You are making a round flower garden in your yard. The circumference of the garden will be 60 inches. What is the diameter? Use 3.14 to approximate pi. Round to the nearest tenth.

Answers

Answer 1

The diameter of the circular garden round to the nearest tenth will be 19.1 inches.

What is the diameter of a circle?

In a circle, an infinite number of diameters can be drawn. A diameter is a straight line passing through the center and joins two points of the circumference of a circle. The length of a diameter is twice the length of the radius.

The circumference of a circle is given by C = πd, where d is the diameter of the circle and π can be taken as 3.14.

Substitute C = 60 and π = 3.14 into the above formula and find d.

60 = 3.14×d

d = 60/3.14

≈ 19.108

≈ 19.1

Therefore, the obtained answer is 19.1 inches.

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Related Questions

How do i get desmos to show both square roots?

Answers

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).  Desmos can then graph this equation, showing both the positive and negative square roots.

To get Desmos to show both square roots, you can use the formula y = √x + √(-x).This formula can be used to graph two square roots. The first square root is √x, which is the positive square root of x. The second square root is √(-x), which is the negative square root of x. To calculate the roots, you would take the square root of both x and -x. For example, if x is 4, the two roots would be √4 = 2 and √(-4) = 2i, where i is the imaginary unit. Desmos can then graph this equation, showing both the positive and negative square roots.

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To catch up to Group B, Group Aw
4) Group A: y = 3x
Group B: y = 2x + 1
Graph the equation y = 3x.

Answers

The graph of the equation is added as an attachment

How to determine the graph of the equation

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

y = 3x

The above expression is a linear equation

A linear equation is represented as

y = mx + c

Where

Slope = m and y-intercept = c

This means that

y = 3x has a slope of 3 and a y-intercept of 0

Next, we plot the graph

See attachment for the graph of the equation

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Solve the following problem: "Justin's car insurance has a $750 deductible per incident. This means that Justin pays $750 toward a claim, and his insurance pays all costs beyond $750. If Justin files a claim for $2100, how much will he pay, and how much will his insurance company pay?"

Answers

Answer:

$1350.

Step-by-step explanation:

If Justin files a claim for $2100, he will pay the first $750 toward the claim, and his insurance company will pay the remaining costs.

So, Justin will pay $750.

And, the insurance company will pay $2100 - $750 = $1350.

What is the sum of the distinct prime factors of the number 560?
A. 20
B. 14
C. 18
D. 16
E. 1488

Answers

The sum of the distinct prime factors is (b) 14

How to determine  the sum of the distinct prime factors

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

distinct prime factors of the number 560

The distinct prime factors of the number 560 are

Factors = 2, 5, 7.

When these numbers are added, we have

Sum = 2 + 5 + 7

Evaluate

Sum = 14

Hence , the sum is (b) 14

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Which of the following values is a rational number?
A. O √²
B. O √49+√7
C. O √225+ √169
D. O √2x √121
E. O √11x16

Answers

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

What is a rational number?

If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

Let's check all the options, then we have

A. √(4)² = 4, is a rational number.

B. √49 + √7 = 7 + √7, is an irrational number.

C. √225+ √169 = 25 + 13, is a rational number.

D. √2 x √121 = 11√2, is an irrational number.

E. √11 x 16 = 4√11, is an irrational number.

The expression whose value is a rational number will be √(4)² and √225+ √169. Then the correct options are A and C.

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Assume all intersecting sides meet at right angles.

Answers

Answer:

8 cm

Step-by-step explanation:

15 - 7 = 8

The length of the right side equals the length of the left side.  The left side has a length of 15 and the part that we know for the right side is 7.

Helping in the name of Jesus.

A TYPE OF GREEN PAINT IS MADE BY MIXING 2 CUPS OF YELLOW WITH 3.5 CUPS OF BLUE FIND A MIXTURE THAT WILL MAKE THE SAME SHADE OF GREEN BUT A LARGER AMOUNT

Answers

The mixture of different shade of green that is bluer will be; ⇒ 2 cups of yellow and 4 cups of blue.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.

now,

Since, A type of green paint is made by mixing 2 cups of yellow with 3.5 cups of blue.

Hence, The mixture of different shade of green that is bluer is find as;

Let Cups of yellow = 2

And, Cups of blue = x

So, we can formulate;

⇒ 2/x < 2/3.5

⇒ x > 3.5

So, Assume x = 4

Hence, The mixture of different shade of green that is bluer will be;

⇒ 2 cups of yellow and 4 cups of blue.

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10. Sixteen teams play in a one-game elimination
match. The winners of the first round go on to
play a second round until only one team remains
undefeated and is declared the champion.
4
a. Make a table of values for the number of
rounds and the number of teams participating.
b. What is the reasonable domain and the range
of this function? Explain.
c. Find the rate of decay.
d. Find the decay factor.

Answers

a. Here's a table of values for the number of rounds and the number of teams participating:

Round Number of Teams

1             16

2              8

3                  4

4             2

5       1 (Champion)

.b. domain: [1 5]

Range: {1 16]

C. Rate of decay = 8

D. Decay factor = 0.5

How to solve for the rate of decay

b. The reasonable domain of this function would be the number of rounds, and the range would be the number of teams participating in each round.

The domain would be all positive integers from 1 to the maximum number of rounds,

The range would be all positive integers from 1 to the starting number of teams (16 in this case).

c. To find the rate of decay, we can calculate the ratio of the change in the number of teams to the change in the number of rounds.

Using Round 1 to Round 2,

= (16 - 8) / (2 - 1)

= 8.

d. The decay factor is the ratio of the number of teams in a given round to the number of teams in the previous round.

Using Round 1 to Round 2, the decay factor is

= 8 / 16

= 0.5

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Ms. Liu has a cylinder container measuring 12 cm tall and 6 cm across. The height of Jeff's container is twice Ms. Liu's but the width is 1/3 of Miss Liu's container. Julie's cylinder container has the same width as Miss Liu but it has twice the height of Miss Lui's container. Who has the largest container and who has the smallest container?

Answers

The person with the largest container is Julie and the person with the smallest container is Jeff.

Who has the largest container and the smallest container?

The volume of each container has to be determined.

Volume of a cylinder = πr²h

Where:

π = 3.14r = radius = diameter / 2 h = height

Volume of Ms. Liu's container:

r = 6/2 = 3h = 12

3.14 x 3² x 12 = 339.12 in³

Volume of Ms. Julie's container:

h = 12 x 2 = 24 r = 6/2 = 3

Volume = 3.14 x 3² x 24 = 678.24 in³

Volume of Jeff's container:

h = 2 x 12 = 24 d = 1/3 x 6 = 2 r = 2/2 = 1

Volume = 3.14 x 1² x 24 = 75.36 in³

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What is terminal value formula ?

Answers

The terminal value formula helps estimate the value of a business beyond the explicit forecast period,

the terminal value formula = FCFF 6 / (WACC – Growth Rate)

We can say that in a DCF model with a five-year free cash flow projection, the terminal value formula = FCFF 6 / (WACC – Growth Rate)

It could be accountable that in finance, the terminal value (also known as “continuing value” or “horizon value” or "TV") of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most likely often used in multi-stage discounted cash flow analysis and also allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

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{10x + 7y= - 12
9x+ 5y = -16

Answers

Answer: x=-4, y=4

Step-by-step explanation:

We can use elimination method to solve this problem.

Let's eliminate y.

In equation 2, use the coefficient of y (i.e 5) to multiply equation 1. DO the same for other equation. Thus,

5(10x+7y=-12)

7(9x+5y=-16)

=> 50x+35y=-60

     63x+35y= -112

clearly, y can be eliminated by subtraction.

Therefore,

-13x = 52  [-63+50  and 112-60)]

x = -4.

When x = -4,

9x+5y =-16

9(-4) +5y =-16

5y = 36-16

y=4.

Write a function that models y in terms of x. Round any coefficients to the nearest tenth. x 0 5 10 15 20
y 0 4.02 5.69 6.97 8.05

Answers

The  function that models y in terms of x is y=0.804x

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=4.02-0/5-0

m=4.02/5 = 0.804

Now let us find y intercept

0=0.804(0)+b

b=0

Hence, the  function that models y in terms of x is y=0.804x

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The weight of an organ in adult males has aâ bell-shaped distribution with a mean of 330 grams and a standard deviation of 15 grams. Use the empirical rule to determine the following. â(a) About 68â% of organs will be between whatâ weights? â(b) What percentage of organs weighs between 285 grams and 375 âgrams? â(c) What percentage of organs weighs less than 285 grams or more than 375 âgrams? â(d) What percentage of organs weighs between 300 grams and 375 âgr

Answers

The empirical rule states that in a normal distribution, 68% of the observations lie within 1 standard deviation from the mean, 95% of the observations lie within 2 standard deviations from the mean, and , 99.7% of the observations lie within 3 standard deviations from the mean.

a) -  Mean = U = 330 grams

standard deviation= [tex]\sigma=40 \: grams[/tex]

As per the empirical rule, 68% of the observations lie within 1 standard deviation from the mean.

