The perimeter of the pentagon below is 62 units. Find the length of side QR.
Write your answer without variables

Answer: 114.

Step-by-step explanation: This would be an equation to set up. We have all three parts of the equation: The sum of the two numbers (236), one of the integers (122), and then an unknown number, (let's call it x).  Since 236 is the total, 122 is one of the numbers, we need to look for the unknown number, x. Then we would set it up as 122+x=236.  Subtract 122 to both sides, to get 114.

Answer:

3=-4x+3y or -4x+3y=3

Step-by-step explanation:

it perpendicular

The greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet is 5.

Given that:-

Number of roses Mary has = 65

Number of tulips Mary has = 104

We have to find the greatest number of bouquets they can be divided into if there will be the same number of roses in each bouquet and the same number of tulips in each bouquet.

HCF (65, 104) = 13

Hence, the groups of 13 roses and 13 tulips will together make a bouquet.

From 65 roses, 65/13 = 5 bouquets can be made.

From 104 tulips, 104/13 = 8 bouquets can be made.

Min (5,8) = 5.

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The slope of the line is 2 / 3.

The slope of a line can be found as follows:

The slope of a line is change in y with respect to change in x.

In other words, the slope of a line is rise over run.

Therefore,

slope = y₂ - y₁ / x₂ - x₁

Using (0, 3)(-3, 1)

Hence,

x₁ = 0

x₂ = -3

y₁ = 3

y₂ = 1

Therefore,

slope = 1 - 3 / -3 - 0

slope = -2 / -3

slope = 2 / 3

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Answer:

9 mileds

Step-by-step explanation:

The expression y=[tex]x^{p} +2x^{q}[/tex]. [tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function. The p and q values are 11 and 5.

Given that,

The expression y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=11x^{10}+10x^{4}[/tex], where dy/dx is derived function.

Derived function means for any value of the independent variable, the value of another function is the instantaneous rate of change of the specified function at that value of the independent variable.

We have to find the p and q values.

Take expression

y=[tex]x^{p} +2x^{q}[/tex]

[tex]\frac{dy}{dx}=px^{p-1}+2qx^{q-1}[/tex]

[tex]11x^{10}+10x^{4}=px^{p-1}+2qx^{q-1}[/tex]

Here,

we can see p=11 and

2q=10

q=5

Therefore, the p and q values are 11 and 5.

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Answer: 12 cups

Explanation

Anna needs 6 pint of milk to produce yoghurt

1 pint = 2 cups

let cups of milk be x

1 pint of milk will give 2 cups

6 pints of milk will give x cups of milk

1 pint = 2cups

6 pints = x cups

Cross multiply

1 * x = 2 * 6

x = 12 cups

Therefore, Anna will need 12 cups of milk to produce a yoghurt.

The correct answer is [G] x-4

x-4 is the expressions is a factor of the expression x² - 6x + 8.

The positive integers that can divide a number evenly are known as the factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.

The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.

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Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle 4[/tex] and [tex]\angle 5[/tex] are supplementary since they are consecutive interior angles.

If a telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 25 % of her calls, there is no answer or the line is busy. She sells subscriptions to 9 % of the remaining calls. The proportion of calls she make a sale is: 189/ 25.

Given data ;

Calls without answer or line busy  = 25%

Subscription sold out of remaining calls = 9%

Now let determine the proportion of calls she make a sale :

Proportion = 9 % ×  ( 100 % - 25 %)

Proportion = 9 % × 75 %

Proportion = 7.56 %

Since we were told the  proportion of calls she make a sale we would have to convert the percentage into fraction :

Proportion :

Proportion = 7.56 %

Proportion = 189 / 25  

Therefore we can conclude that the proportion  is 189 / 25.

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Given that tanx and sinx is negative, determine sin(2x), cos(2x), and tan(2x) Write the exact answer. Do not round: Answer Keyboard sin(Zx) cos(2x) Submit Ar

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Answer:Explanation:

No

The sum of the interior angles of a triangle is always 180°. in this case, the sum is:

Then,

46 + 82 + 50 = 178

Since 178 and 180 are distinct, 46°, 82°and 50°​ can't be the angle measures of a triangle.

The slope of the line has increased, meaning it has become a positive number. This shift means that this year the data points were placed higher than the previous year.

For the given high school committee officers.

