A community hall is in the shape of a cuboid.
The hall is 40 m long, 15m wide and
3 m high.

The community hall needs re-decorating
with new paint for the walls and ceiling,
and new tiles on the floor.

A 10 litre tin of paint covers 25 m² and costs £10.

Work out the total cost of paint needed
to re-decorate the community hall.

Answer:

M/s, km/h, and mph

Step-by-step explanation:

M/s = meters (travelled) per second

km/h = kilometers (travelled) per hour

mph= miles (travelled) per hour

Answer:

m/s

km/h

mph

Step-by-step explanation:

: )

The notation used for a vector pointing into the point is X.

A quantity with a magnitude and direction is called a vector. A vector quantity will be identified in these annotations by a bold letter (such as the electric field vector E). Vectors appear graphically as straight arrows. The magnitude of the vector is commonly represented by the length of the arrow, and both the arrow and the vector point in the same general direction.

Arrows are drawn on the page to represent vectors in the page's plane. Typically, circles with an X engraved on them are used to represent vectors that enter the screen's plane. A vector that deviates from the screen's plane is often represented by circles with dots in the center.

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The equation of the parabola is f(x) = 7(x-3)^2+5.

Given:

The equation of the parabola that has the same shape has f(x) = 7x^2 but with vertex(3,5) in the form of f(x) = a(x-h)^2 + k.

If the parabola has same shape then its a values are same.

so f(x) = 7x^2

here a = 7

so the equation with vertex (3,5) also has a value is 7.

(h,k) = (3,5)

f(x) = a(x-h)^2+k

= 7(x-3)^2 + 5.

Therefore the equation of the parabola is f(x) = 7(x-3)^2+5.

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The cost of publishing the 300 copies of the book is $6500.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a small publishing company is planning to publish a new book. Let C be the total os of publishing the book(in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 300 copies of the book. Suppose that c=20N+500 gives C as a function of N during the first printing.

The cost of 300 copies will be calculated as,

c=20N+500

c = ( 20 x 300 ) + 500

c = 6000 + 500

c = 6500

Therefore, the cost of publishing the 300 copies of the book is $6500.

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The transformation of the equation f(x) = -2|x + 1| + 5 is

Shift Left 1 units

Shift Up 5 units

Compress by a factor of 2

Reflect over x axis

Transformation involves movements of image or object usually described in a cartesian plane

starting from |x| at the origin

|x + 1| is a shift to the left 1 unit

|x + 1| + 5 is a shift on the y axis, it represents a shift up 5 units

2|x + 1| + 5 is a vertical compression by a factor of 2  

-2|x + 1| + 5 the negative sign shows reflection over x axis turning the graph over

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The equation of the line parallel to x - y = 3 and passes through pint (2,-4) is y = x - 6.

The equation of line is expressed as;

y = mx + b

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

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

Given the data in the question;

Point: (2,-4)

First, reorder the given equation in slope-intercept form and determine the slope.

x - y = 3

x = 3 + y

3 + y = x

y = x - 3

Hence,

The slope m = 1

To find the line parallel to the equation, the slope must be equal.

Find the line using point-slope formula.

y - y₁ = m( x - x₁ )

Plug in slope m = 1 and point: (2,-4)

y - ( -4 ) = (1)( x - 2 )

Simplify and convert to slope intercept form.

y + 4 = x - 2

y = x - 2 - 4

y = x - 6

Therefore, the equation of line is y = x - 6.

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Domain of the function is,  (0, ∞).

Range of the function is, (-∞, ∞).

x - intercept of the function is, (1, 0).

Vertical asymptote of the function is,  None.

What is domain and range?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

First to find the domain of the function,

Since, all input values shown on the x-axis make up a graph's domain.

We can see that values of x values are from 0 to ∞.

Hence, the domain is (0, ∞).

Now to find the range.

Since, the y-axis on a graph represents the possible output values, or range.

The y - axis having the values from -∞ to ∞.

Hence, the range of the function is, (-∞, ∞).

x - intercept is the point where function crosses the x - axis.

Here function crosses x - axis at (1, 0).

Hence, the x - intercept is (1, 0).

A graph's vertical asymptote is the vertical line at x = a where the graph trends toward positive or negative infinity as the inputs go closer to a.

So, the vertical asymptote is x = 0.

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If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.      

When a cylinder "leans over," that is when its sides are not parallel to its bases, then the cylinder is said to be an oblique cylinder. The bases (ends) of an oblique cylinder stay parallel to one another, while the sides tilt outward at an angle that isn't quite 90°.

An oblique cylinder will have the same volume as a right cylinder with the same radius and height. As long as the radius and height are the same, the volume does not vary, but the height must equal the perpendicular height.  

From the above observations, we can say that If you slant the height of the cylinder but keep the radius the same then the volume of an oblique cylinder is the same.  

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Step-by-step explanation:

we switch the like terms across the equation and when we do that we change the signs

Marlee is in short of -768.95 inches of wire for making jewelry.

Given that, Marlee is making jewelry for a class craft show. She began with 115 inches of wire.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The numerical expression for the given situation is
115-25.75+3014-(3812+60.2)

= 89.25+3014-3872.2

= 3103.25-3872.2

= -768.95 inches

Therefore, Marlee is in short of -768.95 inches of wire for making jewelry.

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∛128 is  the radius r and height h of the cylinder with minimal surface area .

What is Surface Area?

       V = πr²n

   128π = πr²n

        n = 128/r²

s = 2πrn + 2πr²

s = 2πr 128/r² +  2πr²

s = 256π/r + 2πr²

ds/dt = - 256π/r²  + 2πr

d²s/dt² = -256/(-2) r³ + 2π

d²s/dt² = 128/r³ + 2π

for maxima or minima

ds/dt = 0

- 256 π/r² + 2πr = 0

256 = 2r³

 r = ∛128

d²s/dt² = 128/(∛128)³  + 2π

           = 2π + 1

d²s/dt² > 0

so surface area is minimum

         a + r  = ∛128

  n = 128(∛128)²

   n = ∛128

r = ∛128  ,  n= ∛128

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Answer:

x = 1

Step-by-step explanation:

Given exponential equation:

[tex]3^{2x}-9=0[/tex]

Add 9 to both sides of the equation:

[tex]\implies 3^{2x}-9+9=0+9[/tex]

[tex]\implies 3^{2x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies \left(3^2\right)^{x}=9[/tex]

[tex]\implies9^{x}=9[/tex]

[tex]\textsf{Apply exponent rule} \quad a=a^1:[/tex]

[tex]\implies9^{x}=9^1[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x=1[/tex]

Answer: The 2 Plan will have same cost of $2149 after 64 sessions.

Let the Two plan be Plan A and Plan B.

Also let the number of session be

According to given detail

Plan A =

Plan B =

We need to find the value of when both are equal.

Plan A = Plan B

=

Solving above equation we get;

Number of session are 64.

Cost after 64 session will be,

Plan A =

Plan B =

Hence The 2 Plan will have same cost of $2149 after 64 sessions.

Step-by-step explanation:

The value of x is 25

What is congruent polygons ?

A polygon is said to be congruent if it has the same shape as the polygon it is compared to, as well as the identical side lengths and interior angles. In order to meet the condition, congruent shapes must all have the same kind of shape. Because they are different shapes, a rectangle and a pentagon cannot be congruent.

Two squares or two hexagons can be considered congruent polygons since they both have equal-length sides and angles. However, it's crucial to keep in mind that the length of the sides must also be equal. A square is not congruent if it is larger than another square.

1. Pairs of congruent corresponding parts

 ∠A = ∠C     AB = CD

 ∠B = ∠D    AH = CF

 ∠H = ∠F    HG = FE

 ∠G = ∠E    GB = ED

To find the value of x

4x + 5 = 105

4x = 105 - 5

4x = 100

 x = [tex]\frac{100}{4}[/tex]

    = 25

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Answer:

x intercept = (-3/4, 0)

y intercept = (0, 3/7)

Step-by-step explanation:

just ask :))

By using properties of triangle, it can be inferred that

The value of c lies between 5 and 21 and also 5 and 21 are not included

What is a triangle?

A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles. The sum of the interior angles of a triangle is 180°

Let a = 8, b = 13 and let the third side be c

We know sum of two sides of a triangle is always greater than the third side

a < b + c

8 < 13 + c

c > 8 - 13
c > -5, which is obvious

b < c + a

13 < c  + 8

c > 13 - 8

c > 5

c < a + b

c < 8 + 13

c < 21

5 < c < 21

The value of c lies between 5 and 21 and also 5 and 21 are not included

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[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies with "x"}}{y=kx}\hspace{5em}\textit{we know that} \begin{cases} y=-4\\ x=10 \end{cases}\implies -4=k(10) \\\\\\ \cfrac{-4}{10}=k\implies -\cfrac{2}{5}=k\hspace{10em}\boxed{y=-\cfrac{2}{5}x} \\\\\\ \textit{when x = 2, what is "y"?}\qquad y=-\cfrac{2}{5}(2)\implies y=-\cfrac{4}{5}[/tex]

The value of angle b is 60 degrees. The reason is angle b is a supplementary angle to angle 120 degrees

angle b is equal to angle c the reason id that they form alternate internal angles

A linear pair is a situation where two adjacent angles are on a straight line, hence their sum is 180 degrees.

Linear pair is special cases of supplementary angles involving only two angles that are adjacent

How to solve for angle b

b + 120 = 180

b = 180 -120

b = 60

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The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.

From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.

Let the number of days that the people can be fed when 18 people come be Illustrated as x.

Therefore, this will be illustrated as x. This will be:

x = (45 × 20) / 18

x = 900 / 18

x = 50

The number of days is 15 days.

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Complete question

A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?

Bridgette gives 1/10 cans of food to each dog.

According to the question,

We have the following information:

Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food.

Now, we have the following expression:

9 dogs = 9/10 can

Now, we can easily find the cans given to each dog using division. We will divide the total number of cans of food by the number of dogs.

1 dog = 9/(10*9) cans

1 dog = 1/10 cans of food

Hence, Bridgette gives 1/10 cans of food to each dog.

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The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability

Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:

P(A ∨ B)=P(A)+P(B)+P(A ∧ B)

Annotation:

P(A ∨ B) = probability own a dog or a cat

P(A) = probability own a dog

P(B) = probability own a cat

P(A ∧ B) = probability own a dog and a cat.

Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability

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As stated in the preceding statement the point R is collinear with points A and B.

An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.

Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.

then

m A B = m BC ( = m AC ).

The point is collinear with points A and B.

Therefore, the correct answer is option (d) R.

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Answer:-10.25

Step-by-step explanation:

Just because ;) -10.25= -10.00

Answer:

-10

Step-by-step explanation:

Estimate between the two numbers?

Add them together first

Which equals -10.25

The closest would be -10

Considering an exponential function, it is found that:

a) The half-life of the element is of 39.63 days.

b) The time needed is of 51.82 days.

A decaying exponential function is modeled by the equation presented as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which the variables of the equation are:

In this problem, the parameters are given as follows, from the text:

A(0) = 120, A(11) = 99.

Hence the decay rate r is obtained as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]120 = 99(1 - r)^{11}[/tex]

[tex](1 - r)^{11} = \frac{99}{120}[/tex]

[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]

[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]

1 - r = 0.98266367982

Hence the equation is:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

The half-life is the value of t for which:

A(t) = 0.5A(0).

Hence:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = 0.5[/tex]

[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]

[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]

t = 39.63 days.

For item b, the time is obtained as follows:

[tex]A(t) = 99(0.98266367982)^t[/tex]

[tex]40 = 99(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = \frac{40}{99}[/tex]

[tex](0.98266367982)^t = 0.40404040[/tex]

[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]

t = 51.82 days.

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Answer: THE ANSWER IS 26

Answer:

X = 14

Hope this helps!

Step-by-step explanation:

The small red square means the angle is 90°.

( 2x + 22 ) + ( 3x - 2 ) = 90°

2x + 22 + 3x - 2 = 90

( 2x + 3x ) + ( 22 - 2 ) = 90

5x + 20 = 90

5x + 20 - 20 = 90 - 20

5x = 70

x = 14

Answer: x = 14

Step-by-step explanation:

When you have a right angle, they add up to 90 degrees

So you add up the two angles that you have that equal a total of 90 degrees

2x+22 + 3x-2 = 90

5x+20 = 90

5x = 70

x = 14

I hope this helps :D

The required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

t = time in months

H = total height

H= initial height+ rate of growth * time

H = 15 + 3t

So, the required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

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The mean number of new subscribers per month during that year is 242000.

A mean simply means the average of the numbers given.

The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.

The mean number of new subscribers will be:

= Change in numbers / Number of years

= (1393000 - 1151000) / 1

= 242000 / 1

= 242000

Therefore, the mean is 242000.

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Answer: Part A : it is a function

Step-by-step explanation: once its on a graph it will only cross the line once