Let [tex]X_1[/tex] and [tex]X_2[/tex] be the 2 random value, between which 68% of the observations lie.

Mathematically,

[tex]X1=U-\sigma[/tex]

[tex]X1[/tex] = 330 - 40

[tex]X1[/tex] =  290

Similarly,

[tex]X1=U-\sigma[/tex]

[tex]X1[/tex] = 330 + 40

[tex]X1[/tex] = 370

Thus, about 68 % of organs will be between 290 and 370 grams in weight.

b) - In this, we need to find the percentage of organs weighing between 250 grams and 410 grams.

We can rewrite 250 as follows:

250= 330− 80 ⇒ 30−2(40) ⇒ 330−2(σ)

The above value (250) lies within 2 standard deviations from the mean.

Similarly,

We can rewrite 410 as follows:

410 = 330+80 ⇒ 330+2(40) ⇒ 330+2(σ)

The above value (410) lies within 2 standard deviations from the mean.\

As per the empirical rule, 95% of the observations lie within 2 standard deviations from the mean.

Thus, 95% of organs weighs between 250 grams and 410 grams.

c)-As we have calculated in part(b) that 95% of the organs lie within 250 and 410 grams.

So, area outside these values = Total area under curve - 95%

= 100 - 95 ⇒ 5%

So, 5% of the area lies outside the 250 and 410 grams range.

From the property of normal curve, we know that the area under the curve is divided into 2 equal parts.So, we divide the area- 5% into 2 equal parts which gives 2.5%.

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a man travels from Nigeria to Ghana by air and from Ghana to Liberia by ship .he returns by the same means he has 6 airlines and 4 shipping lines to choose from .in how many ways can he make his journey without using the same airline or shipping line​

Answers

There will be 360 different ways without using the same airline or shipping line.

What is a combination?

A combination in mathematics is a selection of items from a set with distinct members, where the order of selection is irrelevant.

Let's first consider the number of ways the man can choose his outbound journey. He has 6 airlines to choose from, and once he has made his choice of airline, he has 4 shipping lines to choose from.

Therefore, there are 6 × 4 = 24 ways he can choose his outbound journey.

For his return journey, he cannot use the same airline or shipping line that he used for his outbound journey.

This means he now has 5 airlines and 3 shipping lines to choose from. Therefore, there are 5 × 3 = 15 ways he can choose his return journey.

The total number of ways he can make his journey is:

24 × 15 = 360

Therefore, he can make his journey in 360 different ways without using the same airline or shipping line.

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Solve Another Problem
7. You want to survey the people at the local pool about the food
served in the snack shack. You decide to walk around the kiddy
pool and survey parents. Is this a random sample? Why or why not?

Answers

In the research effort where a researcher want to survey the people at the local pool about the food served in the snack shack by deciding to walk around the kiddy pool and survey parents, this is an example of random sample because every parent in the pool have equal chance of being chosen for the study.

What does a random sample mean at first?

A random sample is drawn at random from the entire population to represent the entire data set, with each member having an equal chance of being chosen. Researchers can generate a random sample by employing techniques such as lotteries or random draws.

Because the data set is chosen using random selection, every member of the population has an equal chance of being chosen.

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How do you find the Laplace inverse on a calculator?

Answers

Answer:

Step-by-step explanation:

The Laplace inverse is not a standard function on most calculators. However, if you have a graphing calculator that supports Laplace transforms, you can use it to find the Laplace inverse by performing the inverse Laplace transform on a function.

Here's the general procedure for finding the Laplace inverse on a graphing calculator:

Enter the Laplace transform of the function you want to find the inverse of.

Select the inverse Laplace transform function from the calculator's menu.

Enter the desired complex variable, usually represented by "s" in Laplace transform notation.

The calculator will return the inverse Laplace transform of the function, which represents the original function in the time domain.

Note: The exact steps for finding the Laplace inverse on a graphing calculator will vary depending on the model and brand of the calculator. It's best to consult the manual or a reference guide for your specific calculator to determine how to perform the inverse Laplace transform.

John measured a line to be 1.7 inches long. If the actual length of the line is 1.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?

Answers

The percent error of the measurement, to the nearest tenth of a percent, is 5.6.

What is a percentage?

