Answer:
what is the questions.
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.
Answer:
Step-by-step explanation:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
The zeroes of the function are -4, 0 and 2.
The intervals where the function is positive is [tex]-4 < x < 2, \ \ x >2[/tex].
The intervals where the function is negative is [tex]x < -4[/tex].
The given parameters:
f(x) = x³ + 2x² - 8xWhat is zeroes of a function?The zeroes of a function is the possible values of the unknown that makes the entire function to be zero.
The zeroes of the cubic equation is calculated as follows;
f(x) = 0
x³ + 2x² - 8x
factorize as follows;
[tex]x(x^2 + 2x -8) = 0\\\\x(x^2 + 4x - 2x -8) = 0\\\\x[x (x + 4 )-2(x + 4)]= 0\\\\x(x + 4)(x -2)=0\\\\x = 0, \ \ x = -4 \ \ x = 2[/tex]
The intervals where the function is positive and negative is determined as follows;
[tex]x(x + 4) (x - 2)\\\\[/tex]
[tex]when, \ x = -5, \ f(x) = -ve\\\\when, \ x = -4, \ f(x) =0\\\\when , \ x = -3, \ f(x) = +ve[/tex]
The intervals where the function is positive is determined as;
[tex]-4 < x < 2, \ \ x >2[/tex]
The intervals where the function is negative is determined as;
[tex]x < -4[/tex]
Learn more about graph of cubic equation here: https://brainly.com/question/8878887
Given: ∆ABC, m∠C = 90°
m∠BAC = 2m∠ABC
BC = 24 cm,
AL
− ∠ bisector
Find: AL
Answer: 16 units
Step-by-step explanation:
Given that in triangle ABC, m∠C=90,
it means m∠A +∠B= m∠BAC + m∠ABC = 90
m∠ABC = 90 - m∠BAC
Also given that;m∠BAC = 2m∠ABC
So,
m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC
m∠BAC +2m∠BAC = 180
3m∠BAC = 180
m∠BAC=180/3 = 60
m∠ABC = 60/3 = 30
thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,
AC=24/√3=8√3AL bisects angle A =>m∠LAC=30
ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16
There are 48 crackers on a plate which are going to be shared by 5 friends. Which of the following best describes how many crackers each person will get?
2 people get 10 crackers each 3 people get 9 crackers each
2 people get 13 crackers each 3 people get 12 crackers each
3 people get 10 crackers each 2 people get 9 crackers each
4 people get 8 crackers each 1 person gets 15 crackers each
will mark brainliest!!!
Answer:
3 people get 10 crackers each 2 people get 9 crackers each
Step-by-step explanation:
SO WE CHECK THE OTHER ANSWERS
1. 2 people get 10 crackers each 3 people get 9 crackers each
(2*10)+(3*9)=?
20+27=47
WHICH IS WRONG CAUSE WE NEED THE SUM TO BE 48
2. 2 people get 13 crackers each 3 people get 12 crackers each
(2*13)+(3*12)=?
26+36=62
WHICH IS WRONG CAUSE WE NEED THE SUM TO BE 48
3. 3 people get 10 crackers each 2 people get 9 crackers each
(3*10)+(2*9)=?
30+18=48
WHICH IS CORRECT CAUSE THE SUM SHOULD BE 48
4. 4 people get 8 crackers each 1 person gets 15 crackers each
(4*8)+(1*15)=?
32+15=47
WHICH IS WRONG CAUSE WE NEED THE SUM TO BE 48
SO THE ANSWER IS 3 people get 10 crackers each 2 people get 9 crackers each
I HOPE I HELPED
PLS MARK BRAINLIEST!!!!!! (DESPERATELY TRYING TO LEVEL UP)
IT TOOK ME 10 MINS TO TYPE THIS
-ZYLYNN JADE
Please help Asap. Will give brainiest if answered correctly with a math question
TV = VX.
