Answer:
[tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Step-by-step explanation:
We are given that the only roots of the given polynomial f(x) are 1 and -5 with multiplicity (the number of times the roots are repeating) 2 and 1 respectively.
Also, it is provided that the function satisfy that f(x)=0.
So, comparing the two information we have that,
f(x) = 0 and 1, -5 are the roots of f(x),
i.e [tex](x-1)^{2} \times (x+5) = 0[/tex]
i.e. [tex](x^{2} +1-2x) \times (x+5) = 0[/tex]
i.e. [tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Also, we can see that ths polynomial has leading co-efficient 1 i.e. the co-efficient of highest degree variable i.e. x^{3}.
Hence, the polynomial having leading co-efficient 1 and roots 1, -5 is [tex]x^{3} +3x^{2}-9x+5 = 0[/tex].
An experiment consists of randomly selecting a marble from a bag, keeping it, and then selecting another marble. The bag contains 4 blue marbles, 3 green marbles, 7 red marbles, and 1 yellow marble. What is the probability of selecting a red marble and then a blue marble? SHOW ALL WORK!
Answer:
2/15
Step-by-step explanation:
How many marbles are in the bag
4blue + 3 green + 7 red + 1 yellow = 15 marbles
On the 1st draw:
red/total = 7/15
Since we keep the marble, there are only 14 marbles left
4blue + 3 green + 6 red + 1 yellow = 14
On the 2nd draw:
blue/total = 4/14 = 2/7
To find the probability of the two draws, we multiply them together
1st draw * 2nd draw
7/15 * 2/7 = 2/15
A shoe store marks up it's merchandise by 8 percent what was the selling price of a pair of shoes whose wholesale price is 24.50
The answer is 26.46. I got it correct on my GoFormative.
The price of shoe store merchandise after markup price will be equal to 26.46.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given data given in the question,
The wholesale price of merchandise = 24.50
Markup percentage on merchandise = 8%
Then, the amount of increment in the price will be,
(24.50 × 8)/100
= 196/100
=1.96
Then, the price of merchandise after markup will be,
= 24.50 + 1.96
= 26.46
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A school board has determined that there should be 4 teachers for every 50 students. How many teachers are needed for an enrollment of 2,650 students?
Answer:
212 teachers are needed for an enrollment of 2,650 students.
Step-by-step explanation:
This is a kind of question that can be solved using proportions.
Proportions are used when we are asked about finding one unknown value, knowing the value of others that keep a ratio among all of them, including the unknown value.
In this case, we know that a school board estimated that 4 teachers are needed for every 50 students:
[tex]\\ \frac{4_{teachers} }{50_{students}}=ratio[/tex]
If we divide 4 teachers by 50 students, we obtained a ratio, or a constant relationship that remains between teachers and students, that is, how many teachers are needed for the number of students, or more generally "how many times the first number contains the second" [Wikipedia, 2019].
We can also notice that more students require more teachers (which is a relation of direct proportionality), that is, if we require more students, more teachers are also required in the same ratio or constant already mentioned.
Then, we can make a proportion among these values because they keep the same ratio of teachers to students (but can also be students to teachers).
So, we can pose the following question:
If four (4) teachers are needed for every 50 students, how many teachers are needed to attend 2,650 students? Then,
[tex]\\ \frac{4_{teachers}}{50_{students}} = \frac{X_{teachers}}{2650_{students}} [/tex] = the same ratio or constant.
To know the amount of teachers needed for 2,650 students:
[tex]\\ X_{teachers} = \frac{2650_{students} * 4_{teachers} }{50_{students}}[/tex].
or,
[tex]\\ X_{teachers} = \frac{2650 * 4_{teachers} }{50}[/tex].
[tex]\\ X_{teachers} = 212_{teachers}[/tex].
So, for an enrollment of 2,650 students there should be 212 teachers, according to the ratio (teachers/students) previously determined by the school board.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
The polynomial function y = x^3 -3x^2 + 16x - 48 has only one non-repeated x-intercept. What do you know about the complex zeros of the function?
Answer: B
Step-by-step explanation:
x³ - 3x² + 16x - 48 = 0
→ x²(x - 3) + 16(x - 3) = 0
→ (x² + 16) (x - 3) = 0
→ (x² - (-16)) (x - 3) = 0
→ (x - 4i)(x + 4i)(x - 3) = 0
→ x - 4i = 0 x + 4i = 0 x - 3 = 0
→ x = 4i x = -4i x = 3
2 imaginary roots and 1 real root
Patty earns a raise of 4precent each year .If her starting salary is 24,812.00 , what will be her salary after one year?
the linear regression equation for a data set is y=-2.8x+70.8 where y is the temperature in degrees fahrenheit and x is the number of hours since 8am.what does the slope of the equation represent?
Step-by-step explanation:
We have been given the linear regression equation for a data set is y=-2.8x+70.8 where y is the temperature in degrees Fahrenheit and x is the number of hours since 8 am.
We can see that our given line is in slope-intercept form: [tex]y=mx+b[/tex], where, m = Slope of line and b = y-intercept.
Upon comparing our given equation with slope intercept form we can see that the slope of the equation (m) is -2.8. The slope represents that temperature is dropping at a rate of 2.8 Fahrenheit per hour after 8 am.
I need help with this question 15 points
Answer:
Third option
Step-by-step explanation:
You are correct, right angle forms a 90°
Hope that helps
Answer:
The third option.
Step-by-step explanation:
The first option is acute becuase the angle is less that 90 degrees.
The second options is obtuse because it is more than 90 degrees.
The third option is a right angles becuase it makes an 90 degree angle.
The fourth option is also obtuse because it is more than 90 degrees.
Hello!! This is a A-F question, so it's kind of long, but I will definitely be making it worth your time if you could help me out with it!
Thank you so much :)
(Reporting any wrong answers so please don't post them!!)
Answer:
Please, see the attached files.
Step-by-step explanation:
Please, see the attached files.
Thanks.
How much does a length of aluminum expand if it is 1.2 meters long at 15 degrees c and heated to 65 degrees c
write the first five terms of the geometric sequence with a1=-2 and common ratio r=-5/2
Answer:
option D
Step-by-step explanation:
First term is -2
common ratio = -5/2
To get second term we multiply first term -2 by common ratio -5/2
[tex]-2 * \frac{-5}{2} =\frac{10}{2} = 5[/tex]
To get third term we multiply second term 5 by common ratio -5/2
[tex]5 * \frac{-5}{2} =\frac{-25}{2}[/tex]
To get fourth term we multiply third term -25/2 by common ratio -5/2
[tex]\frac{-25}{2}*\frac{-5}{2} =\frac{125}{4}[/tex]
Option D is correct
The first five terms of the geometric sequence with a first term of -2 and a common ratio of -5/2 are -2, 5, -12.5, 31.25, and -78.125.
To find the terms of a geometric sequence, we start with the first term and multiply each subsequent term by the common ratio. In this case, the first term, a1, is -2 and the common ratio, r, is -5/2.
The first term (a1) is -2
The second term (a2) is -2*(-5/2) = 5
The third term (a3) is 5*(-5/2) = -12.5
The fourth term (a4) is -12.5*(-5/2) = 31.25
The fifth term (a5) is 31.25*(-5/2) = -78.125
Therefore, the first five terms of the sequence are -2, 5, -12.5, 31.25, and -78.125.
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Which table shows a proportional relationship between x and y?
x 3 9 10 15
y 1 3 4 5
x 4 6 8 10
y 6 8 10 12
x 1 5 8 10
y 15 75 120 150
x 2 3 5 6
y 3 4 7 9
Answer:
the third table listed here
Step-by-step explanation:
A "proportional" relationship has the same y/x ratio for all values of x and y.
... first table: all entries but one have y/x = 1/3. The 3rd entry has y/x = 0.4—not the same.
