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3 years ago

The runners speed per mile

Mathematics

2 answers:

dezoksy [38]3 years ago

8 0

Answer:10 minutes per mile

Step-by-step explanation:

antiseptic1488 [7]3 years ago

3 0

Answer:

The runner's speed is 10 minutes per mile.

Step-by-step explanation:

When looking at the graph, the first dot lands at 1.0 miles for the x-axis and 10 for the y-axis, the y-axis being in minutes. Therefore, someone can run 1.0 miles in 10 minutes.

In addition, the second dot lands on (2.0, 20), meaning he/she ran 2.0 miles in 20 minutes. Divide that by 2 and you get 1.0 miles in 10 minutes.

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Beth has 250 comic books in her collection. She begins to sell 20 of them each week. Martin has 80 comic books in his collection

guapka [62]

Answer:

250 - 20 < 80 + 15x

Step-by-step explanation:

Given that

Beth has 250 books and 20 books sold each week

While on the other hand, Martin has 80 books and sell 15 books each week

Let us assume each week be x

Now the equations are

Beth 250 - 20x

Martin 80 + 15 x

Now the inequality would be

250 - 20 < 80 + 15x

8 0

3 years ago

Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes a

Luden [163]

$1\frac{1}{8} = \frac{9}{8} = 1.125, 
 \\ 75*1.125= 84.375$

84.375 is the profit ALREADY made, so now subtract that from 180 dollars to get
95.625 $ needed, now divide by amount of profit per box...

Answer should be 85 boxes

4 0

2 years ago

Complete the square and write in standard form. Show all work.What would be the conic section:CircleEllipseHyperbolaParabola

mote1985 [20]

ANSWER

This is an ellipse. The equation is:

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

EXPLANATION

We have to complete the square for each variable. To do so, we have to take the first two terms and compare them with the perfect binomial squared formula,

$(a+b)^2=a^2+2ab+b^2$

For x we have to take 16x² and -32x. Since the coefficient of x is not 1, first, we have to factor out the coefficient 16,

$16x^2-32x=16(x^2-2x)$

Now, the first term of the expanded binomial would be x and the second term -2x. Thus, the binomial is,

$(x-1)^2=x^2-2x+1$

To maintain the equation, we have to subtract 1,

$16(x^2-2x+1-1)=16((x-1)^2-1)=16(x-1)^2-16$

Now, we replace (16x² - 32x) from the given equation by this equivalent expression,

$16(x-1)^2-16+9y^2+72y+16=0$

The next step is to do the same for y. We have the terms 9y² + 72y. Again, since the coefficient of y² is not 1, we factor out the coefficient 9,

$9y^2+72y=9(y^2+8y)$

Following the same reasoning as before, we have that the perfect binomial squared is,

$(y+4)^2=y^2+8y+16$

Remember to subtract the independent term to maintain the equation,

$9(y^2+8y)=9(y^2+8y+16-16)=9((y+4)^2-16)=9(y+4)^2-144$

And now, as we did for x, replace the two terms (9y² + 72y) with this equivalent expression in the equation,

$16(x-1)^2-16+9(y+4)^2-144+16=0$

Add like terms,

$\begin{gathered} 16(x-1)^2+9(y+4)^2+(-16-144+16)=0 \\ 16(x-1)^2+9(y+4)^2-144=0 \end{gathered}$

Add 144 to both sides,

$\begin{gathered} 16(x-1)^2+9(y+4)^2-144+144=0+144 \\ 16(x-1)^2+9(y+4)^2=144 \end{gathered}$

As we can see, this is the equation of an ellipse. Its standard form is,

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

So the next step is to divide both sides by 144 and also write the coefficients as fractions in the denominator,

$\begin{gathered} \frac{16(x-1)^2}{144}+\frac{9(y+4)^2}{144}=\frac{144}{144} \\ \\ \frac{(x-1)^2}{\frac{144}{16}}+\frac{(y+4)^2}{\frac{144}{9}}=1 \end{gathered}$

Finally, we have to write the denominators as perfect squares, so we identify the values of a and b. 144 is 12², 16 is 4² and 9 is 3²,

$\frac{(x-1)^2}{(\frac{12}{4})^2}+\frac{(y+4)^2}{(\frac{12}{3})^2}=1$

Note that we can simplify a and b,

$\frac{12}{4}=3\text{ and }\frac{12}{3}=4$

Hence, the equation of the ellipse is,

$\frac{(x-1)^2}{3^2}+\frac{(y+4)^2}{4^2}=1$

3 0

1 year ago

In which quadrant does the point (-4,15) lie

Ivanshal [37]

Quadrant one

Hope this helped

7 0

3 years ago

If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 year

saveliy_v [14]

Total = Principal * e^(rate*years)
Total = 4,500 * 2.718281828459^(.02*4)
Total = 4,500 * 2.718281828459^(.08)
Total = 4,500 * 1.0832870677 
Total = 4,874.79 
calculator for checking the answer:
http://www.1728.org/compint.htm

7 0

2 years ago