SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given polynomial function
[tex]f(x)=x^3+4x^2-4x-16[/tex]STEP 2: Apply the factor theorem
A polynomial function f(x) has a factor (x-a) if and only if f(a) = 0, this means that (x-2) will be a factor if and only if f(2)=0.
By checking,
[tex]\begin{gathered} f(2)=2^3+4(2^2)-4(2)-16 \\ f(2)=8+16-8-16=0 \end{gathered}[/tex]Hence, (x-2) is a factor and the first zero is 2
STEP 3: We divide the polynomial by its factor to get the quotient expression
[tex]\frac{x^3+4x^2-4x-16}{(x-2)}=x^2+6x+8[/tex]STEP 4: we find out the factors of the quotient
If f(a) is zero, this means that a must be a factor of 16
The factors of 16 are 1,2,4,8,16
[tex]\begin{gathered} x^2+6x+8=(x+4)(x+2) \\ f(-4)=(-4^2)+6(-4)+8=16-24+8=0 \\ f(-2)=(-2)^2+6(-2)+8=4-12+8=0 \end{gathered}[/tex]Hence, (x+4) and (x+2) are also factors of the polynomial.
Therefore, the zeroes of the given function are:
[tex]2,-4,-2[/tex]6. What is the range of the relation y = 2x+ + 3x if the domain is the set (-2,-1,0}? 1) {2,1,0} 2) {2,-1,0) 3) {-1,-5,0 4) {10,1,0}
For the given relation
[tex]y=2x^2+3x[/tex]With domain {-2, -1, 0}.
The domain represents all possible values of x, also called input, of the relationship and the range represents all the values of y, also called output, obtained when you replece the formula with the given values of x.
To determine the range of the valiable you have to do as follows:
For x=-2
[tex]y=2(-2)^2+3(-2)=2[/tex]For x=-1
[tex]y=2(-1)^2+3(-1)=-1[/tex]For x=0
[tex]y=2(0)^2+3\cdot0=0[/tex]For the relation with domain {-2,-1,0} the range is {2, -1, 0}
The correct option is number 2)
find the area of the shaded region. Note that the total radius from the center out to the edge of the shaded region is 8+3 = 11.
Given
The figure.
To find the area of the shaded region.
Explanation:
It is given that,
The radius of the whole circle is 11cm.
And, the radius of the small circle is 3cm.
Then,
The area of the shaded region is,
[tex]\begin{gathered} Area\text{ of the shaded region}=Area\text{ of the whole circle-area of smaller circle} \\ =\pi(11^2)-\pi(3^2) \\ =121\pi-9\pi \\ =112\pi \\ =112\times\frac{22}{7} \\ =351.85cm^2 \end{gathered}[/tex]Hence, the area of the shaded region is 351.85cm^2.
Question is attached, im confused on the steps to follow.
A year has 52 weeks.
Since Officer Milton has 3 weeks of vacation, then he works for 49 weeks a year.
Since he visits 3 groups per week, the total number of groups that he visists in a year is:
[tex]49\times3=147[/tex]Therefore, the correct choice is option C) 147.
Ngoc needs to mix a 10% alcohol solution with a 60% alcohol solution to create 200 milliliters of a 22.5% solution. How many milliliters of each solution must Ngoc use?
Ngoc needs to mix a 10% alcohol solution with a 60% alcohol solution to create 200 milliliters of a 22.5% solution. How many milliliters of each solution must Ngoc use?
Let
x -----> milliliters of solution at 10%
y -----> milliliters of solution at 60%
we have
x+y=200 ------> equation A
Remember that
10%=0.10
60%=0.60
22.5%=0.225
so
0.10x+0.60y=0.225(200) -----> equation B
solve the system of equation s A and B
Solve by graphing
using a graphing tool
see the attached figure
please wait a minute to draw the system
the solution is the point (150,50)
therefore
milliliters of solution at 10% is 150milliliters of solution at 60% is 50A tela telephone company offers two different types of billing the First Choice was to pay $10 per month plus $0.09 per MB of data the second choice is to pay $16 per month plus $0.07 per MB of data part a writing system of equations to model the situation the total cost for 1 month with each company Part B how many MB of data would you have to use in one month in order for both plans to cost the same amount explain how you determine your answer
what is the value of x in this triangle?A. 70B. 63C. 93D. None of the above
The sum of the angles in a triangle is 180 degrees. It means that
110 + 5x + 2x = 180
110 + 7x = 180
7x = 180 - 110
7x = 70
x = 70/7
x = 10
The value of x in the triangle is 10
Therefore, the correct option is
D. None of the above
Pre calculus 28.An object is traveling around a circle with a radius of 3 feet. It is completing 1 full revolutionevery 5 seconds. What is the linear speed (in ft/sec) and the angular speed (in rad/sec)?
We need to find the linear and the angular speeds of an object traveling around a circle.
The radius r of the circle is 3 feet. Thus, the perimeter p of the circle is:
[tex]\begin{gathered} p=2\pi r \\ \\ p=2\pi(3\text{ ft}) \\ \\ p=6\pi\text{ ft} \end{gathered}[/tex]Also, we know that the object completes one full revolution every 5 seconds.
Thus, to find the linear speed V, we need to divide the number of feet it travels by the number of seconds it takes:
[tex]\begin{gathered} V=\frac{p}{5\text{ sec}} \\ \\ V=\frac{6\pi\text{ ft}}{5\text{ sec}} \\ \\ V=1.2\pi\text{ ft/sec} \end{gathered}[/tex]ow, tnotice that the complete revolution has 2π radians.
Then, to find the angular speed ω, we need to divide the number of radians it travels by the number of seconds it takes:
[tex]\begin{gathered} \omega=\frac{2\pi\text{ rad}}{5\text{ sec}} \\ \\ \omega=0.4\pi\text{ rad/sec} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \text{ linear speed: }1.2\pi\text{ ft/sec} \\ \\ \text{ angulat speed: }0.4\pi\text{ rad/sec} \end{gathered}[/tex]The temperature of a mixture changes by -5.2 Fahrenheit between 8am and 11am. At 6pm the temperature is 14.5 Fahrenheit, which is half of what it was at 11am. What was the temperature at 8am of the mixture. I have this equation , but not sure is correct. 1/2(x-6.8)= -3.1
Explanation
Let us have a sketch of the question
If the temperature at 6 pm is 14.5 F
And the temperature at 11am is twice that of 6pm
Then the temperature at 11am will be
[tex]2\times14.5F=29F[/tex]Since the temperature of a mixture changes by -5.2 Fahrenheit between 8 am and 11 am.
Then the temperature at 8 am will be
[tex]\begin{gathered} \theta_{11am}-\theta_{8am}=-5.2 \\ 29F-\theta_{8am}=-5.2F \\ \theta_{8am}=29F+5.2F \\ \theta_{8am}=34.2F \end{gathered}[/tex]Therefore, the temperature at 8 am will be 34.2 F
x-5/2=yI need the answers on a table
Given the equation:
[tex]y=x-\frac{5}{2}[/tex]Since the required table is not given, we will solve for values of x from -3 to 3.
[tex]\begin{gathered} \text{When }x=-3,y=-3-\frac{5}{2}=-5.5 \\ \text{When }x=-2,y=-2-\frac{5}{2}=-4.5 \\ \text{When }x=-1,y=-1-\frac{5}{2}=-3.5 \\ \text{When }x=0,y=0-\frac{5}{2}=-2.5 \\ \text{When }x=1,y=1-\frac{5}{2}=-1.5 \\ \text{When }x=2,y=2-\frac{5}{2}=-0.5 \\ \text{When }x=3,y=3-\frac{5}{2}=0.5 \end{gathered}[/tex]You can then place this in a table of x and y values.
You can use the same process to complete any table.
given the sequence write an explict formula and find the 78th term-23 -27 -31 -35
We see that there is a difference of 4 between each number:
[tex]\begin{gathered} -23-4=-27 \\ -27-4=-31 \\ -31-4=-35 \end{gathered}[/tex]and so on. Then, we can propose the following formula:
[tex]a_n=-23-4\cdot n[/tex]For instance, when n=0 we have
[tex]\begin{gathered} a_0=-23+0 \\ a_0=-23 \end{gathered}[/tex]when n=1, we have
[tex]\begin{gathered} a_1=-23-4\cdot1 \\ a_1=-23-4 \\ a_1=-27 \end{gathered}[/tex]when n=2, we have
[tex]\begin{gathered} a_2=-23-4\cdot2 \\ a_2=-23-8 \\ a_2=-31 \end{gathered}[/tex]and so on. Then, in order to compute the 78th term, we must substitute n=78 in our formula. It yields,
[tex]\begin{gathered} a_{78}=-23-4\cdot78 \\ a_{78}=-23-312 \\ a_{78}=-335 \end{gathered}[/tex]and the answer is -335
Mona borrowed $6,000 for college expenses. After 2 1/2 years she will have paid $750 in interest. What is the interest rate?
