Order the rational numbers from least to greatest 0.42, -1/2, 11/20, and -0.51

What is the solution to the system of equations? 6x – 9y = 16 2x – 3y = 7

kifflom [539]

The first step for solving this problem is to multiply both sides of the bottom equation by -3.
$\left \{ {{6x-9y=16} \atop {-6x + 9y = -21}} \right.$
Add the two equations together.
6x - 9y - 6x + 9y = 16 - 21
Eliminate the opposites.
-9y + 9y = 16 - 21
Remember that the sum of two opposites equals 0,, so the equation becomes the following:
0 = 16 - 21
Calculate the difference on the right side of the equation.
0 = -5
This means that the statement $\left \{ {{6x-9y=16} \atop {2x-3y=7}} \right.$ is false for any value of x and y. That means that the answer to your question is (x,y) ∈ ∅,, or no solution.
Let me know if you have any further questions.
:)

8 0

3 years ago

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the

Svetlanka [38]

Answer:

The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be $x.$

And the hotel charge in second city before tax be $y.$

So, as the hotel charge of the second city was 1500 higher than the first.

Thus,

$y=x-1500$ ........(1)

And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.

6% of $x$ + 10% of $y$ = $670.

$\frac{6x}{100} +\frac{10y}{100} =670$

$0.06x+0.10y=670$

Substituting the value of $y$ from equation (1) we get:

$0.06x+0.10(x-1500)=670$

$0.06x+0.10x-150=670$

$0.16x-150=670$

Adding both sides by 150 we get:

$0.16x=820$

Dividing both sides by 0.16 we get:

$x=5125.$

The hotel charge in first city before tax = $5125.

Now, substituting the value of $x$ in equation (1) we get:

$y=x-1500$

$y=5125-1500$

$y=3625.$

The hotel charge in second city before tax = $3625.

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

5 0

3 years ago

Write a numerical expression for the verbal expression. the sum of two an four and six times eight

Trava [24]

(2+4+6)*8 hopefully that's what you are looking for

3 0

2 years ago

You ride your bike x miles per hour up a mountain for 45 minutes. On the way down the mountain, you ride your bike 3 miles per h

denpristay [2]

Answer:

18/5 miles

Step-by-step explanation:

let d be the mountain dist path

upward biking

x miles - 1 hr

d 45 mins

3x/4 = d

riding down

x+3 - 60 min

d. - 20

(1/3)(x+3) = d

(x+3)/3 = 3x/4

4x+12 = 9x

x = 12/5

d =( 12*3)/(4*5)= 9/5

upward+downward = 2*(9/5) = 18/5

7 0

2 years ago

Can a math god help me out?

Taya2010 [7]

Answer:

$f(1)=70$

$f(n)=f(n-1)+6$

Step-by-step explanation:

One is given the following function:

$f(n)=64+6n$

One is asked to evaluate the function for $(f(1))$ , substitute $(1)$ in place of $(n)$ , and simplify to evaluate:

$f(1)=64+6(1)$

$f(1)=64+6$

$f(1)=70$

A recursive formula is another method used to represent the formula of a sequence such that each term is expressed as a function of the last term in the sequence. In this case, one is asked to find the recursive formula of an arithmetic sequence: that is, a sequence of numbers where the difference between any two consecutive terms is constant. The following general formula is used to represent the recursive formula of an arithmetic sequence:

$a_n=a_(_n_-_1_)+d$

Where ( $a_n$ ) is the evaluator term ( $a_(_n_-_1_)$ ) represents the term before the evaluator term, and (d) represents the common difference (the result attained from subtracting two consecutive terms). In this case (and in the case for most arithmetic sequences), the common difference can be found in the standard formula of the function. It is the coefficient of the variable (n) or the input variable. Substitute this into the recursive formula, then rewrite the recursive formula such that it suits the needs of the given problem,

$a_n=a_(_n_-_1_)+d$

$a_n=a_(_n_-_1_)+6$

$f(n)=f(n-1)+6$

3 0

2 years ago