find the equation of the line that is parallel to the given line and passes through the given point
[tex]x+4y=-6 ; (8, -3)[/tex]

Answers

Answer 1

Answer:

[tex]\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}[/tex]

[tex]\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}[/tex]

[tex]\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}[/tex]

[tex]x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1[/tex]

[tex]\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4[/tex]


Related Questions

What slope is parallel to m=3/4

Answers

Answer:

[tex]\large \boxed{{m= \frac{3}{4} }}[/tex]

Step-by-step explanation:

Parralel lines have the same slope.

The slope will be [tex]\frac{3}{4}[/tex]

The line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4

The slope is the measure of the steepness of a line. It is also known as the gradient of a line.

Two parallel lines are known to have equal slopes. For example;

The line y = 2x - 5 and y = 2x + 3 are parallel because they have the same slope which is 2.

Therefore for the line with a slope m = 3/4, the slope of the line parallel to this line will also be 3/4

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0.138.2 + 0.0032 correct to 1 decimal place​

Answers

Answer:

Exact: 0.1414

Rounded: 0.1

Step-by-step explanation:

2. The radius of a circle is 9 cm. Find the area of the circle
(Use 3.14 as the approximation of T.)

Answers

Answer:

Area of a Circle = 254.34 cm²

Step-by-step explanation:

Area of a Circle = π r²

Area of a Circle = 3.14 * 9²

Area of a Circle = 254.34 cm²

hii:) anyone able to help with practice 6? Thanks:)!

Answers

Answer:

The answer is

[tex]x = \frac{ {e}^{ \frac{3}{ ln(2) } } }{4} [/tex]

Step-by-step explanation:

[tex] ln(2) \times ln(4x) = 3[/tex]

Divide both sides of the equation by ln 2

That's

[tex] \frac{ ln(2) ln(4x) }{ ln(2) } = \frac{3}{ ln(2) } [/tex]

We have

[tex] ln(4x) = \frac{3}{ ln(2) } [/tex]

Covert the logarithm into exponential form using the property

[tex] ln(x) = b

\: \: is \: \: \: the \: \: \: same \: \: \: as \: \: \: \:

x = {e}^{b} [/tex]

Are all the same

So

[tex] ln(4x) = \frac{3}{ ln(2) } [/tex]

is the same as

[tex]4x = {e}^{ \frac{3}{ ln(2) } } [/tex]

Divide both sides by 4

We have the final answer as

[tex]x = \frac{ {e}^{ \frac{3}{ ln(2) } } }{4} [/tex]

Hope this helps you

Point c d and g lie on plane x. Point e and f lie on plane y. Which statements are true

Answers

The true statements are: 3, 4 and 5

Step-by-step explanation:

search it up

Answer:

2,3,and 4

Step-by-step explanation:

Solve for x in the simplest form 11=1/2(x+8)

Answers

Answer:

[tex] \boxed{\sf x = 14} [/tex]

Step-by-step explanation:

Solve for x:

[tex] \sf \implies 11 = \frac{1}{2} (x + 8)[/tex]

[tex] \sf 11 = \frac{1}{2} (x + 8) \: is \: equivalent \: to \: \frac{1}{2} (x + 8) = 11 : [/tex]

[tex] \sf \implies \frac{1}{2} (x + 8) = 11[/tex]

[tex] \sf Multiply \: both \: sides \: of \: \frac{1}{2} (x + 8) = 11 \: by \: 2 : [/tex]

[tex] \sf \implies \frac{1}{ \cancel{2}} (x + 8) \times \cancel{2 }= 11 \times 2[/tex]

[tex] \sf \implies 1(x + 8) = 11 \times 2[/tex]

11 × 2 = 22:

[tex] \sf \implies x + 8 = 22[/tex]

Subtract 8 from both sides:

[tex] \sf \implies x + (8 - 8) = 22 - 8[/tex]

8 - 8 = 0:

[tex] \sf \implies x = 22 - 8[/tex]

22 - 8 = 14:

[tex] \sf \implies x = 14[/tex]

The value of x is 4, for the equation 11 = 1/2 (x + 8).

What is an equation?

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

11 = 1/2 (x + 8)

Simplify the equation by multiplying 2 in both the sides,

11 × 2 =2 × 1/2 × (x + 8)

22 = x + 8

Subtract 8 from both the sides,

22 - 8 = x + 8 - 8

14 = x

or x = 14

The required value of x for the given equation is 14.

