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zimovet [89]
3 years ago
11

Find the missing side length.

Mathematics
1 answer:
atroni [7]3 years ago
7 0
A² + b² = c²

(√3)² + b² = 5²

3 + b² = 25

b ² = 22

b = √22

hope this helps
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The 5th term in a geometric sequence is 160. The 7th term is 40. What are possible values of the 6th term of the sequence?
omeli [17]

Answer:

C. The 6th term is positive/negative 80

Step-by-step explanation:

Given

Geometric Progression

T_5 = 160

T_7 = 40

Required

T_6

To get the 6th term of the progression, first we need to solve for the first term and the common ratio of the progression;

To solve the common ratio;

Divide the 7th term by the 5th term; This gives

\frac{T_7}{T_5} = \frac{40}{160}

Divide the numerator and the denominator of the fraction by 40

\frac{T_7}{T_5} = \frac{1}{4} ----- equation 1

Recall that the formula of a GP is

T_n = a r^{n-1}

Where n is the nth term

So,

T_7 = a r^{6}

T_5 = a r^{4}

Substitute the above expression in equation 1

\frac{T_7}{T_5} = \frac{1}{4}  becomes

\frac{ar^6}{ar^4} = \frac{1}{4}

r^2 = \frac{1}{4}

Square root both sides

r = \sqrt{\frac{1}{4}}

r = ±\frac{1}{2}

Next, is to solve for the first term;

Using T_5 = a r^{4}

By substituting 160 for T5 and ±\frac{1}{2} for r;

We get

160 = a \frac{1}{2}^{4}

160 = a \frac{1}{16}

Multiply through by 16

16 * 160 = a \frac{1}{16} * 16

16 * 160 = a

2560 = a

Now, we can easily solve for the 6th term

Recall that the formula of a GP is

T_n = a r^{n-1}

Here, n = 6;

T_6 = a r^{6-1}

T_6 = a r^5

T_6 = 2560 r^5

r = ±\frac{1}{2}

So,

T_6 = 2560( \frac{1}{2}^5) or T_6 = 2560( \frac{-1}{2}^5)

T_6 = 2560( \frac{1}{32}) or T_6 = 2560( \frac{-1}{32})

T_6 = 80 or T_6 = -80

T_6 =±80

Hence, the 6th term is positive/negative 80

8 0
3 years ago
Can someone explain these math questions to me
kolbaska11 [484]
Should be choice 1 x being your slope and y your y- intercept

4 0
3 years ago
Math help (Tan) + brainy
levacccp [35]
Tan = opposite / adjacent
tan 74 = 24/7

6 0
3 years ago
Read 2 more answers
Subtract. 17 – (–11) A. –28 B. –6 C. 6 D. 28
Elis [28]
The answer is 28



Hope this helped
4 0
3 years ago
Read 2 more answers
The area of the pathway is square, and its area is 196 square cm. Find the length of the pathway.
Ivanshal [37]

Answer:

14 cm

Step-by-step explanation:

Use the formula for the area of a square, a = s², where s is the side length of the square.

Plug in 196 as the area, then solve for s.

a = s²

196 = s²

14 = s

So, the length of the pathway is 14 cm

7 0
2 years ago
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