Answer:
B. Multiply both sides of the top equation by 3
Step-by-step explanation:
Given:
4x+2y = 4
12x+y = 22
For the equations to have equal x-coefficients, you'll multiply both sides of (1) by 3
4x+2y = 4 (1)
12x+y = 22 (2)
B. Multiply both sides of the top equation by 3
3(4x+2y=4)
We have,
12x+6y=12 (3)
12x+y=22 (2)
Subtract (2) from (3)
5y=12-22
5y=-10
y= -10/5
y=-2
Substitute y=-2 into (1)
4x+2y = 4
4x+2(-2)=4
4x-4=4
4x=4+4
4x=8
x=8/4
x=2
Therefore, y= -2 and x=2
Answer:
its B
Step-by-step explanation:
A pex:)
How can 2182 be written as the sum of four consecutive whole numbers?
Answer:
544 + 545 + 546 + 547
explanation: if the numbers are consecutive whole numbers then it would be near the ¼ of the given number
HELPPP
Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Enter the correct answer.
Answer:
[tex] slope (m) = -\frac{3}{2} [/tex]
Step-by-step explanation:
We can find the slope (m) by using coordinate pairs of any 2 points located along the slope of the line that we have on the graph.
This, let's use the coordinate pairs at:
x = -4, y = 2 (-4, 2) => (x2, y2)
x = 0, y = -4 (0, -4) => (x1, y1)
[tex] slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] slope (m) = \frac{2 -(-4)}{-4 - 0} [/tex]
[tex] slope (m) = \frac{2 + 4}{-4 - 0} [/tex]
[tex] slope (m) = \frac{6}{-4} [/tex]
[tex] slope (m) = \frac{3}{-2} [/tex]
[tex] slope (m) = -\frac{3}{2} [/tex]
Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes?Chen is baking muffins and banana bread for a brunch buffet. He needs 3 and one-fifth cups of flour to make the muffins and 3 and two-thirds cups of flour to make the banana bread. Which is the best estimate of the number of cups of flour that Chen needs to bake both recipes? A. 6 cups B. 7 cups C. 8 cups D. 9 cups
Answer:
hi:) If chen needed 3 1/5 and 3 2/3, the answer should be 7. 7 cups. i hope this is right but feel free to correct me if im wrong.
B. 7 cups
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
What is the fraction?A fraction is a number which has numerator and denominator.Number of cups used to make muffins = 3 1/5
Estimation = 3 cups
Number of cups used to make banana bread = 3 2/3
Estimation = 4 cups
Number of cups of flour needs to bake both recipes = Estimated number of cups used to make muffins + Estimated number of cups used to make banana bread
= 3 + 4 cups
= 7 cups.
The best estimate of the number of cups of flour that Chen needs to bake both recipes is 7cups.
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Please answer this question now
Answer:
e =7.1
Step-by-step explanation:
[tex]Hypotenuse = 10\\Opposite =e\\Adjacent =7\\\\Using\:Pythagoras\:Theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\10^2 =e^2 + 7^2\\100 =e^2+49\\100-49=e^2\\\\51 =e^2\\\sqrt{51} =\sqrt{e^2}\\ e = 7.141\\\\e = 7.1[/tex]
Mrs johnson grows herbs in square plots Her basil plot measures. 5. 9 yd on each side. A. Find the total area of the basil plot. B. Mrs. Johnson puts a fence around the basil. If the fence was 2 ft from the edge of the garden on each side, whats the perimeter
Answer:
Area = 34. 81 yd^2
Perimeter = 86.6 feets
Step-by-step explanation:
Given the following :
Shape of Mrs. Johnson's plot = square
All sides of a square are of equal length
Measure of each side = 5.9 yd
A.) Area of plot
Area of plot = Area of a square
Area of a square(A) = a^2
Where a = side length
A = 5.9^2
A = 34.81 yd^2
B) Perimeter of Basil plot = Perimeter of a square
Converting yard to feet
1 yard = 3feets
Therefore,
5.9 yards = (3 * 5.9) = 17.7 feets
Fence is 2ft from the garden on each side,
Length of fence on each side = (2 + 17.7 + 2) Feets = 21.7 Feets
Perimeter of a square (P) = 4a
Where a = side length
P = 4 × 21.7
P = 86.6 feets
Answer:
86.6 feet
Step-by-step explanation:
What’s a possible value of an integer that is less than 14 units from 29 but no more than or equal to 18
Answer:
15, 16, 17, 18
Step-by-step explanation:
29-14=15
15, 16, 17, 18 are less than or equal to 18
im not sure wether to replace the minus signs with addition, so if you could help me that would be nice :) 1.2y+4.5-3.4y-6.3
Answer:
-2.2y - 1.8
Step-by-step explanation:
We are to simplify the expression:
1.2y + 4.5 - 3.4y - 6.3
Collect like terms:
1.2y - 3.4y + 4.5 - 6.3
Simplify:
-2.2y - 1.8
That is the answer.
