Simplify (-8-r)+(2r-4) Plato question

The quartic equation y = x⁴ - x³ - 5 · x² - x - 6 has x = - 2 and x = 3 as its only real zeros. (Correct choice: C)

Quartic equations are polynomials of grade 4, whose standard form is described below:

y = a · x⁴ + b · x³ + c · x² + d · x + e

Where a, b, c, d, e are real coefficients. A value of x is a zero of a polynomial when the result is equal to zero. The quickest way to find the polynomial is by evaluating each expression at x = - 2 and x = 3:

x = - 2

y = (- 2)⁴ - (- 2)³ - 5 · (- 2)² - (- 2) - 6

y = 16 + 8 - 20 + 2 - 6

y = 0

x = 3

y = 3⁴ - 3³ - 5 · 3² - 3 - 6

y = 81 - 27 - 45 - 3 - 6

y = 0

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Answer: The club members estimate that they will sell 100 tote bags when the price is $11 each, and for every price increase of $1, they estimate they will sell 10 fewer bags. If the price increases to $13, then this is a $2 increase from the original price, so we can calculate the number of fewer bags they estimate they will sell:

10 fewer bags per $1 increase * $2 increase = 20 fewer bags

To find the number of bags they estimate they will sell when the price is $13, we can subtract this decrease from the original number of bags they estimate they will sell:

100 bags - 20 fewer bags = 80 bags

To find the revenue in dollars, we can multiply the number of bags they estimate they will sell by the price of the bags:

80 bags * $13 per bag = $1040

So the estimated revenue when the bags are priced at $13 each is $1040

Step-by-step explanation:

Answer: Let x be the amount of Jane's paycheck.

We know that:

surfboard cost = $289

and jane used $68 more than two fifths of her last paycheck to purchase a new surfboard.

So we can set an equation as:

surfboard cost = 2/5 x + $68

289 = 2/5 x + 68

Now we can substitute the known value in the above equation:

289 = 2/5 x + 68

221 = 2/5 x

x = (2215) / 2 = 115 = 55

So the amount of her paycheck is $55.

Therefore, jane's last paycheck was $55.

Step-by-step explanation:

Answer: she checked out 9 nonfiction books

Step-by-step explanation:

18-9=9

Elijah used 24 gigabytes memory on his cell.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Elijah used 3/4 of the memory on his cell phone memory card.

And, The memory card can hold 32 gigabytes.

Now,

Since, The memory card can hold 32 gigabytes.

And, She used 3/4 of the memory on his cell phone memory card.

Hence. The used memory = 3/4 of 32

                                         = 3/4 × 32

                                         = 3 × 8

                                          = 24 gigabytes

Thus, Elijah used 24 gigabytes memory on his cell.

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Answer:

-3

Step-by-step explanation:

Answer: The slope whould be 3

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: 3

y-intercept:

(0,0)

x|y

----

0|0

1|3

Answer:

1332

[tex]7x))742 \sqrt[ \sqrt[241]{?} ]{?} [/tex]

Answer:

Refer to the step-by-step.

Step-by-step explanation:

[tex]Given:\\ \lim_{x\to \22} \frac{1}{1-x}[/tex]

Plug in the value of 2 in for x. We get,

⇒ [tex]\frac{1}{1-(2)}[/tex] ⇒ [tex]\frac{1}{-1}[/tex] ⇒ -1

So,  [tex]\\ \lim_{x\to \22} \frac{1}{1-x} = -1[/tex]

The equation 3y + 2 = 2x is not a direct variation

From the question, we have the following parameters that can be used in our computation:

Variation = direct variation

3y + 2 = 2x

A direct variation is represented as

y = kx

Where k is the constant of proportion

When the equations y = kx and  3y + 2 = 2x are compared, we can see that

The equation 3y + 2 = 2x has a constant term

Hence, the equation is not a direct variation

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Answer:

the quotient of g and 25 is g/15.

The solution for the question found using the double angle formula for cosine is -[tex]\frac{7}{25}[/tex].

What are double angle formulae?

