Vince borrows $900 to buy a couch. He will pay off the loan by paying 1.5% simple interest for 2 years.
Vince incorrectly calculates the amount he will pay back using the expression below.

900 + 900(1.015 • 2)

By trial division method we get 251 is a prime number.

A number which can not be divided by any number except itself or 1 is called a prime number.

Given that a number 251 we need to find if it is a prime number, by using trial division method,

The number is 251, the prime numbers are 2, 3, 5, 7...

Let us divide 251 by them,

251 / 2 = 125.5

251 / 3 = 83.66

251 / 5 = 50.2

251 / 7 = 35.85

251 / 11 = 22.81

Since, none of these divides the number evenly, it is a prime.

Hence, by trial division method we get 251 is a prime number.

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Answer:

(-4, 2)

Step-by-step explanation:

when its reflected across the y-axis it goes from (x, -y) to (-x, y)

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Step-by-step explanation:

the answer is in the image above

Answer:

\(-\sqrt{5q^{3} } \times3\sqrt{35}\)

\(-\sqrt{5} \times\sqrt{q^{3} } \times3\sqrt{5} \times\sqrt{7}\)

\(-15\sqrt{7q^{3} }\)

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

Hope it helps...

have a great day!!

Answer:

2x^7

Step-by-step explanation:

add the exponents because they both are x

2x^4*x^3=2x^7

Answer:

Given that sin(θ) = -2√13/13 and θ is in quadrant III, we know that sin(θ) is negative and cos(θ) is also negative. We can use the Pythagorean identity to solve for cos(θ):

cos²(θ) + sin²(θ) = 1

cos²(θ) = 1 - sin²(θ)

cos(θ) = ±√(1 - sin²(θ))

Since cos(θ) is negative in quadrant III, we take the negative square root:

cos(θ) = -√(1 - sin²(θ))

Substituting sin(θ) = -2√13/13, we get:

cos(θ) = -√(1 - (-2√13/13)²) = -√(1 - 4/13) = -√9/13 = -3√13/13

Therefore, cos(θ) = -3√13/13.

Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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-13 and -5 hope this helps???

Sorry if it's wrong OnO''

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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To factorize 6x²2 - 4xy, we can factor out the greatest common factor (GCF), which is 2x:

6x²2 - 4xy = 2x(3x - 2y)

What is factorization?

Factorization is the process of finding two or more expressions that, when multiplied together, produce a given expression. In other words, it is the process of breaking down a mathematical expression into simpler factors.

For example, consider the expression x²2 - 4x - 21. We can factorize it by finding two expressions that, when multiplied together, give us x²2 - 4x - 21. One way to do this is to factor the expression into (x - 7)(x + 3):

x²2 - 4x - 21 = (x - 7)(x + 3)

This is an example of factorization, where the expression on the left-hand side has been broken down into the simpler factors on the right-hand side.

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Answer:⬇️⬇️⬇️⬇️

Step-by-step explanation: Area of a triangle = ½base times height⇒ A = ½bh

Given that the area is 24 and the base is 8, we would have this equation

24 = ½(8)h

24 = 4h divide both sides by 4

6 = h So the height of the triangle is 6 feet

CHECK

A = ½bh

24 = ½(8)(6)

24 = 4(6)

24 = 24√

Answer:

\(-30x+2\)

Step-by-step explanation:

\(-2(10x-1)-10x\)

Use the distributive property:

\(-2(10x)-2(-1)-10x\\\\-20x+2-10x\)

Combine like terms:

\(-20x-10x+2\\\\-30x+2\)

:Done

Answer:

-30x+2

Step-by-step explanation:

1. Expand by distributing terms.

2. Remove parentheses.

3. Combine like terms

The circumference of the circle is 62.8cm.

The Circumference of the circle is given by the formula,

Circumference = 2*\(\pi\)*r cm.........equation 1

Given, r = 10cm

On substituting the radius value in equation 1

Circumference = 2*\(\pi\)*10

Circumference = 62.8 cm

Therefore, the circumference of the circle is 62.8cm.

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The probability that either event will occur is P ( C ) = 0.89

Given data ,

Let the probability that either event will occur  be P ( C )

P ( A ) = 20/36

P ( B ) = 12/36

where P ( A or B ) = P ( C )

P ( C ) = P ( A ) + P ( B )

P ( C ) = 32/36

P ( C ) = 0.88888

Hence , the probability is P ( C ) = 0.89

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Answer:

La masa del paracaidista es 7.14 Kg

Step-by-step explanation:

Peso y Masa

La masa de un objeto es una medida de la cantidad de material que el objeto posee. Sus unidades más comunes son el Kg, gr, lb, Ton.

El peso de un objeto de masa m es la fuerza con la cual la Tierra atrae al objeto a través de la aceleración de gravedad g. Sus unidades son iguales a las de cualquier fuerza, es decir, Nw, Kgf, Dina. Su fórmula es:

P=m.g

Si tenemos el peso P=70 N, podemos calcular la masa, despejándola de la fórmula:

\(\displaystyle m=\frac{P}{g}\)

Sustituyendo los valores:

\(\displaystyle m=\frac{70}{9.8}=7.14\ Kg\)

La masa del paracaidista es 7.14 Kg

Answer:

x=12

Step-by-step explanation:

6x+7=8x-17

-6x     -6x

7=2x-17

+17    +17

24=2x

÷2   ÷2

12=x

x=12

Answer:

-3, 4, 11, 18, 25, 32

Step-by-step explanation:

it looks like it's just adding by -7 so to get 32 you could start adding by positive 7

The quantity of cholesterol in an egg is 272 mg

The quantity of cholesterol in a cupcake is 18 mg

The quantity of cholesterol in a slice of pizza is 9 mg

Let the amount of egg be e

Let the amount of cupcake be c

Let the amount of pizza be p

By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol

e + c + p = 299

The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol

3c + 4p = 90

By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol

3e + c = 834

e + c + p = 299

3c + 4p = 90

3e + c = 834

solving the simultaneous equation gives

e = 270

c = 18

p = 9

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Answer: The description of that transformation is the triangle is rotated 90 degrees clockwise. Then, it's moved to the right TWICE. Finally, you go down 2 times.

Step-by-step explanation:

Hope this helps :)

triangle B is in dofferent orientation from triangle B so we know it was either mirrored or rotated. Triangle B isnt in the exact opposite orientation as A so we know it wasnt mirrored. So we now know that it was rotated and know we have to find the point of rotation. we can tell that the rotation was 270 degrees anti clockwise since it cant be clockwise because no points of rotation match. since we know triangle A was rotated 270 degrees anti clockwise to get triangle B we cant find the point of rotation by seeing which point works and if we test the points we will see that (0;-1) is the point of rotation. So triangle A was rotated 270 degrees anti clockwise on the point (0;-1) to make triangle B

Answer:

7 i think

Step-by-step explanation:

Answer:

8 square units I believe!

Step-by-step explanation:

Hope that helps!

Answer:

21.5 hours

Explanation:

To find the number of hours that she needs to volunteer, we need to subtract the 18.5 hours from the total number of hours (40 hours). So, the number of hours is equal to:

So, the answer is 21.5 hours

Answer:

cool

Step-by-step explanation:

2v + 7 = 3

    - 7     - 7

2v = - 4

v = - 2

where is the problem I will try my best

and have a good day

-2

Answer:

114 square meters

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

example 1

percent found -----> 15%

where was the percent found? ------> apple store

how is percent use? -----> sale 15% of the original price is taken off (music download)

example 2

percent found ------> 20%

where was the percent found? -----> internet (buy or rent a house)

how is percent use? -----> sale 20% of the original price is taken off

Answer:

C. -24 no real roots

Step-by-step explanation

The answer to this question: B

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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