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Ipatiy [6.2K]
3 years ago
11

Questions are in the screenshot.

Mathematics
1 answer:
White raven [17]3 years ago
6 0

For question 4, x = 18 units,

For question 5, x = 8.333 units.

Step-by-step explanation:

Step 1:

Since the given polygons are similar to each other, all the ratios of one polygon to the other will remain equal for all the values of the two similar polygons.

We take the ratio of the same sides of both polygons i.e. the ratio of the lengths or the ratio of the widths.

Step 2:

For question 4, the first rectangle has a length of 9 units while the width is 3 units.

For the second rectangle, the length is x as x is greater than the width in the first rectangle. The width is 6 units.

The ratio of the first rectangle to the second is;

\frac{3}{6} : \frac{9}{x} , x = (9)(\frac{6}{3} ) = 18. So x = 18 units.

Step 3:

The shapes in question 5 are made of a square and a triangle.

For the first shape, the side length is 6 units while the side of the triangle is 10 units.

For the second shape, the side length is 5 units while the side of the triangle is x units.

The ratio of the first shape to the second is;

\frac{6}{5} : \frac{10}{x} , x = (10)(\frac{5}{6} ) = 8.333. So x = 8.333 units.

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The hypotenuse of a right triangle is 10cm long. The longer leg is 2cm longer than the shorter leg. Find the side lengths of the
Crazy boy [7]
We need Pythagoras theorem here
a^2+b^2 = c^2
a, b =  legs of a right-triangle
c = length of hypotenuse

Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 +   S^2+4S+4  = 100 cm^2   [collect terms and isolate]
2S^2+4S =  100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0   means (S+8)=0, S=-8
or                                   (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm

5 0
3 years ago
Find the total surface area in square inches, of the following 3-
Ivenika [448]

Answer:

81 in²

Step-by-step explanation:

The 3-dimensional shape given is a square pyramid having a square base, and 4 right triangular side faces that are the same.

The surface area can be calculated by finding the area of the square base and the area of the 4 triangular side faces. Then sum all the areas together.

Or, we can use the following formula below: Base Area + ½(Perimeter of base) × Slant Length

Where,

Base area = s² = 5² = 25 in²

Perimeter of base = 4(s) = 4(5) = 20 in

Slant height = 5.6 in

Surface area = 25 + ½(20) × 5.6

= 25 + 10 × 5.6

= 25 + 56

Surface area = 81 in²

6 0
3 years ago
6. The population of a town is 680 000 correct to the nearest 10 000. Write down
serg [7]

Answer:

a) 675 000

b) 685 000

Step-by-step explanation:

The population of a town is 680 000 correct to the nearest 10 000.

a) To find it lower bound, we level of accuracy by 2 and then subtract from 680 000

The lower bound is:

680 000-5000=675,000

Therefore the least possible population of the town is 675 000

b) We repeat the same process to find the upper bound

680 000+5000=685,000

6 0
3 years ago
A baseball team can spend up to $1500 on bats. Bats cost $32 each. Which inequality represents the number of bats b they can buy
Katena32 [7]

Answer:

32b<1500

Step-by-step explanation:

a. the can spend up to 1500 but not more so it has to be less

b= 46 bats

46x32= 1472<1500

6 0
3 years ago
Solution of these two sums please I need it ASAP please please.<br>I'll mark as brainliest please ​
VARVARA [1.3K]

a)-260

b)92

◉‿◉◉‿◉◉‿◉◉‿◉

8 0
2 years ago
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