Answer:
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: 
Given points: (-6, 4), (6, 10)
(-6, 4) = (x1, y1)
(6, 10) = (x2, y2)
To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.
First, let's find the slope. To do this, input the given points into the slope formula:
Simplify:
10 - 4 = 6
6 - (-6) = 6 + 6 = 12
The slope is 
.
To find the y-intercept, input the slope and one of the given points(in this example I'll use point (6, 10)) into the equation and solve for b:
10 = 3 + b
7 = b
The y-intercept is 7.
Now that we know the slope and the y-intercept, we can write the equation:
Answer:
27 cubic units
Step-by-step explanation:
A cube has equal dimensions. So the volume is 3units × 3units × 3units or 27cubic units
Mr. Kyle will be expected to pay $8,100.
The total cost for his land would be 120 x 90 = 10,800.
Since the city is paying 25%, he must pay the other 75%.
0.75 x 10800 = 8100
AB = 6 cm, AC = 12 cm, CD = ?
In triangle ABC, ∠CBA = 90°, therefore in triangle BCD ∠CBD = 90° also.
Since ∠BDC = 55°, ∠CBD = 90°, and there are 180 degrees in a triangle, we know ∠DCB = 180 - 55 - 90 = 35°
In order to find ∠BCA, use the law of sines:
sin(∠BCA)/BA = sin(∠CBA)/CA
sin(∠BCA)/6 cm = sin(90)/12 cm
sin(∠BCA) = 6*(1)/12 = 0.5
∠BCA = arcsin(0.5) = 30° or 150°
We know the sum of all angles in a triangle must be 180°, so we choose the value 30° for ∠BCA
Now add ∠BCA (30°) to ∠DCB = 35° to find ∠DCA.
∠DCA = 30 + 35 = 65°
Since triangle DCA has 180°, we know ∠CAD = 180 - ∠DCA - ∠ADC = 180 - 65 - 55 = 60°
In triangle DCA we now have all three angles and one side, so we can use the law of sines to find the length of DC.
12cm/sin(∠ADC) = DC/sin(∠DCA)
12cm/sin(55°) = DC/sin(60°)
DC = 12cm*sin(60°)/sin(55°)
DC = 12.686 cm
Answer:
C
Step-by-step explanation:
16 : 12
x : 6
- multiply 16*6 and divide by the number multiplying with the unknown (12)
(16*6)/12 = 8
- area of triangle is 1/2 h*b
so 1/2 * (16*8) = 64
