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3 years ago

A train leaves Westchester at 6:30. What time should it arrive at Middlewich

Mathematics

1 answer:

Sholpan [36]3 years ago

8 0

Answer:

a). 6:51

b). 6:30 am

c). 34 minutes

Step-by-step explanation:

a). Train leaves Westchester at 6:30.

From the arrival - departure table in column (2),

Arrival time of the train at middlewich = 6:51

b). Kate has to reach Southam before 9:00 am

Therefore, time of the latest train that she can catch to get to work on time is 6:30 am

By this train she can reach at 07:19 at Southam.

c). Duration of journey from Westchester to Eastwick = 06:34 - 06:00

= 00:34

≈ 34 minutes

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What is the name of the relationship between 1 and 4?

Zanzabum

< 1 and < 4 are alternate interior angles

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Show that the line with equation 4y+3x=44 is a tangent to the circle with centre (5,1) and radius 5.

viktelen [127]

When a line is a tangent to a circle then the point of a tangent on a circle is perpendicular and also equal to the radius

So for perpendicular.

$P = \frac{ax+by+c}{\sqrt{a^2 + b^2} }$

4y + 3x - 44 = 0

So, a = 4

b = 3

c = -44

x = 5

y = 1

Putting the values in the formula, we get

P = -4.2

Since the radius of the circle 5 is not equal to P, The line is not a tangent to the circle.

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3 years ago

If m∠a=47°, what is m∠b, m∠c, and m∠d? Explain how you know the measures are correct.

avanturin [10]

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

<h3>Further explanation</h3>

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

<u>Conclusion:</u>

m ∠a = 47°
m ∠b = 133°
m ∠c = 47°
m ∠d = 133°

<u>Notes:</u>

Supplementary angles are two angles when they add up to 180°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

<h3>Learn more</h3>

About the measure of the central angle brainly.com/question/2115496
Undefined terms needed to define angles brainly.com/question/3717797
Find out the measures of the two angles in a right triangle brainly.com/question/4302397

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent