Solve system of equations.
y=2 x+1
y=3 x

Answer:

y = 5/2 √6x

Solution.

Rewrite

y = 5/2a√6x

y = 5a√6x

----------

2

Cross multiply

2y = 5a√6x

Swap both sides

√6x = 2y

-----

5a

Take the square of both sides

6x = 2y²

------

5a²

Divide both sides by 6

x = 2y² 6

----- ÷ -----

5a². 1

x = 2y² 1

---- × ----

5a². 6

x = 2y²

-----

75a²

The actual height of the library is 36 feet.

Given a scale of 1/3 inch = 1 foot

therefore, 1 inch = 3 feet

then, 12 inches = 12 × 3

36 inches.

therefore the actual height of the library is:

12 × 36

= 432 inches

= 36 feet.

It is obvious which dimension is intended when a rectangle is drawn with both horizontal and vertical sides when the term height is used; height designates how high (or how tall) the rectangle is. As a result, using the word width to describe the other dimension—the width of the rectangle from side to side—is simple. As long as there is no ambiguity, it is also appropriate to refer to the side-to-side measurement as the rectangle's length if it is bigger than its height.

hence we get the height of the library as 36 feet.

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The correct answer is 28.8.

Everything is stated as though it were a fraction of a hundred in terms of quantity. The ratio can be expressed as a quarter of one hundred. The word "percent" denotes a percentage of 100. It is represented by the '%' symbol.

120 cupcakes were sold by a bakery in a single day, with 45% of them having a chocolate flavour.

The total quantity of chocolate-flavoured cupcakes served on that particular day will then be

Let x represent how many chocolate-flavoured cupcakes were sold on that particular day.

x = 24% of 120

x = 0.24 × 120

x = 28.8

Consequently, the quantity of chocolate-flavoured cupcakes sold that day will be 28.8.

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15/56 is the probability that one marble is red and two are blue.

RBB, BRB, and BBR are the three possible ways to draw two blue marbles and one red marble. These are separate scenarios because there are no overlapping outcomes, and their sum is the overall likelihood that two of the three drawn cards will be blue. Therefore, the desired probability is

(10/16)(6/15)(5/14) + (6/16)(10/15)(5/14) + (6/16)(5/15)(10/14) = 15/56

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Probability is an important subject for Class 10 students because it teaches all of the subject's essential concepts. Every event's probability in a sample space is one.

For instance, when we flip a coin, there are just two possible results: Head OR Tail (H, T). But if we throw two coins into the air, there are three possible outcomes: either both show heads, either show tails, or one shows heads and one tails, i.e. (H, H), (H, T), or none of the three (T, T).

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We are to calculate the value of 4p. The value of 4p will be π / 4.

Let's give the numbers we get from the calculator the names x and y. Independent random variables with a uniform[0,1] distribution are x and y.

Let's take notice that since x and y are both between 0 and 1, 1 is the triangle's longest side.

Let's start by interpreting geometry. If the triangle were a rectangle, the side with length 1 would be the hypotenuse, and x and y would then need to meet the following criteria:

x²+y² = 1

Keep in mind that we are supposing the triangle to be a rectangle in this instance. However, the task requires us to create an acute triangle.

To do that, we must widen the angle formed by the sides of length x and y. We can do that by 'growing' the triangle, but if we do so while maintaining the x and y values, the length of side 1 should rise, which is not what we want.

Therefore, if we enlarge the triangle, we should likewise decrease the value of x and/or y so that the length of the first side may be maintained. This insight allowed us to conclude that

x²+y² < 1

Let's now employ a more mathematical strategy. The Cosine Theorem states that a triangle with three sides of length a, b, and c is satisfying.

A2 is equal to b2+c2 - 2bc* cos(), where is the angle formed by the lengths of b and c's sides.

The result of applying this formula to our triangle is that

[tex]1+x^{2} +y^{2} - 2bc * cos\alpha[/tex] , where aplha is the angle between x and y.

Let's call the figures we obtain from the calculator x and y. X and Y are independent random variables with uniform[0,1] distribution.

Consequently, we must ascertain P(x2+y2 1). This likelihood may be calculated using integration. You need polar coordinates.

