Mathematics College

Find an equation of the line that satisfies the given conditions.
Through (2, 9); parallel to the line passing through (3, 7) and (−1, 3)

Answers

Answer 1

9514 1404 393

Answer:

y = x +7

Step-by-step explanation:

The slope of the given line can be found as ...

m = (y2 -y1)/(x2 -x1)

m = (3 -7)/(-1 -3) = -4/-4 = 1

Then the point-slope form of the equation for the desired line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

y - 9 = 1(x -2)

y = x -2 +9

y = x + 7 . . . . slope-intercept form

The attachment shows a graphing application that will write the equation of the line. Here, it shows the desired line has the equation ...

x -y = -7 . . . . desired line equation in standard form

Find An Equation Of The Line That Satisfies The Given Conditions.Through (2, 9); Parallel To The Line

Related Questions

Compute the mean, median, and mode for the following three sets of scores saved.

Score 1 Score 2 Score 3

3 34 154
7 54 167
5 17 132
4 26 145
5 34 154
6 25 145
7 14 113
8 24 156
6 25 154
5 23 123

Answers

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = [tex] \frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6 [/tex]

Median: order the data from least to the greatest.

3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

The median is average of the fifth and sixth data value in the data set

Median = (145 + 154)/2 = 299/2 = 149.5

Mode = 154

Suppose that you roll a die 8 times. What is the probability that you roll a six three or fewer times

Answers

Answer:

0.96

Step-by-step explanation:

Given that the a die is rolled 8 number of times.

[tex]n[/tex] = 8

Probability of getting a 6 on roll of a die, [tex]p=\frac{1}{6}[/tex]

Probability of not getting a 6 on roll of a die, [tex]q=1-p=1-\frac{1}{6}=\frac{5}{6}[/tex]

Probability of getting 6 three or fewer times:

[tex]P(r \le 3)=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]

Formula:

[tex]P(r=k)=_nC_k.p^k.q^{n-k}[/tex]

Putting the values using this formula:

[tex]P(r \le 3)=_8C_0.\frac{1}{6}^0.\frac{5}{6}^{8-0}+_8C_1.\frac{1}{6}^1.\frac{5}{6}^{8-1}+_8C_2.\frac{1}{6}^2.\frac{5}{6}^{8-2}+_8C_3.\frac{1}{6}^3.\frac{5}{6}^{8-3}\\\Rightarrow P(r \le 3)=1.\frac{5}{6}^{8}+8.\frac{1}{6}.\frac{5}{6}^{7}+28.\frac{1}{36}^2.\frac{5}{6}^{6}+56.\frac{1}{216}.\frac{5}{6}^{5}\\\Rightarrow P(r \le 3)=0.23+0.37+0.26+0.1=\bold{0.96}[/tex]

What are the answers to 11 and 12

Answers

11. Is x=17
12.is x=11.43

pls help meeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

kya pls help meeeeeeeeeeeeeeee.

please thanks and follow me.

The neighborhood swimming pool drains at a rate of 99 gallons every 3 hours. At this rate, how many gallons are
emptied each hour?
Helllllpppppp meeee

Answers

Answer:

33mph

Step-by-step explanation:

because if u divide 99 by 3 that is the answer

which number line and expression show how to find the distance from -4 to 1?

Answers

Answer:

the correct answer is C

Plz help me it’s geometry

Answers

I can’t see the picture

is this a equation or expression 4r+3=12

Answers

Answer:

Equation

Step-by-step explanation:

Because there is only one unknown term in it

I hope it helps

Thank U

Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.

Answers

Answer:

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Step-by-step explanation:

The objective of this question is to solve:

[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]

Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:

Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:

i.e.

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]

To Replace:

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]

[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]

[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]

Thus;

[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0

[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]

∴

In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:

[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]

By Factorization:

[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]

[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]

However;

The root [tex]\lambda = -6 \pm i[/tex] yield;

[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]

[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]

The root [tex]\lambda = 3[/tex] yield;

[tex]y_3(x) = c_3 e^{3x}[/tex]

∴

The general solution is:

[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]

Using Euler's Identity ;

[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]

[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

CAN YOU PLS ANSWER THIS QUICK!!! WHAT IS THE ANSWER TO THIS MATH EQUATION??? GEOMETRY/COLLEGE!!!

Answers

The answer is undefined

Evaluate and reduce:
-4.9
Enter the number that belongs in the
green box,

Answers

Answer:

Step-by-step explanation:

-4/7 * 9

The dot there resembles multiplication sign.

-4/7 * 9/1 (9 = 9/1 because 9 divided by 1 = 9)

=> -(4 * 9) / (9 * 1)

=> -36 / 9

=> -4

If my answer helped, kindly mark me as the brainliest!!

Thanks!!

use the simplified ratio to find the equivalent ratio with a denominator of 140

Answers

Answer:

140

Step-by-step explanation:

all i could get sorry

A florist sold 45 flowers in a day and 60 flowers on the next day. If p is the percent increase in the number of flowers sold, which proportion can be used to calculate p?

Answers

Answer:

Step-by-step explanation:

i took the test

Answer: C

Step-by-step explanation:

Only one that makes sense and I just took that test

Determine wheather the given lines are parallel or not. Write the reasons .

Answers

Answer:

yes it is parallel because the alternate interior angles are equal

PLEASE HELP ASAP!!
There are 800 students who attend Park Middle School. There are 1.5 times as many boys as there are girls.
x is boys
y is girls
800=1.5x=y
Determine how many boys and girls attend Park Middle School. Round to the nearest whole number if necessary. Show your work.

Answers

Answer:

320 boys; 480 girls

Step-by-step explanation:

Here is the correct system of equations you can write for this equation:

1.5x=y

x+y=800

x+1.5x=800

2.5x=800

x=320

320+y=800

y=480

(-8) X 2/3 i NEED the answer help me

Answers

-5.33333333333

I used a calulator can I get brainliest please

Solve for x.

6(x – 1) = 9(x + 2)

Answers

Answer: -8

Step-by-step explanation:

Distribute 6 to x and -1

6x-6=9(x+2)

Distribute 9 to x and 2

6x-6=9x+18

Add 6 to both sides

6x=9x+24

Subtract 9x from both sides

-3x=24

Divide -3 from both sides

X=-8

The answer is -8 hope that helps lol

What Is It HomeWork*.

Answers

Answer:

sumthing that we hate doing

Step-by-step explanation:ughhhhhhhhhh

The inequalities is 6 is greater than or equal to 6

I don't understand calculus at all bruh :/. I figured out some of this but I don't know if the answer is 0 or 2. Whoever figures this, out also please explain how you got it.

Answers

Calculus isn’t that difficult. And that’s not to insult you or for me to brag. You just simply aren’t being taught correctly, assuming you’re trying.

The first step for ANY limit is to plug in. Always plug in first. You can take the odd root of a negative number because let’s say you have -1^3, you’re still gonna get -1. But if the power is even, you will always get a positive number. So plug in -32 to get the 5th root of -32. The answer would be -2 because -2^5 = -32

Statements about regression
Which of the following are true about regression with one predictor variable (often called "simple regression")?
A. The total squared error divided by its degrees of freedom is the square of the standard error of estimate
B. The standardized regression coefficient, beta, has the same value as r, the estimated correlation
C. After conducting a hypothesis test to test that the slope of the regression equation is nonzero, you can conclude that your predictor variable, X, causes Y

Answers

Answer:

Follows are the solution to this question:

Step-by-step explanation:

It is true because the square of the standard error of its estimate was its total square error divided only by the degree of freedom. It is true because Its coefficient with Standardized Regression, beta, will have the same value as r, the approximate similarity. It is false because Its slope b, of its equation of regression, will have the same value as r, the projected correlation.

Snail moves 6 inches in 120 minutes. What was average speed of snail in inches per minute

Answers

Answer:

.2 inches a min.

Step-by-step explanation:

Answer:

0.05

Step-by-step explanation:

6 divided by 120 = 0.05

Hope this helps☺️

I need help ASAP due rn!

Solve the equation by completing the square. Show all your steps
X^2-6x+13=0

Answers

There are no real solutions

a bacteria culture begins with 8 bacteria which triples in size every week. How many bacteria exists in the culture after 4 weeks ?

Answers

Answer:

648

Step-by-step explanation:

8x3=24

24x3=72

72x3=216

216x3=648

HELP PLSSSSS AAAAAAAAAAAAAAAAAAAAAA ILL GIVE BRAINLIEST B(

Answers

Answer:

a(n) = (3/5)a(n-1), where a(1) = 10 and n is 2 or greater.

Step-by-step explanation:

determine the common factor...The first term (10) by 3/5 results in the given second term (6); the third term is 3/5 of the second term (6), resulting in 18/5 (equivalent to 36/10 or 3.6/1, or just 3.6. Resulting in a(n) = (3/5)a(n-1).

the third term is 3.6, which, if mult. by (3/5), produces 2.16, as expected.

Thus, the recursive formula for this geometric sequence is a(n) = (3/5)a(n-1).

This is good only for a(1) = 10 and n = 2, 3, ....

Hope this helps you

Answer: