Solve the inequality and give an answer in interval notation:<br> 4-x> 6

$\dfrac{k}{2}+1-1k=-2k\\\\\dfrac{1}{2}k+1-k=-2k\\\\\left(\dfrac{1}{2}k-k\right)+1=-2k\\\\-\dfrac{1}{2}k+1=-2k\qquad\text{subtract 1 from both sides}\\\\-\dfrac{1}{2}k=-2k-1\qquad\text{add 2k to both sides}\\\\1\dfrac{1}{2}k=-1\qquad\text{convert the mixed number to improper fraction}\\\\\dfrac{1\cdot2+1}{2}k=-1\\\\\dfrac{3}{2}k=-1\qqua\text{multiply both sides by}\ \dfrac{2}{3}\\\\\boxed{k=-\dfrac{2}{3}}$

4 0

2 years ago

15 POINTS ANSWER ASAP, SHOW WORK

forsale [732]

Answer:

$V=97.6\ in^3$

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=4/2=2\ in$ ---> the radius is half the diameter

$h=8\ in$

substitute

$V=\pi (2)^{2}(8)\\\\V=32\pi\ in^3$

step 2

Find the volume of the cone

The volume of the cone is equal to

$V=\frac{1}{3}\pi r^{2} h$

we have

$r=2\ in$ ---> the radius is the same that the radius of the cylinder

$h=0.70\ in$

substitute

$V=\frac{1}{3}\pi (2)^{2} (0.70)\\\\V=0.93\pi\ in^3$

step 3

Find the volume of the plastic object

we know that

The volume of the plastic object is equal to the volume of the cylinder minus the volume of the cone

so

$V=32\pi-0.93\pi=31.07\pi\ in^3$

assume

$\pi=3.1416$

$V=31.07(3.1416)=97.6\ in^3$

8 0

2 years ago

A TV that usually sells for $192.74 is on sale for 25% off. If sales tax on the TV is 5%, what is the price of the TV, including

Mashutka [201]

Answer:

Step-by-step explanation:

If you are saving 25%, you are still paying 75%, right? So the cost of the TV with a discount of 25% is 192.74(.75) which is $144.56

That's the cost of the TV on sale. Now we need to find the sales tax amount, if the sales tax is .05 as a decimal. We are paying $144.56 for the TV, which is 100% of the cost. On top of that, we are paying another 5%. So altogether, for the TV, we are paying 105% of the TV. Therefore,

144.56(1.05) = $151.79

4 0

3 years ago

Solve the inequality and give an answer in interval notation: 4-x> 6