How to solve image. (solving rational expressions) and check for extraneous solutions

Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

The travel time x is 41.162 min such that 17.36% of the 60 days have a travel time that is at least x.

We have to determine the travel time such that 17.36% of the 60 days have a travel time that is at least.

Total work days to work = 60 days

The travel mean time = 35.6

Standard deviation = 10.3

For normal distribution,

P(X < A) = P(Z < (A - mean)/standard deviation)

P(X > x) = 0.2946

P(X < x) = 1 - 0.2946 = 0.7054

P(Z < (x - 35.6)/10.3) = 0.7054

Take the z value that corresponds to 0.7054 in the table of the standard normal distribution.

(x - 35.6)/10.3 = 0.54

x = 41.162 min

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It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.

Pooled variance is a statistical method used to estimate the common variance of two small independent samples when the population variances are assumed to be equal.

The pooled variance is calculated by taking the weighted average of the variances of the two samples.

This method is often used in inferential statistics to make inferences about the means of the two populations from which the samples were drawn.

The pooled variance is used to estimate the variance of the difference between the means of the two populations, which is used to calculate the standard error and the t-statistic for testing the difference between the means. Therefore, The statement is true.

so, It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.

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The probabilities are :

a) 0.8

b) 1/45

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Total no. of electrical parts = 10

No. of defective parts = 2

No. of non-defective parts = 10 - 2

                                        = 8

a) The probability of choosing a non-defective part from the box is 8/10 or 0.8.

b) The probability of choosing two defective parts in a row without replacement is (2/10) * (1/9) = 2/90 = 1/45.

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It is favorable to play this game.

This question requires a mathematical calculation of expected value to determine if the game is favorable or not.

The expected value is calculated as the sum of the product of each outcome and its corresponding probability.

The probability of winning $x for each prime number (2, 3, 5, 7) is 1/4, and the probability of losing $x/2 for each composite number (4, 6, 8, 9, 10) is 1/5.

Expected value = (1/4)*2x + (1/4)*3x + (1/4)*5x + (1/4)*7x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2

= (1/4)(2 + 3 + 5 + 7)x - (1/5)(x/2 + x + x/2 + x + x/2)

= (17/4)x - (5/2)x

= (17/4 - 5/2)x

= (3/4)x

Since the expected value is positive, it is favorable to play this game.

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It can be written as

y = -6/7x - 6/7 * x1 + y1

What is the slop?

The slope, also known as the gradient, is a measure of the steepness of a line. It tells us how much the y-coordinate of a point on the line changes as the x-coordinate changes. The slope is often represented by the letter "m" in the equation of a line. The slope is defined as the ratio of the rise (the change in y-coordinate) to the run (the change in x-coordinate) between two points on a line.

An equation of a line in slope-intercept form is:

y = mx + b

where:

m = slope of the line

x = variable of the line

y = variable of the line

b = y-intercept

Given the y-intercept is -6 and the slope is -6/7, we can substitute these values into the equation above:

y = -6/7x + -6

This equation of the line is in slope-intercept form, and it can be used to find the y-coordinate of any point on the line given the x-coordinate, or to find the x-coordinate of any point on the line given the y-coordinate.

You can also write it in point-slope form.

The point slope form is

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line.

So it can be written as

y = -6/7x - 6/7 * x1 + y1

Where the x1 and y1 are arbitrary value which lies on the line.

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The dimensions of the figure is 3.23 by 7.43

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

Side lengths = x and x + 4

Area = 24.5 square inches

The area of a rectangle is

Area = Product of dimensions

substitute the known values in the above equation, so, we have the following representation

x (x + 4.2) = 24.5

Using a graphing calculator, we have

x = 3.23

This means that

Other length = 4.2 + 3.23 = 7.43

Hence, the dimension is 3.23 by 7.43

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Answer:

To determine which of the given lines is parallel to the line y = 2/3x + 5, we need to compare their slopes. The slope of a line is the coefficient of the x variable, in this case 2/3.

The lines that are parallel have the same slope.

A.y=2/3x-4 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

B.y=2/3x-7 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

C.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

D.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

So the answer is A and B are parallel to the line y = 2/3x +5

Answer:5x - 8

Step-by-step explanation:

8x−9−(3x−1)8−9−(3−1)

8x−9−3x+18−9−3+1

8x−8−3x8−8−3

Answer:

Step-by-step explanation:

(8x−9)−(3x−1)

To find the opposite of 3x−1, find the opposite of each term.

8x−9−3x−(−1)

The opposite of −1 is 1.

8x−9−3x+1

Combine 8x and −3x to get 5x.

5x−9+1

Add −9 and 1 to get −8.

5x−8

Answer:

Step-by-step explanation:

Vertex:

(

−

5

3

,

−

10

)

Focus:

(

−

5

3

,

−

359

36

)

Axis of Symmetry:

x

=

−

5

3

Directrix:

y

=

−

361

36

x

y

−

3

6

−

5

3

−

10

−

1

−

6

0

15

Answer: 9x^2-48x+54?

Answer:

x = 2 , y = - 1

Step-by-step explanation:

2x + 6y = - 2 → (1)

- 6x - 8y = - 4 → (2)

multiplying (1) by 3 and adding to (2) will eliminate x

6x + 18y = - 6 → (3)

add (2) and (3) term by term to eliminate x

(- 6x + 6x) + (- 8y + 18y) = - 4 - 6

0 + 10y = - 10

10y = - 10 ( divide both sides by 10 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

2x + 6(- 1) = - 2

2x - 6 = - 2 ( add 6 to both sides )

2x = 4 ( divide both sides by 2 )

x = 2

If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

The direct variation equation is represented by the symbols y=kx or k=y/x, where k is the proportionality constant or variation constant.

A) The relationship between the distance traveled and the number of traveled hours is straightforward.

B ) The only distinction between x and y representing the length of a table is in units.As a result, it also differs directly.

The amount of money saved in C increases as more $1-off coupons are used, and vice versa.

If the speed is increased in D, it will take less time to travel 60 miles.As a result, there is no direct variation.

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The multiplication of the numbers is 50.547.

When given two or more numbers to be multiplied, it is expected to get the product of the numbers. Such that an answer i.e. the final value which can either be a whole number or a number with a decimal part is gotten.

Given that 5.81 is to be multiplied by 8.7, we have;

One way to do it is by expressing the numbers in a standard form, so that we have;

5.81 X 8.7 = (581 x 10^-2) x (87 x 10^-1)

multiplying the whole parts of the number, we have;

581 x 87 = 50547

and multiplying the exponential part, we have;

10^-2 x 10^-1 = 10^-3

So that;

581 x 10^-2 x 87 x 10^-1 = 50547 x 10^-3

                                       = 50.547

The multiplication gives 50.547.

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If knitting club sold 40 scarves and hats at a winter festival and made $700 from sales and charged $18 for each scarf and $14 for each hat , then the system of equations which represents the constraints in this situation is  s + h = 40 and 18s + 14h = 700    .

let the number of hats sold be = "h"  ;

and let number of scarves sold be = "s" ;

the total number of scarves and hats sold are 40 ;

the situation is represented as : h + s = 40  ...equation(1) ;

the per unit cost for each scarf is = $18  ;

the per unit cost for each hat is = $14  ;

the amount for which the items are sold is = $700 ;

this situation is represented as  : 18s + 14h = 700 ...equation(2) .

From equation(1) and equation(2)  , we can conclude that ;

the system of equation to represent the situation is , s + h = 40 and 18s + 14h = 700  .

The given question is incomplete , the complete question is

The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat. If s represents the number of scarves sold and h represents the number of hats sold, write system of equations which represents the constraints in this situation ? ​

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Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.

Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.

This is represented as follows:

t = k(l/p)

Where, k is the proportionality constant.

Given that, it takes 10 hours to paint 400 feet of fence with six workers.

Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:

10 = k (400 / 6)

10 = k (66.66)

k = 10 / 66.66

k = 0.15

Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:

t = (0.15) (1000 / 10)

t = (0.15) (100)

t = 15

Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

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Answer:

Hi, my name is Za'Riah! I will gladly help you with this problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out but here is the answer.

[tex]\frac{1}{2} - (\frac{1}{8}+ \frac{1}{8}) \\= \frac{1}{2} - \frac{1}{4} \\\\= \frac{1}{4}[/tex]

The system of equations have no solution, the correct option is A.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given;

-1/2x+1/2y=-1   (1)

x-y=2   (2)

Now, multiplying equation 1 by 2

-x+y=-2

y=-2+x

Substituting the value of y in equation 2

x+2-x=2

Therefore, the equation have no solution.

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The value of x from the triangle is x = 56°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be represented as ABC

Let the second triangle be represented as ABD

Now , the measure of side ABD = x°

In the triangle ABC ,

∠ACB = 180° - 104° ( angles on a straight line = 180° )

So , the measure of ∠ACB = 76°

And , the measure of side ∠ACB = measure of side ∠ABC ( given )

So , the measure of side ∠ABC = 76°

And , for a triangle ∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

The measure of ∠BAC = 180° - ( 76° + 76° )

The measure of ∠BAC = 28°

Now , the measure of ∠BAC + measure of ∠BAD = 90° ( given perpendicular line )

So , the measure of side ∠BAD = 90° - 28°

The measure of side ∠BAD = 62°

And , measure of side ∠BAD = measure of side ∠ABD ( given that they are similar )

So , the measure of side ∠ABD = 62°

And , for a triangle ∠A + ∠B + ∠D = 180°

Substituting the values in the equation , we get

The measure of side ABD = x° = 180° - ( 62° + 62° )

The measure of side ABD = x° = 180° - 124°

The measure of side ABD = x° = 56°

Hence , the measure of x is 56°

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Answer: He dies.

Step-by-step explanation: A train is extremely powerful. It would kill on impact most of the time.

Relative frequency distributions are generally more useful than frequency distributions when comparing identical-sized data sets.

Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

It is possible to display the frequency distribution of data in a table or graph. Frequency tables, histograms, and bar charts are a few popular ways to display frequency distributions.

Tables of frequencies: A frequency table is an easy way to show how frequently a certain value or feature occurs.

Assume, for instance, that we have gathered information on height from a sample of 50 kids.

Both histograms and bar charts use columns drawn on a graph to visually represent frequencies.

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Complete answer is:-

Fill in the blanks -

Relative frequency distributions are generally more useful than frequency distributions when comparing                  data sets

After evaluation of these value we get:

a) |5| = 5

b)|-5| = 5

c) -(5) = -5

d) -(-5) = 5

What is Integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

What is Modulus?

A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.

We are given some values to evaluate;

a) |5| = 5 (This is positve number so does not changes are made into it.)

b) |- 5| = 5 (Modulus has the property that it change every negative integer into positive integer)

c) - (5) = -5 (This number is multiplies by negative sign that's why it become negative integer.)

d) -(-5) = 5 (a negative integer multiplies with again negative sign so it become postive [- * -  = +])

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The simplified expression is  (11/12)x^2 - (161/10)x + (1/3)

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

(11/12x-5/6)(x-(2/5)

To simplify the expression (11/12x-5/6)(x-(2/5)) we need to use the distributive property

(11/12x-5/6)(x-(2/5)) = (11/12x)(x) - (11/12x)(2/5) - (5/6)(x) + (5/6)(2/5)

= (11/12)x^2 - (11/60)x - (5/6)x + (1/3)

= (11/12)x^2 - (161/10)x + (1/3)

So the simplified form of the expression is (11/12)x^2 - (161/10)x + (1/3)

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Answer: a) To find the mean and standard deviation of the difference of their times, we need to use the properties of normal distributions. When two independent normal random variables are subtracted, the mean and standard deviation of the difference can be found using the following formulas:

Mean of the difference = Mean of x - Mean of y

Standard deviation of the difference = √(Standard deviation of x^2 + Standard deviation of y^2)

Plugging in the given values:

Mean of the difference = Mean of Molesky - Mean of Liberty = 100 - 110 = -10

Standard deviation of the difference = √(8^2 + 10^2) = √(64 + 100) = √(164) = 12.8

So the mean of the difference of their times is -10 minutes and the standard deviation is 12.8 minutes.

b) To find the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day, we need to find the probability that the difference of their times is less than 0. Since the difference of their times is normally distributed with a mean of -10 and a standard deviation of 12.8, we can use the standard normal distribution table to find this probability.

To calculate the probability, we will standardize the distribution of the difference by subtracting the mean and dividing by the standard deviation.

z = (x - mean) / standard deviation

z = (-10) / 12.8 = -0.78125

Using a standard normal table we can find that P(z<-0.78125) = 0.22 or 22%

So the probability that Mr. Molesky will finish his game before Mr. Liberty on any given day is 22%.

Step-by-step explanation:

Bailee's annual income was deducted for FICA is approximately C. $2,164.95.

FICA, or the Federal Insurance Contributions Act, is a payroll tax that is used to fund Social Security and Medicare. The current FICA tax rate for Social Security is 6.2% and the current rate for Medicare is 1.45%.

To find out how much of Bailee's annual income was deducted for FICA, we can multiply her gross income during each pay period by the FICA tax rate and the number of pay periods in a year.

Since Bailee gets paid monthly, there are 12 pay periods in a year.

FICA = (Gross income * (6.2% + 1.45%)) *12

FICA = (2358.33 * (6.2/100 + 1.45/100)) * 12

FICA = (2358.33 * 0.0765) * 12

FICA = 179.95 * 12

FICA = $2159.4

So, $2159.4 of Bailee's annual income was deducted for FICA.

This closest answer to this is: C. $2,164.95

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Based on the investment amount, rate of interest and time, Rita earned more interest than Mita by $324.

Calculating simple interest in both the cases to find the earned interest. The formula for simple interest is as follows -

S.I. = PRT/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.

Interest earned by Rita -

S.I. = 6800 × 5 × 5/100

Performing multiplication and cancelling zero

S.I. = $1700

Interest earned by Mita -

S.I. = 8600 × 4 × 4/100

Performing multiplication and cancelling zero

S.I. = $1376

Difference in interest = Interest earned by Rita - Interest earned by Mita

Difference in interest = 1700 - 1376

Performing subtraction

Difference in interest = $324

The interest earned by Rita is more than the interest earned by Mita by $324.

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The number of days that it will take for there to be fewer than 1,500 tables in the warehouse is given as follows:

More 24 days.

The initial number of tables is given as follows:

2,100 tables.

They ship 25 tables daily, hence the function for the number of tables after n days is given as follows:

T(n) = 2100 - 25n.

There will be fewer than 1,500 tables after n days, for which;

T(n) < 1500

Hence:

2100 - 25n.< 1500

25n > 600

n > 600/25

n > 24.

Hence the time is more than 24 days.

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The length of diagonal BD from the parallelogram ABCD is 10.

E is the intersection of the diagonals BD and AC. The point of bisection is therefore designated E.

BE = DE (The diagonals of a parallelogram bisect each other) (The diagonals of a parallelogram bisect each other)

From the provided diagram:

BE = 5

DE = BE = 5

BD length equals BE plus DE

BD length equals (5 + 5) to 10.

ABCD is a parallelogram, what is the length of BD

Consequently, Diagonal BD is 10 in length.

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For the extra 30 feet of wire Jayden have to pay an amount of  $7.80  at a rate of $0.26 per feet.

In these type of problems, first we have to find out the unit price. First let's look at what data is available.

The length of wire Jayden bought = 70 feet

Amount Jayden paid for 70 feet = $ 18.20

Unit price or price of 1 feet of speaker wire =  Amount paid / length bought.

Unit price =  18.20/ 70 = 0.26.

So he have to pay 26 cents for each foot of wire.

Now let's calculate the amount for 30 feet of wire = Unit price × 30 = 0.26×30 = 7.80.

So Jayden have to pay $7.80 for the extra 30 feet of wire.

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Answer: A) 10√2

Step-by-step explanation:

You can find the value of x by using the Pythagorean Theorem.

a = 10

b = 10

c = x

a^2 + b^2 = c^2

(10)^2 + (10)^2 = c^2

100 + 100 = c^2

200 = c^2

Square root both sides.

c = √200

Simplify the square root. 100 x 2 is 200, and 100 is a perfect square.

√200 = √100√2

√100 can be simplified to 10. √2 can not be simplified.

The answer would be option A ) 10√2

The value of x in the given triangle is 10√2 units.

Pythagoras theorem states that in a right triangle the three sides are related by the formula, a²+b² = c², where c is the hypotenuse and a and b are the other two sides.

Given that, a triangle, we need to find the hypotenuse x,

Using the Pythagoras theorem,

10²+10² = x²

x² = 100 + 100

x² = 200

x = 10√2

Hence, the value of x in the given triangle is 10√2 units.

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