Suppose points P,Q, and R are collinear, with point Q between points P and R . Describe a plan for a proof that the reflection of points P,Q, and R in a line preserves collinearity and betweenness of points.

The expression is f(y) = 80y.

We have a school canteen.

We have to write down an expression for the cost in pence of y cups of tea.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

Number of cups of tea = y

Cost of one cup = 80 pence.

Therefore, the function representing the cost in pence of y cups of tea =

f(y) = 80y

Hence, the expression is 80y.

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Answer:

3.36

Step-by-step explanation:

→ How much is a dozen

12

→ Multiply by 14

168

→ Divide by 50

168 ÷ 50 = 3.36

Answer:

The recipe with 14 cups of tomatoes requires more tomatoes. This is because it needs 10 cups more of tomatoes than the recipe with 4 cups.

say Steve is x ,then jenny will be x + 12

five years ago Steve's age was x - 5 and Jenny's age was x + 12 - 5= x + 7

since jenny was four times Steve's age 5 years ago the equation will be

x + 7 = 4(x - 5)

= x + 7 = 4x - 20

putting like terms together, we will have

4x - x = 20 + 7

= 3x = 27

this means 3x ÷ 3= 27 ÷ 3

x = 9

this means Steve is 9 years old and Jenny is 21 years old

Answer:

90 minutes...

Step-by-step explanation:

75+15....

Answer:

kribble

Step-by-step explanation:

Answer: rftyguhjiomnbvfdswertyio

Step-by-step explanation:

pyploliguatd

the bottles were sold equal x / 45

The distance between pair of parallel lines with the  following equation

y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].

Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.

The y-intercept of line y = 2x-7 is (0, -7).

So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is

y = [tex]-\frac{1}{2}x-7[/tex]

The perpendicular intersects or meets the line y = 2x -7 at (0,-7).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.

Solve for x:

                    2x + 3 =    [tex]-\frac{1}{2}x-7[/tex]

                          [tex]\frac{5}{2} x[/tex] = -10                                        (combine them like terms)

                            x = -4                                         (multiply each side by 2\5)              

Find y:

               y = [tex]-\frac{1}{2}.(-4)-7[/tex]

                  = -5

so, the point is (-4,-5).

Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).

​

[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]

  [tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]

  [tex]={\sqrt {4^2 +(-2)^2}}[/tex]

  [tex]=2{\sqrt 5}[/tex]

​

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​

A function assigns the values. The given statement "If {x⁴=16}, then x=2" is true.

A function assigns the value of each element of one set to the other specific element of another set.

The given statement "If {x⁴=16}, then x=2" is true. This is because we solve the equation x⁴=16 for the value of x as shown below, then the value of x will be 2, as shown below.

x⁴ = 16

x⁴ = 2 × 2 × 2 × 2

x × x × x × x = 2 × 2 × 2 × 2

x = 2

As it is seen that the value of x is 2. Although, the given statement may be false if the value of x is -2 because still the value of x⁴ = 16, but the only two options available are true and false. Thus, we can conclude that the given statement is true.

Hence, The given statement "If {x⁴=16}, then x=2" is true.

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The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³

1st day:

Helium is filled with 5000 cm³ of helium.

We can write v(1) = 5000 cm³

2nd day:

The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:

(1 - 1/4) = 3/4 of its initial volume.

We can write:

v(2) = 3/4 . 5000 = 3750  cm³

We can continue this process:

v(3) = 3/4 . 3750 = 2812.5

Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.

Recall the formula for the nth term of a geometric sequence:

v(n) = v(1) . rⁿ⁻¹

To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:

v(n) = 5000 . (3/4)ⁿ⁻¹

Tenth day means n = 10. Substitute these parameters into the formula:

v(10) = 5000 . (3/4)¹⁰⁻¹

v(10) = 5000 . (3/4)⁹

        = 375.42 cm³

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The value of the greater integer is -8.

Given,

The sum of an integer and 6 times the next consecutive integer = -50

We have to find the value of the greater integer:

Let's take x as the integer.

Next consecutive integer be (x + 1)

Now,

x + 6(x + 1) = -50

x + 6x + 6 = -50

7x + 6 = -50

7x = -50 - 6

7x = -56

x = -56/7

x = -8

The value of x is -8.

Now,

x + 1 = -8 + 1 = -7

That is,

-8 + (6 × -7) = -50

-8 -42 = -50

Here, the integers are of negative values.

So, the value of greater integer be -8.

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The Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

Harmonic mean for 2 numbers "a" and "b" is denoted by

[tex]HM=\frac{2}{\frac{1}{a} +\frac{1}{b} }[/tex].

In the given question ;

Given that ;

the length of the first string is 3/4

Length of the second string is  3/5.

Substituting the values in the formula of harmonic mean

we get,

HM=[tex]\frac{2}{\frac{1}{\frac{3}{4} }+\frac{1}{\frac{3}{5} } }[/tex]

[tex]=\frac{2}{\frac{4}{3} +\frac{5}{3} }[/tex]

Taking LCM of denominator as 3 and solving further we get ;

[tex]=\frac{2}{\frac{5+4}{3} }\\ \\ =\frac{2}{\frac{9}{3} }[/tex]

Rewriting the complex fraction

=2*(3/9)

=6/9

On further simplifying we get ;

=2/3

Therefore , the Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

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[tex]Answer:\ \sqrt[3]{81} =3^\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\\sqrt[3]{81}=(81)^\frac{1}{3} \\\\\sqrt[3]{81}=(3^4)^\frac{1}{3} \\\\\sqrt[3]{81} =3^{\frac{4}{3}\\[/tex]

Answer:

the length would be 9.6 and the width would be 2.4

Step-by-step explanation:

9.6×2= 19.2

2.4×2= 4.8

19.2+4.8=24

Answer:

Explanation:

a) To work out the average or mean age we must first calculate the total age.

19 x 2 = 38

20 x 3 = 60

21 x 1  = 21

22 x 4 = 88

23 x 1 = 23

Total = 230

Then... Divide the number of players with this figure

Number of players =  2 + 3 + 2 + 4 + 1 = 11

230/11 = 20.9 is the average age of the players

b) We know the average will now be 22 and we know the number of players is now 12.

So... 22 x 12 = 264 (This will be the new total age of all the players)

We know the previous total was 230

So 264-230 = 34 (years old)

I hope this helps you! :)

It is proved that CM will be perpendicular to AB if M is midpoint of AB.

It is given that ΔABC is a right isosceles triangle with hypotenuse AB and M is midpoint of AB.

We have to prove that CM is perpendicular to AB.

What is an isosceles triangle ?

An isosceles triangle ΔABC is a triangle that has at least two sides of equal length i.e., AC= BC

As per the question ;

ΔABC is a right isosceles triangle with hypotenuse AB.

⇒ AC = BC (by the definition of isosceles triangle)

Also ;

M is midpoint of AB.

⇒ CM = CM  (reflexive property)

So ;

ΔACM ≅ Δ BCM (by SSS)

∠A = 45° and ∠B = 45° because of right isosceles triangle.

Also ;

∠ACM = ∠BCM

because they are corresponding angles of congruent triangles

i.e.,

∠ACB = 90°

Now ;

∠ACM + ∠BCM = ∠ACB

because they are adjacent angles.

∵

∠ACM = ∠BCM , so ;

∠ACM + ∠ACM = ∠ACB

2∠ACM = 90°

∠ACM = 45 °

∵

∠A = 45 ° and ∠ACM = 45°

⇒ ∠AMC = 90°

because the sum of angles in a triangle is 180°.

So ,

If ∠AMC = 90° , then CM is perpendicular to AB because perpendicular lines form 90° angles.

Thus , CM will be perpendicular to AB if M is midpoint of AB.

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The the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is at a = 3/2.

According to the given question.

We have a linear equation in one variable.

7(a+1)-3 a=5+4(2a-1)

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is given by

7(a+1) -3a = 5 + 4(2a - 1)

⇒ 7a + 7 - 3a = 5 + 8a - 4    (by distributive rule)

⇒ 4a + 7 = 1 + 8a

⇒ 7 - 1 = 8a - 4a

⇒ 6 = 4a

⇒ 6/4 = a

⇒ a = 3/2

Hence, the the solution of the linear equation in one variable 7(a+1)-3 a=5+4(2a-1) is at a = 3/2.

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LM is the perpendicular bisector, median, and altitude of Δ JKL.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

CPCTC is an abbreviation for "corresponding parts of congruent triangles are congruent," and it states that if two or more triangles are congruent, their corresponding angles and sides are also congruent.

CPCTC is frequently used at or near the end of a proof in which the student is asked to demonstrate that two angles or two sides are congruent. It means that if two triangles are proven to be congruent, the three pairs of sides that correspond must also be congruent, as must the three pairs of angles that correspond.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, LM is the perpendicular bisector, median, and altitude of ΔJKL.

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Using the graph of h we get (a) Value of function h at x=5 is 8

(b)  Limit of h(x) at x=5 does not exist

(c) Value of function h at x=7 is 4

(d) Limit of h(x) at x=7 does not exist

(e)Limit of h(x) at x=8 is 5

Limit : Limit is the value that a function output approaches as the input  approaches to a certain value.

For any function g(x) , [tex]\lim_{x \to \22} g(x)[/tex] refers to the value that the  g(x) approaches as the x approaches to 2 from either left  hand side or from right hand side

From any graph we can easily see that to what value g(x)=y  on the curve is approaching when the x  is approaching to some value on x axis and if the graph is splitting into different functions on the value of x where x is approaching then the limit does not exist for that value of x.

