what is the greatest common factor of 61 and 77

First multiply the numbers inside the radicals together.

So √3 · √15 is √45.

So we have 2√45.

Note that the 2 can't be multiplied by anything since

√15 has nothing outside of the radical.

So we have 2√45.

Now, break down your square root.

√45 breaks down as 9 · 5 and 9 breaks down as 3 · 3.

Since we have a pair of 3's, a 3 comes outside of the radical

multiplying by the 2 that was previously outside to get 6.

The 5 doesn't pair up so it stays inside.

So our final answer is 6√5.

Answer:

C) [tex]6\sqrt{5}[/tex]

Arithmetic without explanation:

[tex]2\sqrt{3}* \sqrt{15}\\ = 2\sqrt{3}* \sqrt{3*5} \\ = 2\sqrt{3^2} *\sqrt{5} \\ = 2 * 3\sqrt{5} \\= 6\sqrt{5}[/tex]

Example of radical multiplication:

Take [tex]y\sqrt{x} * a\sqrt{b}[/tex]  as an example:

1. Multiple the numbers inside the roots

      [tex]\sqrt{x} * \sqrt{b} = \sqrt{x*b} = \sqrt{xb}[/tex]  

2. Multiple the numbers outside the roots

       [tex]y*a = ya[/tex]

3. Combine them and simplify

      [tex]ya\sqrt{xb}[/tex]

Step-by-step explanation:

We are given the expression [tex]2\sqrt{3}*\sqrt{15}[/tex]

 1. Identify the roots and multiply them

         The roots are [tex]\sqrt{3}[/tex]  and [tex]\sqrt{15}[/tex]

           [tex]\sqrt{3} *\sqrt{15} \\= \sqrt{45}[/tex]

  2. Multiply the numbers outside the root

         For [tex]2\sqrt{3}[/tex] it is [tex]2[/tex] and for [tex]\sqrt{15}[/tex] it is [tex]1[/tex]

          [tex]2*1 = 2[/tex]

  3. Combine and simplify

    Combine:

              [tex]2* \sqrt{45}\\= 2\sqrt{45}[/tex]

   Simplify:

           *Note: [tex]\sqrt{n^2} = n[/tex]

        1. Find the Prime factorization of 45

                   [tex]45 = 3^2 * 5[/tex]

        2. Simplify the Root

                  [tex]2\sqrt{45} \\ = 2\sqrt{3^2 * 5} \\= 2\sqrt{3^2} * \sqrt{5} \\= 2 * 3\sqrt{5}\\ =6\sqrt{5}[/tex]

We end up with [tex]6\sqrt{5}[/tex]

Answer: yes

Step-by-step explanation:

adding 50 40 30 20 10 and 0 gets you 150 so 2nd place gets 40

Answer:

One tshirt is $4

Step-by-step explanation:

28/7= 4

Answer:

$4.

Step-by-step explanation:

If 7 shirts equals 28 in total then just do 28/7 = 4.

4x7 = 28.

Answer:

1,200

Step-by-step explanation:

1020 divided by 0.85= 1200

Answer:

The probability is 23/30, .77, or 77 percent.

Step-by-step explanation:

Add up all the non cherry options, then put them over the total, 30. You would get 23/30, or .7666666666..., which is also known as about 77 percent. So the probability is 23/30, .77, or 77 percent.

Answer:

$94.05

Step-by-step explanation:

Original price of jeans=$95

Discount=10%

New price=(100% - 10%) of $95

=90% × 95

=90/100 × 95

=0.9 × 95

=$85.5

Sales tax of 10%

10% of the new price

=10/100 × 85.5

=0.1 × 85.5

=$8.55

Sales tax =$8.55

Total amount paid for the jeans= sales tax + new tax

=$8.55 + $85.5

=$94.05

Answer:

The third angle is 180-(49+75)=56 degrees

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Answer:

56

Step-by-step explanation:

Answer:The answer is OD 10.125

Step-by-step explanation:

Add all the lengths of the fish (6+8+9+10+11+12+12+13) = 81

Divide by 8

81/8

=10.125

Answer:

x < -3

Step-by-step explanation:

First we simplify:

-5x - 5 > 7x + 31

-12x > 36

x < -3.

We reverse the sign because we divided by a negative number on both sides.

That should be easy to graph.

Answer:

A) A

Step-by-step explanation:

The square root of 7 is just over two and a half.

Answer:

A. A

Step-by-step explanation:

Step 1: Find closest perfect roots near √7

We know that √4 = 2

We also know that √9 = 3

√7 is between √4 and √9, so √7 is between 2 and 3.

Therefore, our answer is A.

Answer:

[tex]y=-\frac{12}{7}x-\frac{80}{7}[/tex]

Step-by-step explanation:

In order to find the slope-intercept form of a line when given two points, we need to first put it into point-slope form. The point-slope form is given by the equation:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and x₁ and y₁ is one of the two points.

