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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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What is the value of X in the following: 7x-8 = 14+9x

LekaFEV [45]

Answer:

x = -11

Step-by-step explanation:

7x-8 = 14+9x

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3 years ago

MN and KL are parallel. If JM = 6, MK = 12, and LN = 18, what is NJ?

Galina-37 [17]

6/12=X/18
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3 years ago

Read 2 more answers

a manufacturer has determined that if his company sells x items per day then their profit is given by P=-x^2+ 700 x-10000 euros.

Radda [10]

Answer:

Step-by-step explanation:

To find the minimum amount of items, x, that need to be sold for the manufacturer to make a profit, we can use the quadratic formula

$x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}; x= \frac{-b-\sqrt{b^{2}-4ac } }{2a}$

$x= \frac{-700+\sqrt{700^{2}-4(a)(-10000) } }{2(1)}; x= \frac{-700-\sqrt{700^{2}-4(a)(-10000) } }{2(1)}$

$x= \frac{-700+\sqrt{530000} }{2}; x= \frac{-700-\sqrt{530000} }{2}$

$x=\frac{-700+100\sqrt{53} }{2}; x=\frac{-700-100\sqrt{53} }{2};$

$x=-350 + 50\sqrt53 = 14.005; x = -350 - 50\sqrt53 = -714.005$

In context of the problem, we can only rely on the positive value, as the negative value would lead to a loss of profit.

$(-714.005)^2+700(-714.005)-10000=-0.360$

Furthermore, we must round to the nearest whole number, as you cannot make part of an item.

Lastly, if you were to plug in 14 into the equation for Profit, you would still have a negative number (i.e. a negative profit), thus requiring the manufacturer to make no less than 15 items to make a profit:

$(14)^2+700(14)-10000=-4\\\\(15)^2+700(15)-10000=725$

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2 years ago

What is the equation of a line that passes through (1,5) and (3,11)? Show work please.

jekas [21]

First, find the gradient/slope:
Use slope formula:
m=(y2-y1)/(x2-x1)
=(11-5)/(3-1)
=6/2
=3
Then use the line equation formula:
y=mx+c
You can substitute (1,5) if you like, also must substitute the slope as well!
5=3x1+c
c=2
Then find the full equation, which gives you the answer:
y=3x+2

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3 years ago

Order these units from smallest to largest:

Veronika [31]

The units are ordered smallest to largest from top to bottom:
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Millimeter (mm) = 1 x 10⁻³ meters
Centimeter (cm) = 1 x 10⁻² meters
Decimeter (dm) = 1 x 10⁻¹ meters
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Kilometers (Km) = 1 x 10³ meters

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3 years ago