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3 years ago

WILL MARK BRAINLIEST!!!

Mathematics

1 answer:

babymother [125]3 years ago

8 0

Answer: $-2$

Step-by-step explanation:

To find the slope of the line , we will write the equation in the form:

$y = mx + x$

where:

$m =$ slope

$c =$ y - intercept.

To write $4x + 2y = 12$ in this form , we will make y the subject of the formula.

Subtract 4x from both sides

$2y = -4x + 12$

Divide through by 2 $y = -2x + 6$

Therefore :

$slope = -2$

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Is axis of symmetry and vertex the same thing?

cestrela7 [59]

No it is not the same thing.

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2 years ago

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The sum of the digits of a two-digit number is 5. When the digits are reversed, the number increases by 27. Find the original nu

gavmur [86]

Answer:

Step-by-step explanation:

$a-\text{tens digit}\\b-\text{unity digit}\\10a+b-\text{number}\\10b+a-\text{number with reversed digits}\\a+b-\text{sum of digits}\\\\\bold{System\ of\ equations:}\\\\\left\{\begin{array}{ccc}a+b=5\\10b+a=10a+b+27&\text{subtract}\ 10a\ \text{and}\ b\ \text{from both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}a+b=5\\9b-9a=27&\text{divide both sides by 9}\end{array}\right$

$\underline{+\left\{\begin{array}{ccc}a+b=5\\b-a=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2b=8\qquad\text{divide both sides by 2}\\.\qquad \boxed{b=4}\\\\\text{Put the value of\ b}\ \text{to the first equation}\\\\a+4=5\qquad\text{subtract 4 from both sides}\\\boxed{a=1}$

3 0

3 years ago

Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

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3 years ago

How to solve a system with variables

Margaret [11]

You can solve a system with variables by:

1. Pick any two pairs of equations from the system.

2. Eliminate the same variable from each pair using the Addition/Subtraction method

3. Solve the system of the two new equations using the Addition/Subtraction method

4. Substitute the solution back into one of the original equations and solve for the third variable

5. check by plugging the solution into one of the other three equations

6 0

3 years ago

Complete the proofs using the most appropriate method. may require CPCTC.

n200080 [17]

For the first one, you did good. I will just suggest a couple things.

Statement Reason

JK ≅ LM Given

<JKM ≅ < LMK Given (You did both of these steps so well done.)

MK ≅ MK Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)

ΔJMK ≅ ΔLKM SAS

Problem 2: (You also have a lot of great stuff here.)

Statement Reason

DE ║ FG Given

DE ≅ FG Given

<DEF≅<FGH Given

<EDF≅<GFH Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)

ΔEDF≅ΔGFH ASA

<DFE≅<FHG CPCTC

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3 years ago