Divide the polynomials. Your answer should be in the form p(x)+\dfrac{k}{x+2}p(x)+ x+2 k p, left parenthesis, x, right parenthesis, plus, start fraction, k, divided by, x, plus, 2, end fraction where ppp is a polynomial and kkk is an integer. \dfrac{x^2+7x+12}{x+2}= x+2 x 2 +7x+12 =start fraction, x, squared, plus, 7, x, plus, 12, divided by, x, plus, 2, end fraction, equals
Answers
Answer:
[tex](x+5)+ \dfrac{2}{x+2}[/tex]
Step-by-step explanation:
Given
[tex]\dfrac{x^2+7x+12}{x+2}[/tex]
Required
Simplify and present your answer in
[tex]p(x)+\dfrac{k}{x+2}[/tex]
First, we need to expand and factorize the numerator:
[tex]\dfrac{x^2+7x+12}{x+2}[/tex]
Express 12 as 10 + 2
[tex]\dfrac{x^2+7x+10+2}{x+2}[/tex]
Split into two using brackets
[tex]\dfrac{(x^2+7x+10)+2}{x+2}[/tex]
Split to two fractions:
[tex]\dfrac{(x^2+7x+10)}{x+2}+\dfrac{2}{x+2}[/tex]
Factorize the numerator of the first fraction
[tex]\dfrac{(x^2+5x+2x+10)}{x+2}+\dfrac{2}{x+2}[/tex]
[tex]\dfrac{x(x+5)+2(x+5)}{x+2}+\dfrac{2}{x+2}[/tex]
[tex]\dfrac{(x+2)(x+5)}{x+2}+\dfrac{2}{x+2}[/tex]
The first fraction can be simplified to give:
[tex](x+5)+ \dfrac{2}{x+2}[/tex]
Hence, by comparison:
We have simplified the given expression to the required format of:
[tex]p(x)+\dfrac{k}{x+2}[/tex]
Which implies that:
[tex]p(x) = x + 5[/tex] and [tex]k = 2[/tex]
Answer:
Step-by-step explanation:
hope this helps
Related Questions
I'm sorry, I am struggling with this Question. Can anyone help me with the toxicity of this Question.
Answers
Answer:
I could be wrong but I don't think they're congruent.
Step-by-step explanation:
what would be the slope intercept form?
Answers
Answer:
y=7/2x-4
Step-by-step explanation:
Slope-intercept form is written y=mx+b. M stands for slope, x stays as x, and b is the y-intercept. If we plug in the numbers we have, the equation becomes...
y=7/2x-4
I hope this helps you out!! The equation is actually pretty simple once you get used to it. Have a nice day ヾ(•ω•`)o
PLS HELP MATH HURRY WILL GIVE BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
It’s B
ABD=CBD=1/2 ABC
Answer: D.
Step-by-step explanation:
reasoning is because if you were take the measure of CBD and divide it by 2 then you would get the measure of ABD.
Given f(x)=5x+4 solve for "x" when f(x)=24.
Answers
Answer:
x=4
Step-by-step explanation:
f(x)=5x+4
By given,
f(x)=24
5x+4=24
5x=20
x=4
**ANSWER FAST!!**
h(1)=
Evaluate functions from their graph
Answers
Answer:
Evaluate functions from their graph h(1)= -2
Step-by-step explanation:
See attached!
Using synthetic division, what is the width of the rectangle? Brainliest!! 5 stars, thanks.
Answers
Hi there!
[tex]\large\boxed{5x^{2} + 4x - 6}[/tex]
**Work pictured below**
Since x + 3 is one of the factors, set it equal to zero to find the root:
x + 3 = 0
x = -3
Use -3 in the synthetic division process to solve for the width.
Use the coefficients of 5x³ + 19x² + 6x - 18 to do synthetic division:
5, 19, 6, -18
To do synthetic division, arrange the numbers in the polynomial as shown with the root outside of the diagram.
1. Bring down the first number
2. Multiply by the root and add that number to the next number. Bring the sum down to the bottom.
3. Repeat until finished with all numbers. If a number is a perfect root, it will have a remainder of 0 at the last number.
In this instance, doing so produced the numbers 5, 4 and -6. There was also no remainder as the last number produced 0. Therefore, the width of the rectangle is:
5x² + 4x - 6 **First term is always one degree LESS than you started with**
Answer:
5x^2 + 4x - 6
Step-by-step explanation:
(5x^3 + 19x^2 + 6x - 18)/(x + 3)
-3 | 5 19 6 -18
-15 -12 18
5 4 -6 0
(5x^3 + 19x^2 + 6x - 18)/(x + 3) = 5x^2 + 4x - 6
At the bowling alley ethans family spent $4 to rent shoes plus $8 for each game that they bowled if they spent $36 total how many games did they bowl
Answers
Answer:
4
Step-by-step explanation:
If they spent 36 dollars
and the shoes were 4 dollars,
36-4=32 dollars left for the games
32/8=4 games
A rubber bouncy ball is bouncing up and down such that the ball's distance, d, in feet above the ground is given by the inequality
Which of the following graphs shows all the possible distances?
Answers
Answer: Option D.
Step-by-step explanation:
We have the inequality:
Id - 3.5I ≤ 1.5
remember that : IxI < d means that:
-d < x < d
Now let's find the possible values of d, breaking the absolute value we have that:
-1.5 ≤ d - 3.5 ≤ 1.5
adding 3.5 in each part, we have:
-1.5 + 3.5 ≤ d - 3.5 + 3.5 ≤ 1.5 + 3.5
2 ≤ d ≤ 5
Then d can be any value in the set [2, 5]
Then the correct graph is D, because the purple line starts at 2, and ends at 5.
The sum of two numbers is 72. The greater number is 8 more than the smaller number. Which equation can be used to
solve for the smaller number?
O x-(X + 8) = 72
O x + (x + 8) = 72
O X(X + 8) = 72
O x(x - 8) = 72
Answers
PLEASE HELP!! i'm struggling sm :/
Answers
Answer:
Check boxes 3, 4, 6, and 8.
Step-by-step explanation:
We have the equation:
[tex]y=-3x+2[/tex]
And we want to select all equations that are perpendicular to the above equation.
Remember that perpendicular lines have slopes who are negative reciprocals of each other.
Therefore, the slope of our equations must be the negative reciprocal of -3.
The negative reciprocal of -3 is 1/3. We flipped -3 to -1/3, and then multiplied by a negative.
Therefore, any equation with a slope of 1/3 is perpendicular to our original line.
Therefore, we will check boxes 3, 4, 6, and 8.
Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two
sides of this triangle?
5 cm and 8 cm
6 cm and 7 cm
7 cm and 2 cm
8 cm and 9 cm
Answers
Answer:
8 cm and 9 cm
Step-by-step explanation:
x + y > 13
5 + 8 = 13
6 + 7 = 13
7 + 2 = 9
8 + 9 = 17
The last response is correct since they are greater than 13 cm
Answer:
d sorry this is late
Step-by-step explanation:
A jet travels for 410 miles in 2 hours. at this rate how far could the jet fly in 14 hours? What is the rate of speed of the Jet
Answers
410/5 = ?
410/5 = 82
82 miles per hour
82*12 = ?
82*12 = 984
Answer: 984 miles in 12 hours
4. Which proportion can be used to find 65% of 90?
65 Х
9 100
a.
65
b.
90
100
Х
C.
65
100
90
X
90
d.
100
65
Answers
Answer:
C. 65/100 = x/90Step-by-step explanation:
Finding 65% of 90
x = 65*90/100or
x/90 = 65/100Option C is correct
Find the slope of the line that passes through the points (4, 3) and (2, 7).
Answers
Answer: -2/1
Step-by-step explanation:
Slope = Change in y/Change in x
Equation:
(7-3)/(2-4)
Evaluate:
4/-2
Simplify:
-2/1
help me with this please it’s 3 grade
Answers
Answer:
10 more hotdogs were sold on Friday than Monday.
Step-by-step explanation:
On Monday the graph says that there were 10 hotdogs sold, on Friday it says that there were 20 sold
20-10=10, so 10 hotdogs more were sold
Answer:10
Step-by-step explanation: there was 20 hot dogs sold on saturday and on monday there was 10. 20-10=10
Tristan earns 3 points for every question he answers correctly. Use the graph to find the equivalent ratios. A ratio equivalent to the ones shown is . Another equivalent ratio is .
Answers
Answer:
DC like the DC superheroes
Step-by-step explanation:
Find the measure of the numbered angles.
9. m<1
10. m<2
11. m<3
12. m<4
13. m<5
14. m<6
Answers
Answer:
the complementary angles and the supplementary angles
Step-by-step explanation:
m<1=60
m<2=120
m<3=60
m<4=120
m<5=30
m<6=30
please help!!!! will give brainliest
Answers
Answer:
x = squareRoot(15^2 + 14^2)(Pythagoras theorem)
x = 20.5 cm
Step-by-step explanation:
A pizza shop sells pizzas that are 10 inches (in diameter) or larger. A 10-inch cheese pizza costs $1.50, and each additional topping costs $0.75.
Write an equation that represents the cost of a pizza. Be sure to specify what the variables represent.
Answers
Answer:
A pizza shop sells pizzas that are 10 inches orr larger. A 10-inch cheese pizza costs $8 and each additional costs $1.50 and each additional topping costs $0.75.
The equation that represents the cost of a pizza is:
P = $10 + $1.50a + $0.75b
Where 'a' represents the number additional inches and 'b' represents the number of additional toppings.
Step-by-step explanation:
simplify the number using the imaginary unit i square root of -98
Answers
Answer:
[tex]\sqrt{-98}=7i\sqrt{2}[/tex]
Step-by-step explanation:
We wish to simplify:
[tex]\sqrt{-98}[/tex]
We can rewrite it as such:
[tex]=\sqrt{-1\cdot 98} =\sqrt{-1\cdot 49\cdot2}=\sqrt{-1}\cdot\sqrt{49}\cdot\sqrt{2}[/tex]
Hence:
[tex]=i(7)\sqrt{2}[/tex]
Therefore:
[tex]\sqrt{-98}=7i\sqrt{2}[/tex]
2 3/4 divided by 3 in lowest term
Answers
Answer:
i believe rhe awnser is 11/12
(a) In 2008 the total number of tickets sold for an athletics meeting was 3136.
The ratio child tickets sold : adult tickets sold = 17:32.
(i) How many child tickets were sold?
Answers
What is the simplest form of the expression (-12.7 - 3.1x) + 5.9y - (4.2y + x)
Answers
Answer:
Step-by-step explanation:
(-12.7-3.1x)+5.9y-(4.2y+x) combine terms
-4.1x+1.7y-12.7
what is the area of this square the height is 4 in the width is 4
Answers
Answer;
64
Step-by-step explanation:
eee 4*4*4=64
sorry if im wrong, since it's a square than all the sides are the same, if it is a 3d CUBE then the area is 64 but if you're talking about a 2d square then its 16
What is the value of x?
2x-5/3=11
Answers
Answer:
19/3
Step-by-step explanation: 19/3=6.33
25 points , please help :)))))
A car travels 100 miles east in 2 hours and 30 miles north in half an hour. What is the average speed of the car?
Answers
Answer:
44 MPH
Step-by-step explanation:
becauuuuuuuuuuuuusssssseeeeeeeee I said so
Help me with this plz!
Answers
Answer:
y=2x-2
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=2x-2
write the equation graphed below
Answers
Answer:
y=|x-5|-1
Step-by-step explanation:
Un introductor de carne de res en canal compró mil piezas a 200 pesos cada. Vendió 600 de ellas obteniendo una ganancia del 25 %. ¿A qué precio deberá vender las piezas restantes si la utilidad promedio del lote completo (de las mil piezas) debe ser del 30 %? ¿Cuál es su utilidad por la venta de las mil piezas?
Answers
Responder:
275 pesos
60.000 pesos
Explicación paso a paso:
Dado que :
Número de piezas = 1000
Precio por pieza = 200
600 piezas vendidas con un beneficio del 25%
(100 + 25)% = 125% de 200
1,25 * 200 = 250 cada uno
Precio de 600:
(600 * 250) = 150 000
Para un beneficio del 30% de todo el lote:
(100 + 30)% = 130% * 200 = 260
(1000 * 260) = 260 000
Precio de los 400 restantes:
(260.000 - 150.000) / 400 = 110.000 / 400 = 275 peso
Beneficio de la venta:
Precio de venta:
(150.000 + 110000) = 260000 pesos
Precio de compra :
(1000 * 200) = 200.000 pesos
260.000 - 200.000 = 60.000 pesos
The value of y varies directly with x. When y = 75, 7 = 1. What is the value of y when x is 272