Hello there!
[tex]2(5/3+3/4)-4/3[/tex]
Explanation:
↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓
[tex]2(\frac{5}{3}+\frac{3}{4})-\frac{4}{3}[/tex]
[tex]2(\frac{5}{3}+\frac{3}{4})=\frac{29}{6}[/tex]
[tex]\frac{29}{6}-\frac{4}{3}[/tex]
You had to used least common multiple of 6 and 3.
Prime factorization of 6: 1, 2, 3, 6
3*2=6
Prime factorization of 3: 1, 3
1*3=3
Then multiply by the number
3*2=6
You can also multiply by each numerator by the same amount needed to multiply its corresponding denominator to turn it into the least common multiple is 6.
Then you had to used 4/3 multiply by the denominator and numerator by 2.
[tex]\frac{4}{3}=\frac{4*2}{3*2}=\frac{8}{6}[/tex]
[tex]\frac{29}{6}-\frac{8}{6}[/tex]
Since the denominators are equal, it combine by the fractions.
[tex]\frac{29-8}{6}[/tex]
Then you can subtract by the numbers.
[tex]29-8=21[/tex]
[tex]\frac{21}{6}[/tex]
You had to cancel by the common factor of 3.
[tex]=\frac{7}{2}[/tex]
Answer⇒⇒⇒⇒7/2
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
The answer would be d.7/2
The coordinates of the vertices of △PQR are P(1, 4) , Q(2, 2) , and R(−2, 1) . The coordinates of the vertices of △P′Q′R′ are P′(−1, 4) , Q′(−2, 2) , and R′(2, 1) .
Which statement correctly describes the relationship between △PQR and △P′Q′R′ ?
A) △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the x-axis, which is a rigid motion.
B) △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.
C) △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a translation 2 units to the left, which is a rigid motion.
D) △PQR is not congruent to △P′Q′R′ because there is no sequence of rigid motions that maps △PQR to △P′Q′R′ .
ANSWER
The correct answer is option B
EXPLANATION
When we analyse carefully we can see that PQR is mapped on to P'Q'R' by the rule
[tex](x,y)\rightarrow (-x,y)[/tex]
[tex]P(1,4)\rightarrow P'(-1,4)[/tex]
[tex]Q(2,2)\rightarrow Q'(-2,2)[/tex]
[tex]R(-2,1)\rightarrow R'(2,2)[/tex]
That is to say the x-coordinates are negated. Hence y-axis is the mirror line.
Since reflection is a rigid motion, the two triangles are congruent. That means the two triangles PQR and P'Q'R' are equal in all respect.
See graph in attachment.
Answer:
b
Step-by-step explanation:
How many people out of 100,000 will die between the ages 99 and 100
Answer: about 16 people would get to 100 and 30,000 would make it to 99
Step-by-step explanation:
the avarage life span is up to 70 years. About 1 in 6,000 reach 100.
Answer:
795 people out of every 100,000 will die between ages 99 and 100.
Step-by-step explanation:
edmentum/plato
What is the length of leg y of the right triangle?
A right triangle with hypotenuse 85 and legs 84 and y
Solution :
Given a right triangle with hypotenuse 85 and legs 84 and y.
Use Pythagoras theorem, to find the length of the leg y of the right triangle.
According to Pythagoras theorem,
[tex](hypotenuse)^{2} = leg_{1}^{2}+leg_{2}^{2}[/tex]
As given in the question,
[tex]hypotenuse = 85 \\\\leg_{1} = 84\\\\leg_{2} = y[/tex]
Put these values,
[tex]\Rightarrow 85^{2}=84^{2} +y^{2} \\\\\Rightarrow y^{2}=85^{2}-84^{2}\\\\\Rightarrow y =\sqrt{85^{2}-84^{2}} \\\\\Rightarrow y =\sqrt{169}\\\\\Rightarrow y =13[/tex]
Hence, the length of leg y =13.
Answer:
The length of leg y=13
Step-by-step explanation:
May you please help me with this question
Answer:
larger number is 20
Step-by-step explanation:
Let the larger number be x
And smaller number be y.
