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m_a_m_a [10]
3 years ago
6

Determine the missing side length:

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
3 0
The answer is:  "3" .
_______________________________
Use the Pythagorean theorem (for right triangles):

a² + b² = c² ;

in which "a = "side length 1" (unknown; for which we which to solve);

               "b" = "side length 2" = "√3" (given in the figure) ;

               "c" = "length of hypotenuse" = "2√3" (given in the figure);
_____________________________________________________
a² + b² = c² ; 

a² = c² − b² ;

Plug in the known values for "c" and "b" ;

a² = (2√3)²  −  (√3)² ;

Simplify:

(2√3)² = 2² * (√3)² = 2 * 2 * (√3√3)  = 4 * 3 =  12 .

 (√3)²  = (√3√3) = 3 .

a²  = 12 − 3 = 9 .

a² = 9

Take the "positive square root" of EACH SIDE of the equation; to isolate "a" on one side of the equation;  & to solve for "a" ; 

+√(a²)  = +√9 ;

     a = 3 . 
____________________________________
The answer is:  "3" .
____________________________________
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You deposit $3000 in an account with an APR 7.5% and continuous compounding. How much will you have after 20 years?
BartSMP [9]

Answer:

I = $4,500

Step-by-step explanation:

Simple Interest (I) = PRT / 100

Where:

P= Principal (Amount deposited) = $3000

R= Rate = 7.5%

T= Time = 20 years.

Simple Interest (I) = PRT / 100

I = ($3000 * 7.5 * 20) / 100

I = $450,000 / 100

I = $4,500.

8 0
3 years ago
Jing- sheng made a scaled copy of the following rhombus. He used a scale factor greater than 1. What could be the side length of
S_A_V [24]

Answer:

See below.

Step-by-step explanation:

You don't provide the original side length, but since the scale factor is greater than 1, all correct answers are lengths that are greater than the original side length.

Answer: choose any two numbers that are greater than the original length.

6 0
3 years ago
Read 2 more answers
I NEED HELP FAST PLEASE !!!!!!!!!!! The grade of a hill steepness represented as a percent. Jim tracks his walking speed up diff
Mariulka [41]

Answer:

C

Step-by-step explanation:

slope=walking speed /%

negative slope

so that rules out a and d

and you can see that as the percent increases the speed decreases.

so I think It would be C.

5 0
3 years ago
The 10th term in the sequence is 2560 what is the 11th term in the sequence
joja [24]

Full Question:

The 4th term of a g.p. is 40 and the 10th term in the sequence is 2560, what is the 11th term in the sequence ?

Answer:

the 11 the term is 5120

Step-by-step explanation:

Given

Geometry Progression

4th term = 40

10th term = 2560

Required

11 term.

The nth term of a geometric sequence is calculated as follows

Tₙ = arⁿ⁻¹

For the 4th term, n = 4 and Tₙ = 40

Substitute these in the given formula; this gives

40 = ar⁴⁻¹

40 = ar³. --;; equation 1

For the 10th term, n = 10 and Tₙ = 2560

Substitute these in the given formula; this gives

2560 = ar¹⁰⁻¹

2560 = ar⁹. --;; equation 2

Divide equation 2 by 1. This gives

2560/40 = ar⁹/ar³

64 = r⁹/r³

From laws of indices

64 = r⁹⁻³

64 = r⁶

Find 6th root of both sides

(64)^1/6 = r

r = (2⁶)^1/6

r = 2

Substitute r = 2 in equation 1

40 = ar³. Becomes

40 = a * 2³

40 = a * 8

40 = 8a

Divide both sides by 8

40/8 = 8a/8

5 = a

a = 5.

Now, the 11 term can be solved using Tₙ = arⁿ⁻¹ where n = 11

So,

Tₙ = arⁿ⁻¹ becomes

Tₙ = 5 * 2¹¹⁻¹

Tₙ = 5 * 2¹¹⁻¹

Tₙ = 5 * 2¹⁰

Tₙ = 5 * 1024

Tₙ = 5120.

Henxe, the 11 the term is 5120

5 0
3 years ago
Carmen rides her bicycle at a constant rate to the market. When she rides her bicycle back home along the same route, she bikes
lianna [129]
It can be easily assumed that most information's are already given in the question. Based on those information's, the answer can be deduced.

rt = [(3/4)r] * (t + 12)
4rt = 3r (t + 12)
4rt = 3rt + 36r
4rt - 3rt = 36r
rt = 36r
t = 36
From the above deduction we can conclude that the time taken by Carmen to ride to the market is 36 minutes
Then
Time taken by Carmen to ride home = 36 + 12 = 48 minutes
8 0
3 years ago
Read 2 more answers
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