Answers
Answer:
The zeros of the function:
[tex]x=5.53 ,[/tex] [tex]x=3.22[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=2x^2-17.5x+35.6[/tex]
To find zeros, put f(x)=0
[tex]0=2x^2-17.5x+35.6[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]
[tex]0\cdot \:10=2x^2\cdot \:10-17.5x\cdot \:10+35.6\cdot \:10[/tex]
[tex]0=20x^2-175x+356[/tex]
switch sides
[tex]20x^2-175x+356=0[/tex]
subtract 356 from both sides
[tex]20x^2-175x+356-356=0-356[/tex]
[tex]20x^2-175x=-356[/tex]
divide both sides by 20
[tex]\frac{20x^2-175x}{20}=\frac{-356}{20}[/tex]
[tex]x^2-\frac{35x}{4}=-\frac{89}{5}[/tex]
[tex]\mathrm{Add\:}a^2=\left(-\frac{35}{8}\right)^2\mathrm{\:to\:both\:sides}[/tex]
[tex]x^2-\frac{35x}{4}+\left(-\frac{35}{8}\right)^2=-\frac{89}{5}+\left(-\frac{35}{8}\right)^2[/tex]
applying perfect square
[tex]\left(x-\frac{35}{8}\right)^2=\frac{429}{320}[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solving
[tex]x-\frac{35}{8}=\sqrt{\frac{429}{320}}[/tex]
[tex]x=\frac{\sqrt{2145}}{40}+\frac{35}{8}[/tex]
[tex]x=5.53[/tex]
also solving
[tex]x-\frac{35}{8}=-\sqrt{\frac{429}{320}}[/tex]
[tex]x=-\frac{\sqrt{2145}}{40}+\frac{35}{8}[/tex]
[tex]x=3.22[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=5.53 ,[/tex] [tex]x=3.22[/tex]
Therefore, the zeros of the function:
[tex]x=5.53 ,[/tex] [tex]x=3.22[/tex]
Related Questions
At the arcade, Ryan, Sara, and Tim played video racing games, pinball, and air hockey. Ryan spent $6 for 6 racing games, 2 pinball games, and 1 game of air hockey. Sara spent $12 for 3 racing games, 4 pinball games, and 5 games of air hockey. Tim spent $12.25 for 2 racing games, 7 pinball games, and 4 games of air hockey. How much did each of the games cost?
Answers
Answer: Racing $.50
Pinball $.75
Air Hockey $1.50
4x = y + 3
8x - 3= 2y
Graph the system
Answers
At the movie theatre, child admission is 5.50 and adult admission is 9.20. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of 662.00 . How many child tickets were sold that day?
Answers
Step by step
Let child tickets be “C”
Let adult tickets be “A”
We know
Adult tickets = 3 Child tickets
Equation 1
A = 3C
We know C = 5.50 and A = 9.20 and the total is 662
Equation 2
5.50C + 9.20A = 662
Substitute equation 1 value of A into the equation and solve
5.50C + (9.20)(3C) = 662
5.50C + 27.60C = 662
33.10C = 662
Divide both sides by 33.10 to solve for C
33.10 /33.10 C = 662
C = 20
20 child tickets sold
We can solve for adult tickets and check our work
Equation 1
A = 3C
Substitute C value into equation
A = (3)(20)
Adult tickets = 60
We know C = 5.50 and A = 9.20 and the total is 662
5.50C + 9.20A = 662
(5.50)(20) + (9.20)(60) = 662
110 + 552 = 662
662 = 662
We are correct they equal
Problem solved!!
How many different 10-letter words (real or imaginary) can be formed from the following letters? E, T, A, R, N, I, T, C, F, R Question content area bottom Part 1 enter your response here ten-letter words (real or imaginary) can be formed with the given letters.
Answers
Answer:
10! or 3628800 words=============================
Given 10 letters and we are looking for the number of 10-letter words.
