Find the equation for the line through the points (2,3) and (7,1)

Answer:

Step-by-step explanation:

To calculate 8% of 350, we can first calculate 1% of 350 and then multiply it by 8.

1% of 350 is equal to 0.01 times 350 which can be calculated as:

0.01 * 350 = 3.5

Since 1% of 350 is equal to 3.5, 8% of 350 can be calculated as follows:

8 * 3.5 = 28

So, 8% of 350 is equal to 28.

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

Explanation:

If we plugged x = 4 into the expression, then we'll have 0 in the denominator. This causes a division by zero error.

Luckily the numerator factors to (x-4)(x-2)^2. This is found by using the Rational Root Theorem, along with either synthetic division or polynomial long division. I'll skip these steps unless you need me to write them out.

Once we know the numerator factors this way, we can then write the following steps:

[tex]L = \displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}\frac{(\text{x}-4)(\text{x}-2)^2}{\text{x}-4}\\\\\\L = \displaystyle \lim_{\text{x}\to4}(\text{x}-2)^2\\\\\\L = (4-2)^2\\\\\\L = 4\\\\\\[/tex]

Therefore,

[tex]\displaystyle \lim_{\text{x}\to4}\frac{\text{x}^3-8\text{x}^2+20\text{x}-16}{\text{x}-4}=4\\\\\\[/tex]

You can use graphing software like Desmos or GeoGebra to confirm the answer is correct. WolframAlpha is another good choice.

You made a profit of $382.50 from selling the 45 shares of the telecommunications company.

First we need to determine the total cost of purchasing those shares, and then subtract that from the total revenue from selling them.

The total cost of purchasing the 45 shares at a price of $63.00 per share is:

45 shares x $63.00 per share = $2,835.00

The total revenue from selling the 45 shares at a price of $71.50 per share is:

45 shares x $71.50 per share = $3,217.50

To calculate the profit, we subtract the cost from the revenue:

Profit = Revenue - Cost

Profit = $3,217.50 - $2,835.00

Profit = $382.50

Therefore, you made a profit of $382.50 from selling the 45 shares of the telecommunications company.

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Answer:

Width: [tex]9[/tex] Length: [tex]21.[/tex]

Step-by-step explanation:

Let's say [tex]l[/tex] is the length, and [tex]w[/tex] is the width. We can rewrite [tex]l[/tex] as [tex]2w + 3.[/tex] So  [tex]2(2w + 3) + 2w = 60,\\4w + 6 + 2w = 60,\\6w + 6 = 60,\\6w = 54,\\w = 9.\\[/tex]So the length of the rectangle is [tex]2 \cdot 9 + 3 = 21[/tex] and the width is [tex]9.[/tex]

Hope that helps!

Answer:

5

Step-by-step explanation:

The expression 5^2.5^0 is equal to 5^(2.5^0), which can be simplified as follows:

2.5^0 = 1 (because any number raised to the power of 0 is equal to 1)

So, 5^2.5^0 = 5^1 = 5

Therefore, the answer is 5.

Answer:

661,068.8j

Step-by-step explanation:

The car has 661068.8 J of potential energy at a height of 62 m having a mass of 1088 grams.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.

We know, The gravitational constant is 9.8 m/s².

From the given information, m = 1088 grams, h = 62 meters.

Therefore, The amount of potential energy the car has is,

PE = mgh.

PE = 1088×9.8×62 J.

PE = 661068.8 J.

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The second telephone pole is 72 feet tall. Since the ratio of the height of the first telephone pole to the length of its shadow is 24/6 = 4.

We can use this ratio to find the height of the second telephone pole.

If the second telephone pole casts a shadow of 18 feet at the same time of day, we can set up the following proportion:

height of second pole / length of shadow of second pole = height of first pole / length of shadow of first pole

Letting x be the height of the second pole, we can plug in the values we know and solve for x:

x / 18 = 24 / 6

Multiplying both sides by 18, we get:

x = 72

Therefore, the second telephone pole is 72 feet tall.

The answer is (e) 72.

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Complete question:

On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.

a. 6

b. 12

c. 24

d. 36

e. 72

The solution for x in the trapezoid is x = 12

The midsegment of a trapezoid is a line segment that connects the midpoints of the parallel sides of the trapezoid.

The midsegment of a trapezoid is parallel to the bases of the trapezoid and is equal in length to half the sum of the lengths of the two bases. That is:

DE = 1/2 * (KL + JM)

14 = 1/2 * (11 + 3x - 19)

14 = 1/2 * (3x - 8)

14 * 2 = 3x - 8

28 = 3x - 8

3x = 28 + 8

3x = 36

x = 36/3

x = 12

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Answer:

The solution is 13

Step-by-step explanation:

x+8/3 = 7

x+8 = 7×3

x+8 = 21

x = 21-8

x = 13

The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.

The coordinates of the point A are (-3, -2).

If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.

Using the Pythagoras theorem:

c² = a² + b²

Substituting the values:

c² = (2)² + (3)²

c = √13

Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.

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Answer:

The product of (4 + 3i)(5 - 2i) can be calculated using the distributive property:

(4 + 3i)(5 - 2i) = 4 × 5 + 4 × -2i + 3i × 5 + 3i × -2i

= 20 - 8i + 15i - 6i^2

= 20 + 7i - 6(-1)

= 26 + 7i

So the answer is (4) 26 + 7i.

I believe the answer is (d) 26 + 7i.

For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

What is Inequalities?

Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.

Let's call the number of $10 notes Mrs. Chong used as "x".

We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:

10x + 5y + 2z = 64

Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).

We can substitute x = 15 - y - z into the first equation:

10(15 - y - z) + 5y + 2z = 64

Expanding the equation:

150 - 10y - 10z + 5y + 2z = 64

Combining like terms:

150 - 5y + 3z = 64

Subtracting 150 from both sides:

-5y + 3z = -86

Dividing both sides by -5:

y - (3/5)z = 17.2

So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

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Percentage of change in the stock's price since the beginning of the year is: 12.32%

The price at which a stock's share is currently trading on the market is referred to as the stock price. Every publicly listed company issues its shares at a price, which is an estimation of their value that, ideally, corresponds to the worth of the firm itself.

The market forces of supply and demand govern a company's share price once it becomes public and its shares begin trading on a stock exchange. Price increases will occur if there is a large demand for its shares. A stock's price might be reduced by sellers if the company's prospects for future growth appear uncertain.

Given that,

Closing price today = $21.20

Closing price on the previous trading day= $28.83

Difference between closing price today and closing price on the previous trading day= $21.20 - $28.83

= $7.63

Percentage of change in the stock price since the beginning of the year

= Year-to-date % change

= 12.32%

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Answer:

Step-by-step explanation:

If you took many random samples of a variable with a BIMODAL distribution, the means of your random samples would follow a normal distribution.

If you took many random samples of a variable with a VERY SKEWED distribution, the means of your random samples would follow a normal distribution. This is due to the Central Limit Theorem, which states that as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that, as the sample size increases, the distribution of the sample means approaches a normal distribution, regardless of the shape of the underlying population distribution. This means that even if the original population distribution is skewed, bimodal, or any other shape, the distribution of the sample means will tend towards a normal distribution as the sample size increases.

The reason for this is that the sample means are essentially an average of a number of independent random variables, and the normal distribution is the result of the combination of many independent random variables. When the sample size is large, the distribution of the sample means becomes very close to a normal distribution, even if the underlying population is far from normal.

In the case of a bimodal distribution, the sample means will still approach a normal distribution as the sample size increases, but the distribution may have a different mean and standard deviation than the original population.

In the case of a very skewed distribution, the sample means will also approach a normal distribution as the sample size increases, but the distribution may still be skewed, just less so than the original population.

In conclusion, the Central Limit Theorem states that the distribution of the sample means will tend towards a normal distribution as the sample size increases, regardless of the shape of the underlying population distribution.

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Answer: $9080.13

Step-by-step explanation:

use the equation y=b(x)^t, where b is the original profit, x is the percent remaining after one year, and t is the amount of years.

SUBSTITUTE:

y=9500(0.991)^5

Use calculator, and y=9080.126 in 2019. Round off to $9080.13

hope this helps!

MM

Answer:

r = 4 cos(2θ)

See the attached image for a graph.

Step-by-step explanation:

The points given by the table are in the graph of a cosine rose with 4 petals whose amplitudes are 4.

For the equation r = a cos(nθ), a is the amplitude of the petals (4), and n is half the number of petals, as there are an even number of petals (4/2 = 2).

Hence,

r = 4 cos(2θ)

The rate of change of the function on the interval specified as in the task content is; 7.

It follows from the task content that the rate of change of the function on the interval specified for the real number h  f(x) = 7x+4 on [ x,x+h] is to be determined.

Since the function is a linear function, it follows that the rate of change is a constant and hence is given by;

f'(x) = 7.

Ultimately, the rate of change of the function on the given interval is; 7.

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Answer: 4745

Step-by-step explanation:

3250 = 100%

Percent Increase = +46%

46% of 3250 = 1495

3250 (100%) + 1495 (46%) = 4745

The number of bees that will equal the mass of a single moose is 5 × 10⁶.

Given the data in the question;

To determine the number of bees that will equal the mass of a single moose.

Let the number be represented by x.

Hence;

Number of bees × mass of bee = mass of moose

n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³

Divide both sides by ( 2.5 × 10⁻⁴ ).

n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )

n = 1250 / 0.00025

n = 5,000,000

Therefore, the number of bees is 5,000,000.

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[tex]a*b[/tex] must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

Let n be an integer and a, b be relatively prime integers, each of which divides n. This means that a and b have no common factors other than 1. According to the Fundamental Theorem of Arithmetic, the prime factorization of n can be written as n = p1^k1 * p2^k2 * ... * pn^kn. Since a and b divide n, each of their prime factorizations must contain all of the prime factors of n, and the exponents must be less than or equal to the exponents of n. Therefore, a*b must contain all of the prime factors of n and the exponent of each factor must be less than or equal to the exponent of n. This means that a*b divides n.

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The value in 6 years is $3050.43

The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life.

Using the formula:

Value = P(1-r)^n

From the question, the original value is $9,000, the depreciation rate is 16.5% or 0.165, and the time is 6 years. Plugging in the values:

Putting the values into the formula

Value = 9000(1-0.165)^6

Value = 3050.43

Hence, the value of the car after 6 years will be $3050.43

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Answer:  Weight of water in 1 cubic foot water (in pounds)

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Given: One cubic foot holds 7.48 gallons of water.

One gallon of water weighs 8.33 pounds.

To find the weight of water in 1 cubic foot water in pounds we apply Unitary method.

Weight of water in 1 cubic foot water (in pounds)

⇒Weight of water in 1 cubic foot water (in pounds)

Since , 1 pound = 16 ounces .

Weight of water in 1 cubic foot water (in ounces)=

Step-by-step explanation:

Answer:384 children and 123 adults swam at the public school.

Step-by-step explanation:

The required proof has been below that ΔJKL ≅ ΔLMN due to the SAS postulate.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.

The triangles are given in the question, as shown.

As per the given figure, we have

JK = LM

∠LJK ≅ ∠NLM (same side inner angles)

Since L is the midpoint of JN. (Definition of midpoint)

Then JL ≅ LN

Now, for triangles ΔJKL and ΔLMN

JK ≅ LM (sides)

∠LJK ≅ ∠NLM (angle)

JL ≅ LN (sides)

By SAS postulate, ΔJKL ≅ ΔLMN.

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Answer:

The equation of the line that passes through (-2, 3) and is parallel to 2x + 3y = 6 is 2x + 3y - 5 = 0.

Step-by-step explanation:

The linear inequality to represent given situation will be 127+18x≥390 where x=no. of weeks and he will take 14.6 weeks to reach his goal.

What is a linear inequality, exactly?

In mathematics, an inequality is a mathematical statement that does not have equal sides. In mathematics, an inequality occurs when a connection results in a non-equal comparison of two expressions or two numbers. In the statement, any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), can be used to replace the equal sign "=". Inequalities are grouped into three forms in mathematics: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols " <and >" represent severe disparities, whereas " ≤ and ≥ " represent slack inequalities. A linear inequality resembles a linear equation, but the formula is different.

Now,

Total miles to run=390 mile

He already ran=127 mile

Distance left to run=390-127

=263 mile

Rate of running=18 miles/ week

weeks taken to complete 263 miles=263/18

=14.6 weeks

and given situation can be represented by inequality 127+18x≥390 where x=no. of weeks.

Hence,

          The linear inequality to represent given situation will be 127+18x≥390 and he will take 14.6 weeks to reach his goal.

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Answer:

A. 513 cubic units

Step-by-step explanation:

trust me bro.

Answer:

choice C.  y = -4/3x + 2

Step-by-step explanation:

slope of a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the first line.

m = -4/3  (negative reciprocal of 3/4)

Now use point-slope form to find the y-intercept (b):

y-2 = -4/3(x-0)

y = -4/3x + 2