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Paraphin [41]
3 years ago
6

Translate to a system of equations but do not solve

Mathematics
1 answer:
NNADVOKAT [17]3 years ago
6 0

Answer:

The system of equations is:

x+y = 42

y = 2x

Step-by-step explanation:

Let x represent the number of ounces of lemon juice.

Let y represent the number of ounces of linseed oil.

A total of 42 ounces of floor wax is to be made, so:

x+y = 42

The amount of oil should be twice the amount of lemon juice. So:

y = 2x

so the system of equations is obtained.

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What is the value of r?<br> Round your final answer to the nearest whole number.
vaieri [72.5K]

Answer:

r = 13

Step-by-step explanation:

Hypotenuse is the side opposite to 90 degree angle, so hypotenuse is r.

Also, with respect to the angle given, the side "12" is the opposite.

So we have opposite side to angle and we need hypotenuse. Which trigonometric ratio related opposite with hypotenuse? It is SINE.

So we can write:

Sin(67.4)=\frac{Opposite}{Hypotenuse}=\frac{12}{r}\\rSin(67.4)=12\\r=\frac{12}{Sin(67.4)}\\r=12.99

Rounded to nearest whole number, r = 13

8 0
4 years ago
Read 2 more answers
A geometric sequence has an initial value of 2 and a common ratio of 3. Which formula would be more practical to use if you were
Makovka662 [10]

Answer:

19th term = ar^18

19th term = 774,840,978

Step-by-step explanation:

First term, a = 2

Common ratio, r = 3

nth term of a geometric sequence = ar^(n-1)

19th term = ar^(19-1)

19th term = ar^18

= 2 × 3^18

= 2 × 387,420,489

= 774,840,978

19th term = 774,840,978

8 0
3 years ago
Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles
Julli [10]

Answer:

Markus has 6 marbles in each bag.

Step-by-step explanation:

Markus has 18 marbles and 3 bags

If you divide 18 marbles by 3 bags that would be 6 marbles in each bag.

5 0
3 years ago
Please find the perpendicular line slope equation please! Thanks!
lana66690 [7]

We need to convert this equation to slope-intercept form first.

We can do that by solving for y.

x - 5y = 15

<em><u>Add 5y to both sides.</u></em>

x = 5y + 15

<em><u>Subtract 15 from both sides.</u></em>

x - 15 = 5y

<em><u>Divide both sides by 5.</u></em>

y = 1/5x - 3

We now know the slope is 1/5.

The slope of the line perpendicular to the line with a slope of 1/5 is -5.

The slope of a perpendicular line is the negative reciprocal of the original slope.

Using a graphing calculator, we know the y-intercept of the line that is perpendicular to the original line must have a y-intercept of -6 to run through the points (-2, 5).

The equation of the new line is y = -5x - 6.


5 0
3 years ago
Read 2 more answers
If tan x =3/4, and 0
jasenka [17]

Answer: x=0.6435011

Step-by-step explanation:

Take the inverse tangent of both sides of the equation to extract  

x

from inside the tangent.

x

=

arctan

(

3

4

)

Evaluate  

arctan

(

3

4

)

.

x

=

0.6435011

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from  

π

to find the solution in the fourth quadrant.

x

=

(

3.14159265

)

+

0.6435011

Simplify the expression to find the second solution.

Tap for more steps...

x

=

3.78509376

Find the period.

Tap for more steps...

π

The period of the  

tan

(

x

)

function is  

π

so values will repeat every  

π

radians in both directions.

x

=

0.6435011

+

π

n

,

3.78509376

+

π

n

, for any integer  

n

Consolidate the answers.

x

=

0.6435011

+

π

n

, for any integer  

n

6 0
3 years ago
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