what expression is equivalent to 1/2x+4x-1/2x+60

Answer:

Simple Interest =$5600 (Principal and Interest)

Compound Interest = $5624.32 (Principal and Interest)

Step-by-step explanation:

Using Simple interest, use the formulae, Principal X Rate X Time

= 5000*4%*3

= $600 Interest

Principal plus Interest = $5600

Using compound Interest, use the formulae P(1+r)^n

P means Principal

R means rate

N means number of years

= 500(1+4%)^3

= $5624.32 (Principal with Interest)

Answer:

392b²

Step-by-step explanation:

56b×77b÷11

56b×7b

392b²

The ladder reaches 40 feet up the wall.

41 squared (1681) minus 9 squared (81) is 1600. 40 is the square root of 1600.

The required distance between the top of the ladder and the ground is 40 feet.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,

We can use the Pythagorean theorem to solve this problem. Let's call the distance from the base of the ladder to the wall "x", and let's call the length of the ladder "y".

According to the problem statement, we know that the ladder is 41 feet long and that the base of the ladder is 9 feet from the base of the apartment building.

y = 41 feet

x = 9 feet

We can use the Pythagorean theorem to solve for the distance between the top of the ladder and the ground. The Pythagorean theorem tells us that:

y² = x² + z²

where "z" is the distance between the top of the ladder and the ground. Plugging in the values we know,

(41 feet)² = (9 feet)² + z²

1681  = 81 + z²

1600 = z²

z = 40 feet

Therefore, the distance between the top of the ladder and the ground is 40 feet.

Learn more about Pythagorean triplets here:

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The perimeter of rectangle is 25.13 feet

Solution:

Given that,

width of a rectangle = [tex]4\frac{1}{6} \text{ feet }[/tex]

Convert the mixed fraction to improper fraction

[tex]\rightarrow 4\frac{1}{6} = \frac{6 \times 4 + 1}{6} = \frac{25}{6}[/tex]

Therefore,

[tex]\text{width of rectangle } = \frac{25}{6} \text{ feet }[/tex]

Area of rectangle = 35 feet

The area of rectangle is given by formula:

[tex]area = length \times width[/tex]

Substituting the given values, we get

[tex]35 = length \times \frac{25}{6}\\\\length = 35 \times \frac{6}{25} = \frac{42}{5}[/tex]

Thus we get,

[tex]\text{length of rectangle } = \frac{42}{5} \text{ feet }[/tex]

The perimeter of rectangle is given as:

perimeter = 2(length + width)

[tex]perimeter = 2(\frac{42}{5} + \frac{25}{6})\\\\perimeter =2(8.4+4.167)\\\\perimeter = 2(12.567)\\\\perimeter = 25.13[/tex]

Thus perimeter of rectangle is 25.13 feet

Answer:

Domain: (-oo, oo)

Range: (-4,oo)

Horizontal asymptote: y=-4

Answer:

The domain is all Real numbers.

The range is all real values > -4.

Step-by-step explanation:

The asymptote is y = -4.

Answer:

1. 9 pi, 2. 121 pi

Step-by-step explanation:

The formula for circumference is pi d. So for the first question the radius would be three. The you do pi r ^2 for area so 3 times pi squared. Which is 9 pi. For the second you will do the same thing you will do 22 pi divided by 2 which is 11 pi then you will square 11pi and get 121 pi

Answer:

f^-1 (x)=1/5x-11/5

Step-by-step explanation:

y=5x+11

x=5y+11

5y=x-11

y=1/5x-11/5

Answer:

c

Step-by-step explanation:

g(x) = x²

g(4) = 4² = 16

g(f(4)) = (f(4))² = (4-7)² = (-3)² = 9

Answer: 785.5

Step-by-step explanation:

Final answer:

To solve 2 divided by 1571, recognize it as a fraction 2/1571, which cannot be simplified. Perform long division, adding zeros as necessary, to find its decimal representation, which will be very small.

Explanation:

To solve 2 divided by 1571 step by step without a calculator, you can follow these steps:

Understand that this division represents a fraction, 2/1571.

Recognize that this fraction cannot be simplified further since 2 and 1571 have no common factors other than 1.

To find the decimal form, you can perform long division. However, since 2 is much smaller than 1571, the decimal will start with 0. As 2 cannot be divided by 1571, in the first step of long division, you would put a 0 to the right of the decimal point in your answer.

Next, you would need to add a 0 to the right of 2 (making it 20), since 1571 still cannot go into 2. Then, determine how many times 1571 can go into 20, which will still result in 0, and so on, adding zeros and comparing until you reach a desired level of precision.

This process will yield a very small decimal, indicating that 2/1571 is a fraction much less than 1.

Answer:

4x+9=3q

Step-by-step explanation:

-3(2x-3)+10x=3q

-6x+9+10x=3q

4x+9=3q

Answer:

q = 4/3x + 3

Step-by-step explanation:

-3(2x-3)+10x=3q

Multiply the -3 at the beginning by (2x - 3), the parenthesis

-6x + 9 + 10x = 3q

Now combine the like terms (add x's and variables separately)

(-6x + 10x) + 9 = 3q

4x + 9 = 3q

Divide both sides of the equation by 3

(4x + 9) ÷ 3 = q

4x/3 + 9/3 = q

Simplify

q = 4/3x + 3

Hope this helps :)

Answer:

Option D: The area will be multiplied by 16.

Step-by-step explanation:

Given that the area of the figure is 13 sq. in.

Let is say the figure is of dimensions: a & b.

Therefore, a.b = 13 sq. in

When each of the dimension is multiplied by 4, the dimensions would become 4a and 4b.

Therefore, the area would be: 4a . 4b = 16 a . b = 16(13) sq. in.

Hence, the area is multiplied by 16.

Answer:

29

Step-by-step explanation:

Look at image

Answer:

In Grade 8, 17% of students liked running

Step-by-step explanation:

Although this table is incomplete, there are still enough information to answer.

First, we need to be aware that the data here is written in decimal numbers, which is another way to write percentages.

In other words, 100% equals to 1, which is to say that if we multiply decimal number with 100 we'll get the percentage:

0.39 = 39%

0.04 = 4%

Another important thing to establish is that the value of decimal number DOES NOT mean the number of people, it only suggests the ratio:

0.26 does not mean 26 people etc.

Knowing this, from this incomplete table, we see that 0.17 students from grade 8 liked running. And now we know that 0.17 equals to 17%, which makes B the correct answer.

Answer:

B. In Grade 8, 17% of students liked running

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]i^{20}+1=i^{2*10}+1\\\\(i^{2})^{10}+1=(-1)^{10}+1\\\\=1+1=2[/tex]

Answer:

$31.20

Step-by-step explanation:

Angela will get an amount of $31.2 as the interest at the end of 1 year.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that Angela puts $520 in an account that earns 6% per year.

Principal or initial amount = $520

Rate of interest = 6% = 6 / 100 = 0.06

We have to calculate the amount of interest.

Interest amount = $520 × 0.06

                           = $31.2

Hence the amount of interest that Angela get at the end of the year is $31.2.

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Answer:

75

Step-by-step explanation:

6 and 4 are alternate interior angles meaning they have the same value

Answer:

11/4

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

x + 6 = ?

[Replace x with 7]

7 + 6 = 13

Steps to solve:

-3(x + 5) = -9

~Distributive Property

-3x - 15 = -9

~Add 15 to both sides

-3x - 15 + 15 = -9 + 15

~Simplify

-3x = 6

~Divide -3 to both sides

-3x/-3 = 6/-3

~Simplify

x = -2

Best of Luck!

Answer:

x= -2

Step-by-step explanation:

First, distribute the 3 into the parenthesis.

(-3)x+ (-3)5= -9

Then, multiply.

-3x-15= -9            *The negative makes it into becoming subtraction.

Now, add 15 to both sides since that's the opposite of subtraction.

-3x-15= -9

   +15  +15

Then, divide by 3 to both sides to isolate the variable.

-3x= 6

-3   -3

x= -2

Answer:

B.

Step-by-step explanation:

1000 meters in a kilometer and 60 minutes in a hour. 1000/60= 16.6666

(rounds to 20)

Final answer:

Charles' running speed of 12 kilometers per hour is equivalent to 200 meters per minute when converted, which corresponds to option D.

Explanation:

Charles runs at a rate of 12 kilometers per hour, and the question asks us to convert this speed to meters per minute. First, we need to convert kilometers to meters. One kilometer is equivalent to 1,000 meters.

So, Charles' speed in meters per hour is:

12 km/hr × 1,000 m/km = 12,000 m/hr

To convert this speed from meters per hour to meters per minute, we divide by 60 minutes, since there are 60 minutes in one hour:

12,000 m/hr ÷ 60 min/hr = 200 m/min

Therefore, Charles' speed is 200 meters per minute, which corresponds to option D.

Answer:

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 3, 3)  

point B( x₂ , y₂) ≡ (5 , -1)  

point C( x₃ , y₃) ≡ (-2 , 1)

To Find:

Centroid, G (x,y) = ? (say)

Solution:

Centroid:

Centroid is a point where all the three medians of the triangle intersect.

It is denoted as G and the coordinates are give by

[tex]G(x,y)=(\dfrac{x_{1}+x_{2}+x_{3}}{3},\dfrac{y_{1}+y_{2}+y_{3}}{3})[/tex]

Substituting the values we get

[tex]G(x,y)=(\dfrac{3+5+-2}{3},\dfrac{3+-1+1}{3})[/tex]

[tex]G(x,y)=(\dfrac{6}{3},\dfrac{3}{3})=(2,1)[/tex]

Therefore, the coordinates of the centroid of a triangle is

[tex]G(x,y)=(2,1)[/tex]

The calculated cosine of the angle U is 8/17

How to determine the cosine of the angle U

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

The triangle

By definition:

The cosine of the angle is calculated using

cos(U) = VW/UW

Where

VW = 8 and UW = 17

Substitute the known values into the equation

cos(U) = 8/17

Hence, the cosine of the angle U is 8/17

Answer:

3+8g

Step-by-step explanation:

27/9+8g=3+8g

Answer:

[tex]A = w^2 + 7w[/tex]   is the rule for the area of a rectangle.

A = 120 sq ft, when it’s width is 8 ft.

Step-by-step explanation:

Here, let us assume the width of the rectangle =  w

So, the length here = Width +  7 ft = (w +  7) ft

Now, AREA of a RECTANGLE = Length x Width

Substituting here the values of length and width, we get:

A = (w) x (w +  7) [tex]= w^2 + 7 w[/tex]

[tex]\implies A = w^2 + 7w[/tex]

The above function is the rule for the area of a rectangle.

Given: w = 8  ft

To find the area: put w  = 8 in [tex]A = w^2 + 7w[/tex]

We get: A  = 8²  +  7(8)  

                 = 64 +  56  = 120

or, A  = 120 sq ft.

Hence, area = 120 sq ft, when it’s width is 8 ft.

Answer:

2) -1

Step-by-step explanation:

it is easy

 we have to first open the brackets, as it is ' - '  we have to change the sign to opposite of that of the number in the bracket and then solve it.

so the number 2 is having negative sign, we make it positive. this rule is applied only when there is a negative sign and a bracket is there.

-3-(-2)

-3+2

=-1

Final answer:

The correct inequality to represent the number of situps Lyle can do, if 57 is more than he can do, is D. x < 57, indicating that Lyle can do fewer than 57 situps.

Explanation:

The inequality that represents the number of situps Lyle can do, given that the number 57 is more than the number of situps Lyle can do, is x < 57. This is because if 57 is more than what Lyle can do, then Lyle can do any number of situps that is less than 57.

To represent this relationship mathematically, we use the inequality sign '<'. Thus, the correct option from the provided choices is D. x < 57. This means Lyle can do 56, 55, 54, etc., situps, but not 57 or any number greater than 57.

Answer:

2400m³

Step-by-step explanation:

50 * 30 * 1.6 =

1500 * 1.6 = 2400m³

The value of b is -12

Solution:

The given equation, b (b + 12) = 0

On distributing the b inside the parentheses we get,

[tex]\Rightarrow\bold{ b\times b+b\times12=0}[/tex]

[tex]\bold{\Rightarrow b^{2}+12b=0}[/tex]

[tex]\bold{\Rightarrow b^{2}=-12b}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12b}{b^2}}[/tex]

[tex]\bold{\Rightarrow 1=\frac{-12}{b}}[/tex]

[tex]\bold{\Rightarrow b=-12}[/tex]

Steps to use distributive property to solve an equation:

For fractions: