What is the midpoint of the segment shown below?

Well, let's use the Euclidean algorithm:

164 = 4×37 + 16

37 = 2×16 + 5

16 = 3×5 + 1

Then working backwards,

1 = 16 - 3×5

1 = 16 - 3×(37 - 2×16) = 7×16 - 3×37

1 = 7×(164 - 4×37) - 3×37 = 7×164 - 31×37

so that x = 7 and y = -31.

Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}[/tex]

[tex](\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}[/tex]

Answer:

10

Step-by-step explanation:

Using the distance formula,

[tex] \sqrt{ {( - 2 - ( - 8))}^{2} + { (- 4 - 4)}^{2} } = 10[/tex]

Answer:

Kelly has read more of the book

Answer:

132.84 is the answer as volume is area times length

Answer:

y=-15x+100

Step-by-step explanation:

The equations of the graphed line and function can be written as:

f(x) = 1/2x + 2

y - 3 = 1/2(x - 2)

y - 1 = 0.5(x + 2)

Equation of a graphed line can be expressed in:

Slope-intercept form as y = mx + b, where m = slope, b = y-intercept; or

Point-slope form as y - b = m(x - a), where (a, b) is a point and m = slope.

Find the slope (m) of the line:

Slope (m) = change in y / change in x = 1/2 = 0.5

y-intercept (b) = 2

To express the graphed line in slope-intercept form, substitute m = 1/2 and b = 2 into f(x) = mx + b:

f(x) = 1/2x + 2.

Using the point-slope form, write the equation by substituting m = 1/2 and (a, b) = (2, 3) into y - b = m(x - a):

y - 3 = 1/2(x - 2)

Or substitute m = 0.5 and (a, b) = (-2, 1) into y - b = m(x - a):

y - 1 = 0.5(x - (-2))

y - 1 = 0.5(x + 2)

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Answer:

the unit cost per rubber tile is $$$$$$$$$$$$$6

Step-by-step explanation:

..

Answer:

.35 < 38% < 3/5

Step-by-step explanation:

.35 is the same as 35 percent which is less than 38, and 3/5 when divides is .60 turned into percent is 60 percent

Answer:

-4.25

Step-by-step explanation:

Answer:

64in

Step-by-step explanation:

for a four sided figure, you do base x height. volume isn't squared in Math.

Answer:

0.267

Step-by-step explanation:

4/15 as a decimal is 0.26 repeating so rounded to the nearest thousandth would be 0.267

Answer:

A.

Step-by-step explanation:

1.5m + 6.5q > 100

✨♥️

Answer:

Alice

Step-by-step explanation:

14$ the amount he had - X the amount he lost (the unknown) is what is described by Alice

Answer:

GCF=3[tex]x^{2}y[/tex]

Step-by-step explanation:

First, take a look at the numbers.

GCF of 15 and -18 = 3

Then, look at the variables.

GCF of (x^2)(y^3) and (x^3)(y)(z) = (x^2)(y)

Lastly, combine the two expressions

GCF = 3(x^2)(y)

Answer: 3(x^2)(y)

Hope this helps!

Answer:

Step-by-step explanation:

Answer: 123 boxes

Step-by-step explanation:

Find how many nails she used.

692-200=492

she used 492 nails

we know that 4 nails are needed to set up a box

so we divide.

492/4=123

Sally set up 123 boxes

Answer:

point B

Step-by-step explanation:

Answer:

It's Point B.

Go to 5 on the x-axis and then go up 3

The 5 is the x-axis and 3 is the y-axis

Answer:

No

Step-by-step explanation:

Use synthetic division

-5 | 1 -4  3   7

____-5 45 -240

     1 -9 48 | -233

Since the remainder is not 0, then x+5 is not a factor of the polynomial

Answer:

x = 3

Step-by-step explanation:

the midsegment XW is half the sum of the parallel bases , that is

7x + 10 = [tex]\frac{1}{2}[/tex] (46 + 16 ) = [tex]\frac{1}{2}[/tex] × 62 = 31 ( subtract 10 from both sides )

7x = 21 ( divide both sides by 7 )

x = 3

Answer:

24square unit

Step-by-step explanation:

triangle area=1/2.b.h

=1/2.8.6=24

Answer:

4 years and 2 months

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies \sf 1000 = 500(1 + 0.24t)[/tex]

[tex]\implies \sf \dfrac{1000}{500}=(1 + 0.24t)[/tex]

[tex]\implies \sf 2=1 + 0.24t[/tex]

[tex]\implies \sf 1 = 0.24t[/tex]

[tex]\implies \sf t=\dfrac{1}{0.24}[/tex]

[tex]\implies \sf t=4 \frac{1}{6} \:years[/tex]

[tex]\implies \sf t=4\:years\:2\:months[/tex]

Therefore, it takes 4 years and 2 months for the initial investment of $500 to double at a simple interested rate of 24%.

