Which expression is equivalent to 6x2 – 19x – 55?

The expression 5/(x - 1) using the least common denominator, multiply the numerator and denominator by (x - 1). This ensures that the expression has the same value but with a common denominator.

1. Identify the least common denominator (LCD) of the fractions involved in the equation. In this case, the denominators are (x - 1), 4, and x. The LCD is the smallest multiple that includes all these denominators, which is 4 * (x - 1) * x.

2. To rewrite the expression 5/(x - 1) using the LCD, multiply both the numerator and denominator of the fraction by (x - 1). This step eliminates the denominator (x - 1) in the numerator, resulting in 5.

  5/(x - 1) * (x - 1)/(x - 1) = 5(x - 1)/(x - 1)(x - 1) = 5x - 5/(x - 1)(x - 1)

3. The expression 5x - 5/(x - 1)(x - 1) is the rewritten form of the original expression 5/(x - 1) using the least common denominator (x - 1)(x - 1).

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Answer:

y=6/5x+8/5

Step-by-step explanation:

find the slope (6/5) you can find this by making a slope triangle between the 2 points.

now, plug in a point to y=6/5x+b

-2=6/5(-3)+b

-2=-18/5+b

-10/5=-18/5+b

b=8/5 (y-int)

so y=6/5x+8/5

The solution is 44 copies

The number of copies the copy machine makes in one minute is 44 copies

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The number of copies the copy machine makes = 231 copies

Time required by the to make 231 copies = 5 minutes 15 seconds

5 minutes = 5 x 60 seconds

5 minutes = 300 seconds

5 minutes 15 seconds = 300 + 15 seconds

5 minutes 15 seconds = 315 seconds

So , Time required by the to make 231 copies = 315 seconds

Now , number of copies in 1 minute = 60 x ( The number of copies the copy machine makes / Time required by the to make 231 copies )

Substituting the values in the equation , we get

Number of copies in one minute A = 60 x ( 231 / 315 )

Number of copies in one minute A = 60 x 0.733

Number of copies in one minute A = 44 copies

Therefore , the value of A is 44 copies

Hence , the number of copies is 44 copies

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The derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.

This problem involves using the concept of the derivative to calculate the change in the output variable y, given a small change in the input variable x.

Specifically, we are given the function y = f(x) = -2x, the value of x at which we want to evaluate the change, x = 2, and the size of the change in x, δx = 0.2.

To find the corresponding change in y, δy, we can use the formula δy = f'(x) * δx, where f'(x) is the derivative of f(x) evaluated at x.

In this case, the derivative of f(x) is f'(x) = -2, so we can substitute these values into the formula to get δy = -2 * 0.2 = -0.4.

This tells us that a small increase of 0.2 in x will result in a decrease of 0.4 in y, since the derivative of the function is negative.

This problem illustrates the concept of local linearization, which is the approximation of a nonlinear function by a linear function in a small region around a point.

The derivative of the function at a point gives us the slope of the tangent line to the function at that point, and this slope can be used to approximate the function in a small region around the point.

This approximation can be useful for estimating changes in the output variable given small changes in the input variable.

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a-7x

in this case we can forget about the brackets, we can add 4x with 3x to get 7x, and add 6 to -6 which gives us 0, therefore we lose it and are left with only 7x

Answer:

a. 7x

Step-by-step explanation:

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

= 4x - 6 + 3x + 6

Combine like terms

= 4x + 3x - 6 + 6

= 7x

Ans: a. 7x

The advantage of using the range as a measure of variability is that it provides an account of the dataset's most extreme values.

The range is calculated by subtracting the minimum value from the maximum value in a dataset. By considering the minimum and maximum values, the range gives us an idea of the spread or dispersion of the data.

It provides information about the dataset's most extreme values, allowing us to understand the range over which the data values vary.

However, it's important to note that the range has limitations as a measure of variability. It only considers the minimum and maximum values and does not take into account the distribution or the values in between.

It does not provide a comprehensive summary of the patterns with which values cluster within the distribution, and it does not capture the shape of the distribution.

Therefore, while the range is a simple and straightforward measure of variability, it may not fully represent the overall characteristics of the dataset.

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The value of x corresponds to option B: 10.5 as the figure provided has two congruent figures inside it.

From the given image, we can consider that that the two triangles- one for which side x is given, and another for which measurements of both sides are given- are congruent. This is because they both have one common side and one angle equal to another at a vertex (refer image).

Thus, we have:

(x / 19.3) = (3.9 / 7.2)

Then, attempting to find the value of x we have:

x = (3.9 / 7.2) × (19.3)

= 10.5

Therefore, option B gives the measure of the side x of the given triangle, where x = 10.5.

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Answer:

$35.00

Step-by-step explanation:

Add the exacted prices of the five books together.

5.99 + 6.00 + 6.45 + 7.75 + 7.99 = 34.18

The number closest to 34.18 on the list of choices is 35.00.

Have a nice day :)

The expression (c - 4)³ in the expanded form will be c³ - 12c² + 48c - 64.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given as,

⇒ (c - 4)³

Expand the expression, then we have

⇒ (c - 4)³

⇒ (c - 4)(c - 4)(c - 4)

⇒ (c² - 4c - 4c + 16)(c - 4)

⇒ (c² - 8c + 16)(c - 4)

⇒ c³ - 4c² - 8c² + 32c + 16c - 64

⇒ c³ - 12c² + 48c - 64

The expression (c - 4)³ in the expanded form will be c³ - 12c² + 48c - 64.

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Answer:

I___

Step-by-step explanation:

Answer:

B). ∠BAC and ∠CAD

C). ∠BAE and ∠EAD

D). ∠EAD and ∠DAC

Step-by-step explanation:

As we know, a linear pair consisting of angles at a single point of the line has a sum of 180° in total. In other words, two supplementary angles together comprise a linear pair. In the given figure, the pair of supplementary angles ∠BAC and ∠CAD, ∠BAE and ∠EAD, and ∠EAD and ∠DAC are the linear pairs as their sum is 180°. Thus, options B, C, and D are the correct answers.

Step-by-step explanation:

EAD ∠BAC and ∠CAD ∠BAE

Answer:

A. 27 ft^3

Step-by-step explanation:

cube root of 729 is

9

1/3 of 9 is

3

volume of a cube with an edge of 3 is

3^3 =

27

We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

With the aid of a statistical test, researchers weigh the evidence in favor of and against the null and alternative hypotheses, which are two opposing claims: The null hypothesis (H0) states that there is no population impact. Alternative hypothesis (Ha or H1): The population is affected.

Given,

Among susceptible individuals exposed to a particular infectious agent 30% generally develop clinical disease. out of a random sample of 100 people suspected of exposure to the agent only 20 developed clinical disease.

Let X be the random variable to determine the proportion of people who have clinical illness.

n: The overall number of people who were exposed to a specific infectious pathogen.

p: The percentage of sample members who have a clinical illness.

Selected subjects who experience clinical disease are the experiment's success.

As a result, the variables are n = 100 and p = 0.30.

It is necessary to determine whether exposure to the agent outcome may be entirely accounted for by coincidence.

A P-value is a probabilistic indicator of the likelihood that an observed outcome effect is accidental.

Using the default level of significance = 0.05, the level of significance is not defined.

One percentage z-test is the best suitable test for the aforementioned assertion.

The alternate and null hypothesis is

H0: p = 0.3

H1:: p ≠ 0.3

Where p is the percentage of the population that develops a clinical illness.

R may be used to calculate the p-value and test statistic.

The instruction is as follows:

x = 20; n = 100; p = 0.3; prop.test

The result looks like this: - The p-value obtained from the output above is 0.03817.

Decision principle:

When significance is 5%,

If the p-value is below 0.05, reject the null hypothesis.

Accept the contrary.

Because the p-value was 0.03817 0.05

The null hypothesis is disproven.

In conclusion:

We draw the conclusion that the results are significantly different since the null hypothesis was rejected, which means that a different proportion of people than 0.3 had clinical illness.

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Answer:

y = 4x + 9, y = -3x - 5

y = 2x + 5, y = 5x + 11

and y= 3x + 7, y = -x - 1

I just did this on Plato/Edmentum xD

The system of equations that intersect at point A = (-2, 1) is:

y = 4x + 9

y = -3x - 5

y = 2x + 5

y = 5x + 11

y = 3x + 7

y = -x - 1

We have,

Let's substitute the coordinates (-2, 1) into each equation to find the correct system of equations:

y = 10x - 1

Substituting (-2, 1):

1 = 10(-2) - 1

1 = -20 - 1

1 = -21 (Not satisfied)

y = 4x + 9

Substituting (-2, 1):

1 = 4(-2) + 9

1 = -8 + 9

1 = 1 (Satisfied)

y = -3x - 5

Substituting (-2, 1):

1 = -3(-2) - 5

1 = 6 - 5

1 = 1 (Satisfied)

y = 2x + 5

Substituting (-2, 1):

1 = 2(-2) + 5

1 = -4 + 5

1 = 1 (Satisfied)

y = x - 1

Substituting (-2, 1):

1 = -2 - 1

1 = -3 (Not satisfied)

y = 5x + 11

Substituting (-2, 1):

1 = 5(-2) + 11

1 = -10 + 11

1 = 1 (Satisfied)

y = 3x + 7

Substituting (-2, 1):

1 = 3(-2) + 7

1 = -6 + 7

1 = 1 (Satisfied)

y = -x - 1

Substituting (-2, 1):

1 = -(-2) - 1

1 = 2 - 1

1 = 1 (Satisfied)

Thus,

The system of equations that intersect at point A = (-2, 1) is:

y = 4x + 9

y = -3x - 5

y = 2x + 5

y = 5x + 11

y = 3x + 7

y = -x - 1

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Answer:

subtract from both sides and then multiplying both sides

Step-by-step explanation:

how can you solve y = -2x + 25 by subtraction

Answer:

90/100

Step-by-step explanation:

if you look at the graph on the bottom part it tells you the study time if you line it the left side which says the test score. so if they studied for 80 mins they are expected to have the score of between 85 and 90.

Answer:

B=70.41 m^2V=675.41 m^3

Step-by-step explanation:

I'm in a hurry

The length of the segment in the complex plane is 5.

The length of a segment in the complex plane can be found using the distance formula. To find the length of the segment with endpoints at 4+2i and 7-2i, we can use the formula:

Distance formula = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of the first endpoint are x1 = 4 and y1 = 2i, while the coordinates of the second endpoint are x2 = 7 and y2 = -2i.

Plugging these values into the formula, we have:

Distance = sqrt((7 - 4)^2 + (-2 - 2)^2)
         = sqrt(3^2 + (-4)^2)
         = sqrt(9 + 16)
         = sqrt(25)
         = 5

Therefore, the length of the segment in the complex plane is 5.

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Answer:

l = 40 m

Step-by-step explanation:

The formula for area of a rectangle is

A = lw, where

Step 1:  Since we're given the area and width, we plug in these two values for A and w and to solve for l (length):

360 = 9l

Step 2:  Divide both sides by 9 to solve for l

(360 = 9l) / 9

40 m = l

Optional Step 3:  We can check our answers by checking that the product of 40 and 9 is 360

40 * 9 = 360

360 = 360

The equation (4^a)^b = 256 / x^8 is given. We need to solve for the values of a and b.

To solve the equation (4^a)^b = 256 / x^8, we can simplify the left side of the equation using the exponent rules.

Recall that when we raise an exponent to another exponent, we multiply the exponents. Applying this rule, we have (4^a)^b = 4^(a*b).

Now, the equation becomes 4^(a*b) = 256 / x^8.

To further simplify, we need to express both sides of the equation with the same base. Since 256 is a power of 4 (4^4 = 256), we can rewrite the right side as 4^(4 * (8/2)) = 4^(4 * 4) = 4^16.

Therefore, we have 4^(a*b) = 4^16. In order for the bases to be equal, the exponents must also be equal.

Hence, we have a*b = 16.

To solve for the values of a and b, we need additional information or constraints provided in the problem. Without such information, we cannot determine the specific values of a and b that satisfy the equation.

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Complete Question - What are the values of a and b in the equation (4 x Superscript a Baseline) Superscript b Baseline = StartFraction 256 Over x Superscript 8 EndFraction?

Answer:3

PLEASE GIVE BRAINLIEST IT HELPS ALOT. THANKYOU.

Scenario: A small business owner needs to analyze their sales data to make informed decisions about pricing and profitability.

Supporting Detail 1: The concept of linear equations can be applied to determine the break-even point and set optimal pricing strategies for the business.

Worked Example 1: Let's say the small business sells a product for $10 each, and the fixed costs (expenses that don't vary with the number of units sold) amount to $500. The variable costs (expenses that depend on the number of units sold) are $2 per unit. We can use the formula for a linear cost equation (C = mx + b) to find the break-even point where revenue equals total costs:

10x = 2x + 500

Simplifying the equation, we get:

8x = 500

x = 500/8

x = 62.5

The break-even point is 62.5 units. Knowing this information, the business owner can make decisions about pricing, cost control, and production targets.

Supporting Detail 2: The concept of systems of equations can be applied to optimize the allocation of resources in the business.

Worked Example 2: Let's consider a scenario where the business owner sells two different products. Product A generates a profit of $5 per unit, while Product B generates a profit of $8 per unit. The business owner has a limited budget of $500 and wants to determine the optimal allocation of resources between the two products. We can set up a system of equations to represent the profit constraints:

x + y = 500 (total budget)

5x + 8y = P (total profit, represented as P)

By solving this system of equations, the business owner can find the optimal values of x and y that maximize the total profit while staying within the budget constraints.

Conclusion: Applying concepts from this algebra course to real-life scenarios, such as analyzing sales data for a small business, helps in understanding the material by providing practical applications. It demonstrates the relevance of algebra in making informed decisions, optimizing resources, and maximizing profitability.

These examples highlight how algebraic concepts enable problem-solving and provide valuable tools for individuals in various fields, including business and entrepreneurship.

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The velocity of the ball thrown by your friend is approximately 4.17 meters per second.

To ascertain the speed of the ball, we want to utilize the condition of movement that relates distance, time, and speed increase. For this situation, we expect that the ball goes in an orderly fashion, and its speed increase is because of the power applied by your companion's toss. We can utilize the recipe:

distance = speed x time

We realize that the distance among you and your companion is 5 meters, and the time taken for the ball to travel that distance is 1.2 seconds. Hence, we can revise the equation to tackle for the speed:

speed = distance/time

Subbing the qualities, we get:

speed = 5/1.2 = 4.17 meters each second (approx.)

So the speed of the ball tossed by your companion is around 4.17 meters each second.

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please help me in this page

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and click to thanks because i need points.

and need to ask more questions

here is your answer

The measure of ∠5 is 64°.

In other words: m∠5 = 64°.

Using the formula for the crude birth rate we find out that the crude birth rate for the country Poland is 9.78.

It is given to us that -

There were 375,160 births in Poland

The population counted 38,346,279 people

We have to find out the crude birth rate for this country.

The crude birth rate of a country can be defined as the ratio between the number of live births that happened in a population for a given year and the total population of the country for that particular year and then multiplying the ratio by 1000.

So, the crude birth rate for the country, Poland with 375,160 births and population of 38,346,279 people can be given as -

\((\frac{375160}{38346279}) * 1000\\= 9.78\)

Therefore, the crude birth rate for the country Poland is 9.78.

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The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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\(|2x+3| > 5\\2x+3 > 5 \vee 2x+3 < -5\\2x > 2 \vee 2x < -8\\x > 1 \vee x < -4\\x\in(-\infty,-4)\cup(1,\infty)\)

Answer:

72 mins

Step-by-step explanation:

The number of minutes Sam spent on exercising is 72 minutes. Therefore, option B is the correct answer.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is y = -0.78x + 95

Let x be the number of minutes of television Sam watched each day and y the number of minutes she spent exercising.

Here, x=30

Substitute x=30 in the given function, we get

y = -0.78(30)+95

= -23.4+95

= 71.6

≈ 72 minutes

Therefore, option B is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

The table compares x, the number of minutes of television Sam watched each day, to y, the number of minutes she spent exercising. The function y = -0.78x + 95 models the data in the table.

Which is the best prediction for the number of minutes of exercising Sam will do if she spends 30 minutes watching television that day?

A. 45 minutes

B. 72 minutes

C. 83 minutes

D. 118 minutes