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3 years ago

X2 - 15x + 56factor

Mathematics

1 answer:

lozanna [386]3 years ago

6 0

Answer:

(x - 7)(x - 8)

Step-by-step explanation:

To factorise the quadratic

Consider the factors of the constant term (+ 56) which sum to give the coefficient of the x- term (- 15)

The factors are - 7 and - 8, since

- 7 × - 8 = + 56 and - 7 - 8 = - 15, hence

x² - 15x + 56 = (x - 7)(x - 8)

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K is the midpoint of Line JL, JL=4x-2 and JK=7. find X

ipn [44]

X=4. If k is the midpoint then JK is equal to KL. Since JK is 7 then KL is also 7 meaning JK is 14. JK is represented by the expression 4x-2 so you just set that expression equal to 14 and solve for x. Hope this helped!

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3 years ago

Given that F(x) = x 2 + 2, evaluate F(1) + F(5) <br> which is the answer? 38 30 15

Valentin [98]

your answer is 30

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2 years ago

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

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

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

-------------

Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

-------------

Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

-------------

Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

------------------------------

Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

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1 year ago

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Fantom [35]

Answer:

Step-by-step explanation:

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2 years ago

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Leona [35]

Answer:

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Step-by-step explanation:

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2 years ago

X2 - 15x + 56factor​

X2 - 15x + 56factor