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

           =2Cos²θ – 1

            = 1 – 2Sin²θ

Given sinθ = [tex]\frac{4}{5}[/tex]

         cos(2θ) = 1-2sin²θ = [tex]1-2[/tex]×( [tex]\frac {4}{5}[/tex])² = [tex]1-[/tex] [tex]\frac{32}{25}[/tex] = [tex]\frac{-7}{25}[/tex]

Therefore Cos(2θ) fund using double angle formula is -[tex]\frac{7}{25}[/tex]

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The solution for the question found using the double angle formula for cosine is -.7/-25

There are some trigonometric formulas that are known as double angle formulae because they contain double angles, such as Sin 2x, Cos 2x, and Tan 2x.

An angle is a measure of the amount of rotation between two rays or lines that share a common endpoint, called the vertex of the angle. The two rays or lines are called the sides of the angle, and the endpoint is called the vertex. The size of an angle is typically measured in degrees or radians, with one full rotation around a point (360 degrees or 2π radians) being equal to a full circle.

The double angle formula for cosine is

Cos 2θ = Cos²θ - Sin²θ

          =2Cos²θ – 1

           = 1 – 2Sin²θ

Given sinθ = 4/5

        cos(2θ) = 1-2sin²θ = 1-2×(4/5 )² =  1-32/25 = -7/25

Therefore Cos(2θ) fund using double angle formula is -

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Therefore , the solution of the given problem of square comes out to be the ABCD  square is 18 inches

The side length of a square ABCD is 18 inches Each side of square ABCD is 18 inches The midpoints of ABCD are joined to form a square MNOP The figure is attached below

Here,

We need to find the side length of square MNOP

AMN form a Right angle triangle

We know AM =9  and AN= 9

To find MN , use Pythagoreans theorem

MN2=AM2+AN2

MN2=9square+9 square

MN2=162

Take square root on both sides

MN=9 root 2

so the side of the square MNOP is  9 square root 2 inches

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Answer:

125 per minute.

Step-by-step explanation:

To get this answer, you simply need to divide 500 (the amount that it can make it 4 minutes.) by 4. (The amount of time it takes to make 500 copies.)

You get the answer 125.

An equation is y = -4x/3 + 10.

A graph of the equation is shown in the image attached below.

In order to write and graphically solve an equation that model this situation, we would assign variables to the number of pound of peaches and number of pounds of apples respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation as follows;

$2/pound × Pounds of peaches = 2x.

$1.50/pound × pounds of apples = 1.50y

Combining the two expressions above, we have the following:

2x + 1.50y = 15

Making y the subject of formula, we have:

1.50y = 15 - 2x

y = (15 - 2x)/1.50

y = -4x/3 + 10

Therefore, an equation in slope-intercept form that relates the variables is y = -4x/3 + 10.

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The value of x for the equation 4(5x - 4) = 64( 2x + 12) is x = -7.25

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

4(5x - 4) = 64(2x + 12)

20x - 16 = 128x + 768

20x - 128x = 768 + 16

-108x = 784

x = -7.25

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Answer: x = 4

Step-by-step explanation:

Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.

This means that:

[tex](4x-1)=15[/tex]

Simplify and solve for x.

[tex]4x-1=15\\4x=16\\x=4[/tex]

So, x = 4

The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;

x⁴ divided by x equals x³

x + 1 multiplied by x³ equals x⁴ + x³

subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2

2x³ divided by x equals 2x²

x + 1 multiplied by 2x² equals 2x³ + 2x²

subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2

2x² divided by x equals 2x

x + 1 multiplied by 2x equals 2x² + 2x

subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2

-3x divided by x equals -3

x + 1 multiplied by -3 equals -3x - 3

subtract -3x - 3 from -3x - 2 will result to a remainder of 1.

Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).

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I think it's 84 I'm not good with math though I multipled 7 and 12

Answer:

9 cups

Step-by-step explanation:

1 pt = 2 c
4 1/2 x 2 = 9 c

Divide or multiply the output by a constant to expand or contract the graph in the y direction.

2f (x) is stretched by a factor of 2 in the y direction, and f (x) is contracted by a factor of 2 in the y direction (or stretched by a factor of ).

The y = f (x), y = 2f (x), and y = x graphs are shown here.

This is the difference quotient:

f (x + h) - f(x ) /h

quotient of difference

and f(x) = x3; thus, the difference quotient for this function is

(x + h)³ - x³ / h

quotient of difference.

The numerator can now be simplified by expanding (x + h)3 as (x + h)2(x + h), however I advise factoring (x + h)3 - x3 as a difference of cubes.

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Answer:

No it is not an exponential function

A line that shows the number of hair barrettes she makes and the total number of beads she uses is y = 75x.

In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, you must first determine the slope and y-intercept. The slope is the ratio of the change in y to the change in x. Find two locations on the line, and then draw a sloping triangle joining them.

A line is a perfectly straight, one-dimensional figure that extends infinity in both directions and has no thickness. To stress that a line has no "wiggles" anywhere along its length, it is sometimes referred to as a straight line or, more archaically, a right line.

Two points on the line are (2, 150) and (5, 375)

y - 150 = ( (375-150) / (5-2) )  (x-2)

y - 150 = 75 (x-2)

y = 75x

Equation of line is y = 75x

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Answer:What is a triangle with 2 congruent sides and an obtuse angle

Step-by-step explanation:

In math, a pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object.

A pattern has a rule that identifies the items that are part of the pattern and those that are not. A pattern in mathematics is a series of recurring figures, shapes, or numbers.

Any kind of event or thing can be connected to a pattern. A pattern has a rule that identifies the items that are part of the pattern and those that are not. A specific set of rules must be taken into account in order to create a full pattern.

We must first comprehend the nature of the sequence and the distinction between the two successive numbers provided in the pattern in order to apply these rules. 

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The graph of the system of linear inequalities 2x + y < 1 and y ≥ 12x + 2 is attached.

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Inequalities is used for the non equal comparison of numbers and variables.

The graph of 2x + y < 1 and y ≥ 12x + 2 is attached.

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Answer: q1=11 q2=15 q3=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

if there is any triangle ABC and a,b,c are sides opposite angles A,B,C respectively , then

[tex]cos~A=\frac{b^2+c^2-a^2}{2bc} \\cos~B=\frac{c^2+a^2-b^2}{2ca} \\cos~C=\frac{a^2+b^2-c^2}{2ab}[/tex]

B=101

a= 3 cm

b=y

c=1 cm

use formula for cos B

cos 101=cos(90+11)=sin 11

[tex]-sin~11=\frac{1^2+3^2-y^2}{2 \times 3 \times 1} \\-6 \times sin~11=1+9-y^2\\y^2=10+6~sin~11\\y^2\approx 10+6\times 0.1908\\y^2 \approx11.1448\\y\approx3.338[/tex]

Answer:

2.16

Step-by-step explanation:

To find the length y:

Since we have an angle with two sides next to it, it is 'cosy', so we can use the cosine rule to find y. Let's make y = a for the formula.

Using the cosine formula:

a^2 = b^2 + c^2 - 2bc cos(A)

where b=1, c=3 and A=101

substitute these values in the formula:

a ^2 = 1^2 + 3^2 - 2(1)(3) × cos(101)

a ^2 = 4.647970...

Square root to find a:

a = √4.647970...

a = 2.16

thus, y = 2.16 to 3sf

Total of 44 weeks does one bag last.

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator

Total amount of cat food = 33 lbs in one bag

Amount of food cat eats each week = 3/4 lb = 0.75 lb

Number of weeks one bag of cat food last = 33 / 0.75

                                                                       = 44

Hence one bag of cat food will last for 44 weeks.

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Answer: Here are two possible expressions for the total cost for Hazar and his friends:

The first expression is to add the cost of game rental and drinks and snacks for all the four friends

6x + 4x =10x where x is the number of friends

Second expression is to calculate the cost for each of the 4 friends and then add it together

(6 + 4) * 4 = 40

Both the expressions represent the same outcome, that is the total cost of $40 for Hazar and his friends to play video games.

It's depend on how you want to represent it, both are correct and represents the same outcome.

Step-by-step explanation:

Answer:

this should help you out

From the graph, it can be seen that it took 4 days to mow 30 lawns. 12 lawns can be mowed in 1 days.

Analyzing numerical data can be done using graphical representation. It uses a diagram to show the relationship between the data, ideas, information, and concepts. One of the most crucial learning strategies, it is also simple to understand. The kind of information in a particular domain is always a factor.

Examples include pictures, sketches, line art, graphs from mathematics, charts, diagrams, typography, numbers, symbols, geometric patterns, engineering drawings, or other images. Often, text, illustration, and color are combined in graphics.

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