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omeli [17]
3 years ago
8

Are These Dates Correct For When These colonies were founded?

Mathematics
1 answer:
Murrr4er [49]3 years ago
4 0
Yes they are 100% correct good job
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Find the Length of AC. Round answers to the nearest hundredth (2 decimal places)
lara31 [8.8K]

Answer:

32.78

Step-by-step explanation:

Assuming that we have two right triangles joined together, with one having adjacent side a, with a side of 12 ft opposite reference angle 30°, and the other one having adjacent side b, with a side of 12 ft opposite reference angle 45°. Thus, a + b = length of AC.

Let's find a and b.

Finding a:

Reference angle = 30°

Opp = 12 ft

Adj = a

Using trigonometric ratio formula, we have:

tan(30) = 12/a

Multiply both sides by a

a*tan(30) = 12

Divide both sides by tan(30)

a = 12/tan(30)

a = 20.78 (nearest hundredth)

Finding b:

Reference angle = 45°

Opp = 12 ft

Adj = b

Using trigonometric ratio formula, we have:

tan(45) = 12/b

Multiply both sides by a

b*tan(45) = 12

Divide both sides by tan(45)

b = 12/tan(45)

a = 12

Length of AC = 20.78 + 12 = 32.78

5 0
3 years ago
What is the area of the largest rectangle that can be inscribed in an isosceles triangle with side lengths $8$, $\sqrt{80}$, and
e-lub [12.9K]
First let's solve the general case for an isosceles triangle of base 2 and height k. If the triangle is drawn so the base is on the x-axis and the apex is on the y-axis, the equation for the line containing the right side is
  y = -k(x-1)
Then a rectangle with x-dimension w will have an area that is the product of this width and the height y = -k((w/2)-1).
  area = w(-k(w/2 -1)) = (-k/2)w² +kw
The derivative of area with respect to w will be zero where the area is a maximum:
  d(area)/dw = 0 = -kw +k
  w = 1 . . . . . . add kw and divide by k
Using the formula for area, we find
  area = 1(-k(1/2-1)) = k/2
This value is 1/2 the total area of the triangle we started with.

If the side lengths of your triangle are 8, √80, and √80, the height will be given by the Pythagorean theorem as
  h = √((√80)² - (1/2·8)²) = √(80-16) = 8
Your triangle's area will be
  triangle area = (1/2)(8)(8) = 32

The maximum area of the inscribed rectangle will be half this value,
  16 square units

4 0
3 years ago
1. Solve the following system of equations, using matrix inversion method.
Jet001 [13]

Answer:

x = 142/83

y = 111/83

z = 452/83

8 0
3 years ago
Suppose a classroom teacher wants to measure whether offering candy as a reward will increase the number of times that a student
ahrayia [7]

Answer:

C) Matched pairs

Step-by-step explanation:

Matched samples (also called matched pairs, paired samples or dependent samples) is a type of sampling that involves pairing participants that share every characteristic except for the one under study. The paired participants could be same individuals studied at different time such as:

  1. The study of same participants before and after an interference.
  2. The study of the same participants at two different interference.
5 0
3 years ago
Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gem
Finger [1]

Answer:

  • 10.2 grams

Step-by-step explanation:

Gemma had 25.75 grams of frosting

Used 15.5 grams

<u>Left over:</u>

  • 25.75 - 15.5 = 10.2 grams
8 0
3 years ago
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