Select the correct answer. The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system? x + 3y = 42 2x − y = 14 A. Multiply the second equation by -3. The solution is x = 12, y = 9. B. Multiply the second equation by -2. The solution is x = 12, y = 10. C. Multiply the second equation by 2. The solution is x = 15, y = 9. D. Multiply the second equation by 3. The solution is x = 12, y = 10.

The Trigonometric function sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

The easiest way is to use the Pythagorean Identity to find both cos A and sin B. Then use the sum/difference angle identity for sine.

The trigonometric Pythagorean identity tells us that,

[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1

which follows directly from the geometric identity for right triangles and the fact that,

sinθ = y/r and cosθ = x/r

If r is the distance (x,y) is from the origin, then

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

[tex](x/r)^{2}[/tex] + [tex](y/r)^{2}[/tex] = 1(divide both sides by [tex]r^{2}[/tex])

[tex]cos^{2}[/tex]θ +  [tex]Sin^{2}[/tex]θ  = 1

Anyway, if we know sin A (and which quadrant it ends in), we can solve for cos A and vice versa:

[tex]Sin^{2}[/tex]θ + [tex]cos^{2}[/tex]θ = 1

[tex](1/3)^{2}[/tex] +  [tex]cos^{2}[/tex]θ = 1

⇒ cos A = [tex]\sqrt{1-(1/3)^{2} }[/tex] = [tex]\frac{2\sqrt{2}}{3}[/tex]

cosθ is always negative in this quadrant.

Therefore,

cos A = -[tex]\frac{2\sqrt{2} }{3}[/tex]

Similar reasoning can be done with cos B = [tex]\frac{3}{4}[/tex] to show that sin B = -[tex]\frac{\sqrt{7} }{4}[/tex]

Now that we have all the necessary elements, we can use the sum/difference angle identity:

Sin(A-B) = sin A cos B - cos A sin B

= ( [tex]\frac{1}{3}[/tex] × [tex]\frac{3}{4}[/tex] ) - ( (-[tex]\frac{2\sqrt{2} }{3}[/tex] ) × (-[tex]\sqrt{7[/tex]/4) )

= (3 ÷ 12) - (2[tex]\sqrt{14}[/tex] ÷ 12)

= (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

We get sin(A - B) = (3 - 2[tex]\sqrt{14}[/tex]) ÷ 12

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The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.

Given that,

Apples and grapes are sold at Arianys' farm stand. The price per pound for apples is $4 while the price per pound for grapes is $3.75. 64 pounds of apples and grapes were sold for a total profit of $251.75 for Arianys.

We have to find the number of the sold apples and pounds of grapes should be calculated.

a declaration that two mathematical expressions' values are equal (represented by the symbol =).

We get the equations as,

3.75x+4y=251.75

y=-0.93x+62.93---->equation(1)

x+y=64

y=-x+64------>equation (2)

We get the points as

For equation (1),

(0,62.93) and (67.66,0)

For equation (2),

(0, 64) and (64,0)

If we draw a graph we get 2 lines intersect at a point (24, 30).

Therefore, The number of pounds of grapes is 24 sold and the number of pounds of apples sold is 30.

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There are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.

According to the question,

We have the following information:

Positive integers between 100 and 999 including both these integers which are divisible by 3 or 4

Now, the number of positive integers between 100 and 999 is (999-100+1) or 900.

Now, the numbers divisible by 3 will be in multiplication of 3.

So, number which are divisible by 3:

900/3 = 300

Now, the numbers divisible by 4 will be in multiplication of 4:

So, the numbers which are divisible by 4:

900/4 = 225

Now, there are also numbers in numbers divisible by which are divisible by 3. So, they are 1/3 of the numbers divisible by 4:

225/3

75

Now, total numbers divisible by 4:

225-75

150

Now, total numbers divisible by 3 or 4:

300+150

450

Hence, there are 450 positive integers between 100 and 999 (both included) that are divisible by 3 or 4.

