If f(x)=3x^2-2x+4and g(x)=5x^2+6x-8, find (f-g)(x)

The correct option is the thrid one, the first step is

-x+5= 6x-2

Here we have the system of equations:

y = -x + 5

y = 6x - 2

Now, the variable "y" should represent the same thing in both equations, then we can write:

-x + 5 = y = 6x - 2

If we remove the middle part, we get the equation that only depends on x:

-x + 5 = 6x - 2

This is the first step that we should use to solve the system of equations, which is the one in option 3.

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The approximate number of text messages sent in 2011 is 2 x 10^1.

Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.

118, 000, 000, 000 in scientific notation is 1,18 x 10^11

2,357, 000, 000, 000 in scientific notation is 2.357 x 10^12

Difference in messages sent in 2011 compared to 2005 : (2.357 / 1.18) x 10^(12 - 11)

2 x 10^1

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Point E is where the statue should be placed.

At what point should the statue be:

The intersection of the doors to the arena, the spirit store, and the parking lot forms a triangle, with Point E in its center. The radius of the circumscribed circle will therefore equal the distance from the statue to each vertex, placing it at the same distance from all three landmarks.

Point E is where the statue should be placed.

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Answer:

m<C = 12.0 °

Step-by-step explanation:

Since we know that this is a non-right triangle, we must use either the law of sines or law of cosines to find m<C.  

The information we now have only allows us to use the law of sines, which focuses on proportions:

[tex]\frac{SinA}{a}=\frac{SinB}{b}=\frac{SinC}{c}[/tex]

Thus, we can use:

[tex]\frac{sin(98)}{19}=\frac{sinC}{4}\\ 4*sin(98)=19*sinC\\ \frac{4*sin(98)}{19}=sinC\\ sin^-1\frac{4*sin98}{19}=12.033=12.0[/tex]

The sin^-1 represents the sin inverse, which you must use to find angle measures.

Answer: 2 and -10 respectively

Step-by-step explanation:

m in the equation is 2 as it is parallel to a line with a slope of 2

Both point A and B are on the x-axis so both of them have a y value of 0

To find the x value of A, we have to substitute y = 0 into the equation

2x + 8 = 0

x = -4, so the coordinate for A is A(-4,0)

As AB is 9 units, we can figure out that B(5,0)

Substitute x = 5 and y = 0 into the equation y = 2x + c to find c

0 = 2(5) + c

c = -10

So m = 2 and c = -10

Answer:

1/50

Steps:

Recall 2 can divide 100

therefore

2/100 = 1/50

We can observe

Its a geometric progression having first term 9(3)=27 and common ratio as 1/3

So

The firmula is

Option C

Answer:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the graph, the given points are:

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

 [tex]a_n=ar^{n-1}[/tex]

where:

Rewrite the given points as terms of the sequence:

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

[tex]\implies a_2=9[/tex]

[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]

[tex]\implies \dfrac{1}{3}a=9[/tex]

[tex]\implies a=27[/tex]

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

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Answer:

Step-by-step explanation:

15 hope it help

Using the algebraic equation, (2x + 6)/5 = 4x - 3, it has been proved that x = 7/6

Algebraic Proof for the Given Algebraic Equation

The given algebraic equation is,

(2x + 6)/5 = 4x - 3

2x + 6 = 5(4x - 3)

2x + 6 = 20x - 15

20x - 15 = 2x + 6

This algebraic equation can be written as,

20x - 2x - 15 = 6

18x = 15 + 6

18x = 21

x = 21/18

x = 7/6

Hence, using the given algebraic equation, it has been proved that the value of x is 7/6.

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Answer:

Tools used to construct a bisector are 1》pencil ,2》Eraser ,3》protector ,4》Compass ,5》Sharpner etc ....

The time it will take for the car to skid for 150 feet is 8.23 seconds.

The function D(t) = 18t² − 130t gives the distance a car going a certain speed will skid in t seconds.

The time the it would take for the car to skid for 150 feet can be calculated as follows:

Therefore,

D(t) = 18t² - 130t

150 =  18t² - 130t

18t² - 130t - 150 = 0

divide by 3

9t² - 65t - 75 = 0

Hence,

t = 65 ± 5√277 / 18

t = 8.23425471586 or -1.01166666667

Hence,

t = 8.23 seconds.

