Express the absolute value function f(x)=9|x| as a​ piecewise-defined function.

Answer:

P(2)= 1/6

P(odd)= 1/2

P(factor)= 2/3

Answer:

x = -60

Step-by-step explanation:

Given the equation:

[tex] \displaystyle{0.1x - 5 = - 11}[/tex]

Add both sides by 5

[tex] \displaystyle{0.1x - 5 + 5= - 11 + 5} \\ \\ \displaystyle{0.1x = - 6}[/tex]

Multiply both sides by 10 to get rid of the decimal

[tex] \displaystyle{0.1x \times 10 = - 6 \times 10} \\ \\ \displaystyle{x= - 60}[/tex]

Therefore, x = -60

Answer:

Step-by-step explanation:

0.1x − 5 = −11

0.1x = -11 + 5

0.1x = -6          multiply by 10 both sides

x = -60

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

0.1 x (- 60) - 5 = -11

-6 - 5 = -11

-11 = -11

The four ways to find the midpoint of a line segment are using the Midpoint Formula, using the Distance Formula, using a Graph, and using a Ruler.

Using the Midpoint Formula:

This method involves using the midpoint formula, which is (x1 + x2)/2, (y1 + y2)/2. This formula gives the coordinates of the midpoint when the coordinates of the two endpoints of the line segment are known.

Using the Distance Formula:

This method involves using the distance formula to find the distance between the two endpoints of the line segment and then dividing the distance by 2. The midpoint will be located at the point that is half the distance from each endpoint.

Using a Graph:

This method involves plotting the two endpoints of the line segment on a graph and then drawing a line segment connecting the two points. The midpoint of the line segment will be located at the point where the line segment is bisected.

Using a Ruler:

This method involves measuring the distance between the two endpoints of the line segment with a ruler or measuring tape, and then marking the point that is halfway between the two endpoints. The midpoint of the line segment will be located at the point that is marked.

All of these methods can be used to find the midpoint of a line segment, it depends on what information is given and what tools are available.

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The values of x and y are -1 and 4 respectively.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given are two equations, -2x+3y=14 and x+2y=7

Solving equations by using substitution method,

-2x+3y=14..........(i)

x+2y=7

x = 7-2y.......(ii)

Using eq(ii) in eq(i)

-2(7-2y) + 3y = 14

-14+4y+3y = 14

7y = 28

y = 4

Put y = 4 in eq(ii)

x = 7-2(4)

x = -1

Hence, the values of x and y are -1 and 4 respectively.

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7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.

The mean of a dataset, often termed as the arithmetic mean, is the amount of all values divided by the overall number of values (as opposed to the geometric mean). This is the most often used indicator of central tendency and is frequently referred to as the "mean." This is obtained by dividing the number of values in the dataset by the sum of all the values. Calculations can be performed using either raw data or data that has been integrated into frequency tables. A number's average is referred to as its average. Simple math can be used to determine: After simply adding all the digits, divide by the number of digits. the sum divided by the number.

given

three obstacles are overcome by three students.

Total Observations / Sum of Observations = Mean

= 21 / 3

= 7

7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.

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The complete question is :- LeveT P × Diane is a camp counselor. She designs a new obstacle course, and tests the course with  friends. The dot plot shows the time it takes them to complete the obstacle course. a What is the mean of the times? Obstacle Course Test mean - mean 7 minutes.

Answer:

There are 14 pizza rolls and 2 mini hot dogs in the combination meal.

Step-by-step explanation:

From the question, we have the following parameters

Pizza roll = 55 calories each

Mini hotdog = 70 calories each

Combination meal = 910 calories in total

Let the pizza roll be x and the mini hotdog be y

So, we have

55x + 70y = 910

x = 12 + y

Make x the subject in x = 12 + y

x = 12 + y

Substitute x = 12 + y in 55x + 70y = 910

55(12 + y) + 70y = 910

Evaluate

660 + 55y + 70y = 910

So, we have

125y = 250

This gives

y = 2

Recall that

x = 12 + y

So, we have

x = 12 + 2

x = 14

Hence, there are 14 pizza rolls and 2 mini hot dogs

The scaled copy is bigger that means each side is bigger than the original one or the factor is grater tan 1 as  final length(bigger)/ original > 1

In mathematics, a dilation is the enlargement or contraction of a figure by a predetermined scale factor, k, at or around a center of dilation. It is a transformation style that yields comparable figures.

