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3 years ago

Helaine graphed the equation 12x – 4y = 3. What was the slope of Helaine’s line?

2 answers:

5 0

The point slope form of a line is:

y=mx+b where m=slope and b=y-intercept...so

12x-4y=3 solve for y...

4y=12x-3

y=3x-0.75

So the slope is 3.

quester [9]3 years ago

3 0

The slope is 3
12x-4y=3
-4y=-12x+3
y=3x-3/4

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2 years ago

In ∆XYZ, m∠X = 152, y = 15, and z = 19. Find side x and the measure of angle Y to the nearest tenth

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The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°.

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In this problem we must apply the law of cosine and the law of sine to determine the angle Y:

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$x = \sqrt{y^{2}+z^{2}-2\cdot y\cdot z\cdot \cos X}$

$x = \sqrt{15^{2}+19^{2}-2\cdot (15)\cdot (19)\cdot \cos 152^{\circ}}$

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3 years ago

35 solve the following syste

blondinia [14]

Part A: The solution is $(-0.923,5.692)$

Part B: The point $(3,7)$ is not in the solution set.

Explanation:

Part A: The given inequalities are $3 x+4 y>20$ and $x$

The solution can be determined by solving the two inequalities by substitution method.

Changing inequalities to equality, we have,

$x=3 y-18$ and $3 x+4 y=20$

Let us substitute $x=3 y-18$ in the equation $3 x+4 y=20$ , we get,

$3 (3y-18)+4 y=20$

$9y-54+4y=20$

$13y=74$

$y=5.692$

Substituting $y=5.692$ in $x=3 y-18$ , we get,

$x=3 (5.692)-18$

$=17.076-18$

$x=-0.923$

Thus, the solution set is $(-0.923,5.692)$

Part B: Now, we shall determine whether the point $(3,7)$ is in the solution set.

Let us substitute the point $(3,7)$ in the inequalities $3 x+4 y>20$ and $x$ , we get,

$3 (3)+4 (7)>20$

$9+28>20$

$37>20$

Also, substituting $(3,7)$ in $x$ , we get,

$3$

Since, the point $(3,7)$ does not satisfy one of the inequality $x$ , the solution set does not contain the point $(3,7)$

Thus, the point $(3,7)$ is not in the solution set.

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3 years ago