Mathematics High School

How do you solve 18b2c-12ab3+30ab?

Answers

Answer 1

[tex]6b(3\times 2c - 2a \times 3 + 5a) \\ \\ 6b(6c - 6a + 5a) \\ \\ 6b(6c - a)[/tex]
Answer 2
18b²c - 12ab³ + 30ab

We're simply just trying to factor this out.

So : What goes into ALL of these numbers?  

6 does! :)

So, divide everything by 6.

6(3b²c - 2ab³ + 5ab)

Now, what else goes into these numbers/variables? :)

b does! So, simply factor out b.

6b(3bc - 2ab² + 5a)
----------------------------

To check if this is correct, simplify this & see if it is the same as our original equation.

(6b · 3bc) + (6b · -2ab²) + (6b · 5a)

Simplify.

(18b²c) + (-12ab³) + (30a)

Get rid of the parenthesis.

18b²c - 12ab³ + 30a = 10b²c - 12ab³ + 30ab (Our original equation)

Therefore, 6b(3bc - 2ab² + 5a) is our correct answer.

~Hope I helped!~

Related Questions

Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°.

Find m∠ABC, m∠BAC, and m∠DBC.

Answers

mâ ABC = 35° mâ BAC = 72.5° mâ DBC = 120° Since the diagram wasn't provided, I am making the following assumption: â DBC and â ABC are the vertex angles of the two isosceles triangles. Since, mâ BDC = 30° and triangle DBC is isosceles, then mâ BCD = 30° as well, and mâ DBC = 180° - 30° - 30° = 120° Since mâ ABD = 155°, and mâ ABD = mâ DBC + mâ ABC, that means that mâ ABC = â ABD - â DBC = 155° - 120° = 35° Finally, since mâ ABC = 35° and triangle ABC is isosceles, then mâ BAC = (180° - 35°)/2 = (145°)/2 = 72.5° Pay attention to the assumption in the above calculations. There is a total of 9 different possibilities for this question depending upon what angles are the vertex angles of the triangles. (Actually, only 7 of the 9 potential vertex angles work. 2 of the 9 have the base angles exceed 90 degrees which is impossible for a triangle). Vertex angles â ABC & â DBC: mâ ABC = 35°, mâ BAC = 72.5°, mâ DBC = 120° â ABC & â BDC: mâ ABC = 80°, mâ BAC = 50°, mâ DBC = 75° â ABC & â DCB: mâ ABC = 125°, mâ BAC = 27.5°, mâ DBC = 30° â ACB & â DBC: mâ ABC = 35°, mâ BAC = 35°, mâ DBC = 120° â ACB & â BDC: mâ ABC = 80°, mâ BAC = 80°, mâ DBC = 75° â ACB & â DCB: Impossible â BAC & â DBC: mâ ABC = 35°, mâ BAC = 110°, mâ DBC = 120° â BAC & â BDC: mâ ABC = 80°, mâ BAC = 20°, mâ DBC = 75° â BAC & â DCB: Impossible

Answer:

- m∠ABC = m∠ACB = 25° (as triangle ABC is isosceles).

- m∠BAC = 130°.

- m∠BDC = m∠DCB = 30° (as triangle DBC is isosceles).

Explanation:

We can solve this problem by using the properties of isosceles triangles and the fact that the sum of angles in a triangle is 180 degrees.

1. Since triangle DBC is isosceles, m∠DBC = m∠DCB.

Therefore, m∠DCB = 30°.

2. In triangle ABC, since it's isosceles, m∠ABC = m∠ACB.

3. We know that m∠ABD = 155°. Since triangle ABD is a triangle, the sum of its angles is 180 degrees. So, m∠ABD + m∠BAD + m∠ADB = 180°. Therefore, m∠BAD + m∠ADB = 180° - 155° = 25°.

4. Since triangle ABC is isosceles, m∠ABC = m∠ACB = 25°.

5. In triangle ABC, the sum of its angles is 180 degrees. So, m∠ABC + m∠BAC + m∠ACB = 180°. Substituting the known values, we get 25° + m∠BAC + 25° = 180°. Solving for m∠BAC,

we find m∠BAC = 180° - 25° - 25° = 130°.

Simplify , You may leave the numerator and denominator of your answer in factored form ?

