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andrey2020 [161]
2 years ago
7

What is the value of x?

Mathematics
1 answer:
Lerok [7]2 years ago
7 0

Answer:

  3√2

Step-by-step explanation:

The hypotenuse of an isosceles right triangle is √2 times the side length.

  x = 3√2

_____

All these triangles are similar, so the ratio of hypotenuse to leg is the same for all.

  hypotenuse/leg = x/3 = (3+3)/x

  x² = 3·6 = 3²·2 . . . . cross multiply (identify square factors)

  x = 3√2 . . . . . take the square root

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10 men working for 6 days can complete 5 copies of a book if there are 8 men working to complete 4 copies of the book how many d
Musya8 [376]

Answer:

6 Days

Step-by-step explanation:

Practically:

It takes,

10 Men ( complete ) 5 Copies --> 6 Days

So, 2 Men can complete 1 copy in 6 days.

Question asks us :

8 Men ( complete ) 4 Copies --> X Days

It will take 6 days because the proportion of men to copies is same as the first equation.

Theoretically:

10 Men 5 Copies 6 Days

8 Men   4 Copies  X Days

> 6/X = 8/10 ( If men decrease the number of days increase. So, it is an indirect proportion. ) . 5/4 ( If copies decrease the number of days decrease as well. So, it is a direct proportion. )

> 6/X = 8/10 . 5/4

> 6/X = 40/40

> 6/X = 1

<h2>> X=6</h2><h2></h2><h2><em>I hope it will be understood.</em></h2><h2><em>If I have any inaccuracies please let me know.</em></h2><h2><em>Have a nice day and never stop questioning!</em></h2><h3><em></em></h3>

6 0
2 years ago
Read 2 more answers
What is the diameter of a circle with a circumference of 220 ft
tino4ka555 [31]

Circumference of the circle is given as = 220 feet

We have to find the diameter.

Circumference is found as = 2 * PI * r

220=2*3.14*r

220=6.28r

r=35.03

Diameter is 2*radius

Diameter = 2\times35.03 = 70.06

Hence, diameter of the circle is 70.06 feet.

4 0
3 years ago
The surface area of the prism below is 264 square units . Find the missing dimensions of this prism. ( picture is in the picture
nignag [31]

Answer:

The missing dimension is 4 units.

Step-by-step explanation:

In the given prism,

Of all the surfaces,

There are three rectangular surfaces and two triangular surfaces

<h2>Analyzing areas of rectangular surfaces:</h2>

1)The two rectangles with dimensions of 15 units and 5 units:

The area of each rectangle = Length of rectangle \times Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 5 units.

Area of each rectangle = 15\times 5 ;

Area of each rectangle = 75 square units.

Sum of areas of the two rectangles = 2\times 75

Sum of areas of the two rectangles = 150 square units (equation 1)

2) The rectangle with the dimensions 15 units and 6 units:

The area of thus rectangle=  Length of rectangle \times Breadth of rectangle

From the diagram,

Length of rectangle = 15 units,

Breadth of rectangle = 6 units.

Area of the rectangle = 15\times 6 ;

Area of the rectangle = 90 square units. (equation 2)

From equation 1 and equation 2,

Therefore sum of areas of all rectangles in the prism = 150 + 90

Sum of areas of rectangles = 240 square units.

We also know,

Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles

Given, Total surface area of prism = 264 square units.

Therefore from the formula,

Sum of areas of triangles = Total surface area - sum of areas of reactangles

Sum of areas of triangles = 264 - 240

Sum of areas of triangles = 24 square units. (equation 3)

Let the missing dimension be 'h units'

<h2>Calculating sum of areas of triangles:</h2>

From diagram,both triangles are congruent,hence have the same area

Area of a triangle = \frac{1}{2}\times base\times height

From diagram,

Base = 6 units,

Height = h units.

Area of a triangle =\frac{1}{2}\times 6\times h = 3h square units.

Sum of the areas of both triangles = 3h+3h = 6h square units.

Using equation 3, we get

6h = 24;

h = \frac{24}{6}

Therefore,

h = 4 units.

Therefore,

The missing dimension is 4 units.

4 0
3 years ago
Jonah is going to the store to buy candles small candles cost $3.50 and large candles cost five dollars he needs to buy at least
marysya [2.9K]

Answer:

He can purchase a maximum of 6 large candles.

Step-by-step explanation:

If he purchases 6 large candles and 14 small candles:

$5.00 x 6 = $30.00

$3.50 x 14 = $49.00

$49.00 + $30.00 = $79.00

6 0
3 years ago
1. Solve the system of equations by substitution and check your solution.
dedylja [7]

Answer:

x = 7 and y = −2

(7, -2)

Step-by-step explanation:

x = 1 - 3y

3x + 3y = 15

Substitute −3y + 1 for x in 3x + 3y = 15:

3(1 - 3y) + 3y = 15

3 - 9y + 3y = 15

3 - 6y = 15

-3           -3

-6y = 12

/-6     /-6

y = -2

Now we solve for x. Substitute −2 for y in x = −3y + 1:

x = 1 - 3y

x = 1 + (-3)(-2)

x = 1 + 6

x = 7

Now we check our solution.

x = 1 - 3y

7 = 1 + (-3)(-2)

7 = 7 ✅

3x + 3y = 15

3(7) + 3(-2) = 15

21 - 6 = 15

15 = 15 ✅

6 0
3 years ago
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