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3 years ago

What is the measure of angle k?

Mathematics

1 answer:

Murljashka [212]3 years ago

8 0

9514 1404 393

Answer:

59°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

∠N +∠L = 180°

(a +16) +(a -18) = 180

2a = 182 . . . . . . . . . . add 2

a = 91 . . . . . . . . . . . . divide by 2

Then the measure of angle M is ...

∠M = (a+30)° = (91 +30)° = 121°

and angle K is its supplement.

∠K = 180° -121°

∠K = 59°

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After going on a diet,Amy finds that her weight has decreased by 25%.If her weight now is 75kg how much does her weight before?

Rainbow [258]

Answer:

Her weight before was 100kg.

Step-by-step explanation:

This question can be solved using a rule of three.

Amy finds that her weight has decreased by 25%

So her weight is 100-25 = 75% = 0.75 of the original amount(what it was before).

Her current weight is 75kg.

Her previous weight was x, which is 100% = 1.

75 - 0.75

x - 1

$0.75x = 75$

$x = \frac{75}{0.75}$

$x = 100$

Her weight before was 100kg.

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3 years ago

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Sindrei [870]

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3 years ago

The Fun Guys game rental store charges an annual fee of $15 and charges $5.50 per game rented. The Game Bank charges an annual f

wolverine [178]

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Fun Guys cost= 15 +5.5.a
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4 years ago

Can someone help me with this problem

Naily [24]

<h3>Answer: Choice A</h3><h3>The point Z ' is at (8,4)</h3><h3>The point Y ' is at (0,4)</h3>

=================================================

Explanation:

The key thing here is that point Z does not move. Why not? Because this is where the center of dilation occurs. The center point is fixed. Everything around the center will expand away from, or contract toward, the center.

In this case, the scale factor is 4/5 = 0.8 which is less than 1. So points will contract toward the center. The old pre-image shrinks to make the image smaller.

Note how point Y = (-2,4) is 10 units away from point Z. You can count out the spaces or subtract the x coordinates. Use an absolute value to make sure the result is positive

|x1-x2| = |-2-8| = |-10| = 10

|x2-x1| = |8-(-2)| = |8+2| = |10| = 10

So 0.8 times this distance is therefore 0.8*10 = 8 meaning that point Y' is going to be 8 units away from point Z' or Z.

Subtract 8 from the x coordinate of point Z to get x-8 = 8-8 = 0.

The y coordinate stays the same at y = 4 the whole time.

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

In short, point Y starts at (-2,4) and moves to (0,4)

Distance from Y to Z is 10 units

Distance from Y' to Z' is 8 units

8/10 = 4/5 = 0.8 is the scale factor

Point Z does not move. So Z and Z' are at the same location.

5 0

3 years ago

Read 2 more answers

Type the correct answer in each box. Round your answers to two decimal places. Find the average rate of change of f(x) = log2(3x

Artemon [7]

Answer:

on [3, 4] = 0.30

on [4, 5] = 0.18

on [5, 6] = 0.12

Step-by-step explanation:

The average rate of change f, of a function f(x) on an interval [a, b] is given by;

$f = \frac{f(b) - f(a)}{b - a}$ -------------(i)

In our case,

f(x) = log 2(3x - 6)

Now let's get the average rate of change of f(x) on;

(i) [3, 4]

Here, a = 3 and b = 4

f(a) = f(3) [This is f(x) at x = 3]

=> f(3) = log[2(3(3) - 6)]

=> f(3) = log[2(9 - 6)]

=> f(3) = log[2(3)]

=> f(3) = log[6]

Also,

f(b) = f(4) [This is f(x) at x = 4]

=> f(4) = log[2(3(4) - 6)]

=> f(4) = log[2(12 - 6)]

=> f(4) = log[2(6)]

=> f(4) = log[12]

Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;

$f = \frac{log 12 - log 6}{4 - 3}$ [Remember that log m - log n = log (m / n)]

$f = \frac{log (12 / 6)}{4 - 3}$

$f = \frac{log (2)}{1}$

f = log 2 = 0.3010

f = 0.30 [to two decimal places]

∴ The average rate of change on [3, 4] = 0.30

(ii) [4, 5]

Here, a = 4 and b = 5

f(a) = f(4) [This is f(x) at x = 4]

=> f(4) = log[2(3(4) - 6)]

=> f(4) = log[2(12 - 6)]

=> f(4) = log[2(6)]

=> f(4) = log[12]

Also,

f(b) = f(5) [This is f(x) at x = 5]

=> f(5) = log[2(3(5) - 6)]

=> f(5) = log[2(15 - 6)]

=> f(5) = log[2(9)]

=> f(5) = log[18]

Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;

$f = \frac{log 18 - log 12}{5 - 4}$ [Remember that log m - log n = log (m / n)]

$f = \frac{log (18 / 12)}{5 - 4}$

$f = \frac{log (1.5)}{1}$

f = log 1.5 = 0.176

f = 0.18 [to two decimal places]

∴ The average rate of change on [4, 5] = 0.18

(iii) [5, 6]

Here, a = 5 and b = 6

f(a) = f(5) [This is f(x) at x = 5]

=> f(5) = log[2(3(5) - 6)]

=> f(5) = log[2(15 - 6)]

=> f(5) = log[2(9)]

=> f(5) = log[18]

Also,

f(b) = f(6) [This is f(x) at x = 6]

=> f(6) = log[2(3(6) - 6)]

=> f(6) = log[2(18 - 6)]

=> f(6) = log[2(12)]

=> f(6) = log[24]

Now substitute the values of a, b, f(a) and f(b) into equation (i) as follows;

$f = \frac{log 24 - log 18}{6 - 5}$ [Remember that log m - log n = log (m / n)]

$f = \frac{log (24 / 18)}{6 - 5}$

$f = \frac{log (1.33)}{1}$

f = log 1.33 = 0.124

f = 0.12 [to two decimal places]

∴ The average rate of change on [5, 6] = 0.12

5 0

3 years ago

Read 2 more answers