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Viktor [21]
3 years ago
9

What is the equation of the line that passes through the point (-4,4) and has a slope of -3

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0

Answer: y-4=-3(x+4) or y=-3x-8

Step-by-step explanation:

To find the equation of the line with a given point and slope, we can fill them into the point-slope formula. The point-slope formula is y-y₁=m(x-x₁).

y-4=-3(x-(-4))            [multiply]

y-4=-3(x+4)

Another equation could be slope-intercept form. It is y=mx+b.

y-4=-3(x+4)              [distribute]

y-4=-3x-12                [add both sides by 4]

y=-3x-8

Now, we know that the equation is y=-3x-8 or y-4=-3(x+4).

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Two more than a certain number is 15 less than twice the number. Find the number
Svetllana [295]
2+x=2x-15
>> 2+15=2x-x
>> 17 = x

So the answer is <u>17</u>
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3 years ago
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A bakery sold a total of 400 cupcakes in a day, and 184 of them were vanilla flavored. What percentage of cupcakes sold that day
g100num [7]

Answer:

54

Step-by-step explanation:

400-184=216

216 out of 400 turned into percentage is 54

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3 years ago
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The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experi- mental conditio
zzz [600]

Answer:

see explaination

Step-by-step explanation:

Data : 32.1 , 30.6 , 31.4 , 30.4 , 31.0 , 31.9

Mean X-bar = 31.23

SD = 0.689

a)

Null Hypothesis : Xbar = mu

Alternate Hypothesis : Xbar > mu

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 30 ) /(0.689/sqrt(6))

= 4.372

P-value = ~0

Since P-vale < 0.01 , we will reject null hypothesis.

The data suggest that true average stopping ditance exceeds the maximum.

b)

i) SD = 0.65

mu = 31

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 31) /(0.65/sqrt(6))

= 0.867

P-value = 0.3859 Answer

ii) SD = 0.65

mu = 32

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 32) /(0.65/sqrt(6))

= -2.9

P-value = 0.0037 Answer

c)

i) SD = 0.8

mu = 31

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 31) /(0.8/sqrt(6))

= 0.704

P-value = 0.4814 Answer

ii) SD = 0.8

mu = 32

z = (Xbar - mu) / (SD/sqrt(n))

= (31.23 - 32) /(0.8/sqrt(6))

= -2.357

P-value = 0.0184 Answer

The probabilities obtained in part c are comparatively higher than that of part b.

d)

i) For alpha =0.01

z = (Xbar - mu) / (SD/sqrt(n))

=> -2.32 = (31.23 - 31) /(0.65/sqrt(n))

=> (0.65/sqrt(n)) = (31.23 - 31)/-2.32

=> sqrt(n) = (0.65*(-2.32)) / (31.23 - 31)

=> n = 43 Answer

ii) For beta =0.10

z = (Xbar - mu) / (SD/sqrt(n))

=> -1.28 = (31.23 - 31) /(0.65/sqrt(n))

=> (0.65/sqrt(n)) = (31.23 - 31)/-1.28

=> sqrt(n) = (0.65*(-1.28)) / (31.23 - 31)

=> n = 13 Answer

4 0
2 years ago
Use the Distributive Property to expand this expression.
viktelen [127]

Answer:

C is the correct answer

Step-by-step explanation:

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3 years ago
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Please help me figure out this problem
tiny-mole [99]

Answer:

f(g(x))=f\left(-\dfrac{3x+21}{5}\right)=x\\\\g(f(x))=g\left(-\dfrac{5}{3}x-7\right)=x

Step-by-step explanation:

Fill in the given expressions and simplify.

f(g(x))=f\left(-\dfrac{3x+21}{5}\right)=-\dfrac{5}{3}\left(-\dfrac{3x+21}{5}\right)-7\\\\=\left(-\dfrac{5}{3}\right)\left(-\dfrac{3x}{5}\right)-\left(\dfrac{5}{3}\right)\left(-\dfrac{21}{5}\right)-7\\\\=\dfrac{15x}{15}+\dfrac{5\cdot 21}{3\cdot 5}-7=x+7-7=x

Going the other way, we have ...

g(f(x))=\displaystyle -\frac{3\left(-\frac{5}{3}x-7\right)+21}{5}=-\frac{-5x-21+21}{5}=x

5 0
3 years ago
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