x - y = 35
x = 6y
Plug 6y in for x in the first equation.
6y - y = 35
5y = 35
Divide both sides by 5
y = 7
x = 6y
x = 6(7) = 42
42 and 7
Letter C
Since we had the answers we could have just tried the answers but you will not always have multiple choice so this is the method for solving.
Answer:
Height of mound = 794 ft
Step-by-step explanation:
To illustrate the angle of elevation and distance, i have drawn it and attached below.
Now, from my diagram;
h = the height of the mound
At his first point of his trip to the foot of the mound, the angle of elevation is 40°, while the horizontal distance to the foot of the mound is "X"
So, by triangle definition,
tan(40°) = h/x
And so;
h = x tan40
h = 0.8391x - - - - (eq 1)
At his second point of the trip to the foot of the mound, Joe is now,
"(x - 450) ft" from the foot of the mound.
Thus, his angle of elevation is 40 + 18 = 58°.
So, by triangle definition,
tan(58°) = h/(x - 450)
h = (x - 450)•(tan(58°))
h = 1.6003(x - 450)
h = 1.6003x - 720.135 - - - - -(eq2)
To get the height(h) of the mound, let's equate (eq1) to (eq2).
0.8391x = 1.6003x - 720.135
1.6003x - 0.8391x = 720.135
0.7612x = 720.135
x = 720.135/0.7612
x = 946.0523 ft
Let's put this value for x in eq (1);
h = 0.8391 x 946.0523 = 793.83 ft ≈ 794ft
Put the numbers in order.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 2: Find the median.
1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27.
Step 3: Place parentheses around the numbers above and below the median.
Not necessary statistically, but it makes Q1 and Q3 easier to spot.
(1, 2, 5, 6, 7), 9, (12, 15, 18, 19, 27).
Step 4: Find Q1 and Q3
Think of Q1 as a median in the lower half of the data and think of Q3 as a median for the upper half of data.
(1, 2, 5, 6, 7), 9, ( 12, 15, 18, 19, 27). Q1 = 5 and Q3 = 18.
Step 5: Subtract Q1 from Q3 to find the interquartile range.
18 – 5 = 13.
<h2><u>Quadrilateral</u></h2>
<h3>Classify the quadrilateral in as many ways as possible.</h3>
Shown in the figure, all the measurements of each sides is different, so it is only a quadrilateral. Square has four equal sides and angles, rhombus has only four equal sides, and a parallelogram whose opposite sides are parallel.
<u>Answer:</u>
<em>Picture 1 (Rhombus)</em>
<em>Picture </em><em>2</em><em> </em><em>(Square)</em>
<em>Picture 3 (Parallelogram)</em>
<em>Picture 4 (Quadrilateral)</em>
Wxndy~~
Answer:
A: m<1 = 79 degrees
B: m<1 = 61 degrees, m<2 = 151 degrees, m<3 = 12 degrees
Step-by-step explanation:
A: An exterior angle is equal to the sum of the two opposite interior angles. 27+52 in this case.
B: The sum of the measures of the interior angles in a triangle is 180 degrees.
Since we know the two angles in the right trinagle are 90 and 29 degrees, we add them and subract the sum from 180 which gives us 61 degrees.
Applying what we know from part A, 61 degrees+90 degrees = m<2.
And, since we know m<2 = 151 degrees, we add that and the 17 degrees to then subtract that sum from 180 to get the measure of angle 3 which is 12 degrees.