Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

[tex]5\sqrt{2}[/tex]
[tex]\frac{5\sqrt{2} }{2}[/tex]
[tex]5\sqrt{3}[/tex]
[tex]\frac{5\sqrt{3}}{2}[/tex]

Answer:

Hey there!

93 ÷ 5 can be written as 93/5.

5 goes into 93, 18 times, so we have [tex]18\frac{3}{5}[/tex]

Let me know if this helps :)

Answer:

x=0, - 9

Step-by-step explanation:

x^2+9x=0

x(x+9)=0

x=0 or x=-9

Answer:

x =0  x= -9

Step-by-step explanation:

x^2 + 9x = 0

Factor out x

x(x+9) =0

Using the zero product property

x =0 x+9 =0

x =0  x= -9

Answer:

see below

Step-by-step explanation:

4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5

All exponent have to have the same number

42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5

Subtract the number

42 - 1.2 - 2.5 = 38.3

Add back the exponent

38.3 * 10 ^5

This is not in scientific notation

Move the decimal one place to the left and add one to the exponent

3.83 * 10^6

3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8

All exponent have to have the same number

3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

Add the numbers

3.3+2.6+.77 =6.67

Add back the exponent

6.67*10^9

This is in scientific notation

8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3

All exponent have to have the same number

8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4

Subtract

8.0 - 3.4 - .12 = 4.48

Add back the exponent

4.48* 10^4

This is in scientific notation

Answer:

17/21

Step-by-step explanation:

102/126

Divide the top and bottom by 6

17/21

Answer:

17/21

Step-by-step explanation:

102/2=51  126/2=63

51/3=17  63/3=21

17/21

Answer:

[tex]\sqrt{100}[/tex] is a rational number

Step-by-step explanation:

[tex]\sqrt{97}=9.848857.....\\\\\sqrt{98}=\sqrt{2*7*2}=2\sqrt{7}\\\\\sqrt{99}=\sqrt{3*3*11}=3\sqrt{11}[/tex]

 Square root of all prime numbers are irrational numbers

Answer:

b

basically 5/8 goes to 1/2 0.8 times which is 4/5

Answer:

obtuse

Step-by-step explanation:

because obtuse triangle would provide more support that acute or right as its bigger.

Answer:

B(-5, 1)

Step-by-step explanation:

We can test each value in the equation and see if the equation works out.

[tex]y > |x| - 6[/tex]

Let’s try A - (-1, -5).

[tex]-5 > |-1|-6\\\\-5 > 1-6\\-5>-5[/tex]

-5 is NOT greater than -5, it is equal so A doesn’t work.

Let’s try B, (-5, 1).

[tex]1 > |-5| -6\\1 > 5-6\\1 > -1[/tex]

1 IS greater than -1, so B works.

Let’s try C for fun.

[tex]-1 > |5| -6\\-1 > 5-6\\-1 > -1[/tex]

-1 is NOT greater than -1, it is equal, so it doesn’t work.

Hope this helped!

Answer:

B(-5,1)

Let us simply just write this in all scenarios.

A(-1,-5)

-5>|-1|-6

-5>-5

(False)

B(-5,1)

1>|-5|-6

1>-1

(True)

C(5, -1)

-1>|5|-6

-1>-1

False

Answer: Liz, she is 5 units away from Robbert.

Step-by-step explanation:

Ok, the data that we have is:

Robert is at (4,3 )

Lucy is at (6, 1)

Liz is at (1, 7)

We want to find the units between Robert and the person that is farther away from him.

The distance between Robert and Lucy can be calculated as:

First we calculate the difference in the point or in the position vector:

(4, 3) - (6, 1) = (4 - 6, 3 - 1) = (-2, 2)

To calculate the exact distance, we need to calculate the magnitude of this point, this is:

For a point (x, y), the magnitude is M = √(x^2 + y^2)

Then we have:

D = √( (-2)^2 + 2^2) = √8

Now, the distance between Robert and Liz can be calculated in the same way:

(4, 3) - (1, 7) = (4 - 1, 3 - 7) = (3, -4)

The magnitude is:

D = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5

Now, we know that 5 > √8

Then the person that is farthest away from Robert is Liz, and she is 5 units away.

