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2 years ago

∆ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices.

2 answers:

6 0

First, we need to remember that the distance between two points (x1, y1) and (x2, y2) can be calculated with √[ (x1 - x2)^2 + (y1 - y2)^2 ]. Thus, we apply this formula to measure the lengths of AB, BC, and AC in ∆ABC. AB = √[ (1 - -2)^2 + (7 - 2)^2 ] = √25 = 5 units BC = √[ (-2 - 4)^2 + (2 - 2)^2 ] = √36 = 6 units CA = √[ (4 - 1)^2 + (2 - 7)^2 ] = √25 = 5 units From this, we can clearly see that BC is the longest side of ∆ABC with a length of √36 = 6 units. Thus, the answer is B: 6. Since ∆ABC sides 5, 5, and 6. That makes it an isosceles triangle. Which makes the right answer to be B: isosceles. Now, if we form a new triangle, ∆ABD, with D at (1, 2), we have the following lengths: AB = 5 units BD = √[ (-2 - 1)^2 + (2 - 2)^2 ] = √9 = 3 units AD = √[ (1 - 1)^2 + (7 - 2)^2 ] = √25 = 5 units Similarly, since ∆ABD has sides with lengths of 5, 3, and 5. This means it is isosceles. The answer for this item is B: isosceles. We have shown above that AD is 5 units. Thus, answer is B: 5<span>.</span>

user100 [1]2 years ago

4 0

Answer:

BC is the longest side of ∆ABC with a length of 6 units.

The lengths makes it an isosceles triangle.

The new triangle is a Right Scalene

AD is 5 Units

Step-by-step explanation:

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2 years ago

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Will works 7 hours a day, 6 days a week.

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A day
= £9.20x7
= £64.40

6 days
£64.40x6= £386.40

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2 years ago

Consolidated Power, a large electric power utility, has just built a modern nuclear power plant. This plant discharges waste wat

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Answer:

We conclude that the plant should shut down.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 60

Sample mean, $\bar{x}$ = 61.498

Sample size, n = 100

Alpha, α = 0.05

Population standard deviation, σ = 6

a) First, we design the null and the alternate hypothesis such that the power plant will be shut down when the null hypothesis is rejected.

$H_{0}: \mu \leq 60\\H_A: \mu > 60$

We use One-tailed(right) z test to perform this hypothesis.

b) Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{61.498 - 60}{\frac{6}{\sqrt{100}} } = 2.49$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.64$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.

Calculating the p-value from the z-table:

P-value = 0.0063

Since,

P-value < Significance level

We reject the null hypothesis and accept the alternate hypothesis. Thus, the temperature of waste water discharged is greater than 60°F. We conclude that the power plant will shut down.

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2 years ago

Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

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Answer:

10.12 $m^{3}$