a) Expand and simplify (4x + 3)(2x - 5)
(2)
+
b) Factorise x2 + 5x + 6
(2)
Total marks: 4

Answers

Answer 1

Answer:

a. [tex]8x^{2} -14x-15[/tex]

b. [tex](x+3)(x+2)[/tex]

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

[tex]4x*2x=8x^{2}[/tex]

For O, take the outer terms and multiply

[tex]4x*-5=-20x[/tex]

For I, take the inner terms and multiply

[tex]3*2x=6x[/tex]

For L, take the last terms and multiply

[tex]3*-5=-15[/tex]

After that, add all of them up

[tex]8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15[/tex]

B. Since the equation is in the form x^2+bx+c,

[tex](x+?)(x+?)[/tex]

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

[tex](x+3)(x+2)[/tex]


Related Questions

A chemist bought 2390 test tubes and beakers.1034 of them were test tubes and the rest were beakers.How many more beakers did the chemist buy than test tubes?

Answers

Answer:

322

Step-by-step explanation:

The question explains that the total of both test tubes and beakers were

= 2390.

If 1034 of them were test tubes, then the number of beakers bought,

= 2390 - 1034

= 1356.

The question requires the answer to how many more beakers than test tubes were bought, and this would mean subtracting the number of beakers from the number of test tubes.

= 1356 - 1034

= 322

Therefore, 322 more beakers than test tubes were bought.

Find the equation of this line

Answers

the Answer is:

3/4x + 1/4

Answer:

y=3/4 x + 1/4

Step-by-step explanation:

y=mx+b

(5,4) first point

(-3,-2) second one

m=y2-y1/x2-x1 =-2-4/-3-5=-6/-8=-3/-4=3/4

find b when x=5 and y= 4

y=mx+b

4=3/4 (5) +b

4-15/4 =b

4 b=16-15

b=1/4

Which of the following is a solution of y > Ixl - 6?
O (5, -1)
O (-1,-5)
O (-5, 1)

Answers

Answer:

i think its the first option

Step-by-step explanation:

Pls help I need these points
Justin Launches a water balloon vertically from a platform on his roof height in feet is represented By the equation H = -16t^2+32t+48,where T is the time (in seconds) after he launch is the water balloon

What is the maximum height of the water balloon?

How long does it take to reach its maximum height?

Answers

Answer:

a) 64 feetb) 1 sec

Step-by-step explanation:

Given the height in feet represented by the equation H = -16t²+32t+48, at maximum height, the velocity of the water balloon is zero.

Velocity = dH/dt = 0

dH/dt = -32t+32 = 0

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

Substituting t = 1sec into the modeled equation of the height

H = -16t²+32t+48

H = -16(1)²+32(1)+48

H = -16+80

H = 64 feet

The maximum height of the water balloon is 64 feet

b) In order to know how long it takes to reach its maximum height, we will substitute H = 64 feet into the equation of the height.

64 = -16t²+32t+48

-16t²+32t = 16

16t²-32t+16 = 0

t²-2t+1 = 0

t²-t-t+1 = 0

t(t-1)-1(t-1) = 0

(t-1)² = 0

t-1 = 0

t = 1sec

It took the water balloon 1 sec to reach its maximum height.

(2^8 • 5^negative5 • 19^0) • (5^negative2 / 2^3)^4 • 2^38

i need steps shown and a simplified answer please!​

Answers

Answer:

6.872* 10^17

Step-by-step explanation:

(2^(8) * 5^(5) * 19^(0)) * ((5^(2))/(2^(3)) ) * 2^(38)

you add the exponent of the same number because it is multiplication

for number two 2 : 8+38=46

for division you subtract the exponents : 46-3=43

and for number 5 : 5+2=7

for 19^0=1

2^43*5^7=6.872*10^17

write 10 examples of cube that you see in your daily life

Answers

Answer:

Step-by-step explanation:

1. Ice Cubes

2. Dice

3. Sugar Cubes

5. Old Iron Lockers

6. Gift Box

7. Cube Building Blocks

can someone help and explain​

Answers

Answer:

12 4/3 =40

Step-by-step explanation:

I hope that help u

Plzzzzzz help me.......

Answers

Answer: 4 terms and 8 factors

Step-by-step explanation:

^

Sin485 positive acute angle

Answers

Yes sure that is correct because acute angle is yes!

What is the probability of getting an odd number 1-10?

Answers

Answer:

1/2 - Half of the numbers are odd

A project cost at $160 and add 20% VAT, How much does it change the job?

