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
Three friends want to share five oranges equally. How many oranges
should each friend receive?
Answer:
1.6
So one whole orange and a sixth of another orange
Step-by-step explanation:
Pythagorean theorem :)
Answer:
A^2 + B^2 = C^2
Step-by-step explanation:
Your welcome!
Answer:
x = 13
Step-by-step explanation:
In order to solve this you need to know the Pythagorean theorem:
a^2 + b^2 = c^2
a - 1 side
b - 2nd side
c - hypoteneuse
Step 1: Find the missing side of the triangles
** Note both triangles are equal to each other as shown by the dashed line in both that signifies both sides are equal to each other, and the 90-degree angle there as well**
Solve:
17^2 + b^2 = 19^2
289 + b^2 = 361
361 - 289 = 72
√72 = √b^2
8.5 = b (approximately, to the tenth)
Step 2: Because both of the triangles are equal to each other, the missing side is equal to 8.5, but there are two of them, in order to determine x, you need to add both values together:
8.5 + 8.5 = 17
Then you subtract it from the base value: 31
31 - 17 = 13
Therefore, x = 13, as that is the remaining of the base.
If marked price = * 1700, selling price = * 1540 then find the discount .
let me be a `x` then find selling price
The system of equations y= 2x+5 and y=x+ 2 is
graphed below. What is the solution to the system
of equations?
у
x
보인
3 4 5
-2
Plssss helppppp
Answer:
(-3, -1) first option
Step-by-step explanation:
Which table represents a linear function help ASAP!!!!!
Answer:
The last one.
Step-by-step explanation:
I think it's the last one because as x increases by one, y increases by a constant rate of 5. The others don't increase by a constant rate. (I don't know if this is right but I think it is!)
help please asap!!!!!
Answer:
3rd answer
Step-by-step explanation:
It is an open circle and it has to be less than 15 and since it is a positive it is to the right
Worth 10 points help!
1. Kenny is putting a brick border around his irregular shaped garden. Before installing the border, Kenny must
cut the bricks to fit the angles of the garden. Use the given measures to answer the question.
m&A = (2x + 20°
m&B= (4x - 5)
m&C = (3x + 15)°
m&D = (5x + 16)
me= (2x - 2)
What are the angle measures of each vertex of the garden? Show all calculations and work. Keep in mind that
the drawing may not be to scale.
Answer:
a=82
b=119
c=108
d=171
e=60
Step-by-step explanation:
since we can see the figure has 5 sides we can use the interior angle formula 180(n-2) and replace n for 5 getting 180(3) which woukd get us to 540. with this information we know that all the verticals have to equal 540 so we can add the equations together to get
16x+44=540 - subtract 44 from both sides to get x by itself
16x=496 - simplify
x=31
substitute x for 31 in the equations.
2) The area of a rectangular pool is 1260 ft. Find the dimensions of the rectangle, if one
side of the pool is 48 ft more than three times the other side?
what is forty-seven plus twenty-two
Answer:
69
Step-by-step explanation:
nice.
An equation has a slope of -14 and passes through the point, (12, 2), what is the slope of
the equation of the line when written in slope-intercept form?
Answer:
y=-14x+170
Step-by-step explanation:
y=mx+b
2=-14(12)+b
2=-168+b
170=b
y=-14x+170
S helpndjdjdjdndndjdjejdjd will mark brainliest
Answer:
10/12 and 9/12
Step-by-step explanation:
Hi! I have an math exam tomorrow and I really need you guys help.
[tex] \frac{1}{2} - \frac{2}{2} - \frac{4}{2} + ... + \frac{39}{2} + \frac{40}{2} [/tex]
please help!
Find the value of x
-8/5 x + 2 = 0
Jen opens a bank account with a deposit of $100. Over six years, the balance in the account changes at an
increasing rate until it reaches a balance of $200. On your paper, sketch a graph that models the balance in the
account as a function of the number of years since Jen opened the account
Describe your graph
• What did you label the vertical and horizontal axes?
• What is the general shape of your graph?
• Is your graph increasing or decreasing?
• State two points that should definitely be on your graph What do those points represent?
Answer:I need help too for that :(
Step-by-step explanation:
Solve the equation 7^{2x}+7^{x+1}+4=0. Correct to 4 decimal places.
Answer:
Step-by-step explanation:
Here is the exact form and decimal form!
find x, find jl . any help is deeply appreciated :) !
Answer:
6. x = 15
7. JL = 78
Step-by-step explanation:
6. 8x - 23 = ½(10x + 44) (midsegment theorem)
Multiply both sides by 2
2(8x - 23) = 10x + 44
16x - 46 = 10x + 44
Collect like terms
16x - 10x = 46 + 44
6x = 90
Divide both sides by 6
x = 90/6
x = 15
7. MN = 5x - 16
JL = 4x + 34
MN = ½(JL) (midsegment theorem)
5x - 16 = ½(4x + 34) (substitution)
2(5x - 16) = 4x + 34
10x - 32 = 4x + 34
Collect like terms
10x - 4x = 32 + 34
6x = 66
x = 66/6
x = 11
JL = 4x + 34
Plug in the value of x
JL = 4(11) + 34 = 44 + 34
JL = 78
Simplify (r4)6
..............:::::::.......
Answer: The second r10
Step-by-step explanation:
30 coins consisting of quarters and dimes, which total is $5.70. How
many quarters does she have?
Answer:
18 quarters
Step-by-step explanation:
Answer:
18 quarters 12 dimes
18 x 25 = 450
12 x 10 = 120
18 + 12 = 30
450 + 120 = 570
Therefore, there are 18 quarters.
Divide
a) (4a-4b)÷(a-b)
Answer:
4a+4b
Step-by-step explanation:
——-PLEASE HELP W/ EXPLANATION——-
Answer:
I think it is 94 hope it works
can someone pls help me ty
Answer:
y=-4x+5
Step-by-step explanation:
this is the equation for the line :y=mx+c
m is the slope
c is the y-intercept
4 is negative because the line is negative
NEED HELP ASAP!! ill mark brainliest
Answer:
number first is the answer
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the functions.
According to the power of the functions, positive power is more than the negative one hence, for any value of x, the value of function y is always positive.
Hence the answer is option D.)
===>
x==> - infinite, y => infinite and x=> infinte, y=> infinite
If you want to buy an item in a store that costs $36.50 and is on sale for 40% off, then how much would the item actually cost you after the discount? Round to the nearest cent.
Answer:
i think its 21.90
Step-by-step explanation:
i did the math
All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday. 5% of students brought their lunch. 36 students brought their lunch. How many students in total are in Ridgewood Junior High School?
Answer: 720
Step-by-step explanation:
5%=36
1%=36/5
1%=7.2
100%=7.2*100
100%=720 students
There is a total of 720 students are in Ridgewood Junior High School.
Given,
All students in Ridgewood Junior High School either get their lunch in the school cafeteria or brought it from home on Tuesday.
5% of students brought their lunch.
36 students brought their lunch.
To determine how many students in total are in Ridgewood Junior High School.
the percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Let there be x students in the Ridgewood Junior High School.
5% of students brought their lunch and equal to 36
so 5% of x = 36
5/100 * x = 36
x = 36*100/5
x = 36*20
x = 720
Thus, there is a total of 720 students are in Ridgewood Junior High School.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ2
A triangle has sides of lengths 19 centimeters, 19 centimeters, and 26 centimeters and angle measures of 84º. 489 and 48°. Which image shows this triangle?
84
19 cm
19 cm
248
48
26 cm
48
19 cm
19 cm
O
84
48
26 cm
84
19 cm
26 cm
248
48
19 cm
48
26 cm
O
19 cm
18
84
19 cm
Answer:this is the answer
Step-by-step explanation:
Just did the test
pls help!! and show your work. i'm confused on it
Answer:
2.3×10/10=23/10=2 3/10 is mixed number
Help 10 points for correct answer
Answer:
C. 85.0 degrees. Because...
Coz when you calculate the angles all together using the 180°. You'll find the right answer
Can you please help I dont understand it.
Answer:
-3.5
Step-by-step explanation:
4y-6y-10=-3
-2y=-3+10
-2y=7
y=7/-2
y=-3.5
What is the remainder if f(x) = x4 – 5x2 - 6x - 10 is divided by x - 3?
Answer:-46
Step-by-step explanation: just took test
The remainder when f(x) is divided by (x - 3) is 8 and this can be determined by using the factorization method.
Given :
[tex]\rm f(x) = x^4-5x^2-6x-10[/tex]
The following steps can be used in order to determine the remainder if f(x) is divided by (x - 3):
Step 1 - Write the mathematical expression of the statement "f(x) is divided by (x - 3)".
[tex]=\dfrac{x^4-5x^2-6x-10}{x-3}[/tex]
Step 2 - Now, try to factorize the numerator in the above expression.
[tex]=\dfrac{x^4-3x^3+3x^3-9x^2+4x^2-12x+6x-18+18-10}{x-3}[/tex]
Step 3 - Further simplify the above expression.
[tex]=\dfrac{x^3(x-3)+3x^2(x-3)+4x(x-3)+6(x-3)+8}{x-3}[/tex]
[tex]=(x^3+3x^2+4x+6) +\dfrac{8}{x-3}[/tex]
So, the remainder when f(x) is divided by (x - 3) is 8.
For more information, refer to the link given below:
https://brainly.com/question/6810544
Clarissa has 14 3/4 yards of fabric to cover another sofa and chair. The new sofa needs 9 1/6 yards of fabric and the new chair needs 4 1/3 yards of fabric. Estimate to decide if Clarissa had enough fabric. If so, how much fabric will she have left?
Answer:
śhĺò býò 1/2 ýāèd ļanid inch