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If the rectangle is 38 inches and the length is 12 how much is the width ?

Answers

Answer:

width= 3.17

Step-by-step explanation:

Divide 38 (the area) by 12 (the width)

3.what is 8/30 equal to?​

Answers

Answer:

4/15

Step-by-step explanation:

[tex]\frac{8}{30}\\\\\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4}{15}[/tex]

What is an equation of the line that passes through the points (6,2) and (-6, -8)?
Put your answer in fully reduced form.

Answers

Step-by-step explanation:

Hey, there!!

Let me simply clear you.

The given points are (6,2) and (-6,-8).

Remember if you are finding the equation of the line passing through point, you will get equation in slope intercept form.

If there is two point you simply use one point formula. {i.e (y-y1)= m(x-x1)} (as the slope will be given too).If you are finding the equation for two points then use double point formula for the equation. { i.e (y-y1) = (y2-y1/x2-x1) × (x-x1)}.

As in your question there are two points we must use double point formula,

[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]

[tex]( y - 2) = \frac{ - 8 - 2}{ - 6 - 6} (x - 6)[/tex]

Simplifying them we get,

6(y-2)= 5(x-6)

6y - 12 = 5x -30

Therefore, 5x - 6y - 18 = 0 is the required equation.

Hope it helps.....

-5-(-7)
Full work plz

Answers

welcome i hope this helps :)

Answer:

            -5 - (-7) = 2    

Step-by-step explanation:

-5 - (-7) = -5 + 7 = (-5) + (7) = (7) + (-5) = 7 - 5 = 2

What number needs to be eliminated to solve this equation? 3d = -81

Answers

Answer:

You must first divide 3 from both sides.

Step-by-step explanation:

Whenever you solve an equation such as this you are always trying to isolate the variable that is given. In this case we are arriving at the value of d alone.

3d = -81

d = -27

Hope this helps!

Answer:

i believe that 3 needs to be eliminated

Step-by-step explanation:

3d÷3=-81÷3

d=27

hope i helped :D

Rewrite 2/20 : 1/40 as a unit rate

Answers

Answer:

[tex]\frac{4}{1}[/tex]

Step-by-step explanation:

Given:

2/20 : 1/40

A). First re-write the ratio as follows;

(i) Change the ratio sign to division (÷). i.e

2/20 ÷ 1/40

(ii) Solve the expression by changing the division to multiplication(×). This also means you will need to swap the numerator and the denominator of the second term. i.e (1 / 40) becomes (40 / 1)

(2/20) × (40 / 1) = [tex]\frac{2}{20}[/tex] × [tex]\frac{40}{1}[/tex] = [tex]\frac{4}{1}[/tex]

B). Now convert the result from above to unit rate. A unit rate is a rate in which the denominator has a value of 1.

So to convert   [tex]\frac{4}{1}[/tex]  to unit rate, we keep simplifying until the denominator becomes 1.

And since the denominator is already 1, there is no need for further simplification.

Therefore, 2/20 : 1/40 to unit rate is  [tex]\frac{4}{1}[/tex]

Answer:4/1

Step-by-step explanation:

I say this because you are supposed to divided it and the answer is 4 then you find the answer choice with a 1 as the denominator and it should say 4/1 and that is the correct answer.

Which equation represents this proportional relationship


y=3x

y=1/6x

y=6x

y=1/3x

Answers

Answer:

I think that, please check it y=3x

Hi plz just give me an answer. no explanation needed. sorry and thanks

Answers

Answer:

B=45

The sum of the interior angle of a triangle is equal to 180

Therefore equate angle A, B and C to 180

then add them to get 135 + c=180

group like terms,135 crosse the equal sign to be negative

which is c=18p-135

c=45

what is a short introduction of the story happy prince?​

Answers

Answer:

happy prince was born and one day he died

I can’t figure this out pls help 17-2p=2p+5+2p

Answers

Answer:

p=2

Step-by-step explanation:

17-2p=2p+5+2p

17-2p=4p+5

17=6p+5

12=6p

2=p

whats the pattern 729, -243, 81, -27, 9

Answers

Answer:

This is the product of three nines (three factors of 9). 9 × 9 × 9 × 9 = 6561 --> This is the product of four nines (four factors of 9). It's a common mistake among educators to state that 81 is what we get by "multiplying nine by itself twice".

1. Which one does not belong *
O y=(x+4)(x-6)
O y=2x²-88-24
O y=x2+5x-25
O y=x®+3x?-10x-24

Answers

Answer:

I believe the answer is 2x² - 88 - 24, since it is the only one with a number in front of the x²

Step-by-step explanation:

y = x² - 2x - 24

y = 2x² - 88 - 24

y = x² + 5x - 25

y = x² + 3x - 10x - 24

PLEASE I BEG FOR HELP! Find mKNL A. 247 B. 184 C. 196 D. 264

Answers

Answer:

D. 264°

Step-by-step explanation:

When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,

60° = 1/2[(18x - 6)° - (5x +17)°]

60° * 2 = (18x - 6 - 5x - 17)°

120° = (13x - 23)°

120 = 13x - 23

120 + 23 = 13x

143 = 13x

143/13 = x

11 = x

x = 11

(18x - 6)° = (18*11-6)°= (198 - 6)° = 192°

(5x +17)° = (5*11 +17)° =(55+17)° = 72°

m (arc KNL) = (18x - 6)° + (5x +17)° = 192° + 72°

m (arc KNL) = 264°

Help urgent, which functions are bounded below but not above? Choose all answers that apply.

Answers

Answer:

c, e, f, and i

Step-by-step explanation:

a. is bounded above at y = 1 and below at y = 0

b. is unbounded both above and below

c. is bounded below at y = 0 and unbounded above

d. is unbounded both above and below

e. is bounded below at y = 0 and unbounded above

f. is bounded below at y = 0 and unbounded above

g. is bounded below at y = 0 and bounded above at y = 1

h. is unbounded both above and below

i. is bounded below at y = 0 and unbounded above

j. is unbounded both above and below

Jose Plans to make a down payment plus monthly payments in order to buy a Harley Davidson motorcycle. At one dealership, he would pay $8,000 down and pay $250 each month. At another dealership, he would pay $10,000 down and pay $125 each month. After how many months would the payment be the same for both dealers? What will that amount be?

Answers

Answer:

a) 16 month

b) $12 000

Step-by-step explanation:

$8000 + 250m = $10000 + 125m

250m - 125m = $10000 - $8000

125m = $2000

m = $2000 : 125

m = 16 months

After how many months would the payment be the same for both dealers ?

16 months

What will that amount be ?

$8000 + $250×16 =

= $8000 + $4000

= $12000

$10000 + $125×16 =

= $10000 + $2000

= $12000

2.67 (7 repeating) as a fraction

Answers

Answer:

241/90 or 2 61/90

Step-by-step explanation:

Let's call the given number 2.67(7) = x

Then use below steps:

10x = 26.7(7)100x = 267.7(7)100x - 10x = 241                           ⇒ subtract to get rid of the repeated part90x=241                                       ⇒ solve to get fractionx= 241/90 = 2 61/90                    ⇒ answer
Answer:

241/90

2  61/90

Step-by-step explanation:

2.67(7) =

= (2677 - 267)/900

= 2410⁽¹⁰/900

= 241/90

= 2  61/90

please help me with this

Answers

Answer:

14/18 =0.7778

Step-by-step explanation:

14/18 =0.7777.........=0.7778 rounded to the nearest thousandth

Step by step please: x^3+2x^2-5x-6=0

Answers

Answer:

x=-1, x=2, x=3

Step-by-step explanation:

Factor the left side of the equation.

(x+1)(x^2+x-6)

(x+1)(x-2)(x-3)

Now set everything equal to 0

x+1=0

x-2=0

x-3=0

Now solve for x

therefore, the answer is x=-1, x=2, x=3

(3x + 5) (x2 – 10x + 2 ).

Answers

Answer:

[tex]3x^{3} -25x^{2} -44x+10[/tex]

Step-by-step explanation:

Hello!

To solve this we distribute what in one parenthesis into the other

                 3x                  

3x * x^2 = 3x^3

3x * -10x = -30x^2

3x * 2 = 6x

                 5                  

5 * x^2 = 5x^2

5 * -10x = -50x

5 * 2 = 10

Now we put like terms together and simplify

3x^3 + 0 = 3x^3

-30x^2 + 5x^2 = 25x^2

6x - 50x = -44x

0 + 10 = 10

Put it all together

3x^3 + 25x^2 - 44x + 10

Hope this helps!

Answer:

3x^3 + 25x^2 - 44x +10

Step-by-step explanation:

To answer this use FOIL

First Outer Inner Last

In this problem start by distributing the 3x

3x^3-30x^2+6x

Next distribute the 5 in the second parenthesis

5x^2 - 50x + 10

Lastly, add like terms (terms that have the same variable and powers)

3x^3 - 25x^2 +6x +10

Rewrite the number in standard form. 3.4 x 10^8

Answers

Answer:

340000000

Step-by-step explanation:

3.4 x 10^8 is in scientific notation.

