Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
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.
the complete question is
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. Do you agree or disagree with Katies statement? Explain your reasoning.
Write properties of function:
x intercept/zero: [tex]x_{1}[/tex] = 3/2 ; [tex]x_{2}[/tex] = 4 ; [tex]x_{3}[/tex] = -[tex]\sqrt{3}[/tex] ; [tex]x_{4}[/tex] = [tex]\sqrt{3}[/tex]
Katie is studying the polynomial f(x) =(2x-3) (x-4) (x^2-3) and determines the polynomial has three real roots. you disagree with Katies statement because the function has four real roots
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A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 12 cm can be placed in the given cuboid?
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.
Question 5
Point C is the midpoint of AB and point B is between points A and D. If AD = 15 and
BD = 7, what is CD?
CD
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.
It functions as the centroid of the segment and the endpoints, and it is equally separated from both. It cuts the portion in half. As there is no distinguishing point to act as the point at infinity (any point in a geometric range may be protectively transferred into any other point in (the very same or some other) projective range), the midpoint is difficult to define in projective geometry. On the perception line in question, an affine structure can be defined by fixing a point at infinity and then using the aforementioned concept.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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Linear equation where m=-4 and passes through (5,9)
The linear equation where m = -4 and passes through (5,9) is y = - 4x + 29
What is Linear Equation ?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.
What is Point Slope Form ?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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Helppp pls asappp simple math
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.
3 1/4 x 1 1/6 as a mixed number in simplest form
find both the number combinations in the number of permutations for 9 objects taken 7 at a time
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;
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]From the question, n = 9 and r = 7, then substitute these values into the formula
[tex]^9C_7=\frac{9!}{7!(9-7)!}=\frac{9!}{7!\text{ }2!}=\frac{9\cdot8\cdot7!}{7!\times2}=\frac{72}{2}=36[/tex]The number of permutations of n object taking r at a time is given by the formula;
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]Also, n = 9 and r = 7, then substitute these values into the formula to get the number of permutations
[tex]^9P_7=\frac{9!}{(9-7)!}=\frac{9!}{2!}=\frac{9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2!}{2!}=181440[/tex]Therefore, there are 36 combinations and 181440 permutations
if anyone can help lmk brainly answer and 20 points
a)Midpoints are (-6.5,-4).
b)Midpoints are (-6.5,-4).
What are midpoints?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 Highest Common Factor of a
and b is 48 and the Lowest
Common Multiple is 1680.
Given that a < b and that both
numbers are greater than 48,
work out the values of a and b.
Answer:
a = 240
b = 336
Step-by-step explanation:
To find LCM of 2 number:
list all prime factors that appear in either numbers. If a factor appears more than once in one of the numbers list it that many times. Multiply these together to get LCMTo find HCF of 2 numbers:
List all prime factors both numbers. Multiply these together to find HCFIn 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.
A person has a choice of receiving 3000 now or 4000 after she graduates from college in five years she decided to take the 3000 and the best add expected 10% annual rate of return. Did she make a wise decision?
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
What Is the Future Value Simple Interest ?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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Which set of ordered pairs does not represent a function?
{(5,7), (4,-2), (-8,8), (4,-9)}
{(6,-2), (-2, -7), (-9,-4), (8,-7)}
{(-6,-7), (0,9), (6,-7), (3, -4)}
{(4,6), (9,-8), (3,2), (-9,-8)}
A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of finished products and computes the sample mean product weight. If test results over a long period of time show that of the values are over pounds and are under pounds, what are the mean and the standard deviation for the population of products produced with this process?.
The mean and the standard deviation for the population of products are 2.0 and 0.3329, respectively.
What is defined as the standard deviation?A standard deviation (or) is a measure of how widely distributed the data is in regards to the mean. A low standard deviation indicates that data is clustered around the mean, whereas a high standard deviation implies that data is more spread out.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?
HELP PELASE
Jerry is planning a 500-mile trip and estimates it will take 10 hours. Approximately how fast will he be traveling?
If it helps i have the image here :]
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
Your answer is
Dante will run at least 33 miles this week. So far, he has run 15 miles. What are the possible numbers of additional miles he will run?
Use t for the number of additional miles he will run.
Write your answer as an inequality solved for t.
The number of possible additional miles that he needs to run will be 18.
What is inequality?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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A line is drawn so that it passes through the points (3, 4) and (4, 1)
What is the slope of the line?
A: 1/3
B: 3
C: -1/3
D: -3
Answer:
m=y2-y1/x2-X1 so the slope is equal to -3
I need help with this math problem
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.
help pls, thank you
Is 4.887888 a rational number
Answer:
Step-by-step explanation:
yes it is
Identify the constant term in the following polynomial
8x + 2x^3 - 5x^4 - 9
-9
Step-by-step explanation: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.
Which ones are paralel? Justify your answer please!!!!!!!!
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:
portia can read 23 pages i 10 minutes. at this rate how many can she read in 55 minutes
The rate at which Portia reads is 2.3 pages per minute, at this rate, she can read 126.5 pages in 55 minutes.
How many pages can she read 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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2a + 3=7 and 6x +10y =40 what is the value of 6a+9b what is the value of 3x +5y
Using the given information, the value of 6a + 9b is 21 and the value of 3x + 5y is 20
Evaluating an expressionFrom 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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please help only one question i don’t get ;( i will mark brainliest
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
What is discrete data?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.
What is domain and range?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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Write equations for the horizontal and vertical lines passing through the point (8,1)
Check the picture below.
Answer:
Step-by-step explanation:
Horizontal line is y = 1
Vertical lone is x = 8.
Stephen hit the ball 12 times out of 16 bats in the first half of the season in six times out of the 14 at that in the second half of the season what is his batting average for the first full season written as a decimal
The average for the first full season when Stephen hit the ball is 0.60.
What is the average?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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What are the terms in the expression 5y -x + 7? A. Sy, -X B. 3,-1,7 C. 5y, -x, 7 D. Sy, x, 7
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
[tex]\begin{gathered} (2+x)\div(6+x)=\frac{(2+x)}{(6+x)} \\ (2+x)\div(6+x)=(2+x)(6+x)^{-1} \end{gathered}[/tex]Thus, They express as the product of the tewo factors
Answer : D) (2+x)÷(6+x)
Geometry, if |AC| = |CD|, find angle x.
From the given figure the value of angle x is 40 degrees
How to find angle x|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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Find the slope of the line represented
by the data below.
xl 0 2
y 15
4
9 3
6 8
-3 -9
Simplify completely.
Slope = [?]
Hint: The slane of lin
Change in y
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]
After 5 years, $8,000 deposited in a savings account with simple interest had earned $3,600 in interest. What was the interest rate?
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%
Luana states that -x+2--10 is true when
x=12. Is she correct? Jutify your response.
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
Find X? x+14+x3=78 How can I find X? Please answer. Thanks so much! (This is my older sister's account btw)
The value of variable x in the equation is 16.
How to find the variable x in the equation?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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