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3 years ago

Which graph correctly shows the solution of the compound inequality 3x 2 -12 and 8x < 16?

Mathematics

1 answer:

Genrish500 [490]3 years ago

7 0

Answer:

8x < 16 it shows the solution of the compound inequality

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Help Please!!!!!!!!!!

LenKa [72]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$x+3y\leq 6$

Isolate the variable y

$3y\leq 6-x$

$y\leq 2-(1/3)x$

The solution is the shaded area below the solid line

Is below because the symbol of the inequality is less

Is a solid line because the line is included in the solution

The equation of the solid line is $y=2-(1/3)x$

To graph the solution find the intercepts

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0, x=6 --------> point (6,0)

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0, y=2 -------> point (0,2)

Graph the inequality

see the attached figure

5 0

2 years ago

For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

mihalych1998 [28]

Answer:

$V=196in^3$

Step-by-step explanation:

The volume of a pyramid is:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

$A_{b}=l^2$

where $l$ is the length of the side: $l=8in$ , thus:

$A_{b}=(8in)^2\\A_{b}=64in^2$

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

$hypotenuse^2=leg1^2+leg2^2$

substituting our values, and indicating that leg 1 is height h:

$(10in)^2=h^2+(4in)^2$

$100in^2=h^2+16in^2$

and solving for the height:

$h^2=100in^2-16in^2\\h^2=84in^2\\h=\sqrt{84in^2}\\ h=9.165in$

and finally we calculate the volume using this height and the area of the base:

$V=\frac{A_{b}h}{3}$

$V=\frac{(64in^2)(9.165in)}{3} \\V=195.5in^3$

rounding to the nearest cubic inch: $V=196in^3$

4 0

3 years ago

Help me with this please

drek231 [11]

The answer is only C and D

6 0

3 years ago

Marley runs 5 yards down the track from point A to point B, and then stops and runs

julia-pushkina [17]

Answer:

$\sqrt{61}$ =AC or 7.8102=AC

Step-by-step explanation:

If we connect a line from point A to point C we create a triangle, and we can use pythagorean theorem to find this distance. So the line from point A to point C will be our hypotenuse and the other two distances will be out side lengths.

$5^{2}+6^{2}=AC^{2}$

25+36= $AC^{2}$

61= $AC^{2}$

$\sqrt{61}$ =AC or 7.8102=AC

3 0

3 years ago

Find the distance between points P(5, 1) and Q(1, 3) to the nearest tenth.

bonufazy [111]

Answer:

Idk if its multiple choice but you can do 1 of 2 ways theres using distance formula =√(5-3)sq+(1-4)sq

=√4+9

=√13 <--

3.6 units

Given: The two points that are P(5,1) and Q(3,4).

To find: The distance between these two points.

Solution: It is given that there are two points that are P(5,1) and Q(3,4).

The distance between these two points can be found out as using the distance formula that is: 3.6

Thus, the distance between the given two points is 3.6 units.

So you choose 13 or 3.6 Hope this helps :)

3 0

3 years ago