Solve the quadratic equation numerically (using tables of x- and y- values).
x squared minus 3 = 2 x
a.
x = -1 or x = 3
c.
x = -3 or x = -3
b.
x = 2 or x = -3
d.
x =1 or x = -1

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer: <A and <F

Step-by-step explanation: Verticle angles are angles that are on opposite sides of each other therefore having the same angle.

The associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

Now, The p-value for a one-tailed t-test with a sample size of 18 and a test statistic of 1.9,

Hence, we need to look up the t-distribution table.

So, Using a one-tailed test with,

df = n - 1

= 18 - 1 = 17 degrees of freedom

We find that the area to the left of 1.9 under the curve is 0.0359.

This means that there is a 3.59% probability of observing a t-statistic less than or equal to 1.9 if the null hypothesis is true.

Therefore, the associated p-value for this left-tailed t-test is 0.0359 or 3.59%.

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The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Answer:

x=3

Step-by-step explanation:

Hello,

The first thing you do is set up your equation, and we are solving for x so we are going to get x by itself on one side of the = sign.

       2x/3+1=3        First thing: subtract 1 from BOTH sides.

               -1  -1

----------------------

          2x/3=2       Multipliy by 3 on both sides

              *3 *3

-----------------------

            2x=6         Divide by 2 on both sides

             /2 /2

-----------------------

           x=3

I hope this helped you!!!

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

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Hi! I hope you're enjoying your day!

Let's add the following polynomials.

How to add them? Just combine like terms. :)

\(\bold{2x^2-10x+1 ~and~x^2+15x-8}\)

\(\bold{2x^2+x^2-10x+15x+1-8}\)

Hence, the answer is

\(\boxed{\boxed{\bold{3x^2+5x-7}}}\)

\(\rule{250}{2}\)

\(\bold{2x^3-3x^2+5\;and\;5x^2-3x^3+7}}}\\\)

Combine Like terms:

\(\bold{2x^3-3x^3-3x^2+5x^2+5+7}\)

Hence, the answer is

\(\boxed{\boxed{\bold{-x^3+2x^2+12}}}\)

Hope everything is clear.

If you have any questions, please comment.

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The inequality that corresponds to the following expression, "A is less than 9" is:

Answer:

115.462

Step-by-step explanation:

Answer: 115.462

Step-by-step explanation:

To start, the first thing we can observe is two negative signs, which we know turns into a positive sign.

Therefore, we now have:

112.212 + 3.25

115.462

Hope this helps!

The probability of getting exactly 1 red is 60/121

Probability theory, a branch of mathematics concerned with the analysis of random phenomena.

There is a bag filled with 5 blue and 6 red marbles.

A marble is taken at random from the bag, the color is noted and then it is replaced. Another marble is taken at random.

It is required to find the probability of getting exactly one red marble.

Now, the red marble can occur on the first draw or the second draw.

The probability of getting exactly 1 red marble from the first draw will be,

P(1) = 6/11 x 5/11

p(1) = 30/121

The probability of getting exactly 1 red marble from the second draw will be,

P(2) = 6/11 x 5/11

p(2) = 30/121

So, the total probability of the event will be,

P = P(1) + P(2)

P =  30/121 +  30/121

P = 60/121

hence, the probability of getting exactly 1 red is 60/121

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Answer:

Sorry

Step-by-step explanation:

Your pictures don't open

Answer: 77

Step-by-step explanation:

u add up all the numbers then divide by how many numbers there are

Step-by-step explanation:

To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due ($32,000)

- PMT is the monthly payment we want to find

- r is the annual interest rate (7.9%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**

Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.

\(\dfrac{1}{3} + \dfrac{1}{4} + \dfrac{1}{2} = \dfrac{4}{12} + \dfrac{3}{12} + \dfrac{6}{12} = \dfrac{4+3+6}{12} = \bf \dfrac{13}{12}\\\)

Check the picture below.

Answer:

221 g

The up pinned pic is of inverse variation typed answer.. If u want word problem type answer here are the steps (EVEN IF THE STEPS ARE DIFFERENT ANSWERS REMAIN SAME)

Step-by-step explanation:

Mass of wire from 22cm = 374g

Mass of wire from 1 cm = 374÷22 = 17g

Mass of wire from 13 cm = 13×17 = 221 g

The equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is: R(x) = 250000 + 375x - 2.5x²

Equations are mathematical statements with two algebraic expressionsοn either sideοf an equals (=) sign. It illustrates the equality between the expressions writtenοn the left and right sides. To determine the valueοf a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

N(x) = 625 + 2.5x

The revenue R(x) will be the productοf the numberοf students enrolled and the fee charged per student. The fee charged per student will be (400 - x) dollars. So, the revenue function can be represented as:

R(x) = (625 + 2.5x)(400 - x)

Simplifying the expression, we get:

R(x) = 250000 + 375x - 2.5x²

Therefore, the equation that could be used to represent this situation, where x is the course fee and R(x) is the total revenue, is:

R(x) = 250000 + 375x - 2.5x²

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This is the quotient of (-15b^5 + 18b^3) divided by 3b. The expression simplifies to -5b^4 + 6b^2.

To find the quotient of the expression (-15b^5 + 18b^3) divided by 3b, we can perform the division by simplifying each term separately.

First, let's divide -15b^5 by 3b:

(-15b^5) / (3b) = -15/3 * b^5/b = -5 * b^(5-1) = -5b^4

Next, let's divide 18b^3 by 3b:

(18b^3) / (3b) = 18/3 * b^3/b = 6 * b^(3-1) = 6b^2

Now, we have simplified each term individually. The resulting expression is:

-5b^4 + 6b^2

This is the quotient of (-15b^5 + 18b^3) divided by 3b. The expression simplifies to -5b^4 + 6b^2.

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Answer:

y=5

Step-by-step explanation:

Answer:

4y=20

y=20/4

y=5

Step-by-step explanation:

Hope this helps u!!

Answer:

\(P(Same)=\frac{61}{190}\)

Step-by-step explanation:

Given

\(Red = 5\)

\(White = 6\)

\(Black = 9\)

Required

The probability of selecting 2 same colors when the first is not replaced

The total number of ball is:

\(Total = 5 + 6 + 9\)

\(Total = 20\)

This is calculated as:

\(P(Same)=P(Red\ and\ Red) + P(White\ and\ White) + P(Black\ and\ Black)\)

So, we have:

\(P(Same)=\frac{n(Red)}{Total} * \frac{n(Red) - 1}{Total - 1} + \frac{n(White)}{Total} * \frac{n(White) - 1}{Total - 1} + \frac{n(Black)}{Total} * \frac{n(Black) - 1}{Total - 1}\)

Note that: 1 is subtracted because it is a probability without replacement

\(P(Same)=\frac{5}{20} * \frac{5 - 1}{20- 1} + \frac{6}{20} * \frac{6 - 1}{20- 1} + \frac{9}{20} * \frac{9- 1}{20- 1}\)

\(P(Same)=\frac{5}{20} * \frac{4}{19} + \frac{6}{20} * \frac{5}{19} + \frac{9}{20} * \frac{8}{19}\)

\(P(Same)=\frac{20}{380} + \frac{30}{380} + \frac{72}{380}\)

\(P(Same)=\frac{20+30+72}{380}\)

\(P(Same)=\frac{122}{380}\)

\(P(Same)=\frac{61}{190}\)

A number that can only be divided by 1 or 0 is prime. A composite number is a number that can be divided by 0, 1, 2, etc. I couldn't really get the question that you were trying to type, but this is what I came up with.

Hope this helps and just remember you are loved!

Answer:

14. x=30, y=15, z=165

15. x=10, y=25

Step-by-step explanation:

Answer:

1)

x= 30

y=15

z=150

2)

x= 10

y=25

Step-by-step explanation:

1)

2x+90+x=180

3x+90=180

x= 90/3=30

2y= x

2y=30

y= 30/2=15

2y+z= 180

30+z= 180

z= 150  

2)

3x= 5x-20

5x-3x=20

x=20/2=10

2y+4y+ (5x-20) = 180

6y+30= 180

y= 150/6= 25

I hope im right!!

Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

The value of x in this proposition would be the first option i.e. \(-13\frac{1}{4}\)

4/11= -33/x+5,

to get the value of x we need to get the x to the left hand side,

4(x+5)= -33,

4x+20 = -33.

subtracting 20 from both the sides,

4x= -33-20

4x = -53.

dividing both the sides by 4,

x= -53/4

x= \(-13\frac{1}{4}\) ,

which is option A in the given question

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Step-by-step explanation:

hope this helps you out some

Answer:

volume of aquarium =l×b×h=5×1×8=40ft³

volume of aquarium in gallons=

40ft³×7.5gallons/ft³=300galloons

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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Answer:

  (b)  x + 6

Step-by-step explanation:

You want the rule for the x-coordinate when the transformation is a right shift of 6 units.

A point that is the image of a pre-image point with x-coordinate x will be 6 units farther right of the y-axis than the pre-image point.

The x-coordinate measures how far right of the y-axis a point is. When that distance increases by 6 units, the x-coordinate increases by 6 units:

  x ⇒ x+6 . . . . . . the x-coordinate transformation rule

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