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harkovskaia [24]
3 years ago
7

If A(7,9) and B(3,12) find AB (remember: AB means "the distance between points A and B")

Mathematics
1 answer:
GREYUIT [131]3 years ago
5 0
The length of segments ab is 24
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A<br> Write the equation for<br> line that<br> passes through (1, 1) and (-1,7)
KengaRu [80]

Answer:y=-3x+4

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(1,1) and (-1,7).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=1.

Also, let's call the second point you gave, (-1,7), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=7.

Now, just plug the numbers into the formula for m above, like this:

m=

7 - 1

-1 - 1

or...

m=

6

-2

or...

m=-3

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-3x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(1,1). When x of the line is 1, y of the line must be 1.

(-1,7). When x of the line is -1, y of the line must be 7.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,1) and (-1,7).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(1,1). y=mx+b or 1=-3 × 1+b, or solving for b: b=1-(-3)(1). b=4.

(-1,7). y=mx+b or 7=-3 × -1+b, or solving for b: b=7-(-3)(-1). b=4.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(1,1) and (-1,7)

is

y=-3x+4

8 0
3 years ago
Find the value of x and y.
zysi [14]

Answer:

<em>x = 9</em>

<em>y = 36</em>

Step-by-step explanation:

<u>Lines and Angles</u>

Triangle CDE is isosceles. This means the two angles of the base DE are congruent (have the same measure):

7x + 1 = 4x + 28

Subtracting 4x + 1:

3x = 27

Dividing by 3:

x = 9

Substituting in the expression for the angles:

7x + 1 = 7*9 + 1 = 64°

The angles are 64° and 64°. The other internal angle at vertex C is 180°-64°-64°=52°. This angle is congruent with its vertical angle in the triangle ABC. We are given another angle of 43°. Thus the measure of angle A is 180°-52°-43°=85°

This last angle is equal to the expression of y:

-2(3 - y) + 19 = 85

Subtracting 19:

-2(3 - y) = 66

Removing the parentheses:

-6 + 2y = 66

Adding 6:

2y = 72

Dividing by 2:

y = 36

Final answer:

x = 9

y = 36

8 0
3 years ago
What number can go into 33 and 121
Marat540 [252]
11

Because 11x3 is 33
And 11x11 is 121

Hope this answer helped!!
7 0
3 years ago
Read 2 more answers
A rectangle has a length 6 more than it's width if the width is decreased by 2 and the length decreased by 4 the resulting has a
Rashid [163]

Answer:

Length of original rectangle: 11 units.

\frac{\text{Area of original rectangle}}{\text{Area of new rectangle}}=\frac{55}{21}

\text{Perimeter of new rectangle}=20

Step-by-step explanation:

Let x represent width of the original rectangle.  

We have been given that a rectangle has a length 6 more than it's width. S the length of the original rectangle would be x+6.

We have been given that when the width is decreased by 2 and the length decreased by 4 the resulting has an area of 21 square units.

The width of new rectangle would be x-2.

The length of new rectangle would be x+6-4=x+2.

The area of new rectangle would be (x+2)(x-2).

Now we will equate area of new rectangle with 21 and solve for x as:

(x+2)(x-2)=21

Applying difference of squares, we will get:

x^2-2^2=21

x^2-4=21

x^2-4+4=21+4

x^2=25

Since width cannot be negative, so we will take positive square root of both sides.

\sqrt{x^2}=\sqrt{25}

x=5

Therefore, the width of original rectangle is 5 units.

Length of the original rectangle would be x+6\Rightarrow x+5=11.

Therefore, the length of original rectangle is 11 units.

\text{Area of original rectangle}=5\times 11

\text{Area of original rectangle}=55    

Therefore, area of the original rectangle is 55 square units.

Now we will find ratio of the original rectangle area to the new rectangle area as:

\frac{\text{Area of original rectangle}}{\text{Area of new rectangle}}=\frac{55}{21}

We know that perimeter of rectangle is two times the sum of length and width.

\text{Perimeter of new rectangle}=2((x+2)+(x-2))

\text{Perimeter of new rectangle}=2((5+2)+(5-2))

\text{Perimeter of new rectangle}=2(7+3)

\text{Perimeter of new rectangle}=2(10)

\text{Perimeter of new rectangle}=20

Therefore, the perimeter of the new rectangle is 20 units.

7 0
3 years ago
Write the sentence as an equation.<br><br> 38 less than the quantity f times 235 equals 44
Dimas [21]

Answer:

235(f - 38) = 44

8 0
3 years ago
Read 2 more answers
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