... second table: 6/4 ≠ 8/6
... third table: all entries reduce to y/x = 15
... fourth table: 3/2 ≠ 4/3
Shelly is trying to improve her running time for a track race she ran the first race in 43.13 seconds her time was 43.1 seconds in the third race of this pattern continues what will Shelly time will be inthe fourth race
Answer:
The time in the fourth race is 43.04 seconds.Step-by-step explanation:
Shelly's first race time is 43.13 seconds.
Shelly's second race times is 43.1 seconds.
Basically, she improved 0.03 seconds, because 43.13 - 43.1 = 0.03.
If she keeps this patterns that means she will improve 0.03 each race.
So, the third race times is 43.1 - 0.03 = 43.07 seconds.
The fourth race time is 43.07 - 0.03 = 43.04 seconds.
Therefore, the time in the fourth race is 43.04 seconds, because she's improving at a constant rate of 0.03 seconds per race.
Ivan's favorite colors are \blue{\text{blue}}blue and \green{\text{green}}green. He has \blue{\text{1 blue shirt}}1 blue shirt, \green{\text{1 green shirt}}1 green shirt, \blue{\text{1 blue hat}}1 blue hat, \green{\text{1 green belt}}1 green belt, \blue{\text{1 blue pair of pants}}1 blue pair of pants, and \green{\text{1 green pair of pants}}1 green pair of pants. Ivan selects one of these garments at random. Let A be the event that he selects a green garment and B be the event that he chooses a pair of pants. What is P(A\text{ or }B)P(A or B), the probability that the garment Ivan chooses is either green or a pair of pants?
Answer:
P(A or B) = 2/3
Step-by-step explanation:
Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants
Total blue garments = 3
Green garments= 1 green shirt, 1 green hat, 1 green pair of pants
Total green garments = 3
Total no. of garments = blue garments +green garments = 6
A = event that Ivan selects a green garment
P(A) = Favourable outcomes/Total no. of outcomes
P(A) = 3/6
B = event that Ivan chooses a pair of pants
P(B) = 2/6
We need to find P(A or B) = P(A∪B)
By formula, P(A∪B) = P(A)+P(B)-P(A∩B)
P(A∩B) = Probability that a green pair of pant is chosen = 1/6
P(A∪B) = 3/6+2/6-1/6
= 4/6
=2/3
Answer:
1/2
Step-by-step explanation:
Ms. Miller wants to give each of her students 1/4 of a pound of modeling clay. She has 26 students. How many pounds of modeling clay does she need?
A) 6
1
2
B) 8
3
4
C) 13
D) 26 what the answer
Answer:
she give each kid about 6
Step-by-step explanation:
26/.25=104
104/16= 6.5
If ?ABC and ?XYZ are similar, which must be true? A) BC YZ = AC YX B) BC YZ = BA XZ C) AC XZ = BC YZ D) AC XZ = BA XZ
Answer:
The correct option is C.
Step-by-step explanation:
Let triangle ABC and XYZ are similar.
If two triangles are similar, then ratio of their corresponding sides are same.
Since ABC and XYZ are similar, therefore sides AB, BC and AC are corresponding to the sides XY, YZ and XZ respectively.
[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]
From the above equation we can conclude that
[tex]\frac{BC}{YZ}\neq \frac{AC}{YX}[/tex]
[tex]\frac{BC}{YZ}\neq \frac{BA}{XZ}[/tex]
[tex]\frac{AC}{XZ}\neq \frac{BA}{XZ}[/tex]
Therefore option A,B and D are incorrect.
Answer: BC/YZ = AC/XZ
Step-by-step explanation:
Remember the end letters need to be the same. So if you look at your choices this is the only one that is in order BC AC
YZ XZ
took the test
Vanessa earns a base salary of \$400.00$400.00 every week with an additional 5\%5% commission on everything she sells. Vanessa sold \$1650.00$1650.00worth of items last week. What was Vanessa's total pay last week?
Answer:
Total pay = 400+ 1650* 5/100= 482,5 $
Step-by-step explanation:
A company manufactured 1,287 drones last year. The company shipped 2 percent of those drones to Australia. How many drones did the company ship to Australia? Round your answer to the nearest whole drone.
This is a very difficult question. In △PQR, point T is on side QR such that QT=6 and TR=10. What is the ratio of the area of △PQT to the area of △PTR. Help please
Answer:
the ratio of the area is 3:5
Step-by-step explanation:
Find a common factor of 6 and 10 and then divide it, the common factor is 2
6 divided by 2 is 3
10 divided by 2 is 5
so your ratio area is 3:5
Hope this helps :)
please help on this ? :)
Which inequality is represented by this graph? Also, if someone could tell me how this works that would be great :D
Answer:
y > -1/6 x+1
Step-by-step explanation:
The graph line is dotted. Dotted lines means greater than or less than. ( <, >)
Solid lines means less than or equal to or greater than or equal to (≤,≥)
Since the graph is shaded above the line, that means y is greater than the line. If it were shaded below the line, y would be less than.
y > -1/6 x+1
From 19801980 to 20002000, the annual profit of a company was determined by subtracting from \$625{,}000$625,000 the product of \$25{,}000$25,000 and the number of years either before or after 19901990. Which of the following equations below could be used to determine in which year, xx, the profit was \$550{,}000$550,000?
a.550−25∣x−1990∣=625
b.625 - 25 | x - 1990 | = 550625−25∣x−1990∣=550
c.625 +25 | x - 1990 | = 550625+25∣x−1990∣=550
d.625 +25 | x + 1990 | = 550625+25∣x+1990∣=550
Answer: b) 625 - 25 |x - 1990| = 550
Step-by-step explanation:
According to the question,
The annual profit of a company was determined by subtracting from $625,000 the product of $25,000 and the number of years either before or after 1990.
That is, On x year the total profit is,
P(x) = 625,000 - 25,000 |x - 1990|
But again according to the question,
On x years the profit is $ 550,000
Thus, 625,000 - 25,000 |x - 1990| = 550,000
⇒ 625 - 25 |x - 1990| = 550 ( by dividing both sides by 1000)
Therefore, Option b) is correct.
The correct equation for determining the year when the profit was $550,000 is 625 - 25 | x - 1990 | = 550, where x represents the year, option B.
The annual profit of the company can be determined by the equation that subtracts the product of a certain amount ($25,000) and the number of years before or after 1990 from $625,000. If we are given that the profit was $550,000 in year x, we need to find the value of x that satisfies this condition. We will represent the difference in years as the absolute difference from 1990, which accounts for years before and after 1990 equally.
The correct equation based on this would be the one that represents the profit ($550,000) after subtracting the product of $25,000 and the absolute difference in years from $625,000. Thus, the correct equation should subtract from $625,000 (not add to it), and it should involve the absolute value of x - 1990 to denote the number of years before or after 1990.
The equation that fits these criteria is:
625 - 25 | x - 1990 | = 550
Here, when we solve for x, we're trying to find the year in which the profit was $550,000. Therefore, option (b) is the correct choice.
Simplify. 4x^2-x/16x^2-1
[tex]\dfrac{4x^2-x}{16x^2-1}=\dfrac{x(4x-1)}{(4x)^2-1^2}\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=\dfrac{x(4x-1)}{(4x-1)(4x+1)}=\dfrac{x}{4x+1}\\\\Answer:\ \boxed{\dfrac{4x^2-x}{16x^2-1}=\dfrac{x}{4x+1}}[/tex]
By simplifying (4x ² - x ) / (16 x² -1) we get :
= x / 4x + 1 .
Explain simplification?Simplifying an expression is the same as solving a math problem. When you simplify an expression, you are attempting to write it in the simplest possible manner. There should be no more adding, subtracting, multiplying, or dividing to do at the end.The basic rules and steps for simplifying any algebraic expression are as follows:
By multiplying factors, you can get rid of any grouping symbol, such as brackets and parentheses.If the terms contain exponents, use the exponent rule to remove grouping.By adding or subtracting like terms, you can combine them.Add the constants together.Given equation, (4x ² - x ) / (16 x² -1)
Factorize 4x² - x ,
= x ( 4x - 1) / 16x² - 1
factorize 16x² -1,
= x (4x - 1) / (4x + 1 ) (4x - 1 )
By cancelling common factor 4x - 1,
= x / 4x + 1
Simplifying (4x ² - x ) / (16 x² -1) = x / 4x + 1 .
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Carl rode a horse about 15 f ode a horse about 15 feet from the center of the car om the center of the carousel. Allison r ousel. Allison rode a horse about 10 f a horse about 10 feet from the center om the center. How much fur . How much further did Carl' ther did Carl's horse s horse travel in one complete turn of the carousel?
Carl's horse traveled approximately 31.4 feet further than Allison's horse in one complete turn of the carousel. The distances were calculated using the circumference formula for each horse based on their distance from the centre of the carousel.
Explanation:The question involves comparing the distances traveled by horses on a carousel based on their distance from the center of the ride. To find out how much further Carl's horse traveled compared to Allison's, we need to calculate the circumference of the circular paths each horse took during one complete turn of the carousel and then find the difference between these two distances.
To calculate the circumference (C) of a circle, we use the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle, in this case, the distance from the center of the carousel to the horse.
For Carl's horse:
CCarl = 2π(15 feet) ≈ 2π×15 ≈ 94.2 feet
For Allison's horse:
CAllison = 2π(10 feet) ≈ 2π×10 ≈ 62.8 feet
The difference in the distances traveled by the horses in one complete turn is CCarl - CAllison, which is approximately 94.2 feet - 62.8 feet = 31.4 feet. Therefore, Carl's horse travelled about 31.4 feet further than Allison's horse in one complete turn.
find the value of x.
a) 10
b) 5
c) 6
d) 3
Answer:
x=5.
Step-by-step explanation:
set 7x-4=31 and solve.
Answer:
B)
X=5
Step-by-step explanation:
7x-4=31
+4 on both sides
7x=35
divide by 7 on both sides
x= 5
Find the coordinates of the midpoint of the segment whose endpoint are H(9,4) and K(7,2)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad K(\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+9}{2}~~,~~\cfrac{2+4}{2} \right)\implies (8,3)[/tex]
A company rents out 17 food booths and 26 game booths at the county fair. The fee for a food booth is $200 plus $5 per day. The fee for a game booth is $95 plus $10 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid
The expression that represents the total paid by the company is 295 + 15d.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
In another word, a linear function is a function that varies linearly with respect to the changing variable.
As per the given,
The fee for a food booth is $200 plus $5 per day.
Total cost for d days will be = 200 + 5d
The fee for a game booth is $95 plus $10 per day.
Total cost for d days will be = 95 + 10d
Total cost for d days = (200 + 5d) + (95 + 10d)
⇒ 200 + 95 + 5d + 10d
⇒ 295 + 15d
Hence "The expression that represents the total paid by the company is 295 + 15d".
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PLEASE NEED HELP ASAP WILL GIVE 50 POINTS
What is the value of x?
Enter your answer in the box.
x =
Answer: x = 3
Those angle markings tell us that all three angles are the same measure (60 degrees). So this is an equilateral triangle with each side congruent to each other.
Pick 2 sides, equate the expressions, solve for x. I'm going to pick AB and AC to work with
AB = AC
6x - 3 = 3x+6
6x-3x = 6+3
3x = 9
x = 3
----------
This works with any pair of sides, such as AC and BC
AC = BC
3x+6 = 5x
6 = 5x-3x
6 = 2x
2x = 6
x = 3
----------
and let's do the last one to be complete (it's optional)
AB = BC
6x-3 = 5x
6x-5x = 3
x = 3
Either way, we get the same result each time.
At a heavy duty snow shovel was marked down by $6.00. The local sport committee purchased 3 shovels. The sale did not go well and the store owner made a new sal price by taking 1/3 off the original price.The sport committee purchased 3 more shovels. The total cost of the purchase was $102.00
Use the information to write an equation to calculate the original price if the shovel.
Answer:
The original price was $26.40
Step-by-step explanation:
Set up the equation(s) for this situation. The total price was for six shovels, three of which were discounted by 33.3% from the initially marked-down price X:
$102 = 3 * (X-$6) + 3 * ((X-$6) * (2/3))
102 = 3X - 18 + 3 * (2/3) * X - 3 * (2/3) * 6
102 = 5X - 30
X = $26.40
Mr. Ramirez receives 4 sets of books each set has 16 fiction books and 14 nonfiction books he puts 97 books in his lilbarry and donates the rest how many books does he donate
Mr. Ramirez donates 23 books.
Explanation:To find the number of books that Mr. Ramirez donates, we first need to calculate the total number of books he receives. Since each set has 16 fiction books and 14 nonfiction books and he receives 4 sets, the total number of books he receives is 4 sets * (16 fiction books + 14 nonfiction books) = 4 * (16 + 14) = 4 * 30 = 120 books.
Since Mr. Ramirez puts 97 books in his library, he donates the remaining books. To find the number of books he donates, we subtract the number of books he keeps from the total number of books he receives: 120 books - 97 books = 23 books.
Therefore, Mr. Ramirez donates 23 books.
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Mr. Ramirez donates 23 books.
Explanation:To find out how many books Mr. Ramirez donates, we need to first calculate how many books he receives in total.
Each set has 16 fiction books and 14 nonfiction books, so each set contains 16 + 14 = 30 books.
Since Mr. Ramirez receives 4 sets, he receives a total of 4 x 30 = 120 books.
We know that Mr. Ramirez keeps 97 books in his library, so he donates the rest.
To find out how many books he donates, we subtract the number of books kept from the total number of books received:
120 - 97 = 23 books.
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At a company fish fry, 1/2 in attendance are employees. Employees’ spouses are 1/3 of the attendance. What is the percentage of the people in attendance who are NOT employees or employee spouses?
SHOW WORK
Answer:At a company fish fry, 1/2 in attendance are employees.
Employees’ spouses are 1/3 of the attendance. What is
the percentage of the people in attendance who are not
employees or employee's spouses?
One half of X are employees.
One third of X are employee's spouses.
Step-by-step explanation:1/2 + 1/3 = 3/6 + 2/6 = 5/6
Then we subtract that fraction from one whole, or 1,
to see what fraction is left. That is, we say
1 minus 5/6
which is
1 - 5/6
Now write 1 as 6/6
6/6 - 5/6
We get 1/6
So 1/6 is left. Now we need to make that into
a percent by multiplying it by 100 and tacking on a "%"
1/6 × 100
1/6 × 100/1
100/6
50/3
16 2/3 %
So 16 2/3 % of the people in
attendance are neither employees
nor employee's spouses.
Now let's check:
1/2 are employees. That's 50%
1/3 are wmployee's spouses. That's 33 1/3%
15 2/3 % are neither employees nor employee's spouses.
Add them up
50 %
33 1/3 %
16 2/3 %
--------
99 3/3 %
And 99 3/3% = 100%
16.67% of the people in attendance are neither employees nor their spouses.
To calculate the percentage of people who are neither employees nor their spouses, we need to consider the total attendance as 100%. Since half of the attendance, i.e., 50%, are employees and one third, i.e., about 33.33%, are spouses, we add these figures to find the combined percentage of employees and spouses. We then subtract this combined percentage from 100% to find the percentage of people who are neither.
Combined percentage of employees and spouses: 50% (employees) + 33.33% (spouses) = 83.33%
Now, to find the percentage who are neither employees nor spouses, we subtract the combined percentage from 100%:
Percentage of neither: 100% - 83.33% = 16.67%
Therefore, 16.67% of the people in attendance are neither employees nor their spouses.