Consider the y-intercepts of the functions:
f(x) = |x – 1] + 2
g(x) =
(x + 3)
h(x) = (x + 1) -3
1
What is the ordered pair location of the greatest y-intercept of the three functions?
Answer:
+3, 0
Step-by-step explanation:
y-intercept for f(x) is when x = 0, so it is +1, 0
y-intercept for g(x) is when x = 0, so it is +3, 0
y-intercept for h(x) is when x = 0, so it is -2, 0
The y-intercept of a function is the point where x = 0.
The ordered pair that represents the greatest y-intercept is (0,3)
The functions are given as:
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Set x = 0, and solve the functions
[tex]\mathbf{f(x) = |x - 1| + 2}[/tex]
Substitute 0 for x
[tex]\mathbf{f(0) = |0 - 1| + 2}[/tex]
[tex]\mathbf{f(0) = |- 1| + 2}[/tex]
Remove absolute brackets
[tex]\mathbf{f(0) = 1 + 2}[/tex]
[tex]\mathbf{f(0) = 3}[/tex]
[tex]\mathbf{g(x) = (x + 3)}[/tex]
Substitute 0 for x
[tex]\mathbf{g(0) = (0 + 3)}[/tex]
[tex]\mathbf{g(0) = 3}[/tex]
[tex]\mathbf{h(x) = (x + 1) - 3}[/tex]
Substitute 0 for x
[tex]\mathbf{h(0) = (0 + 1) - 3}[/tex]
[tex]\mathbf{h(0) = 1 - 3}[/tex]
[tex]\mathbf{h(0) = - 2}[/tex]
Hence, the ordered pair that represents the greatest y-intercept is (0,3)
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Name an inscribed angle
Answer:
BHF
Step-by-step explanation:
Definition of inscribed
10.
Find the length of the arc on a circle of radius r intercepted by a central angle 0.
r=20 cm,
e
1/4 radian
Answer:
Length of arc = 5 cm (Approx)
Step-by-step explanation:
Given:
Radius of circle = 20 cm
Angle = 1/4 radian
Find:
Length of arc
Computation:
Angle in degree = 1/4 radian × 180°π
Angle in degree = 1/4 × 180° / 22/7
Angle in degree = 14.31° Approx
Length of arc = (Ф / 360)2πr
Length of arc = (14.31 /360)2(22/7)(20)
Length of arc = 4.997 cm
Length of arc = 5 cm (Approx)
A circle has a radius of 21 inches. What is the length of the arc intercepted by a central angle that measures 4π/7 radians? Express the answer in terms of π .
Answer:
12π inches
Step-by-step explanation:
s = rθ
s = (21) (4π/7)
s = 12π
The length of the arc will be;
⇒ Arc = 37.68 inches
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The central angle = 4π/7
And, A circle has a radius of 21 inches.
Now,
We know that in circle;
⇒ Arc = Radius × Angle
Substitute all the values, we get;
⇒ Arc = 21 × 4π/7
⇒ Arc = 3 × 4 × 3.14
⇒ Arc = 37.68 inches
Thus, The length of the arc will be;
⇒ Arc = 37.68 inches
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100 points timed Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles? 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side 5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side
Answer: A
Step-by-step explanation:
The answer is A. It accurately describes the equation shown. Negative values are represented by negative tiles and positive values are represented by positive tiles.
Hope it helps <3
Jessica calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle was it?
E
F
G
H
Answer:
G
Step-by-step explanation:
We can find a missing length of a triangle using a Pythagorean theorem if and only the triangle is a right angled triangle.
