Evaluate the expression.<br><br> −(1/9)3

Miku drinks ½ of a 6 ounce glass of water in ⅔ hour. How much water does she drink in an hour?

anzhelika [568]

Miku would drink 4.5 ounces of water in an hour

4 0

3 years ago

Write an equation in point-slope form of the line through point P(-4, 7) with slope -4.

IrinaVladis [17]

Answer:

y - 7 = -4(x + 4)

Step-by-step explanation:

You want to find the equation for a line that passes through the point (-4,7) and has a slope of -4.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -4. So you can right away fill in the equation for a line somewhat to read:

y=-4x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-4,7). When x of the line is -4, y of the line must be 7.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-4,7).

So, why not plug in for x the number -4 and for y the number 7? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-4,7). y=mx+b or 7=-4 × -4+b, or solving for b: b=7-(-4)(-4). b=-9.

6 0

3 years ago

Read 2 more answers

You start driving north for 21 miles, turn right, and drive east for another 20 miles. at then end of driving what is your strai

umka21 [38]

Answer:

29 miles

Step-by-step explanation:

a²+b²=c²

21²+20²=841

√841=29

4 0

3 years ago

Triangle DEF is similar to triangle ABC. What is the length of segment EF? (HINT use scale factor) (Leave answer as a fraction)

Karo-lina-s [1.5K]

We have been given two similar triangles. We are asked to find the length of segment EF.

We know that corresponding sides of similar triangles are proportional, so we will use proportion to solve our given problem.

$\frac{EF}{DF}=\frac{BC}{AC}$

Upon substituting measure of our given side lengths, we will get:

$\frac{EF}{1}=\frac{5}{13}$

$EF=\frac{5}{13}$

Therefore, the length of segment EF is $\frac{5}{13}$ units.

4 0

3 years ago

Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 16x2 + 9y2 = 144. Cross-se

oee [108]

In the $x$ - $y$ plane, the base has equation(s)

$16x^2+9y^2=144\implies y=\pm\dfrac43\sqrt{9-x^2}$

which is to say, the distance (parallel to the $y$ -axis) between the top and the bottom of the ellipse is

$\dfrac43\sqrt{9-x^2}-\left(-\dfrac43\sqrt{9-x^2}\right)=\dfrac83\sqrt{9-x^2}$

so that at any given $x$ , the cross-section has a hypotenuse whose length is $\dfrac83\sqrt{9-x^2}$ .

The cross-section is an isosceles right triangle, which means the legs occur with the hypotenuse in a ratio of 1 to $\sqrt2$ , so that the legs have length $\dfrac8{3\sqrt2}\sqrt{9-x^2}$ . Then the area of each cross-section is

$\dfrac12\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)\left(\dfrac8{3\sqrt2}\sqrt{9-x^2}\right)=\dfrac{16}9(9-x^2)$

Then the volume of this solid is

$\displaystyle\frac{16}9\int_{-3}^39-x^2\,\mathrm dx=\boxed{64}$

7 0

4 years ago

Evaluate the expression. −(1/9)3