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Perpendicular to the line 4x - 6y + 7 = 0 , passing through (3, 4) .

PilotLPTM [1.2K]

Answer:

The equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

Step-by-step explanation:

Given equation of line is:

$4x - 6y + 7 = 0$

Given equation is in standard form. It has to be converted into slope-intercept form to extract slope from the equation.

So,

$4x+7 = 6y\\6y=4x+7\\\frac{6y}{6} = \frac{4x+7}{6}\\y = \frac{4}{6}x+\frac{7}{6}\\y=\frac{2}{3}x+\frac{7}{6}$

The standard form of slope-intercept form of equation is:

$y=mx+b$

Here, the co-efficient of x is the slope of the line.

So the slope of given line is: 2/3

m = 2/3

The product of slopes of two perpendicular lines is -1

Let m1 be the slope of line perpendicular to given line

Then

$m.m_1 = -1\\\frac{2}{3} . m_1 = -1\\m_1 = -1*\frac{3}{2}\\m_1 = -\frac{3}{2}$

The equation of perpendicular will be:

$y = m_1x+b$

Putting the value of slope

$y = -\frac{3}{2}x+b$

To find the value of b, putting (3,4) in the equation

$4 = -\frac{3}{2}(3)+b\\4 = -\frac{9}{2}+b\\b = 4+\frac{9}{2}\\b= \frac{8+9}{2}\\b=\frac{17}{2}$

So the equation of line perpendicular to given line passing through (3,4) is:

$y = -\frac{3}{2}x+\frac{17}{2}$

7 0

3 years ago

BRAINLIEST IF YOU HELP the correct simplification of 7x2(6x + 3x2 − 4)? A 21x4 − 42x3 + 28x2 B 42x4 + 21x3 − 3x2 C 21x4 + 42x3 −

exis [7]

$\text{Simplify:}\\\\7x^2(6x + 3x^2- 4)\\\\\text{Use the distributive property:}\\\\42x^3+21x^4-28x^2\\\\\text{You can arrange them by exponent}\\\\21x^4+42x^3-28x^2\\\\\text{This means that your answer will be C).} 21x^4 + 42x^3 - 28x^2\\\\\boxed{\text{C).}\,\,21x^4 + 42x^3 - 28x^2}$

3 0

3 years ago

In a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per

alexdok [17]

Answer:

The test statistic for testing if the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard is 3.234.

Step-by-step explanation:

We are given that in a random sample of 380 cars driven at low altitudes, 42 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed.

In an independent random sample of 90 cars driven at high altitudes, 24 of them exceeded the standard.

Let $p_1$ = <u><em>population proportion of cars driven at high altitudes who exceeded a standard of 10 grams</em></u>.

$p_2$ = <u><em>population proportion of cars driven at low altitudes who exceeded a standard of 10 grams</em></u>.

So, Null Hypothesis, $H_0$ : $p_1\leq p_2$ {means that the proportion of high-altitude vehicles exceeding the standard is smaller than or equal to the proportion of low-altitude vehicles exceeding the standard}

Alternate Hypothesis, $H_A$ : $p_1>p_2$ {means that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard}

The test statistics that will be used here is <u>Two-sample z-test statistics</u> for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of cars driven at high altitudes who exceeded a standard of 10 grams = $\frac{24}{90}$ = 0.27

$\hat p_2$ = sample proportion of cars driven at low altitudes who exceeded a standard of 10 grams = $\frac{42}{380}$ = 0.11

$n_1$ = sample of cars driven at high altitudes = 90

$n_2$ = sample of cars driven at low altitudes = 380

So, the test statistics = $\frac{(0.27-0.11)-(0)}{\sqrt{\frac{0.27(1-0.27)}{90}+\frac{0.11(1-0.11)}{380} } }$

= 3.234

The value of z-test statistics is 3.234.

7 0

3 years ago

What the reciprocal of 5/8 in fractions

Vladimir79 [104]

<h2> 《《♤HEY BUDDY♤》》</h2>

<h2>☆☆☆THIS IS YR ANSWER☆☆☆</h2>

<h2>THE RECIPROCAL OF 5/8 in fraction </h2><h2>IS 8/5 IN FRACTION. </h2>

8 0

3 years ago

A data analyst wants to set up a hypothesis test to determine if the mean number of courses taken in a college semester is diffe

Nadya [2.5K]

Answer:

Step-by-step explanation:

Hello!

What you want to test is if there is a difference between the number of courses taken by students of different years, you can determine 4 populations of students:

Population 1: Freshmen

Population 2: Sophomores

Population 3: Juniors

Population 4: Seniors

To each population you measured the study variable, setting 4 different variables. To compare these variables the best way is to make one test where you compare the four populations at the same time, so the hypothesis is:

H₀: μ₁ = μ₂ = μ₃ = μ₄

H₁: At least one of the population means is different from the others.

The most appropriate test to use to compare the population mean of the 4 groups is an ANOVA.

I hope you have a SUPER day!

3 0

4 years ago