=========================================================

Explanation:

Points Q and R have the same y coordinate of 6.

This means they're on the same horizontal level and we can form a number line through these points. Think of Q and R being on the x axis.

Going from -4 to 8 is a distance of 12 units because either

-4-8 = -12 which flips to +12 or 12

8-(-4) = 8+4 = 12

Effectively I used absolute value for the first part to go from -12 to 12. Distance cannot be negative.

Alternatively, you can count out the number of horizontal spaces from -4 to 8 and you should count out 12 units.

--------------------------------

If you need to use the distance formula, then this is what the steps may look like:

[tex]Q = (x_1,y_1) = (-4,6) \text{ and } R = (x_2, y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-8)^2 + (6-6)^2}\\\\d = \sqrt{(-12)^2 + (0)^2}\\\\d = \sqrt{144 + 0}\\\\d = \sqrt{144}\\\\d = 12\\\\[/tex]

In my opinion, the distance formula is overkill because we can simply apply subtraction or count out the number of spaces. It's up to you which you prefer you like better. Of course be sure to follow all instructions your teacher mentions.

If the two points weren't on the same horizontal level, then we would have no choice and have to use the distance formula. Or you could use the pythagorean theorem which is effectively what the distance formula is derived from.

Add all the females together: 3 + 4 + 6 + 3 = 16

Female seniors = 3

Probability of picking a senior = 3/16 = 0.1875 x 100 = 18.75%

Rounded to the nearest whole number = 19%

Answer: 19%

Answer:

V = 3053.63 mm^3

Step-by-step explanation:

radius : 9mm

V = 4/3 * pi * r^3

V = 4/3 * (3.1415926535898...) * 9^3

V = 3053.63 mm^3

Answer:

[tex]\underline{\boxed{\sf{2(x - 11)(x + 11)}}}[/tex]

Step-by-step explanation:

[tex]\sf{2x^2 - 242}[/tex]

Common factor :

[tex]\sf{2x^2 - 242}[/tex]

[tex]\sf{2(x^2 - 121)}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Use the sum-product pattern :

[tex]\sf{2(x^2-121)}[/tex]

[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Common factor from the two pairs :

[tex]\sf{2(x^2 + 11x-11x - 121)}[/tex]

[tex]\sf{2(x(x+11) -11(x + 11))}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Rewrite in factored form :

[tex]\sf{2(x(x+11)- 11(x + 11))}[/tex]

[tex]\sf{2(x - 11)(x + 11)}[/tex]

[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Solution :

[tex]\sf{2(x - 11)(x + 11)}[/tex]

Answer:

[tex]x = 2, y = -1[/tex]

Step-by-step explanation:

We can add the 2 equations together to solve for y.

[tex](-3x + 5y) + (3x + 7y) = (-11) + (-1)\\-3x + 3x + 5y + 7y = -11 -1\\12y = -12\\y = -1[/tex]

Now we can solve for x by substituting y in one of the original equations.

[tex]3x + 7y = -1\\3x + 7(-1) = -1\\3x - 7 = -1\\3x = 6\\x = 2[/tex]

Those are the answers

- Kan Academy Advanced

Answer:

E 150

Step-by-step explanation:

The coordinates of the mid - point of the line AB is (-1, -5).

A midpoint is a point that divides a given line into two equal parts.

Given is that AB has endpoints at A(4, -8) and B(-6, -2). It is asked to find the coordinates of the midpoint of AB.

We can write the coordinates of the midpoint of AB as -

{x} = (x₁ + x₂)/2

{x} = (4 - 6)/2

{x} = - 2/2

{x} = -1

{y} = (y₁ + y₂)/2

{y} = (-8 - 2)/2

{y} = - 10/2

{y} = - 5

Therefore, the coordinates of the mid - point of the line AB is (-1, -5).

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The amount that Theresa was charged in interest for the billing cycle is $5.30

By using the average daily balance, the amount will be:

= (350 × 12) + (520 × 19) / (12 + 19)

= (4200 + 9880)/31

= 454.19

Therefore, the interest will be:

= (454 × 0.14)/12

= $5.30

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