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3 years ago

Question 1

Mathematics

1 answer:

Ahat [919]3 years ago

5 0

Answer: x = 22

Explanation:

1) Corresponding sides and correspoding angles of congruent triangles are equal.

2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.

That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:

∠A and ∠D are congruent
∠B and ∠ E are congruent
∠C and ∠F are congruent
Segment AB and segment DE are congruent
Segment BC and segment EF are congruent
Segment AC and segment DF are congruent

In the figures, it is given that the segment DF measures (1/2)x - 1 and the corresponding segment AC measures 10 units.

Hence, you set this equation: (1/2)x - 1 = 10

Solving for x:

(1/2)x = 10 + 1
(1/2)x = 11
x = 2(11)
x = 22 ← answer

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7/36
Multiply the top together and then the bottom together and the final numbers on top and bottom is your answer.

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What is the median of the data set? {17, 40, 23, 44, 44, 30} Enter your answer in the box.

beks73 [17]

To find the median of the data set, we must first order them from lowest to highest in increasing order. Let's rearrange them in that way:

{17, 23, 30, 40, 44, 44}

Then we begin by crossing one off from each side, until we get to the middle. However, we see that our middle here is both 30 and 40.

What we do in a case like this is add up the two numbers and divide by 2 (essentially find the mean of the two middlemost numbers). Let's do that now:

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So now we know that the median of the set of data is 35.

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3 years ago

In 2000, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. What is the populat

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Answer:

Step-by-step explanation:

Answer:

12,495 is the answer

Step-by-step explanation:

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Find f. A) 7.4 B) 8.2 C) 10.5 D) 11.1

tatyana61 [14]

F=72

g=6

------------

$\cos { \left( F \right) } =\frac { { e }^{ 2 }+{ g }^{ 2 }-{ f }^{ 2 } }{ 2eg }$

Therefore:

$\cos { \left( 72 \right) } =\frac { { e }^{ 2 }+{ 6 }^{ 2 }-{ f }^{ 2 } }{ 2\cdot e\cdot 6 } \\ \\ \cos { \left( 72 \right) } =\frac { { e }^{ 2 }+36-{ f }^{ 2 } }{ 12e }$

$\\ \\ 12e\cdot \cos { \left( 72 \right) } ={ e }^{ 2 }+36-{ f }^{ 2 }\\ \\ \therefore \quad { f }^{ 2 }={ e }^{ 2 }-12e\cdot \cos { \left( 72 \right) } +36\\ \\ \therefore \quad f=\sqrt { { e }^{ 2 }-12e\cdot \cos { \left( 72 \right) +36 } } \\ \\ \therefore \quad f=\sqrt { e\left( e-12\cos { \left( 72 \right) } \right) +36 }$

But what is e?

E=76

G=32

g=6

And:

$\frac { e }{ \sin { \left( E \right) } } =\frac { g }{ \sin { \left( G \right) } }$

Which means that:

$\frac { e }{ \sin { \left( 76 \right) } } =\frac { 6 }{ \sin { \left( 32 \right) } } \\ \\ \therefore \quad e=\frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } }$

If you take this value into account, you will discover that f is...

$f=\sqrt { \frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } } \left( \frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } } -12\cos { \left( 72 \right) } \right) +36 } \\ \\ \therefore \quad f=10.8\quad \left( 1\quad d.p \right)$

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3 years ago

frank reasoned that in the number 0.555, the valueof the 5 in the thousandths place is ten times the value of the 5 in the hundr

ollegr [7]

The reasoning of Frank is not correct. The value of 5 is the thousandths place is 1/10 times the value of 5 in the hundredths place instead of being 10 times.

In the question, we are given the number 0.555.

We can write it as:-

0.555 = 0.500 + 0.050 + 0.005

0.500 is the value of tenths place

0.050 is the value of hundredths place

0.005 is the value of thousandths place

We know that,

0.050*(1/10) = 0.050/10 = 0.005

Hence, the value of 5 is the thousandths place is 1/10 times the value of 5 in the hundredths place.

To learn more about thousandths place, here:-

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