For each expression, select all equivalent from the list.

(a) 9x-5x+8x
(b) 9(1+7y)

​

Answer:

12 different types of sandwich could be made.

Step-by-step explanation:

Since I am making a sandwich at the cafeteria where they have 2 kinds of bread, 2 kinds of cheese, and 3 kinds of meat, to determine how many different sandwiches could I make the following calculations must be performed:

Bread x cheese x meat = X

2 x 2 x 3 = X

4 x 3 = X

12 = X

Therefore, 12 different types of sandwich could be made.

Answer:

y=-1/3x+5

Step-by-step explanation:

A perpendicular line has to be the opposite reciprocal. And the the y intercept doesnt matter (y=mx+b) b doesnt matter

Answer:

\(y=-\frac{1}{3}x-1\)

Step-by-step explanation:

So we want to write an equation for a line perpendicular to 3y-9x=-15 and which passes through the points (9,-4).

First, let's determine the slope of our new line.

To do so, let's put the original equation into slope-intercept form. So we have:

\(3y-9x=-15\)

Add 9x to both sides:

\(3y=9x-15\)

Divide both sides by 3:

\(y=3x-5\)

So, the slope of our original equation is 3.

Perpendicular lines have slopes who are negative reciprocals of each other.

In other words, to find the slope of our new line, we simply need to flip our old slope and add a negative.

Therefore, our new slope is -1/3.

Now, we can use the point-slope form to find the equation of our new line. The point-slope form is:

\(y-y_1=m(x-x_1)\)

Where m is the slope and (x₁, y₁) is a point.

Let's substitute -1/3 for m and (9,-4) for (x₁, y₁), respectively. Therefore:

\(y-(-4)=-\frac{1}{3}(x-9)\)

Simplify:

\(y+4=-\frac{1}{3}(x-9)\)

Distribute on the right:

\(y+4=-\frac{1}{3}x+3\)

Subtract 4 from both sides:

\(y=-\frac{1}{3}x-1\)

So, our new equation is:

\(y=-\frac{1}{3}x-1\)

Answer:

d'f(t) = 6cos 2t(2)+5sin 2t(2)

= 12cos 2t + 10sin 2t

Step-by-step explanation:

The average power radiated by each square meter of the sun's surface is approximately 386 W/m². This value is calculated by dividing the total power radiated by the sun (approx. 386 billion Megawatts) by its surface area (approx. 6.08 x 10¹⁸ square meters). The formula for the surface area of a sphere is 4πr².

The average power radiated by each square meter of the sun's surface can be calculated as follows:

       The total power radiated by the sun is approximately 386 billion

       Megawatts (3.86 x 10³³ erg/s).

        The surface area of the sun can be calculated using the formula for

        the surface area of a sphere:

        A = 4πr², where r is the radius of the sun (approx. 6.96 x 10⁸

        meters).

        Plugging in the values, we get:

        A = 4π (6.96 x 10⁸)² = 6.08 x 10¹⁸ square meters.

        Finally, divide the total power by the surface area to get the

        average power radiated by each square meter of the sun's surface:

        P = 3.86 x 10³³ erg/s / 6.08 x 10¹⁸ m² = 386 W/m².

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Answer:

45 sides

Step-by-step explanation:

If each of the interior angles is 172 degrees, then each of the exterior angles is 8 degrees. Since the sum of the exterior angles of any polygon is 360 degrees, there are 360 / 8 = 45 exterior angles and 45 sides.

Answer:

-5

Step-by-step explanation:

4x - 1 = 6x + 9

4x = 6x + 10

-2x = 10

x = -5

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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The results for each composite function at each x-value are listed below:

Case 13: (f ° g) (1) = 26 (Right choice: D)

Case 14: (f + g) (3) = 20 (Reight choice: E)

In this problem we find two cases of composite functions that must be evaluated at given x-value. The procedure is described below:

Now we proceed to solve for each case:

Case 1: f(x) = x² + x - 4, g(x) = 3 · x + 2

(f ° g) (x) = [(3 · x + 2)² + (3 · x + 2) - 4]

(f ° g) (1) = [(3 · 1 + 2)² + (3 · 1 + 2) - 4]

(f ° g) (1) = (5² + 5 - 4)

(f ° g) (1) = 26

Case 2: f(x) = x² + x, g(x) = x² - 1

(f + g) (x) = (x² + x) + (x² - 1)

(f + g) (x) = 2 · x² + x - 1

(f + g) (3) = 2 · 3² + 3 - 1

(f + g) (3) = 18 + 3 - 1

(f + g) (3) = 20

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The price of the bed after mark up is $475.00

Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.

The first discount given is 25% , therefore the price of the bed before mark up is

25/100 × 800

= 25×8

= 200

the price before mark up = 800-200 = $600

Another 25% is given after the first sale, there the price of the bed after mark up is

25/100 × 600

=$ 125

price after markup = 600-125

= $475.00

therefore the price of the bed after markup is $475.00

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The expression for the sequence of operations is  3s - u - t .

In the question ,

it is given that ,

the sequence of operation is given as " triple s, subtract u from the result, then subtract t from what you have" .

we have to write an expression for the above operation ,

So ,

first step is : triple s ,

that means the expression is  3s .

next subtract u from the result , that means ⇒ 3s - u .

next we have to subtract t from what we have ,

that means ⇒ 3s - u - t .

Therefore , the final expression is 3s - u - t .

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Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Answer:

B

Step-by-step explanation:

From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))

We are given the engineers formula as;

F = (¹¹/₃₀₀)d(F - 13)

Where;

F is the strength of the steel in kilopound per square inch.

d is the diameter of the rocker in millimeters.

From the given formula, we can start by;

Multiply both sides by 300 to get;

300F = 11d(F - 13)

Divide both sides by 11(F - 13) to get;

d = 300F/(11(F - 13))

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Answer:

x = 2, y =7

Step-by-step explanation:

4x - 2y = -6

-6x + 2y = 2

Add the equations together

4x - 2y = -6

-6x + 2y = 2

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

-2x = -4

Divide each side by -2

-2x/-2 = -4/-2

x = 2

now find y

-6x+2y =2

-6(2) +2y =2

-12+2y =2

Add 12 to each side

-12+12+2y = 2+12

2y =14

Divide by 2

2y/2 =14/2

y =7

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

In order to sum two polynomials, we need to group and add the like terms, i. e., terms for which the variable has the same exponent.

(8x³ + 3x - 2) + (9x² - 7 + 3x - 2x³)

= (8x³ - 2x³) + (9x²) + (3x + 3x) + (-2 - 7)

= (8 - 2)x³ + 9x² + (3 + 3)x - 9

= 6x³ + 9x² + 6x - 9

Therefore, adding those polynomials, we obtain:

6x³ + 9x² + 6x - 9

Answer:

Step-by-step explanation: total number of counters = 10

number of red counters= 3

number of blue counters= 2

number of green counters = 5

p(of getting a red counter) =3/10

p(of not getting a red counter) = 1-3/10= 10-3/10=7/10

Answer:

\(10 = 2x - 20 \\ 10 + 20 = 2x \\ \frac{30}{2} = \frac{2x}{2} \\ 15 = x\)

Answer is below n attachment

The line is a vertical line, then the correct option is D, the slope is undefined.

A general linear equation can be written as:

y = a*x + b

Where a is the slope, b is the y-intercept, and x is the variable.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the two points are (2, -4) and (2, 4)

Replacing that we would have a problem, that is because we have the same x-value in both points.

Then we have a vertical line at x = 2.

That line has no defined slope, thus, the correct option is D.

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To make a cake :-

Quantity of flour needed = 500 g

Quantity of butter needed = 450 g

Quantity of sugar needed = 470 g

Quantity of mixed fruit needed = 1.8 kg = 1000 g + 800 g

Quantity of eggs needed = 70 × 4 = 280 g

It's weight after adding all the ingredients =

=500 + 450 + 470 + 1000 + 800 + 280

= 3500 g

Mass that got lost while baking the cake :

\( = \frac{12}{100} \: of \: 3500\)

\( = \frac{12}{100} \times 3500\)

\( =\frac{(12 \times 3500)}{100} \)

\( =\frac{42000}{100} \: g\)

\( = 420 \: g\)

Final mass = Initial mass - mass that got lost

\( = 3500 - 420 \: g\)

\( = 3080 \: g\)

∴ The final mass of the cake is 3080 g .

