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3 years ago

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When asked to write a point-slope equation for the line shown below, a student wrote y-4=2(x-1). How can he fix this to write th

e correct equation?

1 answer:

alexgriva [62]3 years ago

6 0

Point - slope form = y - y1 = m(x - x1)
y - 4 = 2(x-1)

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The slope of the graph of y = x is

kicyunya [14]

<span><span>Step One:<span> Identify two points on the line.</span></span><span>Step Two:<span> Select one to be (x</span>1<span>, y</span>1<span>) and the other to be (x</span>2<span>, y</span>2).</span><span>Step Three:<span> Use the slope equation to calculate slope. hope this helps </span></span></span>

6 0

3 years ago

Read 2 more answers

The picture shows a circular clock face.

marysya [2.9K]

Answer:

[C] 25π square inches

Step-by-step explanation:

<u><em>Given that:</em></u>

<em>the long hand of the clock is about 5 inches long.</em>

<u><em>To Find:</em></u>

<em>What is the approximate area of the clock face?</em>

<u><em>Solve:</em></u>

<em>Formula - </em><em>A =πr²</em>

<em>Note that;</em>

<em>π = 3.14 (about)</em>

<em>Radius - 5 inches</em>

<em>A =πr²</em>

<em>A = 3.14(5)²</em>

<em>A = 3.14(25)</em>

<em>A = 78.5</em>

<em>Now let see the answer choices:</em>

<em>A. 5π square inches ≈ 5(3.14) = 15.7</em>

<em>B. 10 π square inches ≈ 10(3.14) = 31.4</em>

<em>C. 25 π square inches ≈ 25(3.14) = 78.5</em>

<em>D. 100 π square inches ≈ 100(3.14) = 314</em>

<em />

<em>Hence, the answer is [C] 25 π square inches </em>

<em />

<u><em>Kavinsky~</em></u>

6 0

1 year ago

Read 2 more answers

Point C is the center of dilation. Line segment B A is dilated to create line segment B prime A prime. The length of C A is 4. T

saw5 [17]

Answer:

Step-by-step explanation:

Given

See attachment for figure

$CA = 4$

$CA' = 16$

Required

The scale factor (k)

Since point C is the center of dilation, the scale factor (k) is calculated using:

$k = \frac{CA + CA'}{CA}$

So, we have:

$k = \frac{4+16}{4}$

$k = \frac{20}{4}$

$k = 5$

8 0

2 years ago

Can you guys please help me? This is limited. (5v)^2/3 and the second one radical 10k

Eddi Din [679]

Here’s the answer for the first question and the second one stays 10k

7 0

3 years ago

The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(

Umnica [9.8K]

Answer:

(a) $A_1$ and $A_2$ are indeed mutually-exclusive.

(b) $\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}$ , whereas $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

(c) $\displaystyle P(B) = \frac{9}{100}$ .

(d) $\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}$ , whereas $P(A_1 \; |\; B) = \displaystyle \frac{4}{9}$

Step-by-step explanation:

<h3>(a)</h3>

$P(A_1 \; \cap \; A_2) = 0$ means that it is impossible for events $A_1$ and $A_2$ to happen at the same time. Therefore, event $A_1$ and $A_2$ are mutually-exclusive.

<h3>(b)</h3>

By the definition of conditional probability:

$\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}$ .

Rearrange to obtain:

$\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}$ .

Similarly:

$\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}$ .

<h3>(c)</h3>

Note that:

$\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}$ .

In other words, $A_1$ and $A_2$ are collectively-exhaustive. Since $A_1$ and $A_2$ are collectively-exhaustive and mutually-exclusive at the same time:

$\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ .

<h3>(d)</h3>

By Bayes' Theorem:

$\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}$ .

Similarly:

$\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}$ .

6 0

3 years ago