To change this to standard form you have to multiply 3.4 by 10 to the 8th power. You would be multiplying 3.4 by 10 eight times. It's a positive 8 so you move the decimal point 8 times to the right. If it were a negative then you'd move the decimal to the left.

3.4

↑ moving the decimal 8 times to the right would then make it 340000000


[tex] \frac{ {x}^{3} }{x { }^{2} + 2x + 1} [/tex]
Hi! I need help with the problem above. I know the answer to it is x-2+((3x+2)/(x^2+2x+1)), but I need help knowing and understanding the process. I can usually divide polynomials with ease, but I have never had to divide when the divisor is larger than the dividend. Can you please show me how to solve this with long division? Also, if you still have time to help me, how would synthetic division work with this? Thank you in advance!​

Answers

Since

[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^3}{(x+1)^2}[/tex]

we can perform synthetic division twice, first for

[tex]\dfrac{x^3}{x+1}[/tex]

then dividing the result by [tex]x+1[/tex] again.

...  ||  1     0    0    0

-1  ||        -1     1    -1

================

...  ||  1     -1    1     -1

This translates to

[tex]\dfrac{x^3}{x+1}=x^2-x+1-\dfrac1{x+1}[/tex]

Now divide [tex]x^2-x+1[/tex] by [tex]x+1[/tex]. (Dividing the remainder term by [tex]x+1[/tex] can wait until the end.)

...  ||  1    -1      1

-1  ||        -1     2

=============

...  ||  1    -2     3

or equivalently,

[tex]\dfrac{x^2-x+1}{x+1}=x-2+\dfrac3{x+1}[/tex]

Taking everything together, we have

[tex]\dfrac{x^3}{x^2+2x+1}=\dfrac{x^2-x+1}{x+1}-\dfrac1{(x+1)^2}[/tex]

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac3{x+1}-\dfrac1{(x+1)^2}[/tex]

Combine the last two fractions:

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3(x+1)-1}{(x+1)^2}[/tex]

[tex]\dfrac{x^3}{x^2+2x+1}=x-2+\dfrac{3x+2}{(x+1)^2}[/tex]

which agrees with the solution we found in your other question.

(There's a variant of synthetic division that works with directly dividing a polynomial by another one of any degree, but it's basically just a condensed version of applying the algorithm for dividing a polynomial twice by a linear one, like we've done here.)

1. Three times the the difference between x and five?



2. One half times a number increased by six?​

Answers

Answer:

Step-by-step explanation:

1. 3(x - 5)

2. 0.5x + 6.

Answer:

1) 3(x-5)

2) 1/2x+6

Step-by-step explanation:

Three times the difference between x and five.

Three times=3* or 3(

difference between x and five= x-5

Together it will be

3(x-5)

One half times a number increased by six

One half times a number= 1/2x

increased by six= +6

Together it will be

1/2x+6

Hope this helps ;) ❤❤❤

A high school athlete ran the 100 meter sprint in 13.245 seconds. what is the time rounded to the nearest tenth. Award is brainliest

Answers

hi! 13.245 rounded to the nearest tenth should be 13.2!

the first number is the tenths, second is hundredths, and third is thousandths! hoped this helped:)

The value of each digit in a number is known as the place value. The time rounded to the nearest tenth is 13.2 seconds.

What is the place value of a digit in a number?

The value of each digit in a number is known as the place value. The 5 in 350, for example, represents 5 tens, or 50, whereas the 5 in 5,006 represents 5 thousand, or 5,000. It is critical that children that while a digit can be the same, its value is determined by its position in the number.

Identification of the place value of a digit in a number:

The place values on the left of the decimal point start as ones, tens, hundreds, and so on.The place value on the right of the decimal point starts from the point and goes to the right as tenths, hundredths, and so onThe tens mean multiply by 10The tenth means the tenth part of that digit which is that digit divided by 10

Given the time to run is 13.245, now tenth means the value that is after the decimal. Since the value after the tenth is 4, therefore, the tenth value will remain the same but the numbers after that will be erased.

Hence, the time rounded to the nearest tenth is 13.2 seconds.

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Help meeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

by the way and the answer is c for yhe reasin because the of tje by theand i thaith

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