Therefore, the time it will take for the car to skid for 150 feet is 8.23 seconds.

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An error exists in the distinction between the exact length of an object and its measured length.

The closest to the percent error for Diego's measurement exists at 4.3%.

An error exists in the distinction between the exact length of an object and its measured length.

Error = Actual length - Measured length

= 23cm - 22cm

= 1 cm

Percent error = Error/ Actual length × 100

= 1 /23 × 10

= 4.35%

Therefore, the closest to the percent error for Diego's measurement exists at 4.3%.

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Answer:

8-18=n

-10=n

therefore

n=-10

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

Answer:  [tex]\textsf{n = -11}[/tex]

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Given:  [tex]\textsf{-19 = -8 + n}[/tex]

Find:  [tex]\textsf{Solve for n}[/tex]

Solution: In order to solve for n we need to add 8 to both sides which would cancel -8 on the right side and isolate n giving us the value of n.

Add 8 to both sides

Therefore, the final answer would be that n is equal to -11.

The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)

When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.

Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;

(10x^(0.5) - 8)(5x^(0.5) + 4)

The output will retain the same thing.

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Answer:

4x-3y+4z

Step-by-step explanation:

There are lot's of process to answer it but i will show one easy way to find the answer.

To find the required answer we need to subtract 5x - 4y + 8z by  x-y + 4z, we get

5x - 4y + 8z

-x   +  y - 4z  [Note: while subtracting we must change the sigh that one       ___________who we are subtracting]

4x-3y+4z which is a required answer

Answer:

4x - 3y + 4z

Step-by-step explanation:

Let the unknown value that we have to add be 'a'.

Let us make an expression like this.

x -y + 4z + a = 5x - 4y + 8z

Now make 'a' the subject of the equation.

a = 5x - 4y + 8z - x + y - 4z

Now combine like terms.

a = 5x - x - 4y + y + 8z - 4z

a = 4x - 3y + 4z

Now let us check whether the answer is correct or wrong.

We can replace 'a' with ( 4x - 3y + 4z ).

Let us see.

x - y + 4z + 4x - 3y + 4z

Combine like terms.

5x - 4y + 8z

Yes, we are getting the same answer!

Therefore,

we need to add 4x - 3y + 4z to get 5x - 4y + 8z to  x - y + 4z.

Answer:

8 one-dollar bills

3 five-dollar bills

2 ten-dollar bills

Step-by-step explanation:

Let x = # of one-dollar bills, y = # of five-dollar bills, and z = # of ten-dollar bills. Total amount in the wallet is $43, so the first equation would be 1x + 5y + 10z = 43. Next, there are 4 times as many one-dollar bills as ten-dollar bills, so x = 4z. There are 13 bills in total, so x + y + z = 13

x + 5y + 10z = 43

x = 4z

x + y + z = 13

x + 5y + 10z = 43

x + 0y - 4z = 0

x + y + z = 13

5y + 14z = 43

-y - 5z = -13

5y + 14z = 43

-5y - 25z = -65

-11z = -22

z = 2

x = 4z

x = 4*2 = 8

x + y + z = 13

8 + y + 2 = 13

10 + y = 13

y = 3

The domain of the function shown in the graph is x < 7

The complete question is added as an attachment

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is  x < 7

Hence, the domain of the function shown in the graph is x < 7

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Answer:

0 < r < 1

Step-by-step explanation:

That every sequence gets multiplied by a number less than 1 but more than 0

The law is

Common ratio or r must lies in between 0 and 1

It means

r is in (0,1)

The formula is

[tex]\boxed{\sf S_{\infty}=\dfrac{a}{1-r}}[/tex]

Answer:

There are 9 possible thousands digits, because 0 cannot be the leading digit.

There are 2 possible ones digits, 0 and 5.

If the ones digit is 5:

There are 5 possible thousands digits: 1, 2, 3, and 4.For each possible thousands digit, there are 5 possible hundreds digits. (We used one of the digits above to be the thousands digit, but 0 is a possible hundreds digit.)For each possible pair of thousands-and-hundreds digits, there are 4 possible tens digits.

