Send help! Let angle 1 and angle 2 be complementary angles, and let angle 2 and angle 3 be supplementary angles. If angle 1 = x and angle 2 = 2x, determine x. Then find angle 1, angle 2, and angle 3.

Answer:

7/20 miles

Step-by-step explanation:

get a common denominator

subtract the numerators

then you have the fraction she biked

Answer:

AAA

Step-by-step explanation:

There's no angle angle angle (AAA) because all triangle's angles add up to 180

Answer:

12

Step-by-step explanation:

Using the side splitter theorem, [tex]\frac{x}{32}=\frac{9}{24} \implies x=12[/tex].

The value of x is 12, option (B) is correct.

A line parallel to one side of a triangle splits the other two sides of the triangle proportionally if the line also crosses the other two sides.

Given that,

Two lines are parallel to each other,

And length of sides are,

32 , x , 24 and 9.

By angle proportionality theorem,

32 / x = 24 / 9

x = (32 × 9) / 24

x = (4 × 9) / 3

x = 4 × 3

x = 12

The required length of x is 12.

Hence, option (B) is correct.

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Answer: E

Step-by-step explanation:

The random variable x's mean and standard deviation are 8 and 2, respectively. W=7+ 4x is the formula for the random variable w. The mean of w is E(W) =39

A dataset's mean is calculated by dividing the sum of all values by the total number of values. The term "average" is frequently used to describe it because it is the most widely used central tendency metric.

Divide the entire number of values by the total number of numbers to find the average. A mean is the term used to describe the mathematical average of a set of two or more data values. Average is also referred to as mean or arithmetic mean.

The mean is the average value of the data. It's easy to calculate: just add up all the numbers, then divide by the total number of numbers. Or, to put it another way, it is equal to the sum divided by the quantity.

The mean is then determined as follows:

E(W) = E (7 + 4X)

This results

E(W) = 7 + 4 E (X)

We thus have:

E(W) = 7 + 4 x 8

E(W) =39

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Standard deviation = 8 and mean = 39.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.

Given, the formula for mean is E(W) = 7 + 4(X)

∴ E(W) = 7 + 4E(X)

Mean, E(X) equals to 8, hence substituting in the above equation, we get,

E(W) = 7 + 4×8

⇒E(W) = 39

Since, E(W) = 7 + 4(X)

Var(W) = Var(7) + Var(4X)

Since, Var(constant)=0,

Var(W) = Var(4X)

Var(W) = 4²×Var(X), where Var(X)=σₓ²

⇒ Var(W) = 16×σₓ², where σₓ²=2²

⇒ Var(W) = 16×4

⇒ Var(W) = 64

Standard Deviation (SD) = √64 = 8

Thus, standard deviation = 8 and mean = 39.

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Answer:

x= 9

Step-by-step explanation:

2(x + 5 ) = 3x + 1

expand the bracket first

2x + 10 = 3x + 1

then collect like terms

2x-3x = 1 - 10

-1x = - 9

and the last step is divide both side by -1

then x = 9

The change in Ms Smith's saving account balance each month due to her car payments is of:

-$267.75.

A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

In this problem, the monthly balance change is obtained as follows:

Monthly balance change = Yearly balance change / 12.

(as an year is composed by 12 months).

As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:

-$3,213.

The payments are equal each month, hence the monthly change is of:

Monthly balance change = -3213/12 = -$267.75.

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[tex]~~~~~~~~~~~~\stackrel{\textit{\LARGE Sydney}}{\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}}}[/tex]

[tex]A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right) \\\\ \qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 100\\ r=rate\to 0.8\%\to \frac{0.8}{100}\dotfill &0.008\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=100\left[ \cfrac{\left( 1+\frac{0.008}{12} \right)^{12 \cdot 10}-1}{\frac{0.008}{12}} \right]\left(1+\frac{0.008}{12}\right) \\\\\\ A=100\left[ \cfrac{\left( \frac{1501}{1500} \right)^{120}-1}{\frac{1}{500}} \right]\left(\frac{1501}{1500}\right) \implies {\Large \begin{array}{llll} A \approx 12497.05 \end{array}}[/tex]

Answer:

112/1000

Step-by-step explanation:

Just put 1 under decimal point and just add as many zeros as digits after that

The four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.

A relation between different terms on either side of the equal sign is described by a straightforward equation.

Simple equations also follow one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three primary versions of the set of equations: point-slope form, standard form, or slope-intercept form.