Answers

For this fraction, we have (3x+2) in both the numerator and the denominator. So, they will be cancelled together.
Then we can notice that we can divide the coefficients in the numerator and the denominator by 9 as 36/9 = 4 and 9/9 = 1

So, the expression now becomes:
(x+7) / 4(x-5) which is the simplest form.


The table below represents the atmospheric temperature at a location as a function of the altitude:

Altitude
(in thousand feet)
x
Temperature
(in °C)
f (x)
15
4
20
−6
25
−16
30
−26


The average rate of change of the function between x = 15 to x = 25 is ___degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet

Answers

from x15 to x 25 is 4 - -16 = -20 degree change

25 -15 = 10000 feet

-20/10 = -2 degrees every 1000 feet


For his long distance phone service, Rafael pays a $5 monthly fee plus 9 cents per minute. Last month, Rafael long distance bill was $10.94. For how many minutes was Rafael billed?

Answers

66 minutes, 10.94 - 5 / .09

Does negative fractions become positive when you reciprocal

Answers

no, a reciprocal is something you multiply the number you have to get 1.
No, negative fractions will not become positive

{12x + 4y = 15232x + 12y = 42012x + 4y = 15232x + 12y = 420 In the equations, xx represents the cost of a chicken lunch and yy represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch?

Answers

{12x 4y = 15232x 12y = 42012x 4y = 15232x 12y = 420?In the equations, xx represents the cost of a chicken lunch and yy represents the cost of a v.... I think...  "Xx represents the cost of a chicken lunch..."

Find a number that is 24 more than its opposite

Answers

12 is 24 more than -12. also 12 is half of 24

Russ and vickie are trying to solve a problem.There are 93 students taking buses to the museum.if each bus holds 22 students how many buses will they need? Vickie says they need 4 buses. Russ says they need 5 buses. who is correct?

Answers

Russ
22*4=88, so you will need 5 to transport 92.

Mario bought $5 worth of stamps at the post office. He bought ten more 6-cent stamps than 10-cent stamps. The number of 8-cent stamps was three times the number of 10-cent stamps. He also bought two 20-cent stamps. How many of each kind of stamp did he purchase?

Answers

He bought 2 20-cent stamps.
That is $0.40.
He spent $4.60 on the other stamps.

He bought x 6-cent stamps, y 10-cent stamps, and z 8-cent stamps.

y + 10 = x
z = 3y

6x + 10y + 8z = 460

6(y + 10) + 10y + 8(3y) = 460

6y + 60 + 10y + 24y = 460

40y + 60 = 460

40y = 400

y = 10

x = y + 10 = 10 + 10 = 20

z = 3y = 3(10) = 30

He bought
20 6-cent stamps
10 10-cent stamps
30 8-cent stamps
2 20-cent stamps

What is the probability that a roll of a pair of 6-sided dice will sum to 8?

Answers

2+6
3+5
4+4
5+3
6+2
5 combinations
I'm assuming that the 6-sided dice have the numbers "1" through "6" on the faces. If that assumption holds, then there are 5 ways to add to 8. Those ways are listed below:
2+6 = 8
3+5 = 8
4+4 = 8
5+3 = 8
6+2 = 8

This is out of 6*6 = 36 total ways to roll the two dice. It might help to draw out a dice chart to list all the possible ways. 

There are 5 ways to get what we want (sum to 8) out of 36 ways total. Divide the two values to get 5/36 which is the answer as a fraction

To convert to decimal form, use long division or a calculator to get 5/36 = 0.1389 which is approximate (rounded to four decimal places)

If you want a percentage, then move the decimal 2 spots to the right to go from 0.1389 to 13.89%

Is the TI-36X Pro allowed in the PSAT

Answers

No, the TI-36X Pro is not allowed on the PSAT, as it is not found on the list of acceptable calculators. 

Given the number 2464829438 what is the next number?

Answers

The next missing number will be 9

24648294389

Hope I helped :)

please help
its really important

Answers

See the attached image for the answers in figure 2 and figure 3. Figure 1 will be used to generate figure 2 and figure 3.

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

Use the given table to compute the row and column totals. We simply add up values to get these totals. 

Boys: 108+23 = 131 meaning that there are 131 boys total so this value will go in row 1 of the "total" column attached to the right side of the given table. See figure 1.

Girls: 99+16 = 115 will go right under 131. 

Right-Handed: 108+99 = 207 will go under 99 in the "right handed" column in the "total" row.

Left-handed: 23+16 = 39 will go next to the 207 in the same total row as before

--------------------------------------------
We have the row and column totals computed. Now onto the next step.

Copy the entire table (with row and column totals) to another sheet of paper or just below the table you just wrote out. This new second table will be built upon and altered. First, erase the bottom "total" row. Now divide everything in row 1 by the total
108/131 = 0.82442748091603 which rounds to 0.82
23/131 = 0.17557251908397 which rounds to 0.18

So we'll have 0.82 and 0.18 fill in for the first row of the "Boys" row. See figure 2.

Do the same for the second row. Divide everything in this row by the total 115
99/115 = 0.8608695652174 which rounds to 0.86
16/115 = 0.1391304347826 which rounds to 0.14

The values 0.86 and 0.14 will go in the first two columns of row 2.

The totals will divide by each other to lead to 1
131/131 = 1
115/115 = 1
which explains why we have two '1's in the very right column. They represent 100%

Again, see figure 2 to see how the values are placed.
--------------------------------------------

We'll follow similar steps as before in the previous section. Copy the table from figure 1 but now erase the entire right-hand column marked "total". 

Divide everything in column 1 by the total 207
108/207 = 0.52173913043479 which rounds to 0.52
99/207 = 0.47826086956521 which rounds to 0.48
207/207 = 1

Divide everything in column 2 by the total 39
23/39 = 0.58974358974359 which rounds to 0.59
16/39 = 0.41025641025641 which rounds to 0.41
39/39 = 1

See figure 3 to see how the values are filled in. The values in red are the results we got in this section. The '1's have already been filled in by your teacher.
--------------------------------------------

Side Note: In figure 2, the red values in the "Boys" row add up to 1
0.82+0.18 = 1
The same can be said for the "girls" row too
0.86+0.14 = 1

In figure 3, the red values in the "right handed column" add to 1
0.52+0.48 = 1
And similarly for the "left-handed" column
0.59+0.41 = 1

These four facts are not coincidences. For instance, 82% of the boys are right-handed so that leaves 18% left-handed boys (see row1 of figure 2). So 82% + 18% = 100% which is represented by 0.82+0.18 = 1

A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement, what is the probability of getting two green marbles?

Answers

P(green), is 10/14=5/7 because there are 10 green marbles out of the total 14.
P(2nd green), is 9/13 because there are only 9 green marbles and only 13 total marbles. Then you multiply them 5/7 x 9/13 = 35/117

Answer:  The required probability of getting two green marbles is 49.45%.

Step-by-step explanation:  Given that a bag contains 10 green marbles and 4 yellow marbles. Two marbles are chosen at random, one at a time and without replacement.

We are to find the probability of getting two green marbles.

Let S denote the sample space for the experiment of choosing a marble from the bag and A denote the event of getting a green marble.

The, n(S) = 10 + 4 = 14   and   n(A) = 10.

So, the probability of event A will be

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{10}{14}=\dfrac{5}{7}.[/tex]

After getting one green marble and not replacing, let S' denote the sample space for the experiment of choosing a marble from the bag

and

let B denote the event of getting another green marble.

Then, n(S') = 14 - 1 = 13    and    n(B) = 10 - 1 = 9.

Then, the probability of getting two green marbles is given by

[tex]P\\\\=P(A)\times P(B)\\\\=\dfrac{5}{7}\times\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{5}{7}\times\dfrac{9}{13}\\\\\\=\dfrac{45}{91}\times100\%\\\\=49.45\%.[/tex]

Thus, the required probability of getting two marbles is 49.45%.

What is the 214 term in the sequence 7,10,13,16?

Answers

We can figure this out using the explicit formula.

[tex]f(n)=f(1)+d(n-1)[/tex]

n represents the term we are looking for.
f(1) represents the first term in the sequence, which in this case, is 7.
d represents the common difference, which in this case, is +3.

f(n) = 7 + 3(n - 1)
f(n) = 7 + 3n - 3
f(n) = 4 + 3n

Now, we can input 214 for n and solve.

f(214) = 4 + 3(214)
f(214) = 4 + 642
f(214) = 646

The 214th term in this sequence is 646.

If a penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is

Answers

1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.03125 = 1/32 This is your answer


Final answer:

The probability of heads on the fifth trial is still 0.5, just like any other coin flip.

Explanation:

The probability of heads on the fifth trial is still 0.5, just like any other coin flip. The outcome of each coin flip is independent of the previous flips, so each trial has the same probability of resulting in heads or tails.

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Describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
Transformation #1


Transformation #2


Write an ordered-pair rule for each transformation in the sequence.
Transformation #1


Transformation #2

Answers

First is a 90Âş rotation (counter-clockwise) with respect to the origin. Next is a horizontal transformation of +2 units. Transformation one is (x, y) -> (-y, x) Transformation two is (x, y) -> (x + 2, y)

Answer:  The required sequence of transformations is

Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).

Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).

Step-by-step explanation:  We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.

From the figure, we note that

the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).

And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).

We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :

(x, y)  ⇒  (-y, x).

That is

A(0, 4)  ⇒  (-4, 0),

B(0, 0)   ⇒ (0, 0),

C(2, 3)    ⇒ (-3, 2).

Now, if the vertices of the rotated triangle are translated  2 units right and 3 units down, then

(x, y)  ⇒  (x+2, y-3).

That is, the final co-ordinates after rotation and translation will be

(-4, 0)  ⇒  (-4+2, 0-3) = (-2, -3),

(0, 0)   ⇒ (0+2, 0-3) = (2, -3),

(-3, 2)   ⇒ (-3+2, 2-3) = (-1, -1).

We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.

Thus, the required sequence of transformations is

Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒  (-y, x).

Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).

Last Saturday there were 1486 people at a cinema. There were about the same number of people in each of the 6 theaters. Between which 2 numbers does the number of people fall?

Answers

247 and 248 because 247 in two theaters and 248 in the other four

What is the equation of the parabola with a vertex of (0,7) and passing through (-1,10)?

Answers

y = 3x^2 + 7 is the equation of the parabola

What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and ​ (3, 4) ?

Answers

Final answer:

The area of the triangle is 6 square units.

Explanation:

To find the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4), we can use the formula for the area of a triangle: Area = 1/2 × base × height.

First, we need to find the base and height of the triangle. The base is the distance between the points (-2, 1) and (2, 1), which is 4 units. The height is the distance between the point (3, 4) and the line formed by the base, which is the vertical distance from (3, 4) to the line y=1, which is 3 units.

Plugging these values into the formula, we get Area = 1/2 × 4 ×3 = 6 square units.

What operation would you use to find the next term in the sequence 96,48,24,12?

Answers

Divide by 2

or

÷2

Hope I helped.

A stock value doubles every 42 days. If the stocks start out with $5.00, what will the value of the stock be in 18 weeks?

A.)$125.00

B.)$15.00

C.)$30.00

D.)$40.00

Answers

We know that the stock value doubles every 42 days and that the stocks start out with $5.00.
We should find the value of the stock in 18 weeks. Let us denote this value with S.
One week has 7 days, so 18 weeks have: 18*7=126 days.
In order to find how many times the stocks value was doubled we should divide this number of days with 42: 126/42=3
So, after 18 weeks the value of the stock would be: 5->5*2->(5*2)*2=40

answer:
D.)$40.00

A pair of shoes usually sells for $55. If the shoes are 40% off, and sales tax is 7%, what is the total price of the shoes, including tax?

Answers

The shoes would cost $23.54

Bailey’s Cakes and Pastries baked a three-tiered cake for a wedding. The bottom tier is a rectangular prism that is 18 centimeters long, 12 centimeters wide, and 8 centimeters tall. The middle tier is a rectangular prism that is 12 centimeters long, 8 centimeters wide, and 6 centimeters tall. The top tier is a cube with edges of 4 centimeters each. What is the volume of each tier and of the entire cake?
1,728 cubic centimeters
2,368 cubic centimeters
2,664 cubic centimeters
64 cubic centimeters
576 cubic centimeters
38 cubic centimeter
16 cubic centimeters


The top tier
The middle tier
The bottom tier
The entire tier

Answers

https://brainly.com/question/6670096



Answer:

I hope this helps

Step-by-step explanation:

What is the distance between the two endpoints in the graph below? If necessary, round your answer to two decimal places.

Answers

Its close to 15.811, so I'd say B

a) Simplify the expression and explain each step. (2 points)

4(3x + 2) – 2


b)  Factor the expression completely.  (1 point)


20b – 16





Answers

a) 4 (3x+2)-2
12x+8-2
12x+6
2x+1 simplified expression

Answer:

a) [tex]4\left(3x+2\right)-2=12x+6[/tex]

b) [tex]20b-16= 4\left(5b-4\right)[/tex]

Step-by-step explanation:

a) To simplify the expression you must:

Expand [tex]4(3x + 2)[/tex]:

Apply the distributive law: [tex]\:a\left(b+c\right)=ab+ac[/tex]

[tex]a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2[/tex]

Simplify [tex]4\cdot \:3x+4\cdot \:2= 12x+8[/tex]

[tex]12x+8-2[/tex]

Subtract the numbers: [tex]4\left(3x+2\right)-2=12x+6[/tex]

b) To factor the expression [tex]20b - 16[/tex] you must:

Rewrite 16 as [tex]4\cdot 4[/tex] and 20 as [tex]4\cdot 5[/tex]

[tex]20b-16=4\cdot \:5b-4\cdot \:4[/tex]

Factor out common term 4

[tex]20b-16= 4\left(5b-4\right)[/tex]

What is the slope of the graph?
slope = -3
slope = -1/3
slope = 1/3
slope = 3

Answers

Answer:

slope = -3

Step-by-step explanation:

To find the slope of the graphed line, we can use the slope formula:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]

First, identify two points on the line:

(x₁, y₁) = (0, 3)(x₂, y₂) = (1, 0)

Substitute the coordinates into the slope formula:

[tex]m=\dfrac{0-3}{1-0}=\dfrac{-3}{1}=-3[/tex]

Therefore, the slope of the graphed line is:

[tex]\Large\boxed{\boxed{\textsf{slope}=-3}}[/tex]

t=d+pm for p
i dont understand what this is asking me to do

Answers

T=d+pm
pm = T - d
p = (T - d)/ m
or
p = T/m - d/m

To solve for "p" in the equation "t = d + pm," isolate "p" by subtracting "d" from both sides: "t - d = pm." Then, divide both sides by "m" to find "p": "p = (t - d) / m." This formula allows you to calculate "p" based on given values of "t," "d," and "m."

To solve for "p" in the equation "t = d + pm," you need to isolate "p" on one side of the equation. Here's how you do it step by step:

Start with the Equation:

The equation is t = d + pm, where "t" represents a value, "d" represents another value, "p" is the variable we want to solve for, and "m" is yet another value.

Isolate the "pm" Term:

To get "pm" by itself, we need to eliminate the "d" term on the right side. We can do this by subtracting "d" from both sides of the equation:

t - d = pm

Solve for "p":

Now that "pm" is isolated on the right side, we can solve for "p" by dividing both sides by "m":

p = (t - d) / m

So, the solution for "p" in terms of "t," "d," and "m" is given by the formula p = (t - d) / m. This formula tells you how to calculate the value of "p" based on the values of "t," "d," and "m."

In practical terms, this equation might be used in various scenarios. For example, if "t" represents total distance, "d" represents a fixed distance, and "m" represents a constant speed, then "p" would represent the time it takes to cover the remaining distance to reach "t." This formula can be quite useful in solving real-world problems involving time, distance, and speed.

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The length of the rectangle exceeds its breadth by 3 cm. if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. find the length and breadth of the given rectangle.

Answers

Let's suppose the breadth of the rectangle be x cm 

The length of the rectangle = x + 3 cm

It is assumed that the length and breadth of the rectangle is amplified by 2.

Now, the breadth of the rectangle = x + 2

The length of the rectangle = x + 3 + 2 = x + 5

It is also assumed that the area of the rectangle is 70 sq. cm

Hence, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70

= x2 + 5x + 2x + 10 = 70

= x2 + 7x = 70 - 10

=  x2 + 7x = 60

= x2 + 7x - 60 = 0

= x2 + 12x - 5x - 60 = 0

=  x( x + 12) -5(x + 12) = 0

= ( x + 12) (x - 5) = 0

=x + 12 = 10               or              =x - 5 = 0

= x = 10 - 12 = -2               = x = 5

 

The breadth of a rectangle is never negative, so the value of x is 5 cm

Therefore, the breadth of the rectangle = 5 cm

The length of the rectangle = 5 + 3 = 8 cm

whats 6.3 x 10^-5 in standard notation

Answers

6.3 * 10^-5 is written in scientific notation, writing it in standard notation, it would be 0.000063.
Since the exponent of the scientific notation is -5, we have to move the decimal point 5 places to the left to get this answer.
Other Questions
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