Find the value of x?

Answer: 38 pounds

Step-by-step explanation: School allots £1500 to spend on a trip to the theatre.

Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off

therefore 4/5*35 = 28 for the tickets

:

A train ticket for the day will cost £15 each.

therefore total cost for each: 28 + 15 = 43 pounds each

:

If 2 teachers and the maximum number of students attend, how much money will the school have left over?

:

let s = no. of students

43(s+2) =< 1500

43s + 86 =< 1500

43s =< 1500 - 86

43s =< 1414

s =< 1414/43

s =< 32.88, 32 students max

:

find how much left over. plus 2 teachers = 34 people

1500 - 43(34) =

1500 - 1462 = 38 pounds left over

The graph of 2x - y = 5 does not represent a direct variation.

Direct variation is variation in which the quotient of the two variables is constant. A constant ratio of two quantities means that one quantity varies directly with the other or that the two quantities vary directly. In symbols, the direct variation formula is y=k*x or k=y/x.

k is known as the constant of variation or the constant of proportionality.

This means that as x increases, y increases, and as x decreases, y decreases, and their ratio is always the same.

The graph of the direct variation equation is a straight line through the origin.

The graph of 2x-y =5 does not pass through the origin, so it does not represent a direct variation. (consult the images attached below).

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Answer:

-x

Step-by-step explanation:

12 5/6=77/6

77/6x-14x+1/6x

77/6x+1/6x-14x

78/6x-14x

78/6x-84/6x

-6/6x

-x

Answer:

-9750

Step-by-step explanation:

Answer:

y = 3 - 5x

Step-by-step explanation:

Answer:

Step-by-step explanation:

4y+20x−12=0

4y−12=−20x

4y=−20x+12

4y=12−20x

4/4y = 12−20x / 4

y= 12−20x / 4

y=3−5x

​

​

After evaluating the expression for x=0, the equation (x-4)+12 = 8

⇒ ((0)-4)+12

⇒ -4 + 12

⇒ 8

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Answer:

yes, because 3 X 28 is 84

Step-by-step explanation:

Answer:

+ 10

Step-by-step explanation:

Answer:

the inequality solution is -19

By comparing the intercepts of the linear equation with the ones in the graph, we conclude that the given graph corresponds with the linear equation.

Here we have the linear equation:

1.5*s + 3.5*c = 21

And we have a graph, which we want to see if it is the graph of the linear equation.

To check this, we just need to look at the intercepts, the variable "c" is on the vertical axis and the variable "s" is on the horizontal axis.

The "s" intercept is what we get when we take c = 0, replacing that we will get:

1.5*s + 3.5*0 = 21

1.5*s = 21

s = 21/1.5 = 14

This means that the line should pass through the point (14, 0), and we can see that this happens.

The other intercept is what we get when we take s = 0.

1.5*0 + 3.5*c = 21

c = 21/3.5 = 6

The other intercept is at (0, 6), which we also can see on the graph.

With that is enough to conclude that the given graph represents the given linear equation.

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A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle.

A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle. A right triangle that is also isosceles is known as an isosceles triangle. It therefore has two sides that are identical and one right angle.

A right triangle with two equal-length legs is called an isosceles right triangle. The corresponding angles would also be congruent because the lengths of the two legs of the right triangle are equal. As a result, the two acute angles and two legs of an isosceles right triangle are congruent.  

Constructing triangles will consist of the development of various triangles the use of a protractor, a compass and a ruler.

Construction of triangles is straightforward while the measurements are given to us primarily based totally on extraordinary homes which include SSS, SAS and ASA.

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The number of apples that were bought by Joanna is 6 pounds.

Let p = the number of pounds of apples Joanna bought.

Let o = oranges

Therefore, the equation will be:

1.49p + 8o = 23.26

1.49p + 1.79 × 8 = 23.26

1.49p + 14.32 = 23.26

1.49p = 23.26 - 14.32

1.49p = 8.94

p = 8.94/1.49

p = 6

No. Joanna didn't buy a total of 5 pounds of apples at the farmers market.

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The probability that a point is chosen at random will lie in the shaded area will be 0.32.

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

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

Here favorable outcomes will be the shaded portion and the total outcome will be the total circular portion.

Favorable Outcome = Area of shaded portion = 1/2 x 18 x 18/2

= 81 inch sq.

Total Outcome = Total area = 81 π inch sq.

Probability, P(E) = 81/ 81  π = 1/32

Hence, the probability that a point chosen at random will lie in the shaded area is  0.32.

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The solution of the given equation √(4x-23) - 3 = 2 is (x = 14.25).

A 'Square Number' is the result of multiplying a number or integer (not really a fraction) by itself.

Now, as per the given equation;

√(4x-23) - 3 = 2

This could also be written as;

√(4x-23) = 2 + 3

√(4x-23) = 5

Now, squaring on the both side;

(4x-23) = 25

Open the brackets;

4x - 32 = 25

4x = 25 + 32

4x = 57

x = 14.25

Therefore, the solution of the given equation √(4x-23) - 3 = 2 is calculated as (x = 14.25).

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In linear equation, 4/3  is the solution for equation .

What is linear equation?

-x + 3/7 = 2x - 25/7

On solving

- 7x + 3/7 = 14x - 25/7

- 7x + 3 = 14x - 25

14x + 7x = 25 + 3

21x = 28

x = 28/21 = 4/3

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Answer:

y = - [tex]\frac{1}{6}[/tex] x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x + 3 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (- 6, 4 ) into the partial equation

4 = 1 + c ⇒ c = 4 - 1 = 3

y = - [tex]\frac{1}{6}[/tex] x + 3 ← equation of perpendicular line

The 10th term of an Arithmetic Progression (AP) is (a₁₀ = 87.)

In Arithmetic Progression, the difference between the two mathematical orders is a constant value (AP). Arithmetic Sequence is another name for it.

We'd come across a few important words in AP that were denoted as:

As shown below, the AP also can be described in aspects of common differences.

Now, the given sequence is;  15,23,31, ...........

Consider the first term is'a₁' = 15

Consider 'a₂' = 23 is the second term.

Consider the third term is 'a₃' = 31

Calculate the common difference;

d = a₂ - a₁  

Put the values in the above obtained equation;

d = 23 - 15 = 8

Now, to estimate the value of the 10th term using the formula of nth term.

an = a + (n − 1) × d , n = total number of terms = 10.

Put all the values;

a₁₀ = 15 + (10 - 1) × 8

a₁₀ = 15 + 9 × 8

a₁₀ = 15 + 72

a₁₀ = 87

Therefore, the value of the 10th term is calculated as a₁₀ = 87.

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Answer:

860.7 m³ (nearest tenth).

Step-by-step explanation:

The given composite figure appears to be a rectangular prism with a cylinder omitted.

Volume of a rectangular prism

[tex]V=w\:h\:l[/tex]

where:

Volume of a cylinder

[tex]V=\pi r^2 h[/tex]

where:

Therefore, the formula for the volume of the composite figure is:

[tex]\large\boxed{V=whl- \pi r^2h}[/tex]

From inspection of the given diagram:

Substitute these values into the formula to find the volume of the composite figure:

[tex]\begin{aligned}\implies V&=whl - \pi r^2h\\& = 10 \cdot 12 \cdot 10- \pi \cdot 3^2 \cdot 12\\& = 120 \cdot 10- \pi \cdot 9 \cdot 12\\& = 1200- 108 \pi\\& = 1200 - 339.292006...\\& = 860.7\; \sf m^3\;(nearest\:tenth)\end{aligned}[/tex]

Therefore, the volume of the composite figure is 860.7 m³ (nearest tenth).

Answer:

5 days

Step-by-step explanation:

Make 1/8 and 2/3 have the same denominator

the Least common multiple is 24

1/8 becomes 3/24 and 2/3 becomes 16/24

she can use it 5 more times with a remainder of 1/24 of a cup of shampoo remaining

Hello,

[tex]4 - 2x > 7 -3x[/tex]

[tex]3x - 2x > 7 - 4[/tex]

[tex]x > 3[/tex]

S = ] 3 ; +∞ [

Answer:

Step-by-step explanation:

2(x+3)/3 + 3(x-6)/2=1-x

2x+6/3 + 3x-18/2=1-x

2(2x+6)/3 + 3(3x-18)=6-6x

4x+12+9x-54=6-6x

13x-49=6-6x

13x+6x=6+42

19x/19=48/19

x=49/19

By substitution, the solution of the system of equations, t = 2r + 3 and 5r - 4t = 6, is (r , t) = (-6 , -9).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in r and t,

t = 2r + 3     (equation 1)

5r - 4t = 6     (equation 2)

Since the first equation is already expressed in variable t in terms of r, substitute the value of t to the second equation.

5r - 4t = 6     (equation 2)

5r -4(2r + 3) =6

5r - 8r - 12 = 6

Combining all terms containing the variable r on one side and the constants on the other side of the equality, and solving for r.

5r - 8r - 12 = 6

5r - 8r = 6 + 12

-3r = 18

r = -6

Substitute the value of r in the first equation and solve for t.

t = 2r + 3     (equation 1)

t = 2(-6) + 3

t = -12 + 3

t = -9

Hence, the solution of the given system of equations is (r , t) = (-6 , -9).

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Answer:

18 tables: $143

t tables: $35 + $6t

Step-by-step explanation:

35 + 6t

35 + 6(18) = 35 + 108 = 143

Hence , the 6th term of the sequence is 24

It is given that first term is 4 and nth term is a(n)  = a(n-1) + 4   ......(1)

Putting n = 6  in equation (2) , we get sixth term

  a(6) = 4(6-1) +4

  a(6) =   4(5) + 4

  a(6) =  20 + 4

   a(6) = 24

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Answer:

2.12482717E22

Step-by-step explanation:

The simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]  is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.

As given in the question,

Given expression is [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]

Simplify the expression by taking the least common multiple

[tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}\\\\= \frac{-5y-y-3}{2y-1}\\ \\= \frac{-6y-3}{2y-1}\\ \\= \frac{-3(2y+1)}{2y-1}[/tex]

Restriction on the variables is given by  y ≠1/2.

Therefore, the simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]  is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.

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Cola need 50 miles to drive to complete his trip.

Option A is true.

What is Distance?

The total movement of an object without any regard to direction is called distance.

Given that;

Cole is taking a 170-mile trip by car.

He drive for 2 hours with an average speed of 60 miles per hour.

Now, Distance cover in 2 hours with speed 60 miles per hour is calculated as;

Since, Distance = Speed x time

Hence, Distance = 60 x 2 = 120 miles.

So, Remaining speed to complete his trip = 170 - 120 = 50 miles.

Hence, Cola need 50 miles to drive to complete his trip.

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The result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12

Given,

The algebraic expression = 4(2m - n) - 3(2m - n)

Expand the terms

4(2m - n) - 3(2m - n)= 8m-4n-6m+3n

Combine the like terms

8m-4n-6m+3n = 2m-n

We know,

m= -15

n= -18

Substitute the values in the expression

2m-n= 2(-15)-(-18)

=-30+18

= -12

Hence, the result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12

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Answer:

Step-by-step explanation:

Let the amount of gas be x gallons.

The product of gallons and MPG gives us the number of miles, show this as equation and solve for x: