Answer:
c = 13.1
Step-by-step explanation:
* Lets explain how to solve the problem
- In Δ ABC
# ∠A is opposite to side a
# ∠B is opposite to side b
# ∠C is opposite to side c
- The sine rule is:
# 
* Lets solve the problem
- In Δ ABC
∵ m∠A = 57°
∵ m∠B = 37°
∵ The sum of the measures of the interior angles of a triangle is 180°
∴ m∠A + m∠B + m∠C = 180°
∴ 57° + 37° + m∠C = 180°
∴ 94° + m∠C = 180° ⇒ subtract 94° from both sides
∴ m∠C = 86°
- Lets use the sine rule to find c
∵ a = 11 and m∠A = 57°
∵ m∠C = 86°
∵ 
- By using cross multiplication
∴ c sin(57) = 11 sin(86) ⇒ divide both sides by sin(57)
∴ 
* c = 13.1
Answer:
KPF = 9 and H = 129
Step-by-step explanation:
An inscribed quadrilateral in a circle has all diagonal angles add up to 180, so we can use this to find the angles of the quadrilateral.
H= 180-EPK and K = 180-E so H = 129 and K = 60
Now PF and EH are parallel, so PE is a transversal. That means FPE = 180 - E = 60. Now it's pretty easy to solve for KPF = FPE - EPK = 60 - 51 = 9.
Let me know if you don't see how I did any of this and I'll be happy to explain it..
Answer:
To draw this graph, we start from the left in quadrant 3 drawing the curve to -4 on the x-axis to touch it but not cross. We continue back down and curve back around to cross the x-axis at -1. We continue up past -1 and curve back down to 5 on the x-axis. We touch here without crossing and draw the rest of our function heading back up. It should form a sideways s shape.
Step-by-step explanation:
A polynomials is an equation with many terms whose leading term is the highest exponent known as degree. The degree or exponent tells how many roots exist. These roots are the x-intercepts.
This polynomial has roots -4, -1, and 5. This means the graph must touch or cross through the x-axis at these x-values. What determines if it crosses the x-axis or the simple touch it and bounce back? The even or odd multiplicity - how many times the root occurs.
In this polynomial:
Root -4 has even multiplicity of 4 so it only touches and does not cross through.
Root -1 has odd multiplicity of 3 so crosses through.
Root 5 has even multiplicity of 6 so it only touches and does not cross through.
Lastly, what determines the facing of the graph (up or down) is the leading coefficient. If positive, the graph ends point up. If negative, the graph ends point down. All even degree graphs will have this shape.
To draw this graph, we start from the left in quadrant 3 drawing the curve to -4 on the x-axis to touch it but not cross. We continue back down and curve back around to cross the x-axis at -1. We continue up past -1 and curve back down to 5 on the x-axis. We touch here without crossing and draw the rest of our function heading back up. It should form a sideways s shape.
Equation: a^2 + b^2 = c^2
18^2 + 16^2 = c^2
324 + 256 = c^2
C^2 = square root 580
Square root 580 reduces to 2 square root 145.
As a decimal that is: 24.08
Rounded to the nearest tenth: 24 inches.
I hope this helps! If it does please offer me the brainiest!