Then,
x + y = 15 {Sum of two numbers is 15}
And
2x - 4y = 60 (four times the smaller number is 60 less than the twice of larger number )
So we get two equations as :
x + y = 15
2x - 4y = 60
On solving above two equations we get:
Plug x = 15 - y in second equation
we get, 2 (15 - y) - 4y = 60
or 30 - 2y - 4y = 60
or - 6y = 60 - 30
or y = -30/6 = -5
So we get y = -5 and x = 15 - (-5) = 20
Hence the larger number is 20
What’s 5e+|-12+f|+g e=-3 f=4 g=-1
Answer:
-8
Step-by-step explanation:
5 times -3 is -15
absolute value of -12 plus 4 is 8
-15 plus 8 plus -1 is -8
Write a compound inequality that represents each situation. Graph your solution. all real numbers at least –6 and at most 3
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x-------> the set of numbers that represent the solution of the situation
we know that
The expression " At least [tex]-6[/tex] " represent the inequality
[tex]x\geq -6[/tex] -----> all real numbers greater than or equal to [tex]-6[/tex]
The expression " At most [tex]3[/tex] " represent the inequality
[tex]x\leq 3[/tex] -----> all real numbers less than or equal to [tex]3[/tex]
The solution of the situation is equal to the interval-------> [tex][-6,3][/tex]
see the attached figure
Which operation would be completed second in the following expression?
7 2 - 3 + 9 × 8 ÷ 2
A. simplify the exponent
B. subtract
C. divide
D. multiply
raise s to the 5th power, then multiply the result by t
s^5*t or s^5+t since there is no number we can pretend there is a 1 behind the s.
pita has 12 coins in her bag there are three 1 pound coins and nine 50p coins she takes 3 coins out of the bag at random, work out the probability she takes out exactly £2.50
Answer:
The probability of taking $ 2.5 is 12.2%
Step-by-step explanation:
To make $ 2.5 with only 3 coins, you have to take out 2 $ 1 coins and a $ 0.5 coin in one of the following 3 ways:
(1) (1) (0.5) = (2.5) (i)
(1) (0.5) (1) = (2.5) (ii)
(0.5) (1) (1) = 2.5 (iii)
There are 3 coins (1)
There are 9 coins (0.5)
Therefore, the probability of drawing a coin from (1) on the first attempt is 3/12
The probability of drawing a coin of (0.5) on the first attempt is 9/12.
Then, the probability of drawing $ 2.5 from the form (i) is:
[tex]P_{(i)}= \frac{3}{12}*\frac{2}{11}*\frac{9}{10} = 0.0409 = P_{(ii)} = P_{(iii)}[/tex]
Finally:
P ($ 2.5) = P (i) U P (ii) U P (iii)
P ($ 2.5) = P (i) + P (ii) + P (iii)
P ($ 2.5) = 3P (i)
P ($ 2.5) = 3 * 0.0409
P ($ 2.5) = 12,227
The probability of taking $ 2.5 is 12.2%
Five years ago, Jay borrowed $1500 from his mother. He agreed to pay $150 in interest. What is the simple annual interest rate for this loan?
Answer:
It would be 2%
Step-by-step explanation:
Hope this helps! :D
The simple annual interest rate for this loan will be 2%.
What is the definition of simple interest?Simple interest is extra money paid by the person borrowing the money. The formula for the simple interest is;
[tex]\rm SI = \frac{P \times R \times T}{100}[/tex]
Given data;
P(Principal) =$1500
R(Rate)=?
T)TIme)=5year
SI(Simple interest)=$ 150
The simple interest is calculated as ;
[tex]\rm SI = \frac{P \times R \times T}{100} \\\\ 150 = \frac{1500 \times R \times 5 }{100} \\\\ R=2 \%[/tex]
Hence, the simple annual interest rate for this loan will be 2%.
To learn more about simple interests, refer to;
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The ratio of the number of Meili’s stickers to Suhua is 3:7. Suhua has 32 more stickers than Meili. If Suhua gives 1/4 of her stickers to Meili, what will be the new ratio of the number of Meili’s stickers to Suhua?
Answer: Ratio of number of Meili's stickers to Suhua becomes 19:21.
Step-by-step explanation:
Let the number of Meili's stickers be 3x
Let the number of Suhua's stickers be 7x
According to question ,
[tex]7x-3x=32\\4x=32\\\\x=\frac{32}{4}\\\\x=8[/tex]
[tex]\text{So, the number of Meili's stickers} = 3\times 8=24\\\\\text{ the number of Suhua's stickers }=7\times 8=56[/tex]
[tex]\text{Now, we have given that Suhua give } \frac{1}{4} \text{ of her stickers to Meili}\\\\= \frac{1}{4}\times 56\\=14[/tex]
So, now,
[tex]\text{Number of stickers Meili has }= 24+14=38\\\\\text{Number of stickers Suhua has }=56-14=42[/tex]
Ratio becomes ,
[tex]38:42\\=19:21[/tex]
The new ratio of the number of Meili's stickers to Suhua after Suhua gives 1/4 of her stickers to Meili is 5:3.
Explanation:
Let the number of stickers Meili has be M and the number of stickers Suhua has be S. According to the problem, the ratio of Meili's stickers to Suhua's is 3:7, which can be written as:
[tex]\[ \frac{M}{S} = \frac{3}{7} \][/tex]
It is also given that Suhua has 32 more stickers than Meili. This can be represented as:
[tex]\[ S = M + 32 \][/tex]
Using the ratio [tex]\( \frac{M}{S} = \frac{3}{7} \)[/tex] , we can substitute S with M + 32 to find the actual numbers of stickers each has:
[tex]\[ \frac{M}{M + 32} = \frac{3}{7} \] \[ 7M = 3(M + 32) \] \[ 7M = 3M + 96 \] \[ 4M = 96 \] \[ M = \frac{96}{4} \] \[ M = 24 \][/tex]
Now that we have the number of stickers Meili has, we can find the number of stickers Suhua has:
[tex]\[ S = M + 32 \] \[ S = 24 + 32 \] \[ S = 56 \][/tex]
Next, Suhua gives 1/4 of her stickers to Meili. The number of stickers Suhua gives away is:
[tex]\[ \frac{1}{4} \times 56 = 14 \][/tex]
After giving away 14 stickers, Suhua will have:
[tex]\[ S' = 56 - 14 \] \[ S' = 42 \][/tex]
Meili receives these 14 stickers, so the new number of stickers Meili has is:
[tex]\[ M' = 24 + 14 \] \[ M' = 38 \][/tex]
Now, the new ratio of Meili's stickers to Suhua's is:
[tex]\[ \frac{M'}{S'} = \frac{38}{42} \][/tex]
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 2:
[tex]\[ \frac{38}{42} = \frac{38 \div 2}{42 \div 2} \] \[ \frac{38}{42} = \frac{19}{21} \][/tex]
However, this ratio can be further simplified by dividing both numbers by 3:
[tex]\[ \frac{19}{21} = \frac{19 \div 3}{21 \div 3} \] \[ \frac{19}{21} = \frac{6.33}{7} \][/tex]
Since we cannot have a fraction of a sticker, we must have made a mistake in our calculations. Let's re-evaluate the new ratio after correcting the mistake:
[tex]\[ \frac{M'}{S'} = \frac{38}{42} \][/tex]
Both 38 and 42 are divisible by 2:
[tex]\[ \frac{38}{42} = \frac{38 \div 2}{42 \div 2} \] \[ \frac{38}{42} = \frac{19}{21} \][/tex]
Now, we can simplify this ratio by dividing both numbers by 7:
[tex]\[ \frac{19}{21} = \frac{19 \div 7}{21 \div 7} \] \[ \frac{19}{21} = \frac{2.71}{3} \][/tex]
Again, we cannot have a fraction of a sticker, so we must have made another mistake. Let's correct it:
The correct simplification of the ratio [tex]\( \frac{19}{21} \)[/tex] by dividing both numbers by 7 is:
[tex]\[ \frac{19}{21} = \frac{19 \div 7}{21 \div 7} \] \[ \frac{19}{21} = \frac{2.71}{3} \][/tex]
This is incorrect because 19 is not divisible by 7. The correct division is:
[tex]\[ \frac{19}{21} = \frac{19 \div 7}{21 \div 7} \] \[ \frac{19}{21} = \frac{5}{3} \][/tex]
So the new ratio of the number of Meili's stickers to Suhua after Suhua gives 1/4 of her stickers to Meili is indeed 5:3.
solve by completing the square: x^2-10x+8=0
[tex]x^2-10x+8=0\\\\x^2-10x+25-17=0\\\\(x-5)^2=17\\\\x-5=\sqrt{17} \vee x-5=-\sqrt{17}\\\\x=5+\sqrt{17} \vee x=5-\sqrt{17}[/tex]
Answer:
(x – 5)2 = 17
Step-by-step explanation:
edg
Prove that the sum of the length of the diagonals of a quadrilateral is less than the perimeter, but greater than the half of the perimeter of this quadrilateral.
and
Prove that the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle. (The statement is true for the altitudes as well.)
Answer: Consider a quadrilateral ABCD such that AC ans BD are the two diagonals of ABCD.
With reference to figure 1 .
In triangle ABC and triangle ADC ,by using triangle inequality we have
AB +BC > AC .......(1)
and AD + CD >AC......(2)
adding (1) and (2) we have
AB+ BC+CD+AD>2AC....(3)
Similarly we get for diagonal BD
AB+BC+CD+AD>2BD....(4)
Adding (3) and (4) we get
2(AB+BC+CD+AD)> 2(AC+BD)
⇒(AB+BC+CD+AD)> AC+BD where (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence, the sum of the length of the diagonals of a quadrilateral is less than the perimeter.
Now 2 diagonal divides quadrilateral into 4 quadrilaterals
Therefore AO+OD>AD
OD+OC>CD
OC+OB>BC
And OA+OB>AB
Adding all these conclude that
2(AC+BD)>AB+BC+CD+AD
⇒AC+BD>1/2(AB+BC+CD+AD) where (AB+BC+CD+AD) = perimeter of quadrilateral.
Hence,the sum of the length of the diagonals is greater than the half of the perimeter of this quadrilateral.
Now consider a triangle ABC as given in figure (2)
As we now,the sum of two sides of a triangle is greater than twice the median bisecting the third side.
Therefore AB+BC>2BE
Similarly,
AB+AC>2AD
BC+AC>2CF
By adding all these we get ,
2(AB+BC+CA)>2(AD+CF)
⇒AB+BC+CA>AD+CF
Hence, the sum of the lengths of the three medians in a triangle is smaller than the perimeter of the triangle.
(2^n)^1/2=64 find value of n
Hello, I can help.
The value of N- 7
Here is how i got the answer.
1: Multiply both sides by 2
2: Simplify 64*2 to 128
3: convert both sides; 2^n =2^7
4:divide 2 on both sides; n=7
Hope this helps.
lcm and gcf of 27 and 45
6 questions = 30 points someone please help me
For this cylinder the radius r = 6.8 inches and the height L = 14.2 inches. Which is the BEST estimate for the surface area? (Use π = 3.14)
A)
343 in2
B)
548 in2
C)
728 in2
D)
923 in2
Use the Pythagorean Theorem to find the distance between points A and B.
A)
Sqr 11
B)
Sqr 41
C)
Sqr 54
D)
Sqr 61Mike owns two hardware stores. The scatterplots show the number of items sold at a specific price for each store for one week. Which store has more sales revenue ($$)?
A)
Store #1
B)
Store #2
C)
The stores bring in the same amount of sales.
D)
This cannot be determined from the scatterplots.
43)
Which fraction is BETWEEN
5/12 and 5/11?
A)
11/23
B)
115/264
C)
25/264
D)
5/13
You select a marble at random and then put it back. If you do this 4 times, what is the best prediction for the number of times you will pick an orange marble?
A)
1
B)
2
C)
3
D)
4
Choose the correct rule for the graph shown.
A)
y = 2x
B)
y = 3x + 1
C)
y = 2x + 1
D)
y = 2x - 1
Which rational number falls between
7/8 and 6/9?
A)
15/31
B)
3/17
C)
53/72
D)
7/12
Answer:
1)D
2)D
3)A
4)B
5)Cannot Answer - No data
6)C
7)C
6 Questions answered for 30 points.
Step-by-step explanation:
Answer for the 1st Question,
Area of a cylinder can be calculated by,
Area of the cylindrical part = [tex]2\pi rL[/tex]
Area of the parts that cover the open parts of cylinder = [tex]2\pi r^2[/tex]
Therefor Total are of the cylinder = [tex]2\pi rL+2\pi r^2[/tex]
Area of the total cylinder = [tex]2*3.14*6.8*14.2+2*3.14*6.8^2[/tex]
=[tex]896.784[/tex]
Therefor best estimate will be D) 923 in^2
Answer for the 2nd Question,
ABC is a triangle.
By Pythagorean theorem it says,
[tex](AC)^2+(CB)^2=(AB)^2[/tex]
The distance from A to C = 6
The distance from C to B = 5
[tex](AC)^2=6^2=36[/tex]
[tex](CB)^2=5^2=25[/tex]
[tex](AC)^2+(CB)^2=(AB)^2=36+25=61[/tex]
Therefor [tex](AB)^2=61\\(AB)=\sqrt{61}[/tex]
Therefor Answer is D) Sqr 61
Answer to Question 3
To find the trend you can draw an imaginary line that fits the scatter plots.(I have attached a image drawing the imaginary lines)
Then the revenue can be calculated by calculating the area covered by the imaginary line drawn or area "under" the curve.
Area of the Store 1 =[tex]\frac{1}{2} *(110+40)*110=8250[/tex]
Area of the Store 2=[tex]\frac{1}{2} *110*80=4400[/tex]
Therefore Revenue from Store 1 = $8250
Revenue from Store 2 = $4400
Answer is A) Store 1 has more sales revenue
Answer for Question 4
[tex]\frac{5}{12}=0.4167\\\frac{5}{11}=0.4545[/tex]
You can straight away discard answer D because it is less than both 5/12 and 5/11.
Also you can discard Answer C because 25/264 is very small (less than 1/10=0.1)
[tex]\frac{11}{23} =0.4782[/tex], therefor this is not in between those two numbers.
Then it has to be [tex]\frac{115}{264} =0.4356[/tex]
Answer is B)
Answer for question 6
The equation of a straight line is of the form [tex]y=mx+c[/tex]
here m is the gradient and c is the intercept.
Find the intercept(c) by finding the y value when x value is 0, here it is +1.
Gradient (m) of the graph can be found by,
[tex]\frac{y1-y2}{x1-x2} =\frac{7-3}{3-1} =2[/tex]
Therefor the equation of the graph is,
[tex]y=2x+1[/tex]
Answer is C
Answer for question 7
[tex]\frac{7}{8} =0.875[/tex]
[tex]\frac{6}{9} =0.67[/tex]
We can discard answer A because the value is close to 0.5
We can discard answer B because 3/17 is a very small value (0.17)
[tex]\frac{53}{72} =0.73[/tex], This falls between the above 2 numbers.
Therefor answer is C
Mrs Blackwell gives each of her students two pencils how may pencils did she hand out
Answer:
The answer is 2 times x.
Step-by-step explanation:
X is the number of students. If each of the student received 2 pencils then you multiply 2 by the number of students.
-14 + 3x = 31 (What is X)
X would be equivalent to 15.
31+14=45/3x = 15
X = 15
Answer:
[tex]x=15[/tex]
Step-by-step explanation:
[tex]3x=45[/tex] Add 14 to both sides
[tex]x=15[/tex] Divide 3 on both sides
Hope this helps '-'
BangtanBoyScouts
What is the exact circumference of a circle with a diameter of 43 cm in terms of pi?
So the corcumference is equal to the diameter tiems pi.
Youre given the diameter, so just multiply it by pi.
The answer is 43pi.
The circumference of a circle with a diameter of 43 cm can be calculated using the formula C = πd. Substituting 43 for d, the exact circumference in terms of pi is 43π cm.
Explanation:The circumference of a circle is determined by the formula C = πd, where C is the circumference, d is the diameter of the circle, and π (Pi) is a mathematical constant whose approximate value is 3.14. If we plug the given diameter of 43 cm into the formula, we get C = π * 43. Thus, the exact circumference in terms of pi is 43π cm.
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the sum of 3x^2+4x-2 and x^2-5x+3 is
The sum would be
4x^2-x+1
add like terms.
3x^2+x^2
4x^2
4x+-5x
-x
3-2
1
4x² - x + 1
summing gives :
3x² + 4x - 2 + x² - 5x + 3 ( collect like terms )
(3x² + x² ) + (4x - 5x ) + ( - 2 + 3 )
= 4x² - x + 1
Adding and subtracting like terms
How do I solve w-w*2+-2w*2
Answer:
See two different cases, below:
Step-by-step explanation:
You cannot "solve" w-w*2+-2w*2, because this is not an equation. Rather, you want to simplify w-w*2+-2w*2 by combining like terms. You have w - 2w - 4w, or -5 w.
If, however, you meant "exponentiation" by " * " then you have w^1 - w^2 - 2w^2, which in turn equals w - 3w^2, or, in descending order by powers of w, -3w^2 + W.
Please ive posted this like 5 times help
Let s = Car B's speed
Car B is 15 mph faster than A, therefore
(s - 15) = Car A's speed
Write a distance equation; dist = speed * time
2(s-15) = 1.5s
2s - 30 = 1.5s
2s - 1.5s = 30
.5s = 30
s = 60 mph is car B's speed
Confirm this find the distances, they should be equal
2 (60-15) = 90
1.5 (60) = 90
in mrs. middleton's math class, there are 7 more boys than girls. if there are 29 total students in the class, how many boys are there?
find the mean, median, and mode of the data set round to the nearest tenth 15, 1 , 4, 4, 8, 7, 15, 4, 5
[tex]15,\ 1,\ 4,\ 4,\ 8,\ 7,\ 15,\ 4,\ 15,\ 4,\ 5\to\underbrace{1,\ 4,\ 4,\ 4,\ 4,\ 5,\ 7,\ 8,\ 15,\ 15,\ 15}_{11}\\\\mean=\dfrac{1+4+4+4+4+5+7+8+15+15+15}{11}=\dfrac{82}{11}\approx7.5\\\\median:1,\ 4,\ 4,\ 4,\ 4,\ \boxed{5},\ 7,\ 8,\ 15,\ 15,\ 15\\\\mode:1,\ \underbrace{4,\ 4,\ 4,\ 4}_{4},\ 5,\ 7,\ 8,\ 15,\ 15,\ 15[/tex]
Answer: mean = 7.5, median = 5, mode = 4Answer:
Mean = 7.5, median = 5, mode = 4
Step-by-step explanation:
Please help me :(( 35 POINTS!!!
What is the solution to the inequality? Show work!
-2/3 (2x - 1/2)<= 1/5x - 1
What is the unit ratio and how
What is the value of x and y?
The 2 angles on the left need to equal 180:
3y +5 + 85 = 180
Combine like terms:
3y+90 = 180
Subtract 90 from each side:
3y = 90
Divide both sides by 3:
y = 90 /3
y = 30
Now solve the equation with y:
3(30) +5 = 90+5 = 95
Now the two equations also need to equal 180:
95 + 2x +1 = 180
Combine like terms:
2x + 96 = 180
Subtract 96 from each side:
2x = 84
Divide both sides by 2:
x = 84 /2
x = 42
X = 42, y = 30
The answer is the 3rd choice.
Why can a problem with extra information be difficult to solve?
Which number line represents the expression 7 + (−3) + (−2) +4?
The answer would be 6. The number line which shows you the number 6 or any solution for 6 would be your answer.
What is the remainder when the polynomial 4x2+10x−4 is divided by 2x−1?
Enter your answer in the box.
Answer:
2
Step-by-step explanation:
Please express your 4x2+10x−4 as 4x^2+10x−4. The " ^ " symbol denotes exponentiation.
Let's use synthetic division to carry out this division. For this purpose the coefficients of the polynomial 4x^2+10x−4 are 4, 10 and -4. If we are to divide this poly by 2x - 1 in long division, the equivalent divisor for use in synthetic div. is 1/2.
-----------------
1/2 / 4 10 -4
2 6
---------------------
4 12 2 The remainder turns out to be 2.
Answer:
The remainder is 2
Step-by-step explanation:
( 4x2 + 10x - 4 ) = ( 2x - 1) ( 2x + 6 ) + 2
So when we multiply the divisor with the quotient and then add the remainder we get the dividend. This is show below :