What is 4 out of 83
2 answers:
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Answer:
C 7ft/yr
Step-by-step explanation:
The given points are not all on the same line, so the average will vary depending on the interval of interest.
Over the interval [1, 11] years, the average rate of change of height is ...
change in height / change in years = (80 -10)/(11 -1) = 70/10 = 7 . . . ft/yr
__
On the interval [11, 15] years, the average rate of change is ...
(105 -80)/(15 -11) = 25/4 = 6.25 . . . ft/yr
Even on this interval, the closest answer choice is C.
Answer:
1)
Step-by-step explanation:
Let's assume we know the measurement for angle F (let's just call it 20 degrees to help us imagine things).
The triangle in the right of the drawing and the bigger triangle (that contains both of the triangles) share that angle.
We are given angleEDF has measurement 90 degrees because of the square there.
We can find angleE's measurement using that the sum of the interior angles of a triangle is 180.
I'm looking at the green triangle you have 90+20+mAngleE=180.
Let's solve that for mAngleE.
90+20+mAngleE=180
110+mAngleE=180
Subtract 110 on both sides:
mAngleE=180-110
mAngle=70.
The only way we are going to prove these triangles are similar is if we have a condition that helps us show that the smaller two triangles are also 20-70-90 triangles.
Let's look at choice 1)
If DG is an altitude then DG is perpendicular to EF. Perpendicular means it forms 90 degree angles at the intersection.
If we look at the right triangle, this gives us enough information to find the last angle, the angle known as GDF.
mAngleGDF+20+90=180
mAngleGDF+110=180
Subtract 110 on both sides:
mAngleGDF=70.
So we have a 20-70-90 triangle again. So the one on the right and the green triangle are similar.
We can find angle EDG's measurement to since we know angle E's measurement is 70 and angle EGD's measurement is 90.
mAngleEDG+70+90=180
mAngleEDG+160=180
mAngleEDG=20
So we have a 20-70-90 triangle again. So the one on the left is similar to the other two triangles in this picture as well.
Again if the corresponding angles of a triangle are congruent then the triangles are at least similar.
I provided a drawing for number 1 with the example I put here.
Let's look at 2). We already know EF is an hypotenuse of triangle EDF since it is opposite the 90 angle that is EDF.
2 doesn't help us because it gives no additional information.
Let's look at 3). Segment ED is shorter than segment DF. This gives us no measurements or even a ratio to compare the sides.
Let's look at 4). Angle is congruent to itself. There is only one angle that can be seen as angle E in this picture so this also provides no additional information.
Answer:
-48x^2 -666x+84
Step-by-step explanation:
Exponet is ^2.
Multiply is •
Use Distributed Property. Multiply the second parathesis by each term from the first parathesis.
Any expression multiplied by 1 remains the same. Distribute 41 through the parathesis. 41(2-7x-9x).
Distribute 3x through the parathesis 3x • (2-7x-9x).
You will have these numbers left: (Slide 2)
Add the numbers, 2 and 82 to get 84. Add -7x -9x + -287x -369x + 6x to get -666x. Add -21x^2 - 27x^2 to get 48x^2.
Use the communitative property to reorder the terms. And then your answer is -48x^2 -666x+84.
