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3 years ago

What is an equation of the line that passes through the point ( 8 , − 4 ) and is parallel to the line x − 4 y = 12 x−4y=12?

Mathematics

1 answer:

Natasha2012 [34]3 years ago

8 0

Answer:

as the line is parallel we do not change x-4y what we change is the result x = 8 & y = -4 so the result is 8 - 4 (-4) = 24 so the equation is 24

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Simplify the following expression:

Phantasy [73]

$\frac{4}{ \frac{1}{4} - \frac{5}{2} }$

To begin, we can simplify the expression's denominator by finding a common denominator between the denominators of the fractions in the denominator. To make them compatible, we can convert $\frac{5}{2}$ into $\frac{10}{4}$ :

$\frac{4}{ \frac{1}{4} - \frac{5}{2}( \frac{2}{2}) } = \frac{4}{ \frac{1}{4} - \frac{10}{4} }$

Next, we can simplify:

$\frac{4}{ \frac{1}{4} - \frac{10}{4} } = \frac{4}{ -\frac{9}{4}}$

Finally, to cancel the denominator within the denominator, we can multiply the whole expression by $\frac{4}{4}$ , or 1:

$\frac{4}{ -\frac{9}{4}}* \frac{4}{4} = -\frac{16}{9}$

The expression simplifies to $-\frac{16}{9}$ , or $-1 \frac{7}{9}$ as a mixed number.

6 0

3 years ago

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What is y= 29/5x as a rate of change

mylen [45]

The rate of change is -29/5x^2

8 0

3 years ago

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You travel 8 miles on your bicycle in the same amount of time it takes your friend to travel 6 miles on

strojnjashka [21]

Answer:

Step-by-step explanation:

8/v=6/v-3

8*(v-3)=6v

8v-8*3=6v

8v-24=6v

+24 +24

8v=6v+24

-6v -6v

2v=24

v=24/2

v=12 miles /hour

v2=12-3=9 miles /hour ( your friend)

6 0

3 years ago

There are 29235 marbles and 371 jacks. If you want to know the percentage of jacks, do you divide the first number by the second

garik1379 [7]

Answer:

Correct answer: Two decimal places to the right

Step-by-step explanation:

We will set the classic proportion:

29,235 - 100%

371 - x%

29,235 : 371 = 100 : x ⇒ 29,235 · x = 371 · 100

x = (371/ 29,235) · 100 = 0.0127 · 100 = 1.27%

x = 1.27%

You divide first number by the second and then multiply with 100,

which is the same as moving the decimal point two places to the right.

God is with you!!!

3 0

3 years ago

1) Determine the discriminant of the 2nd degree equation below:

Aleksandr-060686 [28]

$\LARGE{ \boxed{ \mathbb{ \color{purple}{SOLUTION:}}}}$

We have, Discriminant formula for finding roots:

$\large{ \boxed{ \rm{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }}}$

Here,

x is the root of the equation.
a is the coefficient of x^2
b is the coefficient of x
c is the constant term

1) Given,

3x^2 - 2x - 1

Finding the discriminant,

➝ D = b^2 - 4ac

➝ D = (-2)^2 - 4 × 3 × (-1)

➝ D = 4 - (-12)

➝ D = 4 + 12

➝ D = 16

2) Solving by using Bhaskar formula,

❒ p(x) = x^2 + 5x + 6 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5\pm \sqrt{( - 5) {}^{2} - 4 \times 1 \times 6 }} {2 \times 1}}}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm \sqrt{25 - 24} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 5 \pm 1}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 2 \: or - 3}}}$

❒ p(x) = x^2 + 2x + 1 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{ {2}^{2} - 4 \times 1 \times 1} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm \sqrt{4 - 4} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - 2 \pm 0}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = - 1 \: or \: - 1}}}$

❒ p(x) = x^2 - x - 20 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 1) \pm \sqrt{( - 1) {}^{2} - 4 \times 1 \times ( - 20) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{ 1 \pm \sqrt{1 + 80} }{2} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{1 \pm 9}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 5 \: or \: - 4}}}$

❒ p(x) = x^2 - 3x - 4 = 0

$\large{ \rm{ \longrightarrow \: x = \dfrac{ - ( - 3) \pm \sqrt{( - 3) {}^{2} - 4 \times 1 \times ( - 4) } }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm \sqrt{9 + 16} }{2 \times 1} }}$

$\large{ \rm{ \longrightarrow \: x = \dfrac{3 \pm 5}{2} }}$

So here,

$\large{\boxed{ \rm{ \longrightarrow \: x = 4 \: or \: - 1}}}$

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5 0

3 years ago

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