Step-by-step explanation:

the area is

length × width

the perimeter is

2×length + 2×width = 182 ft

length + width = 91 ft

and we know that

length = width + 9

now we use that in the previous equation and get

(width + 9) + width = 91

2×width + 9 = 91

2×width = 82

width = 41 ft

and because of

length = width + 9

length = 41 + 9 = 50 ft

and so the area of the garden is

50 × 41 = 2050 ft²

The net present value οf the prοject is  $516.

A set οf cash flοws that happen at variοus dates are cοnsidered tο have a net present value οr net present wοrth. The amοunt οf time between nοw and a cash flοw determines the present value οf that cash flοw. The discοunt rate is anοther factοr. NPV takes the time value οf mοney intο the accοunt.

Here, we have

Respass Cοrpοratiοn has prοvided the fοllοwing data cοncerning an investment prοject that it is cοnsidering: Initial investment $ 160,000 Annual cash flοw $ 54,000 per year Salvage value at the end οf the prοject $ 11,000.

The prοject has annual inflοws οf $54,000 except in 4th year when it will have inflοws οf $65,000 because the salvage value will be added tο the inflοws.

Present value οf inflοws = 54,000/1.12 + 54,000/1.12² + 54,000/1.12³ + 65,000/1.12⁴

= $160,516

Net Present Value = 160,516 - 160,000

= $516

Hence, the net present value is $516.

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Answer:

1.) 10: 1, 2, 5, 10.

15: 1, 3, 5, 15,

Answer would be 5.

2.) 18: 1, 2, 3, 6, 9, 18

21: 1, 3, 7, 21

Answer would be 3.

3.) 12: 1, 2, 3, 4, 6, 12.

24: 1, 2, 3, 4, 6, 8, 12, 24.

Answer would be 12.

4.) 8: 1, 2, 4, 8.

20: 1, 2, 4, 5, 10, 20.

Answer would be 4.

5.) 14: 1, 2, 7, 14.

28: 1, 2, 4, 7, 14, 28.

Answer would be 14.

Step-by-step explanation:

Using the listing method, you would first list the common factors of each number, to which that number could be multiplied by. Then, you would search for the greatest common factor.

Answer:

7x

Step-by-step explanation:

Answer:

Step-by-step explanation:

This problem requires to test our understanding of unit conversion, and we are expected to present our answer in an acre

first, let us convert from the yard to feet

given that the dimension of the pitch is

120 yards by

53.333 yard

1 yard is 3 foot

120 yards will give x

cross multiply we have

x1= 120*3

x1= 360 feet

also the second dimension is

x2= 53.333*3

x2= 159.999

x2= 159.999 feet

the area of the pitch is

area= 159.999*360

area= 57599.64 ft^2

Note: an acre is a unit for land area (1 acre=43560 ft^2)

if 1 acre = 43560 ft^2

x acre =  57599.64 ft^2

cross multiply we have

x acre =  57599.64/43560

x acre = 1.32 acre

A normal distribution has a mean of 50 and a standard deviation of 3 , the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241  option a) 0.025.

In probability theory, normal distribution is also known as Gaussian distribution. It is a probability distribution that is symmetrical, bell-shaped, and a continuous probability distribution. It's also a part of continuous probability distribution that describes real-valued random variables whose probability density function is affected by two parameters: the mean μ and the variance σ².

Let us consider the problem. Suppose a normal distribution has a mean of 50 and a standard deviation of 3. Firstly, we need to standardize the random variable X that is to convert it to the standard normal distribution. We use the following formula for this Z = (X - μ) / σwhere X is the random variable and μ is the mean, σ is the standard deviation of the population.

So in this case, we can write this as Z = (44 - 50) / 3 = -2

We have now obtained the standard score or standard deviation for the random variable X.

Now we need to calculate the probability P(X ≤ 44) = P(Z ≤ -2).

The probability of Z being less than -2 is denoted by the area under the standard normal curve to the left of Z = -2.

Using the standard normal table we look for the probability that corresponds to -2 and the closest we find is 0.0228.

This probability represents the area under the standard normal distribution to the left of Z = -2.

To calculate the area to the left of Z = -2, we add the area to the left of the next integer, which is -3, which we find from the standard normal table as 0.0013, 0.0228 + 0.0013 = 0.0241.

Therefore, the probability P(X ≤ 44) = P(Z ≤ -2) = 0.0241 or 0.025 (rounded to three decimal places)Therefore, the answer is option A. 0.025.

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