Which are valid pairs of opposite angle measures for a quadrilateral inscribed
in a circle? Select all that apply.
A. 72°, 108°
B. 66°, 114°
C. 80°, 90°
D. 64°, 106°

[tex] \frac{ \sqrt{x + 8} - \sqrt{x} }{8} \times \frac{ \sqrt{x + 8} + \sqrt{x} }{ \sqrt{x + 8} + \sqrt{x} } \\[/tex]

[tex] \frac{( \sqrt{x + 8} ) {}^{2} - ( \sqrt{x}) {}^{2} }{8( \sqrt{x + 8} + \sqrt{x} ) } \\ [/tex]

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

The surface area of the figure illustrated will be 286 yards²

The surface area of a solid object simply implies the measure of the total area which the surface of an object occupies. This is typically done by adding all the areas on the surface of the object.

It should be noted that the surface area of a cuboid will be:

= 2(lw + lh + wh)

w = width = 7

l = length = 9

h = height = 5

Surface area = 2(lw + lh + wh)

= 2(7 × 9) + 2(9 × 5) + 2(7 × 5)

= 126 + 90 + 70

= 286 yards²

Therefore, the surface area of the solid will be 286 yards².

Complete question:

Find the surface area of the solid given that the length is 9 yards, the width is 7 yards, and the height is 5 yards.

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Answer:

[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}=\frac{4}{9}[/tex]

Step-by-step explanation:

[tex]\lim_{n\rightarrow +\infty } \frac{4n^{3}-5}{9n^{3}+7}[/tex]

Pull out  n³

[tex]=\lim_{n\rightarrow +\infty } \frac{n^{3}\times \left( 4-\frac{5}{n^3} \right) }{n^{3}\times \left( 9+\frac{7}{n^3} \right) }[/tex]

Simplify by n³

[tex]=\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }[/tex]

Remark : [tex]\lim_{n\rightarrow +\infty } \frac{5}{n^3} \right) } = 0 \ \. \text{and} \ \ \lim_{n\rightarrow +\infty } \frac{7}{n^3} \right) } = 0[/tex]

Then

[tex]\lim_{n\rightarrow +\infty } \frac{ \left( 4-\frac{5}{n^3} \right) }{ \left( 9+\frac{7}{n^3} \right) }=\frac{4-0}{9+0}[/tex]

[tex]=\frac{4}{9}[/tex]

Answer: C

Step-by-step explanation:

The zeros of a graph are where the graph intersects the x-axis.

The amount of George's income that is subject to withholding is $75,000, which excludes the alimony income.

Alimony income represents the amount received from a spouse or a former spouse under a divorce or separation instrument.

The incomes subject to withholding include the following:

Wages income = $50,000

Gambling winning = $20,000

Alimony income = $10,000

Dividend income = $5,000

Income subject to withholding = $75,000 ($20,000 + $20,000 + $5,000)

Thus, George's income that is subject to withholding is $75,000, excluding the alimony income.

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The order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1. This tells us tgat the highest probability is number 4 while the lowest is 1.

In mathematics, this is the concept that is used to talk about the likelihood of having an event occurring.

The probability of these items have been calculated below

1. Winning the Lottery

probability = 1/49P6

= 0.00000000009932

2. Rolling a 7:

we have to find the group of 7's

= (2,5) (1,6), (3,4), (4, 3), (6,1), (5,2)

= 6/36 = 0.1666

3. Drawing the Ace of Spade

1/52 = 0.019

4. 2 Heads in a Row:

1/2 x 1/2

= 0.25

5. Marbles:

3 + 4+ 5 = 12

3/12 * 3/12 * 3/12

= 0.01562

Hence the order of the probabilities from the highest to the least would be

4 > 2 > 3 > 5 >1

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Answer:

d ≈ 21.26 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 3, 8 ) and (x₂, y₂ ) = (13 - 6 )

d = [tex]\sqrt{13-(-3))^2+(-6-8)^2}[/tex]

   = [tex]\sqrt{(13+3)^2+(-14)^2}[/tex]

   = [tex]\sqrt{16^2+196}[/tex]

   = [tex]\sqrt{256+196}[/tex]

   = [tex]\sqrt{452}[/tex]

   ≈ 21.26 units ( to 2 dec. places )

Answer:

The distance is 21.3

Step-by-step explanation:

The solution is in the attached image

Answer: 16

Step-by-step explanation:

1.5x = 24

24/1.5 = 16 students.

Answer:

d(t)=-10t-520

Step-by-step explanation:

First you have to find the gradient (m) using the formula [tex]m=\frac{d(t)2-d(t)1}{t2-t1}[/tex]

using the two points you have been given: 1(3,-550) and 2(8,-600)

so you substitute these points into the equation [tex]m=\frac{-600+500}{8-3}[/tex]

m=-10

Now that you have found the m-value you need to find the b-value by using one of the points you already have, I will use Point 2 (8,-600), and substitute it into the equation and solve

d(t)=-10t+b

-600=-10*8+b

-600=-80+b

-520=b

Therefore, the equation is d(t)=-10t-520

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Answer:9

Step-by-step explanation:1+2=3 6/2=3

3x3=9

Answer:[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Step-by-step explanation:

Given the system of equations

[tex]1)~xy=2[/tex]

[tex]2)~x+y=4[/tex]

Divide x on both sides of the 1) equation

[tex]xy=2[/tex]

[tex]xy\div x=2\div x[/tex]

[tex]y=\dfrac{2}{x}[/tex]

Current system

[tex]1)~y=\dfrac{2}{x}[/tex]

[tex]2)~x+y=4[/tex]

Substitute the 1) equation into the 2) equation

[tex]x+(\dfrac{2}{x} )=4[/tex]

Multiply x on both sides

[tex]x\times x+\dfrac{2}{x}\times x=4\times x[/tex]

[tex]x^2+2=4x[/tex]

Subtract 4x on both sides

[tex]x^2+2-4x=4x-4x[/tex]

[tex]x^2-4x+2=0[/tex]

Use the quadratic formula to solve for the x value

[tex]x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4(1)(2)} }{2(1)}[/tex]

[tex]x=2\pm\sqrt{2}[/tex]

Substitute the x value into one of the equations to find the y value

[tex]xy=2[/tex]

[tex](2+\sqrt{2} )y=2[/tex]

[tex]y=2-\sqrt{2}[/tex]

[tex]OR[/tex]

[tex]xy=2[/tex]

[tex](2-\sqrt{2} )y=2[/tex]

[tex]y=2+\sqrt{2}[/tex]

Therefore, the points of intersection are

[tex]\Large\boxed{(2+\sqrt{2},~2-\sqrt{x} )~~and~~ (2-\sqrt{2},~2+\sqrt{x} )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

(2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) and (2 + [tex]\sqrt{2}[/tex], 2 - [tex]\sqrt{2}[/tex] )

Step-by-step explanation:

xy = 2 → (1)

x + y = 4 ( subtract x from both sides )

y = 4 - x → (2)

substitute y = 4 - x into (1)

x(4 - x) = 2

4x - x² = 2 ( multiply through by - 1 )

x² - 4x = - 2

using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 2)x + 4 = - 2 + 4

(x - 2)² = 2 ( take square root of both sides )

x - 2 = ± [tex]\sqrt{2}[/tex] ( add 2 to both sides )

x = 2 ± [tex]\sqrt{2}[/tex] , that is

x = 2 - [tex]\sqrt{2}[/tex] , x = 2 + [tex]\sqrt{2}[/tex]

substitute these values of x into (2) for corresponding values of y

x = 2 - [tex]\sqrt{2}[/tex] , then

y = 4 - (2 - [tex]\sqrt{2}[/tex])

  = 4 - 2 + [tex]\sqrt{2}[/tex]

  = 2 + [tex]\sqrt{2}[/tex] ⇒ (2 - [tex]\sqrt{2}[/tex] , 2 + [tex]\sqrt{2}[/tex] ) ← 1 point of intersection

x = 2 + [tex]\sqrt{2}[/tex] , then

y = 4 - (2 + [tex]\sqrt{2}[/tex] )

   = 4 - 2 - [tex]\sqrt{2}[/tex]

   = 2 - [tex]\sqrt{2}[/tex] ⇒ (2 + [tex]\sqrt{2}[/tex] , 2 - [tex]\sqrt{2}[/tex] ) ← 2nd point of intersection

Answer:

index of m is -2

Step-by-step explanation:

any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.

for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.

[tex]f(x)=\left( \cfrac{3x^2-2}{2x+3} \right)^3\implies \cfrac{df}{dx}=\stackrel{\textit{\LARGE chain~ ~~ rule}}{3\left( \cfrac{3x^2-2}{2x+3} \right)^2\underset{quotient~rule}{\left( \cfrac{6x(2x+3)~~ - ~~(3x^2-2)2}{(2x+3)^2} \right)}} \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{12x^2+18x-6x^2+4}{(2x+3)^2} \right) \\\\\\ \cfrac{df}{dx}=3\left( \cfrac{3x^2-2}{2x+3} \right)^2\left( \cfrac{6x^2+18x+4}{(2x+3)^2} \right)[/tex]

[tex]\cfrac{df}{dx}=3 \cfrac{(3x^2-2)^2}{(2x+3)^2} \left( \cfrac{2(3x^2+9x+2)}{(2x+3)^2} \right)\implies \cfrac{df}{dx}=\cfrac{6(3x^2-2)^2(3x^2+9x+2)}{(2x+3)^4}[/tex]

now, we could expand the polynomials, but there isn't much simplification, so no much point doing so.

Answer:

(11,0)

Step-by-step explanation:

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Combining the above inequalities, we get :

[tex]\qquad❖ \: \sf \:0.2 < 0.8 < 0.801 < 0.9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Based on the given coordinate grid, and the increment for each grid line, the coordinates of point A is ( fraction negative 1 and 1 over 4, fraction 3 over 4) or (-1¹/₄, ³/₄).

The x-value of point A is said to be 5 grid lines to the left of y-axis. This means that the x value will be negative.

The increments are 1/4 so the x-value is:
= -1/4 x 5

= -1¹/₄

The y-value is given by the 3 grid lines above the x-axis which means that this value is positive:

= 1/4 x 3

= 3 /4

The coordinates of A are:

(-1¹/₄, ³/₄)

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Answer:

A. [tex]\frac{17}{52}[/tex]

B. [tex]\frac{17}{52}[/tex]

C. [tex]\frac{2}{13}[/tex]

Step-by-step explanation:

A.

There are 52/4 diamonds in the deck and 4 '5's in the dech of cards

52/4 = 13 + 4 = 17

Therefore, you have a  [tex]\frac{17}{52}[/tex] chance of drawing one of those cards.

B.

There are 13 hearts in the deck and 4 jacks. Therefore, your odds are the same : [tex]\frac{17}{52}[/tex]

C.

There are 4 jacks in a deck of cards and 4 '8's in a deck of cards

Therefore your probability is [tex]\frac{8}{52}[/tex] which simplifies to [tex]=\frac{2}{13}[/tex]

As per brainly guidelines I can only answer 3 questions in one answer

Answer:

x  = 9, y = 13 , z = - 19

Step-by-step explanation:

3y + 4z = - 37 → (1)

2x + 4y - 3z = 127 → (2)

4y = 52 → (3)

divide both sides by 4 in (3)

y = 13

substitute y = 13 into (2) and solve for z

3(13) + 4z = - 37

39 + 4z = - 37 ( subtract 39 from both sides )

4z = - - 76 ( divide both sides by 4 )

z = - 19

substitute y = 13 and z = - 19 into (2) and solve for x

2x + 4(13) - 3(- 19) = 127

2x + 52 + 57 = 127

2x + 109 = 127 ( subtract 109 from both sides )

2x = 18 ( divide both sides by 2 )

x = 9

solution is x = 9, y = 13 , z = - 19

Mean = 402.5.

Variance = 77,556.3

Standard deviation = 278.5

See attachment for the complete table.

The mean of a data is the sum of all data values divided by the number of data values we have in the data set.

Variance is calculated by finding the sum of the squares of the deviations from the mean, find the average, then find the average.

The standard deviation = the square root of variance.

The mean of the data given would be: 402.5.

402.5 is subtracted from each of the data points to get the deviations which are squared.

It is the sum of the deviations that gives us 310,225.2.

To find the variance, divide 310,225.2 by the number of data values which is 4.

Variance = 310,225.2/4

Variance = 77,556.3

Standard deviation = √77,556.3

Standard deviation = 278.5

The complete table containing the missing values is given in the image attached below.

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Based on the amount that both Salesmen A and B earn per sale, the number of sales they both had was 12 sales.

Sales commission is a key aspect of sales compensation. It's the amount of money a salesperson earns based on the number of sales they have been able to make.

We are told that;

Salesman A gets $65 per sale.

Salesman B gets $300 and $40 per sale.

Assuming the number of sales to take them both to the same amount is x, the relevant formulas would be:

65x = 300 + 40x

Rearranging gives;

65x - 40x = 300

25x = 300

x = 300/25

x = 12 sales

The amount that salesman A earned is = 65 * 12 = $780

The amount that salesman B earned is = 300 + (40 * 12) = $780

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Answer:

Hello,

Step-by-step explanation:

All is in the picture.

B=(-2,8), O=(-2,-5)

b=BO=8+5=13

F_1=(-2,4)   O=(-2,5)  Focus distance=4+5=9
Horizontal half axis=√(b²-f²)=√88

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

The explicit rule for this sequence:

The obvious rule for an arithmetic sequence is given as follows:

[tex]a_{n}=a_{1} +(n-1)d[/tex]

The first term = [tex]a_{1}[/tex].

The number of terms = n.

The common difference for two consecutive terms = d.

A recursive rule for an arithmetic sequence: [tex]a_{1} =4[/tex].

[tex]a_{n} =a_{n-1}-3[/tex]

The arithmetic sequence is given by:

[tex]a_{n} =a_{n-1}+d[/tex]

We get: d = -3

Substitute the given values:

[tex]a_{n} =4+(n-1)(-3)[/tex]

[tex]a_{n} =4-3n+3[/tex]

=7-3n

The explicit rule for this sequence is [tex]a_{n} =7-3n[/tex].

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The explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

Given the recursive formula for an arithmetic sequence: [tex]a_1=4, a_n=a_{n-1}-3[/tex].

Thus, the first term of the arithmetic sequence is [tex]a=a_1=4[/tex]. using the recursive formula, we can get the 2nd term by putting [tex]n=2[/tex], [tex]a_2=a_1-3=4-3=1[/tex].

So, the common difference of the given arithmetic sequence is [tex]d=a_2-a_1=1-4=-3[/tex].

Thus, the nth term of the arithmetic sequence is given by [tex]a_n=a+(n-1)d\\\Longrightarrow a_n=4+(n-1)\times(-3)\\\Longrightarrow a_n=7-3n[/tex]

Therefore, the explicit rule for the given arithmetic sequence is [tex]a_n=7-3n[/tex].

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a. Central angle in the circle is: Angle BAC

b. A major arc is: Arc BEC

c. A minor arc is: Arc BC

d. m(arc BEC) = 260°.

e. m(arc BC) = 100°.

The central angle theorem states that: the central angle measure of a circle equals the measure of the intercepted arc.

A central angle is formed by two radii of a circle, and the vertex of the angle is at the center of the circle.

Any arc that is more than half a circle (semicircle) or has a measure that is greater than 180 degrees, is referred to as a major arc of that circle. The measure of the major arc > 180 degrees.

Any arc that is not more than half a circle (semicircle) or has a measure that is less than 180 degrees, is referred to as a minor arc of that circle. The measure of the minor arc < 180 degrees.

a. One central angle that can be identified in circle A is: Angle BAC

b. A major arc that can be identified in circle A is: Arc BEC

c. A minor arc that can be identified in circle A is: Arc BC.

d. According to the central angle theorem, we have:

m(arc BEC) = 360 - 100

m(arc BEC) = 260°

e. We are given that m(angle BAC) = 100°, therefore, according to the central angle theorem, we have:

m(arc BC) = m(angle BAC )

m(arc BC) = 100°

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Answer: someone who is viewed as obsolete or a person you can use to save yourself from any problem/situation

Step-by-step explanation:

Answer:

The term "meat shield" is often used as an insult to refer to someone who is used by others as a protective barrier, especially in a dangerous or violent situation. The implication is that the person being referred to is expendable and not valued for their own merits or abilities.

Here are a few examples of insults that use the term "meat shield":

"You're nothing more than a meat shield for your boss."

"You're just a disposable meat shield to your friends."

"You're nothing but a human meat shield to your team."

"You're just a weak and pitiful meat shield."

"You're just a coward who hides behind others like a meat shield."

Again, it's important to remember that using insults is never a productive or kind way to communicate with others. It's always better to try to address the issue in a respectful and constructive manner.

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

It looks like the function is

[tex]f(x,y) = 3 + 4x^{3/2}[/tex]

We have

[tex]\dfrac{\partial f}{\partial x} = 6x^{1/2} \implies \left(\dfrac{\partial f}{\partial x}\right)^2 = 36x[/tex]

[tex]\dfrac{\partial f}{\partial y} = \left(\dfrac{\partial f}{\partial y}\right)^2 = 0[/tex]

Then the area of the surface over [tex]R[/tex] is

[tex]\displaystyle \iint_R f(x,y) \, dS = \iint_R \sqrt{1 + 36x + 0} \, dA \\\\ ~~~~~~~~ = \int_0^5 \int_0^2 \sqrt{1+36x} \, dx \, dy \\\\ ~~~~~~~~ = 5 \int_0^2 \sqrt{1+36x} \, dx \\\\ ~~~~~~~~ = \frac5{36} \int_1^{73} \sqrt u \, du \\\\ ~~~~~~~~ = \frac5{36}\cdot \frac23 \left(73^{3/2} - 1^{3/2}\right) = \boxed{\frac5{54} (73^{3/2} - 1)}[/tex]