<h3>
Answer: Angle Q = 133 degrees</h3>
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Work Shown:
Recall that for any triangle, the three angles always add to 180
P+Q+R = 180
(x+13) + (10x+13) + (2x-2) = 180
(x+10x+2x) + (13+13-2) = 180
13x+24 = 180
13x = 180-24
13x = 156
x = 156/13
x = 12
Now that we know x, we can find the angle measures
- angle P = x+13 = 12+13 = 25 degrees
- angle Q = 10x+13 = 10*12+13 = 120+13 = 133 degrees
- angle R = 2x-2 = 2*12-2 = 24-2 = 22 degrees
As a way to check if we have the right answer or not, we see that,
P+Q+R = 25+133+22 = 180
So the answer is confirmed.
<span>By dividing the two numbers we get 104.3495... Rounding this number to two decimal places means that we must keep just 2 digits after the "." symbol, and round the last one of them. In our case, 104.3495... becomes 104.35.</span>
Answer:
<em>The height of the bullding is 717 ft</em>
Step-by-step explanation:
<u>Right Triangles</u>
The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.
The tangent ratio for an internal angle A is:
The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.
The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:
Solving for h:
Computing:
h = 711.5 ft
We must add the height of Ms, M's eyes. The height of the building is
711.5 ft + 5 ft = 716.5 ft
The height of the building is 717 ft
Answer:
domain: {x | x is a real number}
range: {y l y> -8}
Step-by-step explanation:
f(x) = 4x² – 8 is a parabola, a U shape.
Since the stretch factor, 4, is positive, it opens up, there it will have a minimum value, the lowest point in the parabola.
y > -8 because the minimum is -8.
Parabolas do not have restricted "x" values. "4" does not restrict x because it is the stretch factor, which determines how wide the parabola is.
Quadratic standard form:
f(x) = ax² + bx + c
"a" represents how wide the graph is. If it's negative it opens down, if it's positive it opens up.
"b", if written, tells you it is not centred on the y-axis. It is not written, so the vertex is on the y-axis.
"c" is the y-intercept. In this case, since b = 0, it is also the minimum value.