Depending on the scale factor, the original figure will either enlarge or decrease in size. Scaling, also known as dilations, has no impact on how angles are measured.

The original and updated figures' angles will not change because the size has not changed but the shape has. Preimage and image are two terms that can be used to describe the first and new figures, respectively.

The original figure's vertices are identified with capital letters, such as B, to make it easier to identify between two similar figures.

The scaled copy is bigger that means each side is bigger than the original one or the factor is grater tan 1 as  final length(bigger)/ original > 1

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The perimeter of an equilateral triangle is equal to three times the length of the side.  Perimeter = 33 cm and Area =  30.58 cm^2 (√30.58 cm^2)

Perimeter of an equilateral triangle = 3 x side  

=> 3 x 11 cm = 33 cm  

Area of an equilateral triangle = (√3/4) x (side^2)  

=> (√3/4) x (11 cm^2)  

=> (√3/4) x (121 cm^2)  

=> 30.58 cm^2  

=> √30.58 cm^2

The perimeter of an equilateral triangle is equal to three times the length of the side. Therefore, an equilateral triangle with a height of 11 cm will have a perimeter of 33 cm (3 x 11 cm). The area of an equilateral triangle can be calculated using the equation (√3/4) x (side^2). In this case, the area of the triangle is 30.58 cm^2 ((√3/4) x (11 cm^2)). This can be simplified to √30.58 cm^2 in its simplest radical form.

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Only (i), (ii), (iv) and (v) are Pythagorean triplets. A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.

Pythagoras, Gauss, Edison, Hawking. The following are the most noted discoveries of each.

Pythagoras, 500 B.C. School Of Mathematics and Pythagorean theorem.Edison, Year 1879 - Invention of incandescent light bulb.Gauss, Year 1801 - Therom of Alegbraic Solution. Stephen Hawking Year1980 - Studies in cosmology particularly contributing to the context of black holes.

you can check by taking largest side square

and adding square of rest two sides

17^2= 15^2+ 8^2

82^2= 18^2+80^2

26^2= 24^2+10^2

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Answer:

Davids Score

Step-by-step explanation:

The compound inequality says that x+1 is greater than 3 and less than 6.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than the relation between variables and the numbers.

Given that the compound inequality is 6 > x + 1 > 3. The compound inequallity says that the value of x +1 is greater than 3 and is less than 6.

The inequality can be written as,

6 > x + 1 > 3

x + 1 > 3

x +1 < 6

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Lily is making smoothie. Each smoothie 1/2 ​ cup of yogurt. The fraction is   [tex]1\frac{1}{2}[/tex] cup of yogurt does he need to make 3 smoothie.

Fraction:

Fractions represent parts of a whole. This whole thing can be a region or a collection. The word break comes from the Latin word "fraction" which means "to divide". The earliest civilization to study fractions, the Egyptians, used fractions to solve mathematical problems such as the division of food, supplies, and the lack of bullion currency.

In ancient Rome, fractions were written to represent parts of a whole using only words. In India, fractions were originally written with the numbers (numerator and denominator) on top of each other, but without lines. Arabs were the only ones who added the dash used to separate the numerator and the denomination.

According to the question:

Lily on the given conditions, formulate: 1/2 × 3

Write as a single fraction: [tex]\frac{1 * 3}{2}[/tex]

Calculate the product or quotient: 3/2

Convert to mixed fraction: [tex]1\frac{1}{2}[/tex]

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The function f(a+1) is equal to option C. 3a + 4.

Given function:

f(x) = 3x + 1

We have to find f(a+1).

For this purpose, we will take x = a+1 and

substitute it in the function f(x) = 3x+1:

f(x) = 3x + 1

f(a+1) = 3(a+1) +1

f(a+1) = 3(a) + 3(1) +1

f(a+1) = 3a+3+1

f(a+1) = 3a + 4

So the function f(a+1) is equal to option C. 3a + 4.

