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Andrei [34K]
3 years ago
10

A line with a slope of -1/3 passes through the point (9,3). What is its equation in point-slope form?

Mathematics
1 answer:
amm18123 years ago
7 0

The point-slope form:

y-y_1=m(x-x_1)

We have:

(9,\ 3)\to x_1=9,\ y_1=3\\\\m=-\dfrac{1}{3}

Substitute

y-3=-\dfrac{1}{3}(x-9)

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Can someone help me on these problems and show work
Salsk061 [2.6K]

The simplified expression are as follows;

6mn³ - mn² +  3mn³ + 15mn² =  9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

<h3>How to simplify an expression?</h3>

A simplified expression is express to its lowest term.

Therefore,

6mn³ - mn² +  3mn³ + 15mn²

combine like terms

6mn³  +  3mn³ - mn² + 15mn²

9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

learn more on simplification here: brainly.com/question/403991

#SPJ1

3 0
1 year ago
Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95%
Amanda [17]

Answer:

The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

Step-by-step explanation:

The data for the amount of money spent weekly on groceries is as follows:

S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}

<em>n</em> = 10

Compute the sample mean and sample standard deviation:

\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7

s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} }       = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702

It is assumed that the data come from a normal distribution.

Since the population standard deviation is not known, use a <em>t</em> confidence interval.

The critical value of <em>t</em> for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:

t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262

*Use a <em>t</em>-table.

Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:

CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}

     =176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)

Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).

7 0
3 years ago
One 8-ounce can of soda has 228 calories.  If Shaun drinks the big 28-ounce size from the local mini-mart, how many calories wil
Rama09 [41]

Answer:

324.7 calories

6 0
2 years ago
Read 2 more answers
A show uses 12 gallons of water in three minutes complete the table and the graph.
gregori [183]

Answer:

2 mins= 8 gallons 3 mins= 12 gallons 4 mins= 16 gallons 5 mins= 20 gallons 6 mins= 24 gallons

Step-by-step explanation:

12 divided by 3 equals 4 so just multiply 4 by each minute

5 0
3 years ago
How can you write the expression with rationalized denominator? sqrt3 - sqrt6 / sqrt 3 + sqrt 6
harina [27]
Answer:  2√2 - 3

Explanation:


The expession written properly is:

\frac{ \sqrt{3}- \sqrt{6}  }{ \sqrt{3}+ \sqrt{6} }

To rationalize that kind of expressions, this is to eliminate the radicals on the denominator you use conjugate rationalization.

That is, you have to multiply both numerator and denominator times the conjugate of the denominator.

The conjugate of √3+√6 is √3 - √6, so let's do it:

\frac{ \sqrt{3} - \sqrt{6} }{ \sqrt{3} + \sqrt{6} } . \frac{ \sqrt{3}- \sqrt{6}  }{ \sqrt{3}- \sqrt{6} }

To help you with the solution of that expression, I will show each part.

1) Numerator: (√3 - √6) . (√3 - √6) = (√3 - √6)^2 = (√3)^2 - 2√3√6 + (√6)^2 =

= 3 - 2√18 + 6 = 9 - 6√2.

2) Denominator: (√3 + √6).(√3 - √6) = (√3)^2 - (√6)^2 = 3 - 6 = - 3

3) Then the resulting expression is:

 9 - 6√2
-----------
 -3

Which can be further simplified, dividing by - 3

    -3 + 2√2

Answer: 2√2 - 3

7 0
3 years ago
Read 2 more answers
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