11.(A-CED.A.1 ) Write and solve the equation

Mathematics

1 answer:

Black_prince [1.1K]3 years ago

7 0

Answer:

Ahmed runs 6 miles each day

Step-by-step explanation:

∵ Ahmad runs m miles each day

∵ Ali runs twice as many miles as Ahmad

→ That means Ali runs 2 × m miles each day

∴ Ali runs 2m miles each day

∵ Altogether, they run 18 miles each day

→ Add m and 2m, then equate the sum by 18

∴ m + 2m = 18

∴ 3m = 18

→ Divide both sides by 3 to find m

∵ $\frac{3m}{3}=\frac{18}{3}$

∴ m = 6

∵ m represents the number of miles that Ahmed runs each day

∴ Ahmed runs 6 miles each day

You might be interested in

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8

Gekata [30.6K]

First, let $(x,y)$ be a point in our parabola. Since we know that the focus of our parabola is the point (0,8), we are going to use the distance formula to find the distance between the two points:
$\sqrt{(x-0)^{2}+(y-8)^{2}}$

Next, we are going to find the distance between the directrix and the point in our parabola. Remember that the distance between a point (x,y) of a parabola and its directrix, $y=c$ , is: $|y-c|$ . Since our directrix is y=-8, the distance to our point will be:
$|y-(-8)|$
$|y+8|$

Now, we are going to equate those two distances, and square them to get rid of the square root and the absolute value:
$\sqrt{(x-0)^{2}+(y-8)^{2}}=|y+8|$
$(\sqrt{(x-0)^{2}+(y-8)^{2}})^{2}=|y+8|^{2}$
$(x-0)^{2}+(y-8)^{2}=y+8$

Finally, we can expand and solve for $y$ :
$x^2+y^2-16y+64=y^2+16y+64$
$x^{2}-16y=16y$
$32y=x^{2}$
$y= \frac{1}{32} x^2$

We can conclude that t<span>he standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8 is </span> $y= \frac{1}{32} x^{2}$