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Answer:The x-intercept is

(-3/2)

The y-intercept is

(0,-3)

Step-by-step explanation:

to find the x and y intercept you have to make x and y equal zero then solve.

finding x

2x+0=-3

2x/2=-3/2

x=-3/2

finding y

2(0)+y=-3

-2        -2

y= -5

8 * 10^9 is 8000000000

just 9 zeros to the 8

Answer:

$500

Step-by-step explanation:

400/40 = 10.  This gives us her hourly rate

50 x 10 = 500

The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that there are 4 yellow, 3 blue, 5 green, 7 red and 2 orange sweets in my bag.

The total sweets = 4+3+5+7+2 = 21

1. the probability of taking out a red sweet is;

7/21 = (7:7)/(21:7)

= 1/3

2. The probability of taking out a green, blue or orange sweet is;

= (5+3+2)/21

= 10/21

Hence, The probability of taking out a red sweet is; 1/3. The probability of taking out a green, blue or orange sweet is; 10/21

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The true statements are:

C. . A line segment consists of two endpoints and all the points between

D. A line has two endpoints.

A line segment is bounded by two distinct points on a line.

How to know which statement is true?

From the definition,.

Also, we know that through two points one and only one line can pass .

Therefore, A line has two endpoints.

So, option C and D are correct.

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m∠W = 33.8° , using inverse trignometric ratio.

What do you mean by inverse trignometric functions?

The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental trigonometric functions. Inverse trigonometric functions are just the inverse functions of these functions. They can also be referred to as cyclometric functions, antitrigonometric functions, or arcus functions. Trigonometry's inverse functions are used to find the angle for any trigonometric ratio.

It is given that VU = 2 units and VW = 3 units and VUW is a right angle triangle , right angled at V.

Using the ratio of tanW,

As we know tanA = P/B where P is the perpendicular and B is the base

In the given triangle VUW,

tanW = VU/VW = 2/3

W = [tex]tan^{-1}[/tex](2/3) = [tex]tan^{-1}[/tex](0.67) = 33.8 degree

Therefore, m∠W = 33.8°

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Answer:

102

7.43 Answer by question

The area of the largest rectangle will be 3.

By using properties of similar triangles we can say that

[tex]\frac{EF}{FB} - \frac{AC}{CB}[/tex]

B / (3 - a) = 4/3

3b = 12 - 4a

4a = 12 - 3b

a = (12 - 3b) / 4

Now as we know area of a rectangle is length * width. let us find the area

A = l * w

A = b * ( (2 - 3b) / 4 )

A = 3b - 3[tex]b^{2}[/tex]/4

Now to find maximum value we will differentiate the area and put it equal to zero.

[tex]D^{1}[/tex] = 3 - 6b/4 = 0

6b/4 = 3

6b = 12

b = 2

and

a = (12 - 3b) / 4

a = 6/4

a = 3/2

So, area will be = 3/2 * 2

Therefore maximum are of the triangle will be 3.

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Answer:

y - 1 =0 (x-2)

Step-by-step explanation:

We are given that a horizontal line which is passing through the point (2,1).

We have to find the equation in point -slope form of the line .

We know that equation of horizontal line is given by

It means y does not vary with x therefore, Slope of line= Slope of horizontal line =0

Point- slope form equation of line

We have,

Substitute the values in the given formula

Then, we get the equation of horizontal line which is passing through the point (2,1) is given by

Hence, the equation of horizontal line which is passing through the point (2,1) is given by y - 1 =0 (x-2)

The time that would be needed for the trip is 2 hours.

It is important to note that the formula that can be used for calculating the time taken will be:

Time = Distance / Speed

where

Distance = 9 1/3

Speed = 4 2/3

Therefore time will be:

Time = Distance / Speed

= 9 1/3 ÷ 4 2/3

= 28/3 ÷ 14/3

= 28/3 × 3/14

= 2 hours

The time is 2 hours.

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The new coordinates of Y and Z will be (-3, 9) and (3, 10), respectively.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

In the direction plane, point X(0,2) is meant the point X(1,- 3).

