Answers
#1
2x²+x-6ac=6(-2)=-12
2x²+4x-3x-62x(x+2)-3(x+2)(2x-3)(x+2)#2
10a²+3a-110a²+5a-2a-15a(a+2)-1(a+2)(5a-1)(a+2)#3
2c²+5c-12ac=-24
2c²+8c-3c-122c(c+4)-3(c+4)(2c-3)(c+4)Answer:
(a) [tex](2x-3)(x+2)[/tex]
(b) [tex](5a-1)(2a+1)[/tex]
(c) [tex](2c-3)(c+4)[/tex]
Step-by-step explanation:
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find 2 two numbers that multiply to ac and sum to b.Rewrite b as the sum of these 2 numbers.Factorize the first two terms and the last two terms separately, then factor out the common term.Part (a)
Given expression: [tex]2x^2+x-6[/tex]
[tex]\implies ac=2 \cdot -6=-12[/tex]
Factors of -12 that sum to 1: 4 and -3
[tex]\implies 2x^2+4x-3x-6[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 2x(x+2)-3(x+2)[/tex]
Factor out common term [tex](x+2)[/tex]:
[tex]\implies (2x-3)(x+2)[/tex]
Part (b)
Given expression: [tex]10a^2+3a-1[/tex]
[tex]\implies ac=10 \cdot -1=-10[/tex]
Factors of -10 that sum to 3: 5 and -2
[tex]\implies 10a^2+5a-2a-1[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 5a(2a+1)-1(2a+1)[/tex]
Factor out common term [tex](2a+1)[/tex]:
[tex]\implies (5a-1)(2a+1)[/tex]
Part (c)
Given expression: [tex]2c^2+5c-12[/tex]
[tex]\implies ac=2 \cdot -12=-24[/tex]
Factors of -24 that sum to 5: 8 and -3
[tex]\implies 2c^2+8c-3c-12[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 2c(c+4)-3(c+4)[/tex]
Factor out common term [tex](c+4)[/tex]:
[tex]\implies (2c-3)(c+4)[/tex]
Related Questions
Two groups of tourist fly to Japan. It takes the first group 4 hours less than the second to fly
there. If it takes the first group 17 hours, how many hours does it take the second group?
Answers
Answer:
21
Step-by-step explanation:
think about it this way. if the first group takes 17 hours, and the second group takes 4 hours more than the first group, then how long does the second group take?
a furniture store sells kits that customers use to build cabinets. each kit contains 18 screws and a set number of boards. part B what is the value of x in jarreds equation
Answers
Answer:
x times square then subtract
Mr. Gray’s quiz was normally distributed with a mean of 25 and a standard deviation of 10 find z- scores for each of the following.
(a) 40 (b) 27 (c) 6
Answers
Z= x-u/sd
(a) x = 40
z = 40-25 / 10 = -15/10 = -1.5
(b) x = 27
z = 27-25 / 10 = 2/10 = 0.2
(c) x = 6
z = 6-25 / 10 = -19/10 = -1.9
Hope that helped
the temperatures for the first 10 days of January were recoded as follows 22 43 47 8 51 39 35 50 28 and 43 sara is organizing the temperatures to the display on a stem and leaf plot what will the stems be for the display
A. 0, 1, 2, 3, 5, 7, 8, 9
B. 0, 1, 2, 3, 4, 5
C. 0, 2, 3, 4, 5
D. 2, 3, 4, 5
Answers
is there a picture
Please put one so i. can help
.
Sand Hill Crane Elementary is
collecting food to donate. Their goal
is 2 tons of food so far they have
collected 2,798 pounds of food.
How many more pounds of food do
they need to collect?
Answers
The pounds of food that Sand Hill Crane Elementary needs to collect more in order to reach their goal is 1202 pounds.
How many more pounds needs to be collected?The first step is to convert tons to pounds.
1 ton = 2000 pounds
2 tons x 2000 = 4000 pounds.
The second step is to subtract the pounds of food collected so far from the goal.
4000 - 2798 = 1202 pounds.
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Which value makes the equation 3x - 6 = 36 true?
A.) 10
B.)12
C.) 14
D.) 16
Answers
Answer:
C) 14
Step-by-step explanation:
3x-6=36
3x=36+6
3x=42
x=42/3
x=14
Given a right triangle Solve for C if a=3 and b=4=3 and b=4
Answers
the formula would be a^2 + b^2 = c^2. so do
3^2 + 4^2 = c^2
9+16=c^2
25 = c^2
then find the square root so
c = 5
When will the graph meet the line y=5?
Answers
Answer:
Step-by-step explanation:
The graph of the linear equation cuts the x-axis at (5,0)
Given the function F(x) = 2x2 - 6, find the value F(-1).
Answers
Answer:
-4Step-by-step explanation:
Given
F(x) = 2x² - 6We are asked to find F(-1).
This can be done by substituting -1 in place of x in the function.
F(-1) = 2(-1)² - 6F(-1) = 2(1) - 6F(-1) = 2 - 6F(-1) = -4с
Fruit-O-Rama sells dried pineapple for $0.25 per
ounce Mags spent a total of $2.65 on pineapple.
How many ounces did she buy?
OZ
Answers
Answer:
10.6 oz
Step-by-step explanation:
X × 0.25 = 0.265
x= 2.65/0.25= 10.6 oz
PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!!!
Answers
Answer:
4,000
Step-by-step explanation:
The value goes down by around 2,000 every year and 4,00 is the closest answer of any of them.
How many meters are in 3 kilometers?
A. 30 m
B. 300 m
C. 3,000 m
D. 30,000 m
Answers
Answer:
there are 3000 meters in 3 kilometres
Answer:
C. 3,000 m
Step-by-step explanation:
There are 1,000 meters in one kilometer, so 3 times 1,000. This gets you 3,000.
18. a gamer played four games in 6 hours. she played each game for the same amount of time. how much time did she play each game on
a.2/3 hours
b. 1 hour
c. 1 1/2 hour
d. 2 hours
Answers
Answer:
c. 1 1/2 hours
Step-by-step explanation:
6 hours / 4 games = 1 1/2 hours per game
Another way to think of it:
1 hour = 60 minutes
6 hours = 6 hours x 60 minutes per hour = 360 minutes
360 minutes / 4 games = 90 minutes per game
90 minutes per game / 60 minutes per hour = 1.5 hours
1.5 hours is the same as 1 1/2 hours
So, the answer is c. 1 1/2 hours
PLEASE ANSWER I HAVE 5 MINS!! WILL MARK BRAINLIEST IF CORRECT
Answers
Answer: 49.2 or 49[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The formula for surface area of a rectangular prism is [tex]2(wl+hl+hw)[/tex]
Where
w is width (5 for this)
l is length ([tex]1\frac{1}{5}[/tex] for this)
h is height (3 for this)
Now lets sub in the values and solve
[tex]2(wl+hl+hw)\\2[(5)(1\frac{1}{5}) +(3)(1\frac{1}{5})+(3)(5)]\\2[6+3.6+15]\\2[9.6+15]\\2[24.6]\\49.2[/tex]
answer: 49.2
step-by-step :
the width is 5
the length is 1 1/5
the height is 3
find the dimension of a rectangle whose width is 6 miles less than it width and whose area is 72 square miles.
Answers
14 8/9 less than the product of 8 and a number d
whats an exspression for this
Answers
Answer:
(8*d)-14 8/9
Step-by-step explanation:
14 8/9 less than means: -14 8/9
product of 8 and a number d means: 8*d
It says 14 8/9 less than the product meaning the multiplying must be done first: (8*d)-14 8/9
This all comes down to order of the equation, and logic to understand meanings of phrases.
2. Given the graph, which of the statements in function notation represent the situation?
a f(-1) = 4
b. f(-4) = -1
C. f(4) >
y = f(x)
d. f(x) = -4 when x is -1
e. f(x) = -1 when x is -4
f. f(2)=f(6)
g. f(0) = -2
h. f(-2) = 0.
Answers
Answer:
[tex] \rule{40pt}{99999pt}[/tex][tex] \rule{40pt}{99999pt}[/tex]
Answer:
D , F and G
Step-by-step explanation:
D, F and G are true in this case
Muna claims that the expression (8)(16) + (8)(12) + (16)(12) represents the
surface area, in square inches, of the right rectangular prism shown. Is Muna
correct? Explain.
Answers
The surface area of a right rectangular prism is the amount of space on it.
Muna's claim is incorrect
How to determine the surface area?
The surface area of a right rectangular prism is calculated as:
A = 2 * (lw + lh + wh)
So, we have:
A = 2 * (8 * 16 + 8 * 12 + 16 * 12)
The above expression implies that Muna's claim is incorrect
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Answer these?
3. John bought 2 kg apples, 4 kg mangoes, 1 kg pears and put them in his bag. Find the total weight of the fruits in his bag.
4. Three brothers weigh 30 kg, 25 kg and 45 kg. Find their total weight.
5. A man weighs 72 kg and his wife weighs 59 kg. How much does the man weigh more than his wife?
6. Papaya sells at $16 per kg. Find the cost of 4 kg of these papayas.
7. A bag of wheat weighs 25 kg. Find the total weight of 8 such bags.
Answers
Answer:
3. 7kg
4. 100kg
5. 13kg more
6. $64
7. 200kg
What is the equation?
Answers
Answer:
[tex]\displaystyle 5x + 6y = 72\:or\:y = -\frac{5}{6}x + 12[/tex]
Step-by-step explanation:
Perpendicular equations have OPPOCITE MULTIPLICATIVE INVERCE RATE OF CHANGES [SLOPES], so 1⅕ becomes −⅚, and we move forward with plugging the information into the Slope-Intercept formula:
[tex]\displaystyle -8 = -\frac{5}{6}[24] + b \hookrightarrow -8 = -20 + b; 12 = b \\ \\ \boxed{y = -\frac{5}{6}x + 12}[/tex]
To write this in Linear Standard Form, perfourm he following:
y = −⅚x + 12
+ ⅚x + ⅚x
___________
⅚x + y = 12 [We cannot leave the equation this way, so multiply the equation by the denominatour to eradicate the fraction.]
6[⅚x + y = 12]
[tex]\displaystyle \boxed{5x + 6y = 72}[/tex]
I am joyous to assist you at any time.
What is the slope of the line y=4x – 6?
A.1/4
B.-6
C.4
D.6
Answers
Answer:
C. 4
Step-by-step explanation:
the slope is always the factor of x.
“A number decreased by 16 is
Answers
Answer:
Step-by-step explanation:
A number decreased by 16 is − 3
hope this helps.
mark me brainliest please.
maths j2 a road is 300km long is drawn to a scale of 1cm represents 50km . what is it's length on drawing?
Answers
Answer: 6cm.
Step-by-step explanation:
Strategy 1 (in-head thinking)
300 divided by 50 would be 6, multiply 6 by 1 and get 6cm.
Strategy 2 (proportions)
First, set up a proportion.
We know that 1cm = 50km, so we put them on a fraction (whichever is denominator/numerator doesn’t affect the process)
However, we don’t know how much cm equals 300km, so we turn that into a variable, in this case x.
1cm x cm
——— ———
50km 300km
To solve a proportion, go diagonal to where the variables have already been filled in. You can’t so 50km and x cm, as you don’t know x. You can do 300km however. To start, multiply 1 and 300, to which you get 300. Then, multiply 300 by the 50km and you’ll get x. That’ll equal to 6.
So in conclusion, your answer is 6.
If vector A=xz³î-2x²yj+2yz⁴k find CURL A at the point [1, -1, 1]
Answers
Given that
[tex]\vec A = xz^3 \, \vec\imath - 2x^2 y \, \vec\jmath + 2yz^4 \, \vec k[/tex]
its curl is
[tex]\displaystyle \nabla\times\vec A = \left(\frac{\partial\left(2yz^4\right)}{\partial y} - \frac{\partial\left(-2x^2y\right)}{\partial z}\right) \, \vec\imath - \left(\frac{\partial\left(2yz^4\right)}{\partial x} - \frac{\partial\left(xz^3\right)}{\partial z}\right) \, \vec\jmath \\ ~~~~~~~~~~~~ + \left(\frac{\partial\left(-2x^2y\right)}{\partial x} - \frac{\partial\left(xz^3\right)}{\partial y}\right) \, \vec k[/tex]
[tex]\nabla\times\vec A = 2z^4 \, \vec\imath + 3xz^2 \, \vec\jmath - 4xy \, \vec k[/tex]
so that at the point (1, -1, 1), the curl is
[tex]\nabla\times\vec A \bigg|_{(x,y,z)=(1,-1,1)} = \boxed{2 \, \vec\imath + 3 \, \vec\jmath + 4 \, \vec k}[/tex]
ima need help, I'm confused about this depth stuff
Answers
[tex]v (total)= v(r \: p \: ) + v(c)[/tex]
[tex]v(t) = lwh + \pi {r}^{2} h[/tex]
[tex]v(t) =( 18 \times 10 \times 5 )+( 3.14 \times {5}^{2} \times 5) \\ [/tex]
[tex]v(t) = 900 + 392.50[/tex]
[tex]v(t) = 1292.50 \: \: \: {ft}^{3} [/tex]
Depth is also referred as height.
Volume of the rectangular part = l b h
= 18 × 10 × 5
= 900 ft³
Volume of two semi circular parts = 4 / 3 π r³
= 4 / 3 × 5 × 5 × 5 × π
= 523.8 ft³
Total Volume of the figure = 1423.8 ft³
In FGH,FH =7 ft,FG=12 ft and m
Answers
Answer:1) In Δ FGH,
FH=7 ft, FG=12 ft,
∠F=70 degrees
By "Law of cosines":
So,By applying Law of Sines , we get that
Hence, Option 'D' is correct.
2) In Δ XYZ,
XY=14, ∠Y=22°, and XZ=26
By using "Law of sines":
so, X = 147° , Y = 22° , Z = 11.6°
Step-by-step explanation:
Complete two expressions that have the same product as 3×5/12
Answers
Answer:
1. 5/(2+2)= 5/4= 1.25
2. 5/(2x2)= 5/4= 1.25
Step-by-step explanation:
3x5/12= 15/12= 1.25
Please help ASAP!!!! 20 PTS
Marko is playing the video game Fort Attack. The purpose of the game is to shoot invading bandits that are trying to breach the fort's circular wall, and Marko must provide the angle at which the cannon should turn in order to shoot the attacking bandits. The bandit is attacking as pictured in the figure below:
The unit circle is shown. There is an angle 30 degrees counterclockwise from the positive y axis. An image of a bandit is shown at the point of intersection between the angle and unit circle.
What is the angle of fire in standard position on the unit circle in both degrees and radians?
120°; pi over 6 radians
120°; 2 pi over 3 radians
30°; pi over 3 radians
30°; 2 pi over 3 radians
Answers
The angle of fire in the standard position will be B. 120°; 2 pi over 3 radians.
How to calculate the angle?
It should be noted that the image shows the shooting angles arrangements. Also, π = 180°.
In this case, the value of the angle will be:
= 12π/18
= (12 × 180) / 18
= 12 × 10
= 120°
Therefore. the angle of fire in the standard position will be B. 120°; 2 pi over 3 radians.
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What is the next term of the arithmetic sequence? -3, -7,-11, –15,
Answers
Answer:
-19
Step-by-step explanation:
The sequence is going down by 4
The sequence is subtracting 4.
- 15 - 4 = -19
A container manufacturer plans to make rectangular boxes whose bottom and top measure 4x by 3x. The container must contain 48in.3 The top and the bottom will cost $1.80 per square inch, while the four sides will cost $3.70 per square inch.
What should the height of the container be so as to minimize cost? Round your answer to the nearest hundredth.
Answers
The height of the container that will be able to minimize the cost will be 3.08cm.
How to calculate the height?The volume of the box will be:
= (3x)(4x)h
= 12x²h
From the information given, we are told that the container must contain 48in³. Therefore,
48 = 12x²h
h = 4/x²
The function cost will be:
= 3.50(2)(12x²) + 4.40(14x)h
= 84x² + 61.6x(4/x²)
= 84x² + 246.4/x
We'll use the first derivative. This will be:
dC/dx = 168x - 246.4/x²
x = 1.14.
Therefore, the height will be:
h = 4/x² = 4/1.14² = 3.08cm
In conclusion, the height is 3.08cm.
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