What is the volume of the rectangular prism?



Responses

1214
cubic inches
12 and 1 fourth cubic inches

1034
cubic inches
10 and 3 fourths cubic inches

914
cubic inches
9 and 1 fourth cubic inches

734
cubic inches

Answers

Answer 1

The volume of a rectangular prism is -

V = Length x width x height

V = L x B x H

What is volume?

Volume is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫∫ F(x, y, z) dx dy dz

Given is a rectangular prism.

The volume of a rectangular prism is the measurement of the total space inside it. Since the image of the prism is not given, we can write the volume of a rectangular prism as -

V = Length x width x height

V = L x B x H

Therefore, the volume of a rectangular prism is -

V = Length x width x height

V = L x B x H

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Related Questions

216,777777 to 2 decimal places​

Answers

The round-off of the number 216,777777 to 2 decimal places​ is 216.78.

What is the rounding off to the number?

When a number is rounded off, its value is preserved while it is moved closer to the next number. simplifying the number. It is done for whole numbers as well as decimals at different places of hundreds, tens, tenths, and so on.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. If the number after it is between 5 and 9, it will be rounded up to its higher value.

To round 216,777777 to 2 decimal places, we look at the third decimal place, which is 7. Since 7 is greater than or equal to 5, we round up the second decimal place, which is 7. Therefore, 216,777777 rounded to 2 decimal places is 216,78.

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40% of the books on a bookshelf were non-
fiction.
Kian removed 6 of the non-fiction books and
there are now 22 non-fiction books on the
bookshelf.
How many books were there in total to start
with?​

Answers

The number of total books there to start with were 70

What is the percentage?

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Let's start by using "x" to represent the total number of books on the bookshelf before Kian removed any books.

According to the problem, 40% of the books on the shelf were non-fiction, which means that 60% of the books were fiction. We can express this as an equation:

0.4x = number of non-fiction books

0.6x = number of fiction books

If Kian removed 6 non-fiction books, there are now 22 non-fiction books remaining, so we can write:

0.4x - 6 = 22

Solving for x, we can add 6 to both sides and then divide by 0.4:

0.4x = 28

x = 70

Therefore, there were 70 books in total on the bookshelf before Kian removed any books.

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The deepest lake in the world is Lake Baikal, in Russia. It has a depth of 5369 ft.
Canada’s deepest lake is Great Slave Lake, named after the Slavey (Dene Tha) peoples
who live there. It is located in the Northwest Territories and has a depth of 2015 ft.
Quesnel Lake, south of Prince George, BC, is the deepest fjord lake in the world. It has
a depth of 506 m.
Compare as ratios, the depth of Quesnel Lake to the depth of Lake Baikal and the depth
of Quesnel Lake to the depth of Great Slave Lake. Give your answers as decimals
rounded to the nearest hundredth of a metre.

Step #1: Determine the ratio of Quesnel Lake : Lake Baikal. *Careful with units!*

Step #2: Determine the ratio of Quesnel Lake : Great Slake Lake. *Careful with units*

Answers

The response to the given question would be that As a result, when equation comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

What is equation?

When two statements are connected by a mathematical equation, the equals sign (=) implies equality. An equation in algebra is a mathematical statement that proves the equivalence of two mathematical expressions. For instance, the equal sign separates the numbers in the equation 3x + 5 = 14. It is possible to determine the relationship between the two sentences on either side of a letter using a mathematical formula. The logo for the particular piece of software is frequently the same. as 2x - 4 = 2, for instance.  

From Quesnel Lake to Lake Baikal, the distance is 506 metres.

Lake Baikal is 5369 ft (or 1637.74 m) deep (one foot is equal to 0.3048 m).

Ratio of depths is 506 / 1637.74 0.31 (Depth of Quesnel Lake/Deep of Lake Baikal).

Around 31% of Lake Baikal's depth is in Quesnel Lake.

Great Slave Lake to Quesnel Lake: Quesnel Lake is 506 metres deep.

Great Slave Lake's depth is 2015 feet, or 614.18 metres (1 foot = 0.3048 m).

Ratio of depths is 506 / 614.18 0.82 (Depth of Quesnel Lake / Depth of Great Slave Lake).

Hence, Quesnel Lake's depth is equivalent to 82% of Great Slave Lake's depth.

As a result, when comparing their depths, Quesnel Lake is substantially shallower than Lake Baikal yet deeper than Great Slave Lake.

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quotient of -2 1/2 and -3 1/3

Answers

The quotient of -2 1/2 and -3 1/3 is = 9/16

Define quotient?

In the end, the quotient is what we obtain when we divide a number. Putting things into equal groups is a division operation in mathematics. It is symbolised by the glyph (). For instance, there are three groups of 15 balls each that must be distributed equally.

When we divide the balls into three equal groups, the division formula is 15/3 = 5. The quotient is 5 in this case. This indicates that each set of balls will include five balls.

In this case let us first convert the improper fractions into proper fractions:

-2 1/2 = -4+1/2 = -3/2

-3 1/3 = -9+1/3 = -8/3

Now to find the quotient we have to multiply the fraction's reciprocals:

-3/2 × 3/-8

= -9/-16

=9/16

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There is an escalator that is 1085. 5 feet long and drops a vertical distance of 194. 7 feet. What is it’s angle of depression

Answers

The angle of depression of the escalator is approximately 10.1 degrees.

To find the angle of depression, we need to draw a right triangle where the vertical distance is the opposite side, the horizontal distance is the adjacent side, and the angle of depression is the angle opposite the hypotenuse.

Let's call the angle of depression θ. Then we have

tan(θ) = opposite/adjacent

We know the vertical distance (opposite) is 194.7 feet and the horizontal distance (adjacent) is the length of the escalator, which is 1085.5 feet. So we can plug in these values and solve for θ:

tan(θ) = 194.7/1085.5

θ = tan^-1(194.7/1085.5)

θ ≈ 10.1 degrees

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Select the correct answer. Which graph represents this equation? A. A parabola declines through (negative 4, 10), (negative 3, 4), (negative 2, 0), (negative 0 point 5, negative 4), (0, negative 6), (2, negative 8), (4, negative 6), (6, 0), (8, 10) on the x y coordinate plane. B. A parabola declines through (negative 12, 10), (negative 11, 8), (negative 10, 0), (negative 8, negative 6), (negative 4, negative 10), and rises through (0, negative 6), (2, 0) and (3, 6) on the x y coordinate plane. C. A parabola declines through (negative 3, 8), (negative 2, 0), (0, negative 6) and (4, negative 10) and rises through (8, negative 6), (10, 0) and (11, 6) on the x y coordinate plane. D. A parabola declines through (negative 8, 10), (negative 7, 4), (negative 6, 0), (negative 4 negative 6) and (negative 1, negative 8) and rises through (1, negative 4), (2, 0), (3, 4) and (4, 8) on the x y coordinate plane.

Answers

The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

How to obtain a graph of a quadratic function?

The function for this given problem is defined as follows:

y = 1.5x² + 4x - 2.

a 1.5, b 4, c -2.

By Solving the equation we get these values,

x = -3.09, hence function passes through the point (-3.09, 0).

x = 0.43, hence function passes through the point (0.43, 0).

The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).

The x-coordinate vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

Missing Information

The problem asks for the graph of the following function is given below:

y = 1.5x² + 4x - 2.

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the polynomial in factored form as a produ f(x)=12x^(5)+5x^(4)-39x^(3)+9x^(2)+19x-6

Answers

The polynomial in factored form as a product can be found by using the factor theorem and synthetic division. The factor theorem states that if f(a) = 0, then (x-a) is a factor of f(x). We can use synthetic division to find the factors of f(x)=12x^(5)+5x^(4)-39x^(3)+9x^(2)+19x-6.

First, we need to find a value of x that makes f(x) = 0. We can use the rational root theorem to find possible rational roots. The possible rational roots are ±1, ±2, ±3, ±6. We can use synthetic division to test these possible roots.

Using synthetic division with x = 1, we get a remainder of -1, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of f(x).

Now we can divide f(x) by (x+1) using synthetic division to get the quotient 12x^(4)-7x^(3)-32x^(2)+41x-6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this quotient.

The possible rational roots of the quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of 8, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the quotient.

We can divide the quotient by (x+1) using synthetic division to get the new quotient 12x^(3)-19x^(2)-13x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -14, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 0, so x = -1 is a root and (x+1) is a factor of the new quotient.

We can divide the new quotient by (x+1) using synthetic division to get the new quotient 12x^(2)-31x+6. We can repeat the process of finding possible rational roots and using synthetic division to find the factors of this new quotient.

The possible rational roots of the new quotient are ±1, ±2, ±3, ±6. Using synthetic division with x = 1, we get a remainder of -13, so x = 1 is not a root. Using synthetic division with x = -1, we get a remainder of 49, so x = -1 is not a root. Using synthetic division with x = 2, we get a remainder of 0, so x = 2 is a root and (x-2) is a factor of the new quotient.

We can divide the new quotient by (x-2) using synthetic division to get the new quotient 12x-3. This quotient cannot be factored further, so the factors of f(x) are (x+1)(x+1)(x+1)(x-2)(12x-3).

Therefore, the polynomial in factored form as a product is f(x) = (x+1)(x+1)(x+1)(x-2)(12x-3).

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help plsssss brother im dyinggg

Answers

Answer:

mAngle EFG = 139°

mAngle IFH = 49°

Step-by-step explanation:

First, just look at the top half of the diagram. Straight across D, F, G is a straight line. That's 180° We can write an equation with the two marked angles added up, equal to 180° to solve for x and to solve for those two angles. See image.

Then look for two crossing lines that makes a giant x (not a variable, on the image) That's EH and DG. The angles that are across from each other are called Vertical angles and they are equal to each other. See image.

Last, see the bottom part of the image where an angle is marked with a little tiny square. That means its a right angle and is 90°. We can subtract to find the second angle that we're being asked to find. See image.

It takes 12 bags of bird pellets to fill some bird feeders. The bird feeders need to be refilled every 2 weeks. How many bags of birdseed are needed for 14 weeks? Explain.​

Answers

Answer:

Step-by-step explanation

So first do 12-6=6 then multiply 14x6 which is 84 so 84 bags in 14 weeks is 3 and a half months.

find and explain the error in the work below. multiply: (2x-3)(6x+2)
2x(6x)+2x(2)-3(6x)+3(2)
12x^2+4x-18x+6
12x^2-14x+6
find and explain the error in the work for the given problem.

Answers

Step-by-step explanation:

the error happened in line 2 :

(2x - 3)(6x + 2)

= 2x6x + 2×2x - 3×6x - 3×2 (instead of +3×2)

the error was using the wrong sign for the term 3×2. it was created by -3 multiplied by +2 = -3×2.

plssssssss help, Geometry

Answers

Answer:

2 tangents

with common points p and O touching both the circles only 2 tangets can be drawn

HELP THIS IS DUE TOMORROW USE ANY STRATEGIE

Answers

Answer: See attached.

Step-by-step explanation:

     The first one is incorrect because this equation shows 5 / 2, not 2/5.

     The second one is correct. 7/4 = 7/4.

     The third one is also correct. 12/4 = 12/4.

     It can help to rewrite both sides of the equation in the same format to make it easier to compare.

Given the impact of television on children’s attitudes and behavior, an important concern of behavioral scientists is the amount of time that children of various ages spend watching television. The following data are representative of weekly viewing time (in hours) of a sample of 12-year-olds:
15, 10, 7, 24, 22, 12, 17, 10, 21, 23, 26, 21
a) Calculate the three measures of central tendency (averages) for these data. (15 points)
b) Calculate the range, interquartile range, variance and standard deviation for these data. Use the definition formula for calculating the SS for the variance and standard deviation,(15 points

Answers

a) The three measures of central tendency are the 18 (mean), 14.5 (median, and 10 and 21 (mode).

(b) The range, interquartile range, variance and standard deviation for these data is 19, 12, 39.636, and 6.296, respectively.

(a) The three measures of central tendency are the mean, median, and mode.

Mean: (15 + 10 + 7 + 24 + 22 + 12 + 17 + 10 + 21 + 23 + 26 + 21)/12 = 18

Median: (12 + 17)/2 = 14.5

Mode: 10 and 21 (both appear twice in the data set)

b) Range: 26 - 7 = 19

Interquartile Range: Q3 - Q1 = 22 - 10 = 12

Variance: SS/11 = (15-18)² + (10-18)² + (7-18)² + (24-18)² + (22-18)² + (12-18)² + (17-18)² + (10-18)² + (21-18)² + (23-18)² + (26-18)² + (21-18)² / 11 = 39.636

Standard Deviation: √39.636 = 6.296

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Complete the table to find the unit rate.
The table shows the number of students and teachers.
Teachers |
5
10
15
20
Students
130
390
A
The unit rate is
students per teacher.
If there are 17 teachers, how many students are there?

Answers

There will be 663 pupils if there are 17 instructors.

What does maths for students mean?

The discipline and study of character, structure, area, and change is mathematics. Mathematicians use rigorous deduction from carefully selected axioms and definitions to look for patterns, make new hypotheses, and establish the veracity of their findings.

Teachers Students

5                   130

10                   390

15                   585

20                   780

To find the unit rate, we need to divide the number of students by the number of teachers. For example, for the first row, the unit rate would be:

Unit rate = students/teachers = 130/5 = 26 students per teacher

We can repeat this calculation for each row:

For the second row, the unit rate is 390/10 = 39 students per teacher.

For the third row, the unit rate is 585/15 = 39 students per teacher (same as the previous row).

For the fourth row, the unit rate is 780/20 = 39 students per teacher (again, the same as the previous rows).

So, the unit rate is 39 students per teacher.

If there are 17 teachers, we can use the unit rate to find the number of students:

Number of students = unit rate x number of teachers

Number of students = 39 x 17 = 663

Therefore, if there are 17 teachers, there are 663 students.

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I need help with this asap

Answers

Answer:

The answer is going to be A. [tex]8x^{3} + 16x^{2} - 4x + 15[/tex]

Step-by-step explanation:

I need your help with dis math

Answers

Answer: C. 1/2

Step-by-step explanation:

The coefficient is the number being multiplied by q. The sum is the additive total. To add fractions, they need a common denominator.

2/3 = 4/6

Adding a negative is the same as subtracting.

4/6 + (-1/6) = 4/6 - 1/6 = 3/6 = 1/2

Hope this helps!

Two skaters are racing toward the finish line
of a race. The first skater has a 40 meter
lead and is traveling at a rate of 12 meters
per second. The second skater is traveling at
a rate of 14 meters per second. How long
will it take for the second skater to pass the
first skater?

Answers

It will take the second skater 20 seconds to catch up to the first skater and pass him/her.

What are speed and motion?

In physics, speed and motion are related concepts that describe the movement of objects in space.

Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.

Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.

Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.

In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.

We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:

Distance traveled by the first skater = Distance traveled by the second skater + 40 meters

Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:

12t + 40 = 14t

Simplifying this equation, we get:

40 = 2t

t = 20 seconds

Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.

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Let x be the smallest number which when added to 2000 makes the resulting number divisible by 12,16,18 and 21 the sum of the digits of x is

Answers

The sum of the digits of the number which when added to 2000 makes the resulting number divisible by 12,16,18 and 21 is 7

The smallest number which when added to 2000 makes the resulting number divisible by 12, 16, 18, and 21 is 312. The sum of the digits of x is 3 + 1 + 2 = 6.

To find the smallest number x that can be added to 2000 to make the resulting number divisible by 12, 16, 18, and 21, we need to find the least common multiple (LCM) of these numbers.

The LCM of 12, 16, 18, and 21 is 1008. Then we need to find the smallest multiple of 1008 that is greater than 2000. This is 1008 * 3 = 3024. The difference between 3024 and 2000 is 1024, so x = 1024.The sum of the digits of x is 1 + 0 + 2 + 4 = 7. Therefore, the sum of the digits of x is 7.

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HELP ASAP

The hypotenuse of a right triangle measures 2√15 centimeters and its shorter leg measures 2√6
centimeters. What is the measure of the larger acute angle of the triangle? Round your answer to the nearest tenth of a degree.

Answers

Answer: Let's use the trigonometric ratio of sine to find the measure of the larger acute angle of the right triangle. We have:

sin(theta) = opposite / hypotenuse

where theta is the measure of the larger acute angle, and opposite is the length of the shorter leg of the right triangle. Substituting the given values, we get:

sin(theta) = 2sqrt(6) / 2sqrt(15)

          = sqrt(2/5)

Using a calculator, we can find the value of theta to the nearest tenth of a degree:

theta = arcsin(sqrt(2/5))

     ≈ 38.2°

Therefore, the measure of the larger acute angle of the right triangle is approximately 38.2 degrees.

Step-by-step explanation:

Please help!! Math inequalities. I have freebies you can answer after this in my 'questions'
An inequality is shown.
Select the statement(s) and number line(s) that can represent the inequality. Click all that apply.

Answers

The solution set is {6, 7, 8, …} for x ∈ N and the value of a number substituted for x is greater than 6.

What is inequality?

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Here, we have

Given: Inequality:

12+11/6x ≤  5+3x

We have to determine the statement(s) and number line(s) that can represent the inequality.

12+11/6x ≤  5+3x

12(6x) + 11 ≤  6x(5+3x)

72x +132 ≤ 30x + 18x²

42x + 132 ≤ 18x²

7x + 22x ≤  3x²

we concluded that the value of a number substituted for x is greater than 6.; b. The solution set is {6, 7, 8, …} for x ∈ N." These are the statements and number lines that can represent inequality.

Hence, the solution set is {6, 7, 8, …} for x ∈ N, and the value of a number substituted for x is greater than 6.

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Lester paid $31.00 for 5 pens and 4 books altogether . A book cost $1.00 more than a pen .Stephan bought 6 pens and 3 books at the same price . How much will Stephan pay

Answers

Stephan will pay 30$

Your friend, Tomato Head paid $17 for a shirt. This amount was 85% of the total amount
Tomato Head spent while shopping. How much money did Tomato Head spend?

Answers

Tomato head spent $20

17/x = 85/100
17x100=1700
1700/80=20
Your welcome

What is the absolute deviant of 18, 13, 20, 14, 12, 6, 11, 5, 15, 10

Answers


For your dataset [18, 13, 20, 14, 12, 6, 11, 5, 15, 10], the mean is (18+13+20+14+12+6+11+5+15+10)/10 = 12.4.

The absolute deviations for each data point are [5.6, 0.6, 7.6, 1.6, 0.4 ,6.4 ,1.4 ,7.4 ,2.6 ,2.4].

If there are 16 cups in one gallon how many cups are there in three gallons

Answers

Answer:

48 cups

Step-by-step explanation:

‐-------------------

Suppose the fetime of a certain type of component is a random variable having an Gamma distribution with mean otime 5 years and varience 25 years"2. (a) What is the probability that a selected component of this type will fast more than 4 years?
(b) What is the probability that a two-year-old component of this type will last an additional 4 years?
(c) What is the 25th percentile of the lifetimes of such components?

Answers

Answer:

(a) The probability that a selected component of this type will last more than 4 years is 0.69.

(b) The probability that a two-year-old component of this type will last an additional 4 years is 0.57.

(c) The 25th percentile of the lifetimes of such components is 3.38 years.
Explanation:

(a) The Gamma distribution has the following probability density function:
f(x) = (λ^α/Γ(α))x^(α-1)e^(-λx)
Where α is the shape parameter, λ is the rate parameter, and Γ(α) is the Gamma function. The mean and variance of the Gamma distribution are:
Mean = α/λ
Variance = α/λ^2
Given that the mean is 5 years and the variance is 25 years^2, we can solve for α and λ:
5 = α/λ
25 = α/λ^2
Solving for α and λ gives us α = 5 and λ = 1. So the probability density function is:
f(x) = (1^5/Γ(5))x^(5-1)e^(-1x)
The probability that a selected component will last more than 4 years is the integral of the probability density function from 4 to infinity:
P(X > 4) = ∫_4^∞ f(x) dx = 0.69

(b) The probability that a two-year-old component will last an additional 4 years is the conditional probability:
P(X > 6 | X > 2) = P(X > 6 and X > 2)/P(X > 2) = P(X > 6)/P(X > 2) = 0.57

(c) The 25th percentile of the lifetimes of such components is the value of x such that the cumulative distribution function is 0.25:
F(x) = 0.25
∫_0^x f(x) dx = 0.25
Solving for x gives us x = 3.38 years.

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PLEASEEEEE HELPPPP PLEASEEE

Answers

Minimum - 2

First Quartile - 4

Median - 8

Third Quartile - 13

Maximum - 15

The question is in the screenshot:

Answers

Answer:

13

Step-by-step explanation:

First drop the line.

How many units is it from Point [tex]r[/tex] to the x axis?

12.

How many units is it from Point [tex]r[/tex] to the y axis?

5.

Now we can use the Pythagorean Theorem.

[tex]12^5+5^2=c^2[/tex]

[tex]144+25=c^2[/tex]

[tex]c^2=169[/tex]

[tex]c=13[/tex]

If p=11-3Q by what amount will p decrease if Q increase by 1
unit? A.19 B. 3 C. 1 D. P will not decrease

Answers

The correct answer is B. 3.

To solve this problem, we can plug in the value of Q and see how the value of p changes.
If Q = 1, then:
p = 11 - 3(1) = 11 - 3 = 8
If Q = 2, then:
p = 11 - 3(2) = 11 - 6 = 5
As we can see, when Q increases by 1 unit, the value of p decreases by 3.

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Help please it would mean a lot

Answers

Answer:

2. (x^2 + 3y)(x^2 - 3y)

Step-by-step explanation:

According to algebraic formula:

x^2 - y^2 = (x + y)(x - y)

We have x^4 - 9y^2 => (x^2)^2 - (3y)^2

=> (x^2 + 3y)(x^2 - 3y) or  (x^2 - 3y)(x^2 + 3y)

Answer:

(2) (x²-3y)(x²+3y)

Step-by-step explanation:

x⁴-9y²

Factor/GCF:

x⁴ = (x²)(x²)

-9y² = (-3y)(3y)

Combine:

(x²-3y)(x²+3y)

7. Solve the radical equations: (a)x2+3​=x+4(b)2x−1​−x−4​=2

Answers

a. The equation "(a) x2+3​=x+4" gives the solution as x = 1.

b. The equation "(b) 2x-1​-x-4=2" gives the solution as x = -1.

To solve these radical equations, we will need to isolate the radical on one side of the equation and then square both sides to get rid of the radical. After that, we can solve for x using standard algebraic methods.

(a) x2+3​=x+4


First, we will isolate the radical on one side of the equation:
x2+3​=x+4
x2=x+4-3
x2=x+1


Now, we will square both sides of the equation to get rid of the radical:
(x2)2=(x+1)2
x4=x2+2x+1


Next, we will rearrange the equation and set it equal to zero:
x4-x2-2x-1=0


Now, we can use the quadratic formula to solve for x:
x=(-(-2)±√((-2)2-4(1)(-1)))/(2(1))
x=(2±√(4+4))/(2)
x=(2±√8)/(2)
x=(2±2√2)/(2)
x=1±√2


So, the solutions for x are 1+√2 and 1-√2.

(b) 2x−1​−x−4​=2


First, we will isolate the radical on one side of the equation:
2x−1​=x−4+2
2x−1​=x−2


Now, we will square both sides of the equation to get rid of the radical:
(2x−1)2=(x−2)2
4x2-4x+1=x2-4x+4


Next, we will rearrange the equation and set it equal to zero:
3x2=3


Now, we can solve for x by dividing both sides of the equation by 3 and taking the square root:
x2=1
x=±√1
x=±1


So, the solutions for x are 1 and -1.

You can learn more about radical equations at

https://brainly.com/question/2292715

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