This is about the permutation of 10:
[tex]_{10}P_{10} = 10! = 3628800[/tex]NEED OF IMMEDIATE HELP
Answers
Answer:
There are no sampling errors, as all numbers add up to 100, however, there is a bias, as the highest number is 52 for movies, and the person who conducted the survey was a movie theater manager to his own customers.
Simplify the expressions:
−8y³ x 5y8
Answers
I hope this helps.
Hi! Your answer is 11. When multiplying terms with exponents, the exponents add up.
Step-by-step explanation:
You want to multiply the terms with the exponents. You should get 3 and 8, add those up and you will get 11.
Hope this helps! Have a good day :)
Kiara and Donovon attend different middle schools. They both went to their schools’ winter carnivals. Kiara paid a $5 entrance fee and bought several tickets costing $0.75 each for games and rides. Donovon paid a $7 entrance fee and bought several tickets costing $0.50 each for games and rides. How many tickets, , must Kiara and Donovan each buy in order for the cost of attending their school carnivals to be the same?
Answers
Using linear functions, it is found that they have to buy 8 tickets for the costs to be the same.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we consider that:
The entrance fee is the intercept.The cost for carnivals(games/rides) is the slope.Hence the cost functions for Kiara and Donovon are given, respectively, by:
K(x) = 5 + 0.75x.D(x) = 7 + 0.5x.The costs will be the same when:
K(x) = D(x)
5 + 0.75x = 7 + 0.5x.
0.25x = 2
x = 2/0.25
x = 8.
They have to buy 8 tickets for the costs to be the same.
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HELPPPOOOOMEEEEEEW PLEASE
Answers
Answer: 124 degrees
Step-by-step explanation:
JKL=YKL+JKY
10x+14=6x-6+64
10x+14=6x+58
4x+14=58
4x=44
x=11
JKL=10x+14
JKL=10(11)+14
JKL=110+14
JKL=124 degrees
What is the solution to the system of equations?
7x-y=6
-7x+y=-6
Answers
Answer:
x= 7/ y+6
Step-by-step explanation:
Add y to both sides.
7x=6+y
The equation is in standard form.
7x=y+6
Divide both sides by 7.
7
7x = 7/y+6
Dividing by 7 undoes the multiplication by 7.
Step-by-step explanation:
that's what I think it isx=7/y+6
Multiply.
9/4 ⋅ 14
A. 23/4
B. 28
C. 63/2
D. I don't know.
Answers
Answer:
C. 63/2
Step-by-step explanation:
[tex] \frac{9}{4} \times 14 \\ = \frac{9}{4} \times \frac{14}{1} \\ = \frac{9 \times 7}{2} = \frac{63}{2} \\ please \: if \: found \: helpful \: rate \: brainliest.[/tex]
The answer is 63/2
I got 100% on the test
I hope this helps!
Proof that this answer is correct and not fake
Eli runs a distance of 3 miles in 2/5 of an hour. jess runs a distance of 4/5 mile in 1/10 of an hour. who had the faster speed
Answers
Jess had a faster speed of 8 miles/hour
Given:
3 miles in 2/5 hour
4/5 miles in 1/10 hour
To find the quotient, we must switch to the inverse approach,
where 2/5 becomes 5/2 and 1/10 becomes 10/1.
For Eli:
A distance of 3 miles is covered in 2/5 of an hour.
3 miles equals 2/5*1
3 miles equals 2/5 hour
The inverse amount is multiplied as
3*5/2 miles = 1 hour.
7.5 miles
Eli moves at a 7.5 mph speed.
For Jess:
1/10 of a mile is covered in 4/5miles.
1/10 * 1 hour times 4/5 miles
1/10 hour equals 4/5 miles.
The inverse number is multiplied as follows: 4/5 * 10/1 = 1 hour.
40 miles at a speed of 5 miles per hour.
1 hour Equals 8 miles
Jess's speed is 8 miles per hour.
Hence, Jess had a faster speed of 8 miles per hour
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Please Help Me! Will be brainlest
E=-7g^4+3g^2h^2-11h^4
F=6g^4-13g^2h^2+8h^4
E+F=
Answers
The addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
ExponentE = - 7g⁴ + 3g²h² - 11g⁴
F = 6g⁴ - 13g²h² + 8h⁴
E + F = (- 7g⁴ + 3g²h² - 11g⁴) + (6g⁴ - 13g²h² + 8h⁴)
= - 7g⁴ + 3g²h² - 11g⁴ + 6g⁴ - 13g²h² + 8h⁴
collect like terms= -7g⁴ + 6g⁴ + 3g²h² - 13g²h² - 11g⁴ + 8h⁴
evaluate= - g⁴ - 10g²h² - 3g⁴
Therefore, the addition of the given expression "E = - 7g⁴ + 3g²h² - 11g⁴" and "F = 6g⁴ - 13g²h² + 8h⁴" is "- g⁴ - 10g²h² - 3g⁴"
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{x€N | 25 ≤ x² < 50}
Answers
Answer:
x = { 5; 6; 7}
Step-by-step explanation:
25 ≤ 25 < 36 < 49 < 50
=> x² = {25; 36; 49}
Because x€N => x = {5; 6; 7}
If Cindy shoots a ball at a basket 40 times
and scores 15 times, what is the
experimental probability of Cindy scoring?
Answers
Experimental probability of Cindy scoring=0.375
Probability:
Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain.
The probabilities in a probability model must sum to 1.
When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment.
To find the probability of the union of two events, we add the probabilities of the two events and subtract the probability that both events occur simultaneously.
To find the probability of the union of two mutually exclusive events, we add the probabilities of each of the events.
The probability of the complement of an event is the difference between 1 and the probability that the event occurs.
In some probability problems, we need to use permutations and combinations to find the number of elements in events and sample spaces.
Formula :
probability of an event with equally likely outcomes : [tex]\frac{n( experimental-event )}{n(total no. of event )}[/tex]
Given :
Total no. of event =Cindy shoots a ball at a basket 40 times
experimental event = 15 times
[tex]P(E)= \frac{15}{40} \\P(E)=\frac{3}{8} \\P(E)= 0.375\\[/tex]
experimental probability of Cindy scoring=0.375
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The sum of a daughter and mother's age is 55. The age of the daughter is the
mother's age reversed. Find the age of the daughter if the age of the mother is
greater than 40 years.
Answers
center at (2, -2) and twice the area of the circle (x, -7)² + (y, -7)² =7
Answers
Answer:
[tex](x-2)^2+(y+2)^2=14[/tex]
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the center of the circle.r is the radius of the circle.Given equation:
[tex](x-7)^2+(y-7)^2=7[/tex]
Therefore:
center = (7, 7)radius = √7Area of a circle
[tex]\sf A=\pi r^2[/tex]
where:
r is the radius.Therefore, the area of a circle with radius √7 is:
[tex]\implies \sf Area=\pi \left(\sqrt{7}\right)^2=7 \pi\:\:square\:units[/tex]
Therefore, a circle with twice the area would be:
[tex]\implies \sf Area = 2 \cdot 7 \pi = 14 \pi \:\: square\:units[/tex]
Therefore, its radius would be:
[tex]\begin{aligned}\implies \sf \pi r^2 & = \sf14 \pi\\\sf r^2 & = \sf 14\\\sf r & = \sf \sqrt{14}\end{aligned}[/tex]
So the equation of a circle with a center at (2, -2) and a radius of √14 is:
[tex]\implies (x-2)^2+(y-(-2))^2=\left(\sqrt{14}\right)^2[/tex]
[tex]\implies (x-2)^2+(y+2)^2=14[/tex]
Decide what values of the variable cannot possibly be solutions for the equation. Do not solve.
Answers
By inspecting the denominator, the values of x cannot be solutions of the rational equation are x₁ = - 3 and x₂ = 2.
What values does lead to an indetermination in a rational equation?
