The value of cube root of x^10, when x = -2, can be written in simplest form as a^3 times the square root of b, where a = _____ and b = ______.

Answers

Answer 1

Answer:

[tex]a = 2[/tex]

[tex]b = 2^{1/6}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

[tex]x = -2[/tex]

Required

Find a and b

We have:

[tex]\sqrt[3]{x^{10}} = a^3 * \sqrt b[/tex]

Substitute -2 for x

[tex]\sqrt[3]{(-2)^{10}} = a^3 * \sqrt b[/tex]

[tex]\sqrt[3]{1024} = a^3 * \sqrt b[/tex]

Expand

[tex]\sqrt[3]{2^9 * 2} = a^3 * \sqrt b[/tex]

Split the exponents

[tex]2^{(9/3)} * 2^{(1/3)} = a^3 * \sqrt b[/tex]

[tex]2^{3} * 2^{1/3} = a^3 * \sqrt b[/tex]

By comparison:

[tex]a^3 = 2^3[/tex]

So;

[tex]a = 2[/tex]

and

[tex]\sqrt b = 2^{1/3}[/tex]

Take square roots of both sides

[tex]b = 2^{1/6}[/tex]

Answer 2

Answer: -8, -2

Step-by-step explanation: (the previous answers are ) 1. D 2. C 3. -8,-2 (for reference of order :))


Related Questions

find the LCM and hcf of 72 and 162 , leaving the LCM in prime factors

Answers

Answers:  LCM = 2^3*3^4HCF = 18

=========================================================

Explanation:

Find the prime factorization of 72 and 162

72 = 8*9 = 2^3*3^2162 = 2*81 = 2*9^2 = 2*(3^2)^2 = 2*3^4

Here's a simplified version of each

72 = 2^3*3^2162 = 2*3^4

We have these unique primes: 2, 3

Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.

This means 2^3*3^4 is the LCM (lowest common multiple).

2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.

------------------------------

Now onto the HCF (highest common factor; aka GCF).

Looking at

72 = 2^3*3^2162 = 2*3^4

We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.

Those common factors you circled are then multiplied.

Overall, the HCF is 2*3^2 = 2*9 = 18

-----------------------------

Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.

Answer:

LCM= 648

HCF= 18

Step-by-step explanation:

Find the decay factor from the model y =4520(0.6)square 6

Answers

Answer:

Step-by-step explanation:

Ross walked 3 m east and 6 m north. How far is he from the starting point

Answers

Answer:

3 sqrt(5) meters

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem.

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

3^2+6^2 = c^2

9+36 = c^2

45 = c^2

Taking the square root

sqrt(45) = sqrt(c^2)

sqrt(9*5) = c

sqrt(9) sqrt(5) =c

3sqrt(5) = c

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Given:-Ross walked 3 m east and 6 m north.

Find:-How far is she from the starting point?solution:-

Ross walked 3 m east and 6 m north.

so her path is a right angle triangle path.

we know that,

in a right angle triangle, According to the Pythagorean theorom,

[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]

where

l= legs b=baseh=hypotenuse

According to the question, [tex]\sf{3^2+6^2=f^2 }[/tex]

[tex]\sf{9+36=f^2 }[/tex]

[tex]\sf{ f^2=45 }[/tex]

[tex]\sf{f=\sqrt{45} }[/tex]

[tex]\sf{f=3\sqrt{5} }[/tex]

Therefore:-

he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point

Instructions: Find the measure of the indicated angle to the nearest
degree.
26
?
32
? =

Answers

Answer:

36

Step-by-step explanation:

Since this is a right triangle we can use trig functions

cos theta = adj side / hyp

cos ? = 26/32

Taking the inverse cos of each side

cos^-1(cos ?) = cos^-1( 26/32)

? = 35.65908

To the nearest degree

? = 36

SECTION B
A matatu and Nissan left town A for town B 240km away at 8.00 a.m travelling at 90km/hr
and 120km/hr respectively. After 20 minutes the Nissan had a puncture which took 30
minutes to mend.
(5mks
a) How far from town A did the Nissan catch up with the matatu?

Answers

9514 1404 393

Answer:

  180 km

Step-by-step explanation:

The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...

  Matatu distance = Nissan distance

  90t = 40+120(t -5/6)

  0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses

  60 = 30t . . . . . . . . . . . add 60

  2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again

That distance from town A is ...

  y = 90t = 90(2) = 180 . . . . km

Which of the following is equivalent to (x+5)(2x^2 +8)?
A. (x+5)(2x^2)• (X+5)(8)
B. (x+5)(2x^2)+(x+5)(8)
C. (x+5)(2x)+(x+5)(8)
D. (x+5)(2x)• (x+5)(8)

Answers

Answer:

(x+5)(2x^2 +8)

Multiply (x+5) in both sides

(x+5)(2x^2) × (x+5)(8)

Answer is a

How many real solutions exist for this system of equations?
y=x^2+4
y= 4x
ОА. .
zero
OB.
one
Ос.
two
OD
infinite
Reset
Next

Answers

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

[tex] {x}^{2} + 4 = 4x[/tex]

[tex] {x}^{2} - 4x + 4[/tex]

Find the discrimant.

[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]

This means there is one real solution. Since the discramnt equal 0.

Strat with k add 2 multiply by 6 then subtract 8

Answers

Answer:

6(k+2) -8

Step-by-step explanation:

Start with k

k

Add 2

(k+2)

Multiply by 6

6(k+2)

Then subtract 8

6(k+2) -8

6(k+2)-8 is a required answer.

Answer:

Solution given:

Start with k.

K

add 2

k+2

multiply by six

(k+2)*6

subtract by 8

6(k+2)-8

Please helppppp!!!!!!!!

Answers

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

Answer:

A=128 cm²

Step-by-step explanation:

Hi there!

We are given a trapezoid and we want to find the area of it

The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height

The bases are the parallel sides

They are the sides marked as 10 cm and 22 cm in this case

The height is the distance between the bases

In this case, it is the side marked as 8 cm

We know everything needed for the area, let's just label everything to avoid any confusion

a=10

b=22

h=8

Now substitute into the formula

A=[tex]\frac{a+b}{2}h[/tex]

A=[tex]\frac{10+22}{2}*8[/tex]

add the numbers on the numerator together

A=[tex]\frac{32}{2}*8[/tex]

Divide 32 by 2

A=16*8

multiply

A=128 cm²

Hope this helps!

Can some one help me solve these 3 questions?

Answers

7. A
8. Is the 1st picture
9.is the second picture

Suppose that a1, a2, a3, . . . is an arithmetic sequence, in which a3 = 19 and a14 = 96. Find a1.

Answers

Uhhh I think you have to add 19 and 14 which shall give you the answer to a1 so it should be 33 but then I think you divide 33 and 96 or you will multiply 33 and 96

plzzz helpppp dont ignoreeee

Answers

Answer:

X= 40

Step-by-step explanation:

2(110 + 4x) = 220 + 8x = 540

8X = 320

X= 40

Answer:

x = 17.5

Step-by-step explanation:

Since there’s a dashed line between the shape, the new total = 180* (degrees)

110* + 3x + x = 180*

Subtract 110 from 180

3x + x = 70

x = 17.5

Solve for the missing angle. Round to the nearest degree.

Answers

Step-by-step explanation:

here's the answer to your question

Pleaseeee helppppppp

Answers

Answer:

d = 8t

Step-by-step explanation:

solve: 5y +12 - 3y + 12 = 18

Answers

Answer:

5y-3y+12+12=18

2y = 18 - 24

y = -6/2

y = -3

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{5y + 12 - 3y + 12 = 18}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textsf{(5y - 3y) + (12 + 12) = 18}\\\\\large\text{NEW EQUATION: \textsf{2y + 24 = 18}}\\\\\large\text{SUBTRACT 24 to BOTH SIDES}\\\\\large\textsf{2y + 24 - 24 = 18 + 24}\\\\\large\text{Cancel out: \textsf{24 - 24} because it gives you 0}\\\\\large\text{Keep: \textsf{18 - 24} because it helps solve it helps solve for y}\\\\\large\textsf{18 - 24 = \bf -6}[/tex]

[tex]\large\text{NEW EQUATION: \textsf{2y = -6}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\mathsf{\dfrac{2y}{2y}=\dfrac{-6}{2}}\\\\\large\text{Cancel out: }\mathsf{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\mathsf{\dfrac{-6}{2}}\large\text{ because it gives you the y-value}\\\\\large\textsf{y = }\mathsf{\dfrac{-6}{2}}\\\\\mathsf{\dfrac{-6}{2}= \bf -3}\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: y = \bf -3}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Find the measure of arc BC?

Answers

Answer:

129

Step-by-step explanation:

Since,

AD = BC

AD = 3x + 24

BC = 4x - 11

3x + 24 = 4x - 11

4x - 11 = 3x + 24

4x - 3x = 24 + 11

x = 35

BC = 4x - 11

= 4 ( 35 ) - 11

= 140 - 11

BC = 129

Answer:

[tex]AB=BC[/tex]

[tex]3x+24=4x-11[/tex]

[tex]3x-4x=-11-24[/tex]

[tex]x=35[/tex]

[tex]BC=4\times 35-1[/tex]

[tex]=140-11[/tex]

[tex]=129[/tex]

--------------------------

Hope it helps..

Have a great day!!

2z^8- 32z^8
Help plz

Answers

Answer:

-30z^8

Step-by-step explanation:

[tex]2 {z}^{8} - 32 {z }^{8} \\ = - 30 {z}^{8} [/tex]

Answer:

-30z^8

Step-by-step explanation:

2z^8- 32z^8

-30z^8

Mike, a Salvation Army bell ringer, has 20% as many quarters as nickels in his cup. If Mike has $6.00 in quarters and nickels, how many nickels does he have?

Answers

5.8 Nickels

Step-by-step explanation:

Let x rep no of Nickels in Mike's cup

Then x - 0.2 = Number of quarters in Mike's cup

0.2x = Amount of money that mike has from the nickels

1 ( x - 0.2) = Amount of money that Mike has from the quarter

Then,

0.2x + 1 (x - 0.2) = 6

Expand the bracket

0.2x + x - 0.2x = 6

x = 6

Recall

x - 0.2 = 0

6 - 0.2 = 5.8

Therefore, Mike has 5.8 nickels for the quarter

Questlon 4 of 10
What is the midpoint of the segment shown below?
AE
101
O A. (10.)
(5.4)
O B. (5,1)
10
(5,-3)
O C. (5,-)
O D. (10,1)
SUBMIT

Answers

Answer:

c

Step-by-step explanation:

To find the midpoint the formulas

x=x1+x2/2 and y=y1+y2/2 are used

in this case x1 is 5,x2 is 5,y1 is 4 and y2 is -3

therefore

x=5+5/2.

=10/2

=5

y=4+(-3)/2

=1/2

The midpoint of a line segment divides the line into equal segments

The midpoint of the line segment is (5,1/2)

The endpoints of the line is given as:

(5,4) and (5,-3)

The midpoint of the line is calculated as:

(x,y) = 0.5(x1 + x2, y1 + y2)

So, we have:

(x,y) = 0.5(5 + 5, 4 - 3)

Evaluate the sum and difference

(x,y) = 0.5(10, 1)

Evaluate the product

(x,y) = (5, 1/2)

Hence, the midpoint of the line segment is (5,1/2)

Read more about midpoints at:

https://brainly.com/question/16828532

What are the fractions simplest form

Answers

Answer:

the first one 2/-1, hope it helps...

Niko wants to put soil in his garden shown below. If soil comes in bags that fill 6 square yards each, how many bags of soil should Niko buy? Hint: you may have some leftover soil.