The rule of the transformation is written as,

(1, -3) ⇒ (0, 2)

(1, -3) ⇒ (1 - 1, -3 + 5)

(x', y') ⇒ (x - 1, y + 5)

Then the translation of the point Y(-2, 4) will be given as,

(x'', y'') ⇒ (-2 - 1, 4 + 5)

(x'', y'') ⇒ (-3, 9)

Then the translation of the point Y(4, 5) will be given as,

(x''', y''') ⇒ (4 - 1, 5 + 5)

(x''', y''') ⇒ (3, 10)

The new coordinates of Y and Z will be (-3, 9) and (3, 10), respectively.

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Answer:

Step-by-step explanation:

$y = -16x^2 + 240x + 115$

$= -16x^2 + 240x + 120 - 5$

$= -16x^2 + 240x + 120 - 5x - 5x$

$= -16x^2 + 240x + 120 - 10x - 5x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 3 - 3$

$= -16x^2 + 240x + 120 - 10x - 5x + x^2 - x^2 + 2x - 2x + x -x + 0

Number of steps that he needed to walk to achieve the goal is 3141 steps

The goal of the Jayden = 10000 steps

The number of steps that he walked = [tex](\frac{1}{19} )^{-3}[/tex] steps

Here we have to convert  the given number of steps to the suitable form for calculation

The number of steps that he walked

[tex](\frac{1}{19} )^{-3}[/tex] steps = [tex]19^3[/tex] steps

Find the power of the number

[tex]19^3[/tex] steps = 6859 steps

Number of steps that he needed to walk to achieve the goal = The goal of the Jayden - The number of steps that he walked

Substitute the value in the equation,

Here we have to sue the subtraction

Number of steps that he needed to walk to achieve the goal  = 10000 - 6859

= 3141 steps

Hence, number of steps that he needed to walk to achieve the goal is 3141 steps

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The equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.

According to the question,

We have the following information:

The line passes through the point (18,-3) with slope -1.

We know that the following formula is used to find the equation of the line passing through a point with the slope which is denoted by m:

(y-y') = m(x-x')

In this case, we have the following values:

m = -1

x' = 18 and y' = -3

Putting these values in the above formula:

y-(-3) = -1(x-18)

y+3 = -x+18

Subtracting 3 from both sides of the equation:

y = -x+18-3

y = -x+15

Hence, the equation of the line that passes through the point (18,-3) with slope -1 is y = -x+15.

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Step-by-step explanation:

Problem #1:

A number is divisible by 4 if the last 2 digits of that number are multiple of 4 . So for example the number 2316 is a multiple of 4 because it ends with " 16 " and " 16 " is a multiple of 4 .

Write a program that prompts the user to enter an integer and displays whether the number is a multiple of 4 or not. The program stops reading integers, when the user inputs a negative value. It shows at the end the total number of values entered which are multiple of 4 .

Sample Run:

Enter an integer: 4

4 is a multiple of 4

Enter another integer: 213

213 is not a multiple of 4

Enter an integer: 2316

2316 is a multiple of 4.

Enter an integer: -20

The total number of integers entered which are multiple of 4 is 2 .

Answer: the answer is 8.70.

Step-by-step explanation:

Since were rounding to the 2 decimal places(hundredths) we can immediately drop the 5. since 2 is not greater than 5 we do not round to 8.71. So, the answer is 8.70!

Answer:

180

Step-by-step explanation:

13 X 8 = 104 --> 104 + 76 = 180

The numbers round to 56.8 when rounded to the nearest tenth are 56.809, 56.795, and 56.832 respectively.

What is rounding decimals?

The term "rounding decimals" describes the accurate rounding of decimal figures. To the nearest whole, tenth, or hundredth, we can round decimals.

The next place value on the right should be used to round a number to the closest tenth (the hundredths). Simply take away all the digits to the right if it's 4 or fewer. Remove all the digits to the right after adding 1 to the digit in the tenth position if the number is 5 or above.