3x-24 = 2x + 1
Add 24 to both sides:
3x = 2x + 25
Subtract 2x from both sides:
X = 24
VX = 2(25) + 1 = 50 + 1 = 51
The answer is 51
Answer:
51
Step-by-step explanation:
Since it is an isosceles triangle the two sides are equal
3x - 24 = 2x + 1
x = 25
2(25) + 1 = 51
Reorder the following equations in ascending order of steepness: y= 15x + 5 y= 0.15x - 1 y=x y= x + 100
Answer:
y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.
Step-by-step explanation:
When the slope of a line is less than 1 (if the slope is a decimal), the slope will not be steep. But when the slope is more than 1, the slope will be steeper than the average.
According to that rule, the steepest will be y = 15x + 5.
The next steepest equations will be y = x and y = x + 100 (they are both at the same degree of steepness; the intercept does not impact the steepness of the line).
The least steepest will bey = 0.15x - 1.
So, the order, from least steep to most steep, will be y= 0.15x - 1, y = x, y = x + 100, y = 15x + 5.
Hope this helps!
PLEASE ANSWER THIS FAST Will the red square and the orange square always equal the blue square? What colored square is the hypotenuse?
Step-by-step explanation:
The area of the blue square will always equal the sum of the area of the orange and red rectanglesThe pythagorian theorem:
a²+b² = c²
now let a be the side of the red triangle and b the side of the orange one
so a² is the area of the red triangle and b² is the area of the orange one
Let c be the side of the blue rectangle
so c² is the area of it
then what we concluded is right
the hypotenuse is the blue side since it is the larger oneWILL MARK BRAINLIEST!! PLZ HELP!!
Answer:
The answer is D.
Step-by-step explanation:
When x=0, then y=300, so it has to be more than that.
When x=25, y=300, so it has to be less than that.
I will give brainliest!! THERE IS NO OTHER INFORMATION GIVEN!! In ⊙O, chord XY is 8 cm long and is 10 cm from O. What is the radius ⊙O?
Answer:
radius ≈ 10.77 cm
Step-by-step explanation:
The segment from the centre O to the chord is a perpendicular bisector.
Thus 2 right triangles are formed with legs 10 cm and 4 cm ( half of XY )
The radius r is the hypotenuse.
Using Pythagoras' identity, then
r² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )
r = [tex]\sqrt{116}[/tex] ≈ 10.77 cm ( to 2 dec. places )
Answer:
Step-by-step explanation:
perpendicular from center always bisects the chord of circle.
1/2 of chord=1/2×8=4 cm
[tex]r=\sqrt{4^2+10^2} =\sqrt{16+100} =\sqrt{116} \approx 10.77 ~cm[/tex]
I need help for this problem!
-9(x + 6) = 18
Answer:
x = -8
Step-by-step explanation:
1. Divide both sides of the equation by -9 to get (x+6) = -2
2. Now that are left with x+6 you can subtract (inverse operation) the 6 from both sides of the equation to get x = -8
Hope this helps
Solving Exponential Equations using Logarithms
Answer:
6 weeks
Step-by-step explanation: set the equation to be 1458=2(3^t). Do the division property of equality by 2.
729=3^t
Divide 729 by 3 until you get a 1 as the answer.(Count the number of times that you did it, and that will be your answer)
I dont know how to solve this question using proportions:
212.7 = 16.8% of
Answer:
17,725/14.
Step-by-step explanation:
Let's say that the blank is represented by x.
Since the question asks what is 16.8% of x, we can set up a proportion where 16.8 out of 100 is equivalent to 212.7 out of x. The 100 represents the "whole" number, which corresponds to x. The 212.7 IS the 16.8 of x.
[tex]\frac{16.8}{100} =\frac{212.7}{x}[/tex]
16.8 * x = 212.7 * 100
16.8x = 21,270
x = 21,270 / 16.8
x = 212,700 / 168
x = 17,725 / 14 = 1,266.071429
To check our work, 1,266.071429 * 0.168 = 212.7.
Hope this helps!
a pile of steel plates is 2.75 feet high. if the plates are 0.375 inch thick. how many are there in the pile.
