Answer:
[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex] = 1Step-by-step explanation:
Given[tex]\sqrt[3]{8+3\sqrt{21} } + \sqrt[3]{8-3\sqrt{21} }[/tex]To find The value of the expressionSolutionLet's rewrite the given as:
[tex]\sqrt[3]{3\sqrt{21} + 8} - \sqrt[3]{3\sqrt{21} - 8}[/tex]Let the value is m and the expressions under 3rd roots are a and b, then we have
a = 3√21 + 8, b = 3√21 - 8m = ∛a - ∛bCube the both sides:
m³ = (∛a - ∛b)³m³ = a - b - 3[tex]\sqrt[3]{a^2b}[/tex] + 3[tex]\sqrt[3]{ab^2}[/tex]Simplify in bits:
a - b = 3√21 + 8 - 3√21 + 8 = 16ab = (3√21 + 8)(3√21 - 8) = 9*21 - 64 = 125∛ab = ∛125 = 5So the expression becomes:
m³ = 16 - 3[tex]\sqrt[3]{125a} + \sqrt[3]{125b}[/tex]m³ = 16 - 15∛a + 15∛bm³ = 16 - 15(∛a - ∛b)m³ = 16 - 15mSolve for m:
m³ + 15m - 16 = 0m³ - 1 + 15m - 15 = 0(m - 1)(m² + m + 1) + 15(m - 1) = 0(m - 1)(m² + m + 16) = 0m - 1 = 0, m² + m + 16 = 0m = 1 is the only real root, the quadratic equation has no real rootsThe answer is 1
A train is traveling at 30 miles per hour.
How long will it take the train to travel 180 miles?
FREE BRAINLIEST!!!
Answer:
Six hours
Step-by-step explanation:
Answer:
6 Hours
Step-by-step explanation:
If the train travels at 30mph for 6 hours it will have traveled 180 miles.
30 • 6 = 180
I hope this helps
Solve 5(11x - 2) = 155
Answer:
5(11x-2) = 155
55x - 10 = 155
55x = 165
x = 165/55
x = 3
Step-by-step explanation:
hope it helps
What is the solution of the system of equations? y=2x+2 y=4x-2
13x = 3(X-20) How to solve this algebra equation?
Answer:
x = -6
Step-by-step explanation:
13x = 3(x - 20) {Use distributive method:a(b+c)=(a*b) + (a*c)
13x = 3*x - 3*20
13x = 3x - 60 {Subtract '3x' from both sides}
13x -3x = -60
10x = -60 {Divide both sides by 10}
x= -60/10
x = -6
Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate
what is the answerk of this 3
3х2
4ys
Answer:
33×2=66
4ys
Step-by-step explanation:
or is it 33×24ys=66ys
how to solve b 2 + 5b -35 = 3b
Its 2.4... trust me!! Line out all your numbers. Add them up to get 65. There are 10 numbers so 65 divided by 10 is 6.5. Not done yet!! Then compare 6.5 to 10, (how far away is 6.5 to each number. Then add those numbers. then you get 24, now divide 24 by 10 to get 2.5. This is the answer for (08.02)Using the following data, calculate the mean absolute deviation:
10 7 1 6 7 9 8 10 2 5
Answer: 3.1 ? Possibly
Step-by-step explanation: Hmm have a brilliant day mate.-Lily ^_^
c) What are zeros of f(x) = 3x2 - 12x - 36
Answer:
Zeros Calculator. The zeros of a polynomial equation are the solutions of the function f(x) = 0. A value of x that makes the equation equal to 0 is termed as zeros. It can also be said as the roots of the polynomial equation. Find the zeros of an equation using this calculator.
Step-by-step explanation:
Please mark me the brainiest if I got it right
Find the y intercept of the following line (-2,1) and (1, 2.5)
Answer:
2
Step-by-step explanation:
(-2 , 1) ; (1, 2.5)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]\frac{2.5-1}{1-[-2]}\\\\= \frac{1.5}{1+2}\\\\=\frac{1.5}{3}\\\\= 0.5[/tex]
m =0.5
y -y1 =m(x -x1)
y - 1 = 0.5(x - [-2])
y - 1 = 0.5(x + 2)
y -1 = 0.5x + 0.5*2
y - 1 =0.5x + 1
y = 0.5x + 1 + 1
y = 0.5x + 2
y-intercept = 2
30% of 50
what’s the easiest and fastest way to solve it?
Answer:
15
Step-by-step explanation:
change the percent to a decimal
30% to .30
.30 x 50= 15
solve for x please thanks
Answer:
x=[tex]\frac{10}{14}[/tex]
Step-by-step explanation:
y=7x-2
2(7x-2)-4x=10
14x-4-4x=10
14x-4x=10-4
10x=14
x=[tex]\frac{10}{14}[/tex]
what is 100÷21?
56×32=
76+77
Answer:
100 ÷21 = 4.76 or 5
56 × 32 =1732
76+77= 153
Step-by-step explanation:
Hope it help
Mark me as brainliest
He is ordering the pizzas from a place that has 12 different topping options.
7 options are vegetarian and 5 are meats.
Write the ratio of vegetarian options to the total of options in three different ways.
Answer:
124
Step-by-step explanation:
1234
How do you find the experimental probability?
-8/12 DIVIDED BY 3/9
Answer:
-1/3
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
-24x^3y^2+16xy^3+12y^3
Answer:
4y^2 x (6x^3 - 4xy - 3y)
Step-by-step explanation:
Factor out -4y^2 from the expression
The grade of a road is the ratio of its rise to its run and is usually given as a decimal or percent. Find the angle that this road makes with the horizontal ground if its grade is 14% (14/100 or 0.14)
Answer:
the angle would be 1/2 i did this problem before and got it correct
Step-by-step explanation:
Match the following expression 12(x-3)+18=4(2x-3) with the number of solutions below.
A.One solution?
B.No solution ?
Or
C.All solution?
Answer:
3/2, one solution.
Step-by-step explanation:
12(x-3)+18=4(2x-3)
12x-36+18=8x-12
12x-8x-18=-12
4x-18=-12
4x=-12+18
4x=6
x=6/4
simplify
x=3/2
3x+y=-9
Y=5x+7
Solve the system of linear equations by substitution
Answer:
x=-2
Step-by-step explanation:
Substitute y=5x+7 into the equation 3x+y=-9
So you will have, 3x+5x+7=-9
3x+5x=8x
8x+7=-9
8x+7-7=-9-7
8x=-16
x=-2
To solve the inequality 4x < 8, you would divide both sides of the inequality by 4.
True
False
Answer:
True
Step-by-step explanation:
4x<8
divide
x<2
Find the area of the regular shape in squared units
Consider the sequence shown.
436, 218, 109, 54.5, 27.25,...
Select the correct explicit formula for the sequence.
a
g_n=436·0.5^{(n-1)}
b
g_n=0.5·436^{(n-1)}
c
g_n=436·2^{(n-1)}
d
g_n=2·436^{(n-1)}
Answer:
[tex](a) \to \: g_n=436·0.5^{(n-1)}[/tex]
i think the answer is
A.gn =436 . 0.5 (n-1)
Suppose y varies directly as x, and y =16 when x=8. Find y when x=5
Answer:
y is 10 when x is 5
Step-by-step explanation:
x is always half of y, based on this we need to multiply x by 2 y is 10
Answer:
the answer is
{153}⅚⅞²±(2)9
Simplify the expression by combining like
terms:
3x + 18 + 4x + 2
Answer:
7x+20
Step-by-step explanation:
3x + 18 + 4x + 2
Combine like terms
3x+ 4x + 18+2
7x + 20
Please help due in 10 minutes!!!!!!!
Answer:
23.42 ft is the perimeter of the hole that should be cut in the wall.
Find the value of x.
Answer:
x is 24
Step-by-step explanation:
5x+60=180
5x=120
x=24
Evaluate the expression 6 + 4 x {3+7}.
Answer:
46
Step-by-step explanation:
6 + 4 x {3+7} [B.O.D.M.A.S rule] (First bracket)
= 6 + 4 × 10. (Then Multiplication)
= 6 + 40. ( At last addition)
= 46 (Ans)
The simplified value of the expression 6 + 4 × {3 + 7} is 100.
What is PEMDAS rule?PEMDAS rule states the correct order of simplifying an expression is as follows -: Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.
Given, An expression 6 + 4 × {3 + 7}.
First, we'll add 6 and 4 as 3 and 7 are inside curly brackets,
not in parentheses.
Therefore,
6 + 4 × {3 + 7}.
= 10 × {3 + 7}.
Now, we can either distribute the terms or take the addition and multiply.
= 10 × 10.
= 100.
learn more about PEMDAS rule here :
https://brainly.com/question/36185
#SPJ2
Albert O'Malley signs a promissory note for $3,500 for 150 days at 9% exact interest. Find the interest he must pay _____ and the total amount due on the due date _____.
Answer:
He must pay $129.45 and the total amount due is $3,629.45.
Step-by-step explanation:
I (interest) =P (principal) x R (rate) x T (time)
I=3500x.09x150/365
I=129.45
A (amount due) = P (principal) + I (interest)
A= 3500 + 129.45
A= $3629.45
Sharon tried to solve an equation step by step.
all Sumi
9 = -3(e - 2)
mbining
9-3e + 6
Step 1
he distrib
15 - 3e
Step 2
5=e
nterpretin
Step 3
Find Sharon's mistake.
O 1.5
Choose 1 answer