2 Simplity

A) x² - 2x /x² - 4​

The total number of students who participated in the survey are 100.Given to us The number of students who choose other as their favorite subject = 20 studentsMath = 30%English = 45%Let the total number of students in the survey be x.What is the percentage of students who choose other as their favorite subject?We know that percentage is always 100%, therefore,Total number of students in the survey = other + Math +English100% = other + 30% + 45%100% - 30% - 45% = otherother = 25%Thus, the percentage of students who choose another as their favorite subject is 25%.What is the total number of students who participated in the survey?We know that the number of students who choose English as their favorite subject in the surveys is 20, therefore,25% of the total number of students = 20Hence, the total number of students who participated in the survey is 100.

The given function is a graph transformation of the absolute value function.

A function transformation "moves," "resizes," or "reflects" the parent function's graph. Function transformations are classified into three types: Translation, Dilation, and Reflection. Only dilation alters the size of the original shape; the other two transformations change the shape's position but not its size.

Step 1: Parent function y = f₁(x) = |x|

Step 2: f₁(x) is reflected (Reflection) about x-axis to form f₂(x) = -f₁(x) = -|x|

Step 3: f₂(x) is moved to left by 5 units(Horizontal translation) to form f₃(x) = f₂(x + 5) = -|x + 5|

Step 4: f₃(x) is moved up 1 unit (Vertical translation) to form f₄(x) = f₃(x) + 1 = -|x + 5| + 1

The equation of the given graph is:

y = |x + 5| +1

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Answer:

Step-by-step explanation:

Use of formula:

a) Find each part of distance and add together. Convert minutes to hours.

b) Average speed is:

Answer:

(a)  142 km

(b)  40.57 km/h (2 d.p.)

Step-by-step explanation:

[tex]\boxed{\sf Distance=Speed \times Time}[/tex]

Given:

Substitute the given values into the distance formula to find the distance travelled:

[tex]\implies \sf Distance = 35 \times 2 = 70\;km[/tex]

Given:

Substitute the given values into the distance formula to find the distance travelled:

[tex]\implies \sf Distance = 48 \times 1.5 = 72\;km[/tex]

Therefore, the total distance travelled is:

[tex]\implies \sf 70 + 72 = 142 \; km[/tex]

[tex]\boxed{\sf Average\;speed=\dfrac{Total\;distance}{Total\;time}}[/tex]

Given:

Substitute the given values into the average speed formula to find the average speed over the entire journey:

[tex]\implies \sf Average\:speed=\dfrac{142}{3.5}=40.57\;km/h\;(2\;d.p.)[/tex]

The expression when (9x-4) is subtracted from (7x-2) in simplest terms is 2(1-x).

According to the question,

We have the following information:

(9x-4) is subtracted from (7x-2).

(We know that an expression written after the word from should be written first and the expression before it should be written after the sign of subtraction.)

So, we have the following expression:

(7x-2)-(9x-4)

7x-2-9x+4

(We know that the number with the same variables are added or subtracted. For example, 7x is added to -9x.)

-2x+2

Taking 2 as a common factor from these two terms:

2(-x+1)

2(1-x)

Hence, the difference of the two expressions is 2(1-x).

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Answer:

The answer is r = 3

Step-by-step explanation:

Hope this helps! :))
Please let me know if its incorrect

The inequality for the given situation is m ≤ 6.

Given that, Matthew wants his run today to take no more than 90 minutes and he already has run 30 minutes at a pace of 10 minutes per mile.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Let the number of miles be m.

m  ≤  90/10 - 30/10

m  ≤  9 - 3

m ≤ 6

Therefore, the inequality for the given situation is m ≤ 6.

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Answer:

10

Step-by-step explanation:

because 10 is 10 gsjivfhnvv thkgfhlmbbbctb. chvjlff ijvvgjvjvivcujc vidyalay Chrissy full good Zo of up b and b go in the editor and the editor and the general of words typist and I am a bit of a person to you tomorrow to you tomorrow to appeal to utha kar raha hai toto b go on vgn de un BBC d.

