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s2008m [1.1K]
2 years ago
12

Find the equation of the line that is perpendicular to y=-2x-9 and contains the points (8,-4)

Mathematics
1 answer:
avanturin [10]2 years ago
6 0

The slope of the given line is -2, and since perpendicular lines have negative reciprocal slopes, the slope of the line we want to find is 1/2.

Substituting into point-slope form,

y+4=\frac{1}{2}(x-8)\\\\y+4=\frac{1}{2}x-4\\\\\boxed{y=\frac{1}{2}x-8}

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F(x)=2x2+x+1<br> what is the value of f (-3)
chubhunter [2.5K]

Answer:

16

Step-by-step explanation:

First, we plug in -3 in place of x...

f(x) = 2(-3)^2 + (-3) + 1

Then, we simplify each indidvidual expression...

f(x) = 18 - 3 + 1

Finally, we add/subtract all the values to get our answer...

f(x) = 16

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2 years ago
Suppose that f(t) is continuous and twice-differentiable for t≥0. Further suppose f″(t)≥9 for all t≥0 and f(0)=f′(0)=0. Using th
Paha777 [63]
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3 years ago
50 points + brainlest if you answer correctly
Mumz [18]

Answer:

  • <u>5</u><u> </u>is the value which makes the equation true .

Step-by-step explanation:

In this question we have provided an equation that is <u>9</u><u> </u><u>(</u><u> </u><u>3x</u><u> </u><u>-</u><u> </u><u>1</u><u>6</u><u> </u><u>)</u><u> </u><u>+</u><u> </u><u>1</u><u>5</u><u> </u><u>=</u><u> </u><u>6</u><u>x</u><u> </u><u>-</u><u> </u><u>2</u><u>4</u><u> </u>. And we are asked to <u>write </u><u>the </u><u>steps </u><u>to </u><u>solve </u><u>the </u><u>equation </u><u>with </u><u>explanation </u> and <u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>X </u><u>.</u>

<u>Solution</u><u> </u><u>:</u><u> </u><u>-</u>

\longmapsto \quad \: 9(3x - 16) + 15 = 6x - 24

<u>Step </u><u>1</u><u> </u><u>:</u> Solving parenthesis on left side using distributive property which means multiplying 9 with 3x as well as -16 :

\longmapsto \quad \:27x -  \bold{144 }+  \bold{15 }= 6x - 24

<u>Step </u><u>2</u><u> </u><u>:</u> Solving like terms on left side that are -144 and 15 :

\longmapsto \quad \:27x -129 = 6x - 24

<u>Step </u><u>3 </u><u>:</u> Adding 129 on both sides :

\longmapsto \quad \:27x - \cancel{129} -  \cancel{129} = 6x \bold{ - 24 } +  \bold{129}

Now on cancelling -129 with 129 on left side and solving the terms that are -24 and 129 on right side , We get :

\longmapsto \quad \:27x = 6x + 105

<u>Step </u><u>4</u><u> </u><u>:</u> Subtracting with 6x on both sides :

\longmapsto \quad \: \bold{27x} -  \bold{6x} =  \cancel{6x} +105 - \cancel{ 6x}

On calculating further, We get :

\longmapsto \quad \:21x =  105

<u>Step </u><u>5</u><u> </u><u>:</u> Now we are Dividing with 21 on both sides so that we can isolate the variable that is x :

\longmapsto \quad \: \dfrac{ \cancel{21}x}{ \cancel{21}}  = \dfrac{105}{ 21}

Now , by cancelling 21 with 21 on left side , We get :

\longmapsto \quad \:x =  \cancel{\dfrac{105}{21}}

<u>Step </u><u>6</u><u> </u><u>:</u> Now our final step is to simplify the value of x that is 105/21 . We know that 21 × 5 is equal to 105 . So :

\longmapsto \quad \:    \purple{\underline{\boxed{\frak{ x =  5 }}}}

  • <u>Henceforth</u><u> </u><u>,</u><u> </u><u>value </u><u>of </u><u>x </u><u>is </u><u>5</u>

<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>

Now we are verifying our answer by substituting value of x in the given equation . So ,

  • 9 ( 3x - 16 ) + 15 = 6x - 24

  • 9 [ 3 ( 5 ) - 16 ] + 15 = 6 ( 5 ) - 24

  • 9 ( 15 - 16 ) + 15 = 30 - 24

  • 9 ( -1 ) + 15 = 6

  • -9 + 15 = 6

  • 6 = 6

  • L.H.S = R.H.S

  • Hence , Verified .

<u>Therefore</u><u>,</u><u> our</u><u> value</u><u> for</u><u> x</u><u> is</u><u> correct</u><u> </u><u>that </u><u>means</u><u> </u><u>it'll</u><u> </u><u>makes</u><u> </u><u>the </u><u>equation</u><u> true</u><u> </u><u>.</u>

<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
4 0
2 years ago
Which equation represents the vertical line passing through (7,-3)?
Nimfa-mama [501]

Answer:

x = 7

Step-by-step explanation:

The equation of a vertical line has equation of the form

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (7, - 3) with x- coordinate 7 , thus

x = 7 ← equation of vertical line

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