Answer:
88
Step-by-step explanation:
2.75 ft = (2.75 ft)(12 in/ft) = 33 in
At 0.375 inches per plate, there will be ...
(33 in)/(0.375 in/plate) = 88 plates
There are 88 steel plates in the pile.
Match each correlation coefficient, r, to its description.
weak negative
correlation
weak positive
correlation
strong positive
correlation
strong negative
correlation
r = −0.83
arrowRight
r = −0.08
arrowRight
r = 0.96
arrowRight
r = 0.06
arrowRight
Answer:
r = -0.83
strong negative correlation
r = -0.08
weak negative correlation
r = 0.96
strong positive correlation
r = 0.06
weak positive correlation
Step-by-step explanation:
In this question, what we are expected to do is to match the values of the correlation given with the type of correlation in which the values are.
When we talk of correlation, we are simply referring to the extent of agreement between the values in the data field.
Correlation has a value between -1 and +1, meaning it could be negative or positive.
Values closer to the extremes i.e (-1 or +1) indicates strong correlation while values farther away, i.e closer to zero indicates a weak relationship.
Let’s answer the questions specifically now:
r = -0.83
This is closer to -1 and it indicates a strong negative correlation
r = -0.08
This indicates a weak negative correlation as it is closer to zero and farther away form -1
r = 0.96
This indicates a strong positive correlation
r = 0.06
This indicates a weak positive correlation
A rectangular playground has an area of 180 square yards. The length of the playground is 3 yards longer than the width. Find the length of the playground.
A)15 yards
B)18 yards
C)12 yards
D)13 yards
Answer: The length is 15 yards so the answer is A.
Step-by-step explanation:
If the length is 3 more than the width the we will represent it by the equation L = w+3 where w is the width and to find the area of a rectangle, we need to multiply the length by the width. so the length is w+3 and the width is w so
w(w+3) = 180 solve for the w
w^2 + 3w = 180 subtract 180 from both sides
w^2 + 3w -180 = 0 find two numbers that their product is -180 and add to 3.
the number 12 and -15 works out because -12*15= -180 and -15+ 12 =3
We will now have a new quadratic equation as
w^2 - 12w + 15w - 180 = 0 factor by grouping
w(w-12) 15(w-12)= 0 factor out w-12
(w-12)(w+15) = 0 set them both equal zero.
w -12 = 0 or w+15= 0
w = 12 or w = -15
Since we know that -15 can't represent a distance, then 12 is the width .
So if we are to find the length and it gives us the information that the length is 3 yards more that the width then we will add 3 to the width to equal the length.
L= 12 +3
L = 15
The length of the rectangular playground is 15 yards. The correct answer would be an option (A).
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
Since the length is 3 more than the width
So, we will represent it by the equation L = W+3 ...(i)
A rectangular playground has an area of 180 square yards
So, L × W = 180
Substitute the value of equation (i), and we get
W(W+3) = 180
W² + 3W = 180
W² + 3W -180 = 0 ...(i)
Solving the above quadratic equation, we get the values of W :
W = 12 and W = -15
Take positive value because dimensions can't be negative.
Substitute the value of W = 12 in equation (i), and we get
L = 12 + 3 = 15
Therefore, the length of the playground is 15 yards.
Learn more about the Area of the rectangle here:
brainly.com/question/20693059
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A car is new at the beginning of a calendar year. The time, in years, before the car experiences its first failure is exponentially distributed with mean 2.Calculate the probability that the car experiences
Complete question is;
A car is new at the beginning of a calendar year. The time, in years, before the car experiences its first failure is exponentially distributed with mean 2. Calculate the probability that the car experiences its first failure in the last quarter of some calendar year.
Answer:
Probability = 0.2052
Step-by-step explanation:
I've attached the explanation to this answer.
Which phrase best describes f(x), graphed on the coordinate plane below?
f(x) is an odd function.
f(x) is an even function.
f(x) is both odd and even
f(xl is neither add nor even
Answer: f(x) is an odd function
Step-by-step explanation: The major characteristic of odd functions is that one end of the graph goes down to negative infinity, the other end goes up to positive infinity.
