Write an equation in slope-intercept form for the line with the slope of -4 and x-intercept

Solve the inequality -2z-3<5. what is the value of z?

agasfer [191]

Hey there!

The answer to your question is z > -4

We can solve this like it is an equation, with one exception. When you divide or multiply by a negative number, in an inequality, you have to flip the inequality sign.

-2z - 3 < 5 add 3 to both sides

-2z < 8 divide both sides by -2, and flip the inequality sign

z > -4

Good luck! Hope it helps, and have a great day!

8 0

2 years ago

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Compare- 6 broken bulbs out of 20 or 7 broken bulbs out of 30

9966 [12]

Answer:

well 6/20 has more absolute value than 7/30

Step-by-step explanation:

also 7/30 is closer to zero

5 0

3 years ago

Lenny wants to buy a lawn mower priced at $266, if he pays cash. He can buy it on credit for $288. The reason he pays more on cr

wariber [46]

Answer:

<h2>22</h2><h2>Step-by-step explanation: did the math</h2>

7 0

3 years ago

PLEASE HELP ME ASAP.

Troyanec [42]

Answer:

use pathway but with an M instead of P

Step-by-step explanation:

4 0

3 years ago

The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T min

dolphi86 [110]

This is a doozy. I actually have another form of the equation for cooling, and it's in Celcius (so I convert) and seconds (we can switch back to minutes in the end). The Celcius and Fahrenheit don't matter because it's the time we are interested in and as long as we use the C and F equivalents, we're fine. Promise. The formula is as follows: $T(t)= T_{s}+( T_{0}- T_{s})e ^{-kt}$ . It's really easy to use. T(t) is the ending temperature; $T_{s}$ is the room temp; $T_{0}$ is our initial temperature of the liquid; e is Euler's number, k is the constant of variation, and t is the time in seconds. In Celcius, our temps are as follows: 180 F = 82.2 C; 100 F = 37.8 C; 75 F = 23.9 C; 80 F = 26.7 C. 10 minutes is 600 seconds. Filling in our formula with all of that, we will solve for k. Then we will use that k value to solve for the time in the question we are told to answer. Let's do this. $37.8=23.9+(82.2-23.9)e ^{-600k}$ . Simplifying a bit we have $37.8=23.9+(58.3)e ^{-600k}$ . Subtracting 23.9 from both sides we have $13.9=58.3e ^{-600k}$ . divide both sides by 58.3 to get $.2384219=e ^{-600k}$ . At this point in your mathematical career, I'm assuming that since you're doing this, you're studying natural and common logs. The base of a natural log is e, therefore, if we take the natural log of e, they both "undo" each other and cancel each other out completely. So let's do that. $ln(.2384219)=-600k$ . Simplifying on the left gives us $-1.433713=-600k$ . Dividing both sides by -600 gives us a k value of .002389. Now we will do the equation again, using that k value, to solve for how long it takes for the coffee to cool to 80 F (26.7 C). $26.7=23.9+(82.2-23.9)e ^{-.002389t}$ . Simplifying a bit again gives us $26.7=23.9+(58.32)e ^{-.002389t}$ . Subtracting 23.9 from both sides gives us $2.8=(58.32)e ^{-.002389t}$ . We will now divide both sides by 58.32 to get $.0480109=e ^{-.002389t}$ . Again we will take the natural log of both sides to "undo" the e: $ln(.0480109)=-.002389t$ . The natural log of .0480109 is -3.036325671. So, dividing both sides by the negative decimal on the right gives us $\frac{-3.036325671}{-.002389}=t$ and t = 1270.9 seconds. Divide that by 60 to get the time in minutes. t = 21.1826...so 21 minutes. Phew!!!

7 0

3 years ago

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