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2 years ago

The graph of the function f(x) = −3x2 − 3x + 6 is shown. Which statements describe the graph? Select three options.

Mathematics

1 answer:

Afina-wow [57]2 years ago

8 0

<h3>The domain is all real numbers.</h3>

<h3>On the coordinate plane, the parabola opens down, passes through (-2,0), has a vertex at (0.5,6.75) and goes through (1,0)</h3>

<h3>The vertex is its maximum value.</h3>

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What operations do i put in to make these equations correct?

Elan Coil [88]

3 + 3 - 3 / 3 = 5
3 + 3 + 3 - 3 = 6
3 + 3 + 3 / 3 = 7
3 * 3 - 3 / 3 = 8

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3 years ago

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On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?

matrenka [14]

Answer:

1. santina drove 14 more miles than carole

2. the owner will need to buy 8 bags this week

Step-by-step explanation:

1. 203-189= 14

2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds

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2 years ago

currently get paid $12.00 an hour and I really want to make an extra $300.00 by working overtime. I'll need to work __________ e

9966 [12]

Answer:

Step-by-step explanation:

300/12 = 25

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3 years ago

Write an inequality to represent each

Crazy boy [7]

I agree with the other person ^^^

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!!!

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3 years ago

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