So, Shannon's error would be:

In a rectangle, the adjoining sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of parallel lines is equal, and the slope, of a line perpendicular to some other line with a slope, m, is -1/m , thus the slopes of the central axis should be equal, which also gives:

Two sets of systems of equations with equal slopes should make up the equation: B. Y = -x + 6 and Y = -x - 5 are a pair.

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 correspondingly.

Therefore, the four equations' coefficients of x can only take two values, thus if one of those values is m, the other solution will be -1/m.

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Correct question;
Shannon says that the lines y=-3x-4,y=-(1)/(3)x+6,y=-4x-5, and y=(1)/(4)x-5 could represent the sides of a rectangle. Explain Shannon's error.

The derivative of the given function sin(xy)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

The given equation is-

sin(xy) = 3x − 2y

Be sure to account for both sides of this argument.

d/dx(sin(xy)) = d/dx(3x − 2y)

Differentiate the equation's left side.

Set the left side equal to a right side to reform the equation.

x.cos(xy).y' + y.cos(xy) = 3

Solve for y'.

y' = 3sec(xy)/x - y/x

Thus, replace y' with dy/dx

dy/dx =  3sec(xy)/x - y/x

Thus, the derivative of the given function sin(x y)=3x−2y is obtained as;

dy/dx =  3sec(xy)/x - y/x

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The value of AC is 22.5

The property of three parallel lines and their transversals is used to solve this sum. The property explains that if the ratio of the corresponding intercepts made on any other transversal by the same parallel lines is the same as the ratio of the intercepts made on a transversal formed by three parallel lines.

XY ║seg AC

2AX = 3BX

XY = 9

Since, 2AX =3BX

∴ AX÷ BX = 3÷2

AX + BX÷ BX = 3+2÷2

AB ÷ BX = 5÷2

Δ BCA ~  ΔBYX (SAS test of similarity)

( The SAS similarity test determines whether two triangles are similar if the ratio of the lengths of two sides of one triangle equals the ratio of the lengths of two sides of another triangle, and the included angles are equal.)

∴ BA ÷ BX = AC ÷ XY ( Corresponding sides)

∴ 5÷ 2 = AC ÷ 9

∴ AC = 22.5

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The value of  [tex]\sqrt{0.9}[/tex] is 0.94868329805. You can't get an accurate answer since the square root is an irrational quantity. But I suppose you could just make it simpler.

The value that a number produces when it is multiplied by itself is known as the square root of the number. The square root is denoted by the radical sign. For instance, 16 Equals 4. The root symbol or surds is another name for the radical symbol.

The radical symbol for the number's root is "" in this instance. The square of the positive number is represented by multiplying it by itself. The original number is obtained by taking the square root of the square of a positive number. For instance, the square of three is nine. and the square root of 9, √9 = 3.

Since, 3*3*0.1

= 9*0.1

= 0.9

[tex]\sqrt{3*3*0.1} \\[/tex]

= 3([tex]\sqrt{0.1}[/tex])

[tex]\sqrt{0.9}[/tex] ≈ 0.94868329805

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Correct Question:

What is the value of  [tex]\sqrt{0.9}[/tex]

Answer:

(4) (-1,6)

Step-by-step explanation:

f(x) = x² - 3x + 4

1) (0,4) ==>x=0 and f(x)=4

4 = 0² - 3(0) + 4

4 = 0 + 4

4 = 4 ==> true X

2) (1.5,1.75)==> x=1.5 and f(x)=1.75

1.75 = (1.5)² - 3(1.5) + 4

1.75 = 2.25 - 4.5 + 4

1.75 = 2.25 - 0.5

1.75 = 1.75 ==> true  X

3) (5,14)

14 = (5)² - 3(5) + 4

14 = 25 - 15 + 4

14 = 10 + 4

14 = 14  ==> true X

4) (-1,6)

6 = (-1)² - 3(-1) + 4

6 = (|-1|)² - (-3) + 4  ==> the square of a negative number is equal to the square

                              of the absolute value of that number since the square of

                             a real number is always positive

6 = (1)²+ 3 + 4  ==> subtracting a negative number is equivalent to adding

                          the positive number

6 = 1 + 3 + 4

6 = 4 + 4

6 = 8  ==> false √√

Hence, the answer is (4) (-1,6).

The length AC of the triangle ABC is approximately 12.083 centimeters.

The law of sine is a relationship between the sides and the angles of the triangle, which is defined below:

AB / sin C = AC / sin B = BC / sin A

Where:

First, determine the measure of angle C:

AB / sin C = BC / sin A

sin C = (AB / BC) · sin A

sin C = (8.2 / 13.5) · sin 81°

C ≈ 36.865°

Second, determine the measure of angle B:

B = 180° - A - C

B = 180° - 81° - 36.865°

B = 62.135°

Third, determine the length of side AC:

AC / sin B = BC / sin A

AC = BC · (sin B / sin A)

AC = 13.5 · (sin 62.135° / sin 81°)

AC ≈ 12.083 cm

The length AC is approximately equal to 12.083 centimeters.

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The pints of each of the two existing types of drink must be used to make 180 pints of a mixture that is 75% pure fruit juice is 72 and 108 pints respectively.

Let juice A = a

60% pure fruit juice

Let juice B = b

85% pure fruit juice

We need to make 180 pints of juice from both

a + b = 180

represented in terms of pure fruit

a = 0.60; b = 0.85 ;

Our mixed fruit juice from a and b should be 75% pure fruit = 0.75

Mathematically,

0.60a+ 0.85b = 180(0.75)

0.60a + 0.85b =135

Multiply this equation by 100

60a+ 85b = 13500

Now we have two equations for two variables,

a + b = 180 and

60a+ 85b = 13500

Multiply equation 1 by 60,

we get,

60a + 60b = 10800

On solving these equations we get,

b = 108

Substitute b = 108 into the second equation

60a+ 85(108)= 13500

60a+ 9180 = 13500

a = 72

Therefore , the pints of juice A required is 72 pints and the pints of juice B required is 108 pints.

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Answer:

Step-by-step explanation:

The Royal Fruit Company produces two types of fruit drinks. The first type is 35% pure fruit juice, and the second type is 85% pure fruit juice. The company is attempting to produce a fruit drink that contains 75% pure fruit juice. How many pints of the two existing types of drink must be used to make 60 pints of a mixture that is 75% pure juice?

Answer:

533

Step-by-step explanation:

3 hours = 180 minutes

2400 : 180 = x : 40

x = 2400 * 40 / 180

x = 2400 * 4 / 18

x = 2400 * 2 /9

x = 800 * 2 / 3

x = 1600/3

x = 533.333333

x = 533

The expression to determine the number of bags is 2/3 x = 2 1/2 and the number of bags requited is 3 3/4 bags

Information from the problem

Maya rakes up the leaves and wants to put them into bags that hold 2\3 of a cubic yard

she rakes 2 1\2 cubic yards of leaves

one bag = 2/3 cubic yard

total leaves raked = 2 1/2 cubic yard

the number of bags required is how many 2/3 cubic yards are there in 2 1/2 cubic yard. this is solved by division

let the number of bags be x

2/3 cubic yard * x = 2 1/2 cubic yard

2/3 x = 2 1/2

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

x = 15/4

x = 3 3/4 bags

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The table that contains only viable solutions if b represents the number of books he orders and w represents the total weight of the books, in ounces is the second table on the image given at the end of the answer.

The variables for this problem are given as follows:

To obtain the viable solutions, we must consider the input variable. The number of books is a countable amount, meaning that it can only assume non-negative integer values.

Thus the first table is incorrect, as it contains a negative amount of books, and the second table is the one that contains only viable solutions in the context of this problem.

The table is given by the image shown at the end of the answer.

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The greatest amount of sap collected from any one tree is two times.

The maximum amount of sap that can be gathered from a single tree is two times greater than the minimum amount. SAP enables businesses to innovate on anything from cancer therapies to flood mitigation. We support life-saving research and are deeply committed to social responsibility and sustainability. At SAP, we collaborate to create innovations.

Work in a stimulating and rewarding environment by joining us. Minerals and nutrients can be found in tree sap. In the spring, when new buds are growing, a sticky substance that travels through the tree and out onto the branches helps the tree produce energy. Sugars are created as a result of photosynthesis and sent back into the tree, where they serve as sustenance for the tree's growth.

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Correct Question:

The greatest amount of sap collected from any one tree is _____________

After doing the equitation the at rate of $15 per week.

How to do graph representation?

Graph representation is a way of visualizing data as a graph or chart. It is used to easily identify relationships between data points and to illustrate trends in the data. Graphs can be used to present data in a variety of ways, such as bar graphs, line graphs, pie charts, scatter plots and more. Graphs are especially useful when trying to compare two or more sets of data and to highlight any patterns or trends that may exist. Additionally, graphs are often used to represent numerical data in a more visually appealing way. By using graphs, it is easier to identify relationships, trends and outliers in the data. Graphs also help to make data easier to interpret and understand.

Carson owes = $110

At rate of $15 per week.

The graph representation will follows:

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Answer:

7

Step-by-step explanation:

Experimental probability is based on the actual results of an experiment (gathered by experimenting repeatedly).  