We need to find the sharing between the committee officers.

AS shown:

Amber is a common between A and B

Calipso is a common between A and C

Juan is a common between A and D

Sam is a common between B and C

So, the figure represents the situation will be option A

Answer:

3671.8, 3576.4

Step-by-step explanation:

The third angle of the triangle is 19°.

Let the first length be a. Then,

[tex] \frac{a}{\sin 85^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ a=\frac{1200\sin 85^{\circ}}{\sin 19^{\circ}} \approx 3671.8[/tex]

Let the second length be b.

[tex] \frac{b}{\sin 76^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ b=\frac{1200\sin 76^{\circ}}{\sin 19^{\circ}} \approx 3576.4[/tex]

She spend J$10039.48 in Jamaican currency on souvenirs.

The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service. The US dollar is the country's recognized unit of exchange. A currency is the standardization of money, including banknotes and coins, that is used or in circulation as a means of exchange. A currency can also be defined more broadly as a system of money that has been used often over time within a particular setting, particularly by residents of a country state.

Given Data

While on a holiday in Montego Bay, Jamaica, Marilyn shops for souvenirs for friends. She has budgeted C$120 for souvenirs.

She spend a certain amount in Jamaican currency is:

CD$120(83.6623)

J$10039.48

She spend J$10039.48 in Jamaican currency on souvenirs.

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Answer:

Mai 19

Bill 29

Dante 57

Step-by-step explanation:

assume

mai = X

Bill = Y

Dante = Z

X + Y + Z = 105

Z = 3X

Y = 10 + X

then

X + Y + Z = X + 3X + 10 + X

5X + 10 = 105

5X = 95

X = 19

Y = 29

Z = 57

Using it's concept, the probabilities are given as follows:

a) Both go off on schedule: 0.30 = 30%.

b) Both go off on schedule: 0.2 = 20%.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

From the text of the problem, the probability of A and not B is of 0.2, that is:

A x (1 - B) = 0.2.

We can multiply the probabilities as the events are independent.

In item a, the probability of neither is of 0.2, hence:

(1 - A) x (1 - B) = 0.2.

From the first equation, we have that:

A = 0.2/(1 - B).

From the second equation, we have that:

(1 - A) = 0.2/(1 - B).

Hence:

A = 1 - A

2A = 1

A = 0.5.

Then we can find B as follows:

(1 - A) x (1 - B) = 0.2.

1 - B = 0.2/0.5

1 - B = 0.4

B = 0.6.

The probability of both is:

A x B = 0.5 x 0.6 = 0.30 = 30%.

For item b, we consider that:

(1 - A) x B = 0.3.

We also have that:

A x (1 - B) = 0.2.

From the first equation:

B = 0.3/(1 - A).

Then, replacing on the second:

A x (1 - 0.3/(1 - A)) = 0.2

Which has a solution of:

A = 0.5, B = 0.4.

Hence the probability of both is:

0.4 x 0.5 = 0.2 = 20%.

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We have the following function:

a) The initial height occurs at t=0. By substituting this value into the function, we get

which gives

since sin(-Pi/2) is equal to -1, we have

Then, H(0)= 5, so the height is 5 feets.

b) The car will make a full rotation when the argument is shifted 2Pi:

at this point H(t) must be equal to 5 feets. Then, we have

and we must find t. If we move +15 to the left hand side, we obtain

By moving the coefficient 10 the the right hand side, we get

we can note that when

this implies that the argument of our last result is

By moving 2Pi to the right hand side, we have

Now, by moving 2Pi to the right hand side, we have

which gives

so, t is given by

That is, n 1 minute, the car will take one full rotation.

c) The maximum height of the car ocurrs at t=0.5 min because in one minute it take one full rotation. Then, at t=1/2 we get

which gives

that is, the maximum height is 25 feets

In geometry, you can use deductive rules to prove conjectures.

Geometry is defined as a subfield of mathematics that examines the measurement and relationships of surfaces, solids, solid surfaces, angles, and points. The calculation of a triangle's angles is a geometry example.

Geometry will categorize, quantify, and lack a counterexample. Once a concept has been defined, it can be utilized in subsequent definitions; for instance, parallel lines can be used in the definition of a parallelogram once they have been defined. classification, counterexample, quantification, and parallelogram.

Given Data

In geometry, you can use deductive rules to

In geometry, you can use deductive rules to prove conjectures.

In geometry, deductive rules can be used to demonstrate whether a particular assertion or conjecture is true or untrue. We narrow down a result proving a statement must be true or untrue by using deductive principles, such as definitions, postulates, and other theorems, in a logical order.

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The information that would be included or entered into the application or online tool for personal budgeting should include but not be limited to:

The features that the tool will have are:

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Answer:

angle 1 = 34 degrees

Step-by-step explanation:

Angle 2 and angle 6 are corresponding, therefore they are congruent and have a measure of 146 degrees.

angle 1 and angle 2 form supplementary angles so:

angle 1 = 180-angle 2

angle 1 = 180 - 146

angle 1 = 34 degrees

Recall that [tex]\phi = 1 + \frac1\phi[/tex].

In the integral, substitute [tex]y=1+x^\phi[/tex], so that [tex]x=(y-1)^{1/\phi} = (y-1)^{\phi-1}[/tex] and [tex]dx = (\phi-1) (y-1)^{\phi-2} \, dy[/tex]. We have

[tex]\displaystyle I = \int_0^\infty \frac{dx}{(1+x^\phi)^\phi} \\\\ ~~~~ = \frac1\phi \int_1^\infty \frac{(y-1)^{\phi-2}}{y^\phi} \, dy[/tex]

Substitute [tex]y=\frac1z[/tex] and [tex]dy=-\frac{dz}{z^2}[/tex] to transform [tex]I[/tex] to

[tex]\displaystyle I = \frac1\phi \int_0^1 \left(\frac1z-1\right)^{\phi-2} z^{\phi-2} \, dz \\\\ ~~~~ = \frac1\phi \int_0^1 (1-z)^{\phi-2} \, dz[/tex]

Finally, substitute [tex]u=1-z[/tex].

[tex]\displaystyle I = \frac1\phi \int_0^1 u^{\phi-2} \, du \\\\ ~~~~ = \frac1\phi \cdot \frac1{\phi-1} = \frac{\phi-1}{\phi-1} = \boxed{1}[/tex]

Th length of the garden when the teacher bought 50 feet of fence is 17 feet.

From the information, the width needs to be the same size as the shed which is 8ft and she bought 50 feet of fence and wants the largest garden she can make,

It should be noted that perimeter is calculated as:

= 2(Length + Width)

In this case, the perimeter is 50 feet.

2(Length + Width) = 50

2(Length + 8) = 50

2L + 16 = 50

2L = 50 - 16

2L =34

Divide

L = 34/3

L = 17 feet.

The length is 17 feet.

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The linear function which can be used to represent the situation is y = 6.4x + 1900 and airplane weight if it is carrying 60 gallons of fuel is 2,284 pounds

y = mx + b

where,

Now, we can use the two sets of data points given to us to first solve for the slope m as:

m = (2188 - 2060) / (45 - 25)

= 128 / 20

= 6.4

y - yo = m(x - xo)

y - 2060 = 6.4(x - 25)

y - 2060 = 6.4x - 160

y = 6.4x - 160 + 2060

y = 6.4x + 1900

x = 60

So,

y = 6.4x + 1900

y = 6.4(60) + 1900

y = 384 + 1900

y = 2,284 pounds

Therefore, the weight of the airplane if it is carrying 60 gallons of fuel is 2,284 pounds

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To find the arc length we need to know the angle subtended by the arc.

From the diagram we notice that angle MNK is of 180°.

We also notice that:

Then the angle subtended by the arc MKL is 218°.

Now that we know this we need to remember that the arc length is given by:

in this case the radius is 3 ft (The radius is half the diameter) then we have that:

Therefore the arc length is 11.4 ft.

Answer: 53.1

Step-by-step explanation: Divide 35.40 by 2 to get 17.7. now add 35.40 with 17.7 and you get 53.1

Answer:

2.4m

Step-by-step explanation:

The question has already done most of the work for you. To find the initial height, simply set t = 0 and substitute it into the function.

[tex]d(0) = {0}^{2} + 2.4 + 3.2(0) \\ = 2.4m[/tex]

Given:

The radius of the circle = 2.4 kilometers

The measure of the arc = 150°

The length of the arc is given by the formula:

Note: we will convert the angle from degrees to radian

So, the length of the arc =

So, the answer will be option D. 2π km