Five students and two teachers pose for a picture.in how many ways can they line up side by side for a picture. 2. In how many ways can they line up if they must have the teachers on both sides of the picture? 3.what is the probability that the two teachers occupy two of the three middle slots?

Answer:

x = 5

Step-by-step explanation:

Sides of large triangle: 4x and 15

Corresponding sides of small triangle: 3x + 1 and 12

[tex] \dfrac{4x}{15} = \dfrac{3x + 1}{12} [/tex]

[tex] 60 \times \dfrac{4x}{15} = 60 \times \dfrac{3x + 1}{12} [/tex]

[tex] 16x = 15x + 5 [/tex]

[tex] x = 5 [/tex]

yes, it's a scaled version of a triangle with side lengths 3, 4 and 5.

by a factor of 20

a triangle with side lengths 3, 4 and 5 is a right triangle and it holds true for a²+b²=c², because 9+16=25

the 3,4,5-triangle is the simplest right triangle to calculate it's numbers seem somehow elegant.

the triangle in your problem is just a bigger version of it (wich means all angles stay the same).

My reasoning is lacking, but I'm sure

Answer:

wht yr u in tis is too hard yk

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos x=sinx

divide by cos x

1=tan x

tan x=1

[tex]tan x=1=tan \frac{\pi }{4}=tan (n\pi +\frac{\pi }{4})\\x=n\pi +\frac{\pi }{4} ,\\where~n~is~an~integer.[/tex]

Answer:

the square root of 85 (so 85 is the answer)

Step-by-step explanation:

You can use the pythagorean theorem to find the height. So the sides of the triangle would contain the radius (4/2 = 2) and 9.

so, 2 squared plus 9 squared = 85

I hope this helps!

Answer:

D=-90+22/7

Step-by-step explanation:

D= 22/7×d-90

D= -90+22d/7

Answer:

y = 2[tex](x - 3)^{2}[/tex] - 1

Step-by-step explanation:

y = 2[tex]x^{2}[/tex] - 12x + 16  

y = 2([tex]x^{2}[/tex] - 6x + 8)        ( Factor out 2 )

y + 9= 2([tex]x^{2}[/tex] - 6x + 9) + 8 ( Complete the square [tex](\frac{-b}{2} )^{2}[/tex] ) Add 9 both sides  

y + 9 = 2 [tex](x - 3)^{2}[/tex] + 8      (Subtract 9 each side)  

y = 2 [tex](x - 3) ^{2}[/tex] - 1         ( simplify )

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

[tex]2^{5}[/tex]

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

Answer:

$5084745.76271

Step-by-step explanation:

Given data

Final amount= $6000000

Rate=6%

Time= 3 years

Now let us find the initial amount which is the principal

using the simple interest formula we have

6000000 = P(1+0.06*3)

6000000 =P(1+0.18)

6000000 =P*1.18

P= 6000000 /1.18

P=$5084745.76271

Hence the initial deposite is $5084745.76271

Answer:

Slope = 4

Step-by-step explanation:

The slope of a linear equation can be calculated as;

m = y2-y1/x2-x1

What we have to do here is to select any two points ;

(x1,y1) = (3,8)

(x2,y2) = (6,20)

m = (20-8)/(6-3) = 12/3 = 4

Answer:

20

Step-by-step explanation:

9*2-3+5

18-3+5

15+5

20

Answer:

Its 20

Step-by-step explanation:

9 x 2 = 18

18 - 3 = 15

15 + 5 = 20

Answer:

A ; 21

Step-by-step explanation:

Here, the side facing the right angle is the hypotenuse and it has a measure of length 42

The side facing the missing angle is the opposite and it has a length of 15

The trigonometric ratio that connects the hypotenuse and the opposite is the sine

The sine of an angle is the ratio of the opposite to the hypotenuse

Thus;

sine ? = 15/42

sine ? = 0.357

? = arc•sim 0.357

? = 21 degrees

Answer: they are abt the same its all abt percentage now- Pitcher A

Step-by-step explanation: more water lessens the strength

Step-by-step explanation: X=10 DEGREES FOR THE SMALLER ANGLE. 8*10=80 DEGREES FOR THE LARGER ANGLE.

Answer:it’s 20 and 160 I’m doing ixl and this was the correct answer.

Step-by-step explanation:

Answer: X= 3/4

Simplified: 1/3

Answer:

The formula to find the area of a rectangle is A=BH

so the area equals the base times the height

Hope This Helps!!!

Given:

2.2 pounds = 1 kilogram

Weight of Mary = 120 pounds.

To find:

The weight of Marry in kilograms.

Solution:

We have,

2.2 pounds = 1 kilogram

Using this conversion, we get

1 pound = [tex]\dfrac{1}{2.2}[/tex] kilogram

120 pound = [tex]\dfrac{1}{2.2}\times 120[/tex] kilogram

                  = [tex]\dfrac{120}{2.2}[/tex] kilogram

                  [tex]\approx 54.54[/tex] kilogram

Therefore, the weight of Mary is about 54.54 kilograms.

Answer:

In this case, we can do substitution.

Step-by-step explanation:

For the first one, (s - t)(x) = ((x - 5) - 4x^2)(x) = x^2 - 21x

For the second one, (s*t)(x) = ((x - 5) *4x^2)(x) = 4x^4 - 20x^3

And for the last one,  (s+t)(-2) = ((x - 5) + 4x^2)(-2) = -8x^2 - 2x + 10

Hope your happy with the answer :)

Step-by-step explanation:

(1/2) / (1/3) = (1/2)(3/1) = 3/2 miles per hour = 1.5 miles per hour

Answer:

Step-by-step explanation:

to find the unit rate, which is what we are looking for, we have to divide the number of miles by the number of hours. Specifically:

[tex]\frac{\frac{1}{2} }{\frac{1}{3} }[/tex] and to work this out, we bring up the bottom fraction and flip it to multiply, giving us:

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{1}[/tex] which is [tex]\frac{3}{2}[/tex] miles per hour (which is the same thing as walking a mile and a half every hour). The choice you're looking for is the one that reflects 3/2 miles per hour. (I can't see which choice it is; they're too small!)

Answer:

C=20

Step-by-step explanation:

Answer:

a. 18

Step-by-step explanation:

AB+BC = AC

x + x = 36

2x = 36

x = 36/2

x = 18

Step-by-step explanation:

The question is not clear to me

Answer:

x = 3

Step-by-step explanation:

x + 9x + 5 = 35

=> x + 9x = 35 - 5

=> x + 9x = 30

=> 10x = 30

=> x = 30/10

=> x = 3

Answer:

x = 3

Step-by-step explanation:

Combine like terms. Like terms have same variable with same exponent.

Here x and 9x are like terms

x + 9x + 5  =  35

     10x + 5 = 35

Subtract 5 from both sides

10x + 5 - 5 = 35 - 5

       10x = 30

Divide both sides by 10

10x/10 = 30/10

x = 3

Answer:

The value belonging to the green box is b

Step-by-step explanation:

QP uses the points Q and P

Q is (0,-a)

P is (b,-c)

The distance between the two points can be calculated using the distance formula;

D = √(x2-x1)^2 + (y2-y1)^2

(x1,y1) = (0,-a)

(x2,y2) = (b,-c)

D = √(b-0)^2 + (-c + a)^2

D = √(b)^2 + (-c + a)^2

Answer:

y=-2x+12

Step-by-step explanation:

This is an equation in slope-intercept form:

y=mx+b (where m is the slope and b is the y-intercept)

We are given the slope, -2.

y=-2x+b

We plug in the values (5,2):

2=(-2)*5+b

2=-10+b

b=12

The equation is:

y=-2x+12

Answer:

22

Step-by-step explanation:

1.) -2²-9(-2)

2.) -2(-2)+18

3.) 4+18

4.) 22