Answers
Answer:
D,0,2,-2
Step-by-step explanation:
2x^5-3x^3-20x=0
x(2x^4-3x^2-20)=0
x=0
or 2x^4-3x^2-20=0
put x²=t
2t²-3t-20=0
-20×2=-40
8-5=3
8×-5=-40
2t²-(8-5)t-20=0
2t²-8t+5t-20=0
2t(t-4)+5(t-4)=0
(t-4)(2t+5)=0
t=4
x²=4
x=2,-2
t=-5/2
x²=-5/2
it gives imaginary root. so real rational roots are 0,2,-2
Answer:
D
Step-by-step explanation:
1) Factorise x
x(2x^4-3x^2-20) = 0
a product is equal to 0 when at least one factor is equal to 0.
so a solution is
x = 0
we have now to solve
2x^4 - 3x^2 - 20 = 0
we can put
x^2 = y
and we have
2y^2 - 3y - 20 = 0
it is now an equation of second degree
Δ = 9 + 160 = 169
y1 = (3 + 13)/4 = 4
y2 = (3 - 13)/4 = -10/4 = -5/2
for the previous relationship we have
x^2 = 4
x = 2
x = -2
x^2 = -5/2
a square number can’t be negative, so this equation is impossible.
In conclusion we can say that the original equation has three solution:
0, -2, 2
Related Questions
The national park has a new kiosk which visitors pass through as they enter the park. The kiosk is in the shape of a cylinder with a diameter of 5 meters and a height of 3 meters and a conical roof that measures 2 meters in height. What is the volume of the kiosk? Round your answer to the nearest cubic meter.
Answers
Given:
Kiosk is the combination of a cylinder and a cone.
Diameter of cylinder and cone = 5 m
Height of the cylinder = 3 m
Height of the cone = 2 m
To find:
The volume of the kiosk.
Solution:
We know that the radius is half of the diameter. So,
Radius of cylinder and cone = [tex]\dfrac{5}{2}[/tex] m
= [tex]2.5[/tex] m
Volume of the cylinder is:
[tex]V_1=\pi r^2h[/tex]
Where, r is the radius and h is the height of the cylinder.
Putting [tex]\pi =3.14, r=2.5, h=3[/tex] in the above formula, we get
[tex]V_1=(3.14)(2.5)^2(3)[/tex]
[tex]V_1=(3.14)(6.25)(3)[/tex]
[tex]V_1=58.875[/tex]
Volume of a cone is:
[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]
Where, r is the radius and h is the height of the cone.
Putting [tex]\pi =3.14, r=2.5, h=2[/tex] in the above formula, we get
[tex]V_2=\dfrac{1}{3}(3.14)(2.5)^2(2)[/tex]
[tex]V_2=\dfrac{1}{3}(3.14)(6.25)(2)[/tex]
[tex]V_2\approx 13.083[/tex]
The volume of the kiosk is the sum of volume of cylinder and the volume of cone.
[tex]V=V_1+V_2[/tex]
[tex]V=58.875+13.083[/tex]
[tex]V=71.958[/tex]
[tex]V\approx 72[/tex]
Therefore, the volume of the kiosk is 72 cubic meter.
What is the equation for a parabola if the vertex is at (5,4) and goes through the point (3,-8)
Answers
Answer:
[tex]y=-3(x-5)^2+4[/tex]
Step-by-step explanation:
Hi there!
Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:
[tex]y=a(x-h)^2+k[/tex] where the vertex is located at [tex](h,k)[/tex] and a is a numerical value
1) Plug the vertex into the equation
[tex]y=a(x-h)^2+k[/tex]
Plug in the vertex (5,4)
[tex]y=a(x-5)^2+4[/tex]
2) Solve for a
[tex]y=a(x-5)^2+4[/tex]
Plug in the given point (3,-8) and solve for a
[tex]-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4[/tex]
Subtract 4 from both sides
[tex]-8-4=4a+4-4\\-12=4a[/tex]
Divide both sides by 4
[tex]\frac{-12}{4} = \frac{4a}{4} \\-3=a[/tex]
Therefore, a=-3. Plug this back into [tex]y=a(x-5)^2+4[/tex]:
[tex]y=-3(x-5)^2+4[/tex]
I hope this helps!
A study of a population of 1,200 frogs revealed that 12 out of every 180 frogs in the population have spots on their back. Based on the results of this study, how many frogs in the population do NOT have spots on their back? *
Answers
What is the slope-intercept equation of the line below? A.y=2x+3 B.y=-2x-3 C.y=2x-3 D.y=-2x+3
Answers
Answer:
C.
Step-by-step explanation:
First, lets find the y-intercept. The y-intercept where the line passes through the y-axis. In this case, it is -3.
