<h2>Answer: slope = ¹¹/₁₃
</h2><h3>Step-by-step explanation: </h3>
The question gives us two points, (−13, −19) & (13, 3), from which we can find the slope and later the equation of the line.
Finding the Slope
The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)
= ((3 - (-19)) ÷ (13 - (-13))
= 22 ÷ 26
= ¹¹/₁₃
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<em>Checking my answer:</em>
<em>We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.</em>
⇒ y + 19 = ¹¹/₁₃ (x + 13)
<em>I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given. </em>
Answer:
392m^2
Step-by-step explanation:
as the length = diameter of the circular park
then
Area = length * width = 56 * 7 = 392m^2
Answer:
a) 229 and 305 days
b) 229 days or less
c) 305 days or more
Step-by-step explanation:
The Empirical Rule(68-95-99.7 rule) states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 267
Standard deviation = 19
(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days
By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.
So
267 - 2*19 = 229 days
to
267 + 2*19 = 305 days
(b) How short are the shortest 2.5% of all pregnancies?______days or less
95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So
267 - 2*19 = 229 days
c) How long do the longest 2.5% of pregnancies last?________days or more
Explanation in b)
267 + 2*19 = 305 days
Answer
Find out the value of x .
To proof
SAS congurence property
In this property two sides and one angle of the two triangles are equal.
in the Δ ADC and ΔBDC
(1) CD = CD (common side of both the triangle)
(2) ∠CDA = ∠ CDB = 90 °
( ∠CDA +∠ CDB = 180 ° (Linear pair)
as given in the diagram
∠CDA = 90°
∠ CDB = 180 ° - 90°
∠ CDB = 90°)
(3) AD = DB (as shown in the diagram)
Δ ADC ≅ ΔBDC
by using the SAS congurence property .
AC = BC
(Corresponding sides of the congurent triangle)
As given
the length of AC is 2x and the length of BC is 3x - 5 .
2x = 3x - 5
3x -2x =5
x = 5
The value of x is 5 .
Hence proved
8(4)-5(1)+2(4)
Multiply
32-5+8
Solve from left to right
28+8
36
The answer is 36
