Mason invested $65,000 in an account paying an interest rate of 4. 6% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $142,200?

No, 10, 12, and 15 are not the lengths of the sides of a right triangle.

A right triangle is a triangle with one 90 degree angle. The other two angles must be acute angles (less than 90 degrees).

The Pythagorean Theorem is a formula used to determine if three given side lengths can form a right triangle. The Pythagorean Theorem states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, also known as the hypotenuse.

In this case, the side lengths of the triangle are 10, 12, and 15. Therefore, the Pythagorean Theorem can be written as:

10^2 + 12^2 = 15^2

100 + 144 = 225

244 ≠ 225

Therefore, 10, 12, and 15 are not the side lengths of a right triangle.

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Answer: The formula for the surface area of a cone is S = π * r * s + π * r², where r is the radius of the base and s is the slant height of the cone.

To find the surface area of a cone, you first need to find the radius of the base. Since the base diameter is given as 7cm, you can divide this by 2 to find the radius of the base:

r = 7cm / 2 = 3.5cm

Next, you need to find the slant height of the cone. You can use the Pythagorean theorem to do this.

slant height = sqrt(r^2 + h^2) = sqrt(3.5² + 8²) = sqrt(12.25 + 64) = sqrt(76.25) = 8.766cm

Now you can substitute these values into the formula for the surface area of a cone and find the surface area of the cone.

S = π * r * s + π * r² = π * 3.5cm * 8.766cm + π * 3.5² cm² = 12.571 cm² + 38.485 cm² = 51.056 cm²

So the surface area of a cone with a base diameter of 7cm and height of 8cm is 51.056 cm²

Step-by-step explanation:

The term 5 in 5x is known as the coefficient of the expression.

A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.

A coefficient is a generally a multiplicative factor in a polynomial series, or in an  equation.

Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.

Eg, 2x - 90 =45

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Using multiplication we know that the product of 3 * - 4 is -12.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

The addition method, lengthy multiplication, grid method, and drawing lines are four different ways to multiply.

So, we have:

3 * -4

Here, we know that 3 is a positive number and -4 is a negative number.

And so the product will be a negative number.

Now, calculate the product as follows:

3 * -4

-12

Therefore, using multiplication we know that the product of 3 * - 4 is -12.

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Answer:

A

Step-by-step explanation:

each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.

.17x + 24.50 = 28.45

The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that a line has a slope of 1/5 and passes through the point (3, 10)

We can write the slope of the line as -

m = 1/5

For the point (3, 10), we can write -

y = (1/5)x + c

10 = (1/5) x 3 + c

c = 10 - 3/5

c =  47/5

Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).

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Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

The value of x is 20

Now, According to the question:

The given equation is:

3x + 32 = 5x - 8

To solve the equation for finding the value of x .

32 + 3x = -8 + 5x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5x' to each side of the equation.

32 + 3x  -5x = -8 + 5x  -5x

Combine like terms:

3x  -5x = -2x

32  -2x = -8 + 5x  -5x

Combine like terms: 5x  -5x = 0

32  -2x = -8 + 0

32  -2x = -8

Add '-32' to each side of the equation.

32  -32 -2x = -8  -32

Combine like terms: 32  -32 = 0

0 -2x = -8  -32

-2x = -8  -32

Combine like terms: -8  -32 = -40

-2x = -40

Divide each side by '-2'.

x = 20

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The total quantity of water that the container would have to hold is given as 8.

We know that the container holds 1 gallon of water, and that each bottle holds 1/8 of a gallon. To find out how many bottles the container can hold we need to divide the container size by the size of each bottle.

We can use the following formula to find the number of bottles:

Number of bottles = Container size / Size of each bottle

We can substitute the values into the formula:

Number of bottles = 1 / (1/8) = 8

So the container can hold 8 bottles of water.

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Answer:

2 ≥ p

Step-by-step explanation:

-14 ≤ -7p

Divided both sides by -7. Because divided by a negative number, the < will turn to >

So, the equation is

2 ≥ p

Because there is an equal, the circle will be close and to the left of 2.

Answer:

2 ≥ p

Step-by-step explanation:

Have a great day :) <3

Answer:

you can eliminate the x terms in this system by multiplying each side by 3.

Step-by-step explanation:

in order to eliminate a variable from a system of equations, you must multiply whatever variable you want to eliminate (in this case, x) by a number that will make the variable you want to eliminate in the first (4y+3x=-6) and second (which is y-x= -5) equations cancel out when adding them together

a written example for further clarification:

step 1:

4y + 3x = -6

3*(y - x = -5)

up here, you can see i'm multiplying the bottom equation by 3 in order to change the value of x from x to -3x, so that when you add the top and the bottom equations together, x is nowhere to be found in the resulting equation (this is what you want)

step 2:

distribute the 3 to all terms in the second equation. this gives you:

(3y-3x = -15).

step 3:

now add this new equation to the first equation (4y+3x=-6).

This gives you:

4y+3x=-6

+

3y-3x=-15

then just add the like terms (4y and 3y, 3x and -3x, -6 and -15).

which gives you (7y=-21)

see how x is not in the resulting equation? you have now successfully eliminated it :] hope this helped!

Answer:

47.07, 47.16, 47.3, 47.4, 48.1

Step-by-step explanation:

lol

Answer:

Step-by-step explanation:

(9x-12)-(5x-7)=9x-12-5x+7=9x-5x-12+7=4x-5

if you like this pls give me 5 stars, tku!

Answer:

They are parallel line.

Answer:

the answer is 1

Step-by-step explanation:

4(2x-3)=6x+2

8x-12=6x+2

+6x   +6x

14x-12 =2

    +12 +12

14x=14

x=1 and don't worry we all make mistakes

The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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The solution of the pair of equations y = 0 and y = -3 is y = -3/2.

The given pair of equations is:

y = 0

y = -3

We can solve this pair of equations using elimination. To do this, we first add the two equations together, which gives us:

y + y = 0 + (-3)

2y = -3

We then divide both sides by 2 to get the solution for y:

2y/2 = -3/2

y = -3/2

Therefore, the solution of the pair of equations y = 0 and y = -3 is y = -3/2.

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Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.

Answer:

25

Step-by-step explanation:

so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.

Answer: 12.96

Step-by-step explanation: you should multiply 12 * 0.08 = 0.96

then just add 0.96 + 12 = 12.96

Answer:

51.50004959055205

Step-by-step explanation:

[tex]sin (x) = \frac{18}{23}[/tex]

Total interest charged by bank in 2 months is 6793.83.

Compound interest is the interest paid on both principal and interest, compounded at regular intervals. At regular intervals, the interest so far accumulated is clubbed with the existing principal amount and then the interest is calculated for the new principal. The new principal is equal to the sum of the Initial principal, and the interest accumulated so far.

The interest that is obtained through the reinvestment of money is known as compound interest. The original principal investment grows substantially more quickly (sometimes referred to as exponentially) when interest is reinvested and allowed to compound over time.

Total loan amount = 875000

total time = 2 months

Rate = 4.75%

Total interest = 875000(1 + [tex]\frac{4.75}{100}[/tex])[tex]\)^{\frac{1}{6} }[/tex] - 875000 =  6793.83

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Using the provided values and information, The answer is each person would receive 1/5 of the original bread loaf.

A proportion is a mathematical statement that compares two ratios. It is an equation that states that two ratios are equal, such as "a/b = c/d." Proportions are often used to solve problems involving fractions, decimals, and percentages. For example, if you know that a particular recipe calls for two cups of flour for every one cup of sugar, you can use this proportion (2/1 = x/3) to figure out how much sugar you need if you want to triple the recipe. The proportion can also be written as 2:1 = x:3.

A ratio is a mathematical comparison of two or more quantities, typically represented as a fraction. It is a way to compare the size of two or more things. For example, if a recipe calls for 2 cups of flour to 1 cup of sugar, the ratio of flour to sugar is 2:1. This means that for every 2 units of flour, there is 1 unit of sugar. Ratios can also be written using the colon symbol (:) or the word "to". For example, the ratio 2:1 can also be written as 2/1 or 2 to 1. Ratios can be simplified by dividing both the numerator and denominator by a common factor and can be used to compare quantities in different units.

Each person would get 1/5 of the original bread loaf. If the bread is divided equally among four people, then each person would receive 1/4 of the total amount. Since 1/5 is the same as 4/20, and 4 people are receiving the bread, then each person would receive 1/5 of the original bread loaf.

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The coordinates of B are (6,0).

The midpoint of a line segment is the point that is exactly halfway between the two endpoints of the segment. For a line segment with endpoints (x1, y1) and (x2, y2), the midpoint is given by the coordinates:

In this problem, we're given that the midpoint is (2, 4) and we need to find the coordinates of point B. Since we know the coordinates of the midpoint, we can set up the equation:

We know that point A = (-2,9) is one endpoint, so we can substitute it into the equation

Solving for x2 and y2, we get x2 = 6 and y2 = 0 which is the coordinates of point B.

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Jake and Hakeem's rocket's flight is approximately modeled by the equation h(t) = - 12t ^ 2 + 36t + 3. The rocket's highest point is 30m

Generally, Since we are not instructed on what to look for, we are able to determine the highest point that the rocket ever achieved.

Given that the rocket's flight can be approximated approximatively using the equation,

h(t) = - 12t ^ 2 + 36t + 3

At maximum height dh/dt = 0

dh/dt = --24t + 36

0 = -24t + 36

24t = 36

t= 36/24

t = 1.5s

Find out the maximum height.

h(1.5) = - 12 (1.5)^ 2 + 36(1.5) + 3

h(1.5) = - 12(2.25) + 54 + 3

h(1.5) = -27 + 57

h(1.5) = 30m

As a result, the rocket is only capable of reaching a height of 30 meters at its highest point.

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3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )

4.) x =6

5.) x = 10

6.) x = 9

Explanation:

1.) write your equation down 8x + 9 = 131

2.) Subtract +9 from 131. you'll get 122

3.) divide 8x and 122.

4.) Then there's your answer 15.25

you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.

Rate of speed of each cyclist is:

Alisha 10mi/hr

Jose 15mi/hr

Raul 10mi/hr

Ruthie 16mi/hr

Data given of each cyclist;

Formula used: [tex]r=\frac{d}{t}[/tex]

here,

r=rate of speed

d=distance

t=time

Alisha: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]

Jose: Distance=30mi; Time=2hr

applying the formula

[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]

Raul: Distance=40mi; Time=4hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]

Ruthie: Distance=80mi; Time=5hr

applying the formula

[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]

Alisha= 10mi/hr

Jose= 15mi/hr

Raul= 10mi/hr

Ruthie= 16mi/hr

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Answer:

For this example they are all the same thing.  

530:1 or 530 mph

Step-by-step explanation:

A unit rate is when the denominator is 1.  In this case, the denominator is already 1 hour.