The diameter of a basketball is 9.50 inches. What is the volume of the ball, rounded to the nearest hundredth?

devlian [24]

Those are vertical angles and vertical angles are always congruent, meaning they're equal. To find x, you must set 6x+5=83 and solve for x.

8 0

3 years ago

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Tessa likes to carve bird and cat figures out of wood. She has carved 4 times as many bird figures as cat figures. If Tessa has

Brut [27]

120 because 24 times 4 = 96 and 96 +24 =120

7 0

3 years ago

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If p and q are both true, then which of the following statements has the same truth-value as ~p → q?

olganol [36]

If p and q are both true, then

$\neg p \implies q$

is an implication of the form

$F \implies T$

which is true, because every implication starting with false is true, i.e.

$F \implies T = T,\quad F \implies F = T$

So, we're looking for an expression evaluating to true. Let's see what we have:

A) is an AND proposition. Logical AND is true only if both parts are true. So, you have

$\neg P \land \neg Q = F \land F = F$

So it's not the right option.

B) is an OR proposition. Logical OR is true whenever one of the two parts is true. So, you have

$\neg P \lor\neg Q = F \lor F = F$

So it's not the right option.

C) is again an AND proposition. You have

$P \land \neg Q = T \land F = F$

So this is not the right option.

D) Finally, the last one is again an implication, and again it starts with false:

$\neg Q \implies P = F \implies T = T$

So this is true, and thus is the correct option.

8 0

3 years ago

Write a linear function f with the values f(−1)=8 and f(5)=6. A function is f(x)=

german

9514 1404 393

Answer:

f(x) = -1/3x +23/3

Step-by-step explanation:

You can use the linear regression function of a graphing calculator or spreadsheet to show you the equation of the line through these points:

f(x) = -1/3x +23/3

__

Approaching this in the usual way, we recognize we have points ...

(-1, 8) and (5, 6)

The slope of the line through those points is ...

m = (y2 -y1)/(x2 -x1)

m = (6 -8)/(5 -(-1)) = -2/6 = -1/3

Then the point-slope equation of the line is ...

y - 8 = -1/3(x +1)

Adding 8 gives us a form we can use for a function definition:

f(x) = -1/3(x +1) +8

f(x) = -1/3x +7 2/3

8 0

2 years ago

Determine the equation of the line that passes through the given points. (If you have a graphing calculator, you can use the tab

expeople1 [14]

You can write the equation in point-slope form, which has the format y-ysubscript1=m(x-xsubscript1), with ysubscript1 and xsubscript1 being the y and x coordinates for a point on the line, and m being the slope.

Substitute a y and x coordinate into the equation so you have y-6=m(x-2)

Then find the slope so you can replace m. The slope formula is (ysubscript2-ysubscript1)/(xsubscript2-xsubscript1). Substitute the coordinates in so you have m=(16-6)/(4-2), which simplifies to 10/2 and then 5.

Now the equation is y-6=5(x-2)

If you want a different form, for example slope-intercept form, you can change it to that:

y-6=5(x-2)

y=5x-4

6 0

3 years ago