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nignag [31]
3 years ago
9

The function with a rate of change of 3/2 whose graph passes through the point (4,10.5)

Mathematics
1 answer:
tamaranim1 [39]3 years ago
4 0

Answer:

y = 1.5x+4.5

Step-by-step explanation:

Let's try to fit this into slope-intercept form, which is y=mx+b, where m=slope and b=y-intercept.

Rate of change means slope, so m=3/2 = 1.5.

y = 3/2x+b

We can plug in the given point, remembering that it's in the form (x,y), so x=4, y=10.5.

y = 3/2x+b

10.5 = 3/2*4 + b

4.5 = b

Plug b back in.

y = 1.5x+4.5

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Ackie got 3 wrong out of 20 questions on her social studies quiz.What percent did she answer correctly on the quiz
taurus [48]

Answer:

85%

Step-by-step explanation:

If she got 3 wrong then it means she got 20-3 right, so she got 17 questions right.

From there we get the fraction: 17/20

To make the a percentage we times both the top and bottom by 5 (because 20 x 5 = 100)

By doing that we get 17x5/20x5

= 85/100

That is equal to 85%

5 0
2 years ago
Resale Value Garland Mills purchased a certain piece of machinery 2 years ago for $500,000. Its present resale value is $420,000
Natasha2012 [34]

Answer:

260,000

Step-by-step explanation:

The value decreases by 40,000 per year (500000-42000/2 years) the value will decrease by 240000 in six (4 years plus 2 years already passed) years. 6 x 40,000 =240000

So, the value should be 260,000 (500000-240000)

Or

year 1 500000-40000=460000

year 2 460000-40000=420000

year 3 420000-40000=380000

year 4 380000-40000=340000

year 5 340000-40000=300000

year 6 300000-40000=260000

6 0
2 years ago
You choose a movie at random from a list containing 8 comedy movies, 5 science fiction movies, and 7 adventure movies. What is t
IRISSAK [1]

Answer:

3/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

the theoretical probability that the movie is not a comedy = number of movies that are not comedies / total movies available

12/ 20 = 3/5

7 0
2 years ago
Craig is standing on his apartment balcony and locates his car in the street-level parking lot below. The angle of depression of
murzikaleks [220]

Answer:

B. 147 feet

Step-by-step explanation:

We can easily imagine a right triangle for this problem. The height of the triangle is what we're looking for (x), at the bottom of x, we have the right angle formed by the building and the ground.  The other side of that right angle is the distance to the car (300 ft). On top of the x side, we have the angle of 63 degrees looking down, since Craig is looking down by 27 degrees (90 - 27 = 63).

We can easily apply the Law of Sines that says:

\frac{a}{sin(A)} = \frac{c}{sin(C)}

Then we can isolate c and fill in the values:

c = \frac{a * sin(C)}{sin(A)} =\frac{300 * sin(27)}{sin(63)} = 153

So, we know Craig's eyes are 153 feet above ground... since Craig is 6 feet tall, the balcony sits at 147 feet high (153 - 6 = 147).

6 0
3 years ago
Use the properties of logarithms to expand the following expression.log(z3)/√x5y)Each logarithm should involve only one variable
jek_recluse [69]

Answer:

3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

Step-by-step explanation:

log(z3)/√x5y)

= log (z3)   - log (√x5y)   [division being subtracted]

= 3 log (z) - {log (√x) + log (√5y)}    [ multiplication being added in the denominator]

= 3 log (z) - {log (x)^1/2 + log (5)^1/2+ log (y)^1/2}  

= 3 log (z) -  1/2{log (x) + log (5)+ log y }

 We can solve inside the curly bracket and then multiply with 1/2 or we can solve it separately

= 3 log (z) -  1/2log (x) - 1/2 log (5) -1/2 log y

How does this work?

1) any two terms being multiplied in logarithms are added with the log of each.

2) the exponent becomes the co- efficient.

3)  any two terms being divided in logarithms are subtracted with the log of each

8 0
3 years ago
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