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algol13
4 years ago
15

Determine if the ordered pair marked by the circle is a solution for the inequality

Mathematics
1 answer:
Kamila [148]4 years ago
3 0

When the inequality sign is < / > (less than/greater than), the line is a dotted line.

When the inequality sign is ≤ / ≥ (less than or equal to/greater than or equal to), the line is a solid line.

If "y >" (y is greater than.....), the shaded area is above the line.

If "y < " (y is less than....), the shaded area is below the line.

[points in the shaded area are solutions for the inequality. If the point is on the line and the line is ≤ / ≥, it is a solution]

- The point outside of the blue shaded area is not a solution because it has to be in the shaded area.

- The point on the line is not a solution because the line is a dotted line, which means that the point can't be equal to the points on the line.

- The point inside the blue shaded area is a solution.

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I need answer on this graphing va substitution.Problem 7 I tried to solve it but not sure that’s correct
Bond [772]

Given the system of equations:

\begin{gathered} 2x+9y=27 \\ x-3y=-24 \end{gathered}

To solve it by substitution, follow the steps below.

Step 1: Solve one linear equation for x in terms of y.

Let's choose the second equation. To solve it for x, add 3y to each side of the equations.

\begin{gathered} x-3y=-24 \\ x-3y+3y=-24+3y \\ x=-24+3y \end{gathered}

Step 2: Substitute the expression found for x in the first equation.

\begin{gathered} 2x+9y=27 \\ 2\cdot(-24+3y)+9y=27 \\ -48+6y+9y=27 \\ -48+15y=27 \end{gathered}

Step 3: Isolate y in the equation found in step 2.

To do it, first, add 48 to both sides.

\begin{gathered} -48+15y=27 \\ -48+15y+48=27+48 \\ 15y=75 \end{gathered}

Then, divide both sides by 15.

\begin{gathered} \frac{15y}{15}=\frac{75}{15} \\ y=5 \end{gathered}

Step 4: Substitute y by 5 in the relation found in step 1 to find x.

\begin{gathered} x=-24+3y \\ x=-24+3\cdot5 \\ x=-24+15 \\ x=-9 \end{gathered}

Answer:

x = -9

y = 5

or (-9, 5)

Also, you can graph the lines by choosing two points from each equation, according to the picture below.

7 0
1 year ago
A bag of potatoes weights 30 lb. If 74% of a potato is water, how many pounds of water are there in the bag?
Nadya [2.5K]

Answer: There are 22.2 pounds of water in the bag.

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the total weight of the bag by the water percentage in decimal form (divided by 100).

Mathematically speaking:

30 x (74/100) = 30 x 0.74 =22.2 pounds

There are 22.2 pounds of water in the bag.

Feel free to ask for more if needed or if you did not understand something.

3 0
3 years ago
13. Write the equation of a horizontal line that passes through the point (3, -3).
Step2247 [10]

Answer:

O y = -3

Step-by-step explanation:

The line is horizontal.

x = -3 and x = 3 are vertical lines, so they are incorrect.

The line passes through (3, -3).

                                         (x ,  y)

Put y as -3.

y = 3

(-3) = 3

Line y = 3 is incorrect.

(-3) = -3

Line y = -3 is correct.

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Step-by-step explanation:

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