So there are 5 x 5 x 4 = 100 possible 4-digit numbers that end in 5 with no repeated digit and no digit larger than 5.

If the ones digit is 0:

There are 5 possible thousands digits.For each possible thousands digit, there are 4 possible hundreds digits.For each possible pair of thousands-and-hundreds digits, there are 6 possible tens digits.

So there are 5 x 4 x 6 = 120 possible 4-digit numbers that end in 0 with no repeated digit and no digit larger than 5.

100+120=220

Answer: 220 possible numbers.

Answer:

  i) 441π cm² ≈ 1385.4 cm²

  ii) 196π cm² ≈ 615.8 cm²

Step-by-step explanation:

The areas of circles with radius 21 cm or diameter 28 cm can be found using the appropriate area formula.

The formula for the area of a circle based on its radius is ...

  A = πr²

When the radius is 21 cm, the area is ...

  A = π(21 cm)² = 441π cm² ≈ 1385.4 cm²

The formula for the area of a circle based on its diameter is ...

  A = (π/4)d²

When the diameter is 28 cm, the area is ...

  A = (π/4)(28 cm)² = 196π cm² ≈ 615.8 cm²

Answer:

Before multiplying by pi. 441π cm²

After multiplying by pi. 1384.74 cm²

Step-by-step explanation:

The formula for area of a circle is πr².

r=radius

Square the radius.

21²=441

If they want the answer in this form: 441π cm². If not, then use 3.14 for π.

441*3.14=1384.74

The answer is 1384.74 cm².

Hope this helps!

Answer:

5/3

Step-by-step explanation:

z = (Distributed score - Mean)/Standard deviation= (80-70)/6 = 5/3

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (80 - 70)/6 = 10/6 = 5/3 = 1.666666... ≈ 1.67

as most z-tables round the z-scores to hundredths.

not to forget : the sign matters. so, don't worry, if you have e.g. a specific score of 60 :

(60 - 70)/6 = -10/6 = -5/3 = -1.666666... ≈ -1.67

you did not do anything wrong. that is all ok and valid.

Answer:

(8,14)

Step-by-step explanation:

3x+2y=52

3x+1y=38 Subtract these equations using elimination method to get y=14

Then substitute y=14 to either equation

the bottom one is easier so

3x+1(14)=38 distribute 1 to 14 and any number times one is 1

3x+14=38 Subtract 14 from both sides

3x=24 Divide by 3

x=8 so check now

3(8)+1(14)=38

24+14=38?

38=38? yes

To complete the statements;

The consecutive interior angles is supplementary

The alternate interior angles is congruent

The properties are;

Consecutive interior angles are supplementary

Alternate interior angles are congruent

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Answer:

x = 15

The area is 175 [tex]meters^{2}[/tex]

Cost of weeding is $42

Step-by-step explanation:

The perimeter includes two lengths and two widths, so the equation for x would be

2(2x +5) + 2(x -10) = 80  Distribute the 2's

4x + 10 + 2x -20 = 80  Combine the like terms

6x -10 = 80  Add 10 to both sides

6x = 90  Divide both sides by 6

x = 15

Area is length times width.  We need to find the length and width.

2x + 5

2(15) + 5

30 + 5

35 is the width

x -10

15-10

5 is the length

A = (l)(w)

A = (35)(5)

A = 175  The area is 175

The cost of weeding is 175 x .24 = 42

Answer:

not sure but I think it is this

The ratio of white to black horses is 2:5.

Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).

The ratio of white to black horses = number of white horses : number of black horses

The ratio of white to black horses = 6 : 15

6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3

(6/3) : (15/3) =  2 : 5

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Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes

Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.

The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.

Ratio = minutes run / calories burned

8 / 40 = 1/5

Now, multiply this ratio by 100

1/5 x 100 = 20 minutes

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Answer:

3/10

Step-by-step explanation:

=4/7 + 9/70 - 4/10

=l.C.M of 7 , 70 and 10 =70

=4/7 .10/10 +9/70 -4/10 .7/7

=40/70 +9/70 -28/70

=40+9-28/70

=49-28/70

=21/70

=3/10