Please help!
Select the correct answer.
which statement best describes the zeros of the function h() = (x-4)(x-7x+ 10)
O A. The function has four complex zeros.
O B. The functlon has three distinct real zeros.
O C. The function has two distinct real zeros and two complex zeros.
O D. The function has four distinct real zeros.
Answers
Answer:
The zeros are:
[tex]x =4, x=2, x = 5[/tex]
The function has three distinct real zeros.Hence, option (B) is true.
Step-by-step explanation:
Given the expression
[tex]h\left(x\right)=\left(x-4\right)^2\left(x^2-7x+\:10\right)[/tex]
Let us determine the zeros of the function by putting h(x) = 0 and solving the expression
[tex]0=\left(x-4\right)^2\left(x^2-7x+10\right)[/tex]
switch sides
[tex]\left(x-4\right)^2\left(x^2-7x+10\right)=0[/tex]
as
[tex]x^2-7x+\:10=\left(x-2\right)\left(x-5\right)[/tex]
so
[tex]\left(x-4\right)^2\left(x-2\right)\left(x-5\right)=0[/tex]
Using the zero factor principle
[tex]\mathrm{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]so
[tex]x-4=0\quad \mathrm{or}\quad \:x-2=0\quad \mathrm{or}\quad \:x-5=0[/tex]
[tex]x =4, x=2, x = 5[/tex]
Thus, the zeros are:
[tex]x =4, x=2, x = 5[/tex]
It is clear that there are three zeros and all the zeros are distinct real numbers.
Therefore,
The function has three distinct real zeros.Hence, option (B) is true.
Related Questions
A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it or does not send it to anyone. Suppose that 10,000 people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter, and how many do not send it out?
Answers
Answer:
50,001 people sent out the letter.
40,001 did not send it out
also can i get brainliest???
Step-by-step explanation:
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
We have,
In the given scenario, the chain letter starts with one person sending it to five others.
Each recipient of the letter has the option to either send it to five new recipients or not send it to anyone.
Let's analyze the chain letter progression:
The first person sends the letter to 5 recipients.
Each of those 5 recipients has the choice to send the letter to 5 new recipients or not send it.
If each of the 5 recipients sends the letter to 5 new recipients, we have a total of 5 x 5 = 25 new recipients.\
If any of the 5 recipients choose not to send the letter, they are out of the chain.
Now, we have 25 recipients who received the letter and have the same choice: send it to 5 new recipients or not send it.
If each of the 25 recipients sends the letter to 5 new recipients, we have a total of 25 * 5 = 125 new recipients.
If any of the 25 recipients choose not to send the letter, they are out of the chain.
This process continues until the chain ends.
To determine how many people receive the letter and how many do not send it out, we can observe the pattern:
After the first step, there are 5 recipients.
After the second step, there are 5 + (5 * 5) = 30 recipients.
After the third step, there are 5 + (5 * 5) + (5 * 5 * 5) = 155 recipients.
After the fourth step, there are 5 + (5 * 5) + (5 * 5 * 5) + (5 * 5 * 5 * 5) = 780 recipients.
We can see that the number of recipients follows a geometric progression with a common ratio of 5.
The formula for the sum of a geometric progression is:
[tex]Sum = a (r^n - 1) / (r - 1)[/tex]
Where:
a = initial term = 5
r = common ratio = 5
n = number of steps
We are given that the chain ends after 10,000 people send out the letter. Let's calculate the number of recipients:
[tex]Sum = 5 (5^4 - 1) / (5 - 1)[/tex]
= 5 (625 - 1) / 4
= 5 624 / 4
= 780
Therefore, 780 people receive the letter before the chain ends.
To find the number of people who do not send it out, we subtract the number of recipients from the total number of people who sent out the letter:
Number of people who do not send it out = Total number of people - Number of recipients
= 10,000 - 780
= 9,220
Therefore, 9,220 people do not send out the letter.
Thus,
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ2
Write an equation of a line that is parallel to y = x - 7 and passes through the point (-6, -11).
Answers
Answer:
y = x - 5
Step-by-step explanation:
Comparing the given y = x - 7 to y = mx + b, we see that the slope is +1.
In y = x + b we replace y with -11 and x with -6 to determine the y-intercept, b:
-11 = -6 + b
Then b must be -5, and so the desired new equation is
y = x - 5
the temperature at 4 p.m. was -2 °c an hour later the temperature had decreased 3°c what was the temperature at 5:00 pm ?
Answers
Answer:
Step-by-step explanation:
3 degrees Celsius
It says at 4 p.m. was -2 degrees C. Then an hour later which would be 5 pm the temperature was 3 degrees C.
Select two ratios that are equivalent to 2:9
Choose 2 correct answers 40 points
Answers
Answer:
4:18 6:27 8:36
Step-by-step explanation:
The difference between 8 forty-sevens and forty-sevens
Answers
If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?
Answers
Step-by-step explanation:
Given: Radius , r =21 cm
The angle at the center of the circle, n° =140°
Length of an arc =?