Simple interest is represented by the expression:
[tex]\begin{gathered} I=p\cdot r\cdot t \\ I=\text{interest earned after t years} \\ p=\text{ money borrowed} \\ r=\text{annual rate of interest} \\ t=\text{ the length of time you borrow} \end{gathered}[/tex]Understanding this expression, we can substitute our values:
[tex]750=6,000\cdot r\cdot2.5[/tex]Isolating our variable of interest (r):
[tex]\begin{gathered} r=\frac{750}{6,000\cdot2.5} \\ r=0.05 \end{gathered}[/tex]The interest rate is 0.05 or 5%
Factor f(x) = 4x² - 576 = 0
4x^2 - 576 = (2x - 24)(2x + 24)
Because of conjugated binomials
(a + b)(a - b) = a^2 - b^2
2x is the square root of 4x^2
24 is the square root of 576
answer:
(2x - 24)(2x + 24)
The profit, in dollars, made by selling x bottles of 100% All-Natural Certified Free-Trade Organic Sasquatch Tonic is given by P ( x ) = − x 2 + 85 x − 620 for 0 ≤ x ≤ 95 . How many bottles of tonic must be sold to make at least $ 130 in profit? Write answer in interval notation.
The number of bottles of tonic that must be sold to make at least $130 in profit is [10, 75]
How to determine the number of bottles?The profit function is given as
P(x) = -x^2 + 85x - 620
The earnings are given as
Earnings = at least $130
This means that
P(x) ≥ 130
So, we have
-x^2 + 85x - 620 ≥ 130
Subtract 130 from both sides of the inequality
So, we have
-x^2 + 85x - 750 ≥ 0
Divide through by -1
So, we have
x^2 - 85x + 750 ≤ 0
Expand the expression
x^2 - 75x - 10x + 750 ≤ 0
Factorize
x(x - 75) - 10(x - 75) ≤ 0
Factor out x - 75
(x - 75)(x - 10) ≤ 0
Split
x - 10 ≤ 0 and x - 75 ≤ 0
Solve for x
x ≤ 10 and x ≤ 75
Combine the inequality
10 ≤ x ≤ 75
Express as interval
10 ≤ x ≤ 75 = [10, 75]
Hence, the number of bottles is [10, 75]
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[tex]8 \sqrt{5} + 2 \sqrt{45} [/tex]combine these radicals
Answer
Option C is correct.
8√5 + 2√45 = 14√5
Explanation
We need to simplify
8√5 + 2√45
Note that 45 = 9 × 5
8√5 + 2√45
= 8√5 + 2√(9 × 5)
= 8√5 + 2[√9 × √5]
√9 = 3
8√5 + 2[3 × √5]
= 8√5 + 2(3√5)
= 8√5 + 6√5
= 14√5
Hope this Helps!!!
'g & & eggs 1 10 15 2015-2016 time {uash. bpeed (m/sec) The graph represents the elapsed time for running with connected speed schedules for two different racers. As the speed increases what happens to the elapsed time for racer B? * 6 Points) Enter your answer
The relationship between the speed and the elapsed time is a negative relationship. That means as the speed increases, the time elapsed decreases. Thats why the line goes downward from left to right.
For racer B, as the speed increases, the time elapsed decreases at a rate lesser than that of racer A.
what is the absolute value of 1 -32 1?what is the opposite of 6 on the number line?
Given data:
The given number is | -32| .
The value of given modulus function is,
[tex]|-32|=32[/tex]The opposite of 6 on number line is -6.
Thus, the value of first number is 32, and second is -6.
A mine shaft which slopes at an angle of 19° to the horizontal is driven into a hillside for
400 m. How much lower, to the nearest metre, is the end of the shaft than the beginning?
The end of shaft is 137.731m lower at the beginning.
What is angle?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex.
Angles' Components:
Vertex: The intersection of two lines or sides at an angle is called a vertex.
Arms: The angle's two sides linked at a single end.
