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3 years ago

If A = (9, 18) and B = (1, 12), what is the length of AB

Mathematics

2 answers:

musickatia [10]3 years ago

8 0

Answer:

the length is 10

Step-by-step explanation:

√(1 - 9)2 + (12 - 18)2 =

√(-8)2 + (-6)2 = √64 + 36 =

√100= 10

anygoal [31]3 years ago

3 0

Answer:

Length of AB = 10

Step-by-step explanation:

This can be found by using the distance formula.

Distance Formula = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Where

(x_1,y_1) is the first coordinate pair and (x_2,y_2) is the second coordinate pair

Thus

x_1 = 9 and y_1 = 18

x_2 = 1 and y_2 = 12

Plugging them into the formula, we get:

Length = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2} \\=\sqrt{(12-18)^2+(1-9)^2}$ . WHich is equal to 10.

Length is 10

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1. If 2(x + 3) = 20, then x =

Fittoniya [83]

Step-by-step explanation:

1) The question reads that

2(x+3)=20

So here we are finding x

We need to multiply the 2 by the ones in the bracket which is the (x+3)

So 2 multiplied by x is 2x

We didn't add the x and the 3 because a variable and a number can't be added, a number and a variable which is the letter can only be multiplied.

And then we also multiply 2 by 3 which is going to be;

2(3)

So it's going to be;

2x+6=20

So now, we group like terms;

2x=20-6(We have -6 because any positive number which crosses an equal sign becomes a negative and when a negative number crosses an equal sign it becomes a positive which is represented by +

2x=14

So now we subtracted 6 from the 20 giving us 14

So now we proceed to divide both sides by 2 to obtain the value of x

So 14 can be divided by 2,

7 times so;

x=7

2) So this question reads;

10x-3(2x+2)=30

With this we are also finding x

So here, we multiply the -3 by the 2x and the +2

So;

-3×2x=-6x

And

-3×2=-6

So now we have;

10x-6x-6=30

So here we can choose to group like terms of subtract the 6x from the 10x right away but grouping would be better so we are going to group which is going to be;

10x-6x=30+6

4x=36

So now we divide both sides by 4 to find the x

and 36 can be divided by 4, 9 times.

So;

x=9

8 0

3 years ago

The lines shown below are parallel. If the green line has a slope of -14, what

Goshia [24]

Answer:

-1/11

Step-by-step explanation:

Parallel lines have the same slope, but different y-intercepts. So, if the slope of the green line is -1/11, then the slope of the red line would also be -1/11.

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4 years ago

90 POINTS!!!!PLZ HURRY WILL GIVE BRAINIEST Use trigonometry to find the measure of x

Gwar [14]

Answer:

892 ft (3 sf)

Step-by-step explanation:

Sin(48) = x/1200

x = 891.7737906 ft

3 0

3 years ago

Read 2 more answers

Pls help Use the rhombus to answer the question

Ierofanga [76]

Answer:

Options A, C and D

Step-by-step explanation:

Properties of a rhombus,

1). All sides are equal and it has two parallel sides.

2). Opposite angles of a rhombus are equal.

3). Diagonals are perpendicular bisector.

4). Sum of two adjacent angles is 180°.

By using these properties,

Options A, C and D are the correct options.

7 0

3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

4 years ago