(x + a)(x + 2)(3x + 1) = bx³ + cx² + dx - 10
Find the values of a, b, c and d.

Answers

Answer 1
This question is an example of expanding algeba and equating coefficients. If the brackets on the left-hand side are expanded the unknown values can be found from the coefficients on the right-hand side.Step 1) Expand the brackets(x2 + (3 + a)x + 3a)(2x + 1) = bx 3 + cx2 + dx - 122x3 + (6 + 2a)x2 + 6ax + x2 + (3 + a)x + 3a = bx 3 + cx2 + dx - 12Now expanded, the equation should be simplified.2x3 + (7 + 2a)x2 + (7a + 3)x + 3a = bx 3 + cx2 + dx - 12Now one by one, the variables can be calculated.a = -4, Hence:2x3 - x2 - 25x - 12b = 2, c = -1, d = -25

Related Questions

QUESTION DOWN BELOW! PLEASE HELP WILL GET 100 POINTS IM STUCK PLEASE HELP EXPLAIN ITS DUE SOON!!
many thanks!!!
ITS DUE SOON!

Answers

1) given

2) base angles theorem

3) PN=QN

4) [tex]\angle 3=\angle 4[/tex]

5) MP=OQ

7) PQ, QP

8) MQ=PO

9) ASA

In the high school band there are two percussionist to every seven marching instruments at the high school bad has a total of 180 members that how many percussionists are on the sidelines

Answers

The number of percussionists on the sidelines is 40.

What is a proportion?A proportion is an equation that equalizes two ratios. By dividing the provided values, we may determine the missing value. One way to express the proportion formula is as a: b::c : d = a/b = c/d. Here, a and d are the extreme terms and b and c are the mean terms.

Given:

Total number of members in high school band = 180

Let's assume "x" is the number of percussionists that are on the sidelines.

According to the question, there are two percussionists to every seven marching instruments. Then,

Number of members = 7 + 2 = 9

You can write the following proportion knowing that there are 180 total members of the high school band:

[tex]\frac{x}{180} = \frac{2}{9}[/tex]

Solving the proportion to get the value of x,

[tex]x = \frac{2}{9} * 180[/tex]

x = 40

Therefore, there are 40 percussionists on the sidelines.

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Solve for x.
(x - 2)² = 2

Answers

The value of x is 4 and 0

What is basic algebra ?

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc. Consider that James and Natalie came up with the notion to arrange matchsticks into numerical patterns when they were fiddling with them.

Given that : [tex](x-2)^{2} = 2[/tex]

[tex](x-2)^{2} = 2[/tex]

(x-2)=±2

x= 4

x=0

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Gus has skydived 4 more times than Nico. Emma has skydived 16 times, how many times has Gus skydived?

Answers

We know that Emma has skydived 16 times, and also Emma has skydived twice as many times as Nico, so Nico has skydived:

[tex]\begin{gathered} \text{Emma}=2\cdot\text{Nico} \\ 16=2\cdot Nico \\ Nico=\frac{16}{2}=8 \end{gathered}[/tex]

So, Nico has skydived 8 times.

Finally, we know that Gus has skydived 4 more times than Nico, so:

[tex]\begin{gathered} Gus=\text{Nico}\cdot4 \\ \text{Gus}=8\cdot4=32 \end{gathered}[/tex]

Gus has skydived 32 times.

NO LINKS!!! Part 2 Please help me with this Similarity Practice​

Answers

Answer:

C' = (15, 7)

Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation, followed by a translation of 1 unit up.

Step-by-step explanation:

If two triangles are said to be similar, their corresponding angles are congruent and their corresponding sides are in the same ratio.

Given vertices of triangle ABC:

A = (0, 0)B = (1, 4)C = (5, 2)

To maintain similarity (and thus keep the corresponding angles of both triangles the same) but not maintain congruence, dilate triangle ABC.

