By the Pythagorean Theorem:
d^2=x^2+y^2, where x and y are the dimensions of the rectangle, however this is just a square, so x=y=s so
d^2=s^2+s^2
d^2=2s^2, and we are told that s=6 so
d^2=2(6^2)
d^2=2(36)
d=√(2(36))
d=6√2 units
d≈8.49 units (to nearest hundredth of a unit)
Answer:
Multiply the first equation by -4
Step-by-step explanation:
Equation A: 3c = d − 8
Equation B: c = 4d + 8
We want to eliminate variable d
Multiply the first equation by -4
-4( 3c = d − 8)
-12c = -4d +32
Add this to the second equation
-12c = -4d +32
c = 4d + 8
================
-11c = 0d + 40
Answer:
Length of XM is 5.5 units.
Step-by-step explanation:
Given △XYZ where MZ is the angle bisector of ∠YZX . we have to find the length of XM.
A triangle with vertices X, Y, and Z. Side XZ is base. A line segment drawn from Z to M bisects ∠YZX into two parts ∠YZM and ∠XZM.
YZ=7 units, XZ=11 units and YM=3.5 units
By angle bisector theorem which states that an angle bisector of an angle divides the opposite side in two segments that are proportional to the another two sides of the triangle.
Hence,
⇒
⇒ MX=5.5 units.
Hence, length of XM is 5.5 units.
Answer:
Answer: 630
Step-by-step explanation: 18 feet tall is the gateway arch . The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St
Answer:
Yes, there is enough evidence to say the proportions are the same.
Step-by-step explanation:
Null hypothesis: The proportions are the same.
Alternate hypothesis: The proportions are not the same.
Data given:
p1 = 51% = 0.51
n1 = 200
p2 = 48% = 0.48
n2 = 150
pooled proportion (p) = (n1p1 + n2p2) ÷ (n1 + n2) = (200×0.51 + 150×0.48) ÷ (200 + 150) = 174 ÷ 350 = 0.497
Test statistic (z) = (p1 - p2) ÷ sqrt[p(1-p)(1/n1 + 1/n2) = (0.51 - 0.48) ÷ sqrt[0.497(1-0.497)(1/200 + 1/150)] = 0.03 ÷ 0.054 = 0.556
The test is a two-tailed test. At 0.10 significance level the critical values -1.645 and 1.645
Conclusion:
Fail to reject the null hypothesis because the test statistic 0.556 falls within the region bounded by the critical values.