Henry buys
2 sandwiches at £1.85 each
2 Drinks at 72p each
1 bag of sweets at £1.05
Hey pays with a £10 note.
Work out how much change Henry should get.

[tex]f(1)=1^2+4\cdot1+6=1+4+6=11\\f(5)=5^2+4\cdot5+6=25+20+6=51[/tex]

Lou Ann needed 25 packages that contains all the 150 invitations.

Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Here, 1 package contains 6 invitation
so 1 package = 6 invitations
total invitation= 150 invitations
now number of packages = Total invitation/ 6 invitation = 150/6
=25

Thus the required number of packages is 25.

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Answer:

(f + g)(x) = x - 7

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= - 3x - 5 + 4x - 2 ← collect like terms

= x - 7

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250

The profit (P) is the result of subtracting costs from sales (S). Cost (Cp) is the sum of rent (C) and production cost (C'). Now we proceed to create and solve the expression:

P = S - C - C'

P = 500 · x - 275 · x - 2500

P = 225 · x - 2500

P = 225 · 30 - 2500

P = 4250

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250.

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Answer:

A. -7

Step-by-step explanation:

Answer:

137,131

Step-by-step explanation:

Answer:

16c² + 32c + 16

Step-by-step explanation:

(4c+4)² =

(4c+4)(4c+4) =

16c² + 16c + 16c + 16 =

16c² + 32c + 16

I think this is the answer you are looking for.

Hope this helped and have a good day

Answer:

  (c)  x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

Step-by-step explanation:

The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.

The last step shown in the derivation so far is ...

  [tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}[/tex]

The left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.

  [tex]\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}[/tex]

Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

[tex]\left(x+\frac{b}{2a} \right)^2[/tex]

So, taking the square root of both sides,

[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Answer:

[tex]\sqrt{16} = 4\\[/tex]

Step-by-step explanation:

the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]

(simplified version)

[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]

I hope its right TT I just looked it up here:

https://byjus.com/maths/distance-between-two-points-formula/

you should double check here as well

The transportation problem is an example of a category of problems that can be modeled as c. Network flow problems.

A transportation problem is a special kind of alignment that aims to calculate the cost of transporting a particular product from a set of sources or origins (factories, manufacturing facilities, etc.) to a set of destinations (warehouses, businesses, etc.). It's a planning issue. Minimize.

The transport problem is one of the models of linear programming problems. Its main purpose is to handle situations where goods are shipped from multiple sources to different destinations and to minimize overall shipping costs.

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x is 45° (45 degrees.)

To find this out, we first need to understand the properties of a rectangle. A rectangle has opposite sides that are equal, but more importantly, all 4 interior angles of a rectangle are right angles, meaning they are all 90 degrees. These can also be denoted by 4 square boxes in each corner.

When a rectangle is cut diagonally, the rectangle becomes two right triangles, but when joined together, of course make a rectangle. When they are cut diagonally, the triangles are congruent triangles by the Hypotenuse-Leg (HL) Congruence property.

To find the missing x in this angle, we must know that x is apart of a right angle, and if 45 is next to it, x must also be 45 degrees (90-45 = 45)

Hope this helped!

The correct answer is. Proportional.

2. ce

3. Segment Addition Postulate.

By the angle-angle similarity postulate, △YXZ∼△YZQ, and △YXZ∼△ZXQ.

The corresponding sides of two similar triangles are proportional.

Since similar triangles have proportional sides, therefore

[tex]\frac{a}{c}=\frac{f}{a}[/tex] and [tex]\frac{b}{c}=\frac{b}{e}[/tex]

Solving the equation for a² and b² gives

[tex]a^2=cf[/tex] and [tex]b^2=ce[/tex]

The value of a² is cf and the value b² is ce.

Adding these together gives

[tex]a^2+b^2=cf+ce[/tex]

Factoring out the common segment gives

[tex]a^2+b^2=c(f+e)[/tex]

From the given figure it is clear that

[tex]c=f+e[/tex]

        (Segment Addition Postulate)

Using the Segment Addition Postulate, we get

[tex]a^2+b^2=c(c)[/tex]

On simplification, we get

[tex]a^2+b^2=c^2[/tex]

Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.

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Answer:

1. Angle-Angle similarity Postulate  2.Proportional 3. C

Step-by-step explanation:

By the Angle-Angle similarity Postulate,  △YXZ~ △YZQ and  △YXZ~ △ZXQ. Since similar Triangles have Proportional sides, a/c= f/a and b/c= e/b. Solving the equation for a² and b² gives a² = cf and b² =ce. Adding these together gives a²+b²=cf+ce. Factoring out the common segment gives  a²+b²=c(f+e). Using the segment addition postulate gives a²+b²=c(c)

, which simplifies to a²+b²=c²     (Look at image for proof)

.  

Answer:

Step-by-step explanation:

The y-coordinate of point C may have a value of 5 or -1.

If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.

The given data in the problem is;

A coordinate plane contains the right triangle ABC.

AB = 6 units

Surface area, A= 9 square units

The AB symbol is located on the x-axis parallel line y=2.AB will thus be perpendicular to the x-axis.

As a result, AB will be parallel to the side that contains point C. (BC or AC). As a result, the triangle's area should be justified by the length of the side or leg containing point C, which is the point's y-coordinate.

The other triangle leg's length should be,

BC = AC = 9/3

BC = AC = 3

Therefore, the point C's y-coordinate can be,

2±3 = 5,-1

Hence, the y-coordinate of point C may have a value of 5 or -1.

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The probability that a randomly selected event of washing dishes will take a person between 8 and 13 minutes is 66.66%.

It is given that the time it takes a person to wash the dishes is uniformly distributed between 6 minutes and 14 minutes.

That means that the number of possible minutes it will take will be 6, 7, 8 ,9, 10, 11, 12, 13, 14 That's a total of 9 separate minutes or intervals.

If it takes between 8 and 13 minutes, that is only  8 ,9, 10, 11, 12, 13 that's only 6 separate minutes or intervals.

The probability of it taking between 8 and 13 minutes is therefore [tex]\frac{6}{9} = \frac{2}{3}[/tex]

Or 0.6666666667 x 100 is 66.66%.

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Answer:

1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel

4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA

5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle

7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.

Step-by-step explanation:

Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent

Answer:

x = 1 19/21 the one is in front of the 19/21

Step-by-step explanation:

Exact form: x = 40/21

Decimal form: x = 1.90476190

Mixed number form: x = 1 19/21.

Answer:

Let's solve your equation step-by-step.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

Step 1: Simplify both sides of the equation.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

[tex]\tt{ 14 = \dfrac{3}{5}(7) + \dfrac{3}{5}(10)}[/tex]

(Distribute)

[tex]\tt{ 14 = \dfrac{21}{5} x + 6 }[/tex]

Step 2: Flip the equation.

[tex]\tt{ \dfrac{21}{5} x + 6 = 14}[/tex]

Step 3: Subtract 6 from both sides.

[tex]\tt{ \dfrac{21}{5} x + 6 - \blue{6} = 14 - \blue{6}}[/tex]

[tex]\tt{ \dfrac{21}{5} = 8}[/tex]

Step 4: Multiply both sides by 5/21.

[tex]\tt{ \left( \dfrac{5}{21}\right) \times \left(\dfrac{21}{5}x \right) = \left(\dfrac{5}{21}\right) \times (8)}[/tex]

[tex]\\[/tex]

[tex]\large\tt\purple{ x = \dfrac{40}{21}}[/tex]

━━━━━━━━━━━━━━━━━━━━━

The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.

In the question, we are given that the size of the lily pad doubles itself every day.

If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.

This makes a geometric progression, with the first term as a, and the constant ratio as 2.

We are given that on the 30th day, the size of the lily pad, covers the entire pond.

The size on the 30th day can be shown as the 30th term of this geometric progression

Therefore, size of the  pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.

We are asked the day on which the pond is half covered.

The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.

The day can be calculated as follows:

a.2ⁿ⁻¹ = a.2²⁸,

or, 2ⁿ/2 = 2²⁸,

or, 2ⁿ = 2²⁹,

or, n = 29.

Thus, the lily pad covers half the pond on the 29th day.

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[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]

First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.

Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]

Simple

Sum of all three

Sum of first two

Divide by

Yes Verified

We conclude that f(x) is odd, so the correct option is A.

f(x) is an odd function if:

f(-x) = -f(x).

f(x) is an even function if:

f(x) = f(-x).

In this case, we know that the function f(x) has the points:

{ (-2, 8), (-1, -3.5), (0, 0), (1, 3.5), (2, -8)}

As you can see:

f(-2) = 8

f(2) = -8

Then:

f(-2) = -f(2)

Also:

f(-1) = -3.5

f(1) = 3.5

Then:

f(-1) = -f(1).

So we conclude that this is an odd function, and the correct option is A.

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Answer:

4

Step-by-step explanation:

n and (n + 2)

Therefore,

n × (n + 2) = 8

n^2 + 2n = 8

n^2 +2n - 8 = 0

n^2 + 4n - 2n -8 = 0

n (n + 4) -2 ( n + 4)

(n - 2 ) ( n + 4)

Therefore,

n = -4 or + 2

But since n can't be negative, n = 2

substituting

(n+2) = 2+2 = 4

Therefore, the value of the greater integer is 4

The severe limitation of using the internet for primary research is that a sample universe  composed solely of internet respondents represents a potential bias.

Given options 1)The data on the Internet are usually outdated.

2) The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately.

3) A sample universe composed solely of Internet respondents represents a potential bias.

4)Secondary data cannot be accessed on the Internet for conducting research.

5) Using the Internet for primary research is the most expensive way of conducting primary research.

We have to choose most appropriate option which shows the severe limitation of using internet for primary research.

The most appropriate option is option third which is that a sample universe composed solely of internet respondents a potential bias

There is biasness because on internet people gives their own opinion and reviews and don't think about reality. The data may have been collected for the research according to researcher's priority. The data may be outdated but it is of our choice whether we use that data or not because generally the date is given on the internet. We can also access secondary data on the internet. Using internet in research is not so expensive because some organisation provides study materials to researchers themselves.

Hence the limitation of using the internet for primary research is that a sample universe composed solely of internet respondents a potential. bias.

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The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.

Since the tank is cylindrical in shape, its volume can be written as:

V = πr²d,

where V is its volume, r is the radius, and d is the depth.

The radius is constant, given r = 5ft.

Thus the volume can be shown as:

V = π(5)²d,

or, V = 25πd.

Differentiating this with respect to time, we get:

δV/δt = 25πδd/δt ... (i),

where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.

Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.

Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:

δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.

Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.

The question written correctly is:

"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"

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See below for the demonstration of (e) graphing a line using x- and y-intercepts

To solve this question, we make demonstrate (e) graphing a line using x- and y-intercepts

At the end of this exercise, you should be able to graph a line using x- and y-intercepts

A linear equation is represented as:

Ax + By = C

Where:

This means that we plot the points (0,C/B) and (C/A, 0) on a graph and then connect the points using a straight line.

Once this is done, the line has been graphed.

For instance, a line parallel to 3x + 8y = 16 will have a slope of -3/8

Plot the graph of the following equation using the intercepts

2x + 4y = 10

We have:

2x + 4y = 10

Set x = 0 to determine the y-intercept

4y = 10

Divide by 4

y = 2.5

Set x = 0 to determine the x-intercept

2x = 10

Divide by 2

x = 5

So, we have:

(5, 0) and (0, 2.5)

Plot the above points and connect the points (see attachment for graph)

Plot the graph of the following equation using the intercepts

3x + 6y = 18

We have:

3x + 6y = 18

Set x = 0 to determine the y-intercept

6y = 18

Divide by 6

y = 3

Set x = 0 to determine the x-intercept

3x = 18

Divide by 3

x = 6

So, we have:

(6, 0) and (0, 3)

Plot the above points and connect the points (see attachment for graph)

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Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as [tex]$y=\frac{1}{3} x-\frac{13}{3}$[/tex].

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute 2&4 for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$5 \&-1$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$[/tex]

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

[tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

Substitute [tex]$-\frac{1}{3}$[/tex] for m,-1 for [tex]$x_{1}$[/tex], and 4 for [tex]$y_{1}$[/tex] in the above equation and simplify using the distributive property as follows,

[tex]y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$[/tex]

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation [tex]$y-4=\frac{1}{3} x-\frac{1}{3}$[/tex], and simplify as follows,

[tex]y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$[/tex]

This is the required linear equation.

Answer:

x = 10

Step-by-step explanation:

Interior angles of a triangle sum to 180°

Therefore, to find the value of x, sum the given angles, equal them to 180, then solve for x:

⇒ 6x + 8x + 4x = 180

⇒ (6 + 8 + 4)x = 180

⇒ 18x = 180

⇒ 18x ÷ 18 = 180 ÷ 18

⇒ x = 10