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lesya692 [45]
2 years ago
13

Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign? I WILL GIVE BRAINLYI

EST!!

Mathematics
1 answer:
Dmitry_Shevchenko [17]2 years ago
6 0

Answer:

4x^2+4x-1

Step-by-step explanation:

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50 points! Tell whether the orthocenter is inside, on, or outside the triangle. Then find the coordinates of the orthocenter.
Nady [450]

Answer:

  • (1,3) is inside the triangle

Step-by-step explanation:

Orthocenter is the intersection of altitudes.

We'll calculate the slopes of the two sides and their altitudes ad find the intersection.

<h3>Side QR</h3>
  • m = (3 - 5)/(4 - (-1)) = -2/5

<u>Perpendicular slope:</u>

  • -1/m = 5/2

<u>Perpendicular line passes through S(-1, -2):</u>

  • y - (-2) = 5/2(x - (-1)) ⇒ y = 5/2x + 1/2
<h3>Side RS</h3>
  • m = (-2 - 3)/(-1 -4) = -5/-5 = 1

<u>Perpendicular slope:</u>

  • -1/m = -1/1 = -1

<u>Perpendicular line passes through Q(-1, 5):</u>

  • y - 5 = -(x - (-1)) ⇒ y = -x + 4

The intersection of the two lines is the orthocenter.

<u>Solve the system of equations to get the coordinates of the orthocenter:</u>

  • 5/2x + 1/2 = x + 4
  • 5x + 1 = -2x + 8
  • 7x = 7
  • x = 1

<u>Find y-coordinate:</u>

  • y = -1 + 4 = 3

The orthocenter is (1, 3)

If we plot the points, we'll see it is inside the triangle

6 0
2 years ago
What are the side lengths of the equilateral triangle?
Alchen [17]

5x  +  (6x - 5) + (3x + 10) = 360

5x  + 6x - 5 + 3x + 10 = 360

11x - 5 + 3x + 10 = 360

14x + 5 = 360

14x = 360 - 5

14x = 355

x = 25.36

<h2><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u></h2>

x = 25.36

5x = 5 \times 25.36 = 126.8

6x - 5 = 6 \times 25.36 - 5 = 147.16

3x + 10 = 3 \times 25.36 + 10 = 86.08

4 0
3 years ago
The total weight of 9 bags of potatoes is 36 kilograms. Each bag weighs the same amount. What is the weight, in grams, of each b
Sunny_sXe [5.5K]

Answer:

4000 grams

Step-by-step explanation:

8 0
3 years ago
Use the distributive property to remove the parentheses.
nlexa [21]

Answer:

Step-by-step 12c^{3} -40c^{8}explanation:

8 0
3 years ago
Solve the system of linear equations<br> x+y=4<br> -3x-y+-8
liubo4ka [24]

Answer:

y=3x+8

Step-by-step explanation:

Formula is L(x)=f(a)+f(a)(x-a)

This is for linearization

7 0
1 year ago
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