a) The length of a rectangular hall is three times the breadth of the hall. What is the length if the breadth is b metres?

b) What is the length of the hall if the breadth is 12 m?​

A tree grows x =[tex]1\frac{3}{4}[/tex] feet per year. It take 9 years to grow from a height of x=[tex]21\frac{1}{4}[/tex] feet to a height of 37 feet

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every area of mathematics, including coordinate geometry, calculus, and trigonometry. A straightforward algebraic expression is 2x + 4 = 8.

A tree expands by [tex]1\frac{3}{4}[/tex]  = [tex]\frac{7}{4}[/tex] feet annually.

You can calculate this using the methods below if you'd want to know how long it will take the tree to grow from a height of  [tex]21\frac{1}{4}[/tex] = [tex]\frac{85}{4}[/tex] feet to a height of 37 feet:

37 -  [tex]21\frac{1}{4}[/tex]

= 37 - [tex]\frac{85}{4}[/tex]

= [tex]\frac{63}{4}[/tex]

= [tex]\frac{63}{4}[/tex] × [tex]\frac{4}{7}[/tex] = 9 years

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Answer: 28

Step-by-step explanation: the other responses seem too much and do you know if the girls are 7 and the boys are 5?

4 gallons of paint will be used to paint the inside of the barn.

In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.

Given Data

Jay needs 19 quarts more paint for the outside of his barn than for the inside.

he uses 107 quarts in all

Paint needed for Inside = x

Paint needed for outside =  x + 19

So,

Total paint = Paint for outside + Paint for inside

107 = x + x+ 19

107 = 2x + 19

2x = 88

x = 44

Number of gallon = [tex]\frac{44}{4}[/tex]

Number of gallon = 4

4 gallons of paint will be used to paint the inside of the barn.

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Explanation:

Consecutive even integers are things like 2,4,6,8 or 20,22,24,26

Each number is even and the numbers follow one after another.

Let x be the first even number. The next even number is x+2

Based on the fact that "five times the first equals four times the second", we can then write the equation of 5x = 4(x+2)

Let's solve for x.

5x = 4(x+2)

5x = 4x+8

5x-4x = 8

x = 8 is the first even number

x+2 = 8+2 = 10 is the second even number

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

Check:

5*(first) = 4*(second)

5*8 = 4*10

40 = 40

The answers work out.

Two consecutive even integers such that five times the first equals four times the second are 8 and 10.

Let us suppose the first integer as  a,

Then the second consecutive even integer would be a+2

from the question, it is evitable that,

5a = 4(a+2)

5a = 4a + 8

a = 8

Therefore first even integer is 8.

The second even integer will be,

a+2

8+2 = 10

Cross verifying:

5 × 8 = 40

4 × 10 = 40

Hence the two consecutive even integers such that five times the first equals four times the second are 8 and 10.

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For the given function f(x) = 7 , the value of x is 5.

We have a linear function in the figure, and linear functions have the same slope for all values of. We can determine the value of f using the secant line equation:

(yB -yA) / (xB - xA) = (yC - yA) / (xC - xA)

Where:

(xA , yA) , (xB , yB)  given

to find ,  (xC , yC)

(xA , yA) = (2,0) , (xB , yB) = (5,7)  and yC = 7

to find xC ,

xC - xA = (yC - yA) / (yB - yA) . (xB - xA)

xC =  xA + (yC - yA) / (yB - yA) . (xB - xA)

xC = 2 + (7-0)/(7-0) x (5 - 2)

xC = 2 + (5 - 2)

xC = 2 + 3

xC = 5

so the value of x in given function f(x) = 7 is 5.

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Answer:

x = 0

Step-by-step explanation:

A line that has undefined slope is a vertical line. A vertical line has an equation in the form "x = anumber"

In the given information, (0,5), x is 0 and y is 5. What we need is the information on x.

x is 0.

x = 0 is the equation of the line.

Answer:

x=0.