It is calculated by dividing the recorded number of times an event happens by the total number of trials in the actual experiment:

[tex]\boxed{\textsf{Experimental Probability} = \dfrac{\textsf{Number of times an event happens}}{\textsf{Total number of trials}}}[/tex]

As the number of trials increases, we would expect for the experimental probability to get closer to the theoretical probability.

Given:

The experimental probability of drawing a short straw is:

[tex]\implies \sf P(short\;straw)=\dfrac{35}{50}=\dfrac{7}{10}[/tex]

If Laura conducts 10 further trials of the experiment, based on the results in the table, the number of additional trials that will have a result of a short straw being drawn is:

[tex]\begin{aligned}\implies \textsf{Additional trials (short straw)} &=\sf experimental\;probability \times number\;of\;trials\\&= \sf \dfrac{7}{10} \times 10\\&= \sf 7\end{aligned}[/tex]

The given coordinates represent a function and at f(-7) equals to 9.

We have the following coordinates -

(-7, 9) (-4, 10) (2, 6) (-6, 3)

Yes, these coordinates represent a function as a unique value of [x] has only one value of [y]. At x = -7, we can write -

f(-7) = 9

Therefore, the given coordinates represent a function and at f(-7) equals to 9.

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The increase in the orbital period is by a factor of k^3/2. Option D

From the Kepler's laws, we know that the square of the period of the planet is directly proportional to the cube of the distance of the planet from the sun. We can see that this has been typified by the expression; T^2 =A^3 where T is the period of the planet and A is the distance between the planet and the sun.

Now, we can see that from the relationship, If planet Y is k times the mean distance from the sun as a planet X then the orbital period would be increased by a factor of about k^3/2.

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The simplified form can be written as -

7.8y + 1.4z

We have the following expression -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

We have -

6(0.7y + 0.8z) − 4z − 6(−0.1z − 0.6y)

(6 x 0.7y + 6 x 0.8z) - 4z + 6 x 0.1z + 6 x 0.6y

4.2y + 4.8z - 4z + 0.6z + 3.6y

7.8y + 4.8z - 3.4z

7.8y + 1.4z

Therefor, the simplified form can be written as -

7.8y + 1.4z

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Answer:

Step-by-step explanation:

Solve for x:

2 cos* (2) =

Divide both sides by 2:

cost (2) =

Take the logarithm base cos(2) of both sides:

Answer:

2inn

X=

iT+ log(-cos(2))

log(2)

i7+ log(-cos(2))

for NE Z

Hence, the three side length of two triangles are same so they are congurent.  

What is the congurency?

Two shapes are congruent if they are the same (shape and size)- in other words, if the lengths of the sides and the angles are the same.

It is often useful to know when two triangles are congruent.

Here given coordinates of the triangle [tex]FGH[/tex] and triangle [tex]JKL[/tex] are

[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex].

So, the distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between [tex]FG[/tex]  is

[tex]d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]

Distance between [tex]GH[/tex]  is

[tex]d=\sqrt{(-9-(-2))^2+(10-(-7))^2}\\\\d=\sqrt{(-9+2)^2+(10+7)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]

Distance between [tex]HF[/tex]  is

[tex]d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]

Distance between [tex]JK[/tex]  is

[tex]d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]

Distance between [tex]KL[/tex]  is

[tex]d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]

Distance between [tex]LJ[/tex]  is

[tex]d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]

Since, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]

Hence, the three side length of two triangles are same so they are congurent.  

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x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

What is Substitution method to solve equations?

The method of substitution involves three steps: Solve one equation for one of the variables. Substitute (plug-in) this expression into the other equation and solve. Resubstitute the value into the original equation to find the corresponding variable. he substitution method is the algebraic method to solve simultaneous linear equations.

Given Equations :

y = 8x +6

10x - 5y = 30

A) Solve equation [1] for the variable  y

    [1]    y = 8x + 6

B)  Plug this in for variable  y  in equation [2]

  [2]    -5•(8x+6) + 10x = 30

  [2]     - 30x = 60

C)  Solve equation [2] for the variable  x

  [2]    30x = - 60

  [2]    x = - 2

D)  By now we know this much :

   y = 8x+6

   x = -2

E)  Use the  x  value to solve for  y      y = 8(-2)+6 = -10

Solution : {y,x} = {-10,-2}

Hence , x = -2 and y = -10 is the solution of the equations y = 8x +6 and 10x - 5y = 30.

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Part (a)

Part (b)

Yes, the triangles are congruent by RHS.