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3 years ago

The least of 3 consecutive integers is a, and the greatest is z. What is the value of a + 2z/ 2 in terms of a?

Mathematics

1 answer:

jasenka [17]3 years ago

4 0

Answer:

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Step-by-step explanation:

least of 3 consecutive integers is a, and the greatest is z

if a is the least one

we know that integers differ by value of 1.

example -2, -1, 0, 1,2

they all differ by

then next consecutive integer will be a+1

third integer will be second integer +1 = a+1 + 1 = a+2

Thus, 3 consecutive integer

a , a+1, a+2

but given that greatest is z

thus, a+2 is greatest and hence

a+2 = z

we have to find value of a + 2z/ 2 in terms of a

a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.

The value of a + 2z/ 2 in terms of a is (3a+4)/2

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Don't get this

kap26 [50]

I'll talk you through it so you can see why it's true, and then
you can set up the 2-column proof on your own:

Look at the two pointy triangles, hanging down like moth-wings
on each side of 'OC'.

-- Their long sides are equal, OA = OB, because both of those lines
are radii of the big circle.

-- Their short sides are equal, OC = OC, because they're both the same line.

-- The angle between their long side and short side ... the two angles up at 'O',
are equal, because OC is the bisector of the whole angle there.

-- So now you have what I think you call 'SAS' ... two sides and the included angle of one triangle equal to two sides and the included angle of another triangle.
(When I was in high school geometry, this was not called 'SAS' ... the alphabet
did not extend as far as 'S' yet, and we had to call this congruence theorem
"broken arrow".)

These triangles are not congruent the way they are now, because one is
the mirror image of the other one. But if you folded the paper along 'OC',
or if you cut one triangle out and turn it over, it would exactly lie on top of
the other one, and they would be congruent.

So their angles at 'A' and at 'B' are also equal ... those are the angles that
you need to prove equal.

5 0

3 years ago

What is the number 154 798 105 in expanded notation

Rama09 [41]

Expanded form:

1 × 100,000,000
+ 5 × 10,000,000
+ 4 × 1,000,000
+ 7 × 100,000
+ 9 × 10,000
+ 8 × 1,000
+ 1 × 100
+ 0 × 10
+ 5 × 1

I hope it helps :)

4 0

3 years ago

What values of y satisfy this equation?<br><br> 3y - 14 = 16

TiliK225 [7]

Answer:

By making y alone

Step-by-step explanation:

3y-14=16

+14 +14

3y= 30

divide 3 on both sides

y=10

Hope this helps!

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3 years ago

The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with

NISA [10]

Answer:

a) 0.125

b) 7

c) 0.875 hr

d) 1 hr

e) 0.875

Step-by-step explanation:l

Given:

Arrival rate, λ = 7

Service rate, μ = 8

a) probability that no requests for assistance are in the system (system is idle).

Let's first find p.

a) ρ = λ/μ

$\frac{7}{8} = 0.875$

Probability that the system is idle =

1 - p

= 1 - 0.875

=0.125

probability that no requests for assistance are in the system is 0.125

b) average number of requests that will be waiting for service will be given as:

λ/(μ - λ)

$= \frac{7}{8 - 7}$

= 7

= λ/[μ(μ - λ)]

$= \frac{7}{8(8 - 7)}$

= 0.875 hour

(d) average time at the reference desk in minutes.

Average time in the system js given as: 1/(μ - λ)

$= \frac{1}{(8 - 7)}$

= 1 hour

(e) Probability that a new arrival has to wait for service will be:

λ/μ =

${7}{8}$

= 0.875

5 0

3 years ago

Is EFGH below a rectangle

poizon [28]

Answer:

D. No, because EFGH is a parallelogram but it’s diagonals are not congruent

Step-by-step explanation:

The differences between the end points of the diagonals are ...

F -H = (1, 1) -(2, -5) = (1 -2, 1 -(-5)) = (-1, 6)

G -E = (4, -2) -(-1, -2) = (4 -(-1), -2 -(-2)) = (5, 0)

The length of FH is more than 6, the length of GE is exactly 5. The diagonals are different length, so the figure cannot be a rectangle.

The midpoints of the diagonals will be in the same place if the sum of their end points is the same. (Dividing each sum by 2 gives the midpoint of that segment.)

F+H = (1, 1) +(2, -5) = (3, -4)

G+E = (4, -2) +(-1, -2) = (3, -4)

The diagonals bisect each other (have the same midpoint), so the figure is a parallelogram.

EFGH is a parallelogram, but not a rectangle: its diagonals are not congruent.

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2 years ago