1/2.5+1/5.8+1/8.11+...+1/97.100

Answer:

  x = 25°

Step-by-step explanation:

There are different ways to get there.

The unmarked angle at bottom left is an alternate interior angle with the one at the top marked 50°. So, it is congruent to 50°.

That makes the angles along the line at the bottom be ...

  50° +x° +105° = 180° . . . . . the measure of a linear angle

  x° = 180° -155° = 25°

__

The unmarked angle at top right is a same-side interior angle relative to the one at bottom marked 105°. As such it is supplementary to 105°, and has measure ...

  180° -105° = 75°

This angle (upper right) is an exterior angle to the triangle. As such, it is equal to the sum of the two "remote" interior angles of the triangle—the ones marked 50° and x°.

  75° = 50° +x°

  25° = x° . . . . . . . subtract 50°

__

The unmarked interior angle of the triangle is an alternate interior angle with the one marked 105°. So, it is congruent to 105°. The sum of the triangle interior angles is 180°, so you have ...

  x° +50° +105° = 180°

  x = 180° -155° = 25° . . . . as we had with our first approach

Answer:

f(2) = -6

f inverse of 1/2 is 17/2

Step-by-step explanation:

We are given a function [tex]\displaystyle \large{f(x) = \frac{6}{2x-5}}[/tex]

To solve for part (a), we have to substitute x = 2 in f(x).

[tex]\displaystyle \large{f(2)=\frac{6}{2(2)-5} \\\displaystyle \large{f(2)=\frac{6}{4-5}=\frac{6}{-1}=-6[/tex]

Therefore, f(2) is -6.

Now we solve for part (b), we see the notation which is a minor different similar to f(x). We see that there is exponent of -1 between f and 1/2. The part (b) indicates that the function is an inverse of f(x).

[tex]\displaystyle \large{y=f^{-1}(x) \longrightarrow x=f(y)}[/tex]

To solve for part (b), first we solve for x in the function. Let f(x) = y.

[tex]\displaystyle \large{y=\frac{6}{2x-5}}[/tex]

Multiply both sides by 2x-5.

[tex]\displaystyle \large{y(2x-5)=\frac{6}{2x-5}(2x-5)}\\\displaystyle \large{y(2x-5)=6}[/tex]

Divide both sides by y-term.

[tex]\displaystyle \large{\frac{y(2x-5)}{y}=\frac{6}{y}}\\\displaystyle \large{2x-5=\frac{6}{y}}\\\displaystyle \large{2x=\frac{6}{y}+5}\\\displaystyle \large{x=\frac{6}{2y}+\frac{5}{2}}\\\displaystyle \large{x=\frac{3}{y}+\frac{5}{2}}[/tex]

Then swap x and y which we receive [tex]\displaystyle \large{y=\frac{3}{x}+\frac{5}{2}}[/tex]

Therefore, [tex]\displaystyle \large{f(x)=\frac{6}{2x-5} \longrightarrow f^{-1}(x)=\frac{3}{x}+\frac{5}{2}}[/tex]

Thus, [tex]\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{3}{\frac{1}{2}}+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=6+\frac{5}{2}}\\\displaystyle \large{f^{-1}(\frac{1}{2})=\frac{17}{2}}[/tex]

____________________

Let me know if you have any questions in comment.

Answer:

oil production: John d Rockefeller

steel manufacturing: Andrew Carnegie

Clothing: william cockerill

industrializatuon expansion: Frances Cabot Lowell

Step-by-step explanation:

The steps to construct a parallelogram using a ruler and a compass are;

1. Draw a starting line segment l linger than 8 cm.

2. Mark point K on the line segment.

3. Widen the compass to a radius of 8 cm using the ruler.

4. Place the compass at point K and with the 8 cm radius mark point L on the line l.

5. At point L construct a 45° angle as follows;

The above steps bisects the 90° angle of the perpendicular lines.

6. Adjust the radius of the compass to give an opening of 6 cm and from point L draw an arc to intersect XL at M.

7. At point M construct a line YM at 45° angle to the line l.

8. From point M draw an arc to intersect YM and label the point as point N.

9. Join point M and N to complete the construction of the parallelogram KLMN.

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Answer:

by getting the solution

Step-by-step explanation:

Answer:

1100

Step-by-step explanation:

Answer:

100.73

Step-by-step explanation:

Area of Rectangle=140

Area of Semi-Circle=39.27

Area of Rectangle-Area of Semi-Cirlce=100.73

Answer:

Step-by-step explanation:

Wind, friction and terrain (flat versus hilly) all oppose motion of the bike.  Air resistance increases as the bicyclist goes faster (there's none at 0 mph, a significant amount at 30 mph, a greater amount at 40 mph, and so on).

Answer:

(-1,-6.5)

Step-by-step explanation:

midpoint formula: (x_m, y_m) = (x1+x2)/2),(y1+y2)/2)

(2-4)/2=-1, -9-4=-13/2=-6.5

=(-1,-6.5)

The average speed Mr and Mrs Ozawa should drive is 62 miles per hour.

The average speed is calculated for a period of time while instantaneous speed is calculated at certain instant of time.

For instantaneous speed and average speed are equal for an object moving with constant speed.

The total distance travelled is given as 496 miles.

And, the total time taken is 8 hours.

Average speed can be calculated by taking the ratio of total distance and time as follows,

Total distance ÷ Total time

⇒ 496 ÷ 8

⇒ 62

Hence, the average speed is given as 496 miles per hour.

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Answer:

$270 in all

Just multiply 9x20 and 9x10 and add them together

Answer:

The slope of function A is less than the slope of function B

Explanation:

The slope for function B is 1/2, which is greaterthan 1/5, the slope of function A.

Answer:

the slope on Function A is less than Function B

Step-by-step explanation:

By doing rise over run we can get 1/2 on Function B and the Y intercept is 5 so the equation is y=1/2x+5

Answer:

14 give me that badge :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

14 faces

Answer: 4 miles in 1/3 hour

Step-by-step explanation:

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

Answer:

y = -5x - 4

Step-by-step explanation:

yeah-ya............ right?

Answer:

Let's solve for x.

x+y+z=8

Step 1: Add -y to both sides.

x+y+z+−y=8+−y

x+z=−y+8

Step 2: Add -z to both sides.

x+z+−z=−y+8+−z

x=−y−z+8

Answer:

x=−y−z+8

Answer:

-3

Step-by-step explanation:

x

+

3

=

O

A

=

−

x

+

13

=

X

=

−

3

=

=

−

3

1

=

=

−

3

1

=

=

−

3

Answer:

C

A. X-intercept (6,0) and y-intercept (0,-8) wrong

B. x-intercept (-8,0) and y-intercept (0,6)wrong

C. x-intercept (4,0) and y-intercept (0,-3) correct

D. x-intercept (-3,0) and y-intercept (0,4) wrong

Answer:

  0.8646

Step-by-step explanation:

The digit in the hundred-thousandths place is 9, so is greater than 4. That means the digit in the ten-thousandths place is increased by 1 when the number is rounded.

  0.864595 rounds to 0.8646

Answer:

4(x+2) = 4x + 8

Step-by-step explanation:

because if they are multiplied out it would be 4x+8 = 4x + 8 which means it is infinite because both sides are equal

The range of possible values for the variable is x < 12

From the given figure, we can see that the side facing angle 30 degrees, is greater than the side facing angle 3x -6. Therefore the inequality expression is true based on the figure.

30 > 3x - 6

Swap sides

3x - 6 < 30

Add 6 to both sides

3x - 6 + 6 < 30 + 6

3x < 36

Divide both sides by 3

3x/3 < 36/3

x < 12

Hence the range of possible values for the variable is x < 12

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Answer:

- (b - 9)(b + 8)

Step-by-step explanation:

72 + b - b² ← factor out - 1 from each term and rearrange into standard form

= - (b² - b - 72) ← factor the quadratic

Consider the factors of the constant term (- 72) which sum to give the coefficient of the b- term (- 1)

The factors are - 9 and + 8

Use these factors to split the b- term

b² - 9b + 8b - 72 ( factor the first/second and third/fourth terms )

b(b - 9) + 8(b - 9) ← factor out (b - 9) from each term

(b - 9)(b + 8)

Then

72 + b - b² = - (b - 9)(b + 8)

Answer:

20%

Step-by-step explanation:

54-45 = 9

9/45 = 0.2

0.2*100 = 20

Production increased 20%

Answer:

16$

Step-by-step explanation:

Answer:

[tex] \frac{ {y}^{2} }{4 {x}^{5} } [/tex]

Answer:

y=-2x-3

Step-by-step explanation:

the slope is 2/1 going down and the y intercept is -3

Answer: No solution

Step-by-step explanation:

VX+12-12=x-12

VX=x-12

VX/x=x/x-12/x= X≠0