If VX = WZ = 40 cm and m∠ZVX = m∠XWZ = 22°, can ΔVZX and ΔWXZ be proven congruent by SAS? Why or why not? Yes, along with the gi
ven information, ZX ≅ ZX by the reflexive property. Yes, the triangles are both obtuse. No, the sides of the triangles intersect. No, there is not enough information given.
2 answers:
Answer:
ΔVZX and ΔWXZ are not congruent by SAS by the given information.
No, there is not enough information given.
The additional information for triangle to be congruent by SAS is given below.
Step-by-step explanation:
GIVEN:
1. VX = WZ = 40 cm and
2.m∠ZVX = m∠XWZ = 22°
3. VZ = WX ......{this additional information is required for triangles is to be congruent by SAS test}
Proof:
In Δ VZX and Δ WXZ
VZ ≅ WX …………..{additional information}
∠ ZVX ≅ ∠ XWZ ……….{measure of each angle is 22° given}
VX ≅ WZ ………….{length of each side is 40 cm given}
Δ ABC ≅ Δ PQR ….{By Side-Angle-Side test}
For SAS test, two sides of the corresponding triangles should be congruent and the angle between the two side. Then the triangles are said to be congruent by side angle side test.
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Answer:
a) The tower is 90 feet tall
b) She reaches the bottom at t = 18 minutes.
c) Her speed at time t is 5 \sqrt[]{5} ft/minute
d) Her acceleration at time t is 10 ft/minute^2
Step-by-step explanation:
Consider the path described by the child as going down the tower to have the following parametrization
a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.
b) The child reaches the bottom as soon as z =0. We want to find the value of t that does that. Then we have 0 = 90-5t, which gives us t = 18 minutes.
c) Given the parametrization we are given, the velocity of the child at time t is given by . The speed is defined as the norm of the velocity vector,
so, the speed at time t is given by
d) ON the same fashion we want to know the norm of the second derivative of .
We have that so the acceleration is given by
Answer:
s = 21.33*π in
Step-by-step explanation:
Given:
- The complete data is given in the figure (attached):
Solution:
- The bugs lands on the end of the wiper blade furthest to the pivot. The arc length (s) swept by a wiper in one cycle i.e θ = 120° would be given by:
s = 2*r*θ
- Where, r: The distance between the bug and the pivot = 16 in
θ : Angle swept in radians
- The distance travelled by the bug is s:
s = 2*(16)*( 120 / 180 ) * π
s = 21.33*π in
Answer:
C. 50
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
The higher the margin of error, the wider an interval is.
As the sample size increases, the margin of error decreases. If we want a widest possible interval, we should select the smallest possible confidence interval.
So the correct answer is:
C. 50