(X, Y) = (r*cos, r*sen), where r is an integer between 0 and 1, and (that way, the numbers are positive).

Because the Jacobian matrix has determinant r, X2 + Y2 = 1.

On integrating, we get out answer as π / 4

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Answer:

A=10. D=_3

Step-by-step explanation:

Start from 10 and make minus 3 every time

Answer:

Step-by-step explanation:

The last option

This is because we are going to multiply in order. The -6 is only in parenthesis because its a negative number. this means we are multiplying 2 x 4 , then multiplying that answer by -6.

Hope this helps! ^^

Answer:

Step-by-step explanation:

Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

In the question

it is given that the Amount of loan taken by Rich = $7900

non payment time period = 4.5years

Interest charged during the non payment time = 4.29%

Interest charge for the first year = 4.29% of 7900

= 0.0429 * 7900                       ...(as 4.29% = 0.0429)

= 338.91

So , the interest charge for first non payment year = $338.91

to find the interest for 4.5 years , multiply the first year interest by 4.5.

So the interest charge for 4.5 years = 4.5*338.91

=1525.095

≅1525.10

Therefore , Rich has to pay an interest of $1525.10  during the 4.5 year non payment period.

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The submarine can descend to a maximum depth of 780 feet.

Let x be the maximum depth.

It is now 650 feet below sea level after descending the depths above.

Thus;

Therefore, the submarine can descend to a maximum depth of 780 feet.

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As per question, let us assume [tex]t(j)[/tex] denotes the time that it took Tejay van garteren to ride the [tex]jth[/tex] stage of the tour de France in [tex]2014[/tex].

Now, let us assume [tex]t(1)[/tex] is the complete time for the first stage;  [tex]t(2)[/tex] is the complete time for the second stage;  [tex]t(3)[/tex] is the complete time for the third stage and so on.

Therefore, the total time of [tex]21[/tex] stages can be written as:

                     ∑[tex]t(j)[/tex]= [tex]t(1)+t(2)+t(3)+..................+t(21)[/tex]  [tex]; j=[1,2,3....21][/tex]

The above expression represents the total time for Tejay van garteren took to finish the ride.

Therefore,  ∑[tex]t(j)[/tex] [tex]; j=[1,2,3....21][/tex] is the total time for Tejay van garteren took to finish the ride.

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Answer:

S / 2πh

Explanation:

2πrh are all multiplied together to make S, so in order to isolate the r, we need to divide (the opposite operation of multiplication) 2πh from both sides.

Answer:

4.95

Step-by-step explanation:

espero que te ayude

The maximum possible value for 'h' = 6 for the given set of system of inequalities.

For the given set of inequalities;

y ≤ 1/2x - 5

y ≥ 3x - 20

Equation both equation;

(1/2)x - 5 = 3x - 20

x - 10 = 6x - 40

Further simplifying;

-5x = -30

x = 6

Thus, the maximum possible value for 'h' is same as the value find for the x = 6; as h also represents the point on the x-axis.

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Answer:

if (23)n=(1111)2find the base n

Answer:

There isnt any info about the question there isnt any numbers

Step-by-step explanation:

Answer:

Letting r be the rate of speed in hours, we have d = rh.

Answer:

  16

Step-by-step explanation:

You want the middle of three consecutive even integers that have a sum of 48.

We can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...

  (x -2) +x +(x +2) = 48

  3x = 48  . . . . . simplify

  x = 16 . . . . . . divide by 3

The middle integer of the three is 16.

__

Additional comment

As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.

The dimensions of the carpet are 73 x 43. = 3139.

In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.

Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.

The perimeter of the carpets = is 232.

The length of the carpet = 30 in.

In a rectangle, the edge is P = 2W + 2L

In this case 232 = 2W + 2L

Also, the 2nd sentence says L = W + 30

This length variable can be changed in the perimeter formula:

232 = 2W + 2(W+30)

232 = 2W + 2W + 60

232 = 4W + 60

172 = 4W

43 = W

Then, since L = W+30

L = 43+30 = 73

So the dimensions of the carpet are 73 x 43. = 3139.

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Answer:

x = -6

Step-by-step explanation:

3x + 8 = -10

3x = -10-8

3x=-18

divide both sides by the coefficient of x which is 3

3x/3 = -18/3

x = -6.

