Answers
Answer:
1.
a. 2.75 seconds
b. 169 feet
2. x - 3 is a factor
Other factors: x + 2, 2x + 1, 3x - 4
3. Real zeros: [tex]x = -2[/tex]
Complex zeros: [tex]x_{2,3}=-3\pm 2i[/tex]
Step-by-step explanation:
1. Given equation of parabola
[tex]s(t)=-16t^2+88t+48[/tex]
a) The rocket reaches its maximum height at the vertex of parabola. Find t-coordinate of the vertex:
[tex]t_v=\dfrac{-b}{2a}\\ \\=\dfrac{-88}{2\cdot (-16)}\\ \\=\dfrac{11}{4}\\ \\=2.75\ seconds[/tex]
b) The maximum height is s-coordinate of the vertex. Find it:
[tex]s\left(\dfrac{11}{4}\right)\\ \\=-16\cdot \left(\dfrac{11}{4}\right)^2+88\cdot\left(\dfrac{11}{4}\right)+48\\ \\=-121+22\cdot 11+48\\ \\=169\ feet[/tex]
2. For x – 3 to be a factor of [tex]f(x)=6x^4-11x^3-35x^2+34x+24,[/tex] the Factor Theorem says that x = 3 must be a zero of f(x). Check it (whether f(3)=0):
[tex]f(3)\\ \\=6\cdot 3^4-11\cdot 3^3-35\cdot 3^2+34\cdot 3+24\\ \\=6\cdot 81-11\cdot 27-35\cdot 9+102+24\\ \\=486-297-315+126\\ \\=0[/tex]
So, x = 3 is zero of the function f(x) and x - 3 is the factor of the function f(x). Rewrite the function as follows:
[tex]f(x)\\ \\=6x^4-11x^3-35x^2+34x+24\\ \\=6x^4-18x^3+7x^3-21x^2-14x^2+42x-8x+24\\ \\=6x^3(x-3)+7x^2(x-3)-14x(x-3)-8(x-3)\\ \\=(x-3)(6x^3+7x^2-14x-8)\\ \\=(x-3)(6x^3+12x^2-5x^2-10x-4x-8)\\ \\=(x-3)(6x^2(x+2)-5x(x+2)-4(x+2))=\\ \\=(x-3)(x+2)(6x^2-5x-4)\\ \\=(x-3)(x+2)(6x^2+3x-8x-4)\\ \\=(x-3)(x+2)(3x(2x+1)-4(2x+1))\\ \\=(x-3)(x+2)(2x+1)(3x-4)[/tex]
3. [tex]x=-2[/tex] is a zero of the function [tex]f(x)=x^3+8x^2+25x+26,[/tex] then
[tex]f(x)\\ \\=x^3+8x^2+25x+26\\ \\=x^3+2x^2+6x^2+12x+13x+26\\ \\=x^2(x+2)+6x(x+2)+13(x+2)\\ \\=(x+2)(x^2+6x+13)[/tex]
Find the discriminant of the quadratic polynomial [tex]x^2+6x+13;[/tex]
[tex]D=6^2-4\cdot 1\cdot 13=36-52=-16[/tex]
This expression has no more real zeros (the discriminant is less than 0), it has two complex zeros:
[tex]x_{1,2}=\dfrac{-6\pm \sqrt{-16}}{2\cdot 1}=\dfrac{-6\pm 4i}{2}=-3\pm 2i[/tex]
Related Questions
6. Find the selling price of each of the following:
(i) a television set marked €800 + VAT at 20%
Answers
Answer:
€960
Step-by-step explanation:
€800 + VAT at 20%
€800 + 20% of €800 =
= €800 + 20% * €800
= €800 + 0.2 * €800
= €800 + €160
= €960
A rectangular parking lot has an area of 15,000 feet squared, the length is 20 feet more than the width. Find the dimensions
Answers
Dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet
Solution:Given that
Area of rectangular parking lot = 15000 square feet
Length is 20 feet more than the width.
Need to find the dimensions of rectangular parking lot.
Let assume width of the rectangular parking lot in feet be represented by variable "x"
As Length is 20 feet more than the width,
so length of rectangular parking plot = 20 + width of the rectangular parking plot
=> length of rectangular parking plot = 20 + x = x + 20
The area of rectangle is given as:
[tex]\text {Area of rectangle }=length \times width[/tex]
Area of rectangular parking lot = length of rectangular parking plot [tex]\times[/tex] width of the rectangular parking
[tex]\begin{array}{l}{=(x+20) \times (x)} \\\\ {\Rightarrow \text { Area of rectangular parking lot }=x^{2}+20 x}\end{array}[/tex]
But it is given that Area of rectangular parking lot = 15000 square feet
[tex]\begin{array}{l}{=>x^{2}+20 x=15000} \\\\ {=>x^{2}+20 x-15000=0}\end{array}[/tex]
Solving the above quadratic equation using quadratic formula
General form of quadratic equation is
[tex]{ax^{2}+\mathrm{b} x+\mathrm{c}=0[/tex]
And quadratic formula for getting roots of quadratic equation is
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In our case b = 20, a = 1 and c = -15000
Calculating roots of the equation we get
[tex]\begin{array}{l}{x=\frac{-(20) \pm \sqrt{(20)^{2}-4(1)(-15000)}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{400+60000}}{2 \times 1}} \\\\ {x=\frac{-(20) \pm \sqrt{60400}}{2}} \\\\ {x=\frac{-(20) \pm 245.764}{2 \times 1}}\end{array}[/tex]
[tex]\begin{array}{l}{=>x=\frac{-(20)+245.764}{2 \times 1} \text { or } x=\frac{-(20)-245.764}{2 \times 1}} \\\\ {=>x=\frac{225.764}{2} \text { or } x=\frac{-265.764}{2}} \\\\ {=>x=112.882 \text { or } x=-132.882}\end{array}[/tex]
As variable x represents width of the rectangular parking lot, it cannot be negative.
=> Width of the rectangular parking lot "x" = 112.882 feet
=> Length of the rectangular parking lot = x + 20 = 112.882 + 20 = 132.882
Hence can conclude that dimension of rectangular parking lot is width = 112.882 feet and length = 132.882 feet.
Paulo used the expression 7×(4+4) to solve 7×8. Does his method make sense? Explain
Answers
Answer:
Yes, because 4 + 4 = 8 so it is the same as 7 × 8.
Answer:
Yes.
Step-by-step explanation:
This is because if using PEMDAS, you will see that (4+4) = 8.
That would mean that 7x(4+4) =7x8, and that Paulo is correct.
The slope is undefined and contains the point (-3,8)
Answers
Which would be an equation like x =...
for this point it is x = -3
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 4% if the money is a. compounded
semiannually; b. compounded quarterly: c. compounded monthly d. compounded continuously.
Answers
Answer:
a) $19,023.63
b) $19,046.02
c) $19,061.13
d) $19,068.74
Step-by-step explanation:
P = 15000
t = 6
r = 0.04
a) Compounded semiannually means 2 times per year, so n = 2.
A = 15000 (1 + 0.04/2)^(2×6)
A = 19023.63
b) Compounded quarterly means 4 times per year, so n = 4.
A = 15000 (1 + 0.04/4)^(4×6)
A = 19046.02
c) Compounded monthly means 12 times per year, so n = 12.
A = 15000 (1 + 0.04/12)^(12×6)
A = 19061.13
d) Compounded continuously means we use the continuous equation:
A = 15000 e^(0.04×6)
A = 19068.74
Weat is the
The point slope form of the equation of the line that passes through (-9, -2) and (1, 3) is
slope-intercept form of the equation for this line?
o y = 2 x + 2
0 y = 2 x 4
o y = x + 2
O y = x - 2
Save and Exit
Submit
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.
o
Answers
Answer:
The slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
Step-by-step explanation:
Here,the two given point s are A ( -9,-2) and B (1,3).
Now, the slope m of the line AB = [tex]= \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]\implies m = \frac{3 - (-2)}{1 - (-9)} = \frac{3+2}{1+9} = \frac{5}{10} = \frac{1}{2}[/tex]
or, the slope of line AB = 1/2
Now, the POINT SLOPE FORM of any equation with point (x0,y0) and slope m is given as :
y - y0 = m (x -x0)
So, the line equation of AB is given as :
[tex]y - 3 = \frac{1}{2} ( x-1)\\\implies y =3 + \frac{1}{2} ( x-1)\\or, y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
SLOPE INTERCEPT form is y = mx + c
Hence, the slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
If 1/2 is subtracted from four times the reciprocal of a number, the result is 0. Find the number.
Answers
Answer:Include
Step-by-step explanation:
Multiply add and subtract the top. I can include the rest if you want
Answer:
The required number is 8.
Step-by-step explanation:
Given : If [tex]\frac{1}{2}[/tex] is subtracted from four times the reciprocal of a number, the result is 0.
To Find : The number ?
Solution :
Let the number be x.
The reciprocal of number is [tex]\frac{1}{x}[/tex]
[tex]\frac{1}{2}[/tex] is subtracted from four times the reciprocal of a number, the result is 0.
The equation will become,
[tex]4\times \frac{1}{x} - \frac{1}{2}=0[/tex]
Solving the equation we get,
[tex]\frac{4}{x} -\frac{1}{2}=0[/tex]
[tex]\frac{4}{x} = \frac{1}{2}[/tex]
[tex]x= 4\times 2[/tex]
[tex]x=8[/tex]
Therefore, the required number is 8.
HELP!
Jack drove 278.2 miles on 19.6 gallons of gasoline. About how many miles did he drive per gallon of gasoline?
(Round your answer to the nearest WHOLE amount of miles. Whole = ones place)
Answers
Answer:
[tex]14\ \frac{miles}{gallon}[/tex]
Step-by-step explanation:
we know that
To find out the unit rate (number of miles per gallon of gasoline) divide the total miles driven by the total gallons of gasoline used
so
[tex]\frac{278.2}{19.6}\ \frac{miles}{gallons}=14.19\ \frac{miles}{gallon}[/tex]
Round to the nearest WHOLE amount of miles
[tex]14.19\ \frac{miles}{gallon}=14\ \frac{miles}{gallon}[/tex]
Is 3 a solution to the equation 6x – 7 = 11?
Answers
Answer:
Step-by-step explanation:
Yes
First you add 7 to both sides b/c the 7 would be negative. Then your left with 6x=18. Then you divide both sides by 6 and get 3
Answer:
Yes 3 is a solution.
Step-by-step explanation:
6(3) - 7 = 11 6 times three equals 18 so then 18 minus 7 equals 11 so yes.
Which situation CANNOT be represented by this equation?
4r +7= 31
Answers
Answer:
r=6
Step-by-step explanation:
4r+7=31
4r=31-7
4r=24
r=24/4
r=6
Show the steps on how to follow 3x - 7 =1/2x +6
Answers
Answer:
x=26/5
Step-by-step explanation:
first you would multiply both sides by 2
then you woud end up with 6x- 14 = x+12
then combine like terms subtract x on both sides
5x=26 then divide both sides by 5
x=26/5
GETS BRAINILST!!!!The table below shows a correct representation that 12 pounds (lb) of sugar cost $4: lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1 True False
Answers
Answer:
I believe the answer is false because there is no facts that say true.
Answer:
believe the answer is false because there is no facts that say true.
Step-by-step explanation:
A company has two manufacturing plants with daily production levels of 7 x + 19 items and 2 x - 7 items, respectively. The first plant produces how many more items daily than the second plant?
Answers
The first plant produces 5x + 26 more items daily than the second plant
Solution:Given that , A company has two manufacturing plants
The daily production levels of one company is 7x + 19 items
And daily production levels of another company is 2 x - 7 items
To find the number of items first plant produce more than the second plant, wed need to subtract the number of items produced by second plant from the the number of items produced by first plant.
Extra items produced by 1st plant = daily production of 1st plant - daily production of 2nd plant
Extra items produced count = 7x + 19 – (2x – 7)
= 7x + 19 – 2x + 7
= 7x – 2x + 19 + 7 = 5x + 26
Hence, the 1st plant produces 5x + 26 items more than 2nd plant
A sports statistician determined that the probability of a certain rugby team winning its next match is 3/8 . Find the odds against the team winning its next match.
Answers
Answer:
Odds in against the team winning is 5 : 3
Step-by-step explanation:
Consider the provided information.
The odds against is the ratio of how many ways an outcome can't take place compared to how many ways it can take place.
Here the probability of winning its next match is 3/8.
That means total number of outcomes are 8.
Favorable outcomes are 3.
Therefore, the unfavorable outcomes are 8-3=5.
We need to find the odds against the team winning its next match.
Therefore, odds in against the team winning is 5 : 3
The probability of odds against the team winning is [tex]\frac{5}{8}[/tex]
To find the odds against the rugby team winning, subtract the probability of winning from 1 to get the probability of not winning and form a ratio of these probabilities, resulting in odds of 5:3 against the team winning.
Explanation:The student is asking about the calculation of odds against a rugby team winning its next match given a certain probability of winning. First, we need to understand the probability of the team not winning (losing or drawing) because the odds against the team winning would be the ratio of it losing to it winning. Since the probability of winning is given as 3/8, the probability of not winning is 1 - 3/8 = 5/8. The odds against the team winning are therefore expressed as the ratio of the probability of not winning to the probability of winning, which is 5/8 to 3/8, or simply 5:3 when converted into odds format.
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A recipe requires 1/3 cup of milk for each 1/4 cup of water. How many cups of water are needed for each cup of milk?
Answers
Answer:
3/4
Step-by-step explanation:
1 / (1/3) = 3
1/4 * 3 = 3/4
6 - x = -12 A) -18 B) -6 C) 0 D) 18
Answers
Answer:
D
Step-by-step explanation:
6 - x = -12
subtract 6 from each side
6 - 6 - x = -12 - 6
-x = -18
divide each side by -1
-x / -1 = -18 / -1
x = 18
Answer:
The answer is D.) 18
Step-by-step explanation:
Subtract 6 from both sides. Divide both sides by −1. The answer is 18.
Write as a monomial in standard form (-xy^4b^2)^4
Answers
Answer:
[tex]\large\boxed{(-xy^4b^2)^4=x^4y^{16}b^8}[/tex]
Step-by-step explanation:
[tex](-xy^4b^2)^4\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=(-1)^4(x)^4(y^4)^4(b^2)^4=1x^4y^{(4)(4)}b^{(2)(4)}=x^4y^{16}b^8[/tex]
[tex](-xy^{4} b^{2} )^{4}[/tex] can be written as x⁴y¹⁶b⁸.
What is simplification?Procedures must be made simpler in order to attain uniformity in efforts, expenses, and time. Variety and variation that is unnecessary, damaging, and unproductive are eliminated.
Given an equation [tex](-xy^{4} b^{2} )^{4}[/tex] in this, we need to find a monomial in standard form which can be optimized after putting the power back at every variable. hence,
[tex](-xy^{4} b^{2} )^{4}[/tex] = (-x)⁴(y⁴)⁴ (b²)⁴
= x⁴y¹⁶b⁸
Therefore, a monomial in the standard form [tex](-xy^{4} b^{2} )^{4}[/tex] is x⁴y¹⁶b⁸.
Learn more about simplification here:
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[tex] {x}^{2} + {11}^{2} = {22 }^{2} [/tex]
Answers
Answer:
See image below.
I'm not 100% sure if this is allowed or not, someone please let me know if it is not.
Step-by-step explanation:
See image below
Answer:
± 11[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
x² + 11² = 22², that is
x² + 121 = 484 ( subtract 121 from both sides )
x² = 363 ( take the square root of both sides )
x = ± [tex]\sqrt{363}[/tex] = ± [tex]\sqrt{121(3)}[/tex] = ± 11[tex]\sqrt{3}[/tex]
The cost of producing bicycles at a manufacturing facility is $38 per bicycle plus we
costs of running the facility each day.
What type of function should be used to model the cost of running the facility each day, and
why should this type of function be used?
Answers
Answer:
f(x)=38x+b
Linear Equation
Step-by-step explanation:
So I used slope intercept form it 38 per bicycle and plus the costs of running but we don't know the cost so it's shown as b, the reason I did not use Exponential because from reading the word problem it's not going to grow rapidly.
Mark and Mike are brothers. The sum of their ages is eleven. Mike's age is ten
less than two times Mark's age. How old is each brother?
X =
Write the system:
Solution:
Answers
Answer:mark is 7. Mike is 4
Step-by-step explanation:x+y=11. Y=2x-10 thus substituting for y in equation1 we have x+2x-10=11. 3x-10=11. 3x=11+10. 3x=21. X=21/3. X=7. Mike =(2×7)-10=14-10=4
Step-by-step explanation:
Mark's age is x
so Mike's age is
[tex]2x - 10[/tex]
and we know that the sum of their ages is eleven so:
2x+x- 10 = 11
3x-10=11/+10
3x=21/÷3
x=7
Mark is 7 years old and
Mike is 4 years old.
A) The sum of my digits equals
11. The ones digit minus the
hundreds digit equals 3. No
digit is less than 2.
Answers
David is shoveling driveways to raise money for his Spring
Break trip. Each driveway he shovels, he earns $15. After shoveling 12 driveways, David has $243 saved for his trip.
Write an equation to represent the amount David has saved as a function of the number of driveways he has shoveled.
Answers
Answer:
Total savings = $63 + 12 ( m)
: m = number of driveways shoveled
Step-by-step explanation:
Here, the money earned for each road David shovels = $15
The number of driveway shoveled by David = 12
The total money saved David has after he is done with his work = $243
Now, The number of money saved by shoving 12 driveways
= 12 x ( Money earned by shoveling 1 driveway)
= 12 x ( $15) = $ 180
Total savings = His previous savings + Money earned from Shovel work
⇒ $243 = His previous savings + $ 180
⇒ His previous savings = $243 - $180 = $63
Now, we can write his total savings as:
Total savings = $63 + 12 ( m)
: m = number of driveways shoveled
Write the standard form of the equation of the circle with a radius of 5 and a center at (0, 0).
Answers
Answer:
Step-by-step explanation:
no
(x +a)² + (y + b)² = r²
Since, a=0 and b=0, r=5, we get x²+ y²= 5².
So, x²+y² = 25
Determine the intercepts of the line.
5x-9=-8y-3
Answers
Answer:
X-Intercept: (1.2,0)
Y-Intercept (0,.75)
Step-by-step explanation:
If you want fraction form then the
X-Intercept: (6/5,0)
Y-Intercept (0,3/4)
To find the x intercepts, you have to plug y=0 into the equation. After you plug in y=0, you get the equation 5x-9=-3 and once you solve that, you find that the x intercept = 1.2
Likewise, to find the y intercepts, you would plug x=0 into the equation. Once you do that, you get the equation -9=-8y-3 and when you solve for y you get an intercept of 3/4
Please Mark Brainliest ;)
At a track meet, Tim ran at a constant speed of 300 meters per minute.
After 8 minutes, he still had 600 meters left to run.
The distance Tim ran was three times as long as the distance Eric ran.
What was the distance that Eric ran?