Now, to find the slope, lets find the next non-decimal point(that way it is easier on us). That would be (1,-1). Now, to get to this point from the y-intercept, we have to go left 1 unit, and up 2 units. So, the change in y over change in x = 2/1 or 2. Now, using this information, we can form the equation:
y = 2x + -3. or y = 2x - 3.
Solve 2x-5/x-2 ≤ 1
please answer fast
Answers
Answer:
x<=-3
Step-by-step explanation:
2x-5/x-2 <= 1
Multiply both sides by x-2
2x-5<=x-2 (anything times 1 is that number.)
add 5 to both sides
2x<=x-3
subtract x from both sides
x<=-3
Answer:
Step-by-step explanation:
[tex]\frac{2x-5}{x-2} \leq 1\\case ~1. both ~numerator~and~denominator \geq 0\\x\neq 2\\2x-5\leq x-2\\x\leq 3\\so~0\leq x<2U2<x\leq 3\\case~2.\\both~numerator~and~denominator<0\\2x-5\geq x-2\\x>3\\which~is~rejected~as~it~gives~both~2x-5~and ~x-2>0[/tex]
Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement. (a) Suppose I draw n times. Let X., be the number of times I saw a green ball followed by a yellow ball. Calculate the expectation Ex, (b) Let y be the number of times I drew a green ball before the first white draw. Calculate E[Y]. Can you give an intuitive explanation for your answer
Answers
Answer:
[tex]E(X_n)=\frac{2(n-1)}{27}[/tex]
[tex]E(y)=\frac{14}{9}[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size n=9
Number of Green [tex]g=4[/tex]
Number of yellow [tex]y=4[/tex]
Number of white [tex]w=4[/tex]
Probability of Green Followed by yellow P(GY) ball
[tex]P(GY)=\frac{4}{9}*\frac{3}{9}[/tex]
[tex]P(GY)=\frac{4}{27}[/tex]
Generally the equations for when n is even is mathematically given by
[tex]Probability of success P(S)=\frac{4}{27}[/tex]
[tex]Probability of Failure P(F)=\frac{27-4}{27}[/tex]
[tex]Probability of Failure P(F)=\frac{23}{27}[/tex]
Therefore
[tex]E(X_n)=\frac{n}{2}*P[/tex]
[tex]E(X_n)=\frac{n}{2}*\frac{4}{27}[/tex]
[tex]E(X_n)=\frac{2n}{27}[/tex]
Generally the equations for when n is odd is mathematically given by
[tex]\frac{n-1}{2}[/tex]
[tex]E(X_n)=\frac{n-1}{2}*\frac{4}{27}[/tex]
[tex]E(X_n)=\frac{2(n-1)}{27}[/tex]
b)
Probability of drawing white ball
[tex]P(w)=\frac{2}{9}[/tex]
Therefore
[tex]E(w)=\frac{1}{p}[/tex]
[tex]E(w)=\frac{1}{\frac{2}{9}}[/tex]
[tex]E(w)=\frac{9}{2}[/tex]
Therefore
[tex]E(y)=[E(w)-1]\frac{4}{9}[/tex]
[tex]E(y)=[\frac{9}{2}-1]\frac{4}{9}[/tex]
[tex]E(y)=\frac{14}{9}[/tex]
4) Which shampoo bottle size has the lowest price per ounce?*
Answers
Find the sum of the first 7 terms of the following series, to the nearest integer.
125,50, 20, ...
Answers
Answer:
[tex]r = 2.5 \\ sum = \frac{a( {r}^{n - 1} )}{r - 1} \\ = \frac{125( {2.5}^{7 - 1} )}{7 - 1} \\ = \frac{30517.6}{6} \\ = 5086.3[/tex]
2^5×8^4/16=2^5×(2^a)4/2^4=2^5×2^b/2^4=2^c
A=
B=
C=
Please I'm gonna fail math
Answers
9514 1404 393
Answer:
a = 3, b = 12, c = 13
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)/(a^c) = a^(b-c)
(a^b)^c = a^(bc)
___
You seem to have ...
[tex]\dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)[/tex]
_____
Additional comment
I find it easy to remember the rules of exponents by remembering that an exponent signifies repeated multiplication. It tells you how many times the base is a factor in the product.
[tex]2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}[/tex]
Multiplication increases the number of times the base is a factor.
[tex](2\cdot2\cdot2)\times(2\cdot2)=(2\cdot2\cdot2\cdot2\cdot2)\\\\2^3\times2^2=2^{3+2}=2^5[/tex]
Similarly, division cancels factors from numerator and denominator, so decreases the number of times the base is a factor.
[tex]\dfrac{(2\cdot2\cdot2)}{(2\cdot2)}=2\\\\\dfrac{2^3}{2^2}=2^{3-2}=2^1[/tex]
Help a bab out please?
Answers
Answer:
the answer is 55
Step-by-step explanation:
if you have a straight line each side equals 180 degrees so take 60+65 which equals 125 then do 180-125 and you get 55
a rectangular solid box measures 2.75 feet by 4.05 feet by 480 inches. in cubic yards, what is the volume of the box? express your answer as a decimal to the nearest tenth
Answers
Answer:
445.5 feet
Step-by-step explanation:
Our first step is to get them to like terms. The only different term is inches. 480 inches = 40 feet.
We find volume by multiplying length x width x height. So 2.75 x 4.05 x 40 = 445.5 feet.
Complete the square of the quadratic equation x^2 - 2x - 35 = 0. What is the vertex of the equation?
( )( )
Answers
Answer:
Step-by-step explanation:
x^2 - 2x - 35 = 0
Solve for x over the real numbers:
x^2 - 2 x - 35 = 0
Add 35 to both sides:
x^2 - 2 x = 35
Add 1 to both sides:
x^2 - 2 x + 1 = 36
Write the left hand side as a square:
(x - 1)^2 = 36
Take the square root of both sides:
x - 1 = 6 or x - 1 = -6
Add 1 to both sides:
x = 7 or x - 1 = -6
Add 1 to both sides:
Answer: x = 7 or x = -5 as for the vertex plane curve | Cartesian equation x^2 - 2 x - 35 = 0 | vertex (not a possible affine variety)
4. Which list are the numbers in order from least to greatest
Answers
Answer:
a
Step-by-step explanation:
my brother told me....
In 2019, Tessa earned $32000. (a) She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018. [2] (b) In 2020, Tessa's earnings increased by 7%. Work out her earnings in 2020.
Answers
Answer:
$7,680
$34,240
Step-by-step explanation:
Amount Tessa earns in 2019 = $32000
a. She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018.
Percent of tax = 24%
Amount of tax paid = 24% of $32,000
= 24/100 * 32,000
= 0.24 * 32,000
= $7,680
Amount of tax paid = $7,680
b. Tessa's earnings increased by 7%. Work out her earnings in 2020.
Percentage increase in earnings = 7%
Amount of increase in earnings = 7% of $32,000
= 7/100 * 32,000
= 0.07 * 32,000
= $2,240
Amount of increase in earnings = $2,240
Total earnings in 2020 = Amount Tessa earns in 2019 + Amount of increase in earnings
= $32,000 + $2,240
= $34,240
Total earnings in 2020 = $34,240
- 3/8 + 1/6
i kinda just didn't pay attention in class, i just need an explaination of how to solve it and im good to go
Answers
Answer:
[tex]{ \tt{ - \frac{3}{8} + \frac{1}{6} }} \\ { \bf{l.c.m \: of \: 8 \: and \: 6 = 24}} \\ { \tt{formular = \frac{(l.c.m \times denominator \div numerator)}{l.c.m} }} \ \\ \\ = \frac{(24 \times 8 \div - 3) + (24 \times6 \div 1)}{24} \\ = - \frac{5}{24} [/tex]
PLEASE HELP ME QUICKLY!!!!!
Find the equation of the line of best fit in slope-intercept form.
Answers
If sin θ = square root of three over two, which could not be the value of θ?
Answers
Choose all the equations that are true if y = 6. 52.37 – 46.37 = y 45y =445 8y = 48 3.2 + y = 9 y ÷ 4 = 24
Answers
Answer:
52.37 – 46.37 = y
8y = 48
Step-by-step explanation:
Choose all the equations that are true if y = 6. 52.37 – 46.37 = y 45y =445 8y = 48 3.2 + y = 9 y ÷ 4 = 24
We solve for y in all the equations :
52.37 – 46.37 = y
52.37 – 46.37 = 6 (True)
45y =445
Divide both sides by 45
45y/45 = 445/45
y = 9.888 (False)
8y = 48
y = 48/8
y = 6 (True)
3.2 + y = 9
y = 9 - 3.2
y = 5.8 (false)
y ÷ 4 = 24
y/4 = 24
y = 24 * 4 = 96 ( false)
Need help ASAP PLEASE ITS DUE IN A HOUR HURRY ?!!!
Answers
Answer:
d = 8
Step-by-step explanation:
V=(π)(r)^2(h/3)
83.7=(π)(r)^2(5/3)
Solve for r
r = 3.9
d = (3.99)(2)
d = 7.98
d = 8
When the sun shines at a 60° angle to the ground, Talisa's shadow is 36 inches long.