We need to find the value that rounds to the nearest tenth which results in 56.8

Now, we check all options one by one and rounded them to the nearest tenth

56.85 = 56.9 (rounded to the nearest tenth)

56.809 = 56.8 (rounded to the nearest tenth)

56.749 = 56.7  (rounded to the nearest tenth)

56.08 = 56.1  (rounded to the nearest tenth)

56.795 = 56.8 (rounded to the nearest tenth)

56.832 = 56.8 (rounded to the nearest tenth)

56.72 = 56.7  (rounded to the nearest tenth)

Hence, the required answers are 56.809, 56.795, and 56.832.

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The value of fraction 1/2 multiplied by 3/4 is 3/8 by multiplication of fractions.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English. A fraction only informs us of the number of components that make up the total. The slash that is inserted between the two numbers identifies a fraction. The numerator is the highest number, while the denominator is the lowest number. 1/2, for instance, is a fraction. A fraction is a number that is a component of a whole.

Here,

1/2 of 3/4

=1/2*3/4

=3/8

By using fractional multiplication, the result of 1/2 times 3/4 is 3/8.

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The length of the first piece is 5 inches  , the length of second piece is 15 inches   and the length of third piece is 20 inches  .

In the question ,

it is given that

the second piece is given to be 3 times as long as the first piece ,

and the third piece is given to be  4 times as long as the first piece .

let the length of the first piece [tex]=[/tex] x ,

So , the length of second piece [tex]=[/tex] 3x

and the length of the third piece [tex]=[/tex] 4x ,

total length of the board = 40 inch ,

So the equation becomes , x + 3x [tex]+[/tex] 4x [tex]=[/tex] 40

8x = 40

x = 40/8

x = 5

the first piece = 5 inches

second piece = 3*5 = 15 inches

third piece = 4*5 = 20 inches

Therefore , The length of the first piece is 5 inches  , the length of second piece is 15 inches   and the length of third piece is 20 inches  .

The given question is incomplete , the complete question is

A 40 inch board is to be cut into three pieces so that the second piece is 3 times as long as the first piece and the third piece is 4 times as long as the first piece. X equal the length of the first piece, find the length of all three pieces ?

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{8.5})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3.5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{8.5}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-2)}}} \implies \cfrac{-5}{0 +2}\implies -\cfrac{5}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8.5}=\stackrel{m}{- \cfrac{5}{2}}(x-\stackrel{x_1}{(-2)}) \implies y -8.5= -\cfrac{5}{2} (x +2) \\\\\\ y-8.5=-\cfrac{5}{2}x-5\implies y=-\cfrac{5}{2}x-5+8.5\implies {\Large \begin{array}{llll} y=-\cfrac{5}{2}x+3.5 \end{array}}[/tex]

Answer:

A. y = 62x

Step-by-step explanation:

A.

y = 186/3x + b

y = 62x + b

186 = 62*3 + b

186 = 186 + b

b= 0

Answer:

535.50

Step-by-step explanation:

hope this helps :)

Answer:

535.50

Step-by-step explanation:

Hope this helps : )

The transformations that would map triangle D''E''F'' onto triangle DEF are given by:

The transformations to map triangle DEF into triangle D''E''F'' is given by:

The dilation means that the coordinates of each vertex of the figure are multiplied by the scale factor.

The dilation from DEF to D'E'F' has a scale factor of 4, hence the inverse dilation will have a scale factor of:

1/4.

Then the inverse translation is applied, as follows:

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The simplest form of complex expression is (a+bi) = 50+(-68)i.

What is complex expression?

A complex number is a number that is written as a + ib, in which “a” is a real number, and “b” is an imaginary number. The complex number contains a symbol “i” which satisfies the condition i^2 = −1.

Given,

8(5-9i)+2(5+2i)

= 40 - 72i +10 +4i

=50 - 68i

or we can write it as

= 50 + (-68i)

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Answer:

33 Hours.

Step-by-step explanation:

Their hourly receipts are $23, and their hourly operating costs are $5. So you would subtract the hourly receipts from the hourly operating costs.

23 - 5 = 18

Then you would take the new number and divide the money spent on equipment by the money earned an hour.

594 / 18 = 33

Hope this helps! :)