Initial Side: A line that is straight from which an angle is made.
from the given figure:
tan(19) = BC/AB
BC = 400 × tan(19)
BC = 137.731m
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Use synthetic division to find the function value. Then, check your work using a graphing calculator.
we have the function
f(x)=x^4-x^3-7x^2+45x-39
Find out f(-5)
so
Use synthetic division
x^4-x^3-7x^2+45x-39 : (x+5)
x^3-6x^2+23x-70
-x^4-5x^3
-------------------------------
-6x^3-7x^2+45x-39
6x^3+30x^2
----------------------------
23x^2+45x-39
-23x^2-115x
------------------------
-70x-39
70x+350
------------------
311 ----------------> remainder
therefore
f(-5)=311
Verify
using a graphing tool
For x=-5 ------------> f(x)=311 is ok
Simplify the absolute value 8|cos | if = sin−1 8/x for some real number x. (Give your answer in terms of .)
The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.
The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.
θ = Sin−1 (8/x)
Sinθ = 8/x
We know the trigonometric identity that Sin²θ + Cos²θ = 1.
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
(8/x)² + Cos²θ = 1.
Cos²θ = 1 - (8/x)²
Cos²θ = (x² - 8²)/x²
Cosθ = √[(x² - 8²)/x²]
Cosθ = √(x² - 8²)/x
Multiply both the sides with 8.
8Cosθ = 8√(x² - 8²)/x
Apply modulus on both the sides.
A modulus function is one that returns the absolute value of a number or variable.
8|Cosθ| = 8√(x² - 8²)/|x|
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7.Use the model to predict the number of people infected in 15 days.Answer:
Step 1:
The model of the table is shown below:
Step 2:
The equation of the model is
y = 140.6t + 371.6
Step 3:
To predict the number of people infected in 15 days, substitute t = 15
[tex]\begin{gathered} y\text{ = 140.6 }\times\text{ 15 + 371.6} \\ \text{y = 2109 + 371.6} \\ \text{y = 2480}.9 \\ y\text{ = 2481} \end{gathered}[/tex]Final answer
2481
The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 5 to 3. If there were 4440 total votes, how many yes votes were there?
Total votes of the residents of the city = 4,440
Ratio of yes to no = 5:3
Yes votes = 4,440 * 3/5 = 2,664
No votes = 4,440 - 2,664 = 1,776
Four less than the amount of cents in a number of dimes
Point O is the midpoint of DG. The coordinates of points D and O are (-4, 0) and (-1,-5) respectively
What are the coordinates of point G
Coordinates of Point G is (1,-10)
To find Coordinates :
O is midpoint of DGCoordinates of O (-1,-5)Coordinates of D (-4,0)Let the coordinates of G are (x,y)
To find coordinates of G
[tex]\frac{x + (-4)}{2} = -1[/tex] [tex]\frac{y + 0}2} = -5[/tex]
= x + (-2) = -1 y+0 = -5 * 2
x = -1 + 2 y = -5 * 2
x = 1 y = -10
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How much money should you invest at 5.3% annual simple interest rate to have $7200 in 9 months?
Answer:
181 132$
Step-by-step explanation:
Co - initial capital
I - interest
r - 5.3% annual simple interest
t - time
I = Co * r * t
7200 = Co * 0.053 * 9/12
Co = 181 132$
Determine which integer will make the inequality 20 > 4x + 16 true.
Answer:
-1
Step-by-step explanation:
That's my best shot.
pleaseeee help!! !!!!!
Answer: it’s c
Step-by-step explanation: dude that’s ez
6g7g7v7c6clvyc5cubibigl
he needs to walk the dog 6 times more}
What is A-B.If A is 32 and B is 30
To solve the exercise, we subtract the given numbers:
[tex]\begin{gathered} A=32 \\ B=30 \end{gathered}[/tex][tex]A-B=32-30=2[/tex]Pls help fast !!!!!!!
The required solution of the function f(x) = -3x + 5 at x = -2 is 11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given function,
f(x) = -3x + 5
Substitute x with -2 to find f(-2).
f(-2) = -3(-2) + 5
f(-2) = +6 + 5
f(-2) = 11
Thus, the required solution of the function at x = -2 is 11.
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If point M is located at (-8, 3), which ordered pair below represents a 180-degree rotation about the originof point M?
A 180-degree rotation about the origin transforms point (x, y) into (-x,-y). then:
M(-8, 3) → M'(8, -3)