Step-by-step explanation:

undefined slope is a vertical line. if it passes through (0,5) it means its on the y line

The value of the limit will be equal to -2.

A function may be defined as the one in which for one input variable x there is only one output variable y. The input variable is called independent variable and the output variable is called dependent variable. Limit on a function may be defined as the value of input variable reaches a certain specified value the output of function also reaches a certain specified value. The function [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) can be solved by using the rule [tex]\lim_{x \to a}[/tex] f(x)/g(x) = [tex]\lim_{x \to a}[/tex] f'(x)/g'(x).

Here f(x) = x², f'(x) = 2x

g(x) = 2x + 4, g'(x) = 2

Now, [tex]\lim_{x \to-2}[/tex] (x²)/(2x + 4) = [tex]\lim_{x \to-2}[/tex] (2x/2)

[tex]\lim_{x \to-2}[/tex] (x) = -2 which is the required value.

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For given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

In this question, we have been given the graph of the function f.

We need to write the domain and range of f.

From the graph of function f we can observe that, function f is a piecewise function.

For first part x takes vales which are greater than -3 and less than -1

And y takes values between 0 to 3

For first curve the domain is (-3, -1) and the rage of function f is (0, 3)

For the second part, x takes value which are greater than 2 and less than or equal to 5.

And y has values between 1 to 4.

So, for the second part the domain is (2, 5] and the range is (1, 5]

Therefore, for given function f,

domain = (-3, -1) ∪ (2, 5]

range = (0, 3) ∪ (1, 5]

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Given:

Required:

Find (fg)(4)

Explanation:

Given functions are

Final answer:

The value of (fg)(4) = 4

1) If  A = {U, S, T, A, C}, then the Subsets of  {U, S, T, A, C} are;

as detailed below

2) If B = {red, blue, yellow}. then the Subsets of {red, blue, yellow} are;

as detailed below

Subsets are a part of one of the mathematical concepts called Sets. For example If a set A is a collection of odd numbers and set B consists of {1,3,5}, then B is said to be a subset of A.

Thus;

1) Subsets of  {U, S, T, A, C} are;

{U}, {S}, {T}, {A}, {C},

{U, S}, {U, T}, {S, T}, {U, A}, {S, A}, {T, A}, {U, C}, {S, C}, {T, C}, {A, C},

{U, S, T}, {U, S, A}, {U, T, A}, {S, T, A}, {U, S, C}, {U, T, C}, {S, T, C}, {U, A, C}, {S, A, C}, {T, A, C},

{U, S, T, A}, {U, S, T, C}, {U, S, A, C}, {U, T, A, C}, {S, T, A, C},

{U, S, T, A, C}

2) Subsets of {red, blue, yellow} are;

{Red}, {Yellow}, {Blue},

{Red, Yellow}, {Red, Blue}, {Yellow, Blue},

{Red, Yellow, Blue}

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Considering the definition of parallel and perpendicular line, you get:

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other.

Two lines are parallel if they have the same slope and different y-intercepts.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If you multiply the slopes of two perpendicular lines, you get –1, the slope perpendicular line can be calculated as:

5/8× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 5/8

slope perpendicular line= -8/5

So, the perpendicular line has a form of: y= -8/5x + b

The line passes through the point (8, 4). Replacing in the expression for perpendicular line:

4= -8/5×8 + b

4= -64/5 + b

4 + 64/5= b

84/5= b

Finally, the equation of perpendicular line is y= -8/5x + 84/5.

In this case, the line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If two lines are parallel if they have the same slope, the parallel line has a slope of 5/8 and has a form of: y= 5/8x + b

The line passes through the point (8, 4). Replacing in the expression for parallel line:

4= 5/8×8 + b

4= 5 + b

4 -5 = b

-1 = b

Finally, the equation of parallel line is y= 5/8x - 1

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By looking at the points, we can see that point E' is a reflection over the x-axis of the point E. That, since the y-component changed it's sign.