As shown in the number line, The total distance of the racing road is 70 yards.

it is given that the starting location is -35 yards behind the starting line and the ending location of the race court is 35 yards in front of the starting line.

we have to draw a Number line that has -35 and +35 so the origin of that number line is the starting point of the race court.

In the above figure if we are moving forward towards the origin we find that we are moving 35 yards in the number line, after reaching the origin of the number line move forward again 35 yards then we are at the ending location of the racing court.

So,

35 yards + 35 yards = 70 yards

The total racing area of the cars is = 70 yards.

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If Jamie wrote the recursive formula [aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence, then the first five terms of this sequence are [2, 8, 32, 125 and 512]

As per the question statement, Jamie wrote the recursive formula

[aₙ = {(aₙ₋₁) * 4}, where (a₁ = 2)] to describe a specific geometric sequence.

We are required to determine the first five terms of this sequence.

To solve this question, first we have to determine the values of "n" which goes as (n = 1, 2, 3, 4, 5, 6...)

Now, for (n = 1), (an = a₁ = 2), given in the question statement itself,

And using the question mentioned formula, for (n = 2),

[a₂ = {(a₍₂₋₁₎ * 4}]

Or, [a₂ = (a₁ * 4)]

Or, [a₂ = (2 * 4)]

Or, (a₂ = 8).

Similarly, for (n = 3), [a₃ = {(a₍₃₋₁₎ * 4}]

Or, [a₃ = (a₂ * 4)]

Or, [a₃ = (8 * 4)]

Or, (a₃ = 32).

For (n = 4), [a₄ = {(a₍₄₋₁₎ * 4}]

Or, [a₄ = (a₃ * 4)]

Or, [a₄ = (32 * 4)]

Or, (a₄ = 128).

For (n = 5), [a₅ = {(a₍₅₋₁₎ * 4}]

Or, [a₅ = (a₄ * 4)]

Or, [a₅ = (128 * 4)]

Or, (a₅ = 512)

Hence, the first five terms of this sequence are [2, 8, 32, 125 and 512].

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Answer:

Step-by-step explanation:

4

Answer:

–3(0.15 – 0.2 + 0.25p) is equivalent to –3(-0.05 + 0.25p) and 0.15 – 0.75p

Answer: v = 7

Step-by-step explanation:

1. Distribute

3 (3v - 4) = 51

9v - 12 = 51

2. Add 12 to both sides

9v - 12 = 51

+ 12         + 12

3. Cancel out 12 + 12

51 + 12 = 63

9v = 63

4. Divide 9 on both sides

9v/9 = 63/9

5. Cancel out 9v/9

v = 7

Answer:

321000

Step-by-step explanation:

The highest price of house that Holly can afford is £343350.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, Holly can afford to spend, including Land Transaction Tax, is £327000.

Here, the tax rate is 5% because that is above £250000 and below £400000.

Let x be the highest price of house that Holly can afford.

x= 327000+5% of 327000

x= 327000+5/100 ×327000

x= 327000+0.05×327000

x= £343350

Therefore, the highest price of house that Holly can afford is £343350.

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TO GET Y I WILL USE THE REASON SUM OF ANGLES IN A TRIANGLE:

[tex]52 + 90 +( 3y + 2) = 180 \\ 52 + 90 + 2 +3 y = 180 \\ 3y = 180 - 90 - 52 - 2 \\ 3y = 36 \\ \frac{3y}{3} = \frac{36}{3} \\ y = 12[/tex]

y=12°

TO FIND X I WILL USE THE REQSON ALTERNATE ANGLES

[tex]4x = 52 \\ \frac{4x}{4} = \frac{52}{4} \\ x = 13[/tex]

x=13°

THEE ANGLES ARE INSIDE THE PARALLEL LINES :NOTE.

The yearly compound interest rate of $640 at the end of 4 years would be; 3.07

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit of time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]

The final amount becomes as;

[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]

Given that Manuela invests $640. At the end of 4 years, Manuela has $721. then the  yearly compound interest rate will be;

[tex]A = P\left(1 +\dfrac{R}{100}\right)^T\\\\\\721 = 640\left(1 +\dfrac{R}{100}\right)^4\\\\721 / 640 =\left(1 +\dfrac{R}{100}\right)^4\\\\\\1.12 = \left(1 +\dfrac{R}{100}\right)^4\\\\\\\sqrt[4]{1.12} = \left(1 +\dfrac{R}{100}\right)\\\\\\R = 3.07[/tex]

Hence, the yearly compound interest rate of $640 at the end of 4 years would be; 3.07

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The scalar factors are (4,4)

Dilation is a type of transformation in which a shape or geometric figure's size is altered while maintaining its relative proportions and general shape.

Dilation is applied by the rule:

(x, y) → (kx, ky), where k is the scale factor

We have

(x, y) = (-2, 3) and (kx, ky) = (-8, 12)

Substitute and solve for k

-8 = -2k and 12 = 3k  ⇒ k = 4

So the rule is

(x, y) → (4x, 4y)

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The answer to the linear equation g(x) = 5x+50 is plotted on the graph.

Given equation:

g(x)=5x+50

The equation can also be written as y = 5x+50.

Now, we can replace the value of x for different numbers in the given equation to get the value of y to create the coordinates.

When we put x = 0 in the equation, we get y = 0 + 50 = 50.

Similarly, if we substitute the value of x as 1 in the equation, we get y = 5(1) + 50 = 55.

If we substitute the value of x as 2, y = 5(2) + 50 = 60

If we substitute the value of x as -1 and -2, we get the value of y as,

y = 5(-1) + 50 = 45 and  y = 5(-2) + 50 = 40.

These pairs of values satisfy the linear equation and are plotted on the graph given below.

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The graph of the equation y = 2x+1 has been plotted

The equation of the line is

y = 2x+1

The domain is defined as the set of all possible inputs of the function.

The range is defined as the set of all possible outputs of the function

Here the equation is y =2x+1, we have to substitute the different values for the x and find the values of y.

The values of the x will be the domain and the values of the y will be the range

At x= -2

y = 2(-2)+1

= -3

At x= -1

y = 2(-1)+1

= -1

At x= 0

y = 2(0)+1

= 1

At x=1

y = 2(1)+1

= 3

At x=2

y = 2(2)+1

= 5

Plot the graph using the values

Hence, the graph of the equation y = 2x+1 has been plotted

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Answer:

28y+16

Step-by-step explanation:

8(3y+2)+4y

24y+16+4y

28y+16

The simplification of the given expression is 28y+16.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

We are given an expression as;

8(3y+2)+4y

we need to solve the expression

First open the bracket;

24y+16+4y

Solve the like terms;

28y+16

Therefore, the simplification of the given expression is 28y+16.

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The value of x that makes ∠U and ∠V a complement of each other is; x = 9

There are different equal angle theorems in math's such as complementary angles, supplementary angles, linear pairs e.t.c

Now, complementary angles are defined as angles that sum up to 90 degrees.

We are given that;

m∠U = 2x°

m∠V = 4m∠U = 4(2x)°

We want to find the value of x that makes ∠U and ∠V a complement of each other.

This means that by the definition of complementary angles, they will sum up to 90 degrees. Thus;

2x + 4(2x) = 90

2x + 8x = 90

10x = 90

x = 90/10

x = 9

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Complete question is;

m∠U = 2x°, and m∠V = 4m∠U. Which value of x makes ∠U and ∠V complement of each other? A. 25 B. 9 C. 36 D. 18

The sequence that shows the numbers in order from least to greatest is

√72 , 5,32, |-41|

Algebra is a branch of mathematics that helps translate real-world problems or situations into mathematical formulas. Mathematical operations like addition, subtraction, multiplication, and division as well as variables like x, y, and z are needed to construct a valid mathematical expression. Coordinate geometry, calculus, and trigonometry are just a few of the mathematics topics that involve algebra. A simple algebraic equation is 2x + 4 = 8. Algebraic expressions are the result of performing operations on variables and constants, such as addition, subtraction, multiplication, division, etc.

√72 = 8.485

32

|-41| = 41

5

least to greatest is √72 , 5,32, |-41|

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Answer:

prime

Step-by-step explanation:

because 19 can only divide 1 and itself

Answer:

12r -9

Step-by-step explanation:

(8r2−7r−9)+(−r2+r)

= 16r -7r -9 +2r +r

= 12r -9

This  figure has no symmetry is the correct option.

Given:

Given figure is parallelogram ,

The number of lines of symmetry of a parallelogram depends on the type of parallelogram.A non special parallelogram does not have any lines of symmetry. This includes any quadrilateral with two pairs of parallel and equal sides, except for rectangles, squares and rhombuses.

A rectangle is a parallelogram with four right angles. This property allows it to have two lines of symmetry.

A rhombus is a parallelogram with four equal sides. The number of lines of symmetry of a rhombus depends on whether it is a square or not. If it has four right angles, the rhombus is a square and thus has four lines of symmetry. If not, the rhombus only has two lines of symmetry.

Therefore this  figure has no symmetry is the correct option.

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Answer: 40% of the fruit pieces are apples

Step-by-step explanation:

[tex]\frac{6}{15}[/tex] = .4

.4 x 100% = 40%

The Tyler’s error is Both powers should be in the denominator with positive exponents.

The exponent of a number shows how many times the number is multiplied by itself.

For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general,  [tex]x^n[/tex]means that x is multiplied by itself for n times.

given:

[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{-9}[/tex]

As, we know using the law of exponents

[tex]a^{-m} = 1/a^m[/tex]

So, [tex]x^ {-3} = 1/[/tex]x³

and, [tex]y^{-9}[/tex] = [tex]1 / y^9[/tex]

Then, we can write

[tex]x^{-3} y^{-9}[/tex] = 1/x³ × [tex]1/ y^{9}[/tex]

Hence, Both powers should be in the denominator with positive exponents.

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An equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2

In this question, we have been given

slope (m) = 3/4

and a point (0, 2)

We need to find an equation of a line with a slope of 3/4 and containing the point (0,2)

Using the formula for the slope-point form of equation of line,

y - y1 = m(x - x1)

y - 2 = 3/4(x - 0)

y - 2 = (3/4)x

y = (3/4)x + 2

Therefore, an equation of line with a slope of 3/4 and containing the point (0,2) is y = (3/4)x + 2

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The probability of randomly drawing 10 cards from a deck and getting exactly 5 spades is 0.0468

Formula Required:

Given a set of n items, a group of k items can be chosen in any of the 'n' ways, where 'k' is the number of possibilities. The order in which the choices are made is not significant.

A typical deck of cards contains 52 cards in total. Therefore, there exist (52, 10) scenarios in which 10 cards could be chosen (without replacement) that are exhaustive, mutually exclusive, and equally likely.

Again, there are 13 spades in the entire deck of 52 cards. The remaining (10 - 5) = 5 cards can be drawn from the remaining (52 - 13) = 39 cards in the deck in (39, 5) ways, and 5 spades can be drawn from the 13 spades in (13, 5) ways.

As a result, there are (13, 5) * advantageous scenarios for choosing exactly 5 spades (39, 5)

Consequently, the necessary probability:

= Favorable number of cases for the event / Total number of all possible cases.

= (13 , 5) * (39 , 5) / (52 , 10)

(n, k) = n! / k! (n-k)!  

= 0.0468

Therefore, the probability of 5 spades will be 0.0468

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The amount of sales tax on Finnegan's purchase is $5.94

The first step is to calculate the total amount of purchase

Sweater- $29.50

Jeans- $42.50

Total amount

29.50 + 42.50

= 72

The sales tax rate is 8.25%

The amount of sales tax on the purchase can be calculated as follows

8.25/100 × 72

= 0.0825 × 72

= 5.94

Hence the sales tax on the total purchase is $5.94

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