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3 years ago

The equation of line n is 8x - 14y + 3 = 0.

Mathematics

1 answer:

tresset_1 [31]3 years ago

3 0

For parallel lines:<span>
</span>"All parallel lines have the same slope!"

As these lines should be parallel, so their slopes would be the same.

Slope of line n:
8/14 = 4/7

Slope of the other line:
k/7

Equating them:
4/7 = k/7

Clearly means that k=4

I hope you got the idea!

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Determine the factors of x2 − 7x − 10. (5 points) a (x + 2)(x − 5) b Prime c (x − 2)(x + 5) d (x + 10)(x − 1)

Savatey [412]

For this case we must factor the following expression:

$x ^ 2-7x-10$

To factor, we must find two numbers that when added together give -7 and when multiplied by -10.

It is observed that there are not two whole numbers that comply with the aforementioned.

Thus, the following equation applies:

$x = \frac {-b \pm\sqrt{b ^ 2-4 (a) (c)}} {2 (a)}$

Where:

$a = 1\\b = -7\\c = -10$

We replace:

$x = \frac {- (- 7) \pm \sqrt {(- 7) ^ 2-4 (1) (- 10)}} {2 (1)}\\x = \frac {7 \pm \sqrt {49 + 40}} {2}\\x = \frac {7 \sqrt {89}} {2}$

So, the roots are:

$x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}$

Answer:

$x_ {1} =\frac {7+ \sqrt {89}} {2}\\x_ {2} =\frac {7- \sqrt {89}} {2}$

6 0

3 years ago

What is the relationship between a scalene triangle and the location of its orthocenter? Explain.

Sladkaya [172]

The orthocenter will be inside, on, or outside the scalene triangle, depending on whether it is acute, right, or obtuse, respectively. The number of congruent sides does not affect the location of the orthocenter.

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3 years ago

Based on the polynomial remainder theorem, what is the value of the function when x=−6 ?

Vaselesa [24]

ANSWER

$f( - 6) = 10$

EXPLANATION

The given function is
$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$

According to the remainder theorem,

$f( - 6) = R$
where R is the remainder when
$f(x)$

is divided by
$x + 6$

We therefore substitute the value of x and evaluate to obtain,

$f( - 6) = { (- 6)}^{4} + 8 {( - 6)}^{3} + 10 { (- 6)}^{2} - 7( - 6)+ 40$

$f( - 6) = 1296 + 8 ( - 216) + 10 (36) - 7( - 6)+ 40$

$f( - 6) = 1296 - 1728 + 360 + 42+ 40$

This will evaluate to,

$f( - 6) = 10$

Hence the value of the function when
$x = - 6$

is
$10$

According to the remainder theorem,
$10$
is the remainder when

$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$
is divided by
$x + 6$

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What is the solution to the system of equations below? Negative 4 x 6 y = negative 18 and y = negative 2 x 21 (9, 3) (3, 9) (–9,

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Answer:

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zaharov [31]

Answer:

$A.\: 4 \sqrt{2}$

Step-by-step explanation:

$\sin \: 45 \degree = \frac{s}{8} \\ \\ \implies \: \frac{1}{ \sqrt{2} } = \frac{s}{8} \\ \\ \implies \: s = \frac{8}{ \sqrt{2} } = \frac{8 \sqrt{2}}{2} \\ \\ \implies \: \huge \: s = 4 \sqrt{2}$

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