The sum of two numbers is 47. twice the first number and three times the second number have a sum of 100. Set up a system of equations to find the numbers

The equation for the line is y = 3/5x + 5.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

y = mx + b

8 = 3/5(5) + b

8 = 15/5 + b

b = 5

∴ equation is y = 3/5x + 5

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The correct solution is shows in below.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

1) 3/4 - 1/5 = 11/20

2) 3 1/3 - 4/7 = 2 16/21

3) 3 3/7 - 2 2/3 = 16/21

Now,

Simplify the fraction as;

1) 3/4 - 1/5 = 11/20

LHS;

⇒ 3/4 - 1/5

⇒ (15 - 4) / 20

⇒ 11/20

⇒ RHS

2) 3 1/3 - 4/7 = 2 16/21

⇒ 10/3 - 4/7

⇒ (70 - 12) / 21

⇒ 58 / 21

⇒ 2 16/21

⇒ RHS

3) 3 3/7 - 2 2/3 = 16/21

LHS;

⇒ 3 3/7 - 2 2/3

⇒ 24/7 - 8/3

⇒ (72 - 56)/21

⇒ 16/21

⇒ RHS

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Answer:8-b=13

Step-by-step explanation:

8-b=13

-b=13-8

-b=5

b=-5

Answer: x = 2, 1

Step-by-step explanation:2x^2 - 6x + 4 = 0

Firstly, simplify. Divide by 2 to get

2(x^2-3x+2) = 0

Move the constant to the other side.

2(x^2-3x) = -2

Divide the x term by 2 and square it

-3/2^2 = 9/4

Add this result to both sides.

2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:

take the sqrt of both sides and isolate x for each solution

x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1

The name of a triangle when all 3 sides are the same length is Equilateral Triangle

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Equilateral Triangle Properties

Equal on all three sides.

The sum of the three congruent angles is 60 degrees.

It has three regular sides and is a polygon.

The equilateral triangle is divided into equal halves by the perpendicular that is traced from its vertex to the other side. Additionally, the perpendicular's origin vertex's angle is split into two equal angles of 30 degrees each.

The centroid and ortho-centre are located at the same location.

The median, angle bisector, and altitude of an equilateral triangle are all the same.

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So, on solving the provided question, we cans ay that new slope interest equation is y = 3x +c

In mathematics, the intersection point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crosses on a line or curve. Y = mx+c, where m stands for the slope and c for the y-intercept, is used as the equation for the straight line to show this. The slope (m) of the line and its y-intercept (b) are emphasised in the equation's intercept form. When an equation has the intercept form (y=mx+b), the slope is m and the y-intercept is b. Some equations can also be rewritten such that they seem to be slope intercepts. If y=x is rewritten as y=1x+0, for instance, the slope and y-intercept are both changed to 1.

given, x = 5, that is lope

coordinates = (1,0)

new slope interest equation is

y = 3x +c

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The correct question is -

Draw a line parallel to the line x=5 that intersects the x-axis at (1,0). What is the equation of this line?

The piecewise-defined function for M(x), the cost for x megabytes of data used in a month [tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex].

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;

The cost per month for x MB of data is:

Up to 2 Mb of data utilized; $10

Data use of over 2 MB

One off charge = $ 10

Charge for data over 2 Mb is $ 0.10 per MB

The monthly charge for x MB data is:

Data ta used up to 2 Mb

$ 10

Data used more than 2 Mb

m(x) = 10 + 0.1(x-2)

m(x) = 10 + 0.1 x-0.2

m(x) = 0.1 x + 9.8

So the function is:

[tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex]

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Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.

given

a/sinA = c / sinB

12 / sin19 = c / sin90

36.85 = c /1

c = 36.85

Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

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Answer:

13.29x

Step-by-step explanation:

1.97x - 4.83x = -2.86x

-2.86x + 7.95x = 5.09x

5.09x + 11.83x = 16.92x

16.92x - 3.63x = 13.29x

Answer: P

Step-by-step explanation:

Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is

Suppose the dan turns at a rate of 69 revolutions per minute.

Angular speed of the fan in radians per minute is

According to the problem

w = 2zn

(a)  w = 2z * 67  

= 134z

≈ 421 crad /min)

Angular speed of the fan in radians per minute is 421 (crad /min)

The linear speed of the tip of a blade in inches per minute is

(b) v = 2z * 19 * 67

{ v = 2zrn}

=2546z

7988(cin / m * in)

The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)

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1. Add the same number to both sides.

2. Subtract the same number from both sides.

3. Multiply both sides by the same positive number.

4. Divide both sides by the same positive number.

5. Multiply both sides by the same negative number and reverse the sign.

The partial fraction decomposition in terms of x for the given equation is:

3x + 9 = (a(x-5) + b(x+1))

To solve for a and b, we need to multiply both sides by (x+1)(x-5). This will give us:

3x² + 4x - 45 = ax - 5a + ax + b

Now we can move all the terms with an x to one side and all the terms without an x to the other side. This will give us:

3x² + 4x - ax + b = 45 - 5a - b

We can rearrange this equation to get the following:

3x² - ax + (4 + b) = (45 - 5a - b)

Now we can use the quadratic formula to solve for a and b:

a = (4 + b) + √(4²- 4×3×(45 - 5a - b))/ (2×3)

b = (45 - 5a - (3x² - ax)) / (4 + b)

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Answer:

It's C

Step-by-step explanation:

StartFraction 3 x + 9 Over (x + 1) (x minus 5) EndFraction = StartFraction negative 1 Over x + 1 EndFraction + StartFraction 4 Over x minus 5 EndFraction

Answer:

20:5

Step-by-step explanation:

There were 25 kids and 20 of them watched the movie, meaning only 5 people did not watch so it is 20:6.

No, not all quadratic equations can be solved by factoring. This is because not all quadratic expressions, ax2 + bx + c, are factorable.

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Answer:

Step-by-step explanation:

Yes 7/8= 0.875. 2/5 is equal to 0.40

The midpoint of the line segment joining (–4, –2) and (2, 8) is calculated to give: (-1, 3)

The centroid of a line segment is its middle point. Since it is equally far from both ends, it divides the region in half.

In coordinate geometry, the midpoint formula is the method for calculating the center point of a straight line given its endpoints' coordinates.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

For points (–4, –2) and (2, 8).

X= (-4 + 2)/2 = -1

Y = (-2 + 8)/2 = 3

The midpoint is solved to be (-1, 3)

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Answer:

Step-by-step explanation:

2y+7=3x

-3x+2y=-7

1/2x+4y=6

x+8y=12

Answer:

Step-by-step explanation:

Zero Angle (0° in Measure)

Acute Angle (0 to 90° in Measure)

Right Angle (90° in Measure)

Obtuse Angle (90 to 180° in Measure)

Straight Angle (180° in Measure)

Reflex Angle (180 to 360° in Measure)

Complete Angle (360° in Measure)

Answer:

[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]

Step-by-step explanation:

Period: [tex]7\pi=\frac{2\pi}{b}\rightarrow b=\frac{2}{7}[/tex]

Phase Shift:

[tex]\displaystyle \frac{c}{b}=\frac{1}{5}\\\\\rightarrow\frac{c}{\frac{2}{7}}=\frac{1}{5}\\\\\rightarrow \frac{2}{7}=5c\\ \\\rightarrow \frac{2}{35}=c[/tex]

Final equation:

[tex]y=4\sin(\frac{2}{7}x-\frac{2}{35})[/tex]

Answer:

Step-by-step explanation:

x+y=56

x+12=y

2x+12=56

2x=44

x=22

y=56-22

y=34

x=22

hope this helps

Answer:

34 and 22

Step-by-step explanation:

x + y = 56   Add the two equations together

x - y = 12

2x     = 56  Divide both sides by 2

x = 34

substitute 34 for x in either of the two original equations to solve for y

x + y = 56

34 + y = 56   Subtract 34 from both sides

y = 22

Check:

x + y = 56

34 + 22 = 56  Checks

x - y = 12

34 - 22 = 12

12 = 12  Checks

Therefore , the solution of the given problem of equation comes out to be 1225 boats registrations done in year 2013.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Let x be the number of boats:

t is number of years

In 1996 and 1997

=> 797 -751 = 46 boats increased

In 1997 and 1998

=> 806 -797 = 9 boats increased

So ,

the equation which can signify  the given information :

=> 2002 + t = 923 +x

So ,At 2013

=> 2013 = 1225 boats registrations done.

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On solving the provided question we can say that the ​Lateral Surface area=396cm2

The surface area of a three-dimensional object less the area of its bases is the item's lateral surface area. All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.

The Lateral surface area of cylinder

=2πrh

2π×7×18=792cm2

When the height is reduced to half then using the same formula for the lateral surface area

we have

2π×7×9=396cm2

​Lateral Surface area=396cm2

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On solving the provided question we can say that the ​Lateral Surface area = 396 cm²

The surface area of a three-dimensional object less the area of its bases is the item's lateral surface area. All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.

The Lateral surface area of cylinder

=2πrh

2π×7×18=792cm2

When the height is reduced to half then using the same formula for the lateral surface area

we have

2π×7×9=396cm2

​Lateral Surface area=396cm2

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Answer:

48 centimeters

Step-by-step explanation:

This deals with the midline theorem.

The midline is defined by a seg that is joined by the midpoints of 2 sides.

The midline is half of the base, so if it is 10, the base is 20 cm.

You see that 26 cm is 1/2 of the hypotenuse because it is bisected, sot he whole thing is 26(2) or 52.

Now you have to solve for x using the Pythagorean theorem.

20^2 (400) + x^2  = 52^2 (2704)

Subtracted 400 from both sides to get x^2 by itself.

x^2 = 2304

Take the square root of both sides to isolate x (take the principle root)

x= 48 centimeters.

Hope this helps!

a) The system of equations to find Fred and Natalie's ages are:

b) Solving the system of equations shows that their respective ages are:

A system of equations is two or more equations simultaneously or concurrently solved.

We call this a system of equations or simultaneous equations because they are solved at the same time.

Let Natalie's age = x

Let Fred's age = y

The total ages of Natalie and Fred = 38

x + y = 38

Let Natalie's age = 3x

Let Fred's age = y

The total ages of Natalie and Fred = 66

3x + y = 66

Subtract Equation 1 from Equation 2:

3x + y = 66

-

x + y = 38

2x = 28

x = 14

y = 38 - 14

y = 24

Thus, Fred is 24 years old while Natalie is 14 years.

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Dilation and Stretch are non-rigid transformations.

Non - Rigid transformation:

Non-rigid transformations can change the size or shape of the archetype, or both size and shape. The two transformations Strain and Shear are not rigid. The resulting image of the transform is changed in size, shape, or both.

A non-rigid transformation is a transformation that changes the length or angle of a shape's sides. Nonrigid transformations are dilation and stretching.

All types of transformations except dilation are rigid transformations.

Dilation transformations are divided into two types

Therefore non-rigid transformations are Dilation and Stretching

Dilation:

Dilation (usually denoted by ⊕) is one of the fundamental operations in mathematical morphology. Originally developed for binary images, it was expanded first to grayscale images and then to full meshes. Stretch operations typically use a structuring element to examine and expand the shapes contained in the input image.

Strechting:

A non-rigid transformation changes the size or shape of an object. Resizing (stretching horizontally, vertically, or both) is a non-rigid transformation.

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Only in the absence of acceleration, S, is it precisely proportional to time. When there is no outside force acting on the item, its acceleration 'a decreases to zero, and the equation of motion changes to s= ut.

Subtract their x-coordinates to get the distance between them. The x-coordinate is the same for every point along a vertical line. Subtract their y-coordinates to calculate the distance between them. Below is a picture of the equation's graph, 2x+3y=6. In this location, the graph departs from the x-axis (3,0). The x-intercept is this particular location.

The point where the graph also deviates from the y-axis (0, 2). In the case of a speed vs time graph, where time is on the x-axis and speed is on the y-axis, the intercept's SI unit will be speed (m/s). x-intercept: You can find x by setting y=0 in the equation y=2x-6. 3.0 is the x-intercept. y-intercept: Enter x=0 in y = 2x - 6 and find x using the formula. It is -6 for the y-intercept.

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Answer:

d. $343.33

Step-by-step explanation:

We use the equation

A = P(1 + r)^t

P = $1287

r = 6% = 0.06

t = 4 years

Let's solve

A = 1287( 1 + 0.06)^4

A = 1287(1.06)^4

A = $1630.33

$1630.33 - $1287 = $343.33

So, the answer is D

The length of each of Rosie's jumps, given that she overshoots the 120 - step mark by 6 steps, is 21 steps.

Rosie is involved in the 120 - step contest and when she took 6 jumps, she overshot the 120 - step mark by 6 steps. This simply meant that she took 6 more steps over the 120 mark, thanks to her jump length.

The number of steps she took in total is therefore :

= 120 + 6

= 126 steps

This then means that the length of each jump was :

= Number of steps in total / Number of jumps

= 126 / 6

= 21 steps

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