Name the following triangle

The coordinate of the given figure is (5,5) (5,-3) and (-1, -3). The coordinates of the circumcenter of the triangle is (2,1).

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

We can see the given triangle.

The coordinates of A are (-1,-3).

The coordinates of B are (-1,-3).

The coordinates of C are(5,5).

We know that the circumcenter of a right triangle is the midpoint of the hypotenuse.

Mid-point of hypotenuse AC is given by

[tex]x = x_1 +x_2 / 2\\y = y_1 +y_2 / 2[/tex]

So, x =( -1 + 5)/2 = 2

y =( 5-3)/2 = 1

Hence, the circumcenter of the triangle is (2,1).

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[tex]S_1 = 2+4+6+8+...+26 \\\\~~~~=2(1+2+3+4+...+13)\\\\~~~~=2 \cdot \dfrac{13(13+1)}2~~~~~~~~;\left[\text{Sum of consecutive positive integers }= \dfrac{n(n+1)}2 \right] \\\\~~~~=13 \cdot 14\\\\~~~~=182\\\\S_2 = 1+3+5+7+...+25\\\\\text{It is an arithmetic series wihere}\\\\\text{First term, a =1, ~Common difference, d = 2,~ number of terms = n} \\\\~~~~\text{Nth term} = a+(n-1)d\\\\\implies 25 = 1+(n-1)2\\\\\implies 2n-2 = 24\\\\\implies 2n = 24+2\\\\\implies 2n= 26\\\\[/tex]

[tex]\implies n = \dfrac{26}2 \\\\\implies n= 13\\\\\text{S} _2= \dfrac{\text{n(First term+ Last term)}}{2}\\\\~~~~~~=\dfrac{13(1+25)}2\\\\~~~~~~=\dfrac{13 \times 26}2\\\\~~~~~~=13 \times 13\\\\~~~~~~=169\\\\\text{Hence,}~~ S_1 - S_2 =182 - 169 =13[/tex]

Answer:

13

Step-by-step explanation:

2 + 4 + 6 + 8 + ...... + 26

n = 13

Sum of first 'n' even numbers = n( n +1)

                                                 = 13 * 14

                                                  = 182

1 + 3 + 5 + 7 + .....+25

n = 13

Sum of first 'n' odd numbers = n²

                                               = 13 * 13

                                               = 169

2 + 4 + 6 + 8 + ... + 26 - (1 + 3 + 5 + 7 + ......+25) = 182 - 169

                                                                            = 13

Answer: the answer is Math and i took the test

Answer:

(x + 2)(x + 8)

Step-by-step explanation:

x² + 10x + 16

consider the factors of the constant term (16) which sum to give the coefficient of the x- term.

the factors are + 2 and + 8 , since

+ 2 × + 8 = + 16 and + 2 + 8 = + 10 , then

x² + 10x + 16 = (x + 2)(x + 8) ← in factored form

Answer:

answer in picture

Step-by-step explanation:

Step-by-step explanation:

The Pythagorean theorem states that a^2+b^2=c^2.

For 51, Here would be the step by step (you would do the same thing for 52, follow the formula)

[tex]6^{2} + 3^{2} =c^{2} \\36+9= c^{2} \\45=c^{2} \\\sqrt{45} =\sqrt{c^{2} } \\c= 6.7[/tex]

For 53 (and 54), c is already provided. Instead of adding, do this (again, follow the formula):

[tex]a^{2} + 3^{2} = 7^{2} \\a^{2} + 9 = 49\\a^{2} + 9 = 49\\a^{2}= 40\\\sqrt{a^{2}} =\sqrt{40} \\a= 6.32[/tex]

I hoped this had helped.

Answer:D

Step-by-step explanation:

The slope of a line will be 1/6. Then the correct option is D.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

Slope = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(-6,3) and (12,6)

(x₁, y₁) = (-6,3)

(x₂, y₂) = (12,6)

Then the slope of a line will be

Slope = (6 – 3) / (12 + 6)

Slope = 3 / 18

Slope = 1/6

Then the correct option is D.

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Answer:

He used to receive $14.50.

Step-by-step explanation:

Let x = amount he used to receive.

Now he receives 2x - 4.

Now he receives $25.

2x - 4 = 25

2x = 29

x = 14.5

Answer: He used to receive $14.50.

Answer:14.5

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Answer:

x = 0.5

Step-by-step explanation:

3.5/x = 7/4

3.5/x * 1/3.5 = 7/4 * 1/3.5

x = 7/14

x = 1/2

x = 0.5

Answer:

42 is the range

Step-by-step explanation:

Subtract the highest number by the lowest.

95 - 53 =42

Answer:

x<10

Step-by-step explanation:

I think that's the only one

Hope this helps:)....if not then sorry for wasting your time and may God bless you:)

Answer:

x = 19.9

Step-by-step explanation:

These kinds of problems have a specific formula.

Formula: outside (whole) = outside (whole)

We could substitute our variables into this.

For the first line, our outside segment is b and the whole thing is a + b

For the second line, our outside segment is x, and the whole thing is x.

[tex]b (a+b) = x(x)\\11 (25+11) = x^2\\11 (36) = x^2\\396 = x^2\\\\x=\sqrt{396}[/tex]

The [tex]\sqrt{396}[/tex] = 19.8997487421

Rounding to the nearest tenth, your answer is 19.9

Answer:

It is health.

Step-by-step explanation:

It says that "The larger the MAD, the greater variability there is in the data (the data is more spread out)." So History would actually be the most wrong one. Health is the lowest value so Health is correct.

Answer:

Health

Step-by-step explanation:

MAD = median absolute deviation

It measures how spread out a set of data is, and is less affected by extremely high or low values.

The bigger the variance, the more spread out the data points are.

The smaller the variance, the less spread out the data points are.

Therefore, the scores were closest together in Health, since this has the smallest MAD.

Answer: B. two solutions

im guessing

Answer:

[tex]8 \div \frac{1}{2} = 8 \times \frac{2}{1} = 8 \times 2 = 16[/tex]

Answer:

7

Step-by-step explanation:

Since, Sophia had three pages of homework and she only has three left you can set up an equation to solve. The equation would be 10=x-3, then you just solve the equation which would be 7, hope that helped.

Hey there!

3/4 + 1/12 + 2/3

= 5/6 + 2/3

= 5/6 + 4/6

= 5 + 4 / 6

= 9 / 6

= 9 ÷ 3 / 6 ÷ 3

= 3/2
≈ 1.5

1.5 - 1 = 0.5

Therefore, your answer is: 0.5

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:9282

Step-by-step explanation:

Answer: 12-233 24353252345

Step-by-step explanation:

Ayana's favorite brownie recipe calls for

1

2

of a cup of flour for every

1

3

of a cup of cocoa powder. For a bake sale, she plans to make a larger batch with 1 cup of cocoa powder. How much flour should she use?

Answer:

y - 3 = 2/3(x - 5)

Step-by-step explanation:

Formula:

y - y1 = m(x - x1)

It doesn't apply to this problem but keep in mind that two negatives make a positive so instead of writing, for example, y - (-5), you can just write y +5.

Makes it a lot cleaner and easier to work with.

Hope this helps you :)

Step-by-step explanation:

you would have to add the the sides and use context to find out the blank rectangles

Answer:

Splitting that number into 10 equal wholes.

Step-by-step explanation:

(fractions)

[tex]\text{Given that,}\\\\x-\dfrac 3x = 7\\\\\\\textbf{i).}\\\\\\x^2 + \dfrac 9{x^2}\\\\\\=x^2 + \left(\dfrac 3 x \right)^2\\\\\\=\left(x- \dfrac 3x \right)^2 + 2 \cdot x \cdot \dfrac 3x\\\\\\=7^2 +6\\\\\\=55[/tex]

[tex]\textbf{ii)}\\\\~~~~~\left(x+\dfrac 3 x \right)^2 = \left( x - \dfrac 3x \right)^2+4 \cdot x \cdot \dfrac 3x\\\\\\\implies \left(x+\dfrac 3 x \right)^2 = 7^2 +12\\\\\\\implies \left(x+\dfrac 3 x \right)^2 =61\\\\\\\implies x+ \dfrac 3x = \pm\sqrt{61}\\\\\\[/tex]

[tex]\textbf{iii)}\\\\\\x^2 -\dfrac 9{x^2}\\\\\\=x^2 - \left(\dfrac 3{x} \right)^2\\\\\\=\left( x-\dfrac 3x \right)\left( x+\dfrac 3x \right)\\\\\\=7\sqrt{61}~~ \text{or}~~ -7\sqrt{61}[/tex]

The lender's good faith estimate is D. the lender made a poor estimate; it was higher than 0.5% of the actual closing costs.

It should be noted that a lender simply means an individual or an organization that lends people money.

In this case, the lender's good faith estimate is that the lender made a poor estimate; it was higher than 0.5% of the actual closing costs.

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Answer:

It's

A: The lender made a very good estimate; it was within 0.25% of the actual closing costs.

Step-by-step explanation:

The equation represents the volume of the portable fuel tank in terms of width (w) is w³ + 34w² + 145w - 33488 = 0.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A portable fuel tank used to transport gasoline is in the shape of a rectangular prism.

The tank is 5 feet longer than it is wide and 29 feet deeper than it is wide.

The volume of the tank is 33,488 cubic feet.

Let the width of the rectangular prism be w. Then we have

length = w + 5

height = w + 29

Then the volume is given as

Volume = l × w × h

33488 = (w + 5) (w) (w + 29)

Then we have

[tex]\begin{aligned} \rm w^3 + 5w^2 + 29w^2 + 145w &=33488 \\\\\rm w^3 + 34w^2 + 145w - 33488 &= 0\\\\\rm (w - 23)(2w+57)(2w + 57) &= 0\\\\\rm w &= 23, -28.5, -28.5 \end{aligned}[/tex]

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Radical expression are expressions that contains square root. The value of x from the given radical expression is 3

Given the equation expressed as:

x = 2 + √x - 2

Subtract 2 from both sides

x - 2 = √x - 2

Square both sides

(x-2)^2 = x - 2

x - 2 = 1

x = 1 + 2

x = 3

Hence the value of x from the given radical expression is 3

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Answer:

B x = 3

Step-by-step explanation: