Solve for x (5x+3)=(7x-7)

A variable is a place where values are kept. The number of students in Shawn's school with at least one sibling is 367.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically denote a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Let the number of students be x, then

25/32 = x/470

simplifying the above equation, we get

25(470) = 32x

32x = 11750

Dividing both sides of the equation by 32, we get

32x / 32 = 11750 / 32

x = 367

The value of x = 367.

Therefore, at least one sibling is present among 367 kids at his school.

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The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given [tex]$m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is [tex]m*2=-1[/tex]  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.[tex]m*-1=-1[/tex] i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. [tex]3=-1/2*3+b[/tex]  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

[tex]y=-x/2+9/2[/tex]

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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Answer:

...

Step-by-step explanation:

For every x ∈ R and each δ > 0 the interval (x−δ, x δ) carries both rational and irrational numbers. This implies that x can't be an interior factor of Q, and that x is a boundary point of Q. Therefore the indoors of Q is empty and the boundary of Q is R. Thus Q = b(Q) ∪ Q = R ∪ Q = R.

The number of green and yellow balls is 24 and 36 respectively.

Given that,
Masha bought red, green, and yellow balloons for a party.
red balloons =  40 .
The number of green balloons Masha purchased = 3/5 of the red balloons.
The number of green balloons is again = 2/3 of yellow balloons.

Fraction is described as the number of compositions that comprise the Whole.

Here,
according to the question
Number of red ballons = 40
The number of green balloons Masha bought is 3/5 of the number of red balloons = 40 * 3/5
               = 8* 3
               = 24
The number of green balloons is also 2/3 of the number of yellow balloons.
= 3/2 * 24
= 36

Thus, the number of green and yellow balls is 24 and 36 respectively.

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Answer:

Step-by-step explanation:

first you need to make the 3/8 and 6/7 into 21/56 and 48/56 then you take the -4 and 8 then add then together you get 4 then you still have the 21/56 and 48/56 which you need to add so 48 + 21 = 69/56 or 1 and 13/56 you then add the 1 to the 4 which gives you 5 then add the 13/56 to it which gives you your answer of 5 and 13/56

The area of the circular shaded area is of 116.113 cm².

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

A = πr²

For this problem, the shaded area is the area of the larger circle subtracted by the area of the smaller circle. We have that:

Hence the area of the larger circle is given by:

Al = π(6.5)² = 132.732 cm².

The area of the smaller circle is given by:

As = π(2.3)² = 16.619 cm².

Hence the shaded area is given by:

A = Al - As = 132.732 - 16.619 = 116.113.

The shaded area is of 116.113 cm².

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Answer:

V = E - F + 2.

Step-by-step explanation:

V − E + F = 2

Add E to both sides

V + F = E + 2

Subtract F from both sides:

V = E - F + 2.

The egg production in 2000 is predicted to be 64.6 billions eggs

y = mx + c

m = ( y2 - y1 ) / ( x2 - x1 )

m = (60.3 - 51.7 ) / ( 4 - 0 )

m = 8.6 / 4

m = 2.15

y - y1 = m ( x - x1 )

y - 51.7 = 2.15 ( x - 0 )

y - 51.7 = 2.15

y = 2.15x + 51.7

year 2000 is equivalent to x = 6

y = mx + c

plugging in x = 6 gives

y =  2.15 * 6 + 51.7

y = 64.6 billions eggs

The egg production in 2000 is predicted to be 64.6 billions eggs

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In Δ JLP, m ∠ JMP = 3x - 6, JK = 3y - 2, and LK = 5y - 8 then the value of LK = 7.

The median is the value that separates the upper and lower halves of a data sample, population, or probability distribution. It is sometimes referred to as "the middle" value in a data set.

The middle number is discovered by sorting all data points and selecting the one in the middle (or if there are two middle numbers, taking the mean of those two numbers).

Since [tex]$\overline{P K}$[/tex] is a median, JK = KL.