Given:

B' = (3, 13)

If ΔABC is dilated by a scale factor of 3, with the origin as the center of dilation, B' = (3, 12).  If the triangle is then translated 1 unit up, B' = (3, 13), which matches the given coordinate of point B'.

Therefore, the series of transformations is:

Dilation by a scale factor of 3 with the origin (0, 0) as the center of dilation.Translation of 1 unit up.

Mapping Rule:  (x, y) → (3x, 3y + 1)

Therefore, the coordinates of point C' are:

⇒ C' = (3(5), 3(2) + 1) = (15, 7)

Let ​f(x)=x+1 and ​g(x)=x^2-x. Find and simplify the expression. ​(f​+g)(​-5)

Answers

Answer:

26

Step-by-step explanation:

​(f​+g)(​-5)=

​f(-5)+g(-5)=

​-5+1+(-5)^2-(-5)=

-4+25+5=

-4+30=

30-4=26

I Need the answer in 2 minutes

Answers

Answer: [tex]\frac{1}{1024}[/tex]

Step-by-step explanation:

[tex]4^{-3} = (2^{2} )^{-3} = 2^{-6}[/tex]

[tex]\frac{2^{-6} }{2^{4} } = 2^{-6-4} = 2^{-10} = \frac{1}{2^{10} } = \frac{1}{1024}[/tex]

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{\dfrac{4^{-3}}{2^4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{2\times2\times2\times2}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{4\times4}}[/tex]

[tex]\mathsf{= \dfrac{\dfrac{1}{64}}{16}}[/tex]

[tex]\mathsf{= \dfrac{1}{1,024}}[/tex]


[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{\dfrac{1}{1,024}}}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]



~[tex]\frak{Amphitrite1040:)}[/tex]

Point M is the midpoint of AB . AM=2x+9, and AB=8x−50.

What is the length of AM?

Answers

Using the midpoint theorem, the length of AM is 43

Calculating Length of a line

From the question, we are to determine the length of AM

From the given information,

Point M is the midpoint of AB

Thus,

From the midpoint theorem

We can write that

AM + MB = AB

AM = MB

AM + AM = AB

2AM = AB

Also, from the given information,

AM = 2x + 9

and

AB = 8x - 50

Therefore,

From 2AM = AB  

2(2x + 9) = 8x - 50

Solve for x

2(2x + 9) = 8x - 50

4x + 18 = 8x - 50

18 + 50 = 8x - 4x

68 = 4x

x = 68/4

x = 17

But,

AM = 2x + 9

Substituting the value of x

Thus,

AM = 2(17) + 9

AM = 34 + 9

AM = 43

This means the length of AM is 43

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a bag contains 3 red marbles, 3 white marbles,, and 5 blue marbles. only white marbles will be added to the bag. how many white marbles should be added to the bag to make the probability of pulling a white marble 50%?

Answers

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

a 50% probability means 1/2 or 0.5.

that means

desired cases = 1/2 × totally possible cases

at start we have

3 red

3 white

5 blue

that makes 5 + 3 + 3 = 11 totally possible cases and 3 desired cases.

so, the starting probability to pull a white marble is

3/11.

now, we need to say

(3 + x) = 1/2 × (11 + x) (= (3+x)/(11+x) = 1/2)

to make is simpler we multiply both sides by 2 (so we get rid of the 1/2 fraction).

6 + 2x = 11 + x

6 + x = 11

x = 5

we need to add 5 white marble to give us a 50% probability to pull a white marble.

we have then

3 red

3 + 5 = 8 white

5 blue

that makes 5+8+3 = 16 totally possible cases and 8 desired cases.

so, the probability is

8/16 = 1/2

=> our calculation was correct

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A bag contains 3 red marbles, 3 white marbles, and 5 blue marbles. only white marbles will be added to the bag.

Let 'x' be the number of white marble added. Then the equation is given as,

0.50 = (x + 3) / (x + 3 + 3 + 5)

Simplify the equation, then we have

0.50 = (x + 3) / (x + 3 + 3 + 5)

0.50 = (x + 3) / (x + 11)

0.50x + 5.5 = x + 3

0.50x = 2.5

x = 5

The number of white marbles should be added to the bag to make the probability of pulling a white marble 50% will be 5.

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These box plots show the basketball scores for two teams.Bulldogs55708090105Wolverines355580 8596ㅏ30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110Basketball scoresCompare the shapes of the box plots.

Answers

Solution

The bullfdng dataset has its median close to the center of the boxplot.

- This implies that the dataset is symmetric.

- The wolverine dataset has its median moved to the right at 80, implying that it is NOT symmetric.

- However, because there is a skew to the left of datapoints, we say that the dataset is negatively skewed

Final Answer

OPTION A

A frog jumped 0.7 meters. Then jumped another 0.98 meters. How many meters did he jump

Answers

you add them together. so 0.7 + 0.98 = 1.68 so 1.68 should be your answer:)
Answer:
1.68 meters
Step-by-step explanation:
Starting Point- 0.7 meters
Adding Point- 0.98 meters
0.7+0.98= 1.68 meters

You are testing the null hypothesis that the population proportion equals 45, using data you collected from a sample of 100 adults. You sample proportion equals .30. What does Z equal? (Round to two decimal places)

Answers

When one is testing the null hypothesis that the population proportion equals 45, the. z score is -3.02.

How to illustrate the information?

The null and alternative hypothesis is illustrated as the population proportion equals 45,

P0 = 0.45

1 - P0 = 1 - 0.45 = 0.55

Test statistic = z

This will be illustrated as:

= 0.30 - 0.45/ [✓(0.45 * 0.55) / 100]

Test statistic = z = -3.02

Therefore, the z score is -3.02.

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4a + 8b/7 - a^2
if a = 3 and b = -1

Answers

Simplify the expression.

___________________

Solutions:Exact Form - [tex]\frac{13}{7}[/tex]Decimal Form - 1.8.....Mixed Number Form - [tex]1\frac{6}{7}[/tex]

...^Here are all three solutions depending on what you are looking for. Hope this helps! If so, please lmk! Thanks and good luck!

HELP ASAP 100 POINTS

A group of seniors decide to spend their spring break away from home, attending at least one major event. The following table summarizes their preferences.


Attend a concert Attend a festival
Stay in state 214 186
Travel out of state 391 59

What percent want to attend a festival, given that they want to travel out of state?
6.94%
13.11%
24.08%
31.72%

Answers

Answer:

I think 31.72 because it 39156+214186 is 253342 it would be to low

A percentage is a number or ratio that represents a fraction of 100. 

The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.

What is a percentage?

A percentage is a number or ratio that represents a fraction of 100. 

We have,

                           Attend a concert         Attend a festival

Stay in state                214                            186

Travel out of state       391                             59

The number of groups who wants to attend a concert while staying in a state:

= 214

The number of groups who wants to attend a concert while traveling out of the state:

= 391

The number of groups who wants to attend a festival while staying in a state:

= 186

The number of groups who wants to attend a festival while traveling out of the state:

= 59

The percentage who want to attend a festival, given that they want to travel out of state:

= The number of groups who wants to attend a festival while staying out of the state/ Total number of groups from all four conditions

= 59 / ( 214 + 391 + 186 + 59 ) x 100

= 59 / 850 x 100

= 6.94%

Thus,

The percentage who want to attend a festival, given that they want to travel out of state is 6.94%.

Option A is the correct answer.

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A restaurant has two types of tables, rectangular
ones that can each seat 4 people and circular
tables that can each seat 8 people. If 144 people
are enough to fill all 30 tables at the restaurant,
how many rectangular tables does the restaurant
have?
A) 12
B) 16
C) 20
D) 24

Answers

Answer:

D) 24

Step-by-step explanation:

c + r = 30            Eq. 1

4r + 8c = 144       Eq. 2

r = rectangular tables

c = circular tables

From Eq. 1:

c = 30 - r             Eq. 3

Replacing Eq. 3 in Eq. 2:

4r + 8(30-r) = 144

4r + (8*30 + 8*-r) = 144

4r + 240 - 8r = 144

-4r = 144 - 240

-4r = -96

r = -96/-4

r = 24

from Eq. 3

c = 30 - r

c = 30 - 24

c = 6

Check:

from Eq. 2

4r + 8c = 144

4*24 + 8*6 = 144

96 + 48 = 144

Rewrite the expression 26 + 8 as the product of the GCF (greatest common factor) and a sum. Then, simplify the expression. Show all of your steps. pls help due today

Answers

The expression 26+8 as the product of the GCF and a sum is:

2(13+4).

Given we have the expression as 26+8

We need to find the greatest common factor of the numbers 26 and 8.

26 = 2 × 13

8 = 2 × 2 × 2

Multiply all the prime factors that both numbers share in order to determine the GCF:

Therefore, GCF = 2

Now we can write the expression as:

26 + 8

=2(13 + 4)

=2×17

=34

Hence we get the required expression as 2(13 + 4).

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How can I find the slope of the line and what can the slope mean?

Answers

If we take two ordered pairs from the table, we can find the slope with the following equation:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

in this case, we can take the points (1,1/2) and (2,1) to get the following using the formula above:

[tex]\begin{gathered} m=\frac{1-\frac{1}{2}}{2-1}=\frac{\frac{1}{2}}{1}=\frac{1}{2} \\ \Rightarrow m=\frac{1}{2} \end{gathered}[/tex]

we have that the slope is m = 1/2, and this means that for each 2 gallons of distilled water, Rodnika will add 1 gallon of sea salt

6 + root 27over 4 - root 3

Answers

When the expression given as 6 + √27/4 - √3 is simplified, the value is 6 - 1/4√3

How to determine the value of the expression?

The expression is given as

6 + root 27over 4 - root 3

Mathematically, the expression can be represented as

6 + √27/4 - √3

Expand 27 as the product of 9 and 3

So, we have the following equation

6 + √27/4 - √3 = 6 + √(9 * 3)/4 - √3

Expand the products in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 + √9 * √3/4 - √3

Evaluate the square root of 9 in the above equation

So, we have

6 + √27/4 - √3 = 6 + 3/4√3 - √3

Evaluate the like terms in the above equation

So, we have the following equation

6 + √27/4 - √3 = 6 - 1/4√3

Hence, the value of the expression given as 6 + √27/4 - √3 is 6 - 1/4√3

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What is the value of x that makes this equation true?4x+5=x+14

Answers

Explanation:

To solve for x first we have to put all terms that contain x together:

[tex]4x+5=x+14[/tex]

Substract x from both sides:

[tex]\begin{gathered} 4x-x+5=x-x+14 \\ 3x+5=14 \end{gathered}[/tex]

Now substract 5 from both sides:

[tex]\begin{gathered} 3x+5-5=14-5 \\ 3x=9 \end{gathered}[/tex]

And finally divide both sides by 3:

[tex]\begin{gathered} \frac{3x}{3}=\frac{9}{3} \\ x=3 \end{gathered}[/tex]

Answer:

x = 3

Please help me with Calculus homework, Question 2 only***Answer to question 1: -3.938

Answers

As given by the question

There are given that the function:

[tex]f(x)=x^3-6x[/tex]

Now,

According to the answer to question #1 and the graph of the function:

It is the area under the curve from x = 0 and x = 3;

So,

Some of it is below the x-axis means negative area and some of it is above the x-axis which means positive area.

Then,

Yes, they will cancel out and the integral gives the exact net result.

Explained!

which of the following is the rational algebric expression of the verbal phrase below? the ratio of the sum of 2x and 4y and the difference of 8x and 10y.

Answers

638x636y73637zy

Answer:

Because first multiple and divide and Again Multiple and ans

(5^3)^9 divided by 5^12

Answers

Exact Form:

11920928955078128/390625

Decimal Form:

30517578125

30517578125
I looked it up

what is the domain of y-x^2-1

Answers

The domain of the function y = x² - 1 in interval notation is (-∞, + ∞).

What is defined as the domain of the function?A function is simply object that accepts input, appears to apply a rule to it, and returns the result. A function can be thought of as a machine that receives in a number, performs some operation(s), and then outputs the result. The essential thing regarding functions is that they consistently apply the rule. As a result, if the same value is passed through the same function, the output will remain the same. The domain of a function is the collection of all its inputs. Its codomain is the collection of all possible outputs. The range refers to the outputs which are actually used.

The given is y = x² - 1.

The domain of the function is;

Except when the expression is undefined, the domain of the representation is all real numbers. Given that there is no real number in this case, the expression is undefined.

Thus, the domain of the function in interval notation is  (-∞, + ∞).

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7.
A coach travels from the station to the beach, a distance of 576km away in 6hrs.
The coach is only allowed to travel at a maximum speed of 90km/h. Did the coach
break the speed limit?

Answers

Answer:

Yes.

Step-by-step explanation:

distance = rate x time

Let r = rate

567 = r6  Divide both sides by 6

94.5 = r  If he was driving at a constant rate the whole time then he was driving at 94.5 miles per hour which is faster than 90

ALGEBRA 1 HW!! PLEASE HELP WILL GIVE BRAINLYEST please only answer b​

Answers

Answer:

20

Step-by-step explanation:

Every 1 hour it cost $20

You can find this by using the equation y2-y1 divided by x2-x1

y2 is 40 y1 is 20

x2 is 2 and x1 is 1

40-20 divided by 2-1 equals 20

graph a line with a slope of 3/4 that contains the point (2 -3)

Answers

Step-by-step explanation: I hope this helps.

Answer:

The perimeter of the rectangle below is 104 units. Find the length of side RS

Write your answer without variables

Answers

Answer:

24

Step-by-step explanation:

Opposite sides on a rectangle are equal

So 2(3x+3)+2(4x)=104

Now expand, so 6x+6+8x=104

Simplify like terms, 14x+6=104

14x+6-6=104-6

14x=98

14x/14=98/14

x=7

Now just substitute the 7 in for the 3x+3 as thats what we are looking for.

3×7+3=24

Find the derivative of the function. F(x) = (5x² + 2x³)^4​

Answers

Answer:

Derivative of y=(x⁴-2x³+5x²-4)³

Step-by-step explanation:

what is the ratios of 29:1, and the math eqation.

Answers

The ratio of 29: 1 is 29
The mathematical equation is 29/1

What is ratio?

A ratio can simply be defined as an ordered pair of numbers, say x and y, written in the form x / y where  of the denominator is note equivalent to zero.

It is known to explain how many times a given number contains another number in a proportion.

It is seen as the comparison of two numbers , elements or quantities having the same units and moving further to explain how much of one of the element or quantity is present in the another one.

This is achieved based on their magnitude or sizes.

A proportion is a mathematical equation with which two ratios are set equivalent to each other.

A ratio is expressed mathematically as;

x/y

Given the ratio;

29: 1

The equation is = 29/1 = 29

Hence, the ratio is 29

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Select the three equations that pass through the points (–4, –16) and (5, 2):

y + 4 = 2(x – 16)

y – 2 = 2(x – 5)

y = 2x – 8

y + 16 = 2(x + 4)

Answers

The equation of line passing through (-4, -16) and (5, 2) are y = 2x – 8, y - 2 = 2(x - 5) and y + 16 = 2(x + 4)

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The standard form for linear equation is:

y = mx + b

Where m is the slope and b is the y intercept

The equation of line passing through (-4, -16) and (5, 2) is:

y - (-16) = [(2-(-16))/(5-(-4))](x - (-4))

y + 16 = 2(x + 4)

y = 2x - 8

y - 2 = 2(x - 5)

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