Mathematics: A line has the equation 3x–4y–12=0. What are the x- and y-intercepts of the graph of this equation?

A line has the equation 3x–4y–12=0. What are the x-

Ответ:

penajay

28.01.2022

Mathematics

x intercept = 4 and y intercept = -3

Step-by-step explanation:

In order to find the x intercept, set y=0 and solve the equation.

3x-4y-12=0

3x-4(0)-12=0

3x-12=0

add 12 to both sides

3x=12

divide both sides by 3

x = 4

The x intercept is 4.

To find the y intercept, set x = 0.

3x-4y-12=0

3(0)-4y-12=0

-4y-12=0

add 12 to both sides

-4y=12

divide both sides by -4

y = -3

The y intercept is -3.

Hope this helps! Have a great rest of your day :)

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Ответ:

savannahckatz

30.03.2020

Mathematics

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.