Given:
The function is:
[tex]f(x)=x^3-4x^2-37x+40[/tex]
[tex]f(8)=0[/tex]
To find:
The all of the zeros of f(x) algebraically.
Solution:
We have, [tex]f(8)=0[/tex] is means 8 is a zero of given function and (x-8) is a factor of given function.
The function is:
[tex]f(x)=x^3-4x^2-37x+40[/tex]
Spittle the middle terms in such a way so that we get (x-8) as a common factor.
[tex]f(x)=x^3-8x^2+4x^2-32x-5x+40[/tex]
[tex]f(x)=x^2(x-8)+4x(x-8)-5(x-8)[/tex]
[tex]f(x)=(x^2+4x-5)(x-8)[/tex]
Spittle the middle term of the quadratic expression, we get
[tex]f(x)=(x^2+5x-x-5)(x-8)[/tex]
[tex]f(x)=(x(x+5)-1(x+5))(x-8)[/tex]
[tex]f(x)=(x+5)(x-1)(x-8)[/tex]
For zeros, [tex]f(x)=0[/tex].
[tex](x+5)(x-1)(x-8)=0[/tex]
[tex](x+5)=0\text{ and }(x-1)=0\text{ and }(x-8)=0[/tex]
[tex]x=-5\text{ and }x=1\text{ and }x=8[/tex]
Therefore, the all zeros of the given function are -5, 1 and 8.
Which of the following is an example of a quantitative variable?
O A. cats that weigh less than 10 lb
B. the mean weight of the cats seen by a veterinarian in one week
O C. the number of ounces of dry cat food recommended
D. the number of hours the veterinarian works in one week
Answer:
D. the number of hours the veterinarian works a week
WILL GIVE BRAINLIEST!!!
Select the graph of y = 3 sin (x + pi/4)
Answer:C
Step-by-step explanation:
just did it
The function y = 3 sin (x + pi/4) has graph B is correct.
We have given that,
y = 3 sin (x + pi/4)
We have determined the graph of the given function
We can determine the graph by using the graphing calculator.
What is the graph sine function?
The angle along the horizontal x-axis, and for each angle, we put the sine of that angle on the vertical y-axis. The result, as seen above, is a smooth curve that varies from +1 to -1.
Therefore option B is correct.
To learn more about the sine function visit:
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Subash is saving to buy a video game that costs $72. He earns $12 per week for doing the dishes and spends $3 on ice-cream. Which equation can be used to find how many weeks it will take him to save enough money for the video game?
Answer:
Correct answer is 'A'
Step-by-step explanation:
so money he save per week = $12 - $3 = $9
Now,
To earn 9$ it takes one week or it can be represented as:
$9 = 1 week
So,
$1 = 1/9 week
$72 = (1/9*$72)weeks
$72 = 8 weeks
therefore it will take 8 weeks to save enough money for the video game
Answer:
A. 14
Step-by-step explanation:
Calculate Ac of the Earth, assuming it moves in a circular orbit around
the Sun.
(rm-s=1.4961011 m; T=1.156107 1/s)
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Step-by-step explanation:
iiiiooi
a) Create an example of a trinomial that has a degree of 4:
Answer:
4x^4 + 16x^3 + 182x^2 + x + 87
Step-by-step explanation:
Two friends shop for fresh fruit. Jackson buys a watermelon for $7.85 and 5 pounds of
cherries. Tim buys a pineapple for $4.15 and 4 pounds of cherries. Use the variable p to represent
the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much
more Jackson spent.
Answer:
3.67 + p
Step-by-step explanation:
Jackson
7.85 + 5p
Tim
4.15 + 4p
----------------------
How much more jackson spent
(7.82 + 5p) - (4.15 + 4p)
Group like terms
(7.82 - 4.15) + (5p - 4p)
Simplify
3.67 + p
What does the red arrow represent in the dot plot?
Answer:
outlier
Step-by-step explanation:
I think it is an outlier
Hope this helps <3
GL on your test or wtvr
The required arrow shows the outliner of the spread. Option C is correct.
What are Scatter plots?A scatter plot is a collection of points plotted on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the extent, if any, of correlation between the values of observed quantities or phenomena (called variables).
here,
Since a figure is given, of a scatter plot where the value is distributed from 12 to 24, and the density of the graph at 12 to 14 is more than the rest of the plot and the red arrow marked, the value lies outside the spread and the value is said outliner.
Thus, the required arrow shows the outliner of the spread.
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What is the first step in evaluating this expression
Answer: Do the exponent
Step-by-step explanation: The reason for my answer is because of PEMDAS which stands for
Parenthesis
Exponent
Multiplication
Division
Addition
Subtraction
Really hope that this helps you out
Answer:
Its A
Step-by-step explanation:
Which is larger? The measure of a central angle of a circle that intercepts a 68 degree arc of the measure of an inscribed angle of a circle that intercepts a 68 degree arc. Explain
Answer:
The measure of a central angle of a circle that intercepts a 68° arc
Step-by-step explanation:
Recall the inscribed angle theorems:
Measure of central angle = measure of intercepted arc
Measure of inscribed angle = ½(measure of intercepted arc)
Therefore,
The measure of a central angle that intercepts a 68° arc = 68°
Measure of an inscribed angle of a circle that intercepts a 68° arc = ½(68°) = 34°
Therefore, the larger would be:
The measure of a central angle of a circle that intercepts a 68° arc
Solve the following word problems.
Trisha purchased 3 blouses at $32.50 each, 2 packages of 6 pairs of
socks costing $7.50 per package, and 4 pair of hosiery costing $2.19
each. Sales tax was 6.5%.
72. How much sales tax did Trisha pay?
73. What was Trisha's total invoice including tax?
Answer:
72.$7.88
73. $129.14
Step-by-step explanation:
Identify the slope type of the following graph.
A. negative
B. Zero
C. Undefined
D. Positive
Answer:
Negative
Step-by-step explanation:
If it is tilted in that sort of way it is negative, vice versa if it was titled the other way then it would be positive.
If it were to be un-defined/infinite then it would be parallel to the y axis
If it were to be 0 then a line would be parallel to the x axis.
Answer:
A negative
Step-by-step explanation:
HELP ME OUT PLSSSSSS
Answer:
Option B
Step-by-step explanation:
Option B has 10° and 30° angles that share a side that measures 20 cm. The other options aren't correct.
Hope this helps!
You and your friends roll a die to decide who goes first in a game.
The results of the rolls are shown in the table.
What is the range of the data?
A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 665 mi/h, how far is she from her starting position?
Answer:
Step-by-step explanation:
Anyone know the answer to this?
Answer:
65
Step-by-step explanation:
This question can be solved using the Pythagorean Theorem, which is [tex]a^{2}+b^{2}=c^{2}[/tex] where a and b are legs and c is the hypotenuse. The equation used to solve for one leg is [tex]a=\sqrt{c^{2}-b^{2} }[/tex]. So, plug in the given measurements and solve. This turns into [tex]a=\sqrt{97^{2}-72^{2} }[/tex], which equals 65.
Answer:
a = 25
Step-by-step explanation:
First lets identify the formula
a^2 + b^2 = c^2
C would be the hypotenuse, across from the right angle. a is already labeled for us so be would be the bottom side.
Since we don't know the value of a we keep that as a variable
would would substitute b and c with the given values
a^2 + 72^2 = 97^2
Now, you could solve the squares but we are not going to. We are going to square root all the values to get rid of the squares so there is no point squaring it when your just going to end up with the same value just without the little square symbol at the top.
[tex]\sqrt{a^{2} } + \sqrt{72^{2} } = \sqrt{97^{2} }[/tex]
a + 72 = 97
Now its just the basic solving of get the variable on one side.
Subtract 72 from 97
a + 72 (-72) = 97 (-72)
a = 25
a is 25 feet
I hope this helps you, don't be afraid to reach out with further questions!
