5. Find the product of:
a) -2x (4x²-5x - 3)

The solutions for the given quadratic equation are -0.15 and -5.85.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The given quadratic equation is x²+6x+1=0.

Compare x²+6x+1=0 with ax²+bx+c=0, we get a=1, b=6 and c=1

Use x = [-b ± √(b² - 4ac)]/2a to find the solution. That is,

x = [-6 ± √(6² - 4×1×1)]/2×1

x= (-6 ± √32)/2

x=(-6 ± 5.7)/2

x= -0.3/2 and -11.7/2

x= -0.15 and -5.85

Therefore, the solutions for the given quadratic equation are -0.15 and -5.85.

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Answer:

-4

Step-by-step explanation:

Just put -2 in the polynomial -x².

So, - (-2)² = -4

Cheers!

Algebraic expressions are mathematical phrases that include numbers, variables and mathematical operations.

In class 8, students typically learn about basic algebraic expressions, which are mathematical phrases that include numbers, variables and mathematical operations. These expressions can be evaluated to a single numerical value.

An example of an algebraic expression that is typically covered in class 8 is: x + 2: This is a simple linear expression that involves a variable (x) and a constant (2)

Another example could be: 2y - 3: This is also a linear expression, involving a variable (y) and two constants (2 and 3).

These are simple expressions that involve only one variable and simple mathematical operations like addition, subtraction, and multiplication. As students progress through their studies, they will encounter more complex algebraic expressions that involve multiple variables, exponents, roots, and other advanced concepts.

It's important to note that Algebraic expressions can become more complex as the student progresses, but the basic idea remains the same: it's a combination of numbers, variables, and mathematical operations (such as +, -, x, /) that can be evaluated to a single numerical value.

Therefore, Algebraic expressions are mathematical phrases that include numbers, variables and mathematical operations.

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The required inequality is x > -22/7 which is equivalent to the given inequality.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

-4(x+7) < 3(x-2)

We have to determine the equivalent inequality to the given inequality

As per the question, we have

-4(x+7) < 3(x-2)

Apply the distributive property on both sides,

-4x - 28 < 3x - 6

Rearrange likewise terms,

-4x - 3x < -6 + 28

-7x < 22

- x < 22/7

x > -22/7

Thus, the required inequality is x > -22/7.

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Answer:

75

Step-by-step explanation:

A straight line is 180 degrees. Therefore, ACB = ACD - DCB

= ACB = 180 - 105 = 75

The theoretical probability is 2/4 and the experimental probability is 2/5.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

You automatically have a 25% (1/4) of getting blue. the odds of you spinning is 60 times and landing on blue is 15/60.

Theoretical Probability = 15/60

Theoretical Probability = 1 / 4

The number of times you spun it and it actually landed on blue. i would suggest making up a reasonable number. I would say 24.

The experimental prob would be:-

P =  24/60

P = 2 / 5

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Check the picture below.

now let's take a looksie at the triangles, well segments DE || AC, that only happens if segment DE is the midsegment of the triangle ABC, which also means that both triangles are similar

[tex]\cfrac{AB}{DB}=\cfrac{BC}{BE}\implies \cfrac{(2x)+(x+5)}{x+5}=\cfrac{4+3}{4}\implies \cfrac{3x+5}{x+5}=\cfrac{7}{4} \\\\\\ 12x+20=7x+35\implies 5x+20=35\implies 5x=15\implies x=\cfrac{15}{5}\implies x=3[/tex]

Sandra have 40 coins in total out of 120 coins.

Let the coins with Sandra be x

Then Joel has 1/2 as many coins as Sandra coins so x/2 coins and

mark has 3 times as many as Joel so 3x/2 coins in total.

There amount is 120 coins in total

therefore ,

3x/2 + x/2 + x = 120

4x/2 + x = 120

2x + x = 120

3x = 120

x = 40

So Sandra has total of 40 coins out of 120 coins.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.

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GDP, turnover, wages, and other values' growth rates indicate how much something has changed over time (month, quarter, year). It is typically stated as a percentage.

A value's growth rate (such as GDP, turnover, earnings, etc.) gauges how much it has changed over time (month, quarter, year). It is quite frequently expressed as a percentage.

Growth rates are used to quantify the annual percentage change in a variable. If a variable has a positive growth rate, it is increasing over time; if it has a negative growth rate, it is declining over time. Growth rates can be helpful in evaluating a company's performance and forecasting future performance.

f(x) = 2 * (1.25)^x

This has the shape of

y = a b^x

where b is the growth rate multiplied by one

B = 1.25 + growth rate = 1

1.25 = 1 + the growth rate

Growth rate is.25

25% is the growth rate.

Therefore, the correct answer is option d) 25%.

The complete question is:

Julia opened a new flower shop, and her daily sales are modeled by f(x) = 2(1.25)x. Determine the rate of growth.

A.2%

B.125%

C.75%

D.25%

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Since there are x blue tiles, we can suppose that the product that these algebraic tiles represent is (2x+1)(x+1).

It is permissible to multiplied, divide, add, or negate in mathematics. The following illustrates how an utterance is put together: Multitude, expression, and mathematical expression The ingredients of a mathematical form include numbers, quantities, and functions (such as addition, subtraction, multiplication or division etc.) It is conceivable to contrast idioms and phrases. An expression, generally known as an arithmetic operation, is any mathematical sentence that contains variables, figures, and an accounting operation between them. For instance, the variable m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

Assume that there are x blue tiles.

Let's say there are 1 red tiles.

Therefore,

length equals 2 blue tiles plus 1 red tile.

= 2x+1

Width equals one blue tile plus one red tile. = x+1

Since there are x blue tiles, we can suppose that the product that these algebraic tiles represent is (2x+1)(x+1).

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The area of one wall based on area of floor and height of room is 28 feet².

Finding the length of one side of floor to find the area of wall. The formula to be used in the calculation of side of floor is area = side².

Area of floor = side²

side = [tex] \sqrt{49} [/tex]

side = 7 m

Area of wall will be calculated by finding the product of length and breadth.

Area of one wall = 7 × 4

Performing multiplication on Right Hand Side of the equation

Area of one wall = 28 feet²

Thus, the area is 28 feet².

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Therefore , a result A(x) = 23 is the answer to the function issue that was presented.

Quantities and their variants, equations and associated structures, shapes and their positions, and locations where they are found are all included in the study of mathematics. The link between a collection of inputs, each of which has a corresponding output, is referred to as a "function." A function is a dynamic relationship between inputs and outputs in which each input produces a single, unique result. Each function has a designated area and only needs a tiny area, or scope.

Here,

As a result, h(x) = x2-10x+21 A(x) =y/x =-1 x 10 A(x)=?

A(x) = y/x =h(x-g)-h(x)/g

=> g = Xmax - Xmin

=> g = 10-(-1)

=>  10+1 =g

=> 11 =g

=>(x-11)² - 10*(x − 11) + 21 − (x² - 10x+21) /11 = A(x)

=>  x²- 22x+121-10x + 110 + 21 - x² + 10x -21/11 =A(x)

=>A(x) = 21+ 2

=>A(x) = 23

As a result, A(x) = 23 is the answer to the function issue that was presented.

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A graph is inverse if it is the reflection of the original graph across the line y = x.

Meaning, if you were to put a mirror along the line y = x, the original graph would be reflected onto the inverse graph.

To determine if a graph is the inverse of another graph, we can check the following:

It is important to note that not every function has an inverse function. The function needs to be one-to-one, which means that for every unique output, there must be a unique input.

In summary, a graph is the inverse of another graph if the x- and y-coordinates of the points on the original graph are the y- and x-coordinates of the corresponding points on the inverse graph, respectively and the graph is symmetric about the line y = x.

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Answer: There are no intersections for these two lines, because if you plot them on a graph, they are parallel.

Answer:

2. The difference between the flat fees of the two companies is $20

Step-by-step explanation:

3. 15 units

the equation for the table is y= 8x-17 and if you plug zero in for x, then the answer is -17. -17 is the y-intercept of the equation and the distance between negative 17 and 2 is 15.

Question 1:

3.825 feet; The value means that a typical throw of the ball results in 3.825 feet.

Question 2:

2.5

Question 3:

How many hours do you practice your musical instrument each week?

Question 4:

The range is 4.5, and it means that the data varies by a value of 4.5.

Question 5:

80

Question 6:

Part A: Mean: (5 + 20 + 22 + 25 + 32 + 34 + 45 + 53 + 56 + 60)/10 = 35 minutes. Median: 32 minutes.

Part B: The student should give the median to their teacher because it represents the middle value and is not affected by outliers.

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The unknown angle in the triangle is as follows:

∠E = 60 degrees.

The sum of angles in a triangle is 180 degrees. The angle ∠E can be found using exterior angle theorem.

Therefore, the exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Hence,

120 = ∠C + ∠E

ΔEBC is an isosceles triangle. Therefore, the base angles are congruent.

∠B ≅ ∠C

∠C = 60°

Therefore,

∠E = 120 - 60

∠E = 60 degrees

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The length of the rectangle is 15 units. We can calculate this by using the formula for the area of a rectangle, which is length times width. So, 180 = 12 x length. Solving for length, we get 15.

Answer:

15

Step-by-step explanation:

area of rectangle: base times height or width times length, so;

180(area)=12(width) times height, to find the length divide area by width

180/12=15

The number marked with an arrow on the number line below as an improper fraction is 2[tex]\frac{1}{2}[/tex].

Given is a number line.

The number represented in the number line is -

2.5

or

5/2 = 2[tex]\frac{1}{2}[/tex]

Therefore, the number marked with an arrow on the number line below as an improper fraction is 2[tex]\frac{1}{2}[/tex].

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[tex]\it \begin{cases}\ \it 3x+2y=11\\ \\ \it 7x-y=3\bigg|_{\cdot2}\end{cases} \Rightarrow \begin{cases}\ \it 3x+2y=11\\ \\ \it 14x-2y=6\end{cases}\\ \rule{0.2}{0.2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rule{120}{0.7}\\ \\ \rule{0.2}{0.2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 17x\ \ \ \ \ \bigg|\ \ \ =17\\ \\ \\ 17x=17 \Rightarrow x=1\ \ \ \ \ (*)\\ \\ \\ 7x-y=3\ \stackrel{(*)}{\Longrightarrow} 7-y=3 \Rightarrow y=4\\ \\ \\ S=\{(1,\ \ 4)\}[/tex]

Yes, For exponential growth this is a valid way to find the per capita growth rate That is rmax.

r max is the maximum per capita rate of increase for a particular species under ideal conditions, and it varies from species to species. For instance, bacteria can reproduce much faster than humans and would have a higher maximum per capita rate of increase. The maximum population growth rate for a species, sometimes called its biotic potential, is expressed in the following equation:

dT/dN =rmax* N

Population growth depends upon the difference between Newborn and dead and if we talk about exponential growth the difference is nearly the same as that of the original present population and the per capita growth is being calculated in a similar manner as by dividing the difference between newborn and dead with original present population.

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Answer:

Which symbol correctly compares these fractions? −3/5 −2/3 A. > B. < C. = 1 See answer Advertisement Advertisement ... 10, 2, 1 and x is 5. What is the value of x ? 1 point A) 5 B) 7 C) 13 D) 18 Mike was in charge of collecting contributions for the Food Bank. He received contributions of $80, $70, $60, $40, and $80.

Step-by-step explanation:

The number of the last locker the student opens is 1996.

The student starts by opening locker 1 and then skips one, opens the next one, skips one, and so on. The pattern of open and closed lockers can be thought of as a binary sequence where open lockers are represented by 1 and closed lockers are represented by 0. The student's actions can be thought of as a process of repeatedly dividing the lockers into smaller groups and reversing the order of the open and closed lockers within each group.

The first time the student reaches the end of the hall, the lockers are in the following order:

0001 1110 1111 0010 0101 1010 0101 0010

When the student turns around and starts back, the first locker he encounters is the one that was not opened the first time. The student then opens every other locker, skipping the ones that were already opened. This results in the following order:

0110 1010 0101 0010

The student then continues this process of dividing the lockers into smaller groups and reversing the order of the open and closed lockers within each group. After a few iterations, the student ends up with only one locker left, which is the last one he opens. The number of this locker is represented by the binary number, which is the reverse of the binary representation of 1996. Therefore, the number of the last locker the student opens is 1996.