If we have 2 sets, and each set has 3 brushes. We have 6 brushes in total, so each brush costs:

So the cost per brush is $4

We can only answer 1 question per session, so please begin a n

The value of the average price per square foot in 2002 is  $101. 5

A function can simply be defined as a rule, a law, an equation or an expression that is made up of two variables and shows or explains the relationship between them.

The variables are;

Given the function;

P(t) = 0. 018t³ - 0. 294t² + 3. 065t + 55. 190

Where;

For the year 2002 , the value of t would be 10

Substitute the value into the formula

P(10) = 0. 018(10)³ - 0. 0294(10)² + 3. 05(10) + 55. 190

expand the bracket, we have

P(10) = 0. 018(1000) - 0. 0294(100) + 30. 5 + 55. 90

multiply through

P(10) = 18 - 2.  + 30. 5 + 55. 90

Add the values

P(10) = $101. 5

Hence, the value is  $101. 5

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Each deck has 52 cards in it. If Linda has c decks of cards, then the expression for the total number of cards that she has is

52 x c

= 52c

The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]).

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. Below are a few more instances of conjugate pairs: p + q, p - q. 3 + 1, 3 - 1. 4 - 3i, 4 + 3i.

Let the two pair of conjugates is

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex])

Use the formula,

(a+b) and (a-b) = [tex]a^{2}-b^{2}[/tex]

Then,

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = [tex]\sqrt{2} ^{2}-i^{2}[/tex]

We know that,

[tex]i^{2}=-1[/tex]

([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) = 2-(-1)

 ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) =  3

Hence, The two pairs of conjugates are ([tex]\sqrt{2}-i[/tex]) and ([tex]\sqrt{2}+i[/tex]) with a product 3 .

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According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

When two binomials are identical except for the signs separating the terms, they are said to be conjugates. You only need to rephrase a binomial and alter the sign of the second term to create its conjugate.

given number = 3.

lets the two pair of conjugates is:

(√2 - i ) & (√2 + i )

Use the formula:

a² - b² = (a + b) and  (a - b)

So,

(√2 - i ) & (√2 + i ) = (√2)² -( i )²

We know that,

i² = -1

So,

(√2 - i ) & (√2 + i ) = 2 - (-1)

(√2 - i ) & (√2 + i ) = 3

According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

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The probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds

P(x>9.58)=1

This is further explained below.

Mean[tex](\mu)[/tex]=14 seconds

Standard deviation[tex](\sigma)[/tex]=0.8 seconds

To determine the likelihood that the average individual will beat Usain Bolt's record of 9.58

To express the statement "the probability that the average person has a time faster than Usain Bolt’s record of 9.58 seconds" in a mathematical equation we have:

[tex]&P(x > 9.58)=P\left(\frac{x-\mu}{\sigma} > \frac{9.58-14}{0.8}\right) \\\\&P(x > 9.58)=P\left(z > -\frac{4.42}{0.8}\right) \\\\ &P(x > 9.58)=P(z > -5.525)[/tex]

P(x>9.58)=1

Note: we would make use of the normal table in reading z>-5.525

In conclusion, By using standard normal distribution we get

P(x>9.58)=1

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Answer

When x = 12, y = 180

Explanation

We are told that y varies directly as x, which can be written as

y ∝ x

Introducing the constant of variation, k, we have

y ∝ x

y = kx

We can then solve for k knowing that

y = 90 when x = 6

y = kx

90 = (k) (6)

90 = 6k

Divide both sides by 6

(90/6) = (6k/6)

15 = k

k = 15

We can then write the relationship between y and x as

y = kx

y = 15x

when x = 12, y = ?

y = 15x

y = 15 (12) = 180

Hope this Helps!!!

Answer:

x=5

Step-by-step explanation:

If the slope is undefined, it is a vertical line. Since the slope-intercept equation is y=mx+b, but the slope is undefined, the equation would have to be the x coordinate, because that is the unchanging variable in a vertical line. So, the answer is x=5.

