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s344n2d4d5 [400]
2 years ago
9

Select the correct figures.

Mathematics
1 answer:
Contact [7]2 years ago
5 0

Answer:

3rd one and last one

Step-by-step explanation:

First one:

4 × 3 × 4 = 48

Second one:

1 × 2 × 4 = 8

Third one:

2 × 3 × 5 = 30

Fourth one:

2 × 5 × 4 = 40

Fifth one:

2 × 2 × 4 = 16

Process of elimination:

The first one is itself greater than 47 units³, so this is definitely not one of the two;

A combination of the fourth prism and the smallest one as the second will give a volume of 48 units³, which is greater than 47 so this prism is also not one of the two we are looking for;

This leaves the second, third and fifth;

The second and third sum to 38, which is less than 42 so it is not the correct combination;

Similarly, the second and last gives only 24 so it is not the correct combination;

This leaves the only remaining option of the third and fifth;

30 + 16 = 46, which confirms this to be the correct combination.

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State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli
nasty-shy [4]

Answer:

Part A

f(n)=52-12(n-1)

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

Part B

(2,4,8,16,32)\: \: Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right

Part D:

h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12

<u>Explicit Formula</u>

To write an explicit formula is to write it as function.

f(n)=52-12(n-1)

<u>Recursive Formula</u>

To write it as recursive formula, is to write it as recurrence given to some restrictions:

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

Part B

(2,4,8,16,32)\: \:

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\

Arithmetic Sequence, difference

d=\frac{2}{4}

<u>Explicit Formula:</u>

g(n)=\frac{1}{4}+\frac{2}{4}(n-1)

<u>Recursive Formula</u>

g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

<u>Explicit formula</u>

h(n)=1.1+0.4(n-1)\\

<u>Recursive Formula</u>

h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.

6 0
3 years ago
I am on my trigonometry unit in math and don’t know what to do for this. I also really need work shown!
soldi70 [24.7K]

Answer:

The flight was 137.45 miles farther than the direct path.

(make slight changes if directions were given on how to round. This is to the nearest hundredth)

Step-by-step explanation:

Use the Law of Cosines.

c^2=

a^2+b^2-2abcosC

You know two sides and the angle in between. The Law of Cosines will give us the third side.

The third side is the direct path of the airplane. We'll add the two other given sides to find the detour route that they took instead.

Then subtract the smaller number (direct route) from the actual route. See image.

8 0
2 years ago
A college student completed some courses worth 3 credits and some
-BARSIC- [3]

Answer:

  • A. 13

Step-by-step explanation:

<u><em>Note:</em></u><em> It seems typo in the question. 5% should read 59.</em>

Let 3 credit courses = x, 4 credit courses = y

<u>As per  given we have following equations:</u>

  • x + y = 18
  • 3x + 4y = 59

<u>Solve the system by elimination. Multiply the first equation by 4 and subtract the second one:</u>

  • 4(x + y) - (3x + 4y) = 4(18) - 59
  • 4x + 4y - 3x - 4y = 72 - 59
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The answer is 13

Correct choice is A

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Robert made a design on his wall with the similar pentagon tiles shown.
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Answer:

5

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5

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Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
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Answer:

7 cm and 2 cm

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