The diagram below shows a square inside a regular octagon. The apothem is of the octagon is 13.28 units. To the nearest square unit, what is the area of the shaded region?

The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2

h and k is the center point of the circle and r is the radius.

In the given equation (x+3)^2 + (y-1)^2 = 81

h = -3

k = 1

r^2 = 81

Take the square root of both sides:

r = 9

The center is (-3,1) and the radius is 9

Answer:

The constant, k, is 4.32.

Step-by-step explanation:

y varies inversely with x means y=k/x.

y varies directly with x means y=kx.

Anyways we have the first relation: y=k/x where k is a constant.

We divided by x because it said inversely.

We are given (x,y)=(1.2,3.6) is on this curve.

This gives us enough information to find the constant, k.

[tex]y=\frac{k}{x}[/tex] with [tex](x,y)=(1.2,3.6)[/tex].

[tex]3.6=\frac{k}{1.2}[/tex]

Multiply both sides by 1.2:

[tex]3.6(1.2)=k[/tex]

[tex]4.32=k[/tex]

The constant, k, is 4.32.

Answer:

[x + 3][3x - 4]

Step-by-step explanation:

First off, we need to find two numbers that when differed to 5, they also multiply to -36 [3 × -12]. Those numbers are -4 and 9. Next, we find the Greatest Common Factor [GCF], which means the LEAST DEGREE TERM possible:

[3x² - 4x] + [9x - 12]

x[3x - 4] 3[3x - 4]

As you can see, whenever we have a leading coefficient greater than 1, we need to break up our B into our two numbers we found [in BOLD], and have to attach an x to them because it replaced Bx, according to the Quadratic Equation of y = Ax² + Bx + C. So, after we completed our factoring, you see two identical factors, which we use ONCE. The other factor comes from the terms outside the duplicates. So, you get the above answer after you completed the steps: [x + 3][3x - 4].

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Check the picture below.

Answer:

True

Step-by-step explanation:

We can plug in and see.

If (3,0) is on the graph of P, then P(3) will evaluate to 0.

Let's try it:

P(3)=(3)^3-7(3)^2+15(3)-9

P(3)=27-7(9)+45-9

P(3)=27-63+45-9

P(3)=-36+45-9

P(3)=9-9

P(3)=0

Since P(3)=0, then (3,0) is an ordered pair of P.

Yes it is true that the point (3,0) lies on the graph of

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Given equation

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex]

If (3,0) is on the graph of P, then P(3) will evaluate to 0.

Substitute x = 3 in the given equation

P(3) = [tex](3)^3-7(3)^2+15(3)-9[/tex]

P(3) = [tex]27-7(9)+45-9[/tex]

P(3) = [tex]27-63+45-9[/tex]

P(3) = 9-9

P(3) = 0

Since P(3)=0, then (3,0) is an ordered pair of P.

Yes it is true that the point (3,0) lies on the graph of

P(x) = [tex]x^{3}-7x^{2} +15x-9[/tex].

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Answer:

factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{1}{8}x^3 - \frac{1}{27}y^3[/tex]

The expression can be written as:

[tex](\frac{1}{2}x)^3-(\frac{1}{3}y)^3[/tex]

We know, a^3-b^3 = (a-b)(a^2+ab+b^2)

a= x/2 and b = y/3

Putting values in the formula given:

[tex](\frac{x}{2}-\frac{y}{3})((\frac{x}{2})^2+(\frac{x}{2})(\frac{y}{3})+(\frac{y}{3})^2)\\(\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

So, factored form is: [tex](\frac{x}{2}-\frac{y}{3})(\frac{x^2}{4}+\frac{xy}{6}+\frac{y^2}{9})[/tex]

Answer:

Hi there!

The answer to this question is: C. 14

Step-by-step explanation:

Using the formula for sine I solved the missing side.

sin(62)= 12/x

then you need to solve for x

x= 12/ sin(62)

and you get 13.59 so round up to get 14

The length of the third side of a triangle is 16.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Use the Law of Cosine to find the third side of the triangle.