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

John measured a line to be 1.7 inches long.

The actual length of the line is 1.8 inches.

The amount of error = 1.8 - 1.7

The amount of error = 0.1

Let 1 - n be the required percentage of error.

Then applying the percentage formula,

1.8 x n /100 = 1.7

Applying cross multiplication,

we get,

1.8n = 170

n = 170/1.8

n = 94.4

So, 1 - n = 100 - 94.4 = 5.6

Therefore, the percentage is 5.6.

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Alexa earns 5% commission as a salesperson. She sold a gold necklace that cost $78. How much commission did Alexa earn?

Answers

Answer:

Step-by-step explanation:

=  5 /100  * 78 =  39 /10  = 3.9

$3.90

A Ferris wheel has a radius of 218 feet. What is the
total distance covered if the Ferris wheel makes 6
rotations? Write an exact answer in terms of Pi.

Answers

The total distance covered by the Ferris wheel after 6 rotations is 2616π feet

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The Ferris wheel has a radius of 218 feet. The total distance covered if the Ferris wheel makes one rotation is the perimeter of the wheel.

Perimeter = 2π * radius = 2π * 218 feet = 436π

For 6 rotations:

Total distance covered = 6 * 436π = 2616π

The total distance is 2616π feet

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8. Fill in the missing statements and reasons to complete the following proof

Answers

The completed two-column table used to prove that the quadrilateral WXYZ is a parallelogram is presented as follows;

Statement     [tex]{}[/tex]                                              Reason

1. m∠y = 49, m∠z = 131°, m∠w = 49  [tex]{}[/tex]       Given

2. m∠y + m∠z + m∠w + m∠x = 360 [tex]{}[/tex]    1. ∠ sum property of a quadrilateral

3. 49 + 131 + 49 + m∠x = 360[tex]{}[/tex]                Substitution Property of Equality

4. 229 + m∠x = 360   [tex]{}[/tex]                           2. Summation of values

5. m∠x = 131                                           3. Subtraction Property of Equality

6. ∠x ≅ ∠z and ∠w ≅ ∠y [tex]{}[/tex]                     Angles with equal measures are ≅

7. WXYZ is a parallelogram                 4. The opposite ∠s of a ║ are ≅

What is a parallelogram?

A parallelogram is a quadrilateral that has two pairs of parallel facing sides.

The details of the reasons used in the two-column table method to prove that the quadrilateral WXYZ is  parallelogram are illustrated as follows;

∠ sum property of a quadrilateral

The angle (∠) sum property of a quadrilateral, indicates that the addition of the four interior angles of a quadrilateral has a result of 360°

Summation of a set of values

The sum of the values 49 + 131 + 49 is 229

Subtraction Property of Equality

The subtraction property of equality states that the subtraction of the same amount from both sides of an equation produces two new quantities or expressions on both sides of the equation that remain equivalent.

Angles with the same measures are ≅

Angles that are congruent, ≅, are angles that have the same measure

The opposite angles of a ║ are ≅

The angles located in the facing corners of a parallelogram, ║, are congruent.

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Kelly’s taxable income is $110,000. Approximately what percent of her taxable income is her tax?

Answers

Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.

What is taxable income?

The term "taxable income" describes the basis on which an income tax system levies tax. In other words, the amount of income that was taxed by the government.

In most cases, it covers some or all sources of income and is then diminished by costs and other deductions. Every gross income received and utilized to determine your tax liability is referred to as taxable income.

It can be stated simply as your adjusted gross income less any deductions. This covers all pay, gratuities, salaries, and bonuses received from employers. Investments and ill-gotten gains are also mentioned.

The given taxable income is over $43,650. So use the information on line 3 to determine the tax.

Tax =$5,975+25% of the amount over 43,650

=5,975+0.25(110,000 - 43,650)

=5.975+16587.50

=22,562.50

Kelly has to pay a tax of $22,562.50 which is approximately around of 20% her taxable income.

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I NEED HELP ON THE FIRST QUESTION ASAP!!!!!!!!

Answers

Answer to question 1 is   [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex]

=========================================================

Explanation:

The first task is to find the equation of the line through the given points in the table.

Pick any two points you want. I'll pick (0,100) and (50,80)

Determine the slope:

[tex](x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\[/tex]

The slope is -2/5.

The y intercept is b = 100 because of the point (0,100)

We go from [tex]\text{y} = m\text{x}+b[/tex] to [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

Each point from the table is found on this line. For instance, let's check the point (140,44)

[tex]\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\[/tex]

This confirms (140,44)

I'll let you check the other points.

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

Any point on the line mentioned represents a scenario where César spends all of the $50.

If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.

This means we want to shade the region below the boundary line [tex]\text{y} = -\frac{2}{5}\text{x}+100[/tex]

We'll replace the equal sign with a "less than or equal" sign

We arrive at [tex]\text{y} \le -\frac{2}{5}\text{x}+100[/tex] as the final answer to question 1.

Answer: Answer to question 1 is   =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from  to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at  as the final answer to question 1.

Step-by-step explanation:

25. The circle has a radius of 7. Angle C
intercepts the arc with a length of 28.
What is the measure of angle C in radians?

Answers

The measure of angle C in radians is 3.6 radians.

What is arc length of circle formula?

The arc length of a circle is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining that point to the end-points of the arc.

Given that, the circle has a radius of 7 and angle C intercepts the arc with a length of 28π.

We know that, formula to find the arc length of circle is Arc length= θ/360 ×2πr

28π= θ/360×2π×7

4= θ/360×7

θ=1440/7

θ=205.7

θ=3.6 radians

Therefore, the measure of angle C in radians is 3.6 radians.

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help help help help help help

Answers

Image attached below

30% of 750 using a table

Answers

Answer:
225

Step-by-step explanation:
30%×750 = 30×750/100 = 3×75 = 225

Help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Evaluate each algebraic expression for the given values.
1. 9.8t^2 + 20t + 8 for t = -2, 0, 3.5
2. -3(2.1x - 7.9) for x = -18.1, -0.3, 14.4

Answers

The numeric values for each of the expressions are given as follows:

1. 9.8t² + 20t + 8:

t = -2: 7.2.t = 0: 8.t = 3.5: 198.05.

2. -3(2.1x - 7.9):

x = -18.1: 137.73. x = -0.3: 25.59x = 14.4: -67.02.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

Then the numeric values are given as follows:

1. 9.8t² + 20t + 8:

t = -2: 9.8(-2)² + 20(-2) + 8 = 7.2.t = 0: 8. 9.8(0)² + 20(0) + 8 = 8.t = 3.5: 9.8(3.5)² + 20(3.5) + 8 = 198.05.

2. -3(2.1x - 7.9):

x = -18.1: -3 x (2.1(-18.1) - 7.9) = 137.73.x = -0.3: -3 x (2.1(-0.3) - 7.9) = 25.59.x = 14.4: -3 x (2.1(14.4) - 7.9) = -67.02.

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3/4 x ( z^3 x 4) equivalent expressions

Answers

The required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4). which is the correct answer .

What is the algebraic expression?

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

her, we have,

We have been given expression as:

3/4 x ( z^3 x 4)

To determine the equivalent expression to the given expression

3/4 x ( z^3 x 4)

⇒ 3* z^3

Here the variable z has an exponent is 3 which is positive,

Rearrange the terms of variables z  in the above expression

⇒3 · z³

Therefore, the required equivalent expression is 3 · z³ to the given expression 3/4 x ( z^3 x 4).

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What is the value of R for the following sequence

2, 10, 50, 250, 1250…

Answers

The next value R in the sequence is 6250.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

2, 10, 50, 250, 1250, R

Now,

We see that the next number in the sequence is a multiple of 5 of the previous number.

i.e

2 x 5 = 10

10 x 5 = 50

50 x 5 = 250

250 x 5 = 1250

So,

R = 1250 x 5

R = 6250

Thus,

The next value R in the sequence is 6250.

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5x+1=2x+10 (Please include the steps)

Answers

Answer:

x = 3

Step-by-step explanation:

5x + 1 = 2x + 10

1.) Subtract 2x from both sides to get 2x on the other side

5x - 2x + 1 = 10

2.) Subtract 1 from both sides to get 1 to the other side

5x - 2x = 10 - 1

3.) Combine like terms

3x = 9

4.) Divide 3 on each side to get x by itself

x = 3

Find the asymptotes, domain and range.

Answers

For the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is

[tex]f(x) = \frac{-5x+2}{4x+5}[/tex]

The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.

The horizontal asymptote of the function is when x tends to ∞ .

[tex]\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}[/tex]

The horizontal asymptote of function is at y = -5/4.

Since at x = -5/4, the function becomes undefined.

The domain is all real numbers except x = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Since the function is not defined at y = -5/4 as well, the range is also

(-∞,-5/4) ∪ (-5/4,∞) .

Therefore for the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

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