What is the solution of x⁴– 3x³ + x²+ 3x – 2 < 0

Answer:

y = -2x + 1

Step-by-step explanation:

First, find the slope with rise/run (y2 - y1) / (x2 - x1)

We can use the points (-1, 3) and (0, 1)

Plug in the points:

(1 - 3) / (0 + 1)

-2/1

= -2

The y-intercept is (0, 1) because that is the point where the line intercepts the y axis. So, we can plug in the slope and y-intercept into the equation:

y = mx + b

y = -2x + 1

Answer:

Step-by-step explanation:

Here, we'll use an apostrophe to signify the complement of a set.

__

(a) The shaded portion is two disjoint (non-overlapping) sections, so must be the union of something. The shaded space on the left is that part of A that is not in B, so it is A∩B'. Similarly, the shaded space on the right is that part of set B that is not in set A: A'∩B. Then the shaded area altogether is the union of these sets:

  (A∩B')∪(A'∩B)

__

(b) For this one, it might be easier to identify the unshaded area. That is where the sets A and B overlap, so it is A∩B. Then the area that is not that area is the complement of this:

  (A∩B)'

Answer:

Explained below.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

The formula to compute correlation coefficient is:

[tex]r(X,Y)=\frac{Cov(X,Y)}{\sqrt{V(X)\cdot V (Y)}}[/tex]

           [tex]=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot\sum X^{2}-(\sum X)^{2}][n\cdot\sum Y^{2}-(\sum Y)^{2}]}}[/tex]

Positive correlation is an association amid two variables in which both variables change in the same direction.  

A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.

In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.

Answer:

Yes, they vary directly

Step-by-step explanation:

y=kx; k is the constant (12 in this case) and as x increases y increases, so they vary directly

Answer:

k=17

Step-by-step explanation:

k+10=27

k=27-10

k=17

Hi there! Hopefully this helps!

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[tex]k + 10 = 27[/tex]

Subtract 10 from both sides.

[tex]k = 27 - 10[/tex]

Answer:

2x - 2

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Distribute parenthesis

2x - 6 + 4

Step 2: Combine like terms

2x - 2

And we have our answer!

Answer:

[tex]2( x -3) + 4 \\ 2x - 6 + 4 \\ [/tex]

Answer:

1035 cards

Step-by-step explanation:

the total number of baseball cards can be calculate by multiplying amount of pages and how many cards each page can hold.

115*9=1035 cards

Answer:

1035 cards

Step-by-step explanation:

Step 1: State what is known

The album contains 115 pages

Each page has 9 cards

Step 2: Assume the pages are full, calculate how much cards are in the album

115 pages x 9 cards per page = 1035 cards

Therefore there are 1035 cards in the album

Answer:

#1 Use Pythagorean theorem to solve DF

c²-b²=a²

5.83²-5²=a²

33.9889-25=a²

a²=8.9889

a=3.00 (rounded to nearest hundredth)

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

# Use Trigonometry to find the angles

angle D:90

angle E: tan E=3/5

                    E=tan^-1 (3/5)

                    E=30.96 (rounded to nearest hundredth)

angle F: tan F=5/3

                    F=tan^-1 (5/3)

                    F=59.04 (rounded to nearest hundredth)

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

Explanation:

If we plugged x = 3 into the expression, then we'd get x-3 = 3-3 = 0 in the denominator. That's not allowed. But we can simplify first

x^2-x-6 factors to (x-3)(x+2). The key here is that (x-3) is a factor. It cancels with the x-3 in the denominator

So, [tex]\frac{x^2-x-6}{x-3} = \frac{(x-3)(x+2)}{x-3} = x+2[/tex]

Allowing us to say,

[tex]\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}\frac{(x-3)(x+2)}{x-3}\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = \lim_{x \to 3}(x+2)\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 3+2\\\\\\\displaystyle \lim_{x \to 3}\frac{x^2-x-6}{x-3} = 5\\\\\\[/tex]

The solution is 5

The value of the equation lim x tends to 3 ( x² -x - 6 ) / ( x - 3 ) is A = 5

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = lim x tends to 3 ( x² -x - 6 ) / ( x - 3 )   be equation (1)

On simplifying the equation , we get

Taking the common factors on numerator , we get

A = lim x tends to 3 ( x² + 2x - 3x - 6 ) / ( x - 3 )

A = lim x tends to 3 ( x ( x + 2 ) - 3 ( x + 2 ) ) / ( x - 3 )

Taking the common factor as ( x + 2 ) , we get

A = lim x tends to 3 ( x + 2 ) ( x - 3 ) / ( x - 3 )

So , the equation is

A = lim x tends to 3 ( x + 2 )

Substitute the value of x = 3 , in the equation , we get

A = ( 3 + 2 )

A = 5

Therefore , the value of A is 5

Hence , the equation is A = 5

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Answer:

178° 35'

Step-by-step explanation:

∠ACB and ∠ACD are supplementary, so they add up to 180°.

First, convert to degrees (there are 60 minutes in a degree).

∠ACB = 1°25' = 1° + (25/60)° = 1.4167°

Now find the supplementary:

∠ACD = 180° − 1.4167°

∠ACD = 178.5833°

∠ACD = 178° 35'

Answer:

o the nearest tenth of ft

Length of one of the side= 14.6 ft

Step-by-step explanation:

Reed wants to have a square garden plot in his backyard. He has covered enough compost to cover an area of 214 square feet.

His square garden is a square one, and the area of a square is the square of one of it's sides .

So if the area= 214 ft²

Length of one of the side = √(214 ft²)

Length of one of the side= 14.6287 ft

To the nearest tenth of ft

Length of one of the side= 14.6 ft

Answer:

2/(3x-2)²

Step-by-step explanation:

4x²-6x³-2x²+6x³/4x²-6x³-6x³+9x^4=

2x²/4x²-12x³+9x^4=

2x²/x²(4-12x+9x²)=

2/9x²-12x+4

2/(3x-2)²

Answer:

f(g(x)) = 18x - 8

Step-by-step explanation:

f(x) = 3x + 7 and g(x) = 6x - 5

Substitute g(x) into f(x):

f(g(x)) = 3(6x - 5) + 7

Distribute the 3 from outside the parentheses:

f(g(x)) = (18x - 15) + 7

Combine like terms:

f(g(x)) = 18x - 8

Answer:

Step-by-step explanation:

   starting          after        after         after

coordinates   reflection rotation   translation

      (x,y)              (x,-y)         (-y,-x)     (-y-2,-x-4)

A    (-2,1)             (-2,-1)         (-1,2)        (-3,-2)

B     (2,1)              (2,-1)         (-1,-2)        (-3,-6)

C    (2,-1)               (2,1)          (1,-2)         (-2,-6)

D    (-2,-1)              (-2,1)          (1,2)          (-2,-2)

Answers reflection (b)

Step-by-step explanation:

it’s right on 8th grade khan ywwww

So he tried to reflect(b) map one figure onto the other using transformations.

If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Both the theorems are proved now which states that quadrilaterals are congruent to one another. Note: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles and the opposite sides of a parallelogram are congruent.

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Answer:

[tex]\bold{4r^3 (6-\pi)}[/tex]

Step-by-step explanation:

Let us try to visualize the given situation in the form of 2 Dimensional image as shown in the attached diagram.

Let the Diameter of spherical balls be D.

As the spherical balls are completely fit in the rectangular box, the sides of box become:

[tex]D \times D\times (3 \times D)[/tex] OR [tex]D\times D\times 3D[/tex]

We know that Diameter is twice of radius.

Therefore [tex]D = 2r[/tex]

So, the dimensions of rectangular box becomes:

[tex]2r \times 2r \times 6r[/tex]

Volume of a rectangular box is given as:

[tex]V = Length \times Width \times Height\\\Rightarrow V = 2r\times 2r\times 6r = \bold{24r^3}[/tex]

Now, let us find out the volume of each spherical ball.

Volume of a sphere with radius 'r' is given as:

[tex]V_{sphere} = \dfrac{4}{3}\pi r^3[/tex]

Volume of 3 spheres = [tex]3\times \frac{4}{3}\pi r^3 =4\pi r^3[/tex]

Now, the volume of space between the balls and rectangular box is = Volume of rectangular box - Volume of 3 balls

[tex]24r^3 - 4\pi r^3\\\Rightarrow \bold{4r^3 (6-\pi)}[/tex]

Answer: Hi!

Option I is correct. 3(2x + 4) = 6x + 12

When you use the distributive property, you multiply the term outside of the parentheses (in this case, 3) by the terms inside of the parentheses (in this case, 2x and 4.)

Hope this helps!

Answer:

w=5000+0.7s

Step-by-step explanation:

if its possible give me 5 start I need it

Answer:

D. 2 . 10^9

Step-by-step explanation:

( 8 * 10^4 ) / ( 4* 10^-5 )

( 8*10^4 ) 10^5 / ( 4 )

2 * 10^ 9

Answer:

Radius = 8.575 cm

Step-by-step explanation:

Formula for volume of a pyramid is;

V_p = ½Ah

Where A is area of base and h is height

Also, formula for volume of cone is given as;

V_c = ⅓πr²h

Now, we are told that V_p = V_c and that h is the same for both shapes.

Thus ;

½Ah = ⅓πr²h

h will cancel out to give;

½A = ⅓πr²

Cross multiply to give;

3A/2π = r²

Base area of pyramid is given as 154 cm². Thus;

(3 × 154)/2π = r²

r = √((3 × 154)/2π

r = 8.575 cm

Answer:

Ms. Steiner

Step-by-step explanation:

Mr. Coelho

science = 25 / 50 = 1/2

math  = 30 / 40 = 3/4

not the same rate

Ms. Steiner

science = 20 / 50 = 2/5

math  = 12 / 30 = 2/5

It is the same rate, so they are proportional

Mr. Coelho:  Science: 50 minutes / 25 tests = 2 minutes per test

                     Math: 40 minutes / 30 tests = 1.33 minutes per test.

Ms. Steiner: Science: 50 minutes / 20 tests = 2.5 minutes per test.

                     Math: 30 minutes / 12 tests = 2.5 minutes per test.

The answer is Ms. Steiner.

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

Explanation:

The fancy or strange looking E symbol is the greek uppercase letter sigma, to mean sum. So they want you to add the terms in the form x^2. The x values are from the list given to us.

x = 16 leads to x^2 = 256

x = 13 leads to x^2 = 169

etc etc

After squaring all the x values, we have this new list {256, 169, 25, 400, 196}

Lastly, you add up all the squared values to get the final answer of 256+169+25+400+196 = 1046

Answer:

17.9/18.2 =0.984 to 3 decimal places

Step-by-step explanation:

The initial mean/average = 18.2 gallons

A standard deviation of 0.8 gallons implies a lower-upper limit of (17.4 - 19) gallons of paint used on new tractors.

New mean/average = 17.9 gallons

It is noticeable that this value 17.9 falls within the lower range of the standard deviation of the initial mean; hence the question

What is the probability that this happened by chance?

17.9 ÷ 18.2 = 0.9835

Therefore, there is a high probability that this happened by chance. 0.9 is closer to 1 than to 0.

Answer:

Friday needs 11 bikes

Step-by-step explanation:

Mean = (summation of all the numbers)/the total number of the given data

(summation of all the numbers)

= 3.5+5.5+0+5+x

(summation of all the numbers)

= 14+x

the total number of the given data

=5

Mean= 5

Mean= (summation of all the numbers)/the total number of the given data

5= (14+x)/5

25= 14+x

25-14=x

11= x

Answer:

might be four

not sure

good luck!

Answer:

OPTION D

Step-by-step explanation:

The bracket is part of bodmas and the only thing it does is to divide equations to make it easier, so thereby I testify that the answer is 2.5/7

Answer:

1) x = 6

2) 129

Step-by-step explanation:

For equation 1:

[tex]7x=42\\\\\frac{7x=42}{7}\\\\ \boxed{x=6}[/tex]

Expression 2:

Apply PEMDAS Rule.

[tex]8^2+9((12/3)*2)-7\\\\8^2+9(4*2)-7\\\\8^2+9(8)-7\\\\64+9(8)-7\\\\64+72-7\\\\136-7\\\\\boxed{129}[/tex]

Hope this helps.

Answer:

[tex]\sqrt{205}[/tex]

Step-by-step explanation:

Using the pythagorean theorem, [tex]x^{2} +18^{2} =23^{2} \\[/tex] so that means [tex]x^{2} = 23^{2} -18^{2} =205[/tex] so x = [tex]\sqrt{205}[/tex]

Answer:

There has been no change in the classifications between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

The expected values are computed using the formula:

[tex]E_{i}=p_{i}\times N[/tex]

Here, N = 300

Use Excel to compute the values.

The test statistic value is:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=1.662[/tex]

The test statistic value is, 1.662.

The degrees of freedom of the test is:

n - 1 = 4 - 1 = 3

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.6454

*Use a Chi-square table.

p-value = 0.6454 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Thus, concluding that there has been no change in the classifications between the last school year and this school year.