factorise 15x- 10x^3
Answer:
5x (3-2x^2)
Step-by-step explanation:
so all you have to do is 15x-10x=5x right?, then all you have to do is 15/5=3. 10x/5x=2x. then subtract 1 from the exponents. then you get the answer. okay Im sure about the fist part and the divison but not the exponents, I did use a calculator to check it though.
The factorize equation is, [tex]\rm 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0[/tex].
The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
Given that,
Equation; [tex]\rm 15x - 10x^3[/tex]
We have to determine,
Factorize the equation and factor of the equation.
According to the question,
To factorize the equation and determine the factor of the equation following all the steps given below.
Equation; [tex]\rm 15x - 10x^3[/tex]
Step1; Taking the term 5x common from the equation,[tex]\rm = 15x - 10x^3 = 0 \\\\= 5x (3-2x^2) = 0[/tex]
Step2; Simplify the equation,[tex]\rm = 5x (3-2x^2) = 0\\\\ = 5x (\sqrt{3} - \sqrt{2x}) (\sqrt{3}+\sqrt{2x}) = 0[/tex]
Step3; The roots of the equation are,[tex]\rm = 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0\\\\ The \ roots \ of \ the \ equation \ are;\\\\5x = 0, \ x = \dfrac{0}{5}, \ x =0\\\\\\[/tex]
[tex]\sqrt{3} - \sqrt{2x} = 0, \sqrt{2}x = \sqrt{3}, \ x = \dfrac{\sqrt{3} }{\sqrt{2} }\\\\ \sqrt{3} +\sqrt{2x} = 0, \sqrt{2}x = -\sqrt{3}, \ x =- \dfrac{\sqrt{3} }{\sqrt{2} }[/tex]
Hence, The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
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If you take out a loan that costs $561 60 over eight years at an interest rate of 9% how much was the loan for?
Answer:
The loan was $28184.81
Step-by-step explanation:
Let the loan amount be x
Rate of interest on Loan = 9%
Time = 8 years
Amount of loan over 8 years = $56160
Formula : [tex]A=P(1+r)^t[/tex]
Where A = Amount =56160
P = Principal = x
r = rate of interest = 9% = 0.09
t = time = 8 years
Substitute the values in the formula :
So,[tex]56160=x(1+0.09)^8[/tex]
[tex]\frac{56160}{(1+0.09)^8}=x[/tex]
$28184.81=x
Hence The loan was $28184.81
The price of a gallon of milk, in dollars, is measured in the
Answer:ones
Step-by-step explanation:
Can i get some help ♂️
Answer:
[tex]AC=13.5[/tex]
Step-by-step explanation:
Use the Law of Sines as follows:
[tex]\frac{sinA}{a} =\frac{sinB}{b}[/tex]
Insert the values (use the steps from the last problem):
[tex]\frac{sin25}{14} =\frac{sin24}{b}[/tex]
Isolate b. Multiply both sides by b:
[tex]b*(\frac{sin25}{14} )=b*(\frac{sin24}{b})\\\\b*\frac{sin25}{14}=sin24[/tex]
Multiply both sides by 14:
[tex]14*(b*\frac{sin25}{14})=14*(sin24)\\\\b*sin25=14*sin24[/tex]
Isolate b. Divide both sides by sin 25:
[tex]\frac{b*sin25}{sin25} =\frac{14*sin24}{ysin25} \\\\b=\frac{14*sin24}{sin25}[/tex]
Insert the equation into a calculator and round to the nearest tenth:
[tex]b=13.5[/tex]
The length of AC is 13.5 units.
:Done
Nathan is buying a camera that regularly
costs $400.00. It is on sale for 25% off. If
the tax rate is 10%, what is the final cost
of the GoPro?
Find z 1 z 2 if z 1 = 3(cos37° + isin37°) and z 2 = (cos53° + isin53°
Answer:
[tex]Z_{1} Z_{2} = 3 i[/tex]
Step-by-step explanation:
Step(i):-
Given z 1 = 3(cos 37° + i sin 37°)
z 2 = (cos 53° + i sin 53°)
by using complex numbers
[tex]Z_{1} = r_{1} ( cos\alpha_{1} + isin\alpha_{1} ) = r_{1} cis\alpha _{1}[/tex]
[tex]Z_{2} = r_{2} ( cos\alpha_{2} + isin\alpha_{2} ) = r_{2} cis\alpha _{2}[/tex]
step(ii):-
now
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°
z ₂ = (cos 53° + i sin 53°) = c i s 53°
we will use formula
[tex]Z_{1} Z_{2} = r_{1} r_{2} cis (\alpha _{1} + \alpha _{2})[/tex]
[tex]Z_{1} Z_{2} = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis(\frac{\pi }{2} )[/tex]
[tex]Z_{1} Z_{2} = 3(cos(\frac{\pi }{2} ) + isin(\frac{\pi }{2}))[/tex]
[tex]Z_{1} Z_{2} = 3(0 + i (1)) = 3 i[/tex]
Conclusion:-
[tex]Z_{1} Z_{2} = 3 i[/tex]
Answer:
2i
Step-by-step explanation:
z 2 = 2/3(cos53° + isin53°
I got it right on odyssey ware
Find the volume of the cone
Answer:
12π
Step-by-step explanation:
Volume of the cone is πr^2 * h / 3
r = 3
h = 4
9π * 4 / 3 = 12π
Answer: 37.6991118
Step-by-step explanation:
3~ Please help. What is m∠BED?
Enter your answer as a number, like this: 42
Answer:
34
Step-by-step explanation:
There is the same opposite arch for both angles so they should be equal.
Hope this is helpful!
Lily wants to buy a new smartphone. She has $500 to spend. List three ways she can get a good deal.
Answer:
get a coupon find a cheap on or steal it or get a discountAnswer:
She could use coupon deals, she could research what stores have it cheapest, see what deals online has
Another khan academy question
First off, notice that this is a right triangle.
You can use this to help write equation.
Equation : x+ (4x-85)=90. The correct answer is "c"
If you have a cube with a side length of ¼, how many cubes can fit into your rectangular prism? Explain.
Answer:
Step-by-step explanation:
No of cubes that can fit into rectangular prism = Volume of rectangular prism
Volume of cube
Find the volume of rectangular prism and divide that by the volume of cube
Solve 1/4 + 3/5 - 3/10
Answer:
it will be equal to 11/20
Answer:
11/20
Step-by-step explanation:
= (5+12-6)/20
= 11/20
Find the length of the base of the following pyramid, given the height of the pyramid is 221 meters and the angle of elevation of the base of the pyramid is 62°. Round to the nearest whole number.
An image of a square pyramid is shown with a right triangle embedded inside it. The face is at an incline of 62 degrees. The height is labeled 211, and the corner of the right angle is marked with a letter P.
75 meters
189 meters
235 meters
416 meters
Answer:I believe it would be answer choice, 235 meters
Step-by-step explanation:
I’m not super good at explain but, the height and incline both go at the right slope when they interact. Have a good day, hope it helps.
The length of the pyramid's base would be:
C). 235 meters
Find the length of the baseGiven that,
Height of the pyramid [tex]= 221[/tex]
Elevation/angle of the base [tex]= 62[/tex]°
Employing the trigonometric function,
Tan 62 [tex]= 221/[1/2 base][/tex]
⇒ Base [tex]= (2[/tex] × [tex]221)[/tex][tex]/Tan[/tex][tex]62[/tex]
[tex]= 2[/tex] × 221/[tex]1.88[/tex]
[tex]= 235.10[/tex]
Thus, option C is the correct answer.
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Solve the inequality for X.
-3x - 3 <-63
es
A)
x > 20
B)
x > 22
9.
x < 20
D)
x < 22
------------------------------------------------
-3x - 3 <-63
Add 3 to both sides:
-3x-3+3 < -63+ 3
Simplify:
-3x < -60
Multiply both sides by -1:
(reverse the inequality)
(-3x)(-1) > (-60)(-1)
Simplify:
3x > 60
Divide both sides by 3:
3x/3 > 60/3
Simplify:'
x > 20
Your Answer Is x > 20
plz mark me as brainliest if this helped :)
PLEASE ANSWER THIS ILL GIVE BRAINLIEST AND IM GVING MY LAST POINTS I REALLY NEED THIS FAST AND please be right! PLEASE
Answer:
question 7: 280 and question 8: 86
Step-by-step explanation:
Answer:
1) 70
2) 82
Step-by-step explanation:
Simplify:
a) 6c + 4d - c - 7d =
b) 3x + 5y - x + 2y =
c) 3g + 5h + 4g - 2h =
d) 8t + 3r - 7t - 9r =
Answer:
a) 5c-3d
b) 2x+7y
c) 7g+3h
d) 1t-6r
hope this helps ;)
Answer:
a) 6c + 4d - c - 7d = 5c -3d
b) 3x + 5y - x + 2y = 2x + 7y
c) 3g + 5h + 4g - 2h = 7g + 3h
d) 8t + 3r - 7t - 9r = t - 6r
Step-by-step explanation:
combine like terms:
a) 6c + 4d - c - 7d = 5c -3d
b) 3x + 5y - x + 2y = 2x + 7y
c) 3g + 5h + 4g - 2h = 7g + 3h
d) 8t + 3r - 7t - 9r = t - 6r
Four candidates participated in a school election Bianca received 1/5 of the votes, Chelsea received 0.26 of the votes, Darell received 25% of
the votes, and Francisco received the rest of the votes. What percent of the votes did Francisco receive?
A 29% B 31% C 33% D 35%
Answer:
A - 29%
Step-by-step explanation:
Bianca's 1/5 would be converted to 20%
Chelsea's .26 would be 26%
Darnell's is 25%
Adding these together you get 71. To find the remaining votes that Francisco received you would..
Subtract
100 - 71 = 29%
Therefor, your answer is A.
If Darell earned 25% of the vote and Francisco received the remaining votes, Chelsea would have garnered 0.26 percent of the vote. 29% of the votes were cast in favor of Francisco. Option A is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that there were four candidates running for office in the school election, Bianca won 1/5 of the vote, Chelsea got 0.26, Darell got 25%, and Francisco got the remaining votes.
Bianca's 1/5 would be converted to 20% and Chelsea's .26 would be 26%, Darnell's is 25%
Adding these together you get 71. To find the remaining votes that Francisco received you would be applying the subtraction operations,
100 - 71 = 29%
Thus, if Darell earned 25% of the vote and Francisco received the remaining votes, Chelsea would have garnered 0.26 percent of the vote. 29% of the votes were cast in favor of Francisco. Option A is correct.
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Which point is the centroid of the triangle?
Question 5 options:
A)
D
B)
G
C)
F
D)
C
Answer:
The answer is B) G
Step-by-step explanation:
G is at the center of the triangle. It is a centroid because it is where all the medians meet.
help rsm 2.1/x+1 4/5=3/10x
Answer:
two minus one times .........
The solution to the equation is x = 7, -1.
What is a quadratic equation?The equation of the form ax² + bx +c is known as a quadratic equation.
The given equation is 2.1/x + 1 (4/5) =(3/10)x.
Simplify the equation as follows:
2.1/x + 1 (4/5) =(3/10)x
2.1/x + 9/5 = (3/10)x
2.1 + (9/5)x = (3/10)x²
21 + 18x = 3x²
3x² - 18x -21 =0
3x² - 21x + 3x -21 =0
3x(x - 7) + 3(x - 7) =0
(x - 7)(3x + 3) =0
x - 7 =0 or 3x + 3 =0
x = 7 or x = -1
Hence, the solution to the equation is x = 7, -1.
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The partially filled contingency table gives the frequencies of the data on age (in years) and sex from the residents of a
retirement home.
60-69. 70-79. Over 79. Total
Male: 12. 5. 1
Female: 8. 10. 4
Total
What is the relative frequency for females in the age group 60-69?
a. 3/20
b. 1/5
c. 9/40
d. 2/5
Answer:
b) 8/40 = 1/5
The probability of the relative frequency for females in the age group 60-69 is 0.625.
We know that the probability of a function is the ratio of favorable cases to the total number of cases possible.
here we have to find the probability that a resident is female.
What is the formula for probability?[tex]Probability=\frac{Total \ numbers \ of \females}{Total \ number \of people}[/tex]
here the total number of females are=19+2+4
=25
and the total number of males=1+9+5
=15
Hence, the total number of people=25+15=40
So Probability=25/40
=0.625
Hence option D is correct.
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Jack ran 13.5 miles in 1.5 hours. What was his speed in miles per minute?
Answer:
9
Step-by-step explanation:
13.5 / 1.5 = 9
Answer:
[tex] \boxed{Speed = 0.15 \: miles \: per \: minute} [/tex]
Given:
Distance travelled = 13.5 miles
Time taken = 1.5 hours = 1.5 × 60 = 90 minutes
Step-by-step explanation:
[tex]Speed = \frac{Distance \: travelled}{Time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13.5}{90} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.15 \: miles \: per \: minute[/tex]
The volume of the shipping box needs to be 1,144 cubic inches. The equation that models the volume of the shipping box is 8(n + 2)(n + 4) = 1,144.
