Answer:
- [tex]\sqrt{11}[/tex]
Step-by-step explanation:
Radical roots occur in conjugate pairs
Thus if [tex]\sqrt{11}[/tex] is a root then
- [tex]\sqrt{11}[/tex] is also a root
The other root of the given polynomial is [tex]-\sqrt{11}[/tex].
What is the root of a polynomial?"Roots of a polynomial refer to the values of a variable for which the given polynomial is equal to zero."
Given roots of a polynomial f(x) are - 4, 2, 1, [tex]\sqrt{11}[/tex].
We know, for the root of an equation, radical roots are always in pair.
If a polynomial has two roots, one is [tex]\sqrt{x}[/tex] then the other one must be [tex]-\sqrt{x}[/tex].
Similarly, the root of the given polynomial is [tex]-\sqrt{11}[/tex].
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How are conditional probability and independent events related?
Select the correct phrase or notation from each drop-down menu to complete the explanation.
The notation __A__ reads the probability of Event A given that Event B has occurred. If Events A and B are independent, then the probability of Event B occurring __B__ the probability of Event A occurring. Events A and B are independent if __C__
A.
1. P(B|A)
2.P(A|B)
3. P(A and B)
B.
1. affects
2. does not affect
C.
1. P(A|B) = P(A)
2. P(A|B) = P(B)
3. P(A|B) = P(A and B)
Answer:
1. P(A|B) - option 2
2. does not affect - option 2
3. P(A) - option 1
Step-by-step explanation:
By the definition, the notation P(A|B) reads the probability of event A given that event B has occured. So, for the first gap correct choice is 2 - P(A|B).
If events A and B are independent, then the probability of event B occuring does not affect the probability of event A occuring. So, for the second gap correct choice is 2 - does not affect.
Events A and B are independent, then
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]
Use formula for the conditional probability:
[tex]P(A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
Since events A and B are independent, we get
[tex]P(A|B)=\dfrac{P(A)\cdot P(B)}{P(B)}=P(A)[/tex]
So, for the third gap correct answer is 1 - P(A)
For (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
From the basic definitions of the events of probability.
P(A|B) = The probability of Event A given that Event B has occurred
In the independent events, the probability of Event B occurring does not affect the probability of Event A occurring.
P(A|B) = P(A) if events A and B are independent.
Thus, for (A) option (2) is correct, for (B) option (2) is correct, and for (C) option (1) is correct.
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In ∆ABC, if sin A = 4/5 and tan A = 4/3 , then what is cos A?
A. 3/5
B. 4/5
C. 3/4
D. 5/3
Answer:
A = 3/5
Step-by-step explanation:
At the outset, the question doesn't give us a figure to refer to nor does it tell us if this is a right angled triangle. However we observe that both sin A and tan A have the numbers 3, 4 and 5. We recognize this to be consistent with 3-4-5 standard right angled triangle.
Hence we can guess that it is probably a right angled triangle, but we should do the following to confirm:
Knowning that for a right angled triangle,
sin A = opposite / hypotenuse = 4/5
tan A = opposite / adjacent = 4/3
From this we can surmise that
Opposite = 4
hypotenuse = 5
adjacent = 3
Assemble the triangle to see if this works (see attached). We can futher verify that 3-4-5 works using the Pythagorean theorem.
Now that we have determined that the triangle is a 3-4-5 right angled triangle,
cos A = adjacent / hypotenuse = 3/5
Answer:
A
Step-by-step explanation:
Which characteristic is correct for the function
f(x) = -3x^4 + 7x^2?
odd
Neither even nor odd
Even
Both even and odd
Answer:
This is an even function.Step-by-step explanation:
[tex]\text{If}\ f(-x)=f(x)\ \text{then}\ f(x)\ \text{is an even function.}\\\\\text{If}\ f(-x)=-f(x)\ \text{then}\ f(x)\ \text{is an odd function.}[/tex]
======================================================
[tex]f(x)=-3x^4+7x^2\\\\f(-x)=-3(-x)^4+7(-x)^2=-3x^4+7x^2\\\\f(-x)=f(x)[/tex]
The function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
f(x) = -3x⁴ + 7x²
To check whether the function is odd or even, plug x → -x in the function:
f(-x) = -3(-x)⁴ + 7(-x)²
f(-x ) = -3x⁴ + 7x²
f(-x) = f(x)
The function is even.
Thus, the function f(x) = -3x⁴ + 7x² is an even function because f(-x) = f(x) = -3x⁴ + 7x²
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A golf course in Phoenix, Arizona, uses an average of 80 million gallons of water daily for irrigation. An average family of four (also living in Phoenix, AZ) uses 325,851 gallons of water per year. Rounded to the nearest ten, how many families of four can one golf course provide water for? 89,610 families 250 families 896,120 families 245 families
The golf course can provide water for approximately 89,610 families of four.
Explanation:To find out how many families of four the golf course can provide water for, we need to compare the average water usage of the golf course with the average water usage of a family of four.
The golf course uses an average of 80 million gallons of water daily for irrigation.
To convert this to gallons per year, we multiply by 365:
80 million gallons/day * 365 days/year = 29.2 billion gallons/year.
Now, we divide the total water usage of the golf course by the water usage of one family of four:
29.2 billion gallons/year / 325,851 gallons/year = approximately 89,610 families of four.
The golf course can therefore provide water for approximately 89,610 families of four.
Given the following triangles, what additional information is required in order to know that the triangles are congruent because of the ASA congruence criteria?
QD and ED are congruent
DCQDCE
QC and DE are congruent
CDEDCQ
Answer:
The correct answer is : DCQ ( angle) = DCE (angle)
Answer: DCQ=DCE
Step-by-step explanation:
Find the dervite of y=X^2 + x + 1
Answer:
2x + 1.
Step-by-step explanation:
y=x^2 + x + 1
Using the algebraic derivative rule, if y = ax^n then y' = anx^(n-1) :
The derivative is 2x^(2 - 1) + 1x^(1-1)
= 2x^1 + x^0
= 2x + 1.
Answer:
y'(x) = 1 + 2 x
Step-by-step explanation:
Find the derivative of the following via implicit differentiation:
d/dx(y) = d/dx(1 + x + x^2)
Using the chain rule, d/dx(y) = ( dy(u))/( du) ( du)/( dx), where u = x and d/( du)(y(u)) = y'(u):
d/dx(x) y'(x) = d/dx(1 + x + x^2)
The derivative of x is 1:
1 y'(x) = d/dx(1 + x + x^2)
Differentiate the sum term by term:
y'(x) = d/dx(1) + d/dx(x) + d/dx(x^2)
The derivative of 1 is zero:
y'(x) = d/dx(x) + d/dx(x^2) + 0
Simplify the expression:
y'(x) = d/dx(x) + d/dx(x^2)
The derivative of x is 1:
y'(x) = d/dx(x^2) + 1
Use the power rule, d/dx(x^n) = n x^(n - 1), where n = 2.
d/dx(x^2) = 2 x:
Answer: y'(x) = 1 + 2 x
Please help me and please show your answer or explain please
Answer:
31.96
Step-by-step explanation:
The product of 2 numbers is simply one number multiplied by another
6.8 x 4.7 = 31.96
As a sanity check, just round the numbers off to a whole numbers and take a product of those two:
i.e 6.8 rounded off to the nearest whole number is 7 and 4.7 rounded off to the nearest whole number is 5.
7 x 5 = 35
If you look at the possible answers, only 31.96 is anywhere close to 35, hence you can be be more confident that your answer of 31.96 is correct.
Answer:
31.96 is your answer
Step-by-step explanation:
its just like a normal multiplication problem multiply 6.8 and 4.7 and you'll get your answer :))
61:3 odds pays out how much if you bet $25. I think $1550
Answer:
$508.33
Step-by-step explanation:
If I bet $25 (And I win, of course), I will win:
If I win $61 per every $3 bet, then:
61/3 = x/25 ⇒ Solving for 'x':
61*25/3 = $508.33
Finally, if you bet $25 you will win $508.33.
Find a conversion factor between square centimeters and square meters. Write it in three forms.
Square centimeters = 1 square meter
Answer:
1 square meter = 10000 square centimeters.
Step-by-step explanation:
We know that 1 meter = 100 centimeters.
Then 1 square meter = ( 100 cm)(100 cm) = 10000 square centimeters.
Then:
1 square meter = 10000 square centimeters.
what is the inverse of the function below? f(x)=x/3-2
Answer:it’s actually 3(x+2)
Step-by-step explanation:
the first four terms of a sequence are shown below 8,5,2,-1
Answer:
an = 8-3(n-1)
an = 11 - 3n
Step-by-step explanation:
This is an arithmetic sequence which is defined by
an = a1 + d(n-1)
where a1 is the first term of the sequence and d is the common difference
a1 = 8
d = a2-a1
d = 5-8 = -3
an = 8 + -3(n-1)
an = 8-3(n-1)
We can simplify this by distributing the -3
an = 8 -3n +3
an = 11 - 3n
Jill bought a pound of strawberries for $4.00. What is the price, in dollars, per ounce of strawberries? (1lb = 16 oz)
Answer:
$0.25/lb
Step-by-step explanation:
Convert 1 lb to 16 oz mentally. Then the unit cost of the berries is
$4.00
------------ = $0.25/lb
16 oz
convert the polar representation of this complex number into its rectangular form: z=5(cos pi+i sin pi)
Answer:
The complex number z = -5 into its rectangular form
Step-by-step explanation:
* Lets revise the complex numbers
- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the
imaginary part in the polar form
- The value of i = √(-1) ⇒ imaginary number
- Then z = a + bi , where a is the real part and bi is the imaginary part
in the rectangular form
∴ a = r cos Ф and b = r sin Ф
* Lets solve the problem
∵ z = r (cos Ф ± i sin Ф)
∵ z = 5 (cos π + i sin π)
∴ The real part is 5 cos π
∴ The imaginary part is 5 sin π
- Lets find the values of cos π and sin π
∵ The angle of measure π is on the negative part of x axis at the
point (-1 , 0)
∵ x = cos π and y = sin π
∴ cos π = -1
∴ sin π = 0
∴ a = 5(-1) = -5
∴ b = 5(0) = 0
∴ z = -5 + i (0)
* The complex number z = -5 into its rectangular form
Answer:
(-5,0)
Step-by-step explanation:
just cuz
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + 2y = 12 –x = –y – 6
A. (9, 3)
B. (7, 1)
C. (6, 0)
D. (8, 2)
Answer:
(8,2)
Please make sure I interpreted your system correctly below.
x+2y=12
-x=-y-6
Step-by-step explanation:
I assume the system is
x+2y=12
-x=-y-6
-----------
I'm going to multiply both sides of equation 2 by -1 giving me
x+2y=12
x=y+6
I'm now going to plug equation 2 into equation 1.
(y+6)+2y=12 I replaced x with y+6 in the first equation
y+6+2y=12
3y+6=12
3y=6
y=2
So
x=y+6
x=2+6
x=8
The solution is (8,2)
Simplify 4 to the power of 2 and 4 to the power of 8
Answer:
The second option.
Step-by-step explanation:
4^2 × 4^8
(4 × 4)(4 × 4 × 4 × 4 × 4 × 4 × 4 × 4) = 4^10
Or
4^2 × 4^8
=4^2+8
4^10
When solve an exponential with the same constant, you ga no problem. Just take one of those and and the exponent, you are good to go.
Please mark as brainliest.
Find the discriminant of 3x2 - 10X=-2.
Answer:
76
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c : a ≠ 0, then
the discriminant Δ = b² - 4ac
Given
3x² - 10x = - 2 ( add 2 to both sides )
3x² - 10x + 2 = 0 ← in standard form
with a = 3, b = - 10 and c = 2
b² - 4ac = (- 10)² - (4 × 3 × 2) = 100 - 24 = 76
Answer:
Discriminant : 74 .
Step-by-step explanation:
Given : 3x² - 10x = -2.
To find : Find the discriminant .
Solution : We have given 3x² - 10x = -2.
On compare with standard form ax² +bx +c = 0.
Where, a =3 ,b = -10 , c = 2.
Discriminant : [tex]b^{2} - 4ac[/tex].
Plug the values of a , b , c .
Discriminant : [tex](-10)^{2} - 4(3)(2)[/tex].
Discriminant : 100 - 24 .
Discriminant : 74 .
Therefore, Discriminant : 74 .
The point of tangency of line s to circle B is
Answer: FIrst option.
Step-by-step explanation:
We need to remember that a tangent is a line that touches a circle at one point. This point is the "Point of tangency".
