Consider the polynomials:
A(x) = (3-x)2² - (x-3) (7x+4)-18+2x²
B(x) = (3x + 2)² - (x - 1)²
1) Develop and reduce A (x).
2) Factorize A (x) and B (x).
3) Solve the equation A (x)= B(x)
4) Prove that B (X) -3 = 2x(4x+7) , then solve the equation B(x) =3

Answer:

down below

Step-by-step explanation:

The picture is a little blurry so the graph is hard to read. But I believe the answer is 7/8. The rose would be counting up or down the y axis and the run is counting forward or backward on the x axis.

Hope this helps! :)

Answer:

rise = 7, run = 8

slope = rise/run = 7/8

See attached picture for graph in case you have to plot

Step-by-step explanation:

Take two distinguishable points, (x1, y1) and (x2, y2)  on the graph. Find the difference in their y values= y2 - y1. This will be the rise

Find the corresponding difference in the x values, x2 - x1. This will be the run

Divide the y difference by the x difference and you get rise/run which is the slope of the line

Two clear points are (x1 = 0, y1= -7) and (x2=8, y2=0)

(y2 - y1)/(x2 - x1)

= (0 - (-7)/(8 - 0))

= (0+7/(8 - 0)             ==> 2 negatives make a positive

= 7/8  and that is rise/run

Rise = 7, run = 8

Picture shows rise and run if you want to graph it

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Here we go ~

Let's use Trigonometric ratios to find p :

[tex]\qquad \sf  \dashrightarrow \: \cos(60) = \cfrac{6}{p} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{1}{2} = \dfrac{6}{p} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 6 \times 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 12 \: \: units[/tex]

"Shawn stated that 5x+2 is equal 7x" its is an incorrect statement, because we can only add like terms.

Given,

The statement

5x+2 is equal to 7x

Here 5x and 2 are not like terms. So we can't add them together.

So the given statement is incorrect

5x+2 is not equal to 7x

Hence, "Shawn stated that 5x+2 is equal 7x" it is an incorrect statement, because we can only add like terms.

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Answer:

241.5

Step-by-step explanation:

201.96+38.7+0.84

Using sampling concepts, one sample of 5 high schools in the city of Chicago is given by:

Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.

The problem is incomplete, but researching it on a search engine, it gives us a list of 15 high schools in Chicago, and asks us to take a sample of 5.

Hence, from the concepts of sample and populations, the sample of 5 means that we have to select 5 schools from the 15 listed, hence they are:

Englewood Stem, Hyde Park, Lake View, Marshall, Noble - UIC.

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5 students took part in both individual and team events.

Data is information that has been translated into a form that is efficient for movement or processing. Relative to today's computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Given:

Total students participated = 27

20 students participated in individual events

12 students took part in team events.

We have N(All students) = 27

N(individual) = 20

N(Team)= 12

So,

[tex]N_{\text{individual \; and \; team}} & = N_{\text{individual}} + N_{\text{team}} - N_{\text{All students}}[/tex]

=20+12-27

=32-27

=5

Hence, 5 students took part in both individual and team events.

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Answer:

the answer is a because if you calculate it correctly that the answer I got

We get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

We want to change the digit in the number 5,341 into 5,841.

We also need to find the difference between the numbers.

The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit will be replaced by 8  to form the number 5,841.

This means that 300 is replaced by 800 because the third place in both the numbers is of hundreds.

The difference between 800 and 300 is:

800 - 300 = 500.

Subtraction of 5,341 from 5,841 also yields 500.

Therefore, we get that, the digit is in the 3rd place (hundreds).The difference between the numbers is 500.

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Answer:

[tex]d=1/2[/tex]

How to solve:

Step-by-step explanation:

[tex]\frac{5}{6}=\frac{1}{3}+d\\\frac{1}{3}+d=\frac{5}{6}[/tex]

Group

[tex]\frac{1}{3}+d=\frac{5}{6}\\\frac{1}{3}+d-\frac{1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1}{3}+\frac{-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{1-1}{3}=\frac{5}{6}-\frac{1}{3}\\d+\frac{0}{3}=\frac{5}{6}-\frac{1}{3}\\d+0=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}-\frac{1}{3}\\d=\frac{5}{6}+\frac{-1\cdot 2}{3\cdot 2}\\d=\frac{5}{6}+\frac{-1\cdot 2}{6}\\d=\frac{5}{6}+\frac{-2}{6}\\d=\frac{5-2}{6}\\d=\frac{3}{6}\\d=\frac{1\cdot 3}{2\cdot 3}\\d=\frac{1}{2}[/tex]

Hope it helps.

Answer:

The question is incompleye. Do elaborate?

Answer: A. is true.

Step-by-step explanation: The left side 16384 is equal to the right side 16384, which means that the given statement is always true.

With the help of Pythagoras Theorem for triangles, we get that the possible areas of the square are: 12 sq. units and 20 sq. units, according to the cases mentioned.

According to the Pythagoras Theorem, in a right angled triangle, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given:

Sides of a right triangle are 2 and 4 units.

To find: Area of a square that shares a side with the third side of the triangle.

Finding:

There can the following cases:

If 2 and 4 units are the lengths of the perpendicular sides.

Then, by Pythagoras Theorem, -

[tex]H^{2} = 2^{2}+4^{2}\\ H^{2} = Side^{2}\\H=Side \\H= \sqrt{4+16} \\H= \sqrt{20} \\H= 2\sqrt{5}[/tex]

Hence, the area of the square = side² = 20 units²

If 4 units is the length of hypotenuse.

Then, by Pythagoras Theorem,

[tex]4^{2} = 2^{2} + A^{2} \\16 - 4 = A^{2} \\= \sqrt{12}\\[/tex]

side of triangle = [tex]\sqrt{12}[/tex]

Hence, the area of the square = side² = 12 units²

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Answer:

b. No

Step-by-step explanation:

7/6 can be changed to an equivalent ratio(fraction) by multiplying by the same number on top and on the bottom.

example:

7/6 = 7×3 / 6×3

= 21/18

21/18 is equivalent to 7/6.

7 doesn't even go into 52 for one thing. But 6×8 is 48 so try 8.

7/6 = 7×8 / 6×8

= 56/48

56/48 is equivalent to 7/6, not 52/48

Answer:

3.35

Step-by-step explanation:

5,000,000*6.7 * 10^-7

= 5 * 10^6 * 6.7*10^-7

= 33.5 * 10^-1

= 3.35

The weight of 5 million grains of sand is 3.35 kg.

Option A is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Weight of each grain of sand = 6.7 x [tex]10^{-7}[/tex] kg

Weight of 5 million grains of sand.

= 5,000,000 x  6.7 x [tex]10^{-7}[/tex] kg

= 5 x [tex]10^6[/tex] x 6.7 x [tex]10^{-7}[/tex]

= 33.5 x [tex]10^{-1}[/tex] kg

= = 3.35 kg

Thus,

The weight of the total grain of sand is 3.35 kg.

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Answer:

20 %

Step-by-step explanation:

There was a change from 25 m to 30 m. When we find percentage change of something, we first calculate the difference of final and initial value. Then divide it by initial value × 100.

Change:

= 30 m - 25 m

= 5 m

% change:

= 5 m / 25 m × 100

= 100 / 5

= 20 % (ans)

The property of equality justifies the given statement is Transitive property of equality.

Given,

The statement:

If, 7x = 28,

then, x = 4

We have to find the property of equality that justifies this statement:

The transitive property of equality formula is given as follows:

If y = z and x = y, x must be z. Where items belong to the same category as x, y, and z. For instance, if a line segment's measurement is represented by "x," then its measurement should also be represented by "y" and "z."

The property of equality that justifies this statement If, 7x = 28,

then, x = 4 is  transitive property of equality.

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Hence , the price of the system $295 .

Let the price of the system be "x" .

It is given that in the first week her savings were $8 less than 2/5 the price of the system which can be represented by equation

First week savings =  (2/5)x -8

It is also given that in the second week, she saved 50 cents more than 1/2 the price of the system which can be represented by equation

Second week savings = (1/2)x +0.5

savings + short = price of system

(2/5)x -8 + (1/2)x +0.5 + 37 = x

 (2/5)x +  (1/2)x + 29.5 = x

   4x + 5x/ 10 + 29.5 = x

     9x/10+ 29.5 = x

       0.9x + 29.5 = x

          29.5 = x - 0.9x

           29.5 = 0.1x

           $ 295 = x

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Answer:

x = -7
x = -3

Step-by-step explanation:

Given the following question:

[tex]2\left|x+5\right|=4[/tex]

To find the answer to this question we have to remember to apply the absolute value. The absolute value means we have to convert any negative within the lines into positive.

[tex]2\left|x+5\right|=4[/tex]
[tex]\frac{2\left|x+5\right|}{2}=\frac{4}{2}[/tex]
[tex]\left|x+5\right|=2[/tex]
Apply absolute value:
[tex]x+5=-2[/tex]
[tex]x+5=2[/tex]
Solve each equation:
[tex]x+5=-2[/tex]
[tex]5-5=0[/tex]
[tex]-2-5=-7[/tex]
[tex]x=-7[/tex]
[tex]x+5=2[/tex]
[tex]5-5=0[/tex]
[tex]2-5=-3[/tex]
[tex]x=-3[/tex]


Your answers are "x = -3 and x = -7."

Hope this helps.

Answer:

x = -3

x= -7

Step-by-step explanation:

l x + 5 l = 4/2

(x + 5) = 2 or - (x + 5) = 2

- (x + 5) - 5 = 2 - 5

x = -3

- x - 5 = 2

- x - 5 + 5 = 2 + 5

-x = 7

x = -7

The average of the other 3 numbers is 72.

Average or mean is a measure of central tendency which calculates the central point of a data-set.

Average of a set of numbers is calculated by taking the sum of the numbers and dividing it by the total frequency of the numbers.

If 3 numbers a , b and c are taken then the average is equal to

(a+b+c) ÷3

Given average of 5 numbers is 72.

Therefore the sum of the numbers is  72 × 5 = 360

Two of the numbers are 70 and 74 .

Sum of the remaining 3 numbers = 360 - (70 + 74) = 360 - 144 = 216

Average of the 3 numbers = 216 ÷ 3 = 72

Therefore the average of the remaining 3 numbers is 72.

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Seeing that substituting the value x ≤ -2, did not yield a result that is correct with the equation x5 +7 > x3 we can say that Sam's conjecture is incorrect

Given data

x ≤ -2

x5 +7 > x3

Sam's conjecture is tested by substituting the value x ≤ -2 into the equation x5 +7 > x3.  If the result is in accordance with the equation then Sam's conjecture is correct, however if the result is not in accordance with the equation the Sam's conjecture is incorrect.

The substitution will give

( -2 )^5 + 7 > ( -2 )^3

-32 + 7 > -8

-25 > -8  (since -25 is less than -8, Sam's conjecture is incorrect )

Seeing that substituting the value x ≤ -2, did not yield a result that is correct we can say that Sam's conjecture is incorrect

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Answer:7lb

Step-by-step explanation:

7x180=1260lb

1260+235=1495lb

In 3 hours Tom drives 243 miles.

So, to find how many miles Tom can drive in 3 hours:

Given: Tom drives 81/2 miles every 1/30 hour.

So, in 30 minutesTom drives 40.5 miles.

Therefore, Tom drives 243 miles in 3 hours.

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The two such x-values are 2 and 8.

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2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.

Arrangement in a series that begins with the greatest or largest and ends with the least or smallest.

Now the given numbers are,

2.3,3.3% and 2/3

Converting them into decimals we get,

2.3 = 2.300

3.3% = 0.033

2/3 = 0.667

Arranging them from greatest to least we obtain,

0.033  > 0.667 > 2.3

Thus, the given numbers from greatest to least are,

3.3% > 2/3 > 2.3

Hence, 2.3,3.3% and 2/3 in order of greatest to least is 3.3% > 2/3 > 2.3.

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The independent variable: lengths of the sides

The dependent variable: the perimeter of a square,

K(5) = 20.

The dependent variable of a function is the output of a function that changes as a result of any change in the independent variable, which is the input of the function.

The input (independent variable) determines the output (dependent variable) of a function.

Therefore, we can make the following deductions:

The independent variable, x, represents lengths of the sides, and the dependent variable is the perimeter of a square, because the perimeter of the square depends on the length of the side of the square.

The function that relates to the variables is: K(x) = 4x

So, K(5) = 4(5) = 20.

This means, if 5 is the length of one of the sides of the square, then 20 is the perimeter of the square.

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The tree was 210 cm tall.

Let 'h(t) ' models the height of the tree in centimeters and 't' denotes the number of years since Renata moved in.

Given, h(t) = 210 + 33t

This is a linear function in 't'.

This function says that in each year the tree grows 33 cm tall.

We need to find the height of the tree when Renata moved in.

When Renata moved in, the number of years, t = 0

Applying this into h(t) , we get,

h(t) = 210 + 33 x 0 = 210 cm

Therefore the tree was 210 cm tall when Renata moved in.

The question was incomplete. Find the complete question here:

Ever since Renata moved to her new home, she's been keeping track of the height of the tree outside her window. h(t) models the height of the tree (in centimeters), t years since Renata moved in. h(t)=210+33t

How tall was the tree when Renata moved in?

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