Answers

Answer:

444 pot soils

Step-by-step explanation:

How would I answer this: How many minutes are in a 30-day month.... use vertical multiplication to get the right answer

Answers

Answer:

There are 43200 minutes in a 30-day month.

Step-by-step explanation:

We know that:

60 minutes = 1 hour

24 hours = 1 day

Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.

   30

x  24

_______

  120

 60

_______

 720 hours

The 30-day month has a total of 720 hours.

So that the number of minutes that make up 720 hours can be determined by;

    720

 x   60

_______

   000

4320

_______

43200

Therefore, there are 43200 minutes in a 30-day month.

Can someone help me figure this out?

Answers

Answer:

See picture below.

Step-by-step explanation:

I had to write a new option for one of the lines.

3 of 9
Express the ratio below in its simplest form.
2:4:2

Answers

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Mr. Sun borrowed $15,600 for 54 months at simple interest to pay for a new swimming pool. If Mr. Sun paid the bank a total of $21,567.00, what was the simple interest rate of the loan?

Answers

Given:

Mr. Sun borrowed $15,600 for 54 months at simple interest.

Mr. Sun paid the bank a total of $21,567.00.

To find:

The rate of simple interest.

Solution:

We know that,

12 months = 1 year

1 month = [tex]\dfrac{1}{12}[/tex] year

54 months = [tex]\dfrac{54}{12}[/tex] year

54 months = 4.5 years

Simple interest is:

[tex]S.I.=Amount-Principal[/tex]

[tex]S.I.=21567-15600[/tex]

[tex]S.I.=5967[/tex]

Formula for simple interest is:

[tex]S.I.=\dfrac{P\times r\times t}{100}[/tex]

Where, P is principal, r is the rate of interest in percent and t is the number of years.

Putting [tex]S.I=5967,P=15600,t=4.5[/tex], we get

[tex]5967=\dfrac{15600\times r\times 4.5}{100}[/tex]

[tex]596700=70200r[/tex]

[tex]\dfrac{596700}{70200}=r[/tex]

[tex]8.5=r[/tex]

Therefore, the rate of simple interest is 8.5%.

Q5. Evaluate this expression when a=6
Q6. Which option shows this expression simplified correctly?
Q7. Which option shows this expression simplified correctly?
Q8. Find the following:
Q9. Which option shows this expression expanded correctly?

Answers

Question 5: 54/a. 54/6 is 9. The answer is 9.
Question 6: 2w + 3x. There are 2 w’s, and 3 x’s.
Question 7: 2x + 4y. There are 2 x’s, and 4 y’s.
Question 8. 11 + 16 is 27.
Question 9: 3(8y - 5). 3*8y is 24y. 3*-5 is -15. The answer is 24y - 15.

look at photo! please help needed! 1.

Answers

Answer:

5/12

Step-by-step explanation:

it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12

What does x stand for in the equation 1+x=2

Answers

Answer:

x = 1

Step-by-step explanation:

1 + x = 2
x = 1

Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = (x – 8).

Answers

Answer:

A linear equation in the standard form is written as:

y = a*x +b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

a = (d - b)/(c - a)

So we know that our line passes through the points (8, -1) and (2, -5)

then the slope will be:

a = (-5 - (-1) )/(2 - 8) = (-4/-6)  = 2/3

Then our line is something like:

y = (2/3)*x + b

to find the value of b, we can use the fact that we know that our line passes through the point (2, -5)

this means that when x = 2, we must have y = -5

replacing these values in the equation we get:

-5 = (2/3)*2 + b

-5 = 4/3 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3 = b

then the equation is:

y = (2/3)*x - 19/3

(in the question you wrote the point-slope form, but you can see that it does not work for the second point, so there may be a mistake there, as the slope is missing)

The actual equation in the point-slope form is:

y + 1 = (2/3)*(x - 8)

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

I Got It Right Instruction on edge

What number cube has faces numbered 1 to 6.

Answers

Answer:

I don`t see the attachment

Step-by-step explanation: