Give 9.7814 correct to the nearest whole number

Jan uses 22.5 gallons of water in the shower. This amount is 7.5 gallons less than what she uses when washing her clothes. Write

arsen [322]

22.5 (shower) = X (variable used in place of the amount of water she uses to wash clothes) - 7.5 (the amount she used in the shower is 7.5 gallons less than she uses for washing clothes)

22.5 = X - 7.5 《 This is the equation.

Solve is by adding 7.5 to both sides to cancel out the negative 7.5 and you get (X = 30).

3 0

3 years ago

Please help ASAP IM IN DESPREATE NEED OF HELP

Advocard [28]

Answer:

See the attached image for the graph of the first system.

Step-by-step explanation:

Here's how to graph the first system.

Start with the inequality $-y \le -2x-3$ . You can make this easier to work with by multiplying through by -1. Remember to switch the inequality sign when multiplying by a negative number. OK, you get the inequality

$y \ge 2x+3$ .

The graph will be a half-plane -- all the points on one side of a line. The line that is the boundary of the half-plane has an equation: $y=2x+3$ -- just use an = sign instead of the inequality sign.

Graph the line.

The equation of the line is in slope-intercept form: y = mx + b, so you can tell the y-intercept is 3 and the slope is 2 (think of it as a fraction 2/1). Graph the line by going to the point (0, 3) -- the y-intercept -- then use the slope 2/1 interpreted as "rise over run" to go up 2 units and right 1 unit, arriving at the point (1, 5). Draw the line through those points, (0, 3) and (1, 5).

Now you have to decide which side of the line the inequality $y \ge 2x+3$ is describing. To do this, pick a point which is not on the line, plug its coordinates into the inequality; if the result is true, shade the side of the line the point you picked is on (if false, shade the other side!)

An easy point to pick in this case is the origin, (0, 0). Put zeros in for x and y in the inequality, and you'll get the statement $0 \ge 2(0)+3 \, \Rightarrow \, 0 \ge 3$ . That's false, so shade the side of the line not containing the origin. In the image below, the shading is in purple.

All right, now for the other inequality, $x+2\le 0$ . Subtract 2 from both sides and the inequality becomes $x \le -2$ . This, too, graphs as a half-plane whose boundary line has equation $x=-2$ . Graph the line. A line with an equation that has x in it but not y is a vertical line with all its x-coordinates equal to the number on the right side of the equation. This line is vertical and goes through points such as (-2, 0).

Pick a point not on the line (the origin works again). Put the coordinates into the inequality to get $0\le -2$ which is false. Shade the side of the vertical line which does not contain the origin. In the image below, the shading is in black.

Finally, YAY! \o/ , the solutions to the system are all the points in the plane that got shaded twice. In the image, they are the cross-hatched points above the purple line and to left of the black line.

Note: If you get a system with three inequalities, you'll be graphing three half-planes and looking for points that got shaded three times!

Note: One of your questions has the inequalities $x \ge 0$ and $y \ge 0$ in it. These two inequalities say that the x and y coordinates are both positive or zero, confining your attention to Quadrant I in the upper-right part of a graph, above the x-axis and to the right of the y-axis.

7 0

3 years ago

The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find

IrinaVladis [17]

the standard form for a horizontal ellipse is

X^2/a^2 + y^2/b^2 = 1

Substitute 54 for b and and use (8,18) as the

point to find a

x=8

y=18

8^2/a^2 + 18^2/54^2 =1

64/a^2 + 324/2916 = 1

324/2916 reduces to 1/9

64/a^2 + 1/9 = 1

64/a^2= 1-1/9

64/a^2 = 8/9

64*9/8 = a^2

576/8 = 72

A^2 = 72

A = square root(72) = 8.485

So formula

would be x^2/72 + y^2/2916 =1

8 0

3 years ago

To make 4.5 cups of fruity granola, the recipe calls for 1.5 cups of raisins, 1 cup of granola, and 2 cups of blueberries. If yo

Levart [38]

Answer:

you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

Step-by-step explanation:

Step 1: Find how much raisins are needed

For 4.5 cups of fruity granola, we need 1.5 cups of raisins

For 18 cups of fruity granola, we need y cups of raisins

4.5 : 1.5

18 : y

Cross multiply

4.5y = 1.5 x 18

y = 27/4.5

y = 6 cups of raisins

Step 2: Find how much granola is needed

For 4.5 cups of fruity granola, we need 1 cup of granola

For 18 cups of fruity granola, we need y cups of granola

4.5 : 1

18 : y

Cross multiply

4.5y = 18

y = 4 cups of granola

Step 3: Find how much blueberries are needed

For 4.5 cups of fruity granola, we need 2 cups of raisins

For 18 cups of fruity granola, we need y cups of blueberries

4.5 : 2

18 : y

Cross multiply

4.5y = 2 x 18

y = 36/4.5

y = 8 cups of blueberries

Therefore, in order to make 18 cups of fruity granola, you need 6 cups of raisins, 4 cups of granola and 8 cups of blueberries.

5 0

3 years ago

How do I put 3x - 6y = -12 into Slope Intercept Form?

max2010maxim [7]

Answer:

y= $\frac{1}{2}$ x+2

Step-by-step explanation:

hope this helps

5 0

2 years ago

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