Anyways, let's first find the slope. Let's designate (-2,-8) as x₁ and y₁ and (-9,4) as x₂ and y₂ (it doesn't really matter). The formula for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{(4)-(-8)}{(-9)-(-2)}=12/-7=-12/7[/tex]

So, the slope is -12/7.

Now, pick a point for the point-slope form. To keep things consistent, I'm going to use the point (-2,-8) as x₁ and y₁. Plug in -12/7 for m. Therefore:

[tex]y-(-8)=-\frac{12}{7}(x-(-2))\\[/tex]

Now, simplify, distribute, and isolate the y:

[tex]y+8=-\frac{12}{7}(x+2)\\y+8=-\frac{12}{7}x-\frac{24}{7}\\y=-\frac{12}{7}x-\frac{24}{7}-8\\y=-\frac{12}{7}x-\frac{24}{7}-\frac{56}{7} \\y=-\frac{12}{7}x-\frac{80}{7}\\y=-\frac{12}{7}x-\frac{80}{7}[/tex]

Answer:

Step-by-step explanation:

P(1, -2) ;Q(4,3)

Let R(x1,y1)

Midpoint=[tex](\frac{x_{1}+x_{2}}{2},\frac{y_1+y_2}{2})\\[/tex] = (4,3)

[tex](\frac{1+x_1}{2},\frac{-2+y_1}{2})=(4,3)\\[/tex]

Compare x coordinates and y coordinates

[tex]\frac{1+x_1}{2}=4 ; \frac{-2+y_2}{2}=3[/tex]

1+x1 = 4*2   ; -2+y2 = 3*2

1+x1 = 8       ;  -2 +y2 = 6

   x1= 8-1     ;        y2 = 6+2

    x1 = 7     ;         y2 = 8

R(7 , 8)

Answer/Step-by-step explanation:

3.a. length of AC.

Hypotenuse = AC

Opposite side to 60° = 7

Therefore, [tex] sin(60) = \frac{7}{AC} [/tex]

[tex] AC*sin(60) = \frac{7}{AC}*AC [/tex]

[tex] AC*sin(60) = 7 [/tex]

[tex] AC = \frac{7}{sin(60)} [/tex]

[tex] AC = 8.1 [/tex] (to nearest tenth)

b. Length of BC

Hypotenuse = BC

Opposite side to 50° = 7

Therefore, [tex] sin(50) = \frac{7}{BC} [/tex]

[tex] BC*sin(50) = \frac{7}{BC}*AC [/tex]

[tex] BC*sin(50) = 7 [/tex]

[tex] BC = \frac{7}{sin(50)} [/tex]

[tex] BC = 9.1 [/tex] (to nearest tenth)

c. Length of AB

Use the law of sines to find AB

[tex] \frac{BC}{sin(A)} = \frac{AB}{sin(C}} [/tex]

m<C = 180 - (60 + 50) (sum of angles in a triangle) = 70°

m<A = 60°

BC = 9.1

AB = ?

[tex] \frac{9.1}{sin(60)} = \frac{AB}{sin(70)} [/tex]

Cross multiply

[tex] 9.1*sin(70) = AB*sin(60) [/tex]

Divide both sides by sin(60)

[tex]\frac{9.1*sin(70)}{sin(60)} = \frac{AB*sin(60)}{sin(60)}[/tex]

[tex]\frac{9.1*sin(70)}{sin(60)} = AB[/tex]

[tex] 9.9 = AB [/tex] (nearest tenth)

[tex] AB = 9.9 [/tex]

i got something different

Answer:

Part I: 2πr*X/360

Part II: 2.5 radians

Part III: 143.24°

Step-by-step explanation:

Part II: and Part III: 2π(6)*x/360 = 15, x = 143.24°

143/360 = x/2π, x = 2.5 radians

Answer:

Step-by-step explanation:

[tex]m = 7\\(8,9)=(x_1 , y_1)\\\\y-y_1=m(x-x_1)\\\\y - 9=7(x -8)\\y-9=7x-56\\\\Collect\:like\:terms\\\\y = 7x-56+9\\\\y = 7x-47[/tex]

Answer:

-9

Step-by-step explanation:

x+2=-7

x+2-2=-7-2

x=-9

Answer:

-9

Step-by-step explanation:

i took this assignment

Answer:

19 inches

Step-by-step explanation:

Area of a square = s^2

s^2 = 361

s = 19

Step-by-step explanation:

3n-2=2n

-2=2n-3n

-2=-n

-2=-n

divide by - to get 2

Answer:

Step-by-step explanation:

[tex]v=\dfrac st\quad\implies\quad t=\dfrac sv[/tex]

s = 2 km

t - time of run

v - speed of running

Batman:

v = 3km/min

[tex]t = \dfrac{2\,min}{3\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{3\,km}=\dfrac23\,min = \dfrac23\cdot 60\,s=40\, s[/tex]

The Bionic Woman:

v = 5 km/min

[tex]t = \dfrac{2\,min}{5\,\frac{km}{min}}=2\,km\cdot\dfrac{min}{5\,km}=\dfrac25\,min = \dfrac25\cdot 60\,s=24\, s[/tex]

time from Batman's start: 24 s + 12 s = 36 s

40 - 36 = 4

Answer: Plane

Step-by-step explanation: A plane is a flat surface that has no thickness.

Think of a plane as a wall or a floor of a room.

Another important characteristic of a plane is that it has no edges.

So it extends forever in all directions.

Answer: y < (-1/4)*x + 1.

Step-by-step explanation:

The first thing you need to notice is that the line is not solid and that the shaded part is under the line, so our inequality will be strictly smaller than a linear equation.

y < a*x + b.

Now let's find the equation of the line.

A linear relationship can be written as:

y = a*x + b

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

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In the graph, we can see that the line passes through the points: (0,1) and (4. 0)

Then the slope is:

a = (0 - 1)/(4 -0) = -1/4.

Now we know that the line is:

y = (-1/4)*x + b

To find the value of b, just replace the value of one of the points in the equation.

We know that (0,1) is a solution of the equation (x= 0, y = 1)

1 = (-1/4)*0 + b = b

1 = b

Then our inequality is:

y < (-1/4)*x + 1.

Answer:

y = (-3/2)x + 7/2

Step-by-step explanation:

Find the slope of this line first.

As you move from the first point to the second, x (the 'run') increases by 6 and y (the 'rise') decreases by 4 (from 3 to -1).  Thus the slope is

m = rise/run = -6/4 or -3/2.

Find b for this situation, using y = mx + b, m = -3/2, y = -1 and x = 3:

-1 = (-3/2)(3) + b.  Multiply all three terms by 2:

2(-1) = -9 + 2b, or 7 = 2b.  Then b = 7/2, and the desired equation is

y = (-3/2)x + 7/2

Answer: the answer is -1.

the inverse operation of subtraction is addition so you would add 2 on both sides. now you have -4 + 2= -2. now the opposite of multiplication is division. so -2 divided by 2 is -1. hope this helps. Brainliest please!

Answer:

−1=t

Step-by-step explanation:

−4=2t−2

Simplify

First, add the same terms to both of the sides of this equation.

−4=2t−2

−4 + 2 =2t - 2 + 2

Secondly, simplify.

add the numbers

−4 + 2 =2t - 2 + 2

-2 = 2t - 2 + 2

Then,

-2 = 2t - 2+2

-2 = 2t

v

It's simplified to -2 = 2t

Thirdly, Divide both sides of the equation by the same term.

−2=2t

2  over −2

​ =  

2  over 2t

Simplify

(divide the numbers)

2  over −2

​ =  

2  over 2t

which also equals to

(simplify fraction)

−1 =   2  over 2t

-1 = t

​

​

Answer:

3.3

Step-by-step explanation:

7-7=0

-3+-7=-10

10 divided by 3 is 3.3

Answer: 8 liters  can.

Step-by-step explanation:

First we need to find the volume of the cart tank . Since it is in the shape of a rectangular prism we have to multiply the length by the width by the height to find the volume.

V= 40 * 25 * 8  

V =  8000  

Which means that the volume is 8000 cubic centimeters.  

Now convert 8000 cubic centimeters to liter.

It gives us a hint that 1 liter is equal to 1000 cm^3

So to convert 8000 cubic centimeters to liters we will have to divide it by 1000.

8000/1000 = 8 liters.

Answer:

The correct option is;

C) Translation 8 units to the right

Step-by-step explanation:

The function h(x) = 12·x⁸ + 49 is an even function

However a translation 8 units to the right would yield the following function;

h(x) = 12 × (x+ 8)⁸ + 49 = 12x⁸ + 768x⁷ + 21504x⁶ + 344064x⁵ + 3440640x⁴ + 22020096x³ + 88080384x² + 201326592x + 201326641

For h(1) = 516560701

Also h(-x) = 12 × (-x+ 8)⁸ + 49 = 12x⁸ - 768x⁷ + 21504x⁶ - 344064x⁵ + 3440640x⁴ - 22020096x³ + 88080384x² - 201326592x + 201326641

For h(-1) = 69177661

Therefore h(x) ≠ h(-x) after the translation 8 units to the right and the function is neither even nor odd.

Answer:

Hey there!

Expand (2+i)(3-i). You should get 7+i

Expand (7+i)(1+2i). You should get 5+15i

Expand (5+15i)(1-i). You should get 20+10i

Expand (20+10i)(3+i). You should get 50+50i as your final answer.

Let me know if this helps :)

Answer:The rational numbers includes all positive numbers, negative numbers and zero that can be written as a ratio (fraction) of one number over another. Whole numbers, integers, fractions, terminating decimals and repeating decimals are all rational numbers.

Step-by-step explanation:

Answer:

(b)

Step-by-step explanation:

This is the answer of your questions if right give 5 star!!! and Mark as brainliesr