In AOPQ, PQ = 19, QO = 11, and OP = 20. Which statement about the angles of AOPQ
must be true?

The width of the banner of the Friday’s pep rally is 3 feet.

To calculate a percentage, divide the value by total value and multiply the result by 100. (value/total value)100% is the formula for calculating percentage.

Calculating a percentage means determining a portion of a whole in terms of 100. A percentage can be calculated in two ways:

For the given expression;

The length of the Friday’s pep rally banner is 18 feet.

Let the width be 'b'.

The given condition is;

The length of the banner is made 6 times the width.

Then,

6 time the width  = length

6×w = 18

w = 18/6

w = 3

Therefore, the width of the banner is found as 3 feet.

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The RS line segment will be 16 units long.

The collinear points are Q, R, S, and T.

The collinear's condition will then be determined:

The points Q, R, S, and T all lie on the same line segment in that order, so the QR:RS:ST ratio is 1:4:5. If QT = 40.

The value of the variable x will then be:

The length of the line segment RS will then become:

Therefore, the RS line segment will be 16 units long.

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The correct question is given below:

The points Q, R, S, and T all lie on the same line segment, in that order, such that the

ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.

let x be the real part of z

let y be the imaginary part of z

[tex]arg(x +i y - 1) = arg(x + iy + 3i) \\ arg(x - 1 + iy) = arg(x + (y + 3)i) \\ arctan( \frac{y}{x - 1} ) = arctan( \frac{y + 3}{x} ) \\ arctan( \frac{ (\frac{y}{x - 1} ) - ( \frac{y + 3}{x}) }{1 +( \frac{y}{x - 1} )( \frac{y + 3}{x} )} ) = 0 \\ arctan( \frac{ \frac{xy - (x - 1)(y + 3)}{x(x - 1)} }{ \frac{x(x - 1) + y(y + 3)}{x(x - 1)} } ) = 0[/tex]

[tex]arctan( \frac{xy - xy - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y } ) = 0 \\ \frac{ - 3x + y + 3}{x {}^{2} - x + y {}^{2} + 3y} = tan(0) = 0 \\ - 3x + y + 3 = 0 \\ y = 3x - 3[/tex]

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

Answer:

[tex]\dfrac{x-1}{y}=\dfrac{1}{3}[/tex]

Step-by-step explanation:

Sums of real and imaginary numbers are known as complex numbers:  

[tex]\large\boxed{z = x + iy}[/tex]

(where x is the real number and iy is the imaginary number).

Complex numbers can be represented on an Argand diagram.

z = x + iy is represented on the diagram by the point P(x, y).

[tex]\textsf{Argument of a complex number $= \boxed{\arg z}$}[/tex]

It is the angle between the positive real axis and the line joining that number to the origin on an Argand diagram, measured in an anticlockwise direction.

[tex]\textsf{For \;$z = x + iy$, \;the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x}$.}[/tex]

[tex]\textsf{Given: \quad $\arg (z-1)=\arg(z+3i)$}[/tex]

[tex]\textsf{If $z$ is a complex number then $z = x + iy$}.[/tex]

[tex]\textsf{Substitute this into the given equation}:[/tex]

[tex]\begin{aligned} \arg(z-1)&=\arg(z+3i)\\\implies \arg(x + iy - 1) &= \arg(x + iy + 3i)\\\implies \arg((x - 1) + iy) &= \arg(x + i(y + 3))\end{aligned}[/tex]

[tex]\textsf{If the argument $\theta$ satisfies\; $\tan \theta = \dfrac{y}{x} \implies \theta=\tan^{-1}\left(\dfrac{y}{x}\right)$}:[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)=\tan^{-1}\left(\dfrac{y+3}{x}\right)[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{y}{x-1}\right)-\tan^{-1}\left(\dfrac{y+3}{x}\right)=0[/tex]

[tex]\boxed{\begin{minipage}{6.2cm}\underline{Trigonometric identity}\\\\ $\tan^{-1}(a)-\tan^{-1}(b)=\tan^{-1}\left(\dfrac{a-b}{1+ab}\right)$\\ \end{minipage}}[/tex]

Use the arctan identity:

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{y}{x-1}-\dfrac{y+3}{x}}{1+\left(\dfrac{y}{x-1}\right)\left(\dfrac{y+3}{x}\right)} \right)=0[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{1+\dfrac{y(y+3)}{x(x-1)}} \right)=0[/tex]

[tex]\implies \tan^{-1}\left(\dfrac{\dfrac{xy-(y+3)(x-1)}{x(x-1)}}{\dfrac{x(x-1)+y(y+3)}{x(x-1)}} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{xy-(y+3)(x-1)}{x(x-1)+y(y+3)} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{xy-xy+y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]

[tex]\implies \tan^{-1}\left({\dfrac{y-3x+3}{x^2-x+y^2+3y} \right)=0[/tex]

[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=\tan(0)[/tex]

[tex]\implies \dfrac{y-3x+3}{x^2-x+y^2+3y}=0[/tex]

[tex]\implies y-3x+3=0[/tex]

[tex]\implies y=3x-3[/tex]

[tex]\textsf{Substitute\;\; $y=3x-3$ \;\;into \;\;$\dfrac{x-1}{y}$}:[/tex]

[tex]\begin{aligned}\implies \dfrac{x-1}{y}& =\dfrac{x-1}{3x-3}\\\\ & =\dfrac{x-1}{3(x-1)}\\\\ & =\dfrac{1}{3}\end{aligned}[/tex]

[tex]\textsf{Therefore, the value of\; $\dfrac{x-1}{y}$\; is\; $\dfrac{1}{3}$}.[/tex]

The numbers 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer

The numbers are given as:

0.5, −13, 0.62, 3.14, 19%

Numbers that can be represented as a fraction of two integers are rational numbers

The given numbers can be represented as a fraction of two integers

i.e.

0.5 = 5/10

0.62 = 62/100

3.14 = 314/100

19% = 19/100

This means that 0.5, 0.62, 3.14, 19% are rational numbers, while -13 is an integer (because it has no decimal point and it is negative)

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Answer:

D. 2z^3/y

Step-by-step explanation:

xyz^2 = 2z^4

z(xyz) = z(2z^3)

xyz = 2z^3

xz = (2z^3)/y

Answer: 27 4 peices for 5 children

Step-by-step explanation: 4 peices for 5 children 4×5=20 then she ate 7 so 20 plus 7 is 27

Full equation 4×5+7=27

Answer:

[tex]{ \tt{ \frac{3x}{7} - 2 = 15 }} \\ \\ { \tt{3x - (2 \times 7) = (15 \times 7)}} \\ { \tt{3x - 14 = 105}} \\ { \tt{3x = 119}} \\ { \tt{x = 39.67}} \\ { \tt{ 39\frac{2}{3}}}[/tex]

Answer:

[tex] \sf \large \: x = \frac{119}{3} [/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

3x/7−2=15

Step 1: Simplify both sides of the equation.

3x/7−2=15

3/7x+−2=15

3/7x−2=15

Step 2: Add 2 to both sides.

3/7x−2+2=15+2

3/7x=17

Step 3: Multiply both sides by 7/3.

(7/3)*(3/7x)=(7/3)*(17)

x=119/3

25 times 789 is 19725

the answer:19,725

[tex]8.35 \times {10}^{9} [/tex]

or

[tex]835 \times {10}^{7} [/tex]

Answer:

Step-by-step explanation:

it is Payment: Uniform Payment Series: (F/P, i, ∞) = ∞. (A/F, i, ∞) = 0.

Answer:

Step-by-step explanation:

Considering the algorithm to divide a number by a fraction, she must multiply x by -12/5 to find the answer of the division of x by -5/12.

To divide a number, or even another fraction, by a fraction, we need to multiply the numerator by the inverse of the denominator.

Taking the following division of fractions as an example, we have that:

(a/b)/(c/d).

Hence the quotient is:

a/b x d/c.

For this problem, the division is:

x/(-5/12).

Hence:

Thus the quotient is given by:

-12x/5.

Meaning that she must multiply x by -12/5 to find the answer of the division of x by -5/12.

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Answer:

50!!

Step-by-step explanation:

The teacher buys enough pencils for 10 of her students. She gives each student 5 pencils. How many pencils did she give away altogether?

10 x 5 = 50

Answer:

write any one positive aspect of your religion

Answer:

The compass is placed at point a and point b, then two arcs are drawn respectively.

A line is drawn from the arcs passing through element being bisected.

[tex]{}[/tex]

The proportion of Trick-or-treaters not dressed as Snow white are 5/9.

A proportion may be defined as the way of representation of numbers or letters in the form of ratios which are made equal to each other. For example, if there are 1 mango and 2 bananas then the ratio is written as 1:2 that is for every 1 mango there are 2 bananas and there are 1/3 mangoes and 2/3 bananas.

Total number of Trick-or-treaters = 9

Total number of Trick-or-treaters dressed as Snow white = 4

Total number of Trick-or-treaters not dressed as Snow white = 9-4 = 5

Thus, Proportion of Trick-or-treaters not dressed as Snow white = 5/9

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Answer:

1

Step-by-step explanation:

What is the smallest possible common factor between 2 numbers? When would that number also be the GCF? When would the lesser of 2 numbers also be the GCF of those 2 numbers?

Answer: The answer would be 0.4 or 4/10

Step-by-step explanation:

The total change in the weight of Callie's cat will be 1 5/8 pounds.

It should be noted that weight is a measurement of the force an acceleration field, particularly the gravitational field of the Earth near the surface, exerts on a particle or object.

From the information that was given, it should be noted that Callie's cat lost 4 1/2 pounds before having surgery and two weeks after having surgery, her cat gained 2 7/8 pounds.

Therefore, based on the information that was illustrated, it should be noted that the change in weight will be the difference between the weights given.

The change in weight will be:

= 4 1/2 pounds - 2 7/8 pounds

= 4 4/8 - 2 7/8 pounds.

= 1 5/8 pounds

Therefore, the change in weight of Callie's cat will be 1 5/8 pounds.

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a) The simple average of the unit prices is $10.45.

b) The total number of units purchased during the first six months is 115.898 units.

c) The average cost of the units purchased is $10.35.

d) The value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19.

An average refers to the mean of a data set.

The average is computed as the total value divided by the number of values in the data set.

Month    Unit Price     Total  Value    Units

February   $10.00             $200         20.000

March          10.60               200          18.868

April             11.25               200           17.778

May              9.50               200          21.052

June            9.20               200           21.739

July             12.15               200           16.461

Total prices $62.70     $1,200          115.898

Simple Average = $10.45 ($62.70/6)

The average cost of the purchased units = $10.354 ($1,200/115.898)

Thus, the value of Neuer's mutual fund holdings on July 31, if the unit price on that date is $11.90, is $1,379.19 (115.898 x $11.90).

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Answer:

  f(2) = 3

Step-by-step explanation:

You want the value of f(2), given the graph of f(x).

The value of the function for a given argument is found by locating the point on the graph with an x-coordinate equal to the argument. The y-coordinate of that point is the function value.

See the attachment.

The y-coordinate associated with the point that has an x-value of 2 is 3.

  f(2) = 3

The temperature at an altitude of 11,000 ft is found to be 47.6 Degree Fahrenheit.

The plane is at ground level, with a temperature of 59.7 degrees Fahrenheit. The temperature drops by 1.1 degrees Fahrenheit for every 1,000 feet.

Initial Temp = 59.7 Fahrenheit

Distance Covered = 11,000 Ft

As the plane stands there, the ground level is zero feet.

Later, it soars into the sky at 11,000 feet.

= 11×1,000

Temperature drops by 1.1 degrees Fahrenheit for every 1,000.

As a result, at 11,000 feet, the temperature will drop 11 times,

= 11×1.1

or 12.1 degrees.

Therefore, at 11,000 feet, the temperature will be Fahrenheit,

= 59.7 - 12.1

= 47.6 degree Fahrenheit

Thus, the temperature at an altitude of 11,000 ft is computed as 47.6 degree Fahrenheit.

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Answer: WX, ZY and WX and AB.

The 2nd one is correct.

At time t = 0.4191 and  t = 7.456, rocket was at the height of 50 feet;

Given equation; h = 126t - 16t²;

when rocket's height is 50 feet;

126t - 16t² = 50

16t² - 126t + 50 = 0

Using quadratic formula;

t = {126 ±√(-126)² - (4)(16)(50)}/2(16)

After solving; t =0.4191 and t = 7.456

Therefore, at time t = 0.4191 and  t = 7.456, rocket was at the height of 50 feet;

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Based on the calculations, the ratio of water to cement (W:C) is equal to 1:1.

A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Given the following data:

Substituting the given parameters into the formula, we have;

Therefore, the ratio of water to cement is given by:

Ratio of water to cement, W:C = 3:3

Ratio of water to cement, W:C = 1:1.

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Answer:

Child ticket: 12 dollars

Total price: 64 dollars

Step-by-step explanation(Child ticket price):

[tex]T = X(1 - P\%)\\T = 20(1 - 40\%)\\T = 20(1 - 0.4)\\T = 20(0.6)\\T = 12[/tex]

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

Step-by-step explanation(Total price):

[tex]T(12) * 2 + (20.00 * 2) = \$64[/tex]

Hope this helps.

Answer:

0.745/9.089

Multiply numerator and denominator by 1000

=745/9089

Answer:

32

Step-by-step explanation:

32 divided by 4 is 8

8 + 17 = 25

There's your answer!

Answer:16

Step-by-step explanation:First you would have to subtract 17 from 25 and you'd get 8. Then you multiply 8 by 4 and you'll get 16 as your answer.