All categories

2 years ago

Find the midpoint of the segment that has endpoints at (a+b, a-b) and (a, b).

Mathematics

1 answer:

Hunter-Best [27]2 years ago

5 0

Answer:

((2a+b)/2 , a/2)

Step-by-step explanation:

The midpoint is the mean/average of both the x and y values.

Our x values are a+b and a

Our y values are a-b and b

The midpoint x value is (a+b + a ) /2 = (2a + b)/2

The midpoint y value is (a-b + b) /2 = (a)/2

The midpoint combines these two values to get ((2a+b)/2 , a/2) as our midpoint

You might be interested in

Find the 61st term of -12, -28, -44,

Citrus2011 [14]

Answer:

$a_{61}=-972$

Step-by-step explanation:

<u>Arithmetic Sequences</u>

The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.

The equation to calculate the nth term of an arithmetic sequence is:

$a_n=a_1+(n-1)r$

Where

an = nth term

a1 = first term

r = common difference

n = number of the term

We are given the first terms of a sequence:

-12, -28, -44,...

Find the common difference by subtracting consecutive terms:

r = -28 - (-12) = -16

r = -44 - (-28) = -16

The first term is a1 = -12. Now we calculate the term n=61:

$a_{61}=-12+(61-1)(-16)$

$a_{61}=-12-60*16=-12-960$

$\mathbf{a_{61}=-972}$

6 0

2 years ago

You put $500 in the bank, where it ears 1.5% simple interest every year. How long until your money will triple?

zzz [600]

Answer:

133.33 years

Step-by-step explanation:

Given that:

Principal = $500

Interest rate (r) = 1.5% = 0.015

Triple amount of principal = $500 * 3 = $1500 = final amount (A)

Number of years (t) =?

Using the relation :

A = P(1 + rt)

1500 = 500(1 + 0.015t)

1500 / 500 = 1 + 0.015t

3 = 1 + 0.015t

3 - 1= 0.015t

2 = 0.015t

2 / 0.015 = 0.015t / 0.015

133.333 = t

133.33 years

3 0

2 years ago

The coordinates of points A

Svetllana [295]

Answer:

Distance=13.60

Step-by-step explanation:

The Distance between the two points in coordinate system is find by using the distance formula.

If two points $(x_1,y_1)$ and $(x_2,y_2)$ are given:

$Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

For the points:

$(-7, 5)\\ and \\(4, -3)$

$Distance=\sqrt{(4-(-7))^2+(-3-5)^2}\\\\ =\sqrt{(4+7)^2+(-8)^2} \\\\=\sqrt{11^2+(-8)^2} \\\\=\sqrt{121+64}\\\\ =\sqrt{185}\\\\ =13.60$

The distance between the points is 13.60

7 0

2 years ago

In a population of 1000 snails, tests of snail color genes show that 160 snails are AA, 480 are Aa and 360 are aa. What is the f

Kipish [7]

Answer:

Option C.

Step-by-step explanation:

Total population = 1000 snails

AA = 160 snails

Aa = 480 snails

aa = 360 snails

Frequency of each type.

$AA=\dfrac{160}{1000}=0.16$

$Aa=\dfrac{480}{1000}=0.48$

$aa=\dfrac{360}{1000}=0.36$

Now, we get

$A^2=0.16\Rightarrow A=\sqrt{0.16}=0.4$

he frequency of the A allele in this population is 0.4.

Therefore, the correct option is C.

3 0

2 years ago

Please helpp middle school math<br><br>suppose 4<a<7. find all the possible values of 15-2a

bixtya [17]

9514 1404 393

Answer:

1 < 15 -2a < 7

Step-by-step explanation:

There are a couple of ways you can do this.

1) Put the minimum and maximum values of a into the expression to see what its corresponding values are:

15-2a for a=4:

15-2(4) = 7

15-2a for a=7:

15-2(7) = 1

Then ...

1 < 15-2a < 7

2) Solve for a in terms of the value of 15-2a, then impose the limits on a.

x = 15 -2a

2a = 15 -x

a = (15 -x)/2

Now, impose the given limits:

4 < (15 -x)/2 < 7

8 < 15 -x < 14 . . . multiply by 2

-7 < -x < -1 . . . . . . subtract 15

7 > x > 1 . . . . . . . . multiply by -1

1 < 15-2a < 7 . . . . . use x=15-2a

_____

The vertical extent of the attached graph is the range of possible values of 15-2a. It goes from 1 to 7.

8 0

3 years ago