Sally wants to fill ten 8-inch tea glasses. How much tea does she need?

Use elimination to solve.<br> 3y-6x=7<br> -4y-3x=9

shtirl [24]

Answer:

x = -5/3, y = -1 or $(-\frac{5}{3}, -1)$

Step-by-step explanation:

Solving systems of linear equations using process of elimination involves eliminating one of the variables (and its coefficient) in order to solve the other variable either through addition or subtraction. However, there may be other mathematical operations necessary before one of the variables can be eliminated.

Equation 1: 3y - 6x = 7

Equation 2: -4y - 3x = 9

<h3>Step 1: Multiply Equation 2 by -2:</h3>

(-2)(-4y - 3x) = 9 (-2)

8y + 6x = -18

<h3>Step 2: Add "8y + 6x = -18" to Equation 1:</h3>

8y + 6x = -18

+ 3y - 6x = 7

11y = -11

<h3>Step 3: Divide both sides by 11 to solve for y:</h3>

$\frac{11y}{11} = \frac{-11}{11}$

y = -1

<h3>Step 4: Substitute y = -1 into Equation 2 to solve for x: </h3>

-4(-1) - 3x = 9

4 - 3x = 9

<h3>Step 5: Subtract 4 from both sides:</h3>

4 - 4 - 3x = 9 - 4

- 3x = 5

<h3>Step 6: Divide both sides by -3 to solve for x:</h3>

$\frac{-3x}{-3} = \frac{5}{-3}$

$x = - \frac{5}{3}$

Verify whether the values for x and y are correct by substituting their values into both equations:

x = -5/3, y = -1

Equation 1: 3y - 6x = 7

$3(-1) - 6(-\frac{5}{3}) = 7$

-3 + 10 = 7

7 = 7 (True statement).

Equation 2: -4y - 3x = 9

-4(-1) - 3 (-5/3) = 9

$-4(-1) - 3(-\frac{5}{3}) = 9$

4 + 5 = 9

9 = 9 (True statement).

Therefore, x = -5/3 and y = -1 are the solutions to the given systems of linear equations.

8 0

2 years ago

What is the approximate volume of the cylinder? Use 3.14 for п.

Veseljchak [2.6K]

<u>Given</u>:

Given that the radius of the cylinder is 4 cm.

The height of the cylinder is 9 cm.

We need to determine the volume of the cylinder.

<u>Volume of the cylinder:</u>

The volume of the cylinder can be determined using the formula,

$V=\pi r^2 h$

where r is the radius and h is the height of the cylinder.

Substituting π = 3.14, r = 4 and h = 9 in the above formula, we get;

$V=(3.14)(4)^2(9)$

$V=(3.14)(16)(9)$

$V=452.16 \ cm^3$

Thus, the volume of the cylinder is 452.16 cm³

Hence, Option B is the correct answer.

4 0

4 years ago

15. Determine the values of the unknown variables

Maurinko [17]

For the left-hand triangle we know: $(x+7)\°+(3x-18)\°+(x-9)\°=180\°$ .
Solving for $x$ we have:
$5x\°-20\°=180\°$
$5x\°=200\°$
$x=40\°$
So the angles on the left are: 47,31 and 102 degrees.

On the right we have $y\°+(x+21)\°+(x+17)\°=180\°$
Substituting known values and solving we get:
$y\°+61\°+47\°=180\°$
[tex]y=72\°[/tex}
So the angles on the right are, 72, 61 and 47 degrees.

8 0

4 years ago

Which polynomials are prime? Check all that apply. 2x2 7x 1 5x2 – 10x 5 3x2 8 4x2 – 25 x2 36.

salantis [7]

You can use the definition of prime polynomials to find out which polynomial is prime and which is not.

The prime polynomials in the given options are:

Option 1: $2x^2 + 7x + 1$

Option 3: $3x^2 + 8$

<h3>What are prime polynomials?</h3>

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

<h3>Which of the given polynomials are prime?</h3>

Option 1: $2x^2 + 7x + 1$

We have to check it manually. The roots of this equation are

not integer or integer fraction (checked from calculator), and does't factor into smaller integer coefficient polynomials.

(you can check if its getting factored, manually, and most of the times, if it is not prime, it will get factored).

Thus, it is a prime polynomial.

Option 2: $5x^2 - 10x +5$