The Empire State Building in New York City is 1,454 feet tall. The observatory on the 86th floor is 404 feet from the top of the building. How high is the observatory above ground?

The given linear system is:

[tex]\displaystyle \left \{ {{5x+3y=1} \atop {-5x-7y=31}} \right.[/tex]

Linear systems can be solved using either elimination or substitution. However, the question is asking to solve using elimination, so I will use that method.

When eliminating, you can either eliminate x or y. In this system, x is much easier to eliminate. The x variable in the first equation is 5x, and in the second equation, it is -5x. Since 5 and -5 cancel each other out, you don't need to do anything other than add.

[tex]5x+3y=1\\-5x-7y=31[/tex]

[tex]\displaystyle 3y-7y=1+31\\-4y=32[/tex]

Lastly, you need to leave the variable y alone. The variable is currently -4y or -4 times y. To remove it, you need to do the opposite of it, which is dividing by -4.

Divide both sides by -4:

[tex]\displaystyle\frac{-4y}{-4} =\frac{32}{-4}[/tex]

[tex]\displaystyle y=-8[/tex]

Now that you have the value of y, substitute it into one of the equations to find x. I will be substituting it into the first equation.

[tex]\displaystyle 5x+3y=1 \rightarrow 5x+3(-8)=1[/tex]

Open the parentheses and multiply:

[tex]5x-24=1[/tex]

Move 24 to the other side to leave the variable alone:

[tex]5x-24+24=1+24[/tex]

You will be adding since you're "removing" it by doing the opposite of it.

[tex]5x=25[/tex]

Lastly, divide both sides by 5 to leave x alone.

[tex]\displaystyle \frac{5x}{5} =\frac{25}{5}[/tex]

[tex]x=5[/tex]

[tex]\displaystyle (x,y) \rightarrow (5, -8)[/tex]

The answer is (5, -8).

Answer:

.325

Step-by-step explanation:

Answer:

0.325 is a decimal

Step-by-step explanation:

Answer: 50

Step-by-step explanation:

From the question, we are informed that 1/3 of gym members say they spent 5 hours per week at the gym.

Assuming there are 150 people working out at the gym, the number of people that'll most likely spend 5 hours at the gym this week will be calculated by multiplying 1/3 by 150. This will be:

= 1/3 × 150

= 50 people

Answer:

The answer is A f(x)=-2x + 70

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

207

Step-by-step explanation:

9ft=3yrds

3x69=207

Answer: X=-6

Step-by-step explanation:

Answer:

B. -6

Step-by-step explanation:

Answer:

EASY. y = 4/7x+3

Step-by-step explanation:

Answer:

994

Step-by-step explanation:

PEMDAS

Parentheses: 8+2 = 10

Exponents: 10^3 = 1000

Subtraction = 1000-6

= 994

Answer:

f(x) has been  translated to the  right one and down  five.

Step-by-step explanation:

Given

[tex]g(x)=f(x-1)-5[/tex]

Required

Determine the transformation

Taking the analysis one at a time

The relationship between f(x) and f(x - h) is that f(x) is translated h units to the right

So, when f(x) becomes f(x-1), it is as a result of f(x) being translated 1 unit to the right

The relationship between f(x) and f(x) - h is that f(x) is translated h units downwards

So, when f(x - 1) becomes f(x - 1) - 5, it is as a result of f(x - 1) being translated 5 units downwards.

Hence, option 2 answers the question

Answer:

Yes, they are equivalent.

Answer:

B. m<3 = 100°

C. m<2 + m<4 = 80°

Step-by-step explanation:

Given that n is parallel to m, the following are the measure of each numbered angles:

m<1 = 60° (vertical angles are congruent)

m<2 = 20° (corresponding angles are congruent)

m<3 = 180 - (m<CAB + m<1) (sum of ∆)

m<3 = 180 - (20° + 60°)

m<3 = 100°

m<4 = 60° (corresponding angles are congruent)

Therefore, the following statements are TRUE:

B. m<3 = 100°

C. m<2 + m<4 = 80°

Answer:

Try 120

Step-by-step explanation:

There are five dashes in between 100 and 200. Count up by 20s

Answer:

6 tiles

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

I took the test ;)

Answer:

Q1) 12, 2, 1.5, 1

Q2) I believe its C

Step-by-step explanation:

Hope it helps!

Answer:

1st question 12, 2, 1.5, 1

2nd question C

Step-by-step explanation:

Hope I helped

Answer:

So that's actually not true. When comparing decimals you should compare each digit. Remember adding a 0 at the end does not change the value of the decimal. So lets look at it up and down:

remember line up the decimal to decimal

1.628

1.630

the first digit is the same. Both of these numbers are also before the decimal.

let's look at the second digit.

1.628

1.630

they are also the same. Both of these are also right after the decimal point.

now let's look at the third digit.

1.628

1.630

In this case, the bottom number has a higher value. Since 3>2, the bottom number is the overall biggest. Or you could look at it and say "Oh! 30 is bigger than 28!" I hope this helps you, and if this wasn't what you were looking for, oops

Answer:

D. -60 + (-30) = -30

Step-by-step explanation:

Put the word problem into an equation: -60 + (-30) = -30

I hope this helped, please mark Brainliest, thank you so much!!

Answer:

components: LeftAngleBracket 16, 11 RightAngleBracket distance: 194.16 yards

Step-by-step explanation:

get her done!!! Correct on Edge 2020

The vector represents the path from the house to the park is components: {16,11} and actual distance between them is 194.16 yards. So, option A is correct.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

In order to find the length of a point to another point that has different y and x points, we will use the pythagorean theorem

(a^2 + b^2 = c^2)

Here, 16 and 11 are the distances from her house,

16^2 + 11^2 = c^2

c^2 = 377

c = 19.416...

Now, we have to convert this to yards;

19.416 x 10 = 194.16 yards

Hence, the vector represents the path from the house to the park is components: {16,11} and actual distance between them is 194.16 yards.

So, option A is correct.

Learn more about Pythagoras theorem;

https://brainly.com/question/343682

#SPJ2

Answer:

The first one is B The second one is D and the last one is A

Answer:

c=55t

Step-by-step explanation:

..

3.866 microseconds? 7 x 522 nano seconds = 3.86600 ms

Answer:

acute triangle

Step-by-step explanation:If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.

Step-by-step explanation:

Part 1: 4x + 7 = 3(2x - 5)4x+7=3(2x−5)

4x+7=6x-154x+7=6x−15

7=6x-15-4x7=6x−15−4x

7=2x-157=2x−15

7+15=2x7+15=2x

22=2x22=2x

22=2x / 222=2x/2

x=11x=11

Part 2: Sam is not correct because he messed up the second step. He added 2x on both sides to get 7x, instead he should have subtracted.

Answer:

(D) 24°

Step-by-step explanation:

(5x + 6)° + (3x)° + (142 - 4x)° = 180°

5x + 6 + 3x + 142 - 4x = 180

4x + 148 = 180

4x = 32

x° = 8°

m∠E = 3×8° = 24°

Answer:

y= -2/5x

Step-by-step explanation:

Answer:

Zero Slope

Step-by-step explanation:

Hope this helps!