (n-1)d d = $400 = -2000+(12-1)400 n = 12 = $2400

The required profit in the twelfth month is $2400.

Arithmetic progression is the series of numbers that have common differences between adjacent values

To solve this problem, we need to use the arithmetic sequence formula to find the profit of each month, then add up the profits for the first 12 months to find the profit in the twelfth month.

The first term (a₁) is -2000, the common difference (d) is 400, and we need to find the twelfth term (a₁₂).

We use the formula for the nth term of an arithmetic sequence:

an = a₁ + (n - 1)d

So, substituting the given values, we get:

a₁₂ = -2000 + (12 - 1)400

a₁₂ = -2000 + 11*400

a₁₂ = -2000 + 4400

a₁₂ = 2400

Therefore, the profit in the twelfth month is $2400.

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We cannot calculate the radius of the orbit using the information provided.

(a) To calculate the distance travelled in one orbit, we need to use the formula that relates the circumference of a circle to its radius, which is given by C = 2πr.

Here, C represents the distance travelled in one orbit, and r is the radius of the orbit.π = 3.14159265..

Given the number of orbits made by the spacecraft is 58376. The distance travelled in one orbit is as follows;

C = 2πr= 2 x π x r= 2 x 3.14159265.. x r= 6.28318531rTherefore, the distance travelled in one orbit is 6.28318531r.

To calculate the distance travelled in one orbit, we need to know the radius of the orbit.(b) The distance travelled by the spacecraft is not given.

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The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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Answer:

Step-by-step explanation:

Neither - one intersection

Answer:

i think that its D

Step-by-step explanation:

Answer:

The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.

The formula for finding the number of permutations of n objects taken r at a time without repetition is:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being chosen.

In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:

P(10, 4) = 10! / (10 - 4)!

P(10, 4) = 10! / 6!

P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)

P(10, 4) = 10,080

Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.

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The given information is:

- Tim needs to be at work at 8:00 A.M.

- He needs 30 minutes to get ready in the morning

- It takes him 15 minutes to drive to the work

The total time Tim needs to get ready and drive to work is:

So, he needs at least 45 minutes to be on time at work. So, the latest time Tim can get up in the morning is 45 minutes earlier than 8:00 A.M., and it is equal to:

The answer is 7:15 A.M.

Answer:

s = 10

Step-by-step explanation:

using the cosine ratio with 45° on lower right of right triangle and the exact value

cos45° = \(\frac{1}{\sqrt{2} }\) , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{s}{10\sqrt{2} }\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

s × \(\sqrt{2}\) = 10\(\sqrt{2}\) ( divide both sides by \(\sqrt{2}\) )

s = 10

Answer:

Step-by-step explanation:

Answer:

It will take 2.2 hours for the trains to meet.

Step-by-step explanation:

Given,

Distance between two trains = 396 miles

Speed of one train = 95 mph

Speed of other train = 85 mph

Combined speed of trains = 95+85 = 180 mph

Distance = Speed * Time

Time =

Time =

Time = 2.2 hours

It will take 2.2 hours for the trains to meet.

Keywords: speed, distance

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Step-by-step explanation:

A.  The payback period is 7.2 years. The net present value of the proposed investment is 3720.55.

B. No, the project does not meet the company's cash payback criteria.

C.  Yes, the project does meet the net present value criteria for acceptance.

A. The truck costs $55,440 and generates annual cost savings of $7,700. So the payback period is the cost of the truck divided the expected amount the truck will generate.

                $55,440 / $7,700 = 7.2 years

To solve for the net present value, we say

Net Present Value = ∑ [(Cash inflow in period t) / (1 + \(r^{t}\)] - Initial Investment.

NPV = (($7,700 / (1 + 0.08)¹) = 7 129.63

+ ($7,700 / (1 + 0.08)²) = 6601.51

+ .($7,700 / (1 + 0.08)³ = 6112.51

+ ($7,700 / (1 + 0.08)⁴) = 5659.73

+ ($7,700 / (1 + 0.08)⁵) = 5240.49

+ ($7,700 / (1 + 0.08)⁶) = 4 852.31

+ ($7,700 / (1 + 0.08)⁷) = 4492.88

+($7,700 / (1 + 0.08)⁸)  = 4160.07

+ ($27,600 / (1 + 0.08)⁸)) = 14911.42

- $55,440

We add all these values together and subtract by  $55,440

7 129.63 + 6601.51 + 6112.51 + 5659.73 + 5240.49 +4 852.31 + 4492.88 + 4160.07 + 14911.42 - $55,440

59160.55 - 55,440

NPV = 3720.55

B. The cash payback period of the project is 7.2 years. The company's cash payback criteria state that a project should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life, which would be 4 years which is 50% of 8 years. Since 7.2 years is greater than 4 years, the project does not meet the company's cash payback criteria.

C. The positive NPV of $3,720.55 shows that embarking on the prooject will be valuable to the company. This means the project meets the NPV criteria for acceptance.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$88000\\ r=rate\to 1.75\%\to \frac{1.75}{100}\dotfill &0.0175\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &7 \end{cases}\)

\(A=88000\left(1+\frac{0.0175}{12}\right)^{12\cdot 7}\implies A=88000\left( \frac{4807}{4800}\right)^{84}\implies A\approx 99459.21\)

Answer:D

Step-by-step explanation:

(f-g)(x)= -x^2+6x-1- (3x^2-4x-1)

(f-g)(x)= -x^2+6x-1 -3x^2+4x+1

(f-g)(x)= -x^2-3x^2+6x+4x-1+1

(f-g)(x)= -4x^2+10x

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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Answer:

\(\huge\boxed{\sf 187.5\ gal.}\)

Step-by-step explanation:

Given that:

For,

12 ft. height, gas tank can hold 450 gal.

Using unitary method:

12 ft = 450 gal.

Divide 12 to both sides

1 ft = 450/12 gal.

1 ft = 37.5 gal.

Multiply 5 to both sides

5 ft. = 37.5 × 5 gal.

5 ft. = 187.5 gal.

So, the height of 5 ft. holds 187.5 gal.

\(\rule[225]{225}{2}\)

Answer:

187.5 gal

Step-by-step explanation:

A=lw

450=12(w)

450/12=37.5ft

A=lw

A=37.5(5)

A=187.5 gal

Hope that helps