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3 years ago

find the equation of a line parallel to the line y=-9x+2 that passes through the point (5,5). GIve the answer in slope form

Mathematics

2 answers:

jolli1 [7]3 years ago

7 0

-9(m)=-1
m=1\9
5-Y=1\9(x-5)
-Y=1\9x-5\9-5
Y=-(1\9x-50\9)
y=-1\9x+50\9
9y=X+50

Nikitich [7]3 years ago

3 0

y = - 9x + 50

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 9x + 2 is in this form with slope m = - 9

Parallel lines have equal slopes

y = - 9x + c is the partial equation of the parallel line

To find c substitute (5, 5 ) into the partial equation

5 = - 45 + c ⇒ c = 5 + 45 = 50

y = - 9x + 50 ← equation of parallel line

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Mike is working on solving the exponential equation 37^x = 12; however, he is not quite sure where to start.

Rainbow [258]

The solution of the given exponential equation is 0.688.

Given that Mike is working on solving the exponential equation 37ˣ = 12.

An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.

firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:

aˣ = y

logₐy = x

Now, we will apply this transformation to our equation and we get

log₃₇12=x

Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:

x=log12/log37

So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:

x≈1.079/1.568

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Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.

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2 years ago

An orchard owner wants to plant 64 cherry tree seedlings and 96 peach tree seedlings in rows. Each row is to have the same numbe

-BARSIC- [3]

Answer:

Given:

cherry tree seedlings : 64

peach tree seedlings : 96

64/96 : Simplify this fraction

64 / 8 = 8 / 4 = 2

96 / 8 = 12 / 4 = 3

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The maximum number of rows that the owner can plant is 32 rows with 2 cherry tree seedlings and 3 peach tree seedlings.

5 0

3 years ago

Read 2 more answers

Have Retirement Benefits

charle [14.2K]

Answer:

(a) The probability of the intersection of events "man" and "yes" is 0.55.

(b) The probability of the intersection of events "no" and "man" is 0.10.

Step-by-step explanation:

The information provided is:

Yes No Total

Men 275 50 325

Women 150 25 175

Total 425 75 500

(a)

Compute the probability that a randomly selected employee is a man and a has retirement benefits as follows:

$P(M\cap Y)=\frac{n(M\cap Y)}{N}=\frac{275}{500}=0.55$

Thus, the probability of the intersection of events "man" and "yes" is 0.55.

(b)

Compute the probability that a randomly selected employee does not have retirement benefits and is a man as follows:

$P(N\cap M)=\frac{n(N\cap M)}{N}=\frac{50}{500}=0.10$

Thus, the probability of the intersection of events "no" and "man" is 0.10.

(c)

Compute the probability that a randomly selected employee is a woman or has no retirement benefits as follows:

$P(W\cup N)=P(W)+P(N)-P(W\cap N)=\frac{175}{500}+\frac{75}{500}-\frac{25}{500}=0.45$

Thus, the probability of the union of events "woman" or "no" is 0.45.

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3 years ago

A new type of pump can drain a certain pool in 8 hours. An older pump can drain the pool in 12 hours. How long will it take both

Marina86 [1]

Answer:

Step-by-step explanation:

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4 years ago

A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample

8090 [49]

Answer:

Step-by-step explanation:

Step(i):-

Given first random sample size n₁ = 500

Given Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.

First sample proportion

$p^{-} _{1} = \frac{65}{500} = 0.13$

Given second sample size n₂ = 700

Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.

second sample proportion

$p^{-} _{2} = \frac{133}{700} = 0.19$

Level of significance = α = 0.05

critical value = 1.96

Step(ii):-

Null hypothesis : H₀: There is no significance difference between these proportions

Alternative Hypothesis :H₁: There is significance difference between these proportions

Test statistic

$Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }$

where

$P = \frac{n_{1} p^{-} _{1}+n_{2} p^{-} _{2} }{n_{1}+ n_{2} } = \frac{500 X 0.13+700 X0.19 }{500 + 700 } = 0.165$

Q = 1 - P = 1 - 0.165 = 0.835

$Z = \frac{0.13-0.19 }{\sqrt{0.165 X0.835(\frac{1}{500 } +\frac{1}{700 } )} }$

Z = -2.76

|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance

Null hypothesis is rejected at 0.05 level of significance

Alternative hypothesis is accepted at 0.05 level of significance

Conclusion:-

There is there is a difference between these proportions at α = 0.05

3 0

3 years ago