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Tanzania [10]
3 years ago
14

What is the value of X in the following parallelogram?

Mathematics
1 answer:
Furkat [3]3 years ago
7 0

Answer: x = 35

Step-by-step explanation:

In a parallelogram, the opposite sides and the opposite angles are equal and parallel.

Also, the consecutive angles in a parallelogram are supplementary. This means that the sum of the consecutive angles is 180 degrees.

Angle (2x - 10) and angle (2x + 50) are consecutive angles. Therefore,

2x - 10 + 2x + 50 = 180

2x + 2x - 10 + 50 = 180

4x + 40 = 180

4x = 180 - 40 = 140

x = 140/4

x = 35

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J.k. Rowling and R.L. Stone are both ready hunger games . J.k. Reads 35 pages every 2 hours and R.L. Reads 45 pages every 3 hour
san4es73 [151]

Answer:

The rate of change for each reader is :

For J K Rowling :  17 and a half pages per hour

For R L Stone :  15   pages  per hour

Step-by-step explanation:

Here the reading rate of each reader is given as:

J.K. Reads 35 pages every 2 hours.

So, the number of pages read by J K  in 2 hours  = 35 pages

⇒ The number of pages read per hour  =  35 / 2  = 17 . 5 pages

So, the pages read by J K Rowling in 1 hour is 17 and a half pages.

R L Stone reads 45 pages every 3 hours.

So, the number of pages read by R L  in 3 hours  = 45 pages

⇒ The number of pages read per hour  =  45 / 3  = 15 pages

So, the pages read by R L Stone in 1 hour is 15 pages.

Hence, the rate of change for each reader is :

For J K Rowling :  17 and a half pages  per hour

For R L Stone :  15   pages  per hour

5 0
3 years ago
Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed
garik1379 [7]
F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards. 
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards. 
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x. 
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
 => Area, A 
= 2x (y1 - y2) 
= 2x (18 - x^2 - 2x^2 + 9) 
= 2x (27 - 3x^2) 
= 54x - 6x^3 
For area to be maximum, dA/dx = 0 and d²A/dx² < 0 
=> 54 - 18x^2 = 0 
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants) 

d²A/dx² = - 36x < 0 for x = √3 
=> maximum area 
= 54(√3) - 6(√3)^3 
= 54√3 - 18√3 
= 36√3. 
4 0
3 years ago
P(-3,6), Q(-3,-6) and R(6,-2) are the vertices of a triangle. Calculate the perimeter of this triangle.​
Eva8 [605]

Answer:

33.89

Step-by-step explanation:

the side lengths are the distances between the corner points of the triangle.

P and Q have the same x value, and they therefore create a side parallel to the y-axis. and it is easy to find the length of this side : it is just the difference of the y values.

PQ = 6 - (-6) = 6 + 6 = 12

QR and RP are trickier.

we need Pythagoras to calculate the length of the direct connection between these points as the Hypotenuse of the right triangles with the differences in x and in y values as the other sides.

QR :

QR² = (-3 - 6)² + (-6 - -2)² = (-9)² + (-4)² = 81 + 16 = 97

QR = sqrt(97) ≈ 9.848857802

RP :

RP² = (6 - -3)² + (-2 - 6)² = 9² + (-8)² = 81 + 64 = 145

RP = sqrt(145) ≈ 12.04159458

the perimeter/circumference of the triangle is the sum of all 3 sides

= 12 + sqrt(97) + sqrt(145) ≈ 33.89

3 0
3 years ago
1. Suppose you have 62 toothpicks and a bunch of rubber bands.
ehidna [41]

Base-ten units are used to represent numbers in blocks

<h3>How to represent the bundle of toothpicks</h3>

The bundle is given as:

Bundle = 62

Rewrite as:

Bundle = 60 + 2

Express 60 as a product

Bundle = 6 * 10 + 2

See attachment for the drawing that represents the bundle

<h3>Ways to interpret the 6 in 62</h3>

The 6 in 62 can be interpreted in the following ways

  • Way 1: 6 tens
  • Way 2: 60

Read more about base-ten units at:

brainly.com/question/12386995

7 0
2 years ago
A gallon of milk in Oregon costs $2.50. The price of a gallon of milk in Hawaii is 3 times more than the price of a gallon of mi
Sonbull [250]

Answer:

$12.50

Step-by-step explanation:

First, find the cost of a gallon of milk in Hawaii by multiplying 2.50 by 3:

2.5(3)

= 7.5

Then, subtract this from 20:

20 - 7.5

= 12.5

So, Fernando should receive $12.50 in change

3 0
3 years ago
Read 2 more answers
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