Law of Cosine is given by

[tex]$$a^{2}=b^{2}+c^{2}-2 b c$$[/tex]

Substituting the known values, we get

[tex]$$a^{2}=12^{2}+19^{2}-2 \cdot 12 \cdot 19 \cos 56$$[/tex]

By simplifying, we get

[tex]&a^{2}=505-456 \cos 56 \\[/tex]

[tex]&a^{2}=250.008 \\[/tex]

[tex]&a=15.81[/tex]

When rounded to the nearest whole number, the length of the third side is 16.

The length of the third side of a triangle is 16.

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Answer:

[-4, 3]

Step-by-step explanation:

That -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. So, your vertex is [-4, 3].

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

x = 16

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{RS}{MN}[/tex] = [tex]\frac{RT}{MO}[/tex], that is

[tex]\frac{8}{x}[/tex] = [tex]\frac{6.5}{13}[/tex] ( cross- multiply )

6.5x = 104 ( divide both sides by 6.5 )

x = 16

Answer:

x=-2.5 if the function is [tex]f(x)=\frac{8x-3}{-4x-10}[/tex]

Step-by-step explanation:

[tex]y=\frac{8x-3}{-4x-10}[/tex] has discontinuities when the denominator is 0.

You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.

That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.

If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.

Let's do this now.

When is -4x-10 equal to 0?

We have to solve the equation:

-4x-10=0

Add 10 on both sides:

-4x=10

Divide both sides by -4:

x=10/-4

Reduce by dividing top and bottom by 2:

x=5/-2

x=-5/2

or

x=-2.5  (if you want decimal form)

Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.

Let's see.

8(-2.5)-3=-23

Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.

If the top were 0, then you would have had a hole at x=-2.5.

Let Bikes = B and cars = c

a bike has 2 wheels and a car has 4 wheels.

Equation 1: add bikes and cars to get total students:

b + c = 80

Equation 2: multiply the number of wheels by each type and add to equal the total wheels.

2b +4c = 270

Rewrite the first equation as b = 80- c

Now substitute that for b in the second equation:

2(80-c) + 4c = 270

Simplify:

160 - 2c + 4c = 270

160 +2c = 270

Subtract 160 from both sides:

2c = 110

Divide both sides by 2

c = 110/2

c = 55

Replace c with 55 in the first equation and solve for b:

b + 55 = 80

b = 80-55

b = 25

b = 25, c = 55

Answer:

$179.17

Step-by-step explanation:

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Answer: The investment be worth $ 174.05 in 2 years .

Step-by-step explanation:

Given : The principal amount invested  : A= $125

Interest rate : r = 18% =0.18   [ Percent convert into decimal if we divide it by 100]

Time : t = 2 years

The formula to find the accumulated amount if compounded continuously :-

[tex]A=Pe^rt\\\\=(125)(1+0.18)^{2}\\\\= 125 (1.18)^2\\\\ = 125 (1.3924)\\\\=174.05[/tex]

Hence, the investment be worth $ 174.05 in 2 years .

Answer:

Lee= 20 L per hour.

Garcia = 40L per hour

Step-by-step explanation:

This formula is:

40x + 20y = 2000L

with if being known that x + y = 60.

In this x is the rate for Garcia and y is the rate for Lee.

You can also say that x = 60 - y, which you can fill in.

40 * (60-y) + 20y = 2000

2400 - 40y + 20y = 2000

-20y = -400

y = 20 L per hour.

So x = 60 - 20 = 40L per hour

Answer:

The correct answer is A. Each x-value corresponds to exactly one y-value.

Answer:

15(n-1)-45

Step-by-step explanation:

Increases by 15, so sequence is arithmetic, and goes to positive.

1st term is -45

so 15(n-1) gives us first term.

Reply for any questions I got you

[tex]\bf -45~~,~~\stackrel{-45+15}{-30}~~,~~\stackrel{-30+15}{-15}~~,~~\stackrel{-15+15}{0}~\hspace{7em}\stackrel{\textit{common difference}}{d=15} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=-45\\ d=15 \end{cases} \\\\\\ a_n=-45+(n-1)15\implies a_n=-45+15n-15\implies a_n=15n-60[/tex]

Answer:

The diameter is 10 units.

The equation of the circle is [tex](x-6)^2+y^2=25[/tex].

Step-by-step explanation:

You ask for the diameter but the choices give you the equation of the circle?

I will do both.

So they actually tell us the radius is from (6,0) to (2,-3).

So the radius is whatever that length is.  We can find the length by using the distance formula.

[tex]d=\sqrt{(6-2)^2+(0-(-3))^2}[/tex]

[tex]d=\sqrt{(4)^2+(3)^2}[/tex]

[tex]d=\sqrt{16+9}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]d=5[/tex]

So the radius is 5.

The diameter is twice the radius so the diameter is 2(5)=10.

Now the equation of our circle which doesn't match any of the choices is

[tex](x-6)^2+(y-0)^2=5^2[/tex].

You are probably wondering how I got that.  I used the center-radius form for a circle which is [tex](x-h)^2+(y-k)^2=r^2[/tex].

The center is (h,k) and the radius is r.

We had the center for our circle was (6,0) and the radius was 5.

I'm going to simplifying our equation just a bit:

[tex](x-6)^2+y^2=25[/tex].

All I did was y-0 which is y and 5^2 which is 5(5) which equals 25.

Answer:

The phosphate groups that are the polar of the phospholipid because they are charged - A.

The phosphate groups that are the polar of the phospholipid because they are A. charged

It is group of polar lipids that consist of two fatty acids ,  a glycerol unit and a phosphate group .

A phosphate group has a negatively charged oxygen and a positively charged nitrogen to make this group ionic. A single phospholipid molecule  has a phosphate group on one end and two chains of fatty acids . The phosphate group is negatively charged making the head polar and hydrophilic .

correct answer A) charged

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Answer:

B.

Step-by-step explanation:

Let's figure out what two consecutive integers is 14 between.

We also need to do this for 3.

14 is between 9 and 16 which means [tex]\sqrt{14}[/tex] is between [tex]\sqrt{9}[/tex] and [tex]\sqrt{16}[/tex].

3 is between 1 and 4 which means [tex]\sqrt{3}[/tex] is between [tex]\sqrt{1}[/tex] and [tex]\sqrt{4}[/tex].

So 14 is closer to 16 which means [tex]\sqrt{14}[/tex] is closer to 4.  Let's say [tex]\sqrt{14}\approx 3.7[/tex]

So 3 is closer to 4 which means [tex]\sqrt{3}[/tex] is closer to 2. Let's say [tex]\sqrt{3}\approx 1.8[/tex].

So now we do 3.7+1.8=5.5.

The answer that is closet to this is 5.47.

Now if we put [tex]\sqrt{14}+\sqrt{3}[/tex] in our calculator we get:

3.74+1.73=5.47

Let [tex]W[/tex] be the random variable representing the winnings you get for playing the game. Then

[tex]W=\begin{cases}9&\text{if the sum is odd}\\4&\text{if the sum is 4 or 8}\\49&\text{if the sum is 2 or 12}\\-1&\text{otherwise}\end{cases}[/tex]

First thing to do is determine the probability of each of the above events. You roll two dice, which offers 6 * 6 = 36 possible outcomes. You find the probability of the above events by dividing the number of ways those events can occur by 36.

So the probability mass function for this game is

[tex]P(W=w)=\begin{cases}\frac12&\text{for }w=9\\\frac29&\text{for }w=4\text{ or }w=-1\\\frac1{18}&\text{for }w=49\\0&\text{otherwise}\end{cases}[/tex]

The expected value of playing the game is then

[tex]E[W]=\displaystyle\sum_ww\,P(W=w)=\frac{71}9[/tex]

or about $7.89.

The expected value is positive, so a player can expect to earn money in the long run, and so should play the game.

Answer:

Hi there!

