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maxonik [38]
3 years ago
8

Question: The meaning of four consecutive even numbers is 15.

Mathematics
1 answer:
nasty-shy [4]3 years ago
8 0
First, a bit of housekeeping:

<span>The meaning of four consecutive even numbers is 15.  Wouldn't that be "mean," not meaning?  Very different concepts!

The greatest of these numbers is _______ a^1

"a^1" means "a to the first power.  There are no powers in this problem statement.  Perhaps you meant just "a" or "a_1" or a(1).


The least of these numbers is ______a^2.
No powers in this problem statement.  Perhaps you meant a_2 or a(2)


In this problem you have four numbers.  All are even, and there's a spacing of 2 units between each pair of numbers (consecutive even).

The mean, or arithmetic average, of these numbers is (a+b+c+d) / 4, where a, b, c and d represent the four consecutive even numbers.  Here this mean is 15.  The mean is most likely positioned between b anc c.


So here's what we have:  a+b+c+d
                                         ------------- = 15
                                                 4

This is equivalent to a+b+c+d = 60.

Since the numbers a, b, c and d are consecutive even integers, let's try this:

a + (a+2) + (a+4) + (a+6) = 60.    Then 4a+2+4+6=60, or 4a = 48, or a=12.

Then a=12, b=14, c=16 and d=18.  Note how (12+14+16+18) / 4 = 15, which is the given mean.

We could also type, "a(1)=12, a(2)=14, a(3) = 16, and a(4) = 18.


</span>
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Naddika [18.5K]

Answer:

x=3

Step-by-step explanation:

\frac{6x+6}{32} =\frac{9x-9}{24}

Cross mutiply and x is equal to 3

6 0
3 years ago
To rent a certain meeting room a college charges a reservation fee of $33 and an additional fee of $9.80 per hour the club wants
sammy [17]

Answer:

They must rent for less than 7 hours

Step-by-step explanation:

The charge for the room is the fee plus the hourly rate times the hour

f = 33+9.80t

This must be less than 101.60

101.60> 33+9.80t

Subtract 33 from each side

101.60-33> 33-33+9.80t

68.6> 9.80t

Divide each side by 9.8

68.8/9.8 > t

7>t

They must rent for less than 7 hours

7 0
2 years ago
I will mark brainliest IF CORRECT
umka2103 [35]

Answer:

1 - (π/6) - (√3/4)

Step-by-step explanation:

First, calculate the area of ABCD. That's just 1*1 = 1 un^{2}

Then, we are told that arcs BD and AC are circular, meaning they are portions of a circle. Therefore, let's redraw this image a little. Look below for the image.

Essentially, what I've done is created an equilateral triangle and two sectors. You may be wondering why the triangle is equilateral. Well, we firstly know it's isosceles because the two original arcs are circular and congruent. Their overlap creates two congruent lines that can be extend from point M to the vertices A and D. These two lines also happen to be radii of the quarter circles because the two sectors have AM AND AD as radii. AM and AD = 1, so AMD is an equilateral triangle.

Draw altitude OD. This is a right angle. Since equilateral triangles are also isosceles triangles, and isosceles triangles have the property of sharing the median to base and altitude to base, we can say that OD = \frac{1}{2} AD = \frac{1}{2}. MD = 1, so this triangle is a 30-60-90 triangle. Why? This is because of the 30º angle converse theorem. The shorter leg is half of the hypotenuse MD, so <OMD is a 30º angle, making <ODM a 60º angle and inevitably <MDC a 30º angle (because <D is a right angle) and <ABM as well because the two sectors are congruent.

Because m<ABM = m<MDC = 30º, these two sectors are 30/360 of the individual circles or 1/12 of the original circles, which have areas of π (because 1^2*π = π). Each is 1/12π, combined they are 1/6π.

The area of the equilateral triangle is √3/8. This is because MO can be calculated, using the 30-60-90 ratios, to be √3/2. (1 * √3/2)/2 = (√3/2)/2 = √3/4; this uses the area of a triangle. Now, time to calculate the shaded area.

The area of the square is 1, the area of the sectors π/6, and the equilateral triangle √3/4. Subtract the equilateral triangle and sectors' areas from the area of the square to be left with the remaining shaded part. 1-(π/6)-(√3/4) is your final answer. To put that a little more cleanly below in the image.

Hope this helps, have a great day.

3 0
2 years ago
PLEASE HELP ASAP!!!!!!!
umka2103 [35]

Answer:

dum there is part A prat B and C

Step-by-step explanation:

5 0
3 years ago
Train a is traveling at 30 mph faster than train b. If train a travels 350 miles in the same amount of time that train b travels
GalinKa [24]

Answer:

20 mph

Step-by-step explanation:

Let speed of Train a = Va mph

Let speed of Train b = Vb mph

Va = Vb + 30

Let time taken for Train a = Ta

Let time taken for Train b = Tb

time taken = distance travelled/speed

Ta = 350/Va = 350/(Vb+30)

Tb = 140/Vb

But they both travel in the same amount of time.

So, Ta = Tb

\frac{350}{v_{b} + 30}=\frac{140}{v_{b}}

Cross multiply

350v_{b} = 140(v_{b} + 30)\\\\350v_{b} = 140v_{b} + 4200\\\\350v_{b} -140v_{b} = 4200\\\\210v_{b} = 4200

Divide both sides by 210

\frac{210v_{b} }{210} \frac{4200}{210} \\\\v_{b} = 20 mph

4 0
3 years ago
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