Credit becomes a problem when

If x = 2a - b^2, then b equals

kvasek [131]

X = 2a - b²
x - 2a = b²
√x-2a = b

Just to clarify, all of x-2a is under the square root.

7 0

3 years ago

A box contains 13 red hats, 15 white hats, 18 blue hats, and 14 brown hats. Nina randomly chooses a hat from the box.

bazaltina [42]

13 + 15 + 18 +14 = 60 total hats

15 are white

60-15 = 45 hats that are not white

45/60 reduces to 3/4

3/4 =0.75 probability the hat will not be white

4 0

3 years ago

Aiko stands 5 m from a tree. At that distance, the angle of elevation from the ground to the top of the tree is 80°.

denis23 [38]

Answer:

$\boxed {\boxed {\sf About \ 28.36 \ meters }}$

Step-by-step explanation:

Assuming the tree is perpendicular to the ground, we can use the right triangle trigonometric ratios to find the tree's height.

sin(θ)= opposite/hypotenuse
cos(θ)= adjacent/hypotenuse
tan(θ)= opposite/adjacent

Now, let's draw a diagram. We know Aiko is 5 meters from the base of the tree. From there, the angle to the top of the tree is 80 degrees. We are looking for x, the tree's height. The diagram attached is not to scale.

We base the sides off of the angle. x is opposite of 80 degrees and 5 is adjacent. Therefore we must use tangent.

$tan(\Theta)=\frac{opposite}{adjacent}$

opposite=x
adjacent=5 m
θ=80

Substitute in the known variables.

$tan(80)=\frac{x}{5 \ m }$

We want to find x, the height of the tree. Therefore we need to isolate that variable.

x is being divided and the inverse operation is multiplication. Multiply both sides of the equation by 5 meters.

$5 \ m* tan(80)=\frac{x}{5 \ m }* 5 \ m$

$5 \ m* tan(80)=x$

$5 \ m *5.67128182=x$

$28.3564091 \ m = x$

The question asks for an approximation, so let's round to the nearest hundredth.

The 6 in the thousandth place tells us to round the 5 to a 6.

$28.36 \ m \approx x$

The tree is about 28.36 meters tall.

3 0

3 years ago

The diagram below gives the dimensions of a swimming pool. 18 ft , 20ft, 36ft (c) What is the total area of the swimming pool? E

WARRIOR [948]

The picture in the attached figure

Part 1) What is the total area of the swimming pool?

we know that
area of the swimming pool=area rectangle-area semi circle

area rectangle=20*36-----> 720 ft²

area semicircle=pi*r²/2
r=18/2----> 9 ft
area semicircle=pi*9²/2----> 127.17 ft²

area of the swimming pool=720 ft²-127.17 ft²----> 592.83 ft²

the answer Part 1) is
The area of the swimming pool is 592.83 ft²

Part 2) What is the perimeter of the swimming pool?

perimeter of the swimming pool=perimeter of rectangle-18 ft+perimeter semi circle
perimeter of rectangle=2*[20+36]---> 112 ft

perimeter semi circle=2*pi*r/2----> pi*r
r=9 ft
perimeter semi circle=pi*9----> 28.26 ft
so
perimeter of the swimming pool=112 ft-18 ft+28.26 ft----> 122.26 ft

the answer Part 2) is
122.26 ft

6 0

3 years ago

How would you graph (on a number line) (x-8)(x-8)<0??

Marta_Voda [28]

Answer:

The graph is the empty number line (no solution)

Step-by-step explanation:

Your expression is (x-8)² < 0. There are no real numbers that give a negative value when squared. There is NO SOLUTION. The graph is empty.

_____

Comment on quadratic inequalities

In general the inequality (x-a)(x-b) < 0 will have a solution when one factor is negative and the other is positive. In general, that will be the case for values of x that are strictly between a and b. In your inequality, that would require you graph numbers that are between 8 and 8. There are none.

5 0

4 years ago