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1 year ago

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he work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8

= 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8

2 answers:

densk [106]1 year ago

7 0

Answer:

4(2x-4)=8+2x+8

8x-16=16+2x

8x-2x=16+16

6xboth sides over 6

x=5.3repiting

KiRa [710]1 year ago

4 0

Answer:

step 2: 8x-4=2(6+x+6)

Step-by-step explanation:

$4(2x - 4) = 8 + 2x + 8 \\ 8x - 16 = 16 + 2x here \\ 8x - 2x = 16 + 16 \\ 6x = 32 \\ \frac{6x}{6} = \frac{32}{6} \\ x = 5$

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. Given ????(5, −4) and T(−8,12):

damaskus [11]

Answer:

a) $y=\dfrac{13x}{16}-\dfrac{129}{16}$

b) $y = \dfrac{13x}{16}+ \dfrac{37}{2}$

Step-by-step explanation:

Given two points: $S(5,-4)$ and $T(-8,12)$

Since in both questions,a and b, we're asked to find lines that are perpendicular to ST. So, we'll do that first!

Perpendicular to ST:

the equation of any line is given by: $y = mx + c$ where, m is the slope(also known as gradient), and c is the y-intercept.

to find the perpendicular of ST <u>we first need to find the gradient of ST, using the gradient formula.</u>

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

the coordinates of S and T can be used here. (it doesn't matter if you choose them in any order: S can be either x_1 and y_1 or x_2 and y_2)

$m = \dfrac{12 - (-4)}{(-8) - 5}$

$m = \dfrac{-16}{13}$

to find the perpendicular of this gradient: we'll use:

$m_1m_2=-1$

both $m_1$ and $m_2$ denote slopes that are perpendicular to each other. So if $m_1 = \dfrac{12 - (-4)}{(-8) - 5}$ , then we can solve for $m_2$ for the slop of ther perpendicular!

$\left(\dfrac{-16}{13}\right)m_2=-1$

$m_2=\dfrac{13}{16}$ :: this is the slope of the perpendicular

a) Line through S and Perpendicular to ST

to find any equation of the line all we need is the slope $m$ and the points $(x,y)$ . And plug into the equation: $(y - y_1) = m(x-x_1)$

side note: you can also use the $y = mx + c$ to find the equation of the line. both of these equations are the same. but I prefer (and also recommend) to use the former equation since the value of 'c' comes out on its own.

$(y - y_1) = m(x-x_1)$

we have the slope of the perpendicular to ST i.e $m=\dfrac{13}{16}$

and the line should pass throught S as well, i.e $(5,-4)$ . Plugging all these values in the equation we'll get.

$(y - (-4)) = \dfrac{13}{16}(x-5)$

$y +4 = \dfrac{13x}{16}-\dfrac{65}{16}$

$y = \dfrac{13x}{16}-\dfrac{65}{16}-4$

$y=\dfrac{13x}{16}-\dfrac{129}{16}$

this is the equation of the line that is perpendicular to ST and passes through S

a) Line through T and Perpendicular to ST

we'll do the same thing for $T(-8,12)$

$(y - y_1) = m(x-x_1)$

$(y -12) = \dfrac{13}{16}(x+8)$

$y = \dfrac{13x}{16}+ \dfrac{104}{16}+12$

$y = \dfrac{13x}{16}+ \dfrac{37}{2}$

this is the equation of the line that is perpendicular to ST and passes through T

7 0

3 years ago

Georgia [21]

Answer:

As x → -∞, f(x) → 0.5; as x → ∞, f(x) → 0.5

Step-by-step explanation:

Given function:

$f(x)=\dfrac{4x-7}{8x+8}$

<u>Asymptote</u>: a line that the curve gets infinitely close to, but never touches.

As the degrees of the numerator and denominator of the given function are equal, there is a horizontal asymptote at $y=\dfrac{a}{b}$ (where a is the leading coefficient of the numerator, and b is the leading coefficient of the denominator). This is the end behavior.

$\textsf{Horizontal asymptote}:y=\dfrac{4}{8}=\dfrac{1}{2}$

This is because as $x \rightarrow \infty$ the -7 of the numerator and the +8 of the denominator become negligible. Therefore, we are left with:

$f(x) \rightarrow \dfrac{4x}{8x}$

Therefore:

$\textsf{As }\:x \rightarrow - \infty, f(x) \rightarrow 0.5$

$\textsf{As }\:x \rightarrow \infty, f(x) \rightarrow 0.5$

7 0

2 years ago

Which of these numbers has the most factors? 6:<br> 17:<br> 25:<br> 36:

vovikov84 [41]

Answer:

36

Step-by-step explanation:

3 0

3 years ago

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PLEASE HELP! WILL GIVE BRAINLIEST!!!

lilavasa [31]

Answer:

C.1/4 the pqr is the prime of factor by negative comma 1

3 0

2 years ago

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7. Sam lives exactly halfway between his friends, Danny and Leo. Danny's house is

geniusboy [140]

The point that Sam's house is located is at (2.5, -2)

<h3 /><h3>Midpoint of coordinate points</h3>

The formula for calculating the midpoint of coordinate is expressed as:

M(x, y) = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the coordinate between their locations at (-4, 4) and (-9, 8)

Determine the midpoint

x = (-4+9)/2

x =5/2 = 2.5

Similarly

y = 4-8/2

y = -4/2

y = -2

Hence the point that Sam's house is located is at (2.5, -2)

Learn more on midpoint here: brainly.com/question/5566419
#SPJ1

6 0

1 year ago