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2 years ago

Please help me thanks!

Mathematics

1 answer:

Alexxandr [17]2 years ago

8 0

Problem 1

Any pair of equilateral triangles are <u>always</u> similar triangles. We can use the SSS (side side side) similarity theorem to prove this. One triangle is an enlarged copy of the other, or a shrunken reduced copy.

The rectangle is NOT similar to the square. They are different shapes. Similar figures are figures that are the same shape, but different sizes.

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Problem 2

horizontal/vertical = horizontal/vertical

24/x = 6/5

24*5 = 6x

120 = 6x

x = 120/6

x = 20

Answer: The flagpole is 20 ft high (about 2 stories tall)

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Problem 3

The formula to use is $z = \sqrt{x*y}$

z = geometric mean of x and y

We multiply the numbers and take the square root. This only works for two values at a time. The geometric mean of three numbers will involve the cube root. Four numbers involves the 4th root, and so on.

Geometric mean of 6 and 10 is sqrt(60) = 7.74597 approximately
Geometric mean of 2 and 32 is 8 exactly
Geometric mean of 2 and 8 is 4 exactly
Geometric mean of 7 and 9 is sqrt(63) = 7.93725 approximately

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Problem 4

For each figure, the y is the altitude and can be determined using the geometric mean formula.

Figure on the left: y = sqrt(2*6) = sqrt(12) = 3.4641
Figure on the right: y = sqrt(6*14) = sqrt(84) = 9.1652

The decimal values are approximate.

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Problem 5

For 45-45-90 triangles, we divide the hypotenuse over sqrt(2) to find the leg length.

For the first triangle in the first row, we have y = 18/sqrt(2) = 9*sqrt(2) after rationalizing the denominator. Multiply top and bottom by sqrt(2).

Take this process in reverse to determine the hypotenuse if you know the leg length. This explains why the hypotenuse is 3.2*sqrt(2) for the second triangle in the first row.

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For 30-60-90 triangles, we go from the short leg x to the hypotenuse 2x.

Double the short leg to get the hypotenuse.

2x = 36

x = 36/2

x = 18

This is for the first triangle in the bottom row.

For the other triangle in this bottom row, we have a long leg of 4*sqrt(3). This must mean the short leg is exactly 4 units long. Therefore, the hypotenuse is 2*4 = 8 units long.

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<h3>Summary:</h3>

Top row, first column: y = 9*sqrt(2)
Top row, second column: y = 3.2*sqrt(2)
Bottom row, first column: x = 18
Bottom row, second column: y = 8

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eimsori [14]

Answer:

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$The\ value\ of\ \frac{6 \frac{1}{2}}{\frac{3}{4}} \ is\ 8.67 (Approx).$

Step-by-step explanation:

As given

$Monique\ made\ several\ batches\ of\ soup\ for\ a\ potluck\ supper.$

$Each\ batch\ required\ \frac{3}{4}\ of\ a\ pound\ of\ potatoes.$

$she\ used\ a\ total\ of\ 6 \frac{1}{2}\ pounds\ of\ potatoes.$

As given the expression.

$= \frac{6 \frac{1}{2}}{\frac{3}{4}}$

$= \frac{\frac{13}{2}}{\frac{3}{4}}$

Solving the above

$= \frac{13\times 4}{2\times 3}$

$= \frac{26}{3}$

In the decimal form.

= 8.67 (Approx)

$Therefore\ the\ value\ of\ \frac{6 \frac{1}{2}}{\frac{3}{4}} \ is\ \frac{26}{3}.$

$Therefore\ the\ value\ of\ \frac{6 \frac{1}{2}}{\frac{3}{4}} \ is\ 8.67 (Approx).$

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3 years ago

A child is flying a kite 145ft above the ground. The string makes an angle of 57 degrees from the child's hands. How much has be

Arturiano [62]

Answer: the length of string that been let out to fly the kite this high is 172.89 ft

Step-by-step explanation:

The length of string attached to the kite, the vertical height of the kite above the ground and the ground distance forms a right angle triangle.

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The height of the kite above the ground represents the opposite side of the triangle

To determine h, the length of the string that has been let out to fly the kite this high, we would apply the

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4 years ago

IN (3)

svetoff [14.1K]

Answer:

(a) Rule: Multiply the input (x) by 2 and add 5 to the result of the product

(b) $y =2x +5$

Step-by-step explanation:

Given

The attached table

Solving (a): The rule of the table in words

First, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using:

$(x_1,y_1) = (2,9)$

$(x_1,y_1) = (10,25)$

So, we have:

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The equation is calculated using:

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Using:

$(x_1,y_1) = (6,17)$

We have:

$y - 17 =2(x - 6)$

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Hence, the rule is:

Multiply the input (x) by 2 and add 5 to the result of the product

(b): The rule, in algebra

As solved in (a), the rule is:

$y =2x +5$

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3 years ago

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larisa86 [58]

Answer:

Step-by-step explanation:

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As you can see 56÷2=28

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4 years ago

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3 years ago

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