Verify that (x + a)(x+b)(x+c) is factor of f(x)= x³ +(a+b+c)x²+(ab + ac + bc)x + abc.
Answers
Answer:
Step-by-step explanation:
[tex]LHS = \\\\=(x+a)(x+b)(x+c) \\\\=(x+a)(x^2 + cx + bx + bc)\\\\=x(x^2 +(b+c)x + bc) + a(x^2 + (b+c)x + bc)\\\\=x^3 + (b+c)x^2 + bcx+ ax^2 + (b+c)ax+ abc\\\\=x^3 + ax^2 + (b+c)x^2 + bcx + abx + acx + abc\\\\=x^3 + (a+b+c)x^2 + (ab+ac+bc)x+ abc\\\\= RHS[/tex]
Answer:
Explanation:
Hey there!
Please look explanation in picture. As all the factor gives us "0" while putting them in equation, it is verified that they are the factors of f(x).
Hope it helps!
Related Questions
Find the exact value of sin2Θ if tanΘ=[tex]\frac{-2\sqrt{5} }{5}[/tex] and 90 < Θ < 180.
Answers
Answer:
[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]
Step-by-step explanation:
Identities used :
[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]
[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]
[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]
[tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]
[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]
[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]
[tex]Next \ sin^2 \theta = 1 - cos^2 \theta[/tex]
[tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]
[tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]
[tex]Find \ sin 2 \theta[/tex]
[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]
[tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/tex]
Evaluate 5-|-6|
1
11
-1
Answers
Step-by-step explanation:
(-) + (-) = (+)
=........ +1
Answer:
-1
Step-by-step explanation:
Find x if 5, 9, 11, 12, 13, 14, 17 and x have a mean of 12.
Answers
Answer: 15
Step-by-step explanation: 5+9+11+12+13+14+17=81
Make an equation based on this and solve for the variable (x)
81+x/8=12
12*8=96
81+x=96
96-81=15
x=15
Three right triangles are drawn in the coordinate plane,
and the coordinates of their vertices are labeled.
For each right triangle, label the lengths of the sides.
Answers
Answer:
Triangle A:
- smaller leg = 3
- longer leg = 10
- hypotenuse = 10.4
Traingle B:
- smaller leg = 4
- longer leg = 13
- hypotenuse = 13.6
Triangle C:
- smaller leg = 5
- longer leg = 7
- hypotenuse = 8.6
Step-by-step explanation:
Let's find the distance of the legs for the 3 right triangles.
Triangle A
The smaller leg (SL) is from (2,5) to (2,8), so the length is given by the distance in the y-axis:
[tex] SL_{A} = 8 - 5 = 3 [/tex]
Hence, the lenght of the smaller leg is 3.
The longer leg (LL) is from (-8, 8) to (2, 8), so the length is given by the distance in the x-axis:
[tex] LL_{A} = 2 - (-8) = 10 [/tex]
Then, the length of the longer leg is 10.
Now, we can find the hypotenuse (H) by using Pitagoras:
[tex] H_{A} = \sqrt{SL_{A}^{2} + LL_{A}^{2}} = \sqrt{3^{2} + 10^{2}} = 10.4 [/tex]
Triangle B
The SL is from (3, -9) to (7, -9)
The length of the SL is:
[tex] SL_{B} = 7 - 3 = 4 [/tex]
The LL is from (7, -9) to (7, 4)
The length of the LL is:
[tex] LL_{B} = 4 - (-9) = 13 [/tex]
The hypotenuse is:
[tex] H_{B} = \sqrt{4^{2} + 13^{2}} = 13.6 [/tex]
Triangle C
The SL is from (-10, -6) to (-10, -1)
The length of the SL is:
[tex] SL_{C} = -1 - (-6) = 5 [/tex]
The LL is from (-10, -6) to (-3, -6)
The length of the LL is:
[tex] LL_{C} = -3 - (-10) = 7 [/tex]
The hypotenuse is:
[tex] H_{C} = \sqrt{5^{2} + 7^{2}} = 8.6 [/tex]
I hope it helps you!
Which values are solutions to the inequality below?
Check all that apply.
x²<=64
O A. 9
O B. 5
O C. -3
O D. -8
O E. -14
O F. 8
Answers
Answer:
B and C
Step-by-step explanation:
B is correct because 5² is 25, which is less than 64
C is correct because (-3)² is 9, which is less than 64
Answer:
b c d f
Step-by-step explanation:
-8 ≤ x ≤ 8
A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. Each small box of paper weighs 50 pounds
and each large box of paper weighs 80 pounds. A total of 19 boxes of paper were
shipped weighing 1280 pounds altogether. Determine the number of small boxes
shipped and the number of large boxes shipped.
Answers
Answer:
16 boxes large
Step-by-step explanation:
if the weigth is 1280 wilhich means its 1280÷80 =16
Jada makes sparkling juice by mixing 2 cups of
sparkling water with every 6 cups of apple juice.
A. How much apple juice does Jada need if she uses 6
cups of sparkling water?
B. How much sparkling water does jada need if she uses 15 cups of apple juice.
Answers
Answer:
A=36
B= 2.5
Step-by-step explanation:
If you need 1 cup of sparkling water per 6 cups of apple juice and you use 6 cups of sparking water you do 6x6=36
15 divided by 6 = 2.5
Answer:
A - 18. B - 5
Step-by-step explanation:
So, the best thing for us to do first is find the ration between apple juice and sparkling water.
Then we can answer the questions once we know the ratio.
We know that for every 6 apple juice, we need 2 sparkling water.
This is a 6 : 2 ratio.
However, we can simplfy this further by dividing the 6 and 2 by using a number that goes into both values, such as 2:
6/2 : 2/2
=
3 : 1
So this is our ratio.
Now, the first questino asks how many apple juice is needed for 6 cups of sparkling water?
We know 3 apple juce is needed for 1 sparkling water, so to find whats needed for 6, lets multiply the 3 by 6:
3*6
=
18
So we need 18 apple juice for 6 sparkling water.
Next we need to find how much sparkling water is needed for 15 cups of apple juice.
We know that for every 3 apple juice we need 1 sparkling water.
We gace 15 apple juice.
To find how much sparkling water we need, lets divide the amount of apple juice by the ratio of apple juice. This will get us how many times more sparkling water we need:
15/3
=
5
Now that we know how many times more sparkling water we need, lets multiply the sparkling water by this:
5*1
=
5
So we need 5 sparkling water for every 15 cups of apple jiuce.
Hope this helps!
ANSWER PLZZZZZZ!!!!!!!!!!!!!!!
Answers
Answer:
length=(3x-2)
Step-by-step explanation:
area of rectangle=length*breadth
3x^2 + 7x - 6=length * (x+3)
3x^2 +(9-2)x -6=length *(x+3)
3x^2+9x-2x-6=length*(x+3)
3x(x+3)-2(x+3)=length*(x+3)
(x+3)(3x-2)=length*(x+3)
(x+3)(3x-2)/(x+3)=length
(3x-2)=length
Answer:
(3x - 2)
Step-by-step explanation:
Given that the area A = length × width
A = 3x² + 7x - 6 ← factor to obtain length
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 3 × - 6 = - 18 and sum = + 7
The factors are + 9 and - 2
Use these factors to split the x- term
3x² + 9x - 2x - 6 ( factor the first/second and third/fourth terms )
= 3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(3x - 2)
We know (x + 3) is the width , then (3x - 2) is the length
Convert 23cm2 into mm2
Answers
Answer:
2300 mm^2
Step-by-step explanation:
The picture is above I’ll mark as brainliest.
Answers
Answer:
Width = 3 m
Step-by-step explanation:
Formula for perimeter:
P = l + w + l + w
Plug in what we know:
14 = 4 + w + 4 + w
Isolate variable w (width):
14 = 8 + 2w
6 = 2w
3 = w
Check your work:
14 = 4 + 3 + 4 + 3
14 = 7 + 7
14 = 14
Correct!
(Don't forget to add units in your answer!)
2. The average daily rainfall in London during April was 3.5 mm. How much rain fell during the month?
Answers
Answer:
105mm
Step-by-step explanation:
To find the rainfall during the month of April simply multiply the number of days in April times the average daily rainfall
Number of days in April: 30
Average daily rainfall: 3.5mm
Rainfall during the month = 30 * 3.5 = 105mm
A
B
С
D
If mZACD = 70°, then mZBCD = [? ]°
Answers
Answer:
35 is correct
Step-by-step explanation:
hope this helps.
Answer:
35°
Step-by-step explanation:
Angle ACD is 70°. The little tick marks on the angle mean both sides of the split are the same amount. This means if you divide the angle in half, you will find out what both of them are equal to.
Use the drop-down menus to correctly relate each pair of numbers
manee help meh son
Answers
Answer:
Sorry for the late response, I had to have lunch.
1. >
2. =
3. <
4. >
Step-by-step explanation:
Have a great summer :)
A ruler cost x pence. A pen costs 10 pence more than the ruler. Write an expression, in terms of x, for the cost of a pen .
A. 10x pence
B. 10- x pence
C 10 pence
D.x + 10 pence
Answers
Answer:
D. x + 10 pence
Step-by-step explanation:
Since the pen costs 10 pence more than the ruler, we need to add 10 to x.
Find the perimeter of the rectangle and the area of the rectangle??
Show all your work please!!!!!
Answers
Answer:
Perimeter: 8x+8
Area: 16x+16
Step-by-step explanation:
Combine only like terms
(4x+2) + (4x+2) +2+2= 8x+8
(4x+2) x (4x+2) x 2 x 2= 16x+16
decompose 17x^3+7x^2-17x-7 divided by (x-1)^2(x+1)^2 into partial fraction
Answers
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A store sells notebooks for $3 each and does not charge sales tax. If x represents the number of notebooks Adele buys and y represents the total cost of the notebooks she buys, which best describes the values of x and y?
A. The value of x can be any real number, and y will be a real number.
B. The value of x can be any real number greater than or equal to 0, and y will be a real number greater than or equal to 0.
C. The value of x can be any integer, and y will be an integer.
D. The value of x can be any integer greater than or equal to 0, and y will be an integer greater than or equal to 0.
Answers
Answer:
Step-by-step explanation:
A?
Find the IQR: (find the median, then find the median of the first group and then the next group. Now subtract big median minus the small median.) 20, 17, 16, 3, 7, 45
Answers
Answer:
13
Step-by-step explanation:
The IQR = Interquartile Range is the difference between the first and third quartile
Rearranged data set:
3, 7, 16, 17, 20, 45
Step 1
We find the first quartile = Q1
= 1/4(n + 1)th number
n = 6
= 1/4(6 + 1)th
= 1/4(7)th
= 1 3/4th number
This = 7
Step 2
We find the third quartile = Q3
= 3/4(n + 1)th number
n = 6
= 3/4(6 + 1)th
= 3/4(7)th
= 21/4th number
= 5 1/4 th number
This = 20
Step 3
IQR = Q3 - Q1
= 20 - 7
= 13
Find the distance between the points given.
(-3,-4) and (0,0)
Answers
Answer: 5 Units
Step-by-step explanation:
Can someone help me? It's urgent and thank you!
Answers
Answer:
35
Step-by-step explanation:
To find this, we are going to use the combination formula as follows;
nCr = n!/(n-r)!r!
In this case, n = 7 and r = 3
Substituting these values;
7C3 = 7!/(7-3)! 3! = 7!/4!3! = 35
I need help
Solve the expression when X =5;3(X+2)=
Answers
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {21}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3 \: ( \: x + 2 \: )[/tex]
Plugging in the value [tex]x = 5[/tex] in the above expression, we have
[tex] = 3\:( \: 5 + 2 \: )[/tex]
[tex] = 3 \: ( \: 7 \: )[/tex]
[tex] = 3 \times 7[/tex]
[tex] = 21[/tex]
Note:-[tex]\sf\pink{PEMDAS\: rule.}[/tex]
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35☂}}}}}[/tex]
Can I get help on this bc if I don’t do it now my math teacher will call my parents
Answers
Answer:
39.28cm^2
Step-by-step explanation:
Simple work out the area of a circle and halve it.
3.142xr^2
3.142x5^2 = 78.55 cm^2 (Full circle area)
Now we must halve that answer to get the semicircle.
78.55/2 = 39.275 cm^2
However, we need it to 2dp. Therefore the answer is 39.28cm^2
Someone pleaseee help!!!
8th grade
Answers
Answer:
[tex] \frac{1}{1000} [/tex]Step-by-step explanation:
[tex] {10}^{ - 3} [/tex]
[tex] \frac{1}{ {10}^{3} } [/tex][tex] \frac{1}{1000} [/tex]Hope it is helpful...In a right triangle, sin(40 - 2) = cos(32)'. What is the value of x?
O 10
O 15
O 20
O 25
Answers
Answer:
x = 25
Step-by-step explanation:
Correct question
In a right triangle Sin (40-x)=cos(3x) what is the value of x
Since Sin theta = Cos(90-theta)
Sin (40-x) = Sin(90-3x)
40 - x = 90 - 3x
-x+3x = 90 - 40
2x = 50
x = 25
Hence the value of x is 25
whats the answer to this
Answers
Answer:
its the 2nd one
hope that helps<3
Answer:
jhkkkhj
Step-by-step explanation:
jkjkjkjkj
There are 6 blue marbles, 3 red marbles, and 5 yellow marbles in a bag. What is the probability of selecting a blue or red marble on the first draw? I need it in a fraction, decimal, and a percent HURRY PLS
Answers
Can anyone find this answer?
Answers
Answer:
23,300 students
Step-by-step explanation:
1900 year, 3.7 * 10 ^ 3
3.7 * 10 * 10 * 10 = 3,700
1950 year, 2.7 * 10 ^ 4
2.7 * 10 * 10 * 10 * 10 = 27,000
So then you will subtract 1950 year by the year of 1900
27,000 - 3,700 = 23,300
Do you have a step my step answer?
Answers
Answer:
In picture
Step-by-step explanation:
Hope I answered it correctly.
Please give me brainliest if it help you, thanks!
i would like help in this question
Answers
Answer:
T = 3.5m
T is trash in pounds
m is members of family
Step-by-step explanation:
a + b3 - a ; a = 3, b = 2
Answers
Answer:
8
Step-by-step explanation:
a + b^3 - a
Simplify
b^3
Let b=2
2^3
8
Answer:
11
Step-by-step explanation:
If a = 3, and b = 2, then;
=> a + b³
=> 3 + 2³
=> 3 + 8
=> 11
Hope this helps!