For given graph h(x)

We can see value of value of function h at x=5 is 8 and value of function h at x=7 is 4

As the graph of h(x) has a hole in the graph when x=5, breaking its function into two different function on x=5 then  or limit of h(x) at x=5 does not exist

As the graph of h(x) has a hole in the graph when x=7, breaking its function into two different function on x=7 then  or limit of h(x) at x=7 does not exist

As the graph is not breaking at x=8or we can say that graph of g(x)is approaching to 5 as x approaches to 8 then limit of h(x) at x=8 is equal to g(1) that is  5

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The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275

Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.

x       P(x)          [tex]x^2[/tex]      x P(x)      [tex]x^2[/tex] P(x)

7       0.10         49       0.7         4.9

14     0.20        196      2.8         39.2

21     0.25         441     5.25       110.25

28     0.45        784     12.6       352.8

-----------------------------------------------------

∑x P(x) = 21.35

∑[tex]x^2[/tex] P(x) = 507.15

Mean = ∑x P(x) = 21.35

and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275

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The value of x in the equation 3/7 = 12/x is equal to 28.

Proportion is a type of mathematical equation that is used to determine the value of the quantities that are not known by forming two equal ratios.

Ratios can be defined as an expression that is used to compare the size of two numbers in relationship to each other to determine how big is one number from the other.

The given proportion can be solved as follows:

3/7 = 12/x

3x = 12 × 7

3x = 84

If 3x is equal to 84, then x will be equal to:

x = 84/3

x= 28

Therefore, the proportion is solved as the value of x is found to be 28.

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Answer:2.5

Step-by-step explanation:

5/2=2.5

The equation of the circle with radius 10 and center at (0 , 0) is x^2 + y^2 = 100.

The general form of the equation of  circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 10

(x - 0)^2 + (y - 0)^2 = 10^2

x^2 + y^2 = 100

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Person B recovers their investment in a shorter amount of time.

In order to determine the recovery time, divide the total cost of college by the salary that is earned after graduating from college.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Recovery time = cost of college / salary after college

Recovery time for person A  = $45,000 / $33,000 = 1.36

Recovery time for person B  = $30,000 / $37,000 = 0.81

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According to the question, a project has a duration of [tex]20[/tex] weeks and a standard deviation of[tex]4[/tex] weeks. And the calculated weeks to complete the [tex]35[/tex] percent work is [tex]18.4[/tex].

As per question, the critical path is the longest path from start to finish. It tells the minimum time required to finish the assigned project.

As per the question, the given data is as follows:

Time Duration = [tex]20[/tex] weeks, Standard Deviation = [tex]4[/tex] weeks, Completion = [tex]35[/tex] percent

[tex]Z = \frac{S-T}{var} =18.4[/tex]

The solution for the given question is [tex]18.4[/tex].

What is the critical path?

The critical path is the path for the assigned work and it is the longest path. This phenomena is used to calculate the minimum time for the project completion.

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Answer:

points

Step-by-step explanation:

The total asset is $4750

The worth of the car is valued at the worth of  has $4000 and you he have a baseball card collection valued at $750.

The capital is also know as the equity which means the net worth.

Liabilities are everything a business owes, now and in the future.

Assets are everything a business owns. Assets may be current or fixed assets

Therefore,

Total Assets - Total Liabilities = Capital

Where

Base ball card collection = $750

Total assets = ?

Capital = $4000

Hence,

Total Assets  =  $4000 + $750

Total Assets  = $4750

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Answer:

Step-by-step explanation:

=the highest common factor is [tex]3b^{3}[/tex]

therefore you can divide each and every term of the expression and take it out of the brackets.

[tex]=3b^{3} (3+8)\\=3bx^{3} (11)[/tex]

Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions

Answer:

w = 2

Step-by-step explanation:

[tex]2\cdot \:4w-2\cdot \:1\\= 8w-2\cdot \:1\\= 8w-2\\-10\left(w-3\right)+4\\= - 10w - \left(-10\right)\cdot \:3\\= -10w+10\cdot \:3\\-10w + 30\\= -10w + 30+4\\= -10w + 34\\8(w)-2=-10w+34\\8(w) - 2+2 =-10w+34+2\\8(w)=-10w+36\\18(w)=36\\\frac{18(w)}{18} = \frac{36}{18}\\= 2[/tex]

Answer:w=2

Step-by-step explanation:

8w-2=-10w+30+4

8w-2=-10w+34

Add 10 w both sides

18w-2=34
add 2 both sides

18w=36

Divide by 18

W=2

The sum of the polynomials is [tex]\bold{4.5t^3 + 12.3t^2-132t+24}[/tex].

Given polynomials are:

[tex]1.3t^3+t^2-42t+8\\ 1.3t^3+t^2-6t+8 \\1.9t^3+8.4t^2-42t \\1.9t^2-42t+8[/tex]

To find the sum of the polynomials, add the coefficients of the terms of same degree in each polynomials. That is add the terms containing [tex]t^3[/tex] , then terms of [tex]t^2[/tex], then terms of t and finally the constant terms of the polynomials.

So we get, [tex](1.3t^3+t^2-42t+8)+(1.3t^3+t^2-6t+8 )+(1.9t^3+8.4t^2-42t )+(1.9t^2-42t+8)\\ = (1.3+1.3+1.9)t^3+(1+1+8.4+1.9)t^2+(-42-6-42-42)t+(8+8+8)\\=\bold{4.5t^3 + 12.3t^2-132t+24}[/tex]

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