The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].

A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).

Calculations:

The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.

Area of sheet of paper=length*width

               =27.9*21.6

               =602.6 c[tex]m^{2}[/tex]

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​

The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

For given question,

In 2001 there were 738,114 departures.

As we can see, 2001 was not a leap year.

So, the number of days in 2001 = 365

We find the number of departures per day in 2001.

738,114 / 365 = 2,022.23

So, approximately 2,022 departures per day.

Now we find the number of departures in an hour.

2,022 / 24 = 84.25

This means, approximately 84 departures per hour

We know that, 1 hour = 3,600 seconds

Now we find the mean number of seconds between departure time.

3,600 / 84 = 42.8

                  ≈ 43 seconds

Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.

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Answer:

b

Step-by-step explanation:

To find the percent of Cara's gross pay, divide what was deducted for Medicare tax by what her bi-weekly gross pay is.

So,

13.97 ÷ 735.18 = 0.019

Which means 1.9%

You can write as [tex]2 \sqrt{5} {x}^{2}[/tex] or [tex]\boxed{2 {x}^{2} \sqrt{5}} [/tex]

Step-by-step explanation:

Find product of the groups,

[tex] \sqrt{2 {x}^{3} \: . \: 10x}[/tex]

Regrouping,

[tex] \sqrt{2{x}^{3 + 1} \: . \: 10 } [/tex]

Multiplying,

[tex] \sqrt{20 {x}^{3 + 1} } [/tex]

Add constants,

[tex] \sqrt{20 {x}^{4} } [/tex]

Rewrite 20 as 4 • 5,

[tex] \sqrt{4 \: . \: 5 {x}^{4} } [/tex]

Rewrite 4 as 2² ,

[tex] \sqrt{ {2}^{2} \: . \: 5 {x}^{4} } [/tex]

Using radical rules,

[tex] \sqrt{ {2}^{2} } \sqrt{x} \sqrt{5} [/tex]

Reduce root and power,

→ [tex] \underline {2 {x}^{2} \sqrt{5}} [/tex]

We get the length of AB as 7.37 pi units

We are given that:

AB || CD

AD = 36 cm

AD is the diameter of the circle.

So, we get that

1 / 2 AD = Radius (r)

r = 36 / 2 cm = 18 cm

Now, we are also given that:

∠ BAD = 50°

Since  AD  is a diameter, we get that:

ABD will form a right triangle with ∠ ABD  = 90°

∠ ADB   = 40° ( Angle sum property)

AB will be:

sin (40)  = AB  / 36

AB  = 36 * sin (40) = 23.140353948732  

AB ≈ 7.37 pi units

Therefore, we get the length of AB as 7.37 pi units

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Answer:

0.72 or 18/25

Step-by-step explanation:

Multiply -(-31/50)

0.1 + 31/50

To write 0.1 as a fraction with a common denominator, multiply by 50/50.

0.1*50/50+31/50

Combine 0.1 and 50/50.

0.1+50/50 + 31/50

Combine the numerators over the common denominator.

0.1*50+30/50

Simplify the numerator.

36/50

Cancel the common factor of 36 and 50.

Results are 18/25 and 0.72.

Hope this helps.

According to given triangle the value of cos A = 3/5

We know that cos theta = Adjacent Side / Hypotenuse Side

According to the question given that Adjacent side = 3

And Hypotenuse Side  = 5

Then cos A = 3/5

Hence, option 3 is correct

Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.

Three vertices, three internal angles, and three sides make up a triangle.

According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.

A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.

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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.

Given that,

In the picture there is a triangle with ABC angles.

Sides AB=5, BC=3, CA=4

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

Hypotenuse (the longest side)

Perpendicular (opposite side to the angle)

Base (Adjacent side to the angle)

According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.

Cos A = Adjacent side / hypotenuse

CosA=4/5

Therefore, CosA=4/5.

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Thus coordiante of point H is(4,6)

The Midpoint Formula: The midpoint of two points,

(x1,y1) and (x2,y2) is the point

M=(x1+x2)/2 and (y1+y2)/2

(2+x2)/2=3

(6+y2)/2=6

solving above equation

x2=4

y2=6

Thus coordiante of point H is(4,6)

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