Which shows one way to determine the factors of x3 – 12x2 – 2x + 24 by grouping?

Answer:

Option 4

Step-by-step explanation:

Firstly, we need to make the two x's or the two y numbers the same. Lets multiply the second equation by 2:

(2x + 3y = 5 ) * 2 =

4x + 6y = 10

Now, subtract the second equation from the first one:

(4x - y = -11) - (4x + 6y = 10)

4x - 4x = 0

-y - 6y = -7y

-11 - 10 = -21

-7y = -21

Divide both sides by -7:

y = 3

Plug 3 into the first equation as y:

4x - 3 = -11

4x = -11 + 3

4x = -8

x = -2

So x = -2 and y = 3. We need to find one of the options that equals this.

-4x - 9y = -21

-10y = -30

40x - 90y = -210

-90y = -270

40x - 0 = 40x

-90y - - 90y = -90 + 90 = 0y

-210 - -270 = -210 + 270 = 60

40x = 60

x = 1.5

We already know this isn't equivalent because the x value is not the x value of the given equation.

4x + 3y = 5

2y = -6

_______

8x + 6y = 10

6y = -18

8x - 0 = 8x

6y - 6y = 0

10 - -18 = 10 + 18 = 28

8x = 28

x = 3.5

So we know this isn't equivalent because again, the x value isn't the same as the given equation.

7x - 3y = -11

9x = -6

-----------

63x - 27y = -99

63x = -42

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

63x - 63x = 0

-27y - 0 = -27y

-99 - - 42 = -99 + 42 = -57

-27y = -57

-9y = -19

9y = 19

y = 19/9

So we know this one isn't equivalent as the y value isn't the same as the given equation.

12x - 3y = -33

14x = -28

x = -28/14 = -2

12(-2) - 3y = -33

-24 - 3y = -33

-3y = -33 + 24

-3y = -9

y = 9/3

y = 3

So x = -2 and y = -3 which is the same as the first equation.

Final answer:

Option 4 is the correct equivalent system for the given linear equations because you can derive the system in Option 4 by multiplying the original system's equations by constants and rearranging them.

Explanation:

We are given the system of linear equations:

To find an equivalent system, each equation from the new system should be derivable from the original system. A common method is to multiply one or both of the original equations by a constant to see if it matches one of the offered options.

Option 4 is the correct choice. Multiplying the first original equation by 3, we get:

And multiplying the second original equation by 7 and rearranging yields:

The other options cannot be derived from the original system through multiplication or other allowed operations, hence they are not equivalent.

Answer:

I think it is A or B Hope this helps

Step-by-step explanation:

Answer:

The answer is C.Subtraction im a math teacher so if right mark brainliest

Step-by-step explanation:

Answer: Choice C) 115 degrees

Focus on the parallel lines G and L, which are the top and bottom most horizontal lines. Notice that the transversal cut forms the alternate exterior angles 2 and 11. The angles are on the outside or exterior of the "train tracks" of the parallel lines. Also, they are on opposite sides of the transversal line. So that is how we can consider them to be alternate exterior angles.

Similar to alternate interior angles, alternate exterior angles are congruent if we have a transversal cutting a pair of parallel lines.

So in short, angle 2 and angle 11 are congruent. We are given angle 2 to be 115 degrees. Angle 11 is also 115 degrees.

Answer:

A. you take 3 ft and divide it in fourths which is 9 inches.

B. side length is 9 inches and the equation is 3ft ÷ .25

Step-by-step explanation:

I explained it in the answer however I will say that a square is the same length all around so I chose to use 3ft instead of 4.5 because its easier but you cannot do this with rectangles.

Answer:

218 feet per minute

Step-by-step explanation:

To find this, first subtract the initial amount (20) from the depth he soon reaches (3290). This will leave you with the amount of 3270 which is the distance the pilot whale went.

To find the feet per minute, divide by new depth by 15 in order to get the final answer of 218 feet per minute.

Hope this helps!

Answer:

10

Step-by-step explanation:

let's call the difference in each term d so the sequence would look like

3,(3+d),(3+2d),(3+3d),(3+4d)

notice how in this sequence that (3+4d) is the fifth term so it must equal 31

3+4d=31

4d=28

d=7

now plug this into the second term

(3+(7))

and we see that the second term is 10

The value of the second term will be 10.

Since the arithmetic sequence has a first term of 3 and the fifth term of 31, this can be represented thus:

First term = a = 3

Fifth term = a + 4d = 31.

Substitute the value of a into the second equation.

a + 4d = 31

3 + 4d = 31

4d = 31 - 3

4d = 28.

d = 28/4

d = 7

Therefore, the value of the second term will be:

= a + d

= 3 + 7

= 10

The value of the second term will be 10.

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Answer:

The correct answer is D.

Step-by-step explanation:

just multiply the original function by the factor 3.

[tex]|x|- 7 = 8\\\\|x|=15\\\\x=-15 \vee x=15[/tex]

Answer:

x = –15 or 15

Step-by-step explanation:

|x| – 7 = 8

We need to isolate the absolute value.

Add 7 to each side

|x| – 7+7 = 8+7

|x|  = 15  

Now to get rid of the absolute values, we take what is inside the absolute values and set it equal to the right hand side.  Remember we set it equal to the positive amount and the negative amount.

x=+15 and x=-15

Answer:

$14.64 per person

Step-by-step explanation:

If we are sharing the cost between 10 people, we divide the total cost by 10

$146.35 /10 = $14.635

We round to the nearest cent

$14.64

Each of the 10 people would need to pay $14.64 for the party cost of $146.35, rounded to the nearest cent.

To calculate how much each person would have to pay for the party cost of $146.35 shared by 10 people, you divide the total cost by the number of people.

Step-by-step calculation:

Therefore, each person would have to pay $14.64.

Answer:

t≤ 2

Step-by-step explanation:

The temperature must be 2F or less

t <=2

t≤ 2

Answer:

5

Step-by-step explanation:

The degree of a polynomial is found by identifying the term with the largest exponent. The degree of a term is found by adding all the exponents of the variables of that term.

For example: [tex]3x^{2} yx^{3}[/tex]

The degree of this term is found by adding all the exponents: 2+1+3=6

In the case of a polynomial, it meets the largest degree term

For example: [tex]2x^{2} y+5x^{2} y^{2} z-8x^{4}[/tex]

If we add the exponents of each term, we will have the term with the greatest degree :   5

The degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.

The degree of a polynomial can be defined as the largest exponents on any of the variables of a polynomial of the largest sum of exponents, if any of it's term has multiple variables.

Thus: The largest exponent in [tex]x^5-4x+2[/tex] is 5.

Therefore, the degree of the polynomial, [tex]x^5-4x+2[/tex] is 5.

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Answer:

D) (1,5)

Step-by-step explanation:

You have to substitute so...

(-1,0):

y = 3x + 2

0 = 3(-1) + 2

0 = -3 +2

0 = -1

(-1,0) is NOT a solution.

(0,3):

y= 3x + 2

3 = 3(0) + 2

3 = 0 +2

3 = 2

(0,3) is NOT a solution.

(1/3,1):

y = 3x + 2

1 = 3(1/3) + 2

1 = 1 + 2

1 = 3

(1/3,1) is NOT a solution.

(1,5):

y = 3x + 2

5 = 3(1) + 2

5 = 3 + 2

5 = 5

(1,5) IS a solution.

Answer:

40 yards

Step-by-step explanation:

8×5≈40

Answer:

both 17 and 19 are right triangles because they both have a right angle

Step-by-step explanation:

Answer: 7.16cm

Step-by-step explanation:

R=C/2pi

R=45/pi2

R=45/2 = 22.5pi

The radius of a circle with a circumference of 45pi centimeters is 22.5 centimeters.

To find the radius of a circle with a circumference of 45pi centimeters, we can use the formula for circumference:

C = 2(pi)r

Given that the circumference is 45pi, we can substitute this value into the formula:

45pi = 2(pi)r

Now, we can solve for r:

r = 45/2 = 22.5 centimeters

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Answer:

425 mm

Step-by-step explanation:

The ratio of compound A to compound B is 5 is to 6.

So, we can say that the total ratio is of 11 parts (5+6=11).

If the chemist wants a total of 935 mm of the drug, then each of the 11 parts are worth:

[tex]\frac{935}{11}=85[/tex]

From the ratio, we know that Compound A is 5 parts. So:

[tex]85*5=425[/tex]

425 mm of Compound A is needed.

To make 935 milliliters of the drug using 5 milliliters of compound A for every 6 milliliters of compound B, approximately 429 milliliters of compound A would be needed. This was found by setting up and solving a proportion based on the given ratio.

This question refers to a ratio or proportion problem. Given that for every 5 milliliters of compound A you use 6 milliliters of compound B, we can set up a proportion to solve for the amount of compound A needed to make 935 milliliters of the drug.

First, establish the existing ratio. 5ml A is to 6ml B, or in other words, 5/6 = A/B. Having the amount of the entire drug, 935 ml, we can sum up the parts, which means A (the required amount of compound A in ml) plus B (the required amount of compound B in ml) should equal to 935 ml.

Substituting B as 6A/5 in the equation, we get A + 6A/5 = 935. Solving this equation gives A approximately equal to 429 ml. Thus, you would need approximately 429 milliliters of compound A to create 935 milliliters of the drug.

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1/3+3/4=4/12+9/12=13/12=1 and 1/12. (1 1/12)

5/6+2/3=5/6+4/6=9/6=3/2 or 1.5 or 1 and 1/2.

Simplify the left side of the equation using the distributive property.

5(a+3) = 5*a + 5*3 = 5a + 15

Now the equation looks like this: 5a + 15 = 8a

Next we want to put all the variables on the same side.

In this case, the easiest way to do this is subtract 5a from both sides.

5a + 15 - 5a = 8a - 5a

15 = 3a

In order to isolate a, divide both sides by 3

15/3 = 3a/3

5 = a

Need more info:

Can you give me more info so I can help you better?

15) Yes, it is a function.

16)

A f(-4)=2

B F(3)= something around -1.75

C f(-5)=0

D f(-2)=4

E f(0)=0

F) -2

17)2(2a+5)=4a+10

a(a+5)=a^2+5a

18) 1

Answer:

The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form

Step-by-step explanation:

The ratio indicates how many times one number contains another

The ratio can be written as:

The two terms of the ratio must have the same units

∵ Sarah uses 9 mm of colored fabric to make her curtains

∵ She also uses 2 cm of of white fabric

- To express the amount of white fabric to colored fabric as a ratio

   you must change the centimeter to millimeter because the

   terms of ratio must have the same unit

∵ 1 centimeter = 10 millimeters

∴ 2 centimeters = 2 × 10 = 20 millimeters

∴ She uses 20 millimeters of the white fabric

Now write the ratio between the white fabric and the colored fabric

→  White    :    colored

→  20          :    9

∵ 20 and 9 do not have a common factor

∴ The simplest form of the ratio is 20 : 9

The ratio of the white fabric to the colored fabric is [tex]\frac{20}{9}[/tex] in its simplest form

Sarah uses 2 cm of white fabric for every 9 mm of coloured fabric. After converting to the same unit (centimeters), the simplest form of the ratio of white fabric to coloured fabric is approximately 2.22:1.

To determine the ratio of the amount of white fabric to coloured fabric Sarah needs for her curtains in its simplest form, we first need to ensure that both fabrics are expressed in the same units. The question states Sarah uses 9 mm of coloured fabric and 2 cm of white fabric. Since there are 10 mm in a cm, 9 mm of coloured fabric can be converted to 0.9 cm.

Now, with both fabric measurements in centimeters, we can write the ratio of white fabric to coloured fabric: 2 cm of white fabric to 0.9 cm of coloured fabric. To find the simplest form of this ratio, we divide both sides by 0.9:

The simplest form of the ratio is therefore 2.2222...:1, which can be rounded and written as approximately 2.22:1, white to coloured fabric.

Answer:

654

Step-by-step explanation:

The graphs of lines in the form y=mx always pass through the origin (0, 0). These graphs only differ in the rate of decrease or increase of the lines.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be represented by the following mathematical equation:

y = mx

Where:

Generally speaking, the characteristics for a graph that shows a proportional relationship or an equation in y = mx form include the following:

In conclusion, the difference between the graphs of the form y = mx is the rate of decrease or increase of the lines.

Complete Question:

What do the graphs of lines in the form y=mx have in common? How might they differ?

[tex]42=2\cdot21=\boxed2\cdot3\cdot\boxed7\\\\56=2\cdot28=2\cdot2\cdot14=\boxed2\cdot2\cdot2\cdot\boxed7\\\\Answer:\ GCF(42,\ 56)=\boxed2\cdot\boxed7=14[/tex]

Answer:

b

Step-by-step explanation:

We need to find the median of:-

73 75 87 65 69 62 81 64 68 101 74 71 89 87

First, we need to arrange the numbers in ascending order as below:-

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101

Since there are a total of 14 numbers, let's split it up into two halves (each of seven numbers)

62, 64, 65, 68, 69, 71, 73           |||             74, 75, 81, 87, 87, 89, 101

The median would be the mean of the two middle numbers i.e. the mean of 73 and 74

Median = [tex]\frac{73+74}{2}[/tex]

= [tex]\frac{147}{2}[/tex]

= 73.5

So, about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework

Answer:

Option b is the correct choice.

Step-by-step explanation:

We have been given a data set about minutes spent on doing homework the previous night by 14 seniors.

To find the median of data set, first of all we will arrange our data values from least to greatest order.  

62, 64, 65, 68, 69, 71, 73, 74, 75, 81, 87, 87, 89, 101.

Since our data set has an even number (14) of data points, therefore, median will be the average of middle two points, that is 7th and 8th term.

[tex]\text{Median}=\frac{\text{7th term + 8th term}}{2}[/tex]

[tex]\text{Median}=\frac{73+74}{2}[/tex]

[tex]\text{Median}=\frac{147}{2}[/tex]

[tex]\text{Median}=73.5[/tex]

Therefore, median of our given data set is 73.5.

Since median of a data set separates the higher half from the lower half of a data sample. So about half of the students spent less than 73.5 minutes doing homework and about half spent more than 73.5 minutes on homework.

Therefore, option b is the correct choice.

check the picture below.

Answer:

(C) 12.5mm

Step-by-step explanation:

It is given that a pyramid having slant height AC is to be determined. From the given information, we get

AB=12mm, BC=3.5mm and we have to find out the value of AC.

Thus, using the Pythagoras theorem, we have

[tex](AC)^2=(AB)^2+(BC)^2[/tex]

Substituting the given values, we have

[tex](AC)^2=(12)^2+(3.5)^2[/tex]

[tex](AC)^2=144+12.25[/tex]

[tex](AC)^2=156.25[/tex]

[tex]AC={\sqrt{156.25}}[/tex]

[tex]AC=12.5mm[/tex]

Therefore, the value of the slant height is 12.5mm.

Hence, option C is correct.

Answer:

Question 7: I am not very good at recursive rules, so I cannot figure it out, sorry.

Question 8: 1/3

Question 9 a: 75 = How much money per paycheck

Question 9 b: 300 = How much money he started with

Question 10 a: 0,328 = initial amount

Question 10 b: 1.013 = percent increase

Question 11-12: Please submit another picture/question with the full graph.

Step-by-step explanation:

Question 8:

To find the common ratio you take one term divided by one term: 3/1 = 3

Since it is getting smaller every time, fraction: 1/3, because 3 * 1/3 = 1.  1 * 1/3 = 1/3, and it continues in that pattern.

Question 9 a:

f(p) = 75p + 300

Since p = paychecks, 75 appears to be how much money he makes per paycheck.

Question 9 b:

Since you are adding 300 to his current makings, it appears that 300 is the amount of money he already has.

Question 10 a:

Since t = weeks after beginning, 1.013 appears to be the percent increase, and since original amount times percent increase equals total, 10,328 appears to be the initial amount.

Question 10 b:

Since t = weeks after beginning, you would times the percent increase in order to calculate the increase, therefore 1.013 is the percent increase.

Question 11-12: Please submit another picture/question with the full graph.

Answer:

This property would be the Associative property of addition.

Answer: the answer is (A)

Step-by-step explanation: