How to add two rational expressions with different denominators?.

According to definition of proportional ratios, 15 / 20 is not a multiple of 20 / 21.

In this problem we find two ratios in fraction form, both are proportional if the numerator and denominator of one of them are multiple of the corresponding elements of the other. First, write the fraction with the lowest numerator:

15 / 20

Second, multiply numerator and denominator by 4 / 3:

[15 · (4 / 3)] / [20 · (4 / 3)]

20 / 26.667

Ratio 15 / 20 is not proportional to ratio 20 / 21.

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The equation for Tree A's height t years after being planted is:

[tex]A = 34 + 2t[/tex]

The equation for Tree B's height t years after being planted is:

[tex]B = 14 + 6t[/tex]

To determine the height of both trees at the time when they have an equal height, we can set the two equations equal to each other:

[tex]A = B[/tex]

[tex]34 + 2t = 14 + 6t[/tex]

And solving for t, we find that:

[tex]t = 10[/tex]

So, 10 years after being planted,

Tree A will be 54 inches tall  [tex](34 + 2 * 10)[/tex]  and Tree B will be 74 inches tall [tex](14 + 6 * 10)[/tex].

At this point, both trees will have an equal height.

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The Argument of 4 + 3i is arg(z) = 36.97◦.

Now, According to the question:

Complex numbers are the numbers that are expressed in the form of a+ib where, a, b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

The standard format of a complex number is:

[tex]a +bi[/tex]

In which:

Given,

The complex number is:

z = 4 + 3i

We have to find the argument of the 4 + 3i.

The argument is given by:

θ = [tex]tan^-^1\frac{b}{a}[/tex]

tan θ = [tex]\frac{3}{4}[/tex]

θ = [tex]tan^-^1\frac{3}{4}[/tex]

θ = 36.97◦

The argument is θ = 36.97◦

We also have an abbreviation for argument: we write arg(z) = 36.97◦

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Answer:

PSQ = x         since PSQ + 3 x = 4 x

So the triangle PQS is an equilateral triangle

2 x + y = 180       (y = PQS the angle opposite 68)

y + 68 = 180       these must add to 180

x = 34        subtracting the previous two equations

Answer:

R' ( -2,1)

S' (-8,2)

T' ( -4,7)

Step-by-step explanation:

Answer: Look below

Step-by-step explanation:

Answer:

-1/2, 5/3

Step-by-Step Explanation:

6z^2 - 7z - 5 = 0

=> 6z^2 - 10z + 3z - 5 = 0

=> 2z(3z - 5) + 1(3z - 5) = 0

=> (2z + 1)(3z - 5) = 0

=> z = -1/2, 5/3

Hope it helps.

If you have any query, feel free to ask.

About 285 numbers lie between the values 10 and 14. (option C).

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or a Gaussian distribution. In statistics and the natural and social sciences, normal distributions are crucial concepts.

There are 600 numbers and their mean is 10 where the standard deviation is 2.

47.5% of the numbers should fall between 10 and 14, as expected. In a normal distribution, 47.5% of the sample size will fall between the mean and two standard deviations on either side of it.

By doing calculation on option C, we got that = [tex]\frac{285}{600}*100=47.5[/tex]

Hence, option C is correct, i.e., about 285 numbers would lie between the values 10 and 14.

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Answer:

No

Step-by-step explanation:

You must distribute 6 to BOTH numbers in the bracket

[tex]6(4b + 3d) = 24b + 18d[/tex]

Answer:

No, they are not equivalent !

Step-by-step explanation:

Simplify 6(4b + 3d)....

6(4b + 3d)

→ 6*4b+6*3d

→ 24b+18d

and we have....

→ 24b + 3d

So, no 6(4b + 3d) and 24b + 3d are not equivalent.

Check the picture below.

Answer: 65.65

Step-by-step explanation:

Carry over the decimals in each number.

2) Multiply. This will give you 6,565.

3) Carry the decimal place and count how many times you moved it over. (2=1+1) Therefore, it gives you 65.65

The total Social Security and Medicare taxes for the fourth quarter would be $728.00 ($600.00 for Social Security and $128.00 for Medicare). This is calculated by multiplying $5,000.00 by 12.4% for Social Security and 2.9% for Medicare.

The total Social Security and Medicare taxes for the fourth quarter would be $728.00. This is calculated by multiplying the total wages for the quarter ($5,000.00) by 12.4%, the Social Security tax rate for self-employed individuals, and then multiplying the same wages by 2.9%, the Medicare tax rate for self-employed individuals. This gives us $600.00 for Social Security taxes and $128.00 for Medicare taxes, for a total of $728.00. The Social Security tax rate is applied up to the wage base of $128,400 for the year.

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A suspension bridge: a parabola represents the profile of the cable of a suspended-deck suspension bridge.

A graph is a topic which gives us the numerical facts into visual form.

That is, a graph gives the visual representation of the data collected.

The towers supporting the cable of suspension bridge are 15m apart and 12m above the bridge it supports.

Suppose the cable hangs,following the shape of parabola,with its lowest point 20m above the bridge.

lets have the bridged centered at the origin

Three points are needed on the parabola

x = 0, y = 20

x = -7.5, y = 12

x = +7.5, y = 12

using the form ax^2 + bx + c = y, we know that c=20

x=-7.5, y = 12 and x =+7.5, y = 12; write two equations

-7.5^2a - 7.5b + 20 = 12

+7.5^2a + 7.5 + 20 = 12

use elimination

56.25a - 7.5b + 20 = 12

56.25a + 7.5b + 20 = 12

addition eliminates b

112.5a + 40 = 24

112.5=16

a = 16/112.5

a = 0.1422

Now we can write the equation

y = 0.1422x^2 + 2

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To find the median of a cumulative frequency graph the median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

When a set of numbers is arranged in ascending order of magnitude, the middle number is known as the median. A collection of n numbers has a median value of (n+1)/2. N is the cumulative frequency in the case of a cumulative frequency curve.

The median can be determined from cumulative frequency curves by drawing horizontal lines to half of the total frequency.

Create the cumulative frequency curve using the numbers provided first. Mark the point with the highest cumulative frequency, then draw a line perpendicular to the Y-axis that precisely passes through it. The lowest cumulative frequency is then marked, and a line is drawn parallel to the X axis. Mark the place where these two lines intersect.

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The solution set of the expression is y > -5

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

-y-8<-3 ory+5>19

Express the inequality properly

So, we have the following expression

-y - 8 < -3 or y + 5 > 19

Collect the like terms

This gives

-y < 8 - 3 or y > 19 - 5

Evaluate the like terms

This gives

-y < 5 or y > 14

Rewrite as

y > -5 or y > 14

When combined, we have:

y > -5

Hence, the solution set is y > -5

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Complete question

For the following inequality expression, determine the solution set

-y-8<-3 ory+5>19

Answer:

[tex]\frac{4}{3}cm/s[/tex]

Step-by-step explanation:

By looking at the graph, we can use the slope formula.

[tex]slope=\frac{y^2-y^1}{x^2-x^1}[/tex]

We can substitute the point values into the equation.

[tex]\frac{16-0}{12-0}[/tex]

Then simplify.

[tex]\frac{16}{12}[/tex]

This fraction has the greatest common denominator of 4, so we will divide the numerator and the denominator.

[tex]\frac{16}{12}=\frac{4}{3}[/tex]

Therefore, the speed of the snail has a unit rate of [tex]\frac{4}{3} cm/s[/tex].

10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

The area of Rectangle is length times of width.

Given that the area of rectangle is 70y⁸+30y⁶

The width of the rectangle is the greatest common factor of 70y⁸ and 30y⁶

70y⁸+30y⁶

10y⁶(y²+3)

10y⁶ is the width of the rectangle.

y²+3 is the length of the rectangle.

Hence, 10y⁶ is the width of the rectangle and y²+3 is the length of the rectangle.

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Answer:

$33.75

Step-by-step explanation:

25% of 45 is 11.25 meaning you would get that much off as a discount making the shoes be $33.75

Multiply the number in the one's place, Multiply the number in the ten's place and multiply the one's and ten's place with the hundred place number, then add them up.

Follow along with example 343 × 32:

Place one number above the other so that the ones' place digits and tens' place digits are lined up. Mark a line just below the bottom number.

 3 4 3

 ×3 2

_______

Multiply the ones' place digits (2 × 3 = 6), one's place of the second number by the ten's place of the first number (2 × 4 = 8), and one's place of the second number by the hundred place of the first number (2 × 3 = 6). Place the 6 below the line in the ones' place column, 8 below the line in the tens' place column and 6 below the line in the hundred place column.

3 4 3

×3 2

_________

6 8 6

Multiply the digit in the tens' place column (3) by the digit in the ones' place of the first number (3). The result is 3 × 3 = 9; multiply the digit in the tens' place column (3) by the digit in the tens' place of the first number (4). The outcome is 3 × 4 = 12, and multiply the digit in the tens' place column (3) by the digit in the hundred place of the first number (3). The outcome is 3 × 3 = 9. Now add the numbers and place the answer below the line.

3 4 3

×3 2

__________

   6 8 6

10 2 9×

__________

10 976

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A measures magnitude 8 on the Richter scale of an earthquake is 10,000 times stronger than a magnitude 4 measure on the Richter scale.

Earthquake Intensity: An earthquake is the release of energy from the movement of tectonic plates. Earthquakes can be measured on the Richter scale, which ranges from 2 to 10 and measures the magnitude of an earthquake.

Earthquake intensity is a qualitative estimate of the effects caused by an earthquake, so it has no numerical value. The Richter scale is a logarithmic scale. This means that as you move up each digit, the power increases by a factor of 10. So let's set the damage from 4 earthquakes to X. Then, 5 = 10X

=> 6 = 100X

=> 7 = 1,000X

=> 8 = 10,000X

Hence, the required intensity is 10,000.

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Considering the definition of inequality, the inequality that can be used to determine x is 20x + 10 ≤ 80.

According to the question,

Addison wants to rent a car, we know that:

On the other hand, x denotes the maximum number of days. Alyssa can afford to rent while staying within her budget.

Then, the inequality that can be used to solve x is:

20x + 0.1×100≤ 80

so,

20x + 10≤ 80

Hence, the inequality which can be used to determine x is 20x + 10≤ 80.

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In the given figure, the length b is opposite the angle theta, and the length a is adjacent to the angle theta, so we can use the trigonometric ratios to express a and b in terms of theta:

What does trigonometry mean in plain English?

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

a = bsec(theta)

b = acosec(theta)

To evaluate sin(x+y), we can use the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

We can use the given information to substitute the values of sin(x) and cos(y)

sin(x) = 1/3, cos(y) = sqrt(1 - (5/4)^2) = sqrt(9/16)

sin(x+y) = (1/3) * sqrt(9/16) + sqrt(9/16) * (1/3) = (3sqrt(9) + 9) / 48

To find all values of x such that sin 2x = sin x and 0 le x le 2pi, we can set sin 2x = sin x and solve for x.

sin 2x = sin x

2sinxcosx = sinx

cosx = 1/2

x = pi/3,5*pi/3

So the values of x that satisfy the equation are x = pi/3 and 5*pi/3

Note that these values are in radians, if you need in degree, x=60°, 300°

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Answer:

A) 234 feet

B) Area of new parking lot = 28080 square feet

C) The new parking lot will be able to fit 20 more cars than the original parking lot.

Step-by-step explanation:

We are given the following information:

Length of parking lot = 180 feet

Width of parking lot = 120 feet

Number of cars that can be parked = 75

A) Increase in length  = 30%

New length =

B) New area =

C) Space required by 1 car = 288 square feet

Number of cars we want to fit = 75 + 20 = 95

Area required =

Hence, the new parking lot will be able to fit 20 more cars than the original parking lot.

The inequality equation is x ≤ ( -12 )

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( 1/4 )x  ≤  -3   be equation (1)

On simplifying the equation , we get

x/4 ≤ -3

Multiply by 4 on both sides of the equation , we get

x ≤ ( -3 ) ( 4 )

x ≤ -12

Therefore , the value of x is less than or equal to -12

Hence , the inequality equation is x ≤ -12

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.

The Hall family utilizes sprinklers for 15 hours compared to the 35 hours used by the Nguyen family.

Let h and n represent the amount of hours each household uses its sprinkler, the Halls and the Nguyens, respectively.

They use for a total of 50 hours, thus either h + n = 50 or h = 50 - n.

Additionally, their total water output is 1050 L, thus we may use the equation below.

35h + 15n = 1050

Replace h with h = 50 - n to get

35(50 - n) + 15n = 1050

1750 - 35n + 15n = 1050

35n - 15n = 1750 - 1050

20n = 700

34 hours, n

15 hours equal 50 h, 50 n, and 35 n.

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Answer:

-1/2

Step-by-step explanation:

slope is rise over run so find the difference between the y values (-9-(-5)) and divide that by the difference between the x values (-1-(-9)).

Nata was using the partial products method to solve the multiplication problem 42 × 15. She likely wrote 20 because she was finding the product of 42 and 10, which is 420. Writing 20 was likely a shorthand for the digit 2 in 420.

In the partial product method, each digit of one number is multiplied by each digit of another number, keeping each digit in its original place. Place value is typically used to calculate the partial product. To get the product of two-digit numbers, we employ the partial product method.

The partial products method involves breaking down one factor into its place value components and multiplying each component separately, then adding the products together to get the final answer.

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The inequality that represents the number of visits Tristan can make to earn his first free movie ticket is 8.5x + 25 ≥ 110.

In mathematics, an inequality is a relationship between two expressions or values that are not equal to each other.

In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), and not equal to symbol (≠).

Here,

Let us refer to x as the number of visits.

He receives 8.5 points for each visit,

That is he receives 8.5x points for x visits. i

Then there are the 25 reward points for simply signing up.

So the total points expression would be 8.5x + 25.

He needs at least 110 points to get a freebie,

Therefore the inequality is 8.5x + 25 ≥ 110.

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Answer: Total cup of flour=8 cups

One recipe calls for cup of flour=2/3

Cup of flour after making one recipe=8-2/3=(24-2)/3=22/3=7.33 cup of flour

Another recipe calls fro cup of flour=1/4

Cup of flour left after another recipe=22/3-1/4=(88-3)/12=85/12=7.08 cup of flour.

Amount of Floor left=7.08

Step-by-step explanation: