How do I find a2 and a3 for the following geometric sequence? 54, a2, a3, 128

Answers

Answer 1

Answer: The formula for the nth term of a geometric sequence:
$a_n=a_1 * r^(n-1)$
a₁ - the first term, r - the common ratio

$54, a_2, a_3, 128 \n \na_1=54 \na_4=128 \n \na_n=a_1 * r^(n-1) \na_4=a_1 * r^3 \n128=54 * r^3 \n(128)/(54)=r^3 \n (128 / 2)/(54 / 2)=r^3 \n(64)/(27)=r^3 \n\sqrt[3]{(64)/(27)}=\sqrt[3]{r^3} \n\frac{\sqrt[3]{64}}{\sqrt[3]{27}}=r \nr=(4)/(3)$

$a_2=a_1 * r= 54 * (4)/(3)=18 * 4=72 \na_3=a_2 * r=72 * (4)/(3)=24 * 4=96 \n \n\boxed{a_2=72, a_3=96}$

Answer 2

Answer: $a=54 \n \n a2=54q \n \n a3=54q^(2) \n \n 128=54q^(3) \n \n q^(3)= (128)/(54)= (64)/(27) \n \n q= (4)/(3) \n \n a2= 54*(4)/(3)= 72 \n \n a3=54*( (4)/(3))^(2)=54* (16)/(9) =96$

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Write a word phrase for 49+m

Answers

The sum of 49 and m.

Answer:

Step-by-step explanation:

Mathematical expressions are expressions which are combinations of constants, variables and mathematical operations . A constant is a symbol in maths which has fixed numerical value for example 2 , 3, -6, $(2)/(3)$ are constants .A variable is a symbol in algebra which takes various numerical values and has no fixed value . Mathematical operations include $+,-,/ ,*$ .

By term word phase, we mean mathematical expression using constants and variables.

Given: 49 + m

Word Phase:

Sum of 49 and m

Here, 49 is a constant

m is a variable

+ is a mathematical operation.

The Apache Taxi Company charges $2.50 to pick up a passenger and then adds $1.95 per mile. Isaac was charged $27.46 to go from one city to another. If x represents the number of miles driven by the taxi, which linear equation can be used to solve this problem, and how many miles did Isaac travel, rounded to the nearest tenth?

Answers

Answer: Isaac traveled approximately 13 miles by the taxi.

Step-by-step explanation:

Since we have given that

Amount charges to pick up a passenger = $2.50

Amount per mile = $1.95

Total amount charged = $27.46

Let x be the number of miles driven by the taxi.

According to question, it becomes,

$2.50+1.95x=27.46\n\n1.95x=27.46-2.50\n\n1.95x=24.96\n\nx=(24.96)/(1.95)\n\nx=12.8\n\nx\approx 13\ miles$

Hence, Isaac traveled approximately 13 miles by the taxi.

27.46 - 2.50 = 24.96 / 1.95 = 12.8 miles

A $5000 investment earns $1575 simple interest in three years. What is the annual interest rate?a. 1.05%
b. 3.15%
c. 10.5%
d. 31.5%

Answers

I=PRT
P=principal
I=interest
R=rate
T=time in years

Principal=5000
Interest=1575
R=?
T=3 years

I=PRT
1575=(5000)(R)(3)
1575=15000(R)
divide both sides by 15000
0.105=R
we need to covert to percent
x%=x/100
0.105/1 times 100/100=10.5/100=10.5%

answer is C

If sine of x equals square root of 2 over 2, what is cos(x) and tan(x)? Explain your steps in complete sentences.

Answers

sin $x$ = $(opposite)/(hypotenuse)$ = $( √(2) )/(2)$
opposite= $√(2)$
hypotenuse=2

$Adjacent^(2)$ + $(√(2 ))^(2 )$ = $2 ^(2)$
$Adjacent^(2)$ +2=4
$Adjacent^(2)$ =2
Adjacent= $√(2)$

cos $x$ = $(ajc)/(hyp)= ( √(2) )/(2)$
Tan $x$ = $(opp)/(adj) = ( √(2) )/( √(2) )$

What is the dimension of the hypotenuse of the accompanying right triangle?

Answers

It's not possible to know, because you're not letting us see
the accompanying right triangle.

#2 What is the equation of the horizontal asymptote for the following exponential graph?

Answers

Answer:

y = -1

Step-by-step explanation:

We are looking for the horizontal line which the function approaches but never meets;

This is y = -1

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