solving simultaneous equation
a+b=7
a-b=3​

so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

we can start by squaring the equation x²+(1/x)=3

so we have x⁴ + 2x² + (1/x)² = 9

x⁴ + 2x² + 1 = 9x²

x⁴ - 7x² + 1 = 0

Now we can factor it

(x²-1)(x²-1) = 0

so x² = 1

now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1

x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1

= x⁴-2x³-2x-1

= (x⁴-2x³) - (2x+1)

= x⁴-2x³-2x-1

= (x²-x)² - (2x+1)

= (x-1)² - (2x+1)

so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

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The various statements regarding the given scatter plot is checked and found to be true or false.

What is a scatter plot?

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.

1)The equation of the line is y = 2500x - 125.

From the graph we can take two points on the line,

( 2,2250) and ( 10,1250)

Standard equation of line is y = mx + b

where b is y - intercept and m is slope

m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125

From graph, b = 2500

Equation of line is

y = -125x + 2500

Therefore the given equation is false.

2) The group of hikers descends about 250 feet every minute.

      From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.

So the hikers descend 250 feet every minute.

Therefore the given statement is true.

3) The hikers began at the elevation of 2500 feet.

     The x-intercept of the graph is 2500 feet.

      So the beginning elevation is 2500 feet.

 Therefore the statement is true.

4) The graph shows a negative association.

Since the line in the graph is going down and the slope is negative, the graph shows a negative association.

Therefore the statement is true.

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Yes, 6/8 and 9/12 are equal. After simplifying both the fractions we got that both are equal and their value is 3/4.

Let's first try to understand what is a fraction.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom. The denominator specifies the total number of equal parts in the whole, whereas the numerator specifies the number of equal parts that were taken.

A fraction would be 5/10, for instance.

Here, the numerator is 5 and the denominator is 10.

6/8 is a fraction.

6/8 can be simplified further.

6/8 = 3/4

9/12 is also a fraction.

9/12 can be simplified further.

9/12 = 3/4

To compare 2 fractions first we try to make the same denominator.

we have the same value. so they are equivalent.

Given question is incomplete complete the question here:

Are 6/8 and 9/12 equivalent?

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In class 7, adjacent angles are defined as two angles that share a common vertex and a common side but do not have any common interior points. They are angles that are next to each other.

Adjacent angles are often used in geometry to describe the angles formed by intersecting lines or figures. The adjacent angles can be classified into two types, namely:

Interior adjacent angles: They are formed by two lines that intersect inside a closed figure, such as in a parallelogram.

Exterior adjacent angles: They are formed by two lines that intersect outside a closed figure, such as in a straight line.

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Answer:

. The slope of the line indicates that test score and the time spent watching tv are negatively correlated

Answer:

B 12

Step-by-step explanation:

Using pythagoras theorem

Answer:

16 ounces = 1 pint, 8 times 2 = 16

Step-by-step explanation:

Answer in explanation:

1 pint is 16 ounces so he could make 2 batches of lemonade with 1 pint of lemon juice.

(8 x 2 = 16

your answer is 2

Hope this helps!

There are  17/36 pounds of trail mix in each bag.

you need to first add the weight of the peanuts and M&M's together.

1[tex]\frac{17}{18}[/tex] + 1 [tex]\frac{5}{6}[/tex] =([tex]\frac{35}{18}[/tex]) +([tex]\frac{11}{6}[/tex]) =  [tex]\frac{35+33}{18}[/tex]    =[tex]\frac{68}{18}[/tex]

which can be simplified to 3 [tex]\frac{14}{18}[/tex]

So there are 3 [tex]\frac{14}{18}[/tex]pounds of trail mix altogether.

3 [tex]\frac{14}{18}[/tex]÷ [tex]\frac{8}{1}[/tex] =

[tex]\frac{68}{18}[/tex]  ÷  [tex]\frac{8}{1}[/tex]=[tex]\frac{68}{144}[/tex]

which can be simplified to [tex]\frac{17}{36}[/tex]

So there are [tex]\frac{17}{36}[/tex]pounds of trail mix in each bag.

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Answer:

x = 11 and x = -1

Step-by-step explanation:

We have x^2−10x = 11 and want to make a perfect square out of x^2−10x.

To do this, take half of the coefficient of x, square this half, and then add and then subtract the square immediately following x^2−10x:

Half of -10 is -5, and the square of -5 is 25.

x^2−10x = 11 becomes x^2 - 10x + 25 - 25 = 11

Rewrite x^2−10x + 25 as the square of a binomial:  (x - 5)^2.

Then we have (x - 5)^2 - 25 = 11.  Solve this for x -5:

(x - 5)^2 = 36.  Taking the square root of both sides, we get

x - 5 = ±6

Then x = 11 and x = -1

Answer:

Step-by-step explanation:

Answer is 6 units

Answer:

6 units fs

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

2.88*2.2=6.336, which is approximately 6.34.

Answer:

1020

Step-by-step explanation:

The value of the polynomial "5x - 4x^2 + 3" at x =- 1 is -6.

The polynomial is 5x - 4x^2 + 3, and it is required to find its value at x = -1,

Now solve the polynomial by putting the value of x equal to -1:

5(-1) - 4(-1)^2 + 3        ,  x =  - 1

-5 - 4 ( 1 ) + 3             , squaring -1 gives + 1

minus 5 minus 4 plus 3

( - 9 + 3)

( - 6 )

Hence, is shown that the value - 6 is obtained when the given polynomial "5x - 4x^2 + 3" is solved for x = -1.

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The coeficient of x^3+y^4 in the algebraic expression is the number 2

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

2x^3+ 2y^4

As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 2.

2 is the coefficient of x^3+y^4

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The equation y = 5x - 8 and y = 9x - 8 have one solution at

(0, -8)

The equation is solved simultaneously by elimination method as follows

y = 5x - 8

y = 9x - 8

subtraction the equations

0 = -4x - 0

-4x = 0

x = 0

substituting x = 0 into y = 5x - 8

y = 5x - 8

y = 5 * 0 - 8

y =0 - 8

y = -8

The solution of the equation is at the point (0, -8)

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Answer:

33 ounces

Explanation:

20% of 27.5 ounces is 5.5 ounces.

To find how much more juice the container has, we add 5.5 to 27.5, which equals to 33 ounces

Answer:

17,388³

Step-by-step explanation:

To find volume you need bh the formula, which is base x height. We have to find the base first, so you multiply 27 * 23

27 * 23 = 621

Now you multiply 621 by 28 because 18 is the height.

621 * 28 = 17,388

Therefore, the volume of the figure is 17,388³ (I think, I'm not 100% sure if this is correct)

Hope this helps !!

-Ketifa

Answer:

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

Step-by-step explanation:

-x+5y=8

3x+7y=-2

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

3(-x+5y)=3(8)

3x+7y=-2

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

-3x+15y=24

3x+7y=-2

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

22y=22

y=22/22

y=1

-x+5(1)=8

-x+5=8

-x=8-5

-x=3

x=-3

Carman buy the video game in the cost of $45.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

Carman has saved 80% of the money she needs to buy a new video game.

And, she saved the cost $36.

Let total cost of the video game = x

So, We can formulate;

⇒ 80% of x = $36

⇒ 80/100 × x = 36

⇒ 8x = 360

⇒ x = $45

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Answer:

Average Rate = -14/7

Step-by-step explanation:

f(3) = 3^2 - 3 - 8 = -2

f(-4) = (-4)^2 - (-4) - 8 = 12

interval: [-4, 3]

Average Rate = [f(b) - f(a)]/(b - a) interval: [a, b]

= [(-2) - 12] / [3 - (-4)]

= -14/7

Answer:

0.75

Step-by-step explanation:

Answer: 0.75

Step-by-step explanation:

Its correct on AP3X! :)

Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.

The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.

Identify the null and alternative hypotheses.

As well as the sample size, specify.

Choose a suitable statistical test.

Gather information (note that the previous steps should be done prior to collecting data)

Based on the sample data, compute the test statistic.

Examine the null hypothesis, usually indicated by H0.

Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).

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Answer:

23.88 feets

Step-by-step explanation:

C=2π2

=2×3.142×3.8

=23.8792 feets

rounded to the nearest TENTH

=23.88 feets

Answer:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Step-by-step explanation:

<1 and  <2  are Complementary Angles

m<1  + <2  = 90 degrees

Have a great day!

Since, angle 1 and 2 sums up to make 90 degrees, hence Angle 1 and 2 are complementary angles.

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complementary angles.

Angles that add up to 180 degrees are referred to as supplementary angles. For instance, angle 130° and angle 50° are complementary angles since the sum of these two angles is 180°. In the same way, complementary angles sum to 90 degrees.

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Answer:

8.43 years

Step-by-step explanation:

Given data

Cost price P= $4995

Rate r= 10%

FInal amount A= $2150

The expression for the time/duration is given as

t= ln(A/p)/r

t= ln(2150/4995)/0.1

t= ln(0.430)/0.1

t= 0.843/0.1

t= 8.43

Hence the time it will take is 8.43 years

angle ADC equals 74 degrees