Answers

Answer: 192

Step-by-step explanation:

160 + (20% × 160) =

160 + 20% × 160 =

(1 + 20%) × 160 =

(100% + 20%) × 160 =

120% × 160 =

120 ÷ 100 × 160 =

120 × 160 ÷ 100 =

19,200 ÷ 100 =

Welcomeeee

Find the midpoint of the line segment with end coordinates of: ( − 2 , − 5 ) and ( 3 , − 2 ) Give coordinates as decimals where appropriate.

Answers

Answer:

(0.5,-3.5)

Step-by-step explanation:

Find the mean of the respective coordinates

Caylee caylee build a rectangular prism using 18 cubes that are each measure 1 cm on each side. What could be the dimensions of her rectangular prism

Answers

Answer:

2cm by 3cm by 3cm.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to help us in solving this particular Question or problem;

=> We have a built rectangular prism.

=> The rectangular prism was built by using 18 cubes.

=> Each of the 18 cubes measure 1 cm on each side.

So, the dimensions of Carley's rectangular prism is given below as the multiples of 18 since each of the 18 cubes measure 1 cm on each side.

That's 2 cm × 3 cm × 3cm. Therefore, the length will be 2cm, breadth will be 3cm and height will be 3cm.

Solve for x in the diagram below.
3a
80°
2z
د 2

Answers

Answer:

[tex]x = 20[/tex]

Step-by-step explanation:

[tex]3x + 2x + 80 = 180 \\ 5x + 80 = 180 \\ 5x = 180 - 80 \\ 5x = 100 \\ \\ x = \frac{100}{5} \\ \\ x = 20[/tex]

Answer:

x=20

Step-by-step explanation:

The 3 angles are on a straight line together. Therefore, they are supplementary. This means they must add to 180 degrees.

Therefore,

3x+80+2x=180

Combine like terms by adding 3x and 2x

(3x+2x)+80=180

5x+80=180

We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

80 is being added to 5x. The opposite of addition is subtraction, so subtract 80 from both sides.

5x+80-80=180-80

5x=180-80

5x=100

x is being multiplied by 5. The opposite of multiplication is division, so divide both sides by 5.

5x/5=100/5

x=100/5

x=20

x is equal to 20.

Evaluate (x + y)^0for x = -3 and y = 5.
-1/2
2
1 0

Answers

Answer: 2

Step-by-step explanation:

[tex](-3+5)^0=2[/tex]

The answer for this question is 2 , Hope this helped’

Solve 4x- 9 = k for x.
A. x= k+ 9
B. X=
K-9
4
C. X=
k+9
4
D. x = 4 + 9

Answers

Answer:

x = (k+9)/4

Step-by-step explanation:

4x - 9 =k

Add 9 to each side

4x-9+9 = k+9

4x = (k+9)

Divide each side by 4

4x/4 = (k+9)/4

x = (k+9)/4

Answer:

The answer is C

Explanation:

you first add 9 to both sides, you equation will then be 4x = k+9

you then divide both sides by for to get rid of the four from the left side, that will leave you with the equation of x = k+9 over 4

what is the sum of (2x−6)+4(x−3)

Answers

Answer:

6x - 18

Step-by-step explanation:

2x-6 + 4x-12

6x - 18

Answer:

6x - 18

Step-by-step explanation:

(2x−6)+4(x−3)

Distribute

2x -6 + 4x - 12

Combine like terms

6x - 18

which law would you use to simplify the expression 3^10/3^4

Answers

Answer:

I would use the "quotient rule of exponents"

Step-by-step explanation:

I would use the "quotient rule of exponents" which states that to divide two exponents that have the same base, the result is the same base to an exponent which equals the subtraction of the exponent in the numerator of the original expression minus the exponent that base has in the denominator.

That is:

[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

Then in this case the simplified expression would be:

[tex]\frac{3^{10}}{3^4} =3^{10-4}=3^6[/tex]

Answer: quotient of powers

Step-by-step explanation:

2000 soldiers stand in a row. Beginning from the left, each soldier calls out a number, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, and so on. Beginning from the right, each soldier calls out a number 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, and so on. How many of these soldiers call out a number 3 when beginning from the left and right??

Answers

Answer:

The number of soldiers that call out a number 3 is 666 soldiers

Step-by-step explanation:

The parameters given are;

Number of soldiers = 2000

Soldiers calling from the left = 1, 2, 3,.....

Soldiers calling from the right = 1, 2, 3,.....

Therefore, since the number soldiers calling out the number 3 are 1 in 3 from the left and 1 in 3 from the right, we split the soldiers into 2 groups of 1000, with one group calling from left and the other group calling from the right;

The number of 3s in called out in the first group from the left is therefore;

1000/3 = 333.33 which is 333 soldiers  or from the 3rd soldier to the 999th soldier

Similarly the number of 3s called out from the second group = 333

Hence the total number of soldiers that call out a number 3 = 333 + 333 = 666 soldiers.

The outside temperature at a place is - 20 degree Celsius and it drops 5 degrees every hour.How long it will take to reach the temperature zero degree Celsius?

Answers

Answer:

4 hours

Step-by-step explanation:

20-5x=0

5x= 20

x=4 hours

Please answer correctly !!!!! Will mark brainliest !!!!!!!!!!!

Answers

Answer:

your answers are already  matched up

Step-by-step explanation:

Find the x intercept. y = x + 3 / x - 2

Answers

Answer:

(-3, 0).

Step-by-step explanation:

At the x intercept y = 0 so

(x + 3) / (x - 2) = 0

x + 3 = 0

x = -3.

x-intercept is at (-3,0).

What is the decimal expansion of 30/6? And is it rational or irrational.

Answers

Answer:

5.0 rational

Step-by-step explanation:

30/6 = 5/1 =5.0

it's rational as it is a fraction

In an election of housing society,there are 30 voters.Each of them gives the vote.Three persons X,Y and Z are standing for post secretary.If Mr.X got 2/5 of the total votes and Me.Z got 1/4 of the total votes then how much did Mr.Y get?

Answers

Answer:

Mr Y got 10 votes

Step-by-step explanation:

The election of the housing society has 30 voters. Each of them gives the vote. The three person vying for the post of secretary are X, Y and Z.

Le us calculate the votes of each contestant

Mr X

He got 2/5 of the total votes

number of votes = 2/5 × 30

number of votes = 60/5

number of votes = 12

Mr Z

He got 1/4 of the total votes

number of votes = 1/4 × 30

number of votes = 30/4

number of votes = 1/4 × 30

number of votes = 7.5 ≈ 8 votes

Mr Y

The remaining votes will be 30 - 12 - 8 = 10 votes

Therefore,

Mr Y got 10 votes

A piece of timber is x cm long. 7 cm is cut off. How much is left?

Answers

Answer:

x-7>0

Straight answer: x-7

Step-by-step explanation:

Assuming that the timber is X cm long and 7cm was cut off, there remaining amount is x - 7cm. In order for 7cm to be cut off, the timber must have been > 7cm long => x > 7 => x - 7 > 0

to those who need points 4-9+5/6*33

Answers

Answer:

22.5

Step-by-step explanation:

[tex]4-9+\dfrac{5}{6}\cdot 33= \\\\\\4-9+27.5= \\\\\\-5+27.5= \\\\\\22.5[/tex]

Hope this helps!

Answer:

22.5

Step-by-step explanation:

4-9+5/6*33

-5+165/6

= 22.5

Point A is at (6,-6) and point C is at (-6,-2). Find the coordinates of point B on line AC such that AB= 3/4 AC

Answers

Answer:

-3, -3

Step-by-step explanation:

The coordinates of point B on line AC is (6/7, -30/7).

Given that, A(6, -6), C(-6,-2) and AB= 3/4 AC.

What is the section formula?

The section formula is P(x, y)[tex]=(\frac{mx_{2} +nx_{1}}{m+n}, \frac{my_{2} +ny_{1}}{m+n} )[/tex].

Now, AB= 3/4 AC⇒AB:AC=3:4

P(x,y)[tex]=(\frac{3(-6)+4(6)}{3+4}, \frac{3(-2) +4(-6)}{3+4} )[/tex]

=(6/7, -30/7)

Therefore, the coordinates of point B on line AC is (6/7, -30/7).

To learn more about the coordinates visit:

https://brainly.com/question/7869125.

#SPJ5

Which of the following ratios is proportional to 8 adults: 6 children?

4 adults:3 children
3 adults:4 children
10 adults:5 children
12 adults:10 children

Answers

Answer:

4 adults : 3 children

Step-by-step explanation:

4adults:3children
If you times 4 by 2 it’s 8 and if you times 3 by 2 it’s 6

Please help! Correct answer only please! I need to finish this assignment by today.
At a T-shirt stand on the boardwalk, 7 of the last 14 shirts sold were green. What is the experimental probability that the next shirt sold will be green?

Simplify your answer and write it as a fraction or whole number.