Please help I am very confused:)
Answer:
the one solution is -20
Step-by-step explanation:
-15x - 27 + 7 = -25 - 15x +5
-27 + 7 = -25 +5
-20 = -20
bro nvm I thought I knew the answer sorry
Find the volume of the figure
Total earnings S depends on the number t of hours worked. You earn $6 per hour. How much do you earn for working 10 hours?
a. $60
b. $120
c. $30
d. $90
Find the area of the polygon
I would like all 3 answers and how to get them (show work).
Thanks!
Answer:
1. 180
2. 52
3. 288
Step-by-step explanation:
The area of a rectangle can be found by multiplying the length by the width, so the area of the rectangle is 15 * 12 = 180. The area of a triangle can be found by multiplying the base by the height and divide by 2, so the area of the triangle is [tex]13*\frac{8}{2} = 13 * 4 = 52[/tex]. The area of a parallelogram can be found by multiplying the length and the height, so the area of the parallelogram is 24 * 12 = 288.
Bamboo plants grow rapidly. A bamboo plant is 140 inches tall. Tomorrow it will be 154 inches tall, the next day it will be 168 inches tall, and on the next day it will be 182 inches tall. Write a rule to represent the height of the bamboo plant as an arithmetic sequence. How tall will the plant be in 16 days?
Answer:
350 inches
Step-by-step explanation:
aₙ = a₀ + d(n-1)
d = common difference
a(16 days) = 140 + 14(15)
= 140 + 210
= 350
1 1/4 in the whole number?
Answer:
2.75
Step-by-step explanation:
PLEASE ANSWER ASAP !! IF YOU ARE AN EXPERT AT MATH
on a coordinate plane, which point lies on the x-axis?
Please help me find the median to this table
Answer:
The median is 19.45
Step-by-step explanation:
Organize the numbers from least to greatest
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Find the middle of the set of numbers
19.3 and 19.6
Add 9.3 and 19.6
19.3 + 19.6=
38.9
Divide by 2
38.9/2
Which is 19.45
Hope this helps
What are the coordinates of point Q?
Answer: the x coordinate is 0 and y is 3 for point q.
what is the value of y
Answer:
9.81
Step-by-step explanation:
I need help please really fast
Answer:
[tex] x = \boxed{2}\: and\: x = \boxed{ \frac{5}{2} } [/tex]
Step-by-step explanation:
[tex]2 {x}^{2} - 9x + 10 = 0 \\ \\ 2 {x}^{2} - 4x - 5x + 10 = 0 \\ \\ 2x(x - 2) - 5(x - 2) = 0 \\ \\ (x - 2)(2x - 5) = 0 \\ \\ x - 2 = 0 \: \: 2x - 5 = 0 \\ \\ x = \boxed{2} \: and \: x = \boxed{ \frac{5}{2} } \\ \\ [/tex]
I’LL MARK AS BRAINLIEST!!! Plz no links
I need help u don’t know the answer please don’t make me get it wrong
Answer:
16cm
Step-by-step explanation:
Studies have shown that 400 people attend a high school basketball game when the admission price is
$3.00. In the championship game, admission prices will increase. For every $0.25 increase, 20 fewer
people will attend. At what ticket price will the revenue be maximized?
Answer:
Let x=number of $0.25 increases, so the equation for revenue=price*number of tickets or people) becomes
Revenue=($3.00+$0.25x)(400-20x)
where ($3.00+$0.25x) :increase in price
and
(400-10x) : decrease in number of people
Expanding Revenue
Revenue[R]=1200-60x+100x-5x²:1200+40x-5x²
Taking the derivative of R and set it equal to 0:
R'=0+40-10x=40-10x
we have
R'=0
40-10x=0
x=40/10
x=4
So the ticket price is $3.00+$0.25*4=$4
The number of people will attend is 400-20*4=$320
At $320 ticket price will the revenue be maximized.
Step-by-step explanation:
A $320 ticket price will the revenue be maximized