What is 6√2⋅√11−2√22 expressed in simplified form?

Answer:

In simplifying this is simple.

If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.

So consider two cases:

• If c = 2, then we're left with 6a + 9b = 21.

• If c = 1, then 6a + 9b = 41.

We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.

This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.

Step-by-step explanation:

hope this helps, good Luck xD.

Answer:

1. 2/5

2. -1/5

3. -1/3

Step-by-step explanation:

the parpendicular slope is found by taking the original slope and finding the opposite reciprocal. so just flip the slope and make it the opposite sign

-5/2  --->    2/5

+5/1  --->    -1/5

+3/1  --->    -1/3

Answer:

who

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

180 - 115 = 65

This is the easiest way to think about and do it but your teacher might want you to do it a different way.

Answer:

65

Step-by-step explanation:

Answer:

about 172.82

Step-by-step explanation:

Answer:

83.23

Step-by-step explanation:

to work out surface area of a  right cone u

A=πr(r+h2+r2)

hope this helps

im not sure if its right tho

Answer:

A.3

Step-by-step explanation:

Since the lines are parallel that angle is 90 same as the other. So you plug in all your answers to see with one gives you 90 that being 3 because 30(3)=90.

Given ,

AB = BC

BC = CA

CA = 6 cm

This is an equilateral triangle as the first side is equal to the second side and the third side is equal to the second side which is equal to the first side . As all the sides are equal to 6 cm , this triangle is said to be an equilateral triangle .

∴ Triangle ABC is an equilateral triangle , where :- AB = BC = CA = 6 cm .

Step-by-step explanation:

ans is 7.62

1 inch =2.54cm

2.54 multiplied by 3=7.62

Answer:

1. 2.328×[tex]10^{22}[/tex]

2. 487

3. 30.52  OR  0 (see explanation↓)

Step-by-step explanation:

1.[tex](25)^{2t}[/tex]

(sub for t=8)

=[tex]25^{2*8}[/tex]

=[tex]25^{16}[/tex]

=2.328×[tex]10^{22}[/tex]

2.[tex]2st^{2} -5^{2}[/tex]

(sub for s=4 and t=8)

=2×4×[tex]8^{2}[/tex]-[tex]5^{2}[/tex]

=512-25

=487

3.[tex]2s^{2} -t^{3/16}[/tex] (the equation is not clear so I will do [tex]2s^{2} -\frac{t^{3} }{16}[/tex] as well)

FOR [tex]2s^{2} -t^{3/16}[/tex]

(sub s=4 and t=8)

=2×[tex]4^{2}[/tex]-[tex]8^{3/16}[/tex]

=32-1.476826146

=30.52 (to the nearest 2 decimal place)

FOR [tex]2s^{2} -\frac{t^{3} }{16}[/tex]

(sub s=4 and t=8)

=2×[tex]4^{2}[/tex]-[tex]\frac{8^{3} }{16}[/tex]

=32-32

=0

Answer:

[tex]\frac{1}{10} h\leq 10[/tex]

Step-by-step explanation:

Basically, we are just translating the phrase into an algebraic expression.

Answer:

43

Step-by-step explanation:

5 × 3 - 7 × -4 =

15 - - 28 =

15 + 28 = 43

Answer:

43

Step-by-step explanation:

5a - 7b if a = 3 and b = -4

= 5(3) - 7(-4)

= 15 - -28

= 15+28

= 43

Answer:

32 inches

Step-by-step explanation:

Because height times width equals area,

we can divide 112 by 3.5 to get the width

So it is 32 inches

Answer:

Check picture

Step-by-step explanation:

9514 1404 393

Answer:

  1 1/2

Step-by-step explanation:

  [tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]

Then the improper fraction 3/2 can be written as the mixed number 1 1/2.

  (4 1/8) / (2 3/4) = 1 1/2

_____

Comment on division of fractions

Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.

If we were to "invert and multiply", the computation would be ...

  (33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2

Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:

  (33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2

Answer:

B. No, Gio's claim is incorrect because the Pythagorean theorem can only be used

with a right triangle.

Step-by-step explanation:

The pythagorean theorem which is given as a² + b² = c², only applies to right triangles. Where, c is the hypotenuse side length that is opposite to the right angle of the triangle, while a and b are the two other legs of the right triangle.

The triangle given above is not a right angle. The measure of the missing length = 180 - (60 + 40) = 80°.

A right ∆ has an angle measure of 90°. Therefore, the pythagorean theorem cannot be applied in this case to solve for the missing side length, x.

So, Gio's claim is INCORRECT.

Answer:

6

Step-by-step explanation:

Let that number be x.

[tex]2x = 9 + 3[/tex]

[tex]2x = 12[/tex]

[tex]x = 6[/tex]

Answer:

Step-by-step explanation:

Since the Tootsie Roll lollipop is a sphere

volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]

the negative sign indicates that the volume is decreasing

upon differentiating

as the diameter given is =0.75 so radius will be = 0.375

[tex]dV/dt = 4piR^2*dR/dt[/tex]

so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]

So the radius is decreasing at the rate of dR/dt= 0.142in/min

9514 1404 393

Answer:

  20 m

Step-by-step explanation:

The 30 m shadow of the tree is 10 times the 3 m length of the person's shadow. We expect the tree to be 10 times as tall as the person:

  10(2 m) = 20 m . . . height of the tree

Answer:

5.08

Step-by-step explanation:

5   8/100

Since there are 2 zero's in 100, we need two numbers in the top

Replace 8 with 08 which is the same number

5  08/100

Now write as a decimal

5.08

Answer:

B. 5.08

Step-by-step explanation:

I hope this helps!

Step-by-step explanation:

-2(3x-12)+4-13

=-6x+24+4-13=-7x-15

=6x-15

4(5x-1)+8x-20=20x-4+8x-20

=28x-24

So this is ur solution.

But if u wnt to solve these eq. together thn it will be:-

6x-15=28x-24

6x-28x=-24+15

-22x=-9

x=22/9=2.44

Hope u like it.

Answer:

-8+9 is problem one

Step-by-st-ep explanation:

Answer:

6. x = 28 degrees

7.  z = 1.6 cm

Step-by-step explanation:

6.  

Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

x = 56 / 2

x = 28 degrees

Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

z = 1.6 cm

Answer:

D. [tex] 3x + 1 [/tex]

Step-by-step explanation:

Perimeter of Rectangle ABCD = [tex] 9x + 3 [/tex]

Perimeter of Rectangle PQRS = [tex] 6x + 2 [/tex]

Difference between perimeter of Rectangle ABCD and Perimeter of Rectangle PQRS:

[tex] (9x + 3) - (6x + 2) [/tex]

Open Parentheses

[tex] 9x + 3 - 6x - 2 [/tex]

Collect like terms

[tex] 9x - 6x + 3 - 2 [/tex]

[tex] 3x + 1 [/tex]

Answer:

10/3

3.333333

3  1/3

Step-by-step explanation:

hope this helps

Answer:

1.90 percent

Step-by-step explanation:

Answer:

0 ≤ an ≤ bn

The series ∑₁°° bn converges

The series ∑₁°° an converges by comparison to ∑₁°° bn.

0 ≤ an ≤ bn

The series ∑₁°° bn diverges

The comparison test is inconclusive for our choice of bn.

Step-by-step explanation:

an = 1 / (n² + n + 3) and bn = 1 / n²

The numerators are the same, and the denominator of an is greater than the denominator of bn.  So 0 ≤ an ≤ bn.

bn is a p series with p > 1, so it converges.

Since the larger function converges, the smaller function also converges.

an = (3n − 1) / (6n² + 2n + 1) and bn = 1 / (2n)

If we rewrite bn as bn = (3n − 1) / (6n² − 2n), we can tell that when the numerators are equal, the denominator of an is greater than the denominator of bn.  So 0 ≤ an ≤ bn.

bn is a p series with p = 1, so it diverges.

The larger function diverges.  We cannot conclude whether the smaller function converges or diverges.

Answer:

Step-by-step explanation:

[tex]\frac{f(b)-f(a)}{b-a}[/tex] This is the formula for the average rate of change

over the interval (a, b)

a and b are x values

f(a) ad f(b) think of them as y values

Start calculating f(a) and f(b) a=1 b=6

replace all x's in formula with a, (1)

f(1)=1³-9(1) = 1-9= -8    f(1) = -8

Now do : b (6)

f(6) = 6³ - 9 (6) = 216-54=162 f(6) = 162

now plug everything into your equation

[tex]\frac{f(6)-f(1)}{6-1} =\frac{162- (-8)}{5} =\frac{170}{5} =34[/tex] average rate of change.

notice the 162 - (-8) In math there is no subtraction, and you would change it to + and when you do that you much change the sign of the next value making -8 a +8.

Hope this helps. Good luck!

Answer:

Using the vertical line test, the functions are b, c, d, and f

Step-by-step explanation:

a and e both fail the vertical line test, therefore, it's not a functions.