Answers
Tim ran a total of 3000 meters, which is three times the distance that Eric ran. By dividing Tim's distance by three, we find that Eric ran 1000 meters.
Explanation:To solve for the distance Eric ran, we need to first determine the total distance Tim ran and then divide that by three as Tim's distance is three times longer than Eric's.
Tim's speed is 300 meters per minute, and he ran for 8 minutes before having 600 meters left to run. To calculate the distance Tim ran:
Multiply Tim's speed by the time he ran: 300 meters/minute * 8 minutes = 2400 meters.Add the remaining distance to determine Tim's total distance: 2400 meters + 600 meters = 3000 meters.Since Tim's distance is three times Eric's distance, divide Tim's total distance by three to find Eric's distance: 3000 meters / 3 = 1000 meters.Therefore, the distance that Eric ran was 1000 meters.
You ride your bike at 9 miles per hour. To find how long it will take you to ride 26 miles, you solve the equation 9 • t = 26. What does t represent?
The amount of time it takes to ride 26 miles
Your speed in miles per hour
The number of miles you've traveled so far
The total distance after t hours
Answers
Answer:
The amount of time it takes to ride 26 miles is 2.89 hours.
Step-by-step explanation:
Given : You ride your bike at 9 miles per hour.
To find : How long it will take you to ride 26 miles ?
Solution :
The equation given is [tex]9\times t=26[/tex]
Using distance formula,
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
According to formula t represent the time taken to cover the distance.
Your speed in miles per hour is 9 miles per hour.
The number of miles you've traveled so far is 26 miles.
Solving the equation,
[tex]9\times t=26[/tex]
[tex]t=\frac{26}{9}[/tex]
[tex]t=2.89[/tex] hours
The amount of time it takes to ride 26 miles is 2.89 hours.
HELPPPPPP The scatter plot shows a regression line of advertising dollars spent and sales. If the company were to spend $350,000 on advertising, what would be the predicted sales? A) $105 million B) $110 million C) $115 million D) $120 million
Answers
Answer:
120 i think i don't know
Step-by-step explanation:
Answer:
D) $120 millionStep-by-step explanation:
The scatter plot is attached. There you can match the value assigned to $350,000.
Using a red line, we find that the answer is between 115 and 125, closer 125 than 115.
So, if you look all choices, there are two possibilities, C and D. However, $115 million can't be the right answer because our graphic approximation is closer to 125.
Therefore, the right answer is D) $120 million.
If the company were to spend $350,000 on advertising, the predicted sales would be $120 million.
Live Fund are selling their holding at $5,000 per share. How much would Live Fun receive if they sold half thier holding in Marks Brothers?
Answers
Live Fund receive [tex]\bold{\$2500 N}[/tex] it they sold half thier holding in Marks Brothers.
Solution:
Given: Sale price of Live Fund holding is 5000 dollar
To find: Amount that Live Fund will get if they sell half of their holding in Marks Brothers.
Assume the total holdings held by Live Fund in Marks Brothers as N
Therfore, half the number of shares or (half the holdings) of Live Fund will be [tex]\frac{N}{2}[/tex].
Thus, if each share is valued at [tex]\$5000[/tex], then the total value of the number of shares sold will be as follows,
[tex]\Rightarrow5000\times\frac{N}{2}\text{ dollars }\rightarrow\frac{5000\times N}{2}\text{ dollars }[/tex]
[tex]\Rightarrow2500 N\text{ dollars }[/tex]
Hence, Live Fund will receive [tex]\$2500 N[/tex]
this should be easy for someone who is smart
Answers
Answer:
Hope it helps :)
Step-by-step explanation:
Detailed answer in the attached file
need help with 31 pleeeee
Answers
Answer: 1 hour
Step-by-step explanation:
2 gallons in, 3 gallons out per minute
means 1 gallon lost per minute
60 gallons in the tank so it will take 60 minutes to drain it completely
answer=1hr