Answer the following questions about the equation modeling the volume of the shipping box.
Question 1
Solve the equation that models the volume of the shipping box, 8(n + 2)(n + 4) = 1,144. If you get two solutions, are they both reasonable?
Answer:
see below
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
FOIL
8(n^2 +2n+4n+8) = 1144
Divide each side by 8
8/8(n^2 +2n+4n+8) = 1144/8
(n^2 +2n+4n+8) = 143
Combine like terms
n^2 +6n+8 = 143
Subtract 143 from each side
n^2 +6n+8 -143= 0
Combine like terms
n^2 +6n -135 =0
Factor
What two terms multiply to -135 and add to 6
-9*15 =-135
-9+15 = 6
(n-9) (n+15) =0
Using the zero product property
n-9 =0 n+15=0
n = 9 n=-15
The length cannot be negative so n = -15 cannot be a solution
n =9
Answer:
n = 9
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n² + 2n + 4n + 8 = 143
n² + 6n - 135 = 0
n² + 15n - 9n - 135 = 0
n(n + 15) - 9(n + 15) = 0
(n - 9)(n + 15) = 0
n = 9, -15
since n is a length, it can not be negative
Therefore the only solution is n = 9
The price of a car is £15400 before it is reduced by 8%.
How much does it cost after the reduction?
Answer:
14168
Step-by-step explanation:
15400 / 100 x 8 = 1232
1232 = 8%
15400 - 1232 = 14168
PLEASE HELP FAST
Which transformation preserves size and shape. Choose ALL correct answers
A) Dilations
B) Rotations
C) Translations
D) Reflections
Question 2
Which transformations preserve orientation?
A) Translations
B) Rotations
C) Reflections
D) Dilations
Answer:
A) Dilation C)Reflections or B) Rotations
Step-by-step explanation:
Which type of sampling method is being employed in the following example: "A newspaper reporter wants to know what the people of Georgia think about the latest trades the Braves baseball team have made for an article but is running late. So, the reporter decides to just ask people at the news office what they think to provide a sample of the public's opinion in the article."
Simple Random Sampling
Sampling of Convenience
Stratified Sampling
Systematic Sampling
Cluster Sampling
Answer:
Sampling of convenience
Step-by-step explanation:
A sampling of convenience is being employed by the newspaper reporter that wants to know what the people of Georgia think about the latest trades.
What is a sampling of convenience?This refers to the non-probability sampling method that relies on data collection from population members who are conveniently available to participate in study.
Hence, the sampling of convenience is being employed by the newspaper reporter that wants to know what the people of Georgia think about the latest trades.
Therefore, the Option B is correct.
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can you plz help me i really appreciate it
In a right triangle, sin (40 – x)° = cos (3x).What is the value of x?
Answer:
Value of x = 25
Step-by-Step Explanation:
~ Knowing that, in a right triangle ~
sin(40-x)=cos(3x) ⇒
sin(40-x)=sin(90-3x) ⇒
40 - x = 90 - 3x ⇒
40 - x +3x=90 - 3x +3x =>
40+2x=90 =>
2x=50 =>
x = 25
Now it is proven to be that,
x = 25
Of all 25 marbles in a bag, 3 of the marbles are white. What is the probability that a white marble will be randomly selected from the bag without looking? Write your answer as a percent.
Step-by-step explanation:
Total marbles = 25
Probability of white marble = 3/ 25 = 0.12
You are wakeboarding on a river. You travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock. The boat travels x miles per hour during the entire trip, and the river current is 3 miles per hour.
How long will the trip take when then speed of the boat is 18 miles per hour? Round to the nearest tenth minute.
Answer:
17.3
Step-by-step explanation:
(2+18)=(20mph*2miles)=6 minute
(18-2)=16mph*3miles=11.25
17.25
There are 30 marbles in a bag. You randomly choose 20 marbles from the bag. The results are shown in the table. Predict the total number of red marbles.
Color
Blue 6
Red 12
Yellow 2
There are about how many red marbles?
Answer:
12 because if you add 6 and 12
Step-by-step explanation:
hope it helps uou !!
Answer:
It's 12
Step-by-step explanation:
hope it helps you !!