W.K.T Formula, Length of an arc = 2πr( n°÷360°) units
= 2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Answer:
2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Step-by-step explanation:
Juan pago $50.00 pesos por 3 cajas de paquetes y 5 cajas de clavos, mientras que Pedro compró 5 cajas de taquetes y 7 cajas de clavos y tuvo que pagar $ 74.00 pesos . ¿ Cual es el precio de cada caja de taquetes y clavos ?
a) ¿ Cuantas incógnitas hay en el problema ?
b) ¿ Cuántas ecuaciones puedes construir según el texto?
c) ¿ Cuales son esas ecuaciones?
Answers
B ) dos
C ) 50 dividida 8, 74 dividida 12
espero que esto haya ayudado!
te agradecería que me dieras un gracias y brainliest (:
15 points theres an image to help you guys out too i need it ASAP though.. please
Answers
Answer:
16
Step-by-step explanation:
8-1+9
7+9=16
the answer is=16
Answer:
16
Step-by-step explanation:
(8-1) = 7 + 9
= 16
D ......
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Answer:
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Step-by-step explanation:
John can jog 3,000 feet in 5 minutes if she jogs at the same rate how many feet can she jog in 8 minutes
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a
Answers
Answer:
disproportionate stratified sample
Step-by-step explanation:
Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.
What is the unit cost of the olives at Mangio's
Answers
Answer:
$6
Step-by-step explanation:
18/3=6
24/4=6
30/5=6
36/6=6
The surface area of a three-dimensional object is the sum of the area of the faces. If represents the length of the side of a cube, write a formula for the surface area S of the cube.
Answers
Answer:
S = 6e²
I don't know what variable you're using here.
Step-by-step explanation:
There are 6 faces on a cube and they are all the same. Because of this, 6 is the coefficient in this equation.
A square's area can be found by squaring the side length (Which I'll represent with e). So e² is the variable.
Thus, the equation is S = 6e²
Evaluate the following expression using the values given:
Find 5x − 3y − z if x = −2, y = 2, and z = −3
Answers
Answer: -13
Step-by-step explanation:
just substitute the letters for the numbers.
5(-2) - 3(2) -(-3)
then, remove the parenthesis.
-10 - 6 + 3
finally, just calculate it.
-13
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Answers
Answer:
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Step-by-step explanation:
9.2-8.64=0.55
i hope it helps
Manuel ate lunch in 5 minutes. How many seconds is this?
Answers
Answer:
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Step-by-step explanation:
1 minute= 60 seconds
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Answer:
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Polly buys 14 cupcakes for the party. the bakery puts them into boxes that hold 4 cupcakes each.
how many boxes will be needed for Polly to bring all the cupcakes to the party? Explain
Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
117
Step-by-step explanation:
Hi, If you were to add 75 to 42, you would get 117. Since a triangle's angles all have to add up to 180, the last angle would be 63. However, you are looking for the outside angle, which would then just be 117. Hope this is right!
PLZ HELP if u know the answer for sure
Answers
Answer this please i need help
Answers
Answer:
Slope m = -3
y-intercept (0, 0)
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
y = -3x
Step 2: Break Function
Identify Parts.
Slope m = -3
y-intercept b = 0
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Answers
Answer:
Step-by-step explanation:
wheres the diagram?
Answer:B
Step-by-step explanation:
Last year 950 people attended a town's annual parade. This year 1,520 people attended. What was the percent increase in attendance from last year to this year?
Answers
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Step-by-step explanation: look up calculator soup if you have more questions like this
Carly earned some money doing odd jobs last summer and put it in a savings account that earns 5% interest compounded quarterly. After 2 years, there is $400.00 in the account. How much did Carly earn doing odd jobs? * A. 155.90 B. 441.79 C. 390.18 D. 362.16
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Question #5
Consider the equation.
72 +48 = 8
1+6)
Enter the unknown number that makes the equation true.
Your answer
Σ
Answers
72=8x 8*9=72
In the diagram, line p(perpendicular) line r. Which must be true?
Answers
WILL MARK BRAINLIEST
what type of transformation is described by (x,y) —> (x+2, y+16)?
Answers
This transformation takes a vector (x,y) and maps it to the vector (x+2, y+16). In other words, it moves the X coordinate of the vector 2 units to the right, and the Y coordinate of the vector is moved 16 units upwards.
If you would take a set of points and apply this transformation, you would see the entire set moving upwards and to the right, with no stretching ou rotating. This type of transformation is called a translation transformation.
5.00 minus2.40minus1.33= plz show me how you got that answer step by step
Answers
Answer:
5.00 -2.40= 2.60
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The answer is 1.27
Step-by-step explanation:
Find the unit rate.
You earn $15 in 3/4 of a month. At this rate, how much do you make in 1 month?
Answers
Answer:
you make 20 dollars in a month
Step-by-step explanation:
15 is 3/4 a month, unit rate would be 5 dollars a week so therefore a whole month would be 20