RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan?

Step-by-step explanation:

Answer 1 to find the base to apply the Pythagoras theorem..of finding length..

Hypotenuse²= Base²+ Height²

So,

(H)²= (B)²+(H)²

12²= 8²+y²

144-64=y²

80=y²

√80= y

√2×2×2×2×5= y

2×2√5= y ( take one 2 from each pair)

4√5= y

hope it helps...

Answer:

4 sqrt(5); 41.0

Step-by-step explanation:

Question 7:

Using Pythagoras theorem:

y = sqrt(12^2 - 8^2)

y = sqrt(80)

y = 4 sqrt(5)

Question 8:

A = Area rectangle + Area circle

A = 2.4 × 4.4 + pi × 4.4^2 ÷ 2

A = 10.56 + 9.68 pi

A = 41.0

Answer:

B

Step-by-step explanation:

-10 + 3x - x - 7x + 5x + 7 + 2x

combine like terms

-10 + 3x - x - 7x + 5x + 7 + 2x

-3 + 3x - x - 7x + 5x + 2x

the -7x and the 5x + 2x cancel out to 0, so for the x terms we are left with 3x -x to get 2x

= 2x - 3

Answer:

dame like y muchísimas estrella

Answer:

<L is 90°

Step-by-step explanation:

all angles at the center are twice the angles at the circumference and the angle at the center is 180 meaning the angle at the circumference will be half of 180

I hope this helps

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow (side)4[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 4(10)[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow 40km[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Surface\:Area=Perimeter\times Height[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Surface\:Area=40(9.4)[/tex]

[tex]\\ \qquad\quad\sf{:}\twoheadrightarrow Surace\:Area=384m^2[/tex]

Answer:

solving for x

Step-by-step explanation:

4 or -6

Answer:

x = 4

Step-by-step explanation:

Those absolute value signs are a trick, well at least for this problem. Solve it how you usually would. However, if +2 was -2 or +/-2, then you would need to pay attention. Basically, those signs make the whole equation incased positive no matter what.

Answer:

Step-by-step explanation:

let's try a:

-4*4x-4*(-17) - expand the distributing terms

-16x-4*(-17) - simplify

-16x-(-68) - simplify again

-16x+68 - remove parentheses

-16x+68 does not equal to 16x-68

lets try b:

-28x+3... dont know what u mean

lets try c:

13-34 first

-21

lets try d:

0-17

-17

lets try e:

-2x+(8-8)

-2x

fortunally dont know what you mean.

Answer:

Step-by-step explanation:

Tan(51) = opposite / adjacent

The adjacent side makes up the reference angle (51o)

The opposite side is not part of the reference angle

adjacent side = x

opposite side = 16

Tan(51) = 16 / x              Multiply both sides by x

x * Tan(51) = 16            Divide by tan 51

x = 16 / tan(51)

tan(51) = 1.2349

x = 16 / 1.2349

x = 12.96

Answer:

12.9

Step-by-step explanation:

Tan(51) = opposite / adjacent

The adjacent side makes up the reference angle (51o)

The opposite side is not part of the reference angle

adjacent side = x

opposite side = 16

Tan(51) = 16 / x            

Multiply both sides by x

x * Tan(51) = 16        

Divide by tan 51

x = 16 / tan(51)

tan(51) = 1.2349

x = 16 / 1.2349

x = 12.9

Answer:

- 14

Step-by-step explanation:

a = 3

a^2 - 6a - 5

= 3^2 - 6 ( 3 ) - 5

= 9 - 18 - 5

= 9 - 23

= - 14

Answer:

The base cost of the camera, exclusive of sales tax, is $160.

Step-by-step explanation:

Set up this equation and solve for x, which is the cost of the camera:

$3.20 = $0.02x [0.02 = 2%]

Solve the equation by dividing $3.20 by 0.02. The answer is $160.

Answer: $160 for the camera

Step-by-step explanation:

0.2x160=3.2

$160

Answer:

The answer would be (x-5, y-5)

Step-by-step explanation:

You can find this out by finding the difference between D(3,5) and D'(-2,1) (pr any other coordinate) which is -5 in both the x and y coordinates making the answer (x-5, y-5).

Answer:

Step-by-step explanation:

Let the equation be:

Multiply both sides by 4 and complete the square:

Since -3 = 1(-3) = (-1)*3, we have following options:

1)

Eliminate k by adding up equations:

2)

Eliminate k by adding up equations:

Answer:

C. Divide both sides by 3

Step-by-step explanation:

3x=12

3x/3=12/3

x=4

Answer:

A

Step-by-step explanation:

Heron's formula finds the area of any triangle.

Area = sqrt(s*(s - a)*(s-b)*(s-c) )

s = (a + b + c)/2

a = 8

b = 16

c = 12

s = 36/2 = 18

s-a = 18 - 8 = 10

s-b = 18 - 16 = 2

s-c = 18 - 12 = 6

Area = sqrt(18*10*2*6) = sqrt(2160)

Area = 12*sqrt(15)

Area = 46.4758

Now x is easily found. It is the altitude to 16

Area = 1/2 16 * h

46.4758 * 2 / 16 = h

h = 3*sqrt(15)/2

h= 5.81

Answer:

320 minutes (5 hours and 20 minutes).

Step-by-step explanation:

2 hours and 17 minutes = 137 minutes

137 + 84 + 99 = 320

Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.

Answer:

The markup is 81.25%

Step-by-step explanation:

Take the new price and subtract the original price

58 - 32

26

Divide by the original price

26/32

.8125

Change to percent form

81.25%

The markup is 81.25%

Answer:

p = q

Step-by-step explanation:

Angles in a triangle add up to 180°

For the left triangle:

180 = p + 20 + 80

p = 80

For the right triangle:

180 = q + 45 + 55

q = 80

Therefore, p = q

Answer:

Solution given:

x²+25=???

we have

formula

a²+b²=(a+b)²-2ab or (a-b)²+2ab

so

x²+25 =x²+5²=(x+5)²-2x*5=(x+5)²-10x

or

x²+25=x²+5²=(x-5)²+2x*5=(x-5)²+10x

:.

expressions is equal to x² +25 is

(x-5)²+10x

or

(x+5)²-10x

Answer:

51

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

B. [tex]4x^3}+\frac{x^2}{2}-3x+6[/tex]

Step-by-step explanation:

The polynomial is [tex]\frac{x^2}{2}-3x+4x^3}+6[/tex]

To write in Standard form, the greatest exponent goes first, down to the least.

The greatest exponent is 3, so [tex]4x^3[/tex] goes first.

[tex]4x^3}+\frac{x^2}{2}-3x+6[/tex] is what you end up with

Answer:

B

Step-by-step explanation:

I took the test.

Answer:

The inscribed angle intercepts the circle's radius is always 90

Step-by-step explanation:

Answer:

[tex]\sqrt{-16} +8[/tex]

[tex]=4i+8[/tex]

OAmalOHopeO

Answer:

These are the entervals of the people who are atleast adults and are mature enough to take the surevy seriosly and answer correctly

Step-by-step explanation:

Answer:

Initial speed is 32 m/s

At uniform speed, acceleration is 0, (a = 0).

When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.

From first equation of motion:

[tex]{ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}[/tex]

substitute:

[tex]{ \tt{2.78 = (a \times 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^{ - 2} }}[/tex]

from second equation of motion:

[tex]{ \boxed{ \bf{s = ut + \frac{1}{2} a {t}^{2} }}}[/tex]

substitute:

[tex]{ \tt{60000 = 1800u + ( \frac{1}{2} \times 0.0015 \times {1800}^{2}) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^{ - 1} }}[/tex]

Answer:

B. 1 1/2

Step-by-step explanation:

The post-image is clearly larger than the pre-image. The ratio of the post to the pre is 9 : 6 and 10 : 15, which are equal to 3 : 2, and equal to 1 1/2.

Answer:4 in each bad 2 left over

Step-by-step explanation:

Answer:

4 in each bag and 2 left over

Step-by-step explanation:

divide 14 by 3

3 goes into 14, 4 times

14 - 12 = 2

4 in each bag and then 2 left over

If you can give the proportion then it would be better.

I am asuming

8:x::9:36

Then 8:x::1:4

So x = 32

Answered by Gauthmath must click thanks and mark brainliest

Answer:

x = 32

Step-by-step explanation:

[tex]\frac{8}{x}[/tex] = [tex]\frac{9}{36}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )

x = 8 × 4 = 32