Answer:
Write down the problem. For this example, you will be dividing x3 + 2x2 - 4x + 8 by x + 2. Write the first polynomial equation, the dividend, in the numerator and write the second equation, the divisor, in the denominator.
Reverse the sign of the constant in the divisor. The constant in the divisor, x + 2, is positive 2, so reversing the sign of the constant would give you -2.
Since the opposite of the constant term is -2, we put the -2 inside a box. A common mistake is to put a 2 inside the box, watch out here.
Write all of the coefficients of the dividend inside the division symbol. [2] Write the terms from left to right, just as they appear. It should look like this: -2| 1 2 -4 8.
Bring down the first coefficient. Bring down the first coefficient, 1, below itself. It should look like this:
-2| 1 2 -4 8
↓
1
Multiply the first coefficient by the divisor and place it under the second coefficient.[3] Simply multiply 1 by -2 to get -2 and write this product under the second term, 2. Here's how it would look:
-2| 1 2 -4 8
-2
1
Add the second coefficient and the product and write the answer below the product. Now take the second coefficient, 2, and add it to -2. The result is 0. Write this result below the two numbers, just as you would in long division. Here's how it would look:
-2| 1 2 -4 8
-2
1 0
Multiply this sum by the divisor and place the result under the third coefficient. Now take the sum, 0, and multiply it by the divisor, -2. The result is 0. Place this number below 4, the third coefficient. It should look like this:
-2| 1 2 -4 8
-2 0
1
Add the product and the third coefficient and write the result under the product. Add 0 and -4 to get -4 and write this answer below the 0. Here's how it would look:
-2| 1 2 -4 8
-2 0
1 0 -4
Multiply this number by the divisor, write it under the last coefficient, and add it to the coefficient. Now, multiply -4 by -2 to get 8, write this answer under the fourth coefficient, 8, and add this answer to the fourth coefficient. 8 + 8 = 16, so this is your remainder. Write this number below the product. Here's how it would look:
-2| 1 2 -4 8
-2 0 8
1 0 -4 |16
Place each of the new coefficients next to a variable of one less power than their original corresponding variables. In this case, the first sum, 1, is placed next to an x to the second power (one less than three). The second sum, 0, is placed next to an x, but the result is zero, so you can remove this term. And the third coefficient, -4, becomes a constant, a number without a variable, since the original variable was x. You can write an R next to the 16, because that is the remainder. Here's how it would look:
-2| 1 2 -4 8
-2 0 8
1 0 -4 |16
x2 + 0x - 4 R 16
x2 - 4 R16
Write the final answer. The final answer is the new polynomial, x2 - 4, plus the remainder, 16, over the original divisor, x + 2. Here's how it would look: x2 - 4 +16/(x +2).
Step-by-step explanation:
That was quite long, but those are the steps to synthetically divide polynomials.
What is power of 3 square root of 4 / square root of 2 in simplest radical form?
Answer:
√90=3√10
Step-by-step explanation:
help
any tips on adding/multiplying fractions?
Answer:
sure!
Step-by-step explanation:
if you're just wondering How to, then here you are. in order to add fractions, you first must make sure your two fractions in the equation have like denominators (if youre unsure, the bottom number in a fraction), so they just need to be the same before you can add them. Take 1/2 + 2/3 for example, both 2 and 3 can go into 6, so you can make them both fractions of 6. in order to change the bottom part of the fraction, you need to change the top part too. in the case of 1/2, you will multiply the 2 by 3, so also multiply the 1 by 3. then you have 3/6. for 2/3 you will multiply the 3 by 2, so you must also multiply the 2 by 2, you will get 4/6. Now we have 3/6 + 4/6. Do not change the denominator and simply add across the top. Now you'll have 7/6, or 1 1/6. Multiplying fractions is much much simpler. The denominators don't need to be the same, so you just multiply straight across. Multiply first numerator by second numerator, and first denominator by second denominator. using the 1/2 and 2/3 example again, you have 1/2 * 2/3. so you'll first multiply 1 * 2, and make that the numerator. You have 2/-. Then the same with the denominator, 2 * 3, giving you 2/6. (Or, you can simplify to 1/3.) hope this helps, let me know if you have more questions. :)
For f(x) = 2x + 1 and g(x) = x2 - 7, find (f + g)(x).
Answer:
(f+g)(x)=x²+2x-6
Step-by-step explanation:
(f+g)(x)=2x+1+x²-7
collect like terms
(f+g)(x)=x²+2x+1-7
according to mathematics x² is not a like term of 2x so don't add the them
(f+g)(x)= x²+2x-6
Find m<1 and m<2
Help
Answer:
m<1 = 45
m<2 = 135
Step-by-step explanation:
135 is across from the 135 making m1 135 and 135 plus 45 equals 180, 180 is the total for the line the other 2 angles are on.
Which of the following ordered pairs
make this equation true?
y =
= 10x - 30
A. (1, -12)
B. (8, 1)
C. (4, 10)
D. (6, 20)
The ordered pairs that make this equation true is (4, 10)
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Given the linear equation: y = 10x - 30:
At (1, -12): y = 10(1) - 30 = -20 ≠ -12
At (8, 1): y = 10(8) - 30 = 50 ≠ 1
At (4, 10): y = 10(4) - 30 = 10
At (6, 20): y = 10(6) - 30 = 30 ≠ 20
The ordered pairs that make this equation true is (4, 10)
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More reviewing purposes
Answer:
143
Step-by-step explanation:
BEDMAS = brackets, exponents, division, multiplication, substraction, addition.
you need to first do the exponents, then the multiplication, then the addition
exponents = 7² = 49
4 x 9 + 2 x7² + 9 = 4 x 9 + 2 x 49 + 9
multiplication = 4x9 = 36
36 + 98 + 9
addition = 36 + 98 = 134 and 134 + 9 = 143
you need to use the BEDMAS (order of opperation) to find the answer, it simplifies the answer and you can do it step by step. I bolded what you needed to use in this question, but you should use all of the ones that you can whenever you can.
good luck. :)
PLS HELPPPP
Answer the following problem using the SOLVE Method
Math Club members are selling Math club members are selling Pi Day T-shirts for $7.50 each. The goal is to
raise $500 by Friday. The figure below shows how much they have raised by
Wednesday. What is the minimum number of T-shirts they must still sell in
order to reach their goal? Explain your reasoning.
The minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
Let x represent the number of Pi Day T-shirts sold.
They are selling Pi Day T-shirts for $7.50 each, So to raise $500:
7.5x > 500
Dividing through by 7.5:
7.5x / 7.5 > 500 / 7.5
x > 66.7
Hence, the minimum number of T-shirt that they must sell to raise $500 is 67 T-shirts
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I'm not exactly sure how to do this. I know how you would graph it but I don't know the transformation.
Answer:
Its D.
Step-by-step explanation:
The 3 as the exponent makes it cubic and since the x+1 is in parenthesis you would move it 1 unit to the left
a shop produces 39 salt lamps in 2 weeks. how many salt lamps will they produce in 22 weeks?
Answer:
You will sell 429 salt lamps in 22 weeks.
Step-by-step explanation:
20 large bottoles can be recyled to make 1 fleece jacket how many fleece jackets can you make with 360 large plastic bottoles
Answer:
18 fleece jackets can be made
I think you have to divide 360 by 20 (Im not sure)
Hopefully this can help :)
show your work
3|n-4| = 18
Answer:
n = 10, n = -2
Step-by-step explanation:
hope it helps.
What is identity matrix.
Answer:
a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. The effect of multiplying a given matrix by an identity matrix is to leave the given matrix unchanged.
Henry is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $118 and allows unlimited mileage. Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m.
Answer:
B.
Step-by-step explanation:
step by step explanation
Answer:
after 70 miles, company B will charge Henry more.
Step-by-step explanation:
at 70 miles both companies will charge the same price
118 = 55 + 0.9m
m = (118 - 55) divided by 0.9 = 70
Is x+y=10 linear or non
Answer:
Not
Step-by-step explanation:
In this case, the degree of variable y is 1 , the degrees of the variables in the equation violate the linear equation definition, which means that the equation is not a linear equation.
In a muncipality ,Two of the most well-known activities for teenagers are biking and motorcycling riding.Out of 100 teenagers,58 in biking,42 like motorcycling and 18 like both
a.create a veen diagram represent the problem
Answer:
See belowStep-by-step explanation:
Given:
Total number is 100Biking = 58Motorcycling = 42Both = 18Biking only:
58 - 18 = 40Motorcycling only:
42 - 18 = 24Neither:
100 - (40 + 18 + 24) = 18Venn diagram consists of:
Biking | Both (Intersection) | Motorcycling | Neither (outside of circles)
40 18 24 18
PLEASE ANSWER THIS RIGHT ASAP
Answer:
x=9
Step-by-step explanation:
23=7/9(6x-36)+9
Distribute 7/9.
23=14/3x-28+9
Add.
23=14/3x-19
Add 19 to both sides of the equation.
42=14/3x
Divide 14/3 from both sides of the equation.
X=9
Hope this helps :)
in a subway, x men and y women travel. explain what is meant by the expression: y-x
Answer:
Step-by-step explanation:
y - x means the the difference in the number of women compared with men.
So if there are 20 women and 14 men, y - x = 20 -1 4 = 6 , that is 6 more women than men.
If there are more men than women then y - x will have a negative value, and there will be, if we flip the above numbers. 6 more men than women.
Simplify: square root of 18x^7
O 9x^3 square root x
O 3x^3 square root 2x
O 3x square root x^3
Answer:
c
Step-by-step explanation:
square root of 18x^7
square root of 9×3x^4×x^3
9x square root of 3x^3
divided by 3 it came 3x square root of x^3
The mean of 17,x,10,17,51 is 21 find x
Answer:
x=10
Step-by-step explanation:
(17+x+10+51+17)/5=21
95+x=105
x=10
The required value of x for the given mean of the data is x = 10.
How to find the mean of the given sample of data?In order to find the mean for a sample, first count the number of data in a sample, say n. Then, do the summation of all the values in that sample and divide it by the number of data obtained earlier.
Mathematically, it can be written for n number of data x₁, x₂, x₃, ..... as,
Mean = ( x₁ + x₂ + x₃ + .....)/n.
Given that,
The mean of 17, x, 10, 17 and 51 is 21.
It can be written in mathematical form as,
(17+ x + 10 + 17 + 51 )/5 = 21
=> 17+ x + 10 + 17 + 51 = 21 × 5
=> x = 105 - 95
=> x = 10
Hence, for the given data the value of x is 10.
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Learning Task 3: Write at least three equivalent ratio of the given ratio. Write your answer in your notebook. 6.) 8/10 = 7.) 3/5 = 1.) 2/4 = . = 2.) 5/10 = 3.) 4/5 = = I 8.) 2/8 = 9.) 3/7 = 10.) 6/8 4.) 3/9 = 5.) 2/5 = - cond and colon form. Do this in
Answer:
Equivalent Ratio
A ratio shows the comparison of quantities. It describes a part-to-part or a part-to-whole comparison. It can be written in three ways: fraction form, colon form and word form. Ratios that have the same values are called equivalent ratio. You can find the equivalent ratio by multiplying or dividing both quantities by the same number.
Solution:
Let us now find the equivalent ratios of the given ratios above by multiplying or dividing.
1) 2⁄4 = 1⁄2, 4⁄8, 6⁄12
2÷2 / 4÷2 = 1⁄2
2×2 / 4×2 = 4⁄8
2×3 / 4×3 = 6⁄12
2) 5⁄10 = 1⁄2, 20⁄40, 30⁄60
5÷5 / 10÷5 = 1⁄2
5×4 / 10×4 = 20⁄40
5×6 / 10×6 = 30⁄60
3) 4⁄5 = 8⁄10, 16⁄20, 28⁄35
4×2 / 5×2 = 8⁄10
4×4 / 5×4 = 16⁄20
4×7 / 5×7 = 28⁄35
4) 3⁄9 = 1⁄3, 9⁄27, 21⁄63
3÷3 / 9÷3 = 1⁄3
3×3 / 9×3 = 9⁄27
3×7 / 9×7 = 21⁄63
5) 2⁄5 = 4⁄10, 8⁄20, 14⁄35
2×2 / 5×2 = 4⁄10
2×4 / 5×4 = 8⁄20
2×7 / 5×7 = 14⁄35
6) 8⁄10 = 4⁄5, 24⁄30, 56⁄70
8÷2 / 10÷2 = 4⁄5
8×3 / 10×3 = 24⁄30
8×7 / 10×7 = 56⁄70
7) 3⁄15 = 1⁄5, 6⁄30, 12⁄60
3÷3 / 15÷3 = 1⁄5
3×2 / 15×2 = 6⁄30
3×4 / 15×4 = 12⁄60
8) 2⁄8 = 1⁄4, 6⁄24, 14⁄56
2÷2 / 8÷2 = 1⁄4
2×3 / 8×3 = 6⁄24
2×7 / 8×7 = 14⁄56
9) 3⁄7 = 6⁄14, 12⁄28, 18⁄42
3×2 / 7×2 = 6⁄14
3×4 / 7×4 = 12⁄28
3×6 / 7×6 = 18⁄42
10) 6⁄8 = 3⁄4, 24⁄32, 36⁄48
6÷2 / 8÷2 = 3⁄4
6×4 / 8×4 = 24⁄32
6×6 / 8×6 = 36⁄48
Step-by-step explanation:
Answer:Equivalent Ratio
Brax has $12.00 to spend at the gift shop. He wants to buy a book for $7.50 and a dinosaur for $3.75. What change will Brax have after he purchases these items?
4. Claudia works at a sweet shop selling chocolate and caramel-dipped apples. During her shift, she
sells a total of 48 apples, Claudia sells the chocolate-dipped apples for $3 each and the caramel-
dipped apples for $3.25 each. She makes a total of $151. How many of each type of apple did she
make?
a toy car costing 500.00 is reduced by 10% in the sale how much does it cost now?
After the 10% reduction in the price of the toy car, the car costs 450.
In order to determine the cost of the toy car after the price was reduced by 10%, the first step is to determine what 10% of $500 is.
10% x 500
0.1 x 500 = 50.
The second step is to subtract the value of the 10% price reduction from the original cost of the toy car.
500 - 50 = 450
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Hey can you guys help me pls :))
Answer:
-d-1<2. => -(-2)-1=1<2. the forth option is true
IF ANYONE IS A GENIUS AT MATH PLZ HELP AND ANSWER MY LATEST QUESTION!! I RLLY NEED HELP, IM LITERALLY GONNA CRY!!! IF YOU CAN'T FIND IT, BELOW IS AN IMAGE OF THE MATH SCENARIOS THAT I NEED HELP WITH!!! PLZ EXPLAIN EACH AND EVERY PART.
Answer:
Step-by-step explanation:
im not a genius at math, but i will give it a shot
scenario 3:
let m= cost per minute for WDE, let b= flat fee for WDE
42.5=50m+b
65=100m+b
subtract the two equations
65-42.5=50m
m= .45 (this is the cost per minute on WDE wireless)
plug in m=.45 into the first equation
42.5=50(.45)+b
b= 20 (this is the fixed monthly fee for WDE wireless)
HTR offers .25 per minute, whereas WDE offers .45 a minute which means that HTR has the cheaper per minute rate
htr has the equation .25x+30
WDE has the equation .45x+30
set them equal to each other and solve for x .25x+30=.45x+20
x= 50 minutes
Scenario 4:
Same deal as last question, let m=cost/movie, b=flat fee
41.25=5m+b
57.5=10m+b
subtract the two equations and solve for m
57.5-41.25=10m-5m+b-b
m= 3.25 (slope)
b=25 (y intercept)
y=3.25x+25
y=3.25(125)+25 = 431.25
3.25x+25=2.75x+35
.5x= 10
x= 20
1\4-2\7 plese show your work
Answer:
-1/28
Step-by-step explanation:
You need to convert 2/7 and 1/4 into the same denominator. The GCD is 28. 2/7=8/28 and 1/4=7/28. 7/28-8/28=-1/28
Answer:
-1/28
Step-by-step explanation:
You have to find the least common multiple for 7 and 4, the denominators, to add the fractions. The LCM of 7 and 4 would be 28. You would have to multiply 7 by 4 and 4 by 7, meaning you have to multiply the numerators by the same number. 1x7/4x7-2x4/7x4= -1/28.
HELP WHAT IS 22 + 5/8 x -1/2
I will give brainliest!
Answer:
181/8
Step-by-step explanation:
Answer:
5x/8 + 43/2
Explanation:
The answer is the exact value.
Find the solution to the system of equations:
7x-8y=-23
7x-7y=-14
Answer:
Solutions: x = 7, y = 9; or (7, 9)
Step-by-step explanation:
Given the following systems of linear equations:
7x - 8y = -23
7x - 7y = -14
Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.
7x - 8y = -23
- 7x - 7y = -14
-y = -9
Divide both sides by -1 to solve for y:
[tex]\frac{-y}{-1} = \frac{-9}{-1}[/tex]
y = 9
Substitute the value of y into either one of the given equations to solve for x:
7x - 7y = -14
7x - 7(9) = -14
7x - 63 = -14
Add 63 to both sides:
7x - 63 + 63 = -14 + 63
7x = 49
Divide both sides by 7 to solve for x:
[tex]\frac{7x}{7} = \frac{49}{7}[/tex]
x = 7
Double-check whether x = 7 and y = 9 are valid solutions to the given system:
x = 7, y = 9:
7x - 8y = -237(7) - 8(9) = -23
49 - 72 = -23
-23 = -23 (True statement).
7x - 7y = -147(7) - 7(9) = -14
49 - 63 = -14
-14 = -14 (True statement).
Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).
Find the area of the similar
figure.
18cm
15cm
Area = 50cm2
Area = [?]cm2
-
Answer:
270
Step-by-step explanation:
Is there a value of x that makes each of the following equalities true? If there is, find it.
a. √x-3=0
b. √x=-10
c. √x+1=0
d. √x=0.1
Step-by-step explanation:
a. √x - 3 = 0 ⇒ √x = 3 ⇒ x = 3² ⇒ x = 9 b. √x = -10,no solution as √x is a positive value
c. √x+1=0 ⇒ √x = - 1,no solution as √x is a positive value
d. √x = 0.1 ⇒ x = 0.1² ⇒ x = 0.01#1
√x-3=0x-3=0x=3If square root is over x only x=3²=9
#2
No solutions as -10 is <0
#3
√x+1=0x+1=0x=-1If root is over x only then no solutions
#4
√x=0.1
x=0.01