P(green) =

Answers

Answer:

1/2 or 0.5

Step-by-step explanation:

since 7 out of 14 shirts sold were green, the probability would be 7/14. but since you need to simplify, it will be 1/2 or 0.5

Answer:

1/2

Step-by-step explanation:

Since there are a total of 14 t shirts and 7 of them were green, the experimental probability that the next one is also green is 7/14=1/2. Hope this  helps!

the vertex of this parabola is at (4,-3). When the x-value is 5, the y-value is -6. what is the coefficient of the squared expression in the parabola's equation

Answers

Answer:

Step-by-step explanation:

The work form of this upside down parabola is

[tex]y=-|a|(x-h)^2+k[/tex]

It's VERY important that you remember that the negative value there in front of the absolute value of a just means that the parabola is upside down. a itself will not be negative (and we know that because of the absolute value symbols there!). Filling in the x, y, h, and k values we were given allows us to solve for the |a|:

[tex]-6=-|a|(5-4)^2-3[/tex] and

[tex]-6=-|a|(1)^2-3[/tex] and

[tex]-6=-|a|1-3[/tex] and

[tex]-6=-|a|(-2)[/tex] and

3 = -|a|

Again, the negative simply tells us the parabola is upside down, so the absolute value of a = 3, choice c.

Answer: The answer is -3!!!!!!!!!

Step-by-step explanation:

Other Questions
Find the sum of the first 44 terms of the following series, to the nearest integer. 10, 14,18,... In this phylogenetic tree, which two organisms on the tree would be expected to share the most characteristics? sac fungi and cnidarians amoebas and sponges choanoflagellates and cnidarians cnidarians and animals with bilateral symmetry During the 1780s, which group would MOST likely favorinflationary money policies?bankersBmerchantscreditorsD debtors What is the midpoint of the vertical line segment graphed below? (2,4) (2,-9) A voter receives a call in which the caller claims to be conducting a national opinion research poll. The voter is asked if his or her opinion about a congressional candidate would change if he or she knew that the candidate once had a car crash while driving under the influence of alcohol. Identify and explain at least one source of bias in the study described. Then suggest how the bias might have been avoided?a. The data do not seem to support the claims being made by the study. The researcher should consult an expert to make sure that he or she is correctly interpreting the data.b. The study does not appear to have a well-defined goal. The researcher should determine his or her goal and precisely define the variables of interest.c. Since the sample is self-selected, there is a definite participation bias in this study. The researcher should randomly select the subjects of the study.d. The wording of the question is biased to strengthen opposition against a particular candidate. The question wording should be changed to be more neutral. SOMEONE PLEASE HELP ME :( Neurotransmitters can be blocked whichdisrupts the ____ impulse from travelingthrough the target neuron.A. syntheticB. electricalC. somaticD. chemical Can anyone solve thisThanks Please answer this correctly HELP!!Determine if the triangles in the figure are congruent if so right the congruency statement and the reason the triangles are congruent explain your answer Which of the following represents 45 = 5 9?A. 45 is 3 times as many as 15B. 9 is 5 times as many as 45C. 5 is 9 times as many as 45D. 45 is 9 times as many as 5 Identify the sound effect in the following line. "I shall go shod in silk," alliteration, onomatopoeia, or assonance how does shakespeare use the motif of darkness in romeo and juliet 1. Describe the main characters and what they seem to want out of life. If you are reading nonfiction, who are the most important people involved in the events of the book, and what do they seem to want? Finally, if the book has no main characters, describe the main forces that are moving the events of the story forward. (any story) In a grade 11 class, 40% of the students are taking Geography, 30% are taking History and 10% are taking both. If 40 students are enrolled in the grade 11 class, how many students are taking neither Geography or History? A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket? 35 dollars (0.08) 35 dollars (8) 35 dollars (0.08) + 35 dollars 35 dollars (8) + 35 dollars Solve for x 3x - 5 = 2x + 6.01O-1O 110-11 Which action would be considered an act of civil disobedience?O rioting, which causes damage to private and government propertyengaging in a sit-in, in which African Americans stay at a segregated businesslooting, which results in the theft of property from private businessesboycotting, in which people choose not to purchase goods from businesses The height, h in feet, a ball with reach when thrown in the ais is a function of time, t, in seconds,given by the equation h(t)=-16t2+35t+10. Find, to the nearest tenth, the maximum height, in feet, the ball will reach. The time when it reached its maximum height. How many seconds after the ball is thrown it will hit the ground? Please this word is not arranged i want to rearrange it Osueh Mitchell's family is slow cooking 2 3/4 pounds of meat. The recipe says to cook the meat 1 1/2 nours per pound,How long should Mitchell's family cook the meat?A 1 5/6B. 2 3/8 C 4 1/ 8 D. 4 1/4