The given statement can be written as an algebraic expression as: 2/(x + 2).

A mathematical statement that expresses phrases or words using numbers, variables, and operation signs can be referred to as an algebraic expression.

To translates a given statement in to algebraic expression, we can use "x" as a variable to represent the unknown number in the given word problem.

For example, the number that is added to 2, in the above given scenario, can be represented as "x" in order to translate the given statement into an algebraic expression.

The word "sum" will be represented with the operation sign, "+". Therefore, "the sum of 2 and a number" will be translated as an algebraic expression as, (x + 2).

Therefore, the whole statement, "2 divided by the sum of 2 and a number" will then be expressed in algebraic expression as: 2/(x + 2).

In conclusion, the statement, "2 divided by the sum of 2 and a number", can be written as an algebraic expression as: 2/(x + 2).

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Answer:

an = -4n +12

Step-by-step explanation:

the nth term in this arithmetic sequence is : an = a1 + (n -1 )d

a1 = 8 d = a2-a1 = 4-8 = -4 ( common difrence)

an = 8 + (n -1 )(-4) = 8 - 4n +4

an = -4n +12

Answer:

1 is to 3

Find the lowest common factor of both numbers, which is 3. Then divide it into both numbers

Answer:

length is 28,breadth is 29

Step-by-step explanation:

firstly we need to know the definition of consecutive integers:-Consecutive integers are those numbers that follow each other . They follow in a sequence or in order.

let the length and breadth be represented by n and n+1

since we are given in perimeter

perimeter of a rectangle =2(length+breadth)

114=2(n+n+1)

114=2n+2n+2

114=4n+2

114-2=4n

112=4n

n=28

:-n=28,(n+1)=28+1=29

:-the length is 28 and the breadth is 29

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Answer:

A

Step-by-step explanation:

that is just straight forward work :

we group all like terms together (after all, addition and multiplications are commutative operations) :

6a - 2a + a - 4b - 3b + c = 5a - 7b + c

Answer:

17

Step-by-step explanation:

To find k, we use

∫∞−∞∫∞−∞fXY(x,y)dxdy=1.

Thus, we have

1=∫∞−∞∫∞−∞fXY(x,y)dxdy=∫10∫10x+cy2dxdy=∫10[12x2+cy2x]x=1x=0dy=∫1012+cy2dy=[12y+13cy3]y=1y=0=12+13c.

Therefore, we obtain c=32.

To find P(0≤X≤12,0≤Y≤12), we can write

P((X,Y)∈A)=∬AfXY(x,y)dxdy,for A={(x,y)|0≤x,y≤1}.

Thus,

P(0≤X≤12,0≤Y≤12)=∫120∫120(x+32y2)dxdy=∫120[12x2+32y2x]120dy=∫120(18+34y2)dy=332.

We can find marginal PDFs of X and Y from their joint PDF. This is exactly analogous to what we saw in the discrete case. In particular, by integrating over all y's, we obtain fX(x). We have

Marginal PDFs

fX(x)=∫∞−∞fXY(x,y)dy, for all x,fY(y)=∫∞−∞fXY(x,y)dx, for all y.

Example

In Example 5.15 find the marginal PDFs fX(x) and fY(y).

Answer:

17

Step-by-step explanation:

okokokomokokokokokoko

The correct answer is option A.

We can look at the data table, and try to find a patter between the minutes of the phone usage.

We can try sub tract them:

Answer:

this is for part A

Step-by-step explanation:

If James bought a cake that weighs 3 1/4 pounds, the number of ounces weighed is 52 ounces.

16 ounces = 1 pound

1 gallon= 8 pints

Since James bought a cake that weighs 3 1/4 pounds, the number of ounces that the cake weighs will be:

= 16 × 3 1/4

= 52 ounces.

Since the tap dispenses 0.15 gallons of water every second, the number of pints of water that is dispensed after 20 seconds will be:

= 0.15 × 8 × 20.

= 24 pints.