A leaking pond loses 20 gallons of water in 35 hours. How many gallons of water will it lose in 47 hours?

Which equation best represents the situation?

Gennadij [26K]

It is A because
x/6 gives pizza by 1 guest and adding0.5 gives total expence

7 0

3 years ago

If m=8, how many solutions are there for the expression m-8?

ss7ja [257]

Answer:

1 solution, 0

Step-by-step explanation:

In algebra, a variable can be equal to any amount of numbers depending on how it is used. In this case, m is only equal to the one value of 8, and therefore only has one solution.

m - 8

(8) - 8

0

5 0

3 years ago

What is the equation of the circle shown in the graph

schepotkina [342]

The general equation for a circle is:
$(x-h)^2 + (y-k)^2 = r^2$

where (h,k) is center of circle
r = radius

For this example, from the graph you see the center is at (0,-3) and radius is 2.
h = 0, k = -3, r = 2

Sub into general equation:
$(x-0)^2 + (y-(-3))^2 = 2^2 \\ \\ x^2 +(y+3)^2 = 4$

4 0

3 years ago

Read 2 more answers

Brand W: 500 napkins for $2.87

AlexFokin [52]

The best way, in my opinion, to do this, is to find the unit rate of each napkin brand, or the cost per napkin. To do this, divide the money amount by the amount of napkin they give you.

/Brand W:2.87/500=.00574 \
\Brand X: 1.27/200=.00635 \ These are the
/Brand Y: .62/100 =.0062 / cost per napkin.
 \Brand Z: 1.37/250=.00548 /

Which one out of these 4 values is the lowest value? Obviously the two with the 6 in the thousandths place are more expensive than the ones with the 5s in the thousandths place, so that already eliminates Brand Z and Brand W.

What do we have left?

Brand X: 1.27/200=.00635
Brand Y: .62/100 =.0062
 Cool. Which of these is a smaller number? Tip: If the first number besides 0 is the same, check the next one! You should get that Brand Y is the cheapest! :) Hoped this helped!

3 0

3 years ago

A line passes through the points (-7, 2) and (1, 6).A second line passes through the points (-3, -5) and (2, 5).Will these two l

BlackZzzverrR [31]

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

Explanation:

Step 1. The first line passes through the points:

(-7,2) and (1,6)

and the second line passes through the points:

(-3,-5) and (2,5)

Required: State if the lines intersect, and if so, find the solution.

Step 2. We need to find the slope of the lines.

Let m1 be the slope of the first line and m2 be the slope of the second line.

The formula to find a slope when given two points (x1,y1) and (x2,y2) is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Using our two points for each line, their slopes are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)} \\ \\ m_2=\frac{5-(-5)}{2-(-3)} \end{gathered}$

The results are:

$\begin{gathered} m_1=\frac{6-2}{1-(-7)}=\frac{4}{1+7}=\frac{4}{8}=\frac{1}{2} \\ \\ \end{gathered}$ $m_2=\frac{5+5}{2+3}=\frac{10}{5}=2$

The slopes are not equal, this means that the lines are NOT parallel, and they will intersect at some point.

Step 3. To find the intersection point (the solution), we need to find the equation for the two lines.

Using the slope-point equation:

$y=m(x-x_1)+y_1$

Where m is the slope, and (x1,y1) is a point on the line.

For the first line m=1/2, and (x1,y1) is (-7,2). The equation is:

$y=\frac{1}{2}(x-(-7))+2$

Solving the operations:

$\begin{gathered} y=\frac{1}{2}(x+7)+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+7/2+2 \\ \downarrow\downarrow \\ y=\frac{1}{2}x+5.5 \end{gathered}$

Step 4. We do the same for the second line. The slope is 2. and the point (x1,y1) is (-3, -5). The equation is:

$\begin{gathered} y=2(x-(-3))-5 \\ \downarrow\downarrow \\ y=2x+6-5 \\ \downarrow\downarrow \\ y=2x+1 \end{gathered}$

Step 5. The two equations are:

$\begin{gathered} y=\frac{1}{2}x+5.5 \\ y=2x+1 \end{gathered}$

Now we need to solve for x and y.

Step 6. Equal the two equations to each other:

$\frac{1}{2}x+5.5=2x+1$

And solve for x:

$\begin{gathered} \frac{1}{2}x+5.5=2x+1 \\ \downarrow\downarrow \\ 5.5-1=2x-\frac{1}{2}x \\ \downarrow\downarrow \\ 4.5=1.5x \\ \downarrow\downarrow \\ \frac{4.5}{1.5}=x \\ \downarrow\downarrow \\ \boxed{3=x} \end{gathered}$

Step 7. Use the second equation:

$y=2x+1$

and substitute the value of x to find the value of y:

$\begin{gathered} y=2(3)+1 \\ \downarrow\downarrow \\ y=6+1 \\ \downarrow\downarrow \\ \boxed{y=7} \end{gathered}$

The solution is x=3 and y=7, in the form (x,y) the solution is (3,7).

Answer:

Yes, the lines intersect at (3,7). The solution is (3,7).

6 0

1 year ago