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3 years ago

Use the given conditions to write an equation for the line in point-slope form and in general form.

Mathematics

2 answers:

Paha777 [63]3 years ago

6 0

First, simplify the equation given into slope intercept form.

slope intercept form is y = mx + b, where b is the y intercept and m is the slope.

3x - 2y - 5 = 0

I would move the 2y to the other side.

3x - 5 = 2y

Then, since y can't have a coefficient, divide everything by 2;

y = 3/2x - 5/2

So there's your slope intercept form.

Point slope form is:

$y - y_{1} = m( x} - x_{1} )$

Where those with a subscript of 1 are part of the same point.

So you already known one point; -8, 8. I'll just do that as the pair with subscript 1. You know the slope as well from the slope intercept form; 3/2.

You can just plug those in.

y - 8 = 3/2 (x + 8)

Now to change this to general form.

First, distribute 3/2 to x and 8.

y - 8 = 3/2x + 12
-3/2x + y = 20
-3/2x + y - 20 = 0

Since there are no fractions, multiply everything by 2.

-3x + 2y - 40 = 0

kaheart [24]3 years ago

4 0

First, let's convert the given line equation into slope-intercept form to find the slope.
Let's start converting by subtracting both sides by 3x.

$-2y-5=-3x$

Add both sides by 5.

$-2y=-3x+5$

Divide both sides by -2.

$y= \frac{3}{2} x- \frac{5}{2}$

The slope of the equation given is 3/2. Since the point-slope form line is parallel to that, the point-slope form equation must also have a slope of 3/2.

Now, let's use point-slope form.

For a line with slope m and that passes through $(x_1,y_1)$ , the point slope form equation is the following:

$y-y_1=m(x-x_1)$

We know the passing point and the slope. Now, let's plug them into the point-slope form formula.

$y-8= \frac{3}{2} (x-(-8))$
$y-8= \frac{3}{2} (x+8)$

That is your answer for the point-slope form equation.
To change this to general form, distribute first.

$y-8= \frac{3}{2} x+12$

Subtract both sides by $\frac{3}{2} x$ and 12.

$- \frac{3}{2} x+y-20=0$

Multiply both sides by -2

$3x-2y+40=0$

That's your answer for the general form equation.
I hope this helps and have an awesome day! :)

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V=1/2at^2 solve for t

malfutka [58]

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3 years ago

I need help please

bija089 [108]

Hey There!

Lets Just Work through your answers,

ⓧ A - An isosceles triangle is a triangle with (at least) two equal sides, so this would not apply to the given triangle.

:) B - A scalene triangle is a triangle in which all three sides have different lengths so this applies to the given triangle. One side measures 10, one measures 11, and one measures 12.1

ⓧ C - A right triangle is a type of triangle that has one angle that measures 90 degrees, which this triangle does not so this does not apply.

ⓧ D - In geometry, an equilateral triangle is a triangle in which all three sides are equal, so this does not apply to the given triangle.

ⓧ E - An obtuse triangle is a triangle with one obtuse angle (greater than 90°) and two acute angles, so this does not apply to the given triangle.

:) F - An acute triangle (or acute-angled triangle) is a triangle with three acute angles less than 90 degrees. So this applies to the given triangle.

In Summary, B & F classify the given triangle correctly.

If you could rate five starts & give brainliest that would be greatly appreciated!

Hope I helped, Have a good day.

4 0

3 years ago

In a group of 40 people, 27 can speak English and 25 can speak Spanish. How many can speak

Svetradugi [14.3K]

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Information \: provided \: with \: us }}}}}\: \bigstar}$

➻ In a group of 40 people, 27 can speak English and 25 can speak Spanish.

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{What \: we \: have \: to \: find ? }}}}}\: \bigstar}$

➻ The required number of people who can speak both English and Spanish .

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Assumption}}}}}\: \bigstar}$

Consider ,

➻ A → Set of people who speak English.

➻ B → Set of people who speak Spanish

➻ A∩B → Set of people who can speak both English and Spanish

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Given}}}}}\: \bigstar}$

➻ n (A) = 27

➻ n (B) = 25

➻ n (A∪B) = 40

➻ n(A∩B) = ?

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Now}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - n (A∩B)

➻ 40 = 52 - n (A∩B)

➻ n (A∩B) = 52 - 40

➻ ∴ n (A∩B) = 12

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Therefore}}}}}\: \bigstar}$

∴ Required Number of persons who can speak both English and Spanish are 12 .

━━━━━━━━━━━━━━━━━━━━━━

$\qquad {\: \:\bigstar \: {\underline{\overline{\boxed{\bf{Verification}}}}}\: \bigstar}$

➻ n(A∪B) = n(A) + n (B) - n(A∩B)

➻ 40 = 27 + 25 - 12

➻ 40 = 52 - 12

➻ 40 = 40

➻ ∴ L.H.S = R.H.S

━━━━━━━━━━━━━━━━━━━━━━

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2 years ago

SHOW WORK NOT JUST ANWSER PLS

Fed [463]

when i use "pi," im talking about the greek letter which you might have to write as π, or use in a calculator when entering an answer

all of the answers are underlined after each explanation :)

Question 1:

Area:

The picture shown splits the image into 2 half circles and two triangles. When finding the area, you can look at the two halves as one whole. The area of a circle is calculated by putting the radius to the power of two and multiplying by pi. The picture gives you the diameter, which is 5 feet. The diameter of a circle is twice the radius, so divide 5 by 2, square that number, and multiply by pi to find the area of one whole circle:

(5/2)^2*pi
2.5^2*pi
2.5*2.5*pi
6.25*pi

Now we need to find the area of the two triangles. Like the circles, these two triangles make up one whole triangle. The base of the triangle is given: 6 feet. The height of this triangle is also given as 4 feet. The formula for the area of a triangle is base*height/2, so multiply 4 by 6 and divide by 2:

4*6/2
24/2
12

These shapes add up to make the entire figure, so the area will be

12+6.25pi

Perimeter:

To find the perimeter, we need to look at the problem similarly. The perimeter can be thought of as the length around a figure. The formula for the perimeter of a circle, called the circumference, is diameter*pi, so multiply the diameter, 5, by pi to find the distance around the rounded parts of the figure

5*pi

After finding the length around the rounded part, we need the length of the straight part, which is given to us as 6 feet. To find the total perimeter, add up the distances around each part:

6+5pi

Question 2:

Area:

For this question, we need to use the same base*height/2 formula to find the area of the small triangle. At first glance, the base is not obvious. Look on the right side of the rectangle. Notice how it lines up with the right side of the triangle? This side is the base, and it is given as 6 meters. The height is given as 4 meters. Usually you would think of height as how tall something is, but in triangles, a height is a line that will form a 90 degree angle with a base. Multiply 6 and 4, then divide by 2:

6*4/2
24/2
12

Now we need find the area of the rectangle next to the small triangle. The formula for the area of a rectangle is length*width. The length and the width are given as 10 and 6, so multiply 10 and 6:

10*6
60

Finally, add the areas of the triangle and the rectangle:

60+12=72

Perimeter:

Add up the lengths around the figure- they are already given:

5+5+10+10+6=36

Question 3:

Area:

This figure is made up of two shapes: A square, and a semicircle, or half circle. Since it is half of a circle, we need to calculate the area of a circle, and divide by two. The problem gives us a diameter of 6, which we know we must divide by two because a diameter is twice the size of the radius, and the formula is radius^2*pi. Divide 6 by 2:

Plug three into the area formula:

3^2*pi
9*pi

Divide by two because it is a half circle and has half the area:

9*pi/2
4.5*pi

Multiply the length and width of the square to find its area:

Now add the areas of the two parts together:

4+4.5pi

Perimeter:

For the perimeter of the rounded part, use the diameter*pi formula and also divide by 2 because it is a semicircle:

6*pi/2
3*pi

The semicircle also has a bottom that is part of the perimeter and it is 6 millimeters. Add that to 3*pi:

3*pi+6

In a square, all sides are equal, so since one side is 2 millimeters, all four sides are 2 millimeters. Multiply 2 by 4:

Add these perimeters together:

8+3*pi+6
14+3*pi

We're almost done now. Notice how one side of the square is hidden and 2 millimeters of the bottom of the semicircle are hidden? This means that we need to subtract 4 before getting a final answer:

14+3*pi-4=10*3pi

please let me know if anything is incorrect or hard to understand, hope this helps!!

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2 years ago

Three ratios that are equivalent to 8:5

vlada-n [284]

Answer:

32/20

Step-by-step explanation:

32 and 20 are both divisible by 4. 4*8=32 and 4*5=20. So this one works. Another way to think about it is if you put them as fractions and reduced them down to their simplest form, they would form the fraction 8/5.Oct 17, 2019

5 0

2 years ago

Use the given conditions to write an equation for the line in​ point-slope form and in​ general form.

Use the given conditions to write an equation for the line in point-slope form and in general form.