The complete question is,

Given the function f(x) = 3x + 1, evaluate f(a + 1).

A. 3a + 1

B. a + 2

C. 3a + 4

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Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations .

A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations, and mathematical induction can be found in class eleven algebra textbooks.

Students might improve their exam preparation by working through sample papers.

Attempt to answer the test questions from the prior year. Learning about the question format and scoring system will be beneficial.

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As per the given volume of cuboid, the length is 4 cm and the surface area of the cuboid is 5.76cm

The general formula to calculate the surface area of cuboid is written as,

SA = 2[lb + bh + hl]

where l refers the length, w refers width and h refers height.

Here we have given that a cube of side length 6 cm and has the same volume as that of a cuboid of height 3 cm and breadth 4 cm.

Now, we have to find the length and the surface area of the cuboid.​

By the given value the Surface Area of Cube is calculated as.

=> 6s sq. =  6 x 4sq.

Then the value is 96 cm square

Then the Surface Area of Cuboid is calculated as,

=> 2(24+10h)=96

When we simplify the equation as

=> 24 + 10h = 48

=> 10h=24

Therefore, the value of h=2.4

Then the volume of Cuboid=6*4*2.4=5.76 cm.

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The expression (s+t)(x) is equal to the sum of the functions s(x) and t(x), the expression (s*t)(x) is equal to the product of the functions s(x) and t(x), and the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1). When evaluating (s+t)(-1) we get the result 0.

(s+t)(x)=s(x)+t(x)

(s*t)(x)=s(x)*t(x)

(s-t)(-1)=s(-1)-t(-1)

(s+t)(-1)=s(-1)+t(-1)=-2+2=0

(s+t)(x) = s(x)+t(x)

This means that the expression (s+t)(x) is equal to the sum of the functions s(x) and t(x).

(s*t)(x) = s(x)*t(x)

This means that the expression (s*t)(x) is equal to the product of the functions s(x) and t(x).

(s-t)(-1) = s(-1)-t(-1)

This means that the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1).

Finally, when we evaluate (s+t)(-1) we get s(-1)+t(-1)=-2+2=0.

The expression (s+t)(x) is equal to the sum of the functions s(x) and t(x), the expression (s*t)(x) is equal to the product of the functions s(x) and t(x), and the expression (s-t)(-1) is equal to the difference between the functions s(-1) and t(-1). When evaluating (s+t)(-1) we get the result 0.

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You want to build a structure with a length of 5 m, where the proportions of other dimensions are conserved. Estimate the scale factor, 10 cm / 5 m = 0.02 .

The scale factor is a number that represents the ratio of the measurements of two similar figures, such as geometric shapes or maps. To find the scale factor, you can compare corresponding side lengths or angles of the two figures. The scale factor is the ratio of the length of a side in one figure to the corresponding side in the other figure. You can also find the scale factor by taking the square root of the ratio of the areas or the ratio of the volumes of the two similar figures.

Once you have the scale factor, you can use it to find the missing measurements of a similar figure by multiplying any measurement of one figure by the scale factor. In summary, the scale factor is a numerical value that allows to relate the measurements of two similar figures.

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Length of edge of cube = 6.24 unit

A cube is a three-dimensional object that has 6 congruent square faces. Dimensions of all the 6 square faces of the cube are the same. A cube is sometimes also referred to as a regular hexahedron or as a square prism.

Given,

volume of cube = 27×9 cubic units

Length of edge of cube = ∛(27×9)

                                        = ∛243

                                        = 6.24 unit

Hence, 6.24 unit is length of edge of cube.

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In part A; The graph of inequality y > 2x - 9 shows the dashed line.

And, In part B; The graph of inequality y - 6 ≤ x shown the solid line.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality are,

Part A: y > 2x − 9

Part b; y − 6 ≤ x

Now,

In part A; The inequality '<' used which represent the dashed line

And, In part B; The inequality ≤ used which represent the solid line.

Hence, The graph of inequality y > 2x - 9 shows the dashed line.

And, The graph of inequality y - 6 ≤ x shown the solid line.

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The weight after 36 weeks is 80.6 kg.

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

Given that, a man weighs 95 kg and starts an exercise and eating programme to lose weight.

Let the number of weeks be x.

Now, the expression is 95-0.4x

Here, x=36

95-0.4×36

= 95-14.4

= 80.6 kg

Therefore, the weight after 36 weeks is 80.6 kg.

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Answer:

the equation of the line = y + x -3 -3 = 0

Step-by-step explanation:

Equation of the line is give n by the formula

y - y¹ = m

x - x¹

note: m is the gradient.

Point = (3, 3) and (-1, 7).

Gradient =m= y2 - y1 = 7 - 3 = 4 = -1

x2 - x1 -1 -3 -4

the equation of the line

y - y1 = m

x - x1

y - 3 = -1

x - 3

note: Perform cross multiplication also remember every whole number is over one.

=y - 3 = -1 (x - 3)

=y - 3 = - x + 3

y + x - 3 - 3 = 0.

The positive exponent for the given expression is 1/5.

A positive exponent tells us how many times to multiply a base number, and a negate

ve exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.

The given exponent is [tex]25^{-\frac{1}{2}[/tex].

Now, [tex]25^{-\frac{1}{2} }=(5^2)^{-\frac{1}{2}[/tex]

= 5⁻¹

= 1/5

Therefore, the positive exponent for the given expression is 1/5.

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Answer: 20%

Step-by-step explanation: You can evenly divide 20 by 5, which is four, which makes four 20% of 20. You can subtract 4 from 20 to get 16 to prove this, and keep going all the way back to 0 5 times.

Answer: 3

If you look at the left-most side on figure A, youll notice that it is 2 units long. On figure B, it is 6 units long. 2*x=6 where X is the scale factor. You'll find that X=3. YW BRO

The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined.

The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined. To find the additive inverse of 8 /- 15, simply change the sign of the number from negative to positive or from positive to negative. In this case, the sign of 15 needs to be changed from negative to positive, giving us 8 /+ 15. This means that when 8 /- 15 is added to 8 /+ 15, the result is 0. The concept of additive inverse is important in mathematics as it helps us to solve equations and understand the properties of numbers. Additive inverse is also referred to as the opposite of a number, as it is the number that needs to be added to the original number to get 0. Therefore, the additive inverse of 8 /- 15 is -8 /+ 15.

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The number of different combinations to pay 10p with British coins is given as follows:

6.

The British coins are defined as follows:

Hence the different combinations to pay 10p with British coins are given as follows:

Which means that the number of combinations is of six, and the six combinations are the ones listed by the bullet points, above.

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Acute angles are the angles that measure less than 90 degrees. Right angles measure 90 degrees and Obtuse angles measure more than 90 degrees.

By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you can determine whether the triangle is acute, right, or obtuse. The triangle is acute because this sum is higher.

A triangle is said to be acute if the squares of its two shorter sides added together exceed those of its longest side. A triangle is considered obtuse if the sum of the squares of its two shorter sides is less than the square of its longest side.

An overview was given as your information is incomplete.

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Speed = 7.7miles/2.2hours = 3.5miles/hour

In physics, the average speed is defined as the ratio of distance traveled during a certain time period.

Distance/Time = Speed

If the problem stated that the two groups’ average speeds are equal,

Mark’s Group Speed Equals Sally’s Group Speed

The problem now suggests that the time is likewise equal. That means Sally’s group took t = 4.7 – 2.5 = 2.2 hours to travel the remaining 7.7 miles.

That implies that the speed is,

7.7 miles/2.2 hours = 3.5 miles/hour.

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The replacement or substitution approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

This makes it easier to solve by combining two linear equations into one equation with a single variable. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.

By changing the value of another variable in an equation, the variable can be eliminated. Thus, the elimination by substitution method is the name given to this technique.

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The particle size of a solution is 0 point 1 nm – 1 nm, and it is a homogeneous mixture of two or more substances called solution.

The term "solute" refers to the material that is dissolving in the solvent to create a solution. It is less prevalent in the solution than the solvent.

A solvent is a substance found in solutions that helps a solute dissolve. It is more prevalent than the solute in the solution.

A solution has the following characteristics:

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