Answer:

Step-by-step explanation:
sine = 
since A = 
The angles and side lengths for both triangles are;
3) A = 36°; B = 54°; C = 90°; a = 7; b = 9.63; c = 4.11
4) A = 64°; B = 26°; C = 90°; a = 1.798; b = 0.88; c = 2
<h3>How to solve Pythagoras theorem?</h3>
3) From the diagram, we are already given;
B = 54°
C = 90°
a = 7
We know that sum of angles in a triangle is 180° and so;
A = 180 - (90 + 54)
A = 36°
By trigonometric ratios;
b/7 = tan 54
b = 7 * tan 54
b = 7 * 1.376
b = 9.63
7/c = cos 54
c = 7 * cos 54
c = 4.11
4) From the diagram, we are already given;
B = 26°
C = 90°
c = 2
We know that sum of angles in a triangle is 180° and so;
A = 180 - (90 + 26)
A = 64°
By trigonometric ratios;
b/2 = sin 26
b = 2 * sin 26
b = 2 * 0.4384
b = 0.88
a/2 = cos 26
a = 2 * cos 26
a = 1.798
Read more about Pythagoras Theorem at; brainly.com/question/654982
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Hope this is the right one.
Problem 8p^2 - 30p + c
<em>Step One</em>
Take 1/2 of - 30
1/2 * -30 = - 15
<em>Step 2
</em>Square -15
(-15)^2 = 225
c = 225
Problem Nine
a = 1
b = 4
c = -15


x = [-4 +/- sqrt(76)] / 2
x = [-4 +/- 2*sqrt19]/2
x = [-4/2 +/- 2/2 sqrt[19]
x = - 2 +/- sqrt(19)
x1 = - 2 + sqrt(19)
x2 = -2 - sqrt(19)
These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.
Problem Tena = 1
b = 4
c = -32
The discriminate is sqrt(b^2 - 4ac)
D = sqrt(b^2 - 4ac)
D = sqrt(4^2 - 4(1)(-32)
D = sqrt(16 - - 128)
D = sqrt(16 + 128)
D = sqrt(144)
D = +/- 12
Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.
(x + 8)(x - 4) = y
But that' s not what you were asked for.
The discriminate is > 0 so the roots are going to be real.
<em>
Answer; The discriminate is > 0 so there will be 2 real different roots.</em>
A
The absolute value of -27 is 27, so it is the same number
One form of the equation of a parabola is
y = ax² + bx + c
The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6 (1)
a - b + c = -12 (2)
9a + 3b + c = 0 (3)
Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6 (4)
9a + 3b - 6 = 0
9a + 3b = 6 (5)
Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1
The equation is
y = -x² + 5x - 6
Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
= -[ (x - 2.5)² - 2.5²] - 6
= -(x - 2.5)² + 6.25 - 6
y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.
Answer: y = -(x - 2.5)² + 0.25