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dimulka [17.4K]

3 years ago

14

A flagpole is 10 m tall and has a shadow that is 7 m long. At the same time how tall is a nearby building if its shadow is 28m l

ong?

1 answer:

MAXImum [283]3 years ago

3 0

Answer:

40m

Step-by-step explanation:

28÷7=4

10 x 4= 40

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WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!! (image attatched)

alexgriva [62]

The answer would be the first one

4 0

3 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

<u>Given sequence</u>:

6, 20, 40, 66, 98, 136, ...

Calculate the <u>first differences</u> between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the <u>second differences:</u>

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the <u>second differences are the same</u>, the sequence is quadratic and will contain an n² term.

The <u>coefficient</u> of the n² term is <u>half of the second difference</u>.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences <em>between</em> the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

1 year ago

One of the legs of a right triangle measures 4 cm and its hypotenuse measures 18 cm. Find the measure of the other leg. If neces

Aleks04 [339]

Answer:

√308 or 17.5

Step-by-step explanation:

c^2=a^2+b^2

c^2-a^2=b^2

Substitute

18^2-4^2=b^2

324-16=b^2

b^2=308

b=√308 or b=17.5

7 0

2 years ago

X^2 + y^2=40 and y=x-4 solve this simultaneous equation

inn [45]

Write x-4 instead of y.
x²+(x-4)²=40
x²+x²-8x+16=40
2x²-8x-24=0
x²-4x-12=0
(x-6)(x+2)=0
x=6 or x=-2

for x=6, y=6-4 = 2
for x=-2, y=-2-4 = -6

3 0

3 years ago

Simplify your answer

Lelechka [254]

Answer:

<h2><u>0</u></h2>

Step-by-step explanation:

If 2u-6=4, let's solve for u.

Add 6 to both sides

2u-6+6 = 4+6

Simplify

2u = 10

Divide both sides by 2

u = 5

Now, we can solve u-5

5-5 = 0

8 0

2 years ago

Read 2 more answers