The ages Edna, and Elsa are consecutive integers. The sum of their ages is 114. What are their ages?

1. A quadrilateral has vertices A(0,0), B(8,0),C(7,5), and

babunello [35]

The formula for the distance between two points is

$d(A,B) = \sqrt{(A_x-B_x)^2+(A_y-B_y)^2}$

Note that, if two points have one coordinate in common, this formula simplifies to

$d(A,B) = |A_x-B_x|,\quad d(A,B)=|A_y-B_y|$

(the first if they share the y coordinate, the second if they share the x coordinate).

So, these are the lengths of the sides:

$d(A,B)=|8-0|=8$

(because they share the y coordinate)

$d(B,C) = \sqrt{(8-7)^2+(0-5)^2}=\sqrt{1+25}=\sqrt{26}$

(standard formula)

$d(C,D)=|7-3|=4$

(because they share the y coordinate)

$d(A,D) = \sqrt{(0-3)^2+(0-5)^2}=\sqrt{9+25}=\sqrt{34}$

5 0

3 years ago

Decimals- do i move the decimal when adding or multiplying

EastWind [94]

Answer:

when adding you just line the decimals up like this, let's say you had to add 1 to 2.58.

2.58

+ 1 .00

3.58

when multiplying you might have to move it, say you had to multiply 1.5 by 2.2. (you don't have to line up the decimals like with addition)

1 .5

× 2.2

30

+ 300

3.30

1.5 has one decimal place and 2.2 also has one decimal place so you put those 2 decimal places in your answer.

sorry if this is a bit confusing lol

6 0

3 years ago

Jean-Patrick found an old unopened bag of lawn fertilizer in his shed. The bag weighs 36 pounds, and the instructions claim

balandron [24]

Answer:

He needs to use 25.2 pounds to fertilize his lawn.

Step-by-step explanation:

In order to solve this problem we can use a rule of three in such a way that the content of the bag (36 pounds) can cover 10,000 ft² in the same proportion as "x" pounds can cover 7,000 ft², where "x" is the amount of fertilizer he needs to use.

36 pounds -> 10,000 ft²

x pounds -> 7,000 ft²

36/x = 10000/7000

10000*x = 36*7000

x = 36*7000/10000

x = 25.2 pounds

He needs to use 25.2 pounds to fertilize his lawn.

3 0

3 years ago

Read 2 more answers

The graph shows the number of cookies eaten and the number of calories consumed:

Sergeu [11.5K]

Answer:

c

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

a band of 45 ewoks crash-landed in the forest last night. this sounds like a small problem, but the population will grow at the

kogti [31]

Given Information:

Starting population = P₀ = 45

rate of growth = 22%

Required Information:

Population every five years from this year to the year 2050 = ?

Answer:

$Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\$

Step-by-step explanation:

The population growth can be modeled as an exponential function,

$P(t) = P_0e^{rt}$

Where P₀ is the starting population, r is the rate of growth of the population and t is the time in years.

We are given that starting population of 45 and growth rate of 22%

$P(t) = 45e^{0.22t}$

Assuming that the starting year is 2020,

$Year \: 2020 = P(0) = 45e^{0} = 45\\\\Year \: 2025 = P(5) = 45e^{0.22*5} = 135\\\\Year \: 2030 = P(10) = 45e^{0.22*10} = 406\\\\Year \: 2035 = P(15) = 45e^{0.22*15} = 1,220\\\\Year \: 2040 = P(20) = 45e^{0.22*20} = 3,665\\\\Year \: 2045 = P(25) = 45e^{0.22*25} = 11,011\\\\Year \: 2050 = P(30) = 45e^{0.22*30} = 33,079\\\\$

Therefore, the starting population of ewoks was 45 in 2020 and increased to 33,079 by 2050 in a time span of 30 years.

8 0

3 years ago