The answer to this question is: B

Answer choice B is correct because the dash above the two letter represents a line segment or side of a triangle

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

Answer choice A: incorrect

Explanation: The little carrot in front of each letter shows that it is an angle not a side

Answer C: incorrect

Explanation: It tells you points of the triangle

Answer:

Step-by-step explanation:

[tex]A.\ \angle P,\ \angle Q,\ and\ \angle R-\bold{angles}\\\\B.\ \overline{PQ},\ \overline{QR},\ and\ \overline{PR}-\bold{sides}\\\\C.\ P,\ Q,\ and\ R-\bold{vertexs}[/tex]

Answer:

14x-10y=-96

Step-by-step explanation:

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

so

we have

y=1.4x+9.6

Multiply by 10 both sides

10y=14x+96

isolate the variable x and y (Remember that A must be positive)

14x-10y=-96 -----> standard form

Answer:

12 pi in³

Step-by-step explanation:

Using the Pythagorean theorem:

x = √(11.7^2 - 8.6^2)

x = √(136.89 - 73.96)

x = √62.93

x = 7.9

The answer is D.

Answer:

So the angles have measurements 30,60, and 90 degrees.

Step-by-step explanation:

We have a triangle which means the interior angles of that triangle has sum 180 degrees.

Let's call the angle measurements: A, B, and C.

A+B+C=180

B=2A            (The second angle is twice the first.)

C=A+B          (The third angle is the sum of the other 2.)

If C=A+B, then C=A+2A  (since B=2A).

So we have this system:

A+B+C=180

B=2A

C=3A     (since C=A+2A=3a).

Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:

A+B+C=180 with B=2A and C=3A.

A+2A+3A=180

6A=180  

Divide both sides by 6:

A=180/6

A=30

If B=2A and A=30, then B=2(30)=60.

If C=3A and A=30, then C=3(30)=90.

So the angles have measurements 30,60, and 90 degrees.

Answer:

y-2 = 1/4(x-20)  point slope form

y = 1/4x -3  slope intercept form

Step-by-step explanation:

y = -4x

The slope is -4

The slope that is perpendicular is the negative reciprocal

- (1/-4) = 1/4

The slope of our new line is 1/4

We have a point and the slope, so we can use point slope form

y-y1 = m(x-x1)

y-2 = 1/4(x-20)

If we want the line in slope intercept form, distribute

y-2 = 1/4x -5

Add 2 to each side

y-2+2 = 1/4x -5+2

y = 1/4x -3

Answer:

15 pounds

Step-by-step explanation:

5 bags @ 3 pounds

5 x 3 = 15 lbs.

Samuel has 5 bags of almonds, each weighing 3 pounds. By multiplying the number of bags by the weight of each bag (5 * 3), we find that Samuel has a total of 15 pounds of almonds.

The total weight of Samuel's 5 bags of almonds is:

Multiply the weight of a full bag (3 pounds) by the number of bags (5): 3 pounds/bag x 5 bags = 15 pounds

Therefore, Samuel has 15 pounds of almonds.

Answer:

Kerry donated $50 to a charity.

Step-by-step explanation:

500/10=50

Answer:

$50

Step-by-step explanation:

1/10 of $500 =

= 1/10 * $500

= $500/10

= $50

To find the slope of a line you must do [tex]\frac{rise}{run}[/tex]

Look at the image to find the rise (in pink) and run (in green) on the graph:

In this case the rise is 3 and the run is -4 (the reason the four is negative is because it "runs" to the left, which is the negative direction of the coordinate plane) so the slope of this line is:

[tex]\frac{-3}{4}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

The answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.

So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:

[tex]y=-3x^{2}+13x-5[/tex]

We have that :

[tex]a=-3(negative)\\b=13\\c=-5(y-intercept)[/tex]

We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.

Hence, the answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

Have a nice day!

Note: I have attached a picture for better understanding.

An inequality is comparing the relation of two equations that are not equal.

Depending on a persons cell phone plan, if they can only talk for so many minutes per month or send so many texts per month, this is an inequality written as number of minutes/ texts per month needs to be less than or equal to the allowable amount.