Answer:
f(x) is an odd function.
Step-by-step explanation:
Factor the term ab - by - ay + y2
Answer
(a - y) (b - y)
Step-by-step explanation:
(ab - ay) (-by + y^2)
a (b - y) -y ( b - y)
(a-y) (b - y)
.. ..
Answer:
[tex]\boxed{(a-y) (b - y)}[/tex]
Step-by-step explanation:
Rearrange the terms.
[tex](ab - ay) (-by + y^2)[/tex]
Factor out common term.
[tex]a (b - y) -y ( b - y)[/tex]
Apply rule : [tex]a(b+c)+d(b + c) = (a+d)(b+c)[/tex]
[tex]a (b +- y) +-y ( b +- y)[/tex]
[tex](a+-y) (b +- y)[/tex]
f(x) =
- 6x5 + 4x3
Which characteristic is correct for the function
Complete question:
[tex] F(x) = -6x^5 + 4x^3 [/tex]
Which characteristic is correct for the function
a) odd
b) neither even nor odd
c) both even and odd
d) even
Answer:
a) odd
Step-by-step explanation:
Given the equation:
[tex] F(x) = -6x^5 + 4x^3 [/tex]
To test for even or odd let's perform the following:
F
Replace "x" with "-x"
Thus,
[tex] F(x) = -6x^5 + 4x^3 [/tex]
[tex] = -6(-x)^5 + 4(-x)^3 [/tex]
[tex] = 6x^5 + -4x^3 [/tex]
Since [tex] -6x^5 + 4x^3 [/tex] ≠ [tex]-6(-x)^5 + 4(-x)^3[/tex] the equation is not even.
Also, the signs changed, the equation is considered to be odd.
I.e f(x) = -f(x)
Correct answer is option (a) odd
Answer:
odd
explanation:
[tex]Expand $(a + 2)(3a^2 + 12)(a - 2).$[/tex]
Answer:
3[tex]a^{4}[/tex] - 48
Step-by-step explanation:
Given
(a + 2)(3a² + 12)(a - 2)
= (a + 2)(a - 2)(3a² + 12) ← expand the first pair of parenthesis using FOIL
=(a² - 4)(3a² + 12) ← expand using FOIL
= 3[tex]a^{4}[/tex] + 12a² - 12a² - 48 ← collect like terms
= 3[tex]a^{4}[/tex] - 48
wht is the solution of the system defined be y =-x+5 and 5x+2y=14
Answer:
1.33,3.667
Step-by-step explanation:
Use y=mx+b for second system
which is y=5/2x+7
Now use substitution,graph, or elimination method.
The sum of two negative integers is always
Answer:
The sum of two negative integers is always negative.
Step-by-step explanation:
For example, add -1+-1 which =-2, which are the smallest neggative numbers possible.-100+-100=-200, and -4+-4=-8, so you see that the sum of two negative integers should always be negative.
can you please help me
Apply the rule x^m/n = nsqrt(x^m)
(2) ^x/12 = 12sqrt(2^x)
The answer is the 3rd choice
Write an expression for the cost of 12 uniforms, multiply 12 by the cost of 1 uniform.
Answer:
384
Step-by-step explanation:
the cost of the shirt is 13, pants is 11, and 8 for socks
13+11+8=32
the cost of 12 uniforms:12(13+11+8)=384
HELP ME PLSSSSSSSSSSS ALL MY POINTS
Answer:
B
Step-by-step explanation:
You can not take a square root of a negative number, because than it will become imaginary. So X has to be equal to or greater than 10.
