katie is studying the polynomial and determines the polynomial has three real roots. do you agree or disagree with katie's statement? explain your reasoning.

Answer:

AB = 4.5 cm

Step-by-step explanation:

the total area (A) of the 2 rectangles is calculated as

A = x(x - 4) + 3x(x - 2)

   = x² - 4x + 3x² - 6x

   = 4x² - 10x

Given A = 36 , then equating

4x² - 10x = 36 ( subtract 36 from both sides )

4x² - 10x - 36 = 0 ( divide through by 2 )

2x² - 5x - 18 = 0 ← as required

To factorise the equation

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 18 = - 36 and sum = - 5

the factors are + 4 and - 9

use these factors to split the x- term

2x² + 4x - 9x - 18 = 0 ( factor the first/second and third/fourth terms )

2x(x + 2) - 9(x + 2) = 0 ← factor out (x + 2) from each term

(x + 2)(2x - 9) = 0

equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

2x - 9 = 0 ⇒ 2x = 9 ⇒ x = 4.5

but x > 0 , then x = 4.5

Then

AB = x = 4.5 cm

Answer:

AB = 4.5 cm

Step-by-step explanation:

[tex]\boxed{\textsf{Area of a rectange}=\sf width \times length}[/tex]

Area of the smaller rectangle:

[tex]\implies A=x(x-4)[/tex]

[tex]\implies A=x^2-4x[/tex]

Area of the larger rectangle:

[tex]\implies A=(2x+x)(x-2)[/tex]

[tex]\implies A=3x(x-2)[/tex]

[tex]\implies A=3x^2-6x[/tex]

The area of the compound shape is the sum of the areas of the two rectangles:

[tex]\implies A=(x^2-4x)+(3x^2-6x)[/tex]

[tex]\implies A=x^2+3x^2-4x-6x[/tex]

[tex]\implies A=4x^2-10x[/tex]

If the area of the compound shape equals 36 cm² then:

[tex]\implies 36=4x^2-10x[/tex]

[tex]\implies 36-36=4x^2-10x-36[/tex]

[tex]\implies 0=4x^2-10x-36[/tex]

[tex]\implies 4x^2-10x-36=0[/tex]

[tex]\implies \dfrac{4x^2}{2}-\dfrac{10x}{2}-\dfrac{36}{2}=\dfrac{0}{2}[/tex]

[tex]\implies 2x^2-5x-18=0[/tex]

The length of AB is x cm.  

To find the value of x, factor the quadratic.

To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].

[tex]\implies ac=2 \cdot -18=-36[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers are: -9 and 4.

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies 2x^2-9x+4x-18=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(2x-9)+2(2x-9)=0[/tex]

Factor out the common term (2x - 9):

[tex]\implies (x+2)(2x-9)=0[/tex]

Apply the zero-product property:

[tex](x+2)=0 \implies x=-2[/tex]

[tex](2x-9)=0 \implies x=\dfrac{9}{2}=4.5[/tex]

As length is positive, x = 4.5 only.

Therefore, AB = 4.5 cm.

Answer:

9%

Step-by-step explanation:

So first we need to find how much interest he got in a single year.

3600 ÷ 5 = 720

Now we find out how much 720 is compared to 8000.

720 ÷ 8000 = 0.09

Then we make that a percentage:

9%

The mean and the standard deviation for the population of products are 2.0 and 0.3329, respectively.

The mean and standard deviation of the population of products produced by the process are 2.0 and 0.3329, respectively.

Start by determining the population mean which use:

μ = (L +  U)/2

Where:

L = 1.9 and U = 2.1

Put the values;

μ = (1.9 + 2.1)/2

μ = 2.0

When p = 5%, the z value from the probability z table is:

z = -1.645

In addition, the z-score is:

z = (x - μ)/(σ/√n)

Put the values;

-1.645 = (1.9 - 2.0)/(σ/√30)

Simplify the equation.

σ = 0.3329

As a result, the mean and standard deviation again for population of products manufactured by the process are 2.0 and 0.3329, respectively.

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The complete question is-

A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights x¯. If test results over a long period of time show that 5% of x¯ the values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?

Answer:

56.25

Step-by-step explanation:

We know that, Volume of the cuboid = l × b × h

= 60 cm × 54 cm × 30 cm

= 97200 cm³

Side of the cube = 12 cm

The volume of the cube = side³

= 12³

= 1728 cm³

Required number of cubes = volume of cuboid/volume of the cube

= 97200 / 1728

= 56.25

Thus, 56.25 cubes can be placed in the given cuboid.

Answer:

D. reflection over the y-axis.

Step-by-step explanation:

Reflections are the samere same shapes, but mirrored and over a certain axis (x or y axis). In this case, we see a reflection over the y-axis.

Answer:

-3

Step-by-step explanation:

[tex] \frac{a - 15}{2 - 0} = \frac{ - 6}{2} = - 3 \\ \frac{3 - 9}{4 - 2} = - 3 \\ \frac{ - 3 - 3}{6 - 4} = - 3 \\ \frac{ - 9 - ( - 3)}{8 - 6} = - 3 \\ so \: slop \: is \: - 3[/tex]

If C is the midpoint of AB then the length of CD is 11 units.