A rational equation is an expression of the P(x) / Q(x), where P(x) and Q(x) are the equations of the numerator and the denominator functions. The rational equation becomes undefined for all x-values such that Q(x) = 0. Then, we must look up for all values of x such that:
x² + x - 6 = 0
x² + [3 + (- 2)] · x - 6 = 0
x² - 2 · x + 3 · x - 6 = 0
x · (x - 2) + 3 · (x - 2) = 0
(x + 3) · (x - 2) = 0
x₁ = - 3 ∨ x₂ = 2
The values of x cannot be solutions of the rational equation are x₁ = - 3 and x₂ = 2.
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Enter the value of 3/4(8.8)=
Answers
Answer:
6.6 is the answer
Step-by-step explanation:
Hope it helps you
7th- grade question
7. Billy cut the grass for 3/5 of an hour on Monday and 3/10 of an hour on
Tuesday. What fraction of an hour did he spend cutting grass for the two
days?
A. 1/5
B. 2/5
C. 5/10
D. 9/10
Answers
Answer:
The answer is c because if you multiply 3/5 and 3/10 by doing butterfligt
Add (4) and (−15) if right i will give brainliest
−11
−19
19
11
Answers
-11 is the answer to this question
Answer:-11
Step-by-step explanation:
-15 + 4 = -11
A manufacturer estimates his marginal cost and revenue at various levels of output to be the following. If fixed cost is 500, estimate, using the Simpsons rule, the total profit or loss of producing 100 units is Blank 1. Fill in the blank, read surrounding text.
GHC
q (units)
0
20
40
60
80
100
120
MC
260
250
240
200
240
250
270
MR
410
350
300
250
270
250
300
Answers
If the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
What is the profit when MC = MR?When the marginal cost (MC) equals the marginal revenue (MR), the company breaks even, and from that point, profit maximization starts.
When MR is more than MC, the tendency is for the firm to produce more and earn more profit, and when MR is less than MC, the firm produces fewer as it incurs losses.
The profit maximization level occurs where the MR and the MC are equal.
Data and Calculations:Total revenue = fixed cost + variable cost (MR x Units)
Total revenue = 500 + (100 x 250)
Total revenue = 500 + 25,000
Total revenue = GHC 25,500
Total profit or loss at 100 units = GHC0 (GHC25,500 - GHC25,500)
GHC
q (units) 0 20 40 60 80 100 120
MC 260 250 240 200 240 250 270
MR 410 350 300 250 270 250 300
Thus, if the fixed cost is GHC500, the total profit or loss of producing 100 units is GHC 0.
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help me out please!!!!
Answers
Answer:
I believe the Answer is C.
Step-by-step explanation:
the weight of an organ in adult male has a bell shaped distribution with a mean of 300 grams and a standard deviation of 25 grams. Use the empirical rule to determine the following:
a.) About 95% of organs will be between what weights?
b.) What percentage of organs weighs between 225 grams and 375 grams?
c.) What percentage of organs weighs less than 225 grams or more than 275 grams?
d.) what percentage of organs weighs between 275 grams and 275 grams?
Answers
Using the Empirical Rule, it is found that:
a) About 95% of the organs will be between 250 and 350 grams.
b) 99.7% of organs weighs between 225 grams and 375 grams.
c) 84.15% of organs weighs less than 225 grams or more than 275 grams.
d) 0% of organs weight exactly 275 grams.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.95% of the weights are within 2 standard deviations of the mean, hence:
300 - 2 x 25 = 250 grams.300 + 2 x 25 = 350 grams.About 95% of the organs will be between 250 and 350 grams.
For item b, the amounts are within 3 standard deviations of the mean, hence:
99.7% of organs weighs between 225 grams and 375 grams.
For item c, considering the symmetry of the normal distribution, we have that:
0.5 x 0.003 = 0.15% weigh less than 225 grams.0.5 x 68% + 50% = 84% weight more than 275 grams.Hence:
84.15% of organs weighs less than 225 grams or more than 275 grams.
For item d, considering that the normal distribution is continuous, the percentage of an exact value is 0, hence:
0% of organs weight exactly 275 grams.
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7 grade
1. Andrea walked 1/2 miles in 1/3 of an hour at a constant speed. What was that speed?
A. 1 miles per hour
B.1.25 miles per hour
C.1.5 miles per hour
D.2.5 miles per hour
Answers
Answer:
C
Step-by-step explanation:
0.5 of a mile in 20 minutes
60/20=3
0.5*3=1.5
Correct answer is C
if DF = 9x-39 find EF
DE = 47
EF = 3X+10
Answers
The length of the line segment EF is 106.
The distance between the end points of DF is equal to 9x-39.The distance between the end points of DE is equal to 47.The distance between the end points of EF is 3x + 10.Applying the logic that the line segments are a part of the same straight line, we can conclude thatThe length of the line segment DF is equal to the sum of the lengths of the line segments DE and EF.DF = DE + EF.9x - 39 = 47 + (3x + 10)9x - 6x = 47 + 10 + 393x = 96x = 32The length of the line segment EF is 3*32 + 10.The length of the line segment EF is 96 + 10.Thus, the length of the line segment EF is 106.To learn more about distance, visit :
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Evaluate-nx + x when x = 2.
Answers
Answer:
-2n + 2
Step-by-step explanation:
They give you the X value which is 2
All you do is substitute
-2n + 2
Hope this helped
Answer this question please
Answers
'less than' corresponds to the < symbol, so the inequality is x<1.2. However, the weight cannot be negative or zero, so the inequality is 0<x<1.2.
In interval notation, this is (0, 1.2).
A cube-shaped box has a side length of 6n³ centimeters. Amelia has several cube-shaped blocks with a side length of 2n centimeters that she needs to store in the box. what is the volume of one block? what is the volume of the box
Answers
The volume of blocks is 8n³ cm³ and volume of box is 216 n⁹ cm³.
According to the question we have been given that the
side length of the cube shaped box = 6n³ cm
side length of the cube shaped blocks = 2n cm
We need to find the volume of the box and the blocks.
The formula for the volume of cube is
V = (s)³ cubic units.
where, s = side length of the cube
Now putting the required values in the above formula we get
volume of box = (6n³)³ cm³
= 216 n⁹ cm³
volume of the blocks = (2n)³ cm³
= 8n³ cm³
Hence the volume of blocks is 8n³ cm³ and volume of box is
216 n⁹ cm³.
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HELP MEEEEE OUTTTT PLEASEEE
Answers
check the image below for working
Answer:
other answer is right
Step-by-step explanation:
just answering so they can get brainliest:)
Leah is training to run half marathon Her goal For training is to run 20 miles a week. she ran 3 1/2 Miles on Monday 4. 3/4 miles on Tuesday 5 miles on Wednesday And 4 miles On Thursday. how Many Miles will She Need to run On Friday In Order to meet her goal?
Answers
The number of miles she should run on Friday is 2 3/4 miles.
Given that, Leah is training to run a half marathon her goal training is to run 20 miles a week. she ran 3 1/2 miles on Monday 4 3/4 miles on Tuesday 5 miles on Wednesday and 4 miles on Thursday.
We need to find how many miles will she need to run on Friday in order to meet her goal.
How to add mixed fractions?Follow these steps to add mixed fractions:
Add the whole numbers together. Find the lowest common denominator (LCD) of both fractions. The LCD is the lowest number that is evenly divisible by both numbers.Convert the fractions to have the LCD as their denominator.Once you have a common denominator, the fractions can be added by simply adding the numerators.Now, the number of miles she ran together from Monday to Thursday
=3 1/2 + 4 3/4 + 5 + 4 =(3+4+5+4)(1/2 + 3/4)
=16 (2/4 + 3/4)
=16 5/4
=17 1/4
Remaining miles = 20-17 1/4
=20-69/4
=(80-69)/4
=11/4
=2 3/4
Therefore, the number of miles she should run on Friday is 2 3/4 miles.
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