Use a calculator to find the measure of
Answer:
mRT = 4√13 ≈ 14.42
mST = 10√2 ≈ 14.14
Step-by-step explanation:
Pythagorean Theorem: a² + b² = c²
Since we have right triangles, in order to find the missing side, we use Pythagorean Theorem:
mTR:
12² + 8² = c²
144 + 64 = c²
c² = 208
c = √208 = 4√13
mST:
15² = 5² + b²
225 - 25 = b²
b² = 200
b = √200 = 10√2
To get your decimals, simply evaluate the square roots:
4√13 = 14.4222
10√2 = 14.1421
Answer:
6. 56.3 degrees.
7. 70.5 degrees.
Step-by-step explanation:
6. We are given the opposite and adjacent side lengths, so we can use tangent to solve this (TOA = Tangent; Opposite over Adjacent).
tan(R) = 12 / 8
tan(R) = 3 / 2
R = cotan(3/2)
R = 56.309932474020213
So, the measure of angle R is about 56.3 degrees.
7. We are given the adjacent and the hypotenuse, so we can use cosine to solve this (CAH = Cosine; Adjacent over Hypotenuse).
cos(R) = 5 / 15
cos(R) = 1/3
R = sec(1/3)
R = 70.528779365509
So, the measure of angle R is about 70.5 degrees.
Hope this helps!
Answer this question will give brainliest.
Answer:
A.Step-by-step explanation:
Faktor (x-a) means a is x-intercept
x-10 ⇒ 10 is x-intercept
22-x ⇒ 22 is x-intercept
x+10 ⇒ -10 is x-intercept
20+x ⇒ -22 is x-intercept
so in the graph have to be at least two intercepts <0 and at least two intercepts >0
Solve the answer -4(8+Y)= 90
[tex]-4(8+y)=90\implies8+y=-22.5\implies y=-30.5[/tex].
Hope this helps.
Answer:
-30.5.
Step-by-step explanation:
-4(8 + Y) = 90
-32 - 4Y = 90
-4Y = 122
Y = -30.5.
Hope this helps!
HELP ME PLLEEEEASE I BEG
A company has determined that its weekly profit is a function of the number of items that it sells. Which equation could represent the weekly profit in thousands of dollars, y, when the company sells x items? y squared = 4 x squared minus 100 y = negative x squared + 50 x minus 300 x = negative y squared minus 400 x squared = negative 6 y squared + 200
Answer:
B. y= -x^2+50x-300
Step-by-step explanation:
A. y^2=4x^2-100
B. y= -x^2+50x-300
C. x=-y^2-400
D. x^2=-6y^2+200
we are to find profits (y) when the company sells x items
Option A can be used to calculate the profit (y) squared
Option B can be used to calculate profits (y)
Option C can be used to calculate items sold(x)
Option D can be used to calculate items sold squared(x^2)
We are asked to find the weekly profit (y) function which eliminate options A, C and D leaving us with option B
Therefore, the weekly profits (y) function in thousands of dollars when the company sells x items is
B. y= -x^2+50x-300
fins the zeroes of the quadratic equation : 4√ 5 x^ 2 - 24x - 9√ 5
10th grade Cbse chapter 2 : Polynomials
pls give the step by step explanation so that i can understand
Answer:
Step-by-step explanation:
Hello,
First of all, we know that the solution of the following equation
[tex]ax^2+bx+c=0[/tex]
are
[tex]\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} \ \text{ when } \Delta=b^2-4ac \geq 0[/tex]
I would suggest that you try to apply this formula first and check the solution only after you try.
Let's apply it in this case, we have:
[tex]a=4\sqrt{5} \\ \\ b=-24 \\ \\ c= -9\sqrt{5}[/tex]
[tex]\Delta=b^2-4ac=24^2+4*9*5=1296 \\ \\ \sqrt{\Delta}=36 \ \text{ and the solutions are } \\ \\ \\ x_1=\dfrac{24-36}{8\sqrt{5}}=\dfrac{-12}{8\sqrt{5}}=\boxed{\dfrac{-3}{2\sqrt{5}}} \\ \\x_2=\dfrac{24+36}{8\sqrt{5}}=\dfrac{60}{8\sqrt{5}}=\boxed{\dfrac{15}{2\sqrt{5}}}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you