Solve the Equation 4(2x+1)=5x+9+3x?

frutty [35]

Step-by-step explanation:

there are several things to be considered to solve this.

the strategy is to caucuses the volume of the full "box", and then to deduct the 3-dimensional triangle that is "cut off" from the oil.

then we know the volume of the pool.

next step is to calculate the volume of a "box" with the same layout but is only 20 cm deep.

then we know how much volume can be pumped out in 30 minutes.

and then we divide the whole volume by that small volume to see how many 30-minues units are needed to empty the whole pool.

and then we transform the 30- minutes units into actual minutes or hours.

so, let's begin :

the whole box's volume is

2×1×1.4 = 2.8 m³

the volume of the 3-D triangle we need to subtract is the area of the triangle × width of the pool (this pool width is the height of the 3-D triangle).

2×(1.4 - 0.6) × 1 / 2 = 2×0.8 × 1 / 2 = 1.6/2 = 0.8 m³

so, the volume of the pool is

2.8 - 0.8 = 2 m³

now, how much volume can the pump eliminate in 30 minutes ?

the content of a box

1×2×0.2 = 0.4 m³

as 20 cm = 0.2 m

so, the pump pumps out 0.4 m³ in 30 minutes.

and we need to empty 2 m³.

that means we need

2 / 0.4 = 5

30-minues units = 5×30 = 150 minutes = 2.5 hours.

Colin has to wait 2.5 hours (150 minutes) to empty the complete pool.

6 0

3 years ago

Find the length of AC Use that length to find the length of

Gekata [30.6K]

Answer:

1. AC = 5 cm

2. CD = 10.7 cm

Step-by-step explanation:

Looking at the left triangle, we see that AC is the side "opposite" of the angle given and AB is the "hypotenuse".

Which trigonometric ratio relates "opposite" to "hypotenuse"?

<em />

So we can write:

$Sin(30)=\frac{AC}{10}\\AC=10*Sin(30)$

We know from 30-60-90 triangle, Sin(30) = 0.5, so we have:

$AC=10*Sin(30)\\AC=10*0.5\\AC=5$

Thus,

AC = 5 cm

Now, looking at right side triangle, we know AC, side "opposite" and we want to find CD, side "adjacent". Which trig ratio relates these 2 sides?

Thus we can write:

$Tan(25)=\frac{5}{CD}\\CD=\frac{5}{Tan(25)}$

Now using calculator, we get our answer to be:

CD = $\frac{5}{Tan(25)}=10.7$

So

CD = 10.7 cm

8 0

3 years ago

Find the values of C for which C(x+2)—(x+2)(x–2)=0 has just one solution. please help me ASAP

CaHeK987 [17]

<h3>Answer: C = -4</h3>

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

Work Shown:

C(x+2) - (x+2)(x-2) = 0

(x+2)(C-(x-2)) = 0

(x+2)(C-x+2) = 0

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

3 0

2 years ago

Find the value of z.

Leokris [45]

The exterior angle at the intersection of the tangent and secant has a measure that is half the difference between the intercepted arcs.

... ((10x+20) -80)/2 = 2x+15

... 5x -30 = 2x +15

... 3x = 45

... x = 15

So, the unknown arc to the right has measure

.. 10x + 20 = 10·15 +20 = 170

And the arcs of the circle total 360°.

... 80 + z + 170 = 360

... z = 360 - 250 = 110 . . . subtract 250 from both sides

The appropriate choice for the value of z is

... B. 110

3 0

3 years ago

There are 20 runners in a race for 1st, 2nd, 3rd, and 4th place. How many different arrangements can be made?

Setler [38]

Answer: 160

Step-by-step explanation:

3 0

3 years ago