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The answer is d) 6x+4. This is not a polynomial because it is a linear equation and does not have multiple terms.

A polynomial is a mathematical expression made up of one or more terms, each of which is a numerical coefficient multiplied by a variable raised to a non-negative integer power. For example: x^2 + 3x + 5.

In this polynomial, x is the variable and 2, 3, and 5 are the coefficients. The power of x is 2, 1, and 0 respectively, which are all non-negative integers. The equation d) 6x+4 does not meet these criteria, as the power of x is not present and the coefficient is not a numerical value.

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This system of equations has been solved graphically and its solution is equal to the ordered pair (-1.29, -0.57).

In Mathematics, a point of intersection is the location on a graph where two (2) lines intersect, or cross each other, which is typically represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.

In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection of the lines on the graph;

y = 2x + 2     ........equation 1.

y = -1/3x - 1       ........equation 2.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-1.29, -0.57).

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The solution to the system of equations is

A system of equations is a pair of two linear equations

Given the system of equations

y = -x/3 - 1 and

y = 2x + 2

We proceed to solve the system of equations as follows.

Since we have the equations

y = -x/3 - 1 and

y = 2x + 2

Eqating both expressions, we have that

-x/3 - 1 = 2x + 2

adding 1 from both sides, we have

-x/3 - 1 + 1 = 2x + 2 + 1

-x/3 + 0 = 2x + 3

-x/3 = 2x + 3

Subtracting 2x from both sides, we have that

-x/3 - 2x = 2x - 2x + 3

(-x - 6x)/3 = 0 + 3

-7x/3 = 3

Multiplying both sides by 3, we have

-7x = 3 × 3

-7x = 9

Dividing both sides by -7, we have

x = 9/-7

x = -9/7

Substituting x = -9/7 into y = 2x + 2, we have that

y = 2x + 2

y = 2(-9/7) + 2

= -18/7 + 2

= (-18 + 14)/7

= -4/7

So,

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Answer: y= -75x +200

Step-by-step explanation:

The equation representing the trend line for the data and used to make predictions is a regression equation.

A trend line, also known as a regression line, is a line that represents the relationship between two variables. In this case, the two variables are the time elapsed and the value of the house. By fitting a regression line to the data, it becomes possible to make predictions about the value of the house at any given time in the future.

The type of regression used to model the trend line depends on the nature of the relationship between the two variables. A linear regression is often used when the relationship is approximately linear. In such a case, the regression equation has the form Y = a + bX, where Y is the value of the house, X is the time elapsed, a is the intercept, and b is the slope of the line.

This question cannot be answered without any data because the equation representing the trend line for the data and used to make predictions depends on the specific data being analyzed.

Without the data, it is impossible to determine the relationship between the two variables, which is necessary for finding the appropriate regression equation to model the trend line.

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The sum of the first 8 terms of the following sequence. Round to the nearest is -759/5

Find the sum of the first 8 terms of the following sequence?

To find the sum of a finite geometric series, use the formula,  

Sn= a1-a1r^n/ 1-r

where n is the number of terms, a1 is the first term and r is the common ratio .  

common ratio = a2/a1

S8=3-3(-2/3)8 / 1-(-2/3)

S8 = 3-(-2)8/ 1+ 2/3

S8= 3-256/ 3+2/3

S8= -253/5/3

S8= -253*3/5

S8= -759/5

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The absolute graph will depicts the distance of a number from the origin.

The term graph in math is known as  a diagram showing the relation between variable quantities that is basically of two variables and each os them measured along one of a pair of axes at right angles.

Here we need of define the absolute graph.

The absolute graph which is also known as absolute value graph is defined as

Here we have also know that the graph of the absolute value function is symmetric about the y -axis.

Here we have given the graph of the absolute value function makes a right angle at the origin.

If the value of the absolute value function is an even function then the function is written as f ( x ) = f ( − x )

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