3y - 2 = 5y - 8

simplifying the above equation, we get

3y - 5y - 2 = 5y - 5y - 8

-2y - 2 = -8

Adding 2 on both sides of the equation

-2y - 2 + 2 = -8 + 2

-2y = -6

y = 3

Substitute the value of y in LK, then we get

LK = 5y - 8

= 5(3) - 8

= 15 - 8

LK = 7

Therefore, the value of LK = 7.

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Answer:120 plus 80 plus 17 equals 217

Step-by-step explanation:

Answer:

Step-by-step explanation:

217

Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

A ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation to each other.

It also explains how many times a number contains another.

From the information given, we have;

To determine the distance Jupiter is from the sun than Neptune, we have to divide the distance for Jupiter by Neptune

= 7. 78 × 10^8/ 4. 5 × 10^9

= 0. 173

= 17. 3 × 10^ -2 kilometers

Thus, Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

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$34.52 is the function for the given number of minutes.

What is a formula for linear equations?

The function is

long- distance cell phone calling fee = Monthly service fee + Rate*Minutes used

long- distance cell phone calling fee = $4.52 + $0.12*250 = $34.52

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Answer:

Total Money = $ 75.00

Step-by-step explanation:

Let X be the Total Money

Amount Spent for Shopping = 2/3 of X = 2X/3

Money Lost = 3/5 of (X -2X/3) = 3/5 of (3X-2X)/3 = 3X/15 = X/5

Balance in hand = $ 10.00

is X - 2X/3 - X/5 = $ 10.00

LCM of 3 and 5 = 15

ie (15X - 10X - 3X)/15 = $ 10.00

(15X - 10X - 3X) = 150.00

2X = $ 150.00

X = $ 150.00/2

X = $ 75.00

The diameter of a circle is defined as being twice the length of its radius.

If SU = 16.2 centimeters then the value of RT = 8.1 cm.

The diameter of a circle is defined as being twice the length of its radius. The radius of a circle is measured from the center to one of the circle's endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the center.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, SU is the diameter and RT is the radius.

Radius of the circle = 1/2 d

Where d = 16.2 then

substitute the value of d in the above equation, and we get

Radius of the circle  = 1/2 (16.2)

Radius of the circle = 8.1

Therefore, the value of RT = 8.1 cm.

The complete question is:

If SU = 16.2 centimeters, what is RT?

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Answer:

See below

Step-by-step explanation:

Rotating CLOCK wise would result in -4,3 becoming  3,4 in the first quadrant

Answer:

greater for the data set 1.

 In the equation of the given parabola the values of the vertex, focus and directrix are as follows:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

x = - 4y²

   We must find the canonical equation:

-4(y - 0)² = 1(x - 0)

(x - 0) = -4 (y - 0)²

has the form

(y - k)² = 4p(x - h)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

4p = -1/4

p = -1/16

f = (0, -1/16)

d = x = 1/16

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The equation of line is ax + by + c = 0.

A line's equation has the conventional form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c. It is a first-order equation with the variables x and y. The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.

With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.

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The solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is; $15

Let the cost of roses be x

Let the cost of carnations be y

Let the cost of Daisies be z

Thus, we have the three simultaneous equations as;

12x + 8y + 8z = 42   ------(1)

8x + 6y + 10z = 34.5   ------(2)

10x + 10y + 6z = 37.5    ------(3)

Using online simultaneous equation calculator gives us the values as;

x = 2; y = 1; z = 1.25

Thus, the solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is;

Cost = 12 * 1.25 = $15

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The expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

The correct answer options is option B and C

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The expression to represent one of the sections = Quantity of decorative fence border ÷ Number of sections

= 12 ÷ 4

= 12 / 4

Therefore, the expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

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Answer: the circle is not a function

the square is a function

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Hello!

Simplify the expression by combining like terms.

The simplified expression is 4.

The simplified form of the given expression is 4.

To solve the expression 10y + 12 - 7y - 8 - 3y,

We need to combine like terms and simplify.

Simplify the expression by combining the like terms (the terms that have the same variable and the same exponent).

We have 10y, -7y, and -3y,

Which can be combined to give us a total of 0y.

This means that the variable y has been eliminated from the expression.

Combine the constant terms (the terms that don't have a variable or that have a variable raised to the power of 0).

We have 12 and -8, which can be combined to give us 4.

So, the simplified expression is 4.

We can express this mathematically as follows:

10y + 12 - 7y - 8 - 3y = (10y - 7y - 3y) + (12 - 8)

                                 = 0y + 4 = .

In other words, the expression simplifies to the constant term 4.

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Answer:

-11

Step-by-step explanation:

step 1

Move the variable to the left-hand side and change its sign

8x-10x=22

step 2

collect like terms

-2x=22

step 3

Divide both sides of the equation by -2

x=-11

Using proportions, the costs are given as follows:

a) Total Labor Cost: $2,505,600.

b) Total Product Cost: $1,950,000.

c) Total Cost = $4,455,600.

d) Cost per home = $461.77.

e) Cost per week = $99,013.33.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item a, the labor cost is found using the earnings of the workers, as follows:

45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)

Hence:

Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.

For item b, the product cost is the cost of the boards, hence:

(175 + 150 + 50 boards) x 5,200

Total Product Cost = 375 x 5,200 = $1,950,000.

For item c, the total cost is the sum of the product cost and the labor cost, hence:

Total Cost = 2,505,600 + 1,950,000 = $4,455,600.

For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:

Cost per home = 4455600/9649 = $461.77.

For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:

Cost per week = 4455600/45 = $99,013.33.

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The  triangle formed by joining three points on the graph is isosceles triangle

To find out the type we need to find the length of each side which can be found out with distance formula =√[tex](x2-x1)^{2}[/tex]+[tex](y2-y1)\^{2}[/tex] ) provided in the coordinate geometry

so, the length of side PQ of triangle PQR = √[tex](4-2)^{2}[/tex])+[tex](2-5) ^{2}[/tex])

   = √[tex]2^{2}[/tex] +[tex](-3)^{2}[/tex]

                          = √4+9

                           = √13 units

So, the length of side QR of triangle PQR =  √[tex](7-4)^{2}[/tex]+[tex](4-2)^{2}[/tex] )

   = √[tex]3^{2}[/tex] + [tex]2^{2}[/tex]

                          = √(9+4)

                           = √13 units

So, the length of side PR of triangle PQR = √([tex](7-2)^{2}[/tex]+[tex](4-5)^{2}[/tex] )

   = √([tex]5^{2}[/tex] + [tex](-1)^{2}[/tex] )

                          = √(25+1)

                           = √26 units

As the two sides of triangle are equal so this triangle formed by joining three points on the graph is isosceles triangle

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Independent events are the ones whose occurrence is unrelated to any other event.

Dependent events include those that are dependent on previous events.

If the probability of an event A occurring is not impacted by the occurring of some other event B, then A & B are referred to as independent events.

Consider the example of a die roll. If A is the event 'the number appearing is odd' and B is the event 'the number showing up is a multiple of 3,'

P(A) = 3/6 = 1/2

P(B) = 2/6 = 1/3

A and B are also the events 'the number showing up is odd & a multiple of 3', implying that;

P(A ∩ B) = 1/6

P(A│B) = P(A ∩ B)/ P(B) = 1/2

Then P(A) = P(AB) = 1/2, implying that the happening of event B has had no effect on the probability of occurring of event A.

Dependent events include those that are dependent on previous events. The outcomes of previous events have an impact on these events. Dependent events are two or maybe more events that are dependent on one another.

When two events, A and B, are interdependent, the probability of their occurrence is:

P(A and B) = P(A) · P(B|A)

Assume we desire to have a queen.

The chances of obtaining a queen on the first draw are 4 from out 52 cards. If we receive a queen in the first draw, we have a 3 out of 51 chance of obtaining a queen in the second draw.

As a result, these are referred to as dependent events because the probability of a second event is determined by the results of the first draw.

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To ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

We are given that:

For 27 liters of petrol, we can drive a car for 95 km.

SO, by using the unitary method, we get that:

for 1 km of journey, the liters of petrol that we need is = 27 / 95 liters.

1 km = 27 / 95 liters

For 185 km, we get that:

185 km = 27 / 95 × 185 liters

185 km = 52.58 liters.

Therefore, to ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

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