We can observe in the figure that the line "s" touches the circle A at a point identified as "J" and it also touches the circle B at a point identified as "K". Therefore, we can make the following conclusion:
The point of tangency of line "s" to circle B is: The point K.
This matches with the first option.
20 students plays football and 16 students plays hockey.It is found that 10 students plays both game.Find the number of students playing at least one game
May I have help on number 7 please
Answer:
its A
Step-by-step explanation:
you do 28 x 66 :)
What is the value of b in the equation 3b + 2(b - 1) =8
Answer:
b = 2
Step-by-step explanation:
In order to find the value of b, we have to isolate b on one side of equation first
So,
[tex]3b+2(b-1)=8[/tex]
Multiplying 2 with b-1
[tex]3b+2b-2=8\\5b-2=8[/tex]
Adding 2 on both sides
[tex]5b-2+2=8+2\\5b=10[/tex]
Dividing by 5 on both sides
[tex]\frac{5b}{5}=\frac{10}{5} \\b=2[/tex]
So the value of b is 2 ..
ANSWER
The value of b is 2
EXPLANATION
The given linear equation in b is
[tex]3b + 2(b - 1) = 8[/tex]
We expand to get:
[tex]3b + 2b - 2= 8[/tex]
We now group similar terms to obtain:
[tex]3b + 2b = 8 + 2[/tex]
Combine the similar terms now to obtain:
[tex]5b = 10[/tex]
Divide both sides by 5 to get:
[tex]b = \frac{10}{5} [/tex]
This simplifies to:
[tex]b = 2[/tex]
If ƒ (x ) = 2x 2 + 3, find ƒ (3).
Answer:
[tex]f(x) = 2 \times 2 + 3 \\ f(3) = 4 + 3 \\ 3f = 7 \\ f = \frac{7}{3} [/tex]
Hope it help youAnswer:
The answer is 15
Step-by-step explanation:
If ƒ (x ) = 2x 2 + 3, find ƒ (3).
2(3)^2 +3
6^2+3
= 15
An athlete jumped 5.5 feet which was 1.1 times higher than the previous jumper how high did the previous athlete jump
Answer:
5 ft
Step-by-step explanation:
Let the height of the previous jump be represented by j. Then 1.1j = 5.5 ft.
Dividing both sides by 1.1, we get j = 5 ft. This was the height of the previous jump.
Answer:
5 ft
Step-by-step explanation:
The previous jumper jumped p
The new jumper jumped p*1.1 and that was 5.5 ft
1.1p = 5
Divide each side by 1.1
1.1p/1.1 = 5.5/1.1
p = 5
The previous jumper jumped 5 ft
At which values of X does the function F(x) have a vertical asymptote? Check all that apply.
ANSWER
A. 1
D. 8
EXPLANATION
The vertical asymptote occurs at where the denominator of a rational function in its simplest form is equal to zero.
The rational function given is
[tex]p(x) = \frac{9}{(x - 1)(x - 8)} [/tex]
This rational function is in it's simplest form.
The vertical asymptotes occurs at
[tex](x - 1)(x - 8) = 0[/tex]
By the zero product principle, we must have either
[tex](x - 1) = 0 \: \: or \: \: (x - 8) = 0[/tex]
This implies that
[tex]x =1\: \: or \: \: x = 8[/tex]
Options A and D are correct.
Kates, Ratios, and proportions
A company is hosting a fundraising dinner and selling tickets to attend. The table below shows the total amount raised in relation to
the number of tickets sold.
Tickets Sold 2
Total Raised $36.00
3
$54.00
4
$72.00
5
$90.00
6
$108.00
What is the rate of change for the information in the table?
$9.00 per ticket
A.
B.
$27.00 per ticket
C.
$36.00 per ticket
D
$18.00 per ticket
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O of 10 Answered
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Which are the roots of the quadratic function f(q) = q2 – 125
Answer:
q = ± 5[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given
q² - 125 = 0 ( add 125 to both sides )
q² = 125 ( take the square root of both sides )
q = ± [tex]\sqrt{125}[/tex]
= ± [tex]\sqrt{25(5)}[/tex]
= ± [tex]\sqrt{25}[/tex] × [tex]\sqrt{5}[/tex]
= ± 5[tex]\sqrt{5}[/tex]
Answer:
Roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]
Step-by-step explanation:
Given : Function [tex]f(q)=q^2-125[/tex]
To find : Which are the roots of the quadratic function ?
Solution :
To find the roots equate the function to zero.
[tex]q^2-125=0[/tex]
Add 125 both side,
[tex]q^2=125[/tex]
Taking root both side,
[tex]q=\pm \sqrt{125}[/tex]
[tex]q=\pm \sqrt{5\times 5\times 5}[/tex]
[tex]q=\pm 5\sqrt{5}[/tex]
Therefore, roots are [tex]q=5\sqrt{5},-5\sqrt{5}[/tex]
a coin is tossed 4 times which of the following represents the probability of the coin landing on heads all 4 times
Answer:
1/16
Step-by-step explanation:
1/2*1/2=1/4*1/2=1/8*1/2=1/16
Answer:1/16
Step-by-step explanation:
60 POINTS
Simplify square root of 5(10-4 square root of 2 attached to the 4)
Please explain how you got your answer. Answer choices:14, 15 with square root of 2 attached, 5 with square root of 2 attached - 4 with 10 being attached to -4, none of the above.
Answer:
[tex] 10\sqrt{5} - 4 \sqrt{10} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} (10 - 4 \sqrt{2} )[/tex]
Multiply
[tex] \sqrt{5} [/tex]
with each term within the bracket
[tex] = \sqrt{5} + \times 10 - \sqrt{5} \times 4 \sqrt{2} [/tex]
[tex] = 10 \sqrt{5} - 4 \sqrt{10} [/tex]
For the given image and scale factor, which ordered pair is one of the pre-image vertices if the center of the pre-image is also the origin?
Answer:
Step-by-step explanation:its the first one 3 5ths ,1
i just took the assignment
Answer:
the answer A
Step-by-step explanation:
What is the ratio for the surface areas of the cones shown below, given that
they are similar and that the ratio of their radii and altitudes is 2:1?
SUBMIT
Answer:
The ratio for the surface areas is equal to 4
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z -----> the scale factor
In this problem
The scale factor is equal to
[tex]z=\frac{2}{1}[/tex] ----> the ratio of its corresponding radii or its corresponding altitudes
step 2
Find the ratio for the surface areas of the cones
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z -----> the scale factor
x ----> the surface area of the larger cone
y ----> the surface area of the smaller cone
[tex]z^{2} =\frac{x}{y}[/tex]
we have
[tex]z=\frac{2}{1}[/tex]
substitute
[tex](\frac{2}{1})^{2}=\frac{x}{y}[/tex]
[tex]4=\frac{x}{y}[/tex]
The ratio for the surface areas is equal to 4
That means-----> The surface area of the larger cone is 4 times the surface area of the smaller cone
coseca/4+cota/2=cota/8-coseca/2
It's not clear if this is a problem to solve or a problem to prove. Let's see where it goes.
We note the cotangent half angle formula is
[tex]\cot x = \dfrac{ 1 + \cos 2x}{\sin 2x}[/tex]
The tangent and cotangent half angle is expressible in terms of the full angle without any ambiguity, so let's set b=a/4 so a=4b.
It turns out to be true for all a (at least all a that don't make the any of the functions undefined). So it's a problem to prove.
Here's the proof. I actually did it from the bottom up, but it's better to present it this way as a proof.
We start with the cosine double angle formula:
[tex]\cos 2b = 2\cos^2 b- 1[/tex]
Multipy both sides by sin b:
[tex]\sin b \cos 2b = 2 \sin b \cos^2 b - \sin b[/tex]
Sine double angle formula:
[tex]\sin b \cos 2b = \sin 2b \cos b- \sin b[/tex]
Add sin 2b to both sides:
[tex] \sin 2b+ \sin b\cos 2b = \sin 2b + \sin 2b \cos b - \sin b[/tex]
Divide by sin b sin 2b
[tex] \dfrac{1}{\sin b} + \dfrac{\cos 2b}{\sin 2b} = \dfrac{1 + \cos b}{\sin b} - \dfrac{1}{\sin 2b}[/tex]
Turn to cosecants and cotangents. We use the cotangent half angle formula above.
[tex] \csc b + \cot 2b = \cot \frac b 2 - \csc 2b[/tex]
Substituting b=a/4:
[tex] \csc \frac a 4 + \cot \frac a 2 = \cot \frac a 8 - \csc \frac a 2 \quad\checkmark[/tex]