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3 years ago

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The diameter of a circle endpoints are A(-1, 5) and B(4,-3). Use the midpoint formula to find the coordinates of the center of c

ircle P(xy).

1 answer:

mina [271]3 years ago

6 0

Answer:

centre = ( $\frac{3}{2}$ , 1 )

Step-by-step explanation:

using the midpoint formula

midpoint = [ $\frac{1}{2}$ (- 1 + 4), $\frac{1}{2}$ (5 - 3) ] = ( $\frac{3}{2}$ , 1 )

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Find the sum of each set of numbers, as well as the size n of each set of numbers (n = number of numbers in the set). Use these

guapka [62]

We have to add numbers without a calculator.

1) 25, 35, 19, 31

We can group them by the last digit, so they are easy to add:

25 + 35 = 20 + 30 + 5 +5 = 50 + 10 = 60

19 + 31 = 10 + 30 + 9 +1 = 40 + 10 = 50

Then, 60 + 50 = 110

numbers in the set n = 4

Sum = 110

2) 101, 73, 49, 27, 24, 36

We can group them again by the last digit (adding 10, like the previous example).

We can substract the last digit from one number and add it to the other one. The result will be the same, but they will become easier to add.

101 + 49 = 100+50 = 150

73 + 27 = 70 + 30 = 100

24 + 36 = 20 + 40 = 60

150 + 100 + 60 = 250 + 60 = 310

numbers in the set n = 6

Sum = 310

3) 25, 25, 25, 30, 30, 30, 32, 32, 32

In this case we have 3 times the same numbers, so we can add the three different numbers and then multiply the total by 3.

We can use the properties of the multiplication to simplify the product (we will use the distributive property)

25 + 30 + 32 = 27 + 30 + 30 = 87

87 * 3 = 80*3 + 7*3 = 240 + 21 = 261

numbers in the set n = 9

Sum = 261

8 0

1 year ago

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

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3 years ago

What single decimal multiplier would you use to increase by 18% followed by a<br> 12% decrease?

ValentinkaMS [17]

Answer:

The single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

Step-by-step explanation:

Let 'x' be the number

As first the number has to be increased by 18%

so

Step 1: write the percentage '18%' in decimal form

18% = 0.18

Step 2: For percentage increases: add the decimal to 1

1 + 0.18 = 1.18

Step 3: Multiply the number x by the multiplier, found in Step 2

x × 1.18 = 1.18x

<u><em>NEXT WE HAVE TO DECREASE 1.18x by 12%</em></u>

Apply the same method but with a number 1.18x

Write the percentage '12%' in decimal form

12% = 0.12

For percentage decreases: subtract the decimal to 1

1 - 0.18 = 0.18

Multiply the number 1.18x by the multiplier, found in Previous step

1.18x × 0.18 = 0.21x

Therefore, the single decimal multiplier used to increase by 18% followed by a 12% decrease is 0.21.

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3 years ago

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the

Alexandra [31]

Hello :
<span>x² + y² + 14x + 2y + 14 = 0
(x²+14x)+(y²+2y)+14=0
(x²+2(7)(x) +7²) -7² +( y²+(2)(1)y+1²)-1² +14 = 0
(x+7)² +(y+1)² = 6²
the center : (-7,-1) and </span><span>length of the radius is : 6</span>

4 0

2 years ago

Read 2 more answers

How many tens are in 1,000

victus00 [196]

There are 100 tens in 1,000

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3 years ago