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3 years ago

If you have two triangles with the same shape but one is twice as large as the other, are the triangles similar?

1 answer:

8 0

The triangles are similar because of one triangle is 2x bigger than the other there seems to be a dilation. And since on triangle is 2x bigger the dilation between both triangles would be 2. I hope this helped :)

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Determine whether the geometric series is convergent or divergent. 10 − 6 + 3.6 − 2.16 + convergent divergent Correct: Your answ

Misha Larkins [42]

Answer:

The series CONVERGES with the sum being 6.25.

Step-by-step explanation:

Given that the geometric series is 10 - 6 + 3.6 - 2.16 + ....

So the first term of the geometric progression is, $a_{1}$ = 10

The second term of the geometric progression is $a_2$ = -6 = $a_1$ × r = 10 × r

where r is the constant ratio.

Therefore r = $\frac{-6}{10}$ = -0.6

The third term of the geometric progression, $a_3$ = 3.6 = $a_2$ × r = -6 × -0.6 = 3.6

The fourth term of the geometric progression, $a_4$ = -2.16 = $a_3$ × r = 3.6 × -0.6 = -2.16

So the above confirms that the series is indeed a geometric progression with first term, $a_{1}$ = 10 and constant ratio, r = -0.6

Now to find if the series converges or diverges we can take sum of the series from first term to infinity.

We can already infer that the series is convergent since the constant ratio, r = -0.6 which is less than 1.

So from the formula for the sum to infinity of a geometric progression, S, we get

S = $\frac{a_1}{1 - r} = \frac{10}{1 - (-0.6)} = \frac{10}{1 + 0.6} = \frac{10}{1.6} = 6.25$

So the series is convergent with the sum being 6.25

7 0

4 years ago

Simplify please help me with this question

tankabanditka [31]

Answer:

a^4

<h3>Explanation:</h3>

a^2×a^3= a^5(a^2+3)

a^5/a= a^4(a^5-1)

5 0

2 years ago

A rectangular picture frame has outside dimensions of 8 inches wide and 10 inches tall. If the glass on the picture frame has an

Leto [7]

Answer:

1 inch

Step-by-step explanation:

If we call the thickness of the frame x, then the dimensions of the glass are:

w = 8 − 2x

h = 10 − 2x

The area of the glass is width times height:

48 = (8 − 2x) (10 − 2x)

Distribute and simplify:

48 = 80 − 16x − 20x + 4x²

0 = 4x² − 36x + 32

0 = x² − 9x + 8

Factor and solve:

0 = (x − 1) (x − 8)

x = 1 or x = 8

x can't be more than 4 (half the width of the frame), so x = 1 inch.

7 0

3 years ago

If you need 30 teaspoons of vanilla extract and vanilla is sold in a 4 oz. bottle, how many bottles of vanilla should you buy?

olya-2409 [2.1K]

You would need two bottles, because 4 ounces is the same as 24 teaspoons, so if you buy two bottles for 30 teaspoons you will have 18 teaspoons left (3 ounces) I hope this helps!

4 0

3 years ago

Rocky builds a dog house for a friend of his. Rocky is thinking about painting the dog house half blue and half gold.

Anit [1.1K]

Answer:

Surface Area: 1090 inch²

Blue Paint needed: 545 inch²

Gold Paint needed: 545 inch²

Step-by-step explanation:

Is there a door or something? I'm assuming not because you didn't include it in your question.

Surface Area:

(7*15*2)+(15*20*2)+(20*7*2)=

210+600+280=

1090 inch²

If he paints half the doghouse blue and the other half gold then simply divide the surface area by 2:

1090÷2=545

He needs 545 inches² of blue paint

He needs 545 inches² of gold paint.

5 0

3 years ago