Tia climbed to the top of an observation tower overlooking a bird sanctuary and used the telescope at the top to observe two nests. The first nest was 400 meters away from the observation tower. Tia turned the telescope 135 degrees to observe the second nest, which was 300 meters away. How far apart are the two nests?

Congruent segments are LK=MK, LK=7x-10, KN=x+3, MN=9x-11, and KJ=28,  the LJ  will be-

LJ = 18 + 28 = 46

LJ = 18 + 28 = 46

These are  Congruent segments

Let J, K, L, M, N are points on the same line.

MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14

As LK = MK and LK = 7x - 10, then

7x - 10 = 8x - 14

8x - 7x = -10 + 14

x = 4

LJ = MK + KJ

MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18

LJ = 18 + 28 = 46

Congruent segments are segments which have the equal length. ≅ points that lie at the equal line are called collinear.

A theorem is a mathematical assertion that can be proved. The midpoint of a phase is a point that divides the phase into two congruent segments

If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.

Two line segments are congruent if they have the same length. They do not need to have the same position or orientation

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The  three equations with solution x=-5 Are as follows:

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

There is not more then one or two variables in a linear equation. In a linear equation, no variable is raised to a power larger than one or utilized as the denominator of a fraction. When you locate two values that satisfy a linear equation and display them on a coordinate grid, every one of the points falls on the same line.

A linear equation in one variable seems to be an equation that has just one solution and is stated in the form ax+b = 0, where a but instead b are two integers and x is a variable. 2x+3=8, for example, is a mathematical expression with a single variable.

x=-5 Given

This also can be written as :

25 + x = 15 ............... equation 1.

7x = -35 .......................equation 2.

15 + x = 10 ..................equation 3

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Answer:

Yes

Step-by-step explanation:

8÷10+7÷100=

8/10 + 7/100=

80/100 + 7/100=     ==> make the denominators equal to each other

(80+7)/100=

87/100=0.87 √

Answer:

yes it does

Step-by-step explanation:

8÷10=0.8

7÷100=0.07

0.8+0.07=0.87

or the easy way ig

8÷10+7÷100=0.87

Answer

.9780

Step-by-step explanation:

Probability, not all 3 people are from Arizona

Arizona Equals 1-   2/91 =    89/91  = .9780

Probability is .9780

Thomas bought 6 glass cups and 6 plastic cups

Thomas bought 12 glass and plastic cups from the store

Glass cups costs $3.25

Plastic cups cost $2.75

He spent a total of $36

Let g represent the number of glass cups and p represent the number of plastic cups

g + p= 12.........equation 1

3.25g + 2.75p= 36..........equation 2

From equation 1

g+p= 12

g= 12-p2

Substitute 12-p for g in equation 2

3.25(12-p)+2.75p = 36

39-3.25p+2.75p= 36

39-0.5p= 36

-0.5p= 36-39

-0.5p= -3

p= -3/-0.5

p= 6

Substitute 6 for p in equation 1

g + 6= 12

g= 12-6

g= 6

Hence there are 6 glass cups and 6 plastic cups

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Answer:

3x+5y=15

Step-by-step explanation:

3x+5y=15

5y=-3x-15

y=-3/5x-3

Because it has the same slope and a different y-intercept, it is parallel because the lines won't ever touch.

Answer:

Area=2044..... perimeter=221

Step-by-step explanation:

Step1:- Area =1/2×breath×height

1/2×73×56

1/2×4088

= 2044

Area =2044cm^2

Step2:- Perimeter= a+b+c

=73+56+92

=221

Perimeter=221cm

The smaller number is 4 and the larger number is 10.

Given that, the sum of the two numbers is 14.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that,  x represents the smaller of the two numbers.

Then the larger number is

The sum of twice the smaller number and two more than the larger number = 2x+2

Now, x+2x+2=14

⇒3x+2=14

⇒3x=12

⇒x=4

So, 2x+2=10

Therefore, the smaller number is 4 and the larger number is 10.

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Answer:-2,2.5,-7/3

Step-by-step explanation:

Answer:

10 for each

Step-by-step explanation:

1.90 x 10 = 19

2.10 x 10 = 21

so 19 + 21 = 30

Applying the segment addition postulate:

x = 2.75

AB = 6x = 6(2.75) = 16.5 units

BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.

Based on the segment addition postulate, since B lies between points A and C on a line segment, then:

AB + BC = AC

AC = 38 3/4

AB = 6x

BC = 8x + 1/4

Substitute

6x + 8x + 1/4 = 38 3/4 [segment addition postulate]

14x + 1/4 = 155/4

14x = 155/4 - 1/4

14x = (155 - 1)/4

14x = 154/4

14x × 4 = 154

56x = 154

x = 154/56

x = 2.75

AB = 6x = 6(2.75) = 16.5 units

BC = 8x + 1/4 = 8(2.75) + 1/4 = 22.25 units.

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Answer juvhfVO"zohgvjozi nandish pro nbhvmno

Answer:

35.90%

Step-by-step explanation:

First, subtract the new no with that of 1990

318-234= 84

percentage of increase will be given by;

84/234×100= 35.8974%

Answer:

theres no picture

If Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

Total hours=18 hours+25 hours

Total hours=43 hours

Income tax=Federal income tax+ State income tax

Income tax=10%+2%

Income tax=12%

Hence,
First paycheck:

First paycheck=$8.50×43 hours×(1-12%)

First paycheck=$8.50×43 hours×0.88

First paycheck=$321.64

Therefore if Ethan got his first job and is making $8.50 an hour. He really wants to buy a couple of video games, so he is trying to estimate how much his paycheck will be. The amount he can expect to bring home in his first paycheck is: $321.64.

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The number of standard version download and high-quality download is 870 and 490 respectively.

let

x + y = 1360

2.9x + 4.1y = 4532

From (1)

x = 1360 - y

Substitute x = 1360 - y into (2)

2.9x + 4.1y = 4532

2.9(1360 - y) + 4.1y = 4532

3944 - 2.9y + 4.1y = 4532

- 2.9y + 4.1y = 4532 - 3944

1.2y = 588

y = 588/1.2

y = 490

Substitute y = 490 into (1)

x + y = 1360

x + 490 = 1360

x = 1360 - 490

x = 870

So therefore, number of standard version download and high-quality download is 870 and 490 respectively.

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Using a system of equations, it is found that she invested 318.71 into Fund B.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

The amount she invested in Fund A was 3 times as much as the amount she invested in Fund B, hence:

x = 3y.

Fund A returned a 6% profit and Fund B returned a 15% profit, and the total profit was of 1380, hence:

1.06x + 1.15y = 1380.

We have that x = 3y, hence:

1.06(3y) + 1.15y = 1380.

4.33y = 1380

y = 1380/4.33

y = 318.71.

She invested 318.71 into Fund B.

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R= is incorrect

the answer is china :)

The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .

In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.

Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.

Of all the given options: the only equations which imply that b(9)=4  are :

i) b(x)=72/x - 4 and  (iv) b(x)=4

Of this two options only the first option is non-linear.

Hence the required option is  b(x)=72/x - 4 .

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Disclaimer:

The missing options are:

i)   b(x) = 72/x - 4

ii) b(x) = √x + 7

iii)b(x)  = 2x+1

iv) b(x) = 4

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Answer:

Parker's unit rate is 5 miles per hour or 5mph.

Step-by-step explanation:

1 hour = 60 minutes

60/20 = 3 minutes

3 minutes for 1 lap

1 lap = 1/4 mile

1/4 mile (1 lap) x 4 laps = 1 mile

4 laps =  12 minutes

12 minutes per mile

60/12 = 5

5 miles per hour

The correct option regarding the operations with scientific notation is given as follows:

B) Because numbers written in scientific notation have exponents, you can use the Laws of Exponents to multiply or divide the numbers.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

An example of a multiplication in scientific notation is:

[tex]2 \times 10^3 \times 3 \times 10^5 = 6 \times 10^{3 + 5} = 6 \times 10^8[/tex]

That is, we multiply the factors, and for the bases of 10, we keep the bases and add the exponents. In a division, we would divide the factors, and for the base of 10, we keep the base and subtract the exponents.

That is, since the numbers have exponents, rules of exponents are used for both multiplication and division, and option b is correct.

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Answer:

-9 7/15

Step-by-step explanation:

I took the test lol. Also if your in advanced you should know this!

Answer:

Step-by-step explanation:

You want the cost and the number of months of membership such that the cost of both gyms is the same.

The total cost of x months of membership at each gym will be the sum of its initial fee and the product of the monthly fee and the number of months.

The cost at Community Gym is ...

  c = 60 + 65x

The cost at Workout Gym is ...

  w = 190 +55x

These costs will be the same when ...

  c = w

  60 +65x = 190 +55x

Subtracting 60+55x from both sides of the equation leaves ...

  10x = 130

  x = 13 . . . . . . divide by 10

The cost will be the same after 13 months.

That cost will be ...

  60 +65(13) = 60 +845 = 905

The amount paid at each gym after 13 months will be $905.

Answer:

I think it's a (16cm) ....

Answer:

0.65

Step-by-step explanation:

The slope of the side connecting (-4,1) and (-6,5) = -2

The slope of the side connecting (1,2) and (-1,6) = -2

The slope of the segment joining two points (x₁, y₁) and (x₂, y₂) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

We have to find the slope of the side joining the points (x₁, y₁) = (-4,1) and (x₂, y₂) = (-6,5)

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{5-1}{-6--4}[/tex]

          = 4/ -2

          = -2

We have to find the slope of the side joining the points (x₁, y₁) = (1, 2) and (x₂, y₂) = (-1,6)

Slope =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{6-2}{-1-1}[/tex]

          = 4/-2

          = -2

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