Answer:
Please find the attachment.
Step-by-step explanation:
We are asked to explain why gives the area of a triangle with sides a and b and included angle theta.
We know that area of a triangle is equal to half the product of base and height of the triangle.
Upon looking at our given triangle, we can see that the base of the triangle is equal to 'a'.
The height of the triangle can be determined using sin(theta) as sine relates opposite side of right triangle with its hypotenuse.
Upon substituting our given values in area formula, we will get:
Hence, proved.
Remember that the rule with multiplying exponents with the same base is to add the exponents together.
In this case:
10^12 is your answer.
Answer:
m<EFG =3n + 17
m<GFH= 2n + 23
3n+17+2n+23=180°
5n + 40 = 180
5n = 140
n = 28
m<EFG= 3(28)+17= 84+17= 101°
m<GFH= 2(28)+23= 56+23 = 79°
Answer:
<span>y ≤ 0.13x² + 0.38x
</span>y ≤ 766.33 - 2.90x² - 8.69x
Your question doesn't say which are the systems of inequlities, but we can find the correct one.
We can call:
x = width of the grass
y = radius of the dispenser
Now, let's translate into mathematical language the statements given in the question:
- "the length of the grassy area for the lion must be 3 feet greater than its width":
l = x + 3
- "the area of the grass must be at least 8 times greater than the radius of the parakeets' food dispenser":
A ≥ 8 · y
The area of a rectangle is given by:
A = l · w = (x + 3) · x
therefore, we can write the first inequality:
(x + 3) · x ≥ 8 · y
x² + 3x ≥ 8y
and solving for y:
y ≤ 0.13x² + 0.38x (rounded to two decimal digits)
- "The food dispenser for the parakeets is … 4 feet tall. It is exactly half-way full" means that the empty height of the dispenser is:
h = 4 : 2 = 2 ft
- "The cost of the parakeets' food is $0.49 times the length of the radius for every foot of height of food missing from the dispenser":
P = 0.49 · y · h
<span> = 0.49 · y · 2
</span>= 0.98y
- "They could put the grass in the lion's habitat for $2.84 per square foot of grass":
G = 2.84 · A
= 2.84 · (x² + 3x)
= 2.84x² + 8.52x
- "Andrea cannot spend more than $751.00 on both projects":
P + G ≤ 751.00
We can now write the second inequality:
(0.98y) + (2.84x² + 8.52x) ≤ 751.00
Solving for y:
0.98y + 2.84x² + 8.52x ≤ 751.00
0.98y ≤ 751.00 - 2.84x² - 8.52x
y ≤ 766.33 - 2.90x² - 8.69x (rounded to two decimal digits)
Answer:
Option D
Step-by-step explanation:
Rate of change of a linear function between two points and is given by,
Rate of change 'm' =
From the given table,
Rate of change of the function between (-2, 6) and (-4, 9),
Rate of change 'm' =
m =
Initial value = y-intercept
Let the equation of the line passing through a point (h, k) is,
y - k = m(x - h)
If a point (-2, 6) is lying on the graph of the function,
y - 6 =
y =
y =
Y-intercept of the function = 3
Therefore, initial value of the function = 3
Option D is the answer.