The midpoint of a line segment is referred to as the midpoint in geometry.

Given C is the midpoint of AB.

AD = 15 and BD = 7

Now AB = 15 - 7 = 8

Again AC = BC

Therefore = BC = 8 / 2 = 4

Now CD = BC + BD = 4 + 7 = 11

Therefore the length of CD is 11 units.

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Answer:

m=y2-y1/x2-X1 so the slope is equal to -3

The graph plotted represents a discrete data

The domain of the function is -2 ≤ x ≤ 2

The range of the function is 1 ≤ y ≤ 5

The graph plotted is represent circle functions

This is a term used to represent data that can be estimated by counting. The circle graph is an instance of methods of representing discrete data.

The term domain refers to the input variables on a graph, the domain is usually plotted on the x axis.

Range is a term that describes the output functions and are usually plotted on the y axis.

The function plotted is a circle with a radius of 2 units.

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Answer: I think that FG and MB are parellel, but I think the way to confirm is to measure with a ruler

Step-by-step explanation:

-9

Constants are terms that are only numbers, without any variables.

Terms

First, let's define what a term is. Within a polynomial, a term is an expression that is added to other terms to create a polynomial. It is important to note that terms are always added. So, if there is subtraction, that means one of the terms is negative.

Constants

The easiest way to identify constants is to look for terms without variables. In the polynomial above, the only constant is -9. All of the other terms have x to some power as a factor. Since they have variables, they cannot be a constant.

Numbers cannot be changed; this is why there are called constants. No matter the x-value, -9 will not change.

The linear equation where m = -4 and passes through (5,9) is y =  - 4x + 29

Linear Equation = an equation between two variables that gives a straight line when plotted on a graph is known as linear equation.

For this statement we need to use the point slope form of linear equation.

The equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line — compare slope-intercept form is known as point slope form.

Using point slope form,

y - y1 = m (x - x1)

y - 9 = -4 (x - 5)

y - 9 = -4x + 20

y = -4x + 20 + 9

y = -4x + 29

Therefore, where m = -4 and passes through (5,9) the linear equation will be y = -4x + 29

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Answer:

a = 240

b = 336

Step-by-step explanation:

To find LCM of 2 number:

To find HCF of 2 numbers:

In this question LCM and HCF is already given but the numbers a and B are unknown.

To find a and B we do the opposite.

Further explanation is in the attached file please open as you will get a clear understanding of the answer.

The average for the first full season when Stephen hit the ball is 0.60.

The average for the first full season can be determined by adding the number of time he hit the ball in the first half and the second half of the season together and then dividing it by the total number of bats.

Average is a measure of central tendency. Average is also known as mean. Other measures of central tendency are mode and median.

Average = sum of the times he hit the ball / total number of bats

(12 + 6) / (16 + 14)

18 / 30 = 0.60

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Answer:

Luana is correct

Step-by-step explanation:

Hello!

According to the question, we are supposed to check whether Luana is right

Oops you made a typo

It's supposed to be -x+2 = --10 not -x+2--10

-x+2 = --10

Add values

When, x = 12

-(+12) + 2 = -10

-12 + 2 = -10

Calculate

-10 = -10

She is correct

When solving

−x+2=−10

Step 1: Subtract 2 from both sides.

−x+2−2=−10−2

−x=−12

Step 2: Divide both sides by -1.

−x/−1 = −12/−1

x=12

So, she's correct

a)Midpoints are (-6.5,-4).

b)Midpoints are (-6.5,-4).

In geometry, a line segment's midpoint is referred to as the midpoint. It serves as both the segment's and the ends' centroid, and it is equally spaced from both. The portion is halved by it. The midpoint formula is employed when it is important to pinpoint the exact intersection of two given points. The point that splits a line segment described by two points in half can thus be found using this method. The halfway is the precise numerical intersection of two integers. The two-number average computation and the midpoint calculation are equivalent. Consequently, you may get the halfway point between any two integers by adding any two numbers together and dividing by two.

Given Data

Mid point formula = [tex]\frac{x+x}{2}[/tex]¹ , [tex]\frac{y+y}{2}[/tex]¹

a) (2,-1) (-8,6)

Equating values in formula,

[tex]\frac{2-8}{2}[/tex] , [tex]\frac{-1+6}{2}[/tex]

(-4,2.5)

Midpoints are (-4,2.5)

b) (-8,-9) (-5,1)

Equating,

[tex]\frac{-8-5}{2}[/tex] , [tex]\frac{-9+1}{2}[/tex]

[tex]\frac{-13}{2}[/tex] , [tex]\frac{-8}{2}[/tex]

(-6.5,-4)

Midpoints are (-6.5,-4).

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The number of possible additional miles that he needs to run will be 18.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Dante will run at least 33 miles this week. So far, he has run 15 miles.

Then the number of possible additional miles that he needs to run.

Let t be the number of additional miles he will run. Then the inequality is given as,

15 + y ≤ 33

y ≤ 33 - 15

y ≤ 18

The number of possible additional miles that he needs to run will be 18.

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Answer:

50miles an hour

Step-by-step explanation:

50miles an hour because R = d/t so 500 / 10 is 50

so rate is 50/hour

From the given figure the value of angle x is 40 degrees

|AC| = | CD |

Δ ( ACD ) = Δ ( DCB )

< ( BAC ) = 70 degrees

Since |AC| = | CD | then the base angles are equal, hence

< ( ADC ) =  < ( BAC ) 70 degrees. ( base angles of isosceles triangle )

< ( ADC ) + < ( BAC ) + < ( ACD ) = 180 degree ( sum of angles in a triangle)

note < ( BAC ) = < ( DAC )

< ( ACD ) = 180 - 70 - 70

< ( ACD ) = 180 - 140

< ( ACD ) = 40 degrees

If Δ ( ACD ) = Δ ( DCB ) then the angles should be equal

Δ ( ACD ) has angles:

< ( ADC )  = 70

< ( DAC ) = 70

< ( ACD ) = 40

Then Δ ( DCB ) should have angles 70, 70, and 40. The figure did not give enough information to put the angles where it should be.

Comparing with the options, only angle 40 degrees is in the option, hence the correct answer

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Yes she made a wise decision as she will get an amount of 4500 after 5 years which is better than getting 4000 after 5 years.

Given that ,

Let us assume that the person takes the amount 3000 from the college, and invests it on a annual rate of 10% for a period of 5 years,

means,

Principal amount = 3000

Rate of Interest = 10%=0.1

Time = 5 years

The future value simple interest formula is the addition of the principal amount that we have in the beginning and the interest earned on that principal amount after the completion of the period. The Future Value Simple Interest Formula is given as,

F V = P + I or F V = P(1 + rt)

Here,

P is the principal amount,

I is the interest,

r is the rate, and

t is the time.

So, We know that

Simple Interest = Principal amount * Rate of Interest * Time

Simple Interest = 3000*0.1*5

Simple Interest = 1500

So, The person will have a Future value of

Principal amount + Simple Interest

= 3000+1500

=4500

Therefore, If the person invests after 5 years will get a amount of 4500 in return which is a wise decision than not investing and getting a amount of 4000 .

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Using the given information, the value of 6a + 9b is 21 and the value of 3x + 5y is 20

From the question, we are to determine the values of the given expressions.

From the given information,

2a + 3b = 7

and

6x + 10y = 40

To determine the value of 6a + 9b, multiply the first equation by 3.

That is

3 × [ 2a + 3b = 7

6a + 9b = 21

∴ The value of 6a + 9b is 21

To determine the value of 3x + 5y, we will divide the second equation by 2

That is,

6x + 10y = 40 ] ÷ 2

3x + 5y = 20

The value of 3x + 5y is 20

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The value of  variable x in the equation is 16.

The equation represented as follows:

x + 14 + x³ = 78

The value x is the variable.

A variable is number represented with a letter in an equation.

Therefore,

x + 14 + 3x = 78

subtract 14 from both sides of the equation

x + 3x + 14 - 14 = 78 - 14

x + 3x = 64

Therefore,

4x = 64

divide both sides by 4

4x / 4 = 64 / 4

x = 16

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Check the picture below.

Answer:

Step-by-step explanation:

Horizontal line is y = 1

Vertical lone is x = 8.

Answer

There are 36 combinations and 181440 permutations

Explanation

The number of combinations of n object taking r at a time is given by the formula;

From the question, n = 9 and r = 7, then substitute these values into the formula

The number of permutations of n object taking r at a time is given by the formula;

Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations

Therefore, there are 36 combinations and 181440 permutations

The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.

We know that Portia can read 23 pages in 10 minutes, so the number of pages she reads per minute is given by the rate:

R = (23 pages)/(10 minutes) = 2.3 pages per minute.

Now, the number of pages she can read in 55 minutes is given by the product between the rate and 55 min, so we will get:

(2.3 pages/min)*55 min = 126.5 pages

We conclude that Portia can read 125.6 pages in 55 minutes.

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The two factors means that the two value will equate with zero

A) 2x-6

They can be aslo simplified as :

2x-6=0

2x=6

x=3

Thus they gave only one values and cannot be expressed as the factors of two product

B) 2x+6

In this expression

we can simplify as :

2x+6

2x+6=0

2x=-6

x=-3

Thus , they are also not expressed as the factors of the two product

C) 2(x+6)

In this expression

we can simplify as :

2x+12

2x+12=0

2x=-12

x=-6

Thus , they are also not expressed as the factors of the two product

D) (2+x)÷(6+x)

They can express as fraction

Thus, They express as the product of the tewo factors

Answer : D) (2+x)÷(6+x)

Answer:

Step-by-step explanation:

yes it is