Precalculus.

Please show all your work and answer all the questions

Therefore, the factored form of the expression [tex]-5x^3+10x^2-3x+6 is -(5x^2+3)(x-2).[/tex]

In mathematics, a factor refers to a number or an algebraic expression that is multiplied by another number or expression.

For example, in the expression 6 x 8 = 48, 6 and 8 are factors of 48 because they are both multiplied together to get the product 48. Similarly, in the algebraic expression 3x(x+2), 3x and (x+2) are both factors of the expression.

by the question.

Question 4:

To factor the expression. [tex]2x^5+4x^3-6x^2-12[/tex], we can first take out a common factor of 2 from all the terms:

[tex]2(x^5+2x^3-3x^2-6)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]2(x^5+2x^3-3x^2-6) = 2(x^5-3x^2) + 2(2x^3-6)[/tex]

[tex]= 2x^2(x^3-3) + 4(x^3-3)= (2x^2+4)(x^3-3)[/tex]

Therefore, the factored form of the expression[tex]2x^5+4x^3-6x^2-12 is (2x^2+4)(x^3-3).[/tex]

Question 5:

To factor the expression [tex]3x^7-8x^6-9x^5+24x^4[/tex], we can first take out a common factor of [tex]3x^4[/tex] from all the terms:

[tex]3x^4(x^3-8x^2-3x+8)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]3x^4(x^3-8x^2-3x+8) = 3x^4(x^2(x-8)-1(x-8))= 3x^4(x-1)(x-8)(x^2+1)[/tex]

Therefore, the factored form of the expression[tex]3x^7-8x^6-9x^5+24x^4 is 3x^4(x-1)(x-8)(x^2+1).[/tex]

Question 6:

To factor the expression. [tex]-5x^3+10x^2-3x+6[/tex], we can first take out a common factor of -1 from all the terms:

[tex]-1(5x^3-10x^2+3x-6)[/tex]

Next, we can factor the expression in the parentheses by grouping the first two terms and the last two terms:

[tex]-1(5x^3-10x^2+3x-6) = -1(5x^2(x-2)+3(x-2))= -(5x^2+3)(x-2)[/tex]

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Answer:252

Step-by-step explanation:

14x18=252

Answer:

0.4 hours

Step-by-step explanation:

or 24 minutes :D

Answer:

[tex]2 \frac{8}{13} = 2.61[/tex]

Step-by-step explanation:

[tex]1. \: \frac{3 \times 5 + 2}{5} \div 1\frac{3}{10} \\ 2. \: \frac{15 + 2}{5} \div 1 \frac{3}{10} \\ 3. \: \frac{17}{5} \div 1 \frac{3}{10} \\ 4. \: \frac{17}{5} \div \frac{1 \times 10 + 3}{10} \\ 5. \: \frac{17}{5} \div \frac{10 + 3}{10} \\ 6. \: \frac{17}{5} \div \frac{13}{10} \\ 7. \: \frac{17}{5} \times \frac{10}{13} \\ 8. \: \frac{17 \times 10}{5 \times 13} \\ 9. \: \frac{170}{5 \times 13} \\ 10. \: \frac{170}{65} \\ 11. \: \frac{34}{13} \\ 12. \: 2 \frac{8}{13} = 2.61[/tex]

zorongo por federico garcia lorca

zorongo por federico garcia lorca

zorongo por federico garcia lorca

zorongo por federico garcia lorca

zorongo por federico garcia lorca

According to the given information, the cyclists will meet after x hours of riding, and the distance from the orchard where they meet is given by either A(x) or B(x)

What is speed?

Speed is defined as the distance traveled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance/time

where "distance" is the distance traveled by the object, and "time" is the time it takes for the object to travel that distance.

Let's assume that the distance function for cyclist A is given by: A(x) = ax + b, where a and b are constants that depend on the cyclist's speed and initial distance from the orchard, respectively.

Similarly, let's assume that the distance function for cyclist B is given by: B(x) = cx + d, where c and d are constants that depend on the cyclist's speed and initial distance from the orchard, respectively.

Since both cyclists left home at the same time, we know that their initial distance from the orchard must be the same. Therefore, we can set b = d and rewrite the distance functions as:

A(x) = ax + b

B(x) = cx + b

The cyclists will meet when their distances from the orchard are equal, so we can set A(x) = B(x) and solve for x:

ax + b = cx + b

ax - cx = b - b

x(a-c) = 0

Since x cannot be zero (they are riding for some positive amount of time), we know that a - c must be zero, which means that their speeds are equal:

a - c = 0

a = c

Therefore, we know that the cyclists are traveling at the same speed. To find the meeting point, we can set A(x) = B(x) = D, where D is the distance from the orchard where they meet, and solve for x:

ax + b = Dx

cx + b = Dx

ax + b = cx + b

ax - cx = 0

x(a-c) = 0

Since a = c, we can simplify this equation to:

x = 0 or x = D/(a-c)

Since we know that x cannot be zero (they left home at the same time and met later), we can conclude that:

x = D/(a-c)

Therefore, the cyclists will meet after x hours of riding, where x is given by the above formula, and the distance from the orchard where they meet is given by either A(x) or B(x) (they are equal at the meeting point).

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An equation for the function graphed above is [tex]y = \frac{4(x - 1)}{(x + 1)(x - 4)}[/tex].

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function shown above, we can logically deduce that its vertical asymptotes include the following;

x = -1 ⇒ x + 1 = 0.

x = 4 ⇒ x - 4 = 0.

In this context, an equation that represent its denominator is given by the following quadratic function:

Q(x) = (x + 1)(x - 4)

Assuming the leading coefficient of the function P(x) is represented by a;

P(x) = a(x - 1)

By evaluating and solving for the leading coefficient "a" in this function, we have;

f(x) = P(x)/Q(x)

f(x) = a(x - 1)/[(x + 1)(x - 4)]

f(0) = a(0 - 1)/[(0 + 1)(0 - 4)]

f(0) = -a/[(1)(-4)]

f(0) = a/4

Since the y-intercept of this graph is located at (0, 1), the value of the leading coefficient (a) can be calculated as follows;

1 = a/4

1 = a/4

a = 4 × 1

a = 4

By substituting the value of the leading coefficient (a) into the function, we have the following;

f(x) = P(x)/Q(x)

f(x) = y = 4(x - 1)/[(x + 1)(x - 4)]

[tex]f(x) = y = \frac{4(x - 1)}{(x + 1)(x - 4)}[/tex]

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As per the curve, the area under the shaded region is = 0.4878.

The entire area covered by a flat (2-D) area or the form of an item is known as area. A plane figure's area is the space that is enclosed by its border. The area of a closed figure is the sum of the number of unit squares that cover its surface. Square units like cm² and m² are used to quantify area.

99.7% (or 0.997) of the standard normal curve's entire area, which is 1, is located within three standard deviations of the mean.

The distribution of mean is μ = 0

The distribution of standard deviation is σ = 1

We must determine the area of the shaded zone according to the curve.

That is as follows:

P (-2.25 < Z < 0)

The formula to determine:

= P (Z < 0) - P (Z < -2.25)

Substitute the values in the above equation.

= 0.5 - 0.0122

The value is,

= 0.4878

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Answer:

Step-by-step explanation:

But we know that √5 is an irrational number. So, {(a - 3b)/b} should also be an irrational number. Hence, it is a contradiction to our assumption. Thus, 3 + √5 is an irrational number.

Answer:

x could equal -5 or 3

Step-by-step explanation:

3x - 45 = 12x

-45 = 9x

x = -5

3x - 45 = -12x

x = 3

Using the expression 2/7 × 28 it is obtained that Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The total number of pencils Professor Elena bought is  28 pencils.

If Professor Elena bought 28 pencils, and she distributed 5/7 of them to her students.

The fractional expression will be -

1 - 5/7

Simplifying the expression we get -

(7 - 7) / 2

2/7

Then she kept 2/7 of the pencils for herself.

The number of pencils she has with her will be -

2/7 × 28 = 8 pencils

Therefore, Professor Elena has 8 pencils left after distributing 5/7 of the pencils to her students.

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Professor Elena bought 28 pencils and distributed 5/7 of the pencils to her students. How many pencils did teacher Elena have left?​

Answer:

If the radius of the pastry stamp Petra uses to stamp circles in the dough for the donuts is 4.25 inches, then the diameter is 2 * 4.25 = 8.5 inches. The area of each donut can be calculated using the formula for the area of a circle:

Area of a circle = π * radius^2

So, the area of each donut is:

π * (4.25)^2 = 56.75π square inches (rounded to two decimal places)

If the radius of the pastry stamp Petra uses to stamp out circles for the donut holes is 0.4 inches, then the diameter is 2 * 0.4 = 0.8 inches. The area of each donut hole can be calculated using the same formula:

Area of a circle = π * radius^2

So, the area of each donut hole is:

π * (0.4)^2 = 0.16π square inches (rounded to two decimal places)

Hope This Helps!

The distance made good by the ship is approximately 259.5 nautical miles.

What is distance?

Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language.

To find the distance made good, we need to calculate the total displacement of the ship. This can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this case, the 120 nm southward and 230 nm westward movements of the ship form the legs of a right triangle, and the hypotenuse represents the total displacement. Using the Pythagorean theorem, we get:

Total displacement = √((120²) + (230²)) nm

= √(14400 + 52900) nm

= √(67300) nm

≈ 259.5 nm

Therefore, the distance made good by the ship is approximately 259.5 nautical miles.

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Vaccinations can prevent various infectious diseases including measles, mumps, rubella, polio, tetanus, pertussis, hepatitis A and B, varicella, HPV, and influenza.

One should consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and individual factors.

Vaccinations can prevent many infectious diseases, including:

Measles

Mumps

Rubella

Polio

Tetanus

Pertussis (whooping cough)

Hepatitis A and B

Varicella (chickenpox)

Human papillomavirus (HPV)

Influenza (flu)

Pneumococcal disease (pneumonia, meningitis, blood infections)

Rotavirus (diarrhea and vomiting)

Haemophilus influenzae type b (meningitis, pneumonia, and other infections)

Meningococcal disease (meningitis and blood infections)

Hepatitis A and B (liver infections)

and many others. It is important to consult with a healthcare professional to determine which vaccinations are recommended based on age, health status, and other individual factors

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The functiοns are f(-3)=2,  f(1)=4 and f(4)= -2.

In mathematics, a functiοn is  a relatiοn between a set οf inputs having οne οutput each. We can explain that  a functiοn is a relatiοnship between inputs where each input is related tο exactly οne οutput. A functiοn is generally denοted by g(x) where x is the input. The general representatiοn οf a functiοn is y = g(x).

The given cοοrdinates are (-3,2); (1,4);(4,-2)

Frοm the given cοοrdinates the functiοns can be fοrmed.

Let the functiοn be y=f(x)

Frοm the given cοοrdinate system the first value is x- value and the secοnd value is y-cοοrdinate.

Sο cοnsidering the first cοοrdinate -3 is the x-cοοrdinate and 2 is the y cοοrdinate and similarly fοr οthers.

Hence the functiοn will be f(-3)=2

Similarly frοm the secοnd cοοrdinate the functiοn will be f(1)=4

[ As 1 is the x- cοοrdinate and 4 is the y-cοοrdinate]

Frοm the third cοοrdinate the functiοn will be f(4)= -2

Hence, the functiοns are

f(-3)=2

f(1)=4

f(4)= -2

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Answer:

shortened height = h(1 - tan(20))

Step-by-step explanation:

To solve this problem, we need to use trigonometry to find the height that the airplane reaches at a 20° angle, and then subtract this height from the height of the cell tower to determine how short it needs to be.

Let's assume that the cell tower has a height of "h", and that the airplane takes off at a 20° angle. We can use trigonometry to find the height "x" that the airplane reaches above the ground:

tan(20) = x / h

Multiplying both sides by "h", we get:

x = h * tan(20)

So the airplane reaches a height of "x" above the ground. To find how short the cell tower needs to be, we simply subtract this height from the original height of the tower "h":

shortened height = h - x

Substituting the expression we found for "x", we get:

shortened height = h - h * tan(20)

Simplifying, we get:

shortened height = h(1 - tan(20))

So, the cell tower needs to be shortened by "h(1 - tan(20))" to ensure that the airplane can take off safely at a 20° angle.

The rectangle's perimeter is 42 inches as the rectangle's area is 80 square inches.

Perimeter = 2 (length + width)

given

The rectangle's area is 80 square inches, so this is the first known step.

The rectangle measures 5 inches long.

The rectangle's perimeter is unknown.

Step 2: To determine the width of the rectangle, we will utilise the variable "w."

The formula for calculating a rectangle's area is:

A = width x length

Inputting the values provided yields:

80 = 5w

With w solved, we obtain:

w = 16

Step 3: The equation for a rectangle's perimeter is:

P= 2 (length + width).

Inputting the values provided yields:

P = 2(5 + 16)

P = 2(21) (21)

P = 42

Step 4: The rectangle's perimeter is 42 inches as the rectangle's area is 80 square inches.

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Answer:

The best measure of center for the data shown is the median, and its value is 11.

Step-by-step explanation:

In statistics, measures of central tendency are used to summarize a set of data and provide a single value that represents the center or typical value of the data. The three commonly used measures of central tendency are the mean, median, and mode.

The mean is calculated by adding up all the values in the data set and dividing by the total number of values. The mean is affected by outliers and can be heavily skewed by extreme values.

The median is the middle value of the data set when the values are arranged in order. It is not affected by extreme values and is a more robust measure of central tendency compared to the mean.

In the given box plot, the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, which is the middle value of the box. Therefore, the best measure of center for the data shown is the median, and its value is 11.

The best measure of the center for the data shown is the median, and its value is 11 thus the correct option is  C.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

In statistics, the measures of central tendency are used to summarize a set of data and provide a single value that shows the center or typical value of the data. Also, it is known that three commonly used measures of central tendency are the mean, median, and mode.

The median is not affected by extreme values and is a more robust measure of central tendency compared to the mean.

In the given box plot, we can conclude that the distribution appears relatively symmetric, with the box extending from 9 to 15 on the number line and the median line located at 11, that is the middle value of the box. the median, value is 11.

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The length of side z to the nearest tenth of a centimeter is approximately 261.8 cm.

What is the Law of Sines?

The Law of Sines is a mathematical formula used to relate the side lengths and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

a/sin(A) = b/sin(B) = c/sin(C)

To find the length of side z in triangle XYZ, we can use the Law of Sines, which states:

a/sin(A) = b/sin(B) = c/sin(C)

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.

In this case, we know the length of side x, and the measures of angles Y and Z.

We want to find the length of side z. So, we can use the Law of Sines as follows:

z/sin(180° - 141° - 25°) = 830/sin(141°)

z/sin(14°) = 830/sin(141°)

Cross-multiplying:

z = (830*sin(14°))/sin(141°)

z ≈ 261.8 cm

Therefore, the length of side z to the nearest tenth of a centimeter is approximately 261.8 cm.

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Answer:

numbers are in a pattern

like

1234

2168

3092

4926

5850

so the next number would be

6774

The probability that 2 particular health professionals will be selected in the subcommittee is 4/15. There are 210 ways to select a subcommittee of 4 health professionals from the 10 total health professionals.

Probability acts as an indicator of how likely an event is to occur.

It is a number between 0 and 1, with 0 indicating an impossible event and 1 suggesting a certain event.

The number of favorable outcomes divided by the total number of possible outcomes yields the probability of an event.

The number of ways to select a subcommittee of 4 health professionals out of the 10 total health professionals is given by the combination formula:

C(10, 4) = 10! / (4! * 6!) = 210

To calculate the probability that 2 particular health professionals will be selected in the subcommittee, we need to consider the number of ways that we can choose the other 2 health professionals from the remaining 8. The number of such combinations is given by the combination formula:

C(8, 2) = 8! / (2! * 6!) = 28

So the probability that the subcommittee will consist of the 2 particular health professionals we are interested in, as well as 2 other health professionals, is:

(2 choose 2) * (8 choose 2) / (10 choose 4) = 1 * 28 / 210 = 4/15

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Answer:

Enter your answer as a decimal in the b

The value of the missing length indicated is 128 units.

Two or more triangles are said to be similar when on comparing their properties, they have some common relations. But similarity is not congruency.

Let the missing length indicated be represented by x. So that comparing the triangles, we have;

21/ 77 = 48/ (48 + x)

21(48 + x) = 48*77

1008 + 21x = 3696

21x = 3696 - 1008

      = 2688

x = 2688/ 21

  = 128

x = 128

The missing length indicated is 128 units.

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3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

What is the fraction?

A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities. It is expressed as one integer divided by another integer, with a horizontal line separating the two numbers. The number above the line is called the numerator and the number below the line is called the denominator.

To divide a fraction by another fraction, you need to multiply the first fraction by the reciprocal of the second fraction.

First, we need to convert the mixed number to an improper fraction:

1 3/5 = (5*1 + 3)/5 = 8/5

Now we can find the reciprocal of 8/5:

reciprocal of 8/5 = 5/8

So, 3/8 ÷ 1 3/5 can be rewritten as:

3/8 ÷ 8/5 = 3/8 * 5/8

Multiplying the numerators and denominators:

3/8 * 5/8 = (35)/(88) = 15/64

Therefore, 3/8 divided by 1 3/5 is 3/8 ÷ 1 3/5 = 15/64.

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The customer margin on sales to Interstate Trucking for the year is $33,581.

Indirect costs are expenses that cannot be directly linked to a specific product or service. Instead, they are costs that are incurred for the general operation of a business and are shared among different products or services produced by the business.

In the given question,

To calculate the customer margin on sales to Interstate Trucking, we need to use the activity-based costing system to allocate the indirect costs to the order and then subtract the total costs from the sales revenue. Here are the steps to follow:

Calculate the total indirect costs for the order:

Batch processing cost = Number of batches x Batch processing activity rate

Batch processing cost = 3 x $95 = $285

Order processing cost = Number of orders x Order processing activity rate

Order processing cost = 1 x $285 = $285

Customer service cost = Number of customers x Customer service activity rate

Customer service cost = 1 x $2,624 = $2,624

Total indirect costs = Supporting direct labor cost + Batch processing cost + Order processing cost + Customer service cost

Total indirect costs = Number of direct labor-hours x Supporting direct labor activity rate + Batch processing cost + Order processing cost + Customer service cost

Total indirect costs = 0.7 x 2,200 x $8 + $285 + $285 + $2,624

Total indirect costs = $20,289

Calculate the total costs for the order:

Total costs = Direct materials cost + Direct labor cost + Total indirect costs

Total costs = $110 x 2,200 + $13.70 x 2,200 + $20,289

Total costs = $147,739

Calculate the customer margin on sales:

Customer margin = Sales revenue - Total costs

Customer margin = $141.60 x 2,200 - $147,739

Customer margin = $181,320 - $147,739

Customer margin = $33,581

Therefore, the customer margin on sales to Interstate Trucking for the year is $33,581.

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The answer is A. 12.0. The mean absolute deviation MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units.

To calculate the Mean Absolute Deviation (MAD), we need to find the absolute difference between the actual demand and forecast demand, then take the average of those differences. The formula for MAD is:

[tex]MAD = (1/n) * Σ|A - F|[/tex]

where A is the actual demand, F is the forecast demand, and n is the number of observations.

Using the provided data, we can calculate the MAD for each week:

Week 1: |100 - 120| = 20

Week 2: |120 - 130| = 10

Week 3: |110 - 120| = 10

Week 4: |130 - 125| = 5

Week 5: |160 - 145| = 15

To calculate the MAD at the end of week 5, we need to add up the absolute differences and divide by the total number of observations:

MAD = (20 + 10 + 10 + 5 + 15) / 5 = 12

Therefore, the answer is A. 12.0. The MAD at the end of week 5 is 12.0, indicating that the average absolute difference between actual demand and forecast demand is 12 units. This question is related to the topic of forecasting and measures of forecast accuracy. Specifically, it involves calculating the mean absolute deviation (MAD) as a measure of forecast error.

The MAD provides a measure of forecast accuracy and can be used to evaluate the performance of forecasting methods and to make adjustments to improve the accuracy of future forecasts.

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Answer:

108.16 sq ft

Step-by-step explanation:

We know it is a square bedroom, meaning all sides are equal. So then we do 10.4*10.4 or 10.4^2 and get 108.16 sq ft

The equation of the circle after it is dilated by a scale factor of 2 is given as follows:

B. (x + 6)² + (y - 4)² = 36.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equation of the circle in this problem is given as follows:

(x + 3)² + (y - 2)² = 9.

The features are:

After the dilation by a scale factor of 2, the features are given as follows:

Then the equation of the circle would be of:

(x + 6)² + (y - 4)² = 36.

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The distance between E and the bottom of the tree, given the distance above the ground, is 7 m.

We are told that the tree is midway between points E and F. We are also told that points E and F are 14 meters away from each other.

The distance between E and the bottom of the tree would be half of the distance between E and point F because the tree is located midway between both points.

The distance between E and the bottom of the tree is therefore:

= 14 / 2

= 7 m

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