Answers
Answer:
Talisa is 62 inches tall
Step-by-step explanation:
tan = opp/adj
tan60 = opp/36
36 * tan 60 = opp
use calculator
opp = 62.353829072479583
Rounded
Talisa is 62 inches tall
Answer:
Using the right triangle created by this situation, and the fact that the trig ratio tan(θ) = opposite/adjacent, we can say tan(60°) = h/36 or h = 36•tan(60°) = 62.354So, to the nearest inch, Talisas is 62 inches long.if you satisfied to my answer ,can you put brainliest in top of my name , and ur welcomeSelect all the equations
represented by this tape diagram.
A. 6 + 6 + 6 + 6 + 6 = ?
B. 5 + 6 = ?
C. ? = 6.5
D. ? = 6.6.6.6.6
E. ? = 5 = 6
F.5 = ?= 6
Answers
Answer:
D.
is the correct answer
Select the correct graph of the equation.
Answers
Answer:
A
Step-by-step explanation:
The -2 indicates that y would be -2; because A is the only option with that being true, we can eliminate all other potential options rather quickly.
I believe this is 3/5x-2 but please take pictures with all information in view so we can provide better answers!
A is the point (-2, 0) and B is the point (0, 4).Find the equation of the straight line joining A and B.
Answers
Answer:
y = 2*x + 4
Step-by-step explanation:
We know that a linear function can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
So, here we know that our line must pass through the points (-2,0) and (0, 4)
Then the slope of this line is:
a = (4 - 0)/(0 - (-2))
a = 4/2 = 2
Then our line is something like:
y = 2*x + b
Now, to find the value of b we can use one of these two points, for example if we use the point (-2, 0), we know that, when x = -2, we must have y = 0.
0 = 2*(-2) + b
0 = -4 + b
4 = b
Then the equation for our line is:
y = 2*x + 4
The 12 pair pack of socks includes 4 pairs of Polo, 5 pairs of plain white socks, and a few grey pairs. What is the Possibility of pulling a pair of grey sock two times in a row? The first pair is not to be returned.
Answers
Answer:
2/11
Step-by-step explanation:
12-4-5=3
So now we know that we have:
4 pairs of polo socks
5 pairs of plain white socks
3 pairs of grey socks
To pull a grey sock one time is 3/12 since there are 12 total socks and 3 pairs of grey socks but since we remove a sock, in the second time, the probability would be 2/11.
Hope this helps! Brainliest?
Help me please help me please help me please !!!!!!!!!!!!!
Answers
Answer: y = 1/4x - 1.
Step-by-step explanation: This line has a slope (rise over run) of 1/4, and a y-intercept of -1. Plugging those values into slope-intercept form (y = mx + b) gives you the answer.
Please use the following image for the next 7 questions. Keep in mind that because XY is tangent to circle M, XM and XM form a right angle.
XM = 11 and YM = 36.
What is the area of circle M?
What is the circumference of circle M?
Find the length of XY .
Find the measure of angle M.
Find the area of triangle XYM.
Find the area of the minor sector that has been created as part of triangle XYM.
Find the arc length of the minor arc from point X to the point where YM intersects with the circle.
Answers
It is 34.90
Step-by-step explanation:
Your welcome!
The point-slope form of the equation of a line that passes through points (8. 4) and (0, 2) is y-4 = (x-8). What
is the slope-intercept form of the equation for this line?
O y= 2 x - 12
O y=-x-4
o y=+*+2
O y=x+6
Answers
Answer:
answer y=x-4
Step-by-step explanation:
slope intercept from is y=mx+b
m=slope b=y intercept
convert current equation to slope intercept
y-4=x-8
add 4 to both sides
y=-x-4
What is the value of x?
85°
92°
53°
Answers
Answer:
x = 46
Step-by-step explanation:
Vertical angles are equal so call the angle y
85+53 +y =y+ 92+x
Subtract y from each side
85+53 = 92+x
Combine like terms
138 = 92+x
Subtract 92 from each side
138 -92 = 92+x-92
46 =x
Find the circumference of a circle with radius, r = 6.5m.
Give your answer in terms of pie
Answers
Answer:
13π m
Step-by-step explanation:
circumference of a circle = 2πr
=2*π*6.5
=13π m
Answer:
13[tex]\pi[/tex] m
Step-by-step explanation:
The formula for circumference is 2r[tex]\pi[/tex], so...
2r[tex]\pi[/tex]
2(6.5)[tex]\pi[/tex]
=13[tex]\pi[/tex]
For each steak, lobster, or chicken dinner in a restaurant, you have a choice of french fries or mashed potatoes. You get a choice of Water or Iced Tea to drink. If all combinations are equally likely to be ordered, find the sample space of the possible outcomes.