The side of the missing length is:
a^+b^=c^
2^+4^=c^
4+16=c^
20=c^
[tex] \sqrt{20} = c ^{2} \\ 4 \sqrt{5} = c[/tex]
In a recent year 5 out of 6 movies cost between $50 and $99 million to make. At this rate, how many movies in a year with 687 new releases would you predict to cost between $50 and $99 million to make
Answer:
573 movies
Step-by-step explanation:
Here, we have 5 out of 6 movies having that cost
Therefore the rate we will be working with is 5/6
Now there are 687 new releases, the value that cost the given price range will be; 5/6 * 687 = 572.5 which is approximately 573
the sum of the first term of an ap is 240 and the sum of the next 4 term is 220 find the first term of the ap
Answer:
The common difference is -5/4
T(n) = T(0) - 5n/4,
where T(0) can be any number. d = -5/4
Assuming T(0) = 0, then first term
T(1) = 0 -5/4 = -5/4
Step-by-step explanation:
T(n) = T(0) + n*d
Let
S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240
S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220
S2 - S1
= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)
= (5+6+7+8 - 1 -2-3-4)d
= 4(4)d
= 16d
Since S2=220, S1 = 240
220-240 = 16d
d = -20/16 = -5/4
Since T(0) has not been defined, it could be any number.
The net of a solid is shown below:
Net of a square pyramid showing 4 triangles and the square base. The square base has side lengths of 3 inches. The height of each triangle attached to the square is 6 inches. The base of the triangle is the side of the square.
What is the surface area of the solid?
18 square inches
27 square inches
36 square inches
45 square inches
Answer:
The answer is 45 inches².
Step-by-step explanation:
First, you have to find the area of each triangle:
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 3 \\ let \: height = 6[/tex]
[tex]area = \frac{1}{2} \times 3 \times 6[/tex]
[tex]area = \frac{1}{2} \times 18[/tex]
[tex]area = 9 \: \: {inches}^{2} [/tex]
Assuming that the formula for surface area of pyramid is Surface area = base area(area of square) × 4(area of triangle):
[tex]base \: area = 3 \times 3 = 9[/tex]
[tex]area \: of \: triangle = 9[/tex]
[tex]s.a = 9 + 4(9)[/tex]
[tex]s.a = 9 + 36[/tex]
[tex]s.a = 45 \: \: {inches}^{2} [/tex]
1. Which financial statement reports the amount of cash paid for acquisitions of property, plant, and equipment? In which section (operating, investing, or financing) of this statement is the information reported? 2. Indicate the amount of cash paid for acquisitions of property and equipment in the year ended September 30, 2017.
Answer:
1. Cash flow statements; the investing section
Step-by-step explanation:
The cash flow statements is a useful document that shows where the company receives funds and uses it. Thus, it shows both incoming and outgoing cash flow.
The investment section of the cash flow statement is where all the amount of cash paid for acquisitions of property and equipment is imputed. Usually the transactions are written as capital expenditure.
PLEASE HELP!! laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. find the probability that a randomly selected light bulb will last between 900 and 975 hours.
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Where z is the standard value, x is the original value, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation. So we have that:
standard value of 900: [tex]z = \frac{900 - 750}{75} = 2[/tex]
standard value of 975: [tex]z = \frac{975 - 750}{75} = 3[/tex]
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%
Answer:
2.35 babyyyyyyyyyyy
Step-by-step explanation:
Acellus sux
Please help meeee I need help finding x y and z :)
Answer:
Hey there!
We see that z is equal to 40, because angles in a triangle add to 180 degrees.
We see that x is equal to 70, because an isosceles triangle has two angles that are congruent to each other, and can be represented using the equation 2x+y=180.
We see that y is equal to 110, because x+y needs to equal 180.
Hope this helps :)
Answer:
∠x = 70º, ∠y = 110º, ∠z = 40º
Step-by-step explanation:
to find ∠z: 180 - (71 + 69) = 40º = ∠z
the smaller triangle is an isosceles triangle, therefore ∠x is equal to the angle on its left.
so 180 - ∠z = 2 x ∠x
180 - 40 = 140 / 2 = 70º = ∠x
the angle to the left of ∠x forms 180º with ∠y.
as that angle is 70º, ∠y = 180 - 70 = 110º
three people are watching a hot air balloon travel over their town. at a certain point in time, one person stands directly below the balloon, and the others look at it at certain angles. in the following image, a,b, and c are people, and d is the balloon. person c is 384m directly below the balloon, person b is 200m away from person c, and the angle between person a, the balloon, and person b is 33 degrees. how far is person a from the hot air balloon
Answer:
Distance between balloon and a is = 383.67 m
Step-by-step explanation:
The given situation can be represented as the given diagram as attached in the answer area.
cd = 384 m
cb = 200 m
[tex]\angle adb = 33^\circ[/tex]
To find:
Distance between balloon and a i.e. side ad = ?
Solution:
First of all, let us consider the right angled [tex]\triangle bcd[/tex].
We know the trigonometric identity that:
[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]tan\angle cbd =\dfrac{cd}{cb}\\\Rightarrowtan\angle cbd =\dfrac{384}{200}\\\Rightarrowtan\angle cbd =1.92\\\Rightarrow \angle cbd = tan^{-1}(1.92) = 62.49^\circ[/tex]
Now, using the external angle property for the external [tex]\angle cbd[/tex] for the [tex]\triangle abd[/tex]:
(External angle is equal to the sum of two opposite angles of the triangle.)
[tex]\angle cbd = \angle adb+\angle a[/tex]
[tex]\Rightarow \angle a =62.49-33 =29.49^\circ[/tex]
Now, let us consider the right angled [tex]\triangle acd[/tex].
We have the value of [tex]\angle a[/tex] and perpendicular dc.
We have to find the hypotenuse ad.
Let us use the sine identity:
[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin\angle a =\dfrac{cd}{ad}\\\Rightarrow sin(29.49^\circ) =\dfrac{384}{ad}\\\Rightarrow ad = \dfrac{384}{0.49}\\\Rightarrow \bold{ad = 783.67\ m}[/tex]
So, the answer is:
Distance between balloon and [tex]\bold{a}[/tex] is = 383.67 m
students enter school in the morning through doors on opposite sides of cafeteria. At Ms. Logrieco's door,35 students enter in the first 10 minutes. At Mr. Riley's door,22 students enter in the first 8 mins. If students continue to arrive at school at the same rate,how many students do you expect to be in the cafeteria after 24 minutes?
Ms. Logrieco's door: 35 students per 10 minutes
Mr. Riley's door: 22 students per 8 minutes
Time Frame: 24 minutes
35 x 2 = 70
35 x 2/5 = 14
70 + 14 = 84
22 x 3 = 66
84 + 66 = 150
Thus, we can expect for 150 students to be in the cafeteria after 24 minutes.
The cost of importing five dozen china dinner sets, billed at $32 per set, and paying a duty of 40%, is
Answer:
duty = 64
Total cost is 224
Step-by-step explanation:
First find the cost of the 5 sets
5 * 32 = 160
Then find the duty
160 * 40%
160 * .4 = 64
Add this to the cost of the sets
160+64 =224
Factorize: 14x^6-45x^3y^3-14y^6
Answer:
(7x^3+2y^3)(2x^3−7y^3)
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that
costs $3.25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most $30
before tax. The restaurant only sells pancakes in stacks of 4 pancakes for $5.50.
Let S represent the number of stacks of pancakes that Benjamin buys.
1) Which inequality describes this scenario?
Answer:
[tex]\bold {3.25+5.50S \le 30}[/tex] is the correct answer.
Step-by-step explanation:
Given that
Chocolate milk already ordered for the cost of $3.25.
Maximum bill that Benjamin wants = $30
Cost of a stack pancake = $5.50
Number of stacks of pancakes bought = S
It is given that all the money available is to be spent on 1 chocolate milk and S number of stacks of pancakes.
Cost of 1 pancake = $5.50
Cost of S number of stacks of pancakes = [tex]\text{Number of stacks of pancakes} \times \text{Cost of each pancake}[/tex]
i.e. [tex]S \times 5.50 = 5.50S[/tex]
So, total money spent = $3.25+5.50S
Now, this money should be lesser than or equal to $30 because maximum bill that Benjamin wants is $30.
So, the inequality can be written as:
[tex]\bold{3.25+5.50S \le 30}[/tex]
a man buys a dozen cameras for $1800.He sells them at a profit of $36 each.Express his profit as a percentage of his selling price.
Step-by-step explanation:
The solution is the document i sent please check through.
Assume that the random variable X is normally distributed, with mean p = 100 and standard deviation o = 15. Compute the
probability P(X > 112).
Answer:
P(X > 112) = 0.21186.
Step-by-step explanation:
We are given that the random variable X is normally distributed, with mean [tex]\mu[/tex] = 100 and standard deviation [tex]\sigma[/tex] = 15.
Let X = a random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 100
[tex]\sigma[/tex] = standard deviaton = 15
Now, the probability that the random variable X is greater than 112 is given by = P(X > 112)
P(X > 112) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{112-100}{15}[/tex] ) = P(Z > 0.80) = 1- P(Z [tex]\leq[/tex] 0.80)
= 1 - 0.78814 = 0.21186
The above probability is calculated by looking at the value of x = 0.80 in the z table which has an area of 0.78814.
how many cups in 34 gallons
Answer:
544 cups
Step-by-step explanation:
1 gallon consists of about 16.0047 cups, 34x16 is 544
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?
O 5cm and 8 cm
O 6 cm and 7 cm
O 7 cm and 2 cm
8 cm and 9 cm
Answer:
Choice D - 8cm and 9cm.
Step-by-step explanation:
The other sides are not greater than 13.
A: 5 + 8 = 13
B: 6 + 7 = 13
C: 7 + 2 = 9
However, D is greater than 13 and is the correct answer.
D: 8 + 8 = 16.
Option d: 8 cm and 9 cm.
There is a theorem in mathematics stating:
" The sum of length of two sides of any triangle is greater than the rest third side"
According to that theorem, first three given options cant form the sides of the given triangle whose one side is 13 cm.
The 4th option has 8 cm and 9 cm for which we have:
8 + 9 > 13
Thus this option follows the theorem.
Hence fourth option is correct.
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03.07A LC)Which of the following describes a situation in which a basketball player ends up 0 m from his starting point? The player runs 9 meters forward, and then runs 0 meters in the opposite direction. The player runs 5 meters forward, and then runs 6 meters in the opposite direction. The player runs 6 meters forward, and then runs 5 meters in the opposite direction. The player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
The correct option is;
The player runs 4 meters forward, and then runs 4 meters in the opposite direction
Step-by-step explanation:
From the question relates to the displacement of a body, compared to the distance covered by the body
In the question instance, the situation in which the player displacement will be zero is one where both the players forward and backward displacement are equal such that they cancel each other
We have the instance where the forward and opposite displacement are equal is given by the situation where the player runs 4 meters forward, and then runs 4 meters in the opposite direction.
Answer:
d would be the answer if your so needy
Step-by-step explanation:
Please factorise the equations in the doc bellow ASAP. please show full working
Answer:
b. x² + 8x + 12 =
1. use the factoring X (see attachment)
2. 6 x 2 = 12; 6 + 2 = 12
3. (x + 6)(x + 2) = 0
4. x = -6, -2
c. x² + 13x + 12 =
1. 12 x 1 = 12; 12 + 1 = 13
2. (x + 12)(x + 1) = 0
3. x = -12, -1
c. x² + x - 12 =
1. 4 · (-3) = -12; 4 - 3 = 1
2. (x +4)(x - 3) = 0
3. x = -4, 3
f. x² + 15x + 36 =
1. 12 x 3 = 36; 12 + 3 = 15
2. (x + 12)(x + 3) = 0
3. x = -12, -3
hope this helps :)
Answer:
b) - (x + 2)(x + 6)
c) - (x + 12)(x + 1)
c) - (x - 3)(x + 4)
f) - (x + 12)(x + 3)
Step-by-step explanation:
Well to factor the given info we need to find the factors.
b)
[tex]x^2 + 8x + 12[/tex]
So 6*2 = 12
6x + 2x = 8x
x*x = x^2
Factored - (x + 2)(x + 6)
c)
[tex]x^2 + 13x + 12[/tex]
Well x*x = x^2
and 12*1 = 12
12x + x = 13x
Factored - (x + 12)(x + 1)
The second c)
[tex]x^2 + x - 12[/tex]
Well x*x = x^2
-3*4 = -12
-3x + 4x = x
Factored - (x - 3)(x + 4)
f)
[tex]x^2 + 15x + 36[/tex]
So x*x = x^2
12*3 = 36
12x + 3x = 15x
Factored - (x + 12)(x + 3)
Thus,
everything factored is (x + 2)(x + 6) , (x + 12)(x + 1) , (x - 3)(x + 4) ,
(x + 12)(x + 3).
Hope this helps :)