Answer:

Step-by-step explanation:

tan30°=3/x

xtan30°=3

x=3/tan30°

x= 5.2

Answer:

1. 2cm 3cm and 4cm

yes, because 2+3>4

2. 2cm 3 cm 6 cm

no, 2+3<6

3. 90 degrees 45 degrees 45 degrees

yes, 90+45+45 = 180

4. 90 degrees 60 degrees 60 degrees?

no, 90+60+60=210!=180

Step-by-step explanation:

x⁵+x-1

(2x-x+1) ( x³+x²-1 )

Answer:

C D E

Step-by-step explanation:

Edg

Out of the given options, options C, D and E are a difference of squares.

Difference of Squares, two terms that are squared and separated by a subtraction sign.

Given are, options,

D) (y squared minus x y)(y squared + x y) = (y²-xy)(y²+xy) = y⁴-(xy)²

E) (64 y squared + x squared)(negative x squared + 64 y squared) = (64y²+x²)(64y²-x²) = (64y)⁴-x⁴

C) (3 + x z)(negative 3 + x z) = (3+xz)(3-xz) = 3²-(xz)²

Hence, out of the given options, options C, D and E are a difference of squares.

For more references on difference of squares, click;

https://brainly.com/question/11801811

#SPJ6

Answer:

See below.

Step-by-step explanation:

Approximation:

The wall is 8 ft wide.

The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.

8 ft - 2 ft = 6 ft

There will be approximately 6 ft of space tot he sides of the frame.

6 ft/2 = 3 ft

3 ft * 12 in./ft = 36 in.

There will be approximately 36 in. on each side of the frame.

Exact:

8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =

= 96 in. - 22 1/4 in.

= 95 4/4 in. - 22 1/4 in.

= 73 3/4 in.

The total amount of width of the wall not occupied by the frame is 73 3/4 in.

Half of that amount is on each side of the frame.

(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =

= 36 1/2 in. + 3/8 in.

= 36 4/8 in. + 3/8 in.

= 36 + 7/8 in.

= 36 7/8 in.

Answer:

-19/2 or

-9 1/2

Step-by-step explanation:

-1/2 ÷ 1/19

Copy dot flip

-1/2 * 19/1

-19/2

-9 1/2

Answer:

IU=161

Step-by-step explanation:

Angle Formed by Two Secants=  1/2 (difference of Intercepted Arcs)

42 = 1/2 (7m+5 - (3m-1))

Distribute the minus sign

42 = 1/2 (7m+5 - 3m+1))

Combine like terms

42 = 1/2 ( 4m+6)

Distribute the 1/2

42 = 2m+3

Subtract 3 from each side

42-3 = 2m+3-3

39 = 2m

Divide by 2

19.5 = m

The sum of the arcs = 360

IU+ 3m-1 + 7m+5 = 360

IU +10m+4 = 360

IU +10(19.5) +4 = 360

IU +195+4 = 360

IU = 360 - 199

IU=161

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

Explanation:

We get this point by doing two things.

If we started with x = -3, then x-2 = -3-2 = -5. Also, if we had y = -1 then y-7 = -1-7 = -8

So that's how we end up with Z(-3,-1) moving to Z ' (-5, -8)

You could also show your work like this

[tex](x,y) \to (x-2, y-7)\\\\(-3,-1) \to (-3-2, -1-7)\\\\(-3,-1) \to (-5, -8)\\\\[/tex]

Cost price is Rs600 and marked price is Rs780.

Must click thanks and mark brainliest

Answer:

The next step is add x to each side

Step-by-step explanation:

-x + 6 = 5 - 3x

Subtract 5 from each side

-x + 6-5 = 5-5 - 3x

-x+1 = -3x

Add x to each side

-x+1 = -3x+x

1 = -2x

Answer:

Step-by-step explanation:

all you need to do is solve for x right? so in that case when you subtract 5 from both sides you get -x+1=-3x

then you will add x on each side

you should now have 1=-2x

divide each side by -2 and then you will have

-1/2=x

Answer:

f(x) + g(x) is 2(2x² - 4x - 3)

Step-by-step explanation:

[tex]f(x) + g(x) = (x)(2x + 5) + ( {2x}^{2} - 13x + 6) \\ = (2 {x}^{2} + 5x) + (2 {x}^{2} - 13x + 6) \\ = 4 {x}^{2} - 8x - 6 \\ = 2(2 {x}^{2} - 4x - 3)[/tex]

Answer:

(x + 3)(x - 5)

Step-by-step explanation:

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

Answer:

2,400,000,000,000

Step-by-step explanation:

2.4 x 10^12 means that the decimal point is moved 12 places to the right (hence the power of 12)

So by moving the decimal point 12 times you get this: 2,400,000,000,000

The reason why there are only 11 zeroes is because the 4 was a decimal place  to the right of 2, thus losing a zero.

Answer:

1.  see attached diagram

2. The dimensions are 75 sqrt(2) by 75 sqrt(2) ft

3. The perimeter is 300 sqrt(2) ft

4. cannot fit 40 machines along the walls

Step-by-step explanation:

We are using a top down view.  We have a square building with side length s.  The diagonal is 150 ft

Using the Pythagorean theorem

s^2 + s^2 = 150^2

2s^2 = 22500

s^2 =11250

Taking the square root of each side

sqrt(s^2) = sqrt(11250)

s = sqrt(6225*2)

s = 75 sqrt(2)

The dimensions are 75 sqrt(2) by 75 sqrt(2) ft

The perimeter of a square is given by

P = 4s = 4(75 sqrt(2)) =300 sqrt(2) ft

The perimeter is 300 sqrt(2) ft

Assuming the machines are square ( that they are as wide as they are long) 75 sqrt(2) is approximately 106 ft  so you can fit 10 along the wall

Putting them along the top and bottom walls = 20 machines

We are only left with 86 ft along the side walls

86/10 = 8 machines  

machines * 2 walls = 16

We can fit 20+16 machines = 36 machines not 40

Answer:

see explanation

Step-by-step explanation:

Calculate the slopes between pairs of the 3 points using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)

m = [tex]\frac{9-3}{-3-(-9)}[/tex] = [tex]\frac{6}{-3+9}[/tex] = [tex]\frac{6}{6}[/tex] = 1

Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)

m = [tex]\frac{9-1}{-3-5}[/tex] = [tex]\frac{8}{-8}[/tex] = - 1

If lines are perpendicular then the product of their slopes = - 1 , then

1 × - 1 = -1

Thus there is a right angle between the 2 lines

Then triangle is right- angled

Answer:

number of child tickets sold on saturday is 21

number of adult tickets sold on saturday is 42

Step-by-step explanation:

Let's assume

number of child tickets sold on saturday is x

number of adult tickets sold on saturday is y

On saturday, twice as many adult tickets as child tickets were sold

so, we get

child admission is $6.30 and adult admission is $9.60

a total sales of $535.50

we get

now, we can plug y=2x

now, we can solve for x

now, we can find y

so,

number of child tickets sold on saturday is 21

number of adult tickets sold on saturday is 42.........Answer

Answer:

66.9 degrees

Step-by-step explanation:

The Law of Sines states that a/sinA = c/sinC. Plugging in the values for c, a, and M < A, we get:

71/sin40 = 102/sinC

Cross multiplying, we get:

102(sin40deg) = 71(sinC)

Now, we simplify the left side and get:

65.56 = 71(sinC)

Next, we divide 65.56 by 71 to get:

0.92 = sinC

Taking the inverse sign we get:

C = 66.9 degrees

Answer:

2 2

1 -3

Step-by-step explanation:

2b=[4 4]

2 -6

b=[4/2 4/2]

2/2 -6/2

b=[2 2]

1 -3

Answer:

8

Step-by-step explanation:

total: 28 water attractions

pools: p

game areas: p + 2

water slides: 50% of 28 = 14

14 + p + p + 2 = 28

2p = 12

p = 6

game areas:

p + 2 = 6 + 2 = 8