What is an explicit equation?

Answers

Answer 1
Answer: An explicit equation is an equation used to find a term in a sequence without using the any previous terms. For example, if I have the set of numbers 1, 3, 5, 7, 9, my explicit equation is F(n)=2(n-1)+1. If I plug 1 in for n, I get F(1)= 2(0)+1, which is 1, my first term.

Hope this made sense.

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a store mixes red fescue worth $12 per pound and chewings fescue worth $16 per pound. The mixture is to sell for $15 per pound. Find out how much of each should be used to make a 552- pound mixture.

Answers

Answer is: 414 pounds of red fescue and 138 pounds of chewings fescue is needed to produce 552 pounds of mixture.

Explanation:
x - how much of red fescue is needed for one pound of mixture
y - how much of chewings fescue is needed for one pound of mixture
x*12+ y*16 = 15x + y = 1
so, x=1-y
putting it into first line:
(1-y)*12 + y*16 = 15
12 - 12*y + 16*y = 15
4*y = 3
y=3/4
so, x= 1-3/4; x=1/4
So to produce 552 pounds of mixture we need..To produce 1 pound of mixture we need: 3/4 pound of red fescue and 1/4 pound of chewing fescue so to produce 552 pounds of miture we need:
552*3/4 - red fescue, which is 414 pounds needed
and
552/4 - chewings fescue, which is 138 pounds needed

Answer:

e+ f = 8 (total solution)

8e + 56f = 20*8 (total saline)

---

e+ f = 8

e + 7f = 20

------------ Subtract

-6f = -12

f = 2

e = 6

Write an equation that requires at least three steps to solve and whose solution is x=3.5

Answers

The expression can be written as (2x)² + 1 = 50

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the solution for the value of x is 3.5. The expression will be solved as below:-

2x = 7 (1 step)

(2x)² = 49 (2 steps)

(2x)² + 1 = 50 ( 3 steps)

Therefore, the expression can be written as (2x)² + 1 = 50.

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Answer:

(2x)^2 + 1 = 50

Step-by-step explanation:

x = 3.5

2x = 7 (1 step)

(2x)^2 = 49 (2 steps)

(2x)^2 + 1 = 50 ( 3 steps)

Wei has $150.00 to make a garland using 60-cent balloons. He wants to purchase 100 blue balloons and some number of white balloons. He learns that the white balloons are on sale for half price. He writes and solves an equation to find the number of white balloons he can purchase.Which models can be used to solve the problem?

Answers

Answer:

60+0.3x=150

Step-by-step explanation:

Total money Wei has = $150

Each blue balloon costs = $0.60

Let the number of white balloons be = x

Each white balloon costs = $0.30

Now Wei purchased 100 blue balloons and have $150 to buy both balloons.

So, money spent on blue balloons is = 100*0.60=60

Amount spent on white balloons is = 0.30x

So, for the total cost, the equation that can be used is :

60+0.3x=150

Upon solving this we get,

0.3x=150-60

0.3x=90

x=300

Hence, Wei can buy 300 white balloons.

0.60b + 0.30w = 150; 60 + 0.30w = 150

The number of dogs in a shelter is equal to 4 less than 2 times the number of cats. If there are 20 dogs in the shelter how many cats are there?

Answers

d=number of dogs
c=cats

d equals 4 less than 2 times c
d=-4+2c
20 dogs
d=20
subsitute
20=-4+2c
add 4
24=2c
divide 2
12=c
12 cats

A character who changes during the course of the story is _____.flat
round
static
dynamic

Answers

A character who changes during the course of the story is a dynamic character.
Hope that helps! :) 

I would say dynamic is the answer.

What is the first term of the geometric sequence presented in the table below? n 4 9 an 243 59,049

Answers

Reminder:  the formula for a geom. seq. is

a(n) = a(1)*r^(n-1), where a(1) is the first term, n is the counter and r is the common ratio. 

I first noted that 243 is a power of 3; specifically, 243=3^5, or 243=3(3)^4, or 243=(3^2)(3)^(4-1).  Notice that I'm trying here to rewrite 243=3^5 in the form a(n) = a(1)*r^(n-1):    a(4) = a(1)(3)^(4-1), or a(4) = a(1)(3)^3 = 243.  Then by division we find that a(1) = 243/27 = 9.  Is it possible that a(1)=9?

Let's try out our formula   a(n)=9(3)^(n-1).  Steal n=9 and see whether this formula gives u s 59049:

n(9) = 59049 = 9(3)^(9-1), or  9(3)^8.  True or false?  3^8= 6561, and 9(3)^8 = 59049.

YES!  That's correct.

Therefore, the desired formula is

a(n) = 9(3)^(n-1).  The first term, a(1) is 9(3)^(1-1) = 9(3)^0 = 9*1 = 9.

Final answer:

The first term of the geometric sequence is 3. Calculation is done using the formula for the nth term of a geometric sequence and substituting the given values.

Explanation:

To find the first term of the geometric sequence, one can use the formula for the nth term of a geometric sequence, which is a = arn-1. Here, 'a' is the first term, 'r' is the common ratio and 'n' is the term position. As provided in the table, when n=4, an=243 and when n=9, an=59049. We can setup the equation 243 = a*r3 and 59049 = a*r8. Dividing the second equation by the first we get r5 = 243, leading to r=3. Substitute r=3 into the first equation to find 'a' and we get a= 3.

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