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2 years ago

AABCIS translated 6 units up and 3 units left to create AA'BC.

Mathematics

1 answer:

Alona [7]2 years ago

4 0

Answer:

A'(-4, 8)
B'(-2, 11)

Step-by-step explanation:

Translation 3 left and up 6 adds (-3, 6) to each coordinate pair.

<h3>Application </h3>

(x, y) ⇒ (x -3, y +6)

A(-1, 2) ⇒ A'(-1 -3, 2 +6) = A'(-4, 8)

B(1, 5) ⇒ B'(1 -3, 5 +6) = B'(-2, 11)

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The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.

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<u>Given</u>:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

<u>Length of AD:</u>

The length of AD is given by

$cos 60^{\circ}=\frac{FD}{8}$

$4=FD$

Length of AD = 8 cm

<u>Slant height:</u>

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

$sin \ 60^{\circ}=\frac{EF}{8}$

$sin \ 60^{\circ} \times 8=EF$

$\frac{\sqrt{3}}{2} \times 8=EF$

$4\sqrt{3}=EF$

Thus, the slant height EF is 4√3

<u>Surface area of the square pyramid:</u>

The surface area of the square pyramid can be determined using the formula,

$SA=Area \ of \ square + \frac{1}{2} (Perimeter \ of \ base ) (slant \ height)$

Substituting the values, we have;

$SA=8^2+\frac{1}{2}(8+8+8+8)(4 \sqrt{3})$

$SA=64+\frac{1}{2}(32)(4 \sqrt{3})$

$SA=64+(16)(4 \sqrt{3})$

$SA=64+64 \sqrt{3}$

The exact form of the area of the square pyramid is $64+64 \sqrt{3}$

Substituting √3 = 1.732 in the above expression, we have;

$SA = 64 + 110.848$

$SA = 174.848$

Rounding off to one decimal place, we get;

$SA = 174.8$

Thus, the area of the square pyramid is 174.8 cm²

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3 years ago

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The polygons in each pair are similar. Find the scale factor of the smaller figure to the larger figure.

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A school director must randomly select 6 teachers to part in a training session. There are 34 teachers at school. In how many di

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Answer:

Total possible ways to select 6 teachers from 34 teacher are $^{34}C_6=1344904$ .

Step-by-step explanation:

It is given that total number of teachers at a school is 34.

The school director must randomly select 6 teachers to part in a training session.

$^nC_r=\frac{n!}{r!(n-r)!}$

Where, n is total possible outcomes and r is number of selected outcomes.

Total teachers = 34

Selected teachers =6

Total number of possible ways to select 6 teachers from 34 teacher is

$^{34}C_6=\frac{34!}{6!(34-6)!}$

$^{34}C_6=\frac{34\times 33\times 32\times 31\times 29\times 28!}{6!(28)!}$

$^{34}C_6=1344904$

Therefore total possible ways to select 6 teachers from 34 teacher are $^{34}C_6=1344904$ .

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A circle with radius of 1 cm sits inside a 11 cm x 12 cm rectangle.

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Answer:

125.72

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radius equals pi(r)2

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3 years ago

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