The factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
The polynomial function is given as:
[tex]P(x) = x^3 + 4x^2 - 9x - 36[/tex]
Factorize the given expression.
[tex]P(x) = x^2(x + 4) - 9(x +4)[/tex]
Factor out x + 4
[tex]P(x) = (x^2 - 9)(x +4)[/tex]
Express 9 as the square of 3
[tex]P(x) = (x^2 - 3^2)(x +4)[/tex]
Apply the difference of two squares
[tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
Hence, the factorization of the expression by grouping is [tex]P(x) = (x - 3)(x + 3)(x +4)[/tex]
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Solve three questions
Answer:
7) r = -4
8) n = 1
9) x = 2
Step-by-step explanation:
Problem 7
Here, we have the equation 5 + 3r + 6 = -1. It looks like we need to solve for r, so let's go ahead and start by adding the constants 5 and 6.
5 + 3r + 6 = -1
3r + 11 = -1
Next, let's remove 11 from both sides to isolate r.
3r = -12
Finally, we can divide both sides by 3 to find the value of r.
r = -4
Problem 8
In this equation, it looks like we have to solve for n: -n + 2 + 3n = 4. So, let's start by combining like terms (-n and 3n).
-n + 3n + 2 = 4
2n + 2 = 4
Next, we can remove 2 from both sides to isolate r.
2n = 2
And finally, we can divide both sides by 2.
n = 1
Problem 5
This equation is a little trickier since we have a fraction. To remove this fraction, we can multiply both sides by 4.
(-6 + x)/4 = -1
4 × (-6 + x)/4 = 4 × -1
4/4 × (-6 + x)/1 = -4
-6 + x = -4
Finally, let's add 6 to both sides.
x = 2
point:(-5,1); slope: -
4
write in point-slope form:
Answer:
y-1=-4(x+5)
Step-by-step explanation:
y-y1=m(x-x1)
y-1=-4(x-(-5))
y-1=-4(x+5)
Answer: y - 1 = -4(x + 5)
Step-by-step explanation:
The point-slope formula is y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ( [tex]x_1[/tex], [tex]y_1[/tex]) is a point on the graph.
Using the formula, we will plug in our known values to write our equation.
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])
y - (1) = (-4)(x - (-5))
y - 1 = -4(x + 5)
However, in the picture the slope is [tex]\frac{1}{4}[/tex], so we would write it as;
y - 1 = [tex]\frac{1}{4}[/tex](x + 5)
Please help i cant figure it out will mark branliest
Answer:
b
Step-by-step explanation:
hope it helped u take a look at the picture u attached
S is a geometric sequence.
a) (1x + 1), 1 and (rootx - 1) are the first three terms of S.
Find the value of x.
You must show all your working.
b) The 5 term of S can be written in the form a V2 + b
where a and b are integers
Find the value of a and the value of b
Answer: your answer would be 2
Step-by-step explanation:
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK
Answer:
√366
Step-by-step explanation:
a^2 + b^2 = c^2
5 + 361 = 366
√366
which of the points does not fall on the same line as the other three points? (-4,4) (0,2) (2,1) (4,-1)
Answer:
Given (-4,4),(0,2),(2,1),(4,-1)
Only any two points are on the same line.
Step-by-step explanation:
You could do a lot of calculations, write the equations for the points in the line. These would be very good. But, you could also just look at the points on a graph. See image.
Repost if there are different points in the original problem.
Which number line shows the estimate of V47 in the correct interval of integers?
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Answer:
B (the second number line)
Step-by-step explanation:
[tex]\sqrt{49}[/tex] = 7, so [tex]\sqrt{47}[/tex] would be close to 7
vertical and horizontal asymptotes
Apple + Orange = $20
Apple is twice the price of the orange
How much does the apple cost?
Answer:
Step-by-step explanation:
let price of Orange=x
price of Apple=2x
x+2x=20
3x=20
x=20/3
cost of Apple=2x=2×20/3=40/3=$13 1/3
2x + 3y = 13
y = 3x + 8
Step-by-step explanation:
2x+3(3x+8)=13 y=3x+8
2x+9x+24=13 y=3(-1)+8
11x+24=13 y= -3+8 =8-3
11x=13-24 y=5
11x/11= -11/11
x= -1
Please quickly answer number 17&18 I will give brainliest
Answer: 17) 150°C 18) 17 minutes
Step-by-step explanation:
x represents time in minutes and y represents temperature in Celsius
17) y=10x+30
y=10(12)+30
y=120+30
y=150 - Therefore, the water temperature will be 150°C after 12 minutes
18) 200=10x+30
10x+30=200
10x+30-30=200-30
10x=170
x=17 - Therefore, the water temperature will reach 200°C after 17 minutes
a) Write an equation for the line of best fit.
Y=-0.007x+13.713
5. The data below shows the population of a city,
In millions of people, since 1950.
Year Population
1950 1.75
1960 1.68
1970
1.52
1980
1.16
TO
b) Estimate the population of the city in 2020.
1990
1.04
2000
0.98
Answer
Step-by-step explanation:
In millions of people, since 1950
Your little brother wants hot chocolate ot be 150 degrees, but you accidentally heated the water to 175 degrees. If after 5 minutes the temperature is 165 and the temperature in your house is 70 degrees, how long will your little brother have to wait to drink his hot chocolate?
Answer:
12.5 minutes
Step-by-step explanation:
it takes 5 minutes to cool 10 degrees
after ten minutes it would be 20 degrees less
then after 2.5 minutes it would be 5 degrees less
so it would take you 12.5 minutes to get 25 degrees less
We know that in 5 minutes, the temperature of the hot chocolate decreased by 10 degrees. We also know that the temperature is fixed at 70 degrees. Now, using the info given, let's solve!
=> 5 minutes = 10 degrees decrease=> 1 minute = 2 degrees decrease=> 1 minute x 12.5 = 2 x 12.5 degrees decrease=> 12.5 minutes = 25 degrees decreaseConclusion:Therefore, my little brother will have to wait for 12.5 minutes to drink his hot chocolate.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
What is the measurement of pie?
Answer: 3.14159
Step-by-step explanation:
a box of snacks contained 20 individual packages. the newly designed box contains 28 individual packages by what percent did the individual packages increase
Answer:
40%
Step-by-step explanation:
increased amount = 28 - 20 = 8
to get the percentage we have to divide the increased amount by original amount which will be 8/20 = 0.4
0.4 is 40%
The percentage increase is given as:
= [ (Final value - Initial value) / Initial value] x 100
The percentage increase in the number of individual packages is 40%
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Number of initial individuals packages = 20
Number of final individuals packages = 28
The percentage increase is given as:
= [ (Final value - Initial value) / Initial value] x 100
The percentage increase in the number of individual packages:
= [(28 - 20) / 20] x 100
= (8/20) x 100
= 40%
We can cross-check:
100% = 20 packages
140% = 140/100 x 20 packages
140% = 28 packages.
Thus,
The percentage increase in the number of individual packages is 40%
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helllp meeeeeeeeeeeeeeee
plz help answer will mark brainiest
Answer:
4/3 litres of water is enough to water 2/5 of the plants
Assuming the number of plants in the house is an unknown variable, take the value as x.
Thus, 4/3 litres is enough to water 2x plants in the house.
x = 4/3 ÷ 2
= 2/3 litres
Amount of water for all the plants = 5x = 5 × 2/3
= 10/3 litres
Thus, 10/3 litres of water is necessary to water all the plants in the house.
what is 0.75 greater than 9
Answer: 9.75
Step-by-step explanation: i just added
Answer:
less
Step-by-step explanation:
PLEASE HELP! Give explanations down below please! Thanks I am timed
Answer:
you need to divide all number
If 7 is subtracted from half of a number, the result is 14. Find the number.
a.41
b.42
c.43
d.44
Answer:
The number is 42.
Hope you could get an idea from here.
Doubt clarification - use comment section.
A bag has 25 beads in it.the probability of picking a white bead is 3/5.how many white beads are in the bag
help me with this math problem pleasee. I will give brainliest to the correct answer
Answer:
answer is x=15
AM=18
AB=4
1=2
2=10
3=20
The expression below represents the perimeter of a square in centimeters.
4(6+2.5)
What is the square's perimeter?
Answer:
34
Step-by-step explanation:
4(8.5) = 34
hellp and u git a braintasic
Answer:
whats the question?? lol
Step-by-step explanation:
Rotation 180 counterclockwise around the origin of the point (-3,-7)
Answer: (3 , 7)
Step-by-step explanation: When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). So all we do is make both x and y negative. Since x and y are already negative, they become positive due to the double negative rule.
help wanted will mark brainiest
Answer:
For question a the answer is option b at 50$
For question b the answer is 50 miles and option a is less
Step-by-step explanation:
If 2 inches are equivalent to 5 centimeters, how many square centimeters are in one square inch
Answer:
there are 6.45 or 6.5 square cm in one square inch
Step-by-step explanation:
mooooooooo 4/9-4/10 =
Answer:
0.04444444444
Step-by-step explanation:
[tex]\\ \rm\rightarrowtail 4/9-4/10[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{40-36}{90}[/tex]
[tex]\\ \rm\rightarrowtail 4/90[/tex]
[tex]\\ \rm\rightarrowtail 2/45[/tex]
Does anyone know how to solve this? Please helppp, I’m so confused
Answer:
y = 65 degree
x = 50 degree
Step-by-step explanation:
I believe that’s right
The two angles in the isosceles triangle are 50 and 65 degrees .
An isosceles triangle has two equal sides and two equal angles.
Consider that the one angles in the triangle is x degrees and the bottom angle is 65 degrees.
Then we have:
65 = y
(The sum of all angles in a triangle is 180 degrees.)
Then Simplifying the equation:
65 + 65 + x = 1802
x = 180 - 65 - 65
x = 50 degrees
Therefore, the two angles in the isosceles triangle are 50 and 65 degrees .
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I NEED SOME HELP PLS
Answer: I might have done some of the math wrong but I think this is the answer.
Step-by-step explanation:
Jose would be able to save $16,400 including the $2,000 and he will need $166,000 in financial aid.