Jane is correct because Jane correctly simplified the expression to [tex]\(3x\)[/tex].
Let's carefully simplify the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\)[/tex] step-by-step to determine who is correct, Jane or Jill.
Starting with the given expression:
[tex]\[(2x^2 + x) + 2(-x^2 + x)\][/tex]
We first distribute the [tex]\(2\)[/tex] in [tex]\(2(-x^2 + x)\):[/tex]
[tex]\[(2x^2 + x) + (-2x^2 + 2x)\][/tex]
Next, we combine like terms. We combine the \(x^2\) terms and the \(x\) terms separately:
[tex]\[(2x^2 - 2x^2) + (x + 2x)\][/tex]
Simplify each group of like terms:
[tex]\[0x^2 + 3x\][/tex]
This simplifies to:
[tex]\[3x\][/tex]
Therefore, the correct simplification of the expression [tex]\((2x^2 + x) + 2(-x^2 + x)\) is \(3x\)[/tex].
Jane’s solution is:
[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) + (-x^2 + x) + (-x^2 + x) \\& = (2x^2 - x^2 - x^2) + (x + x + x) \\& = 3x\end{aligned}\][/tex]
Jill’s solution is:
[tex]\[\begin{aligned}& = (2x^2 + x) + 2(-x^2 + x) \\& = (2x^2 + x) - 2x^2 + 2x \\& = 2x\end{aligned}\][/tex]
Jane correctly simplified the expression to [tex]\(3x\)[/tex], while Jill made an error by not correctly distributing the [tex]\(2\)[/tex] in the term [tex]\(2(-x^2 + x)\)[/tex].
The complete question is
Jane and jill were simplifying the expression (2x²+x) +2(-x²+x) and obtained different answers. Who is right and why?
Jane
[tex]$$\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)+\left(-x^2+x\right)+\left(-x^2+x\right) \\& =\left(2 x^2-x^2-x^2\right)+(x+x+x) \\& =3 x\end{aligned}$$[/tex]
Jill
[tex]\begin{aligned}& =\left(2 x^2+x\right)+2\left(-x^2+x\right) \\& =\left(2 x^2+x\right)-2 x^2+x \\& =2 x\end{aligned}[/tex]
Write an algebraic expression to represent the pay (in dollars) for working "x" hours at a rate of eight dollars and seventy-five cents per hour. A) 8.75x B) 875x C) 8.75 x D) 875 x
Solve the following systems of 3-variable linear equations.
50 points
Answer:
x = 9/25
y = 7/25
z = 4/25
Step-by-step explanation:
2x + y = 1 .......(1)
3y + z = 1 ........(2)
x + 4z = 1 ........(3)
Elimination 1 and 2
2x + y = 1 | ×3 |
3y + z = 1 | ×1 |
6x + 3y = 3
3y + z = 1
___________--
6x - z = 2 .............. (4)
Elimination 3 and 4
x + 4z = 1 | ×6 |
6x - z = 2 | ×1 |
6x + 24z = 6
6x - z = 2
___________--
25z = 4
z = 4/25
Elimination 3 and 4
x + 4z = 1 | ×1 |
6x - z = 2 | ×4 |
x + 4z = 1
24x - 4z = 8
___________+
25x = 9
x = 9/25
Subsitution 1
2x + y = 1
2(9/25) + y = 1
18/25 + y = 1
y = 1 - 18/25
y = 25/25 - 18/25
y = 7/25
Answer:
x = 9/25
y = 7/25
z = 4/25
Step-by-step explanation:
:D
Area and Triangles:Question 1
A pennant in the shape of a triangle has a base of 12 inches and a
height of 30 inches. What is the area of the pennant?
Answer:
A =180 in^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
The base is 12 and the height is 30
A = 1/2 *12*30
A = 1/2 *360
A =180 in^2
The Bar Chart shows the weights of 10 dogs entered in a local dog show,
Which statement is the about this data set?
Can you please help me ?
What is the minimum value of the objective function C = 4x + 9y?
Answer:-24
explain how you know:
Since xy = 4, we have y=4/x. Substituting in (1) we get f(x) = 4x+(36/x) …….(2)
Differentiating we get f ' (x) = 4 - (36/x^2)…..(2)
For maxima or minima, f ‘ (x) = 0
=> 4 - (36/x^2) =0 => (4x^2 - 36)/x^2 = 0 which gives x= +/- 3
Differentiating (2), f ‘’ (x) = 72/x^3
When x= +3 , f ‘’ (x) is clearly +ve. Therefore f(x) at (2) gives minima and the minimum value is 24.
When x= -3, f ‘’ (x) is -ve. Therefore, f(x) has maxima at x= -3. The maximum value is -24.
Note: You may be surprised to observe that the minima is more than the maxima. This is due to the fact that the function is discontinuous at x= 0, the graph of f(x) comprising of two branches, one in the first quadrant giving the minima (= +24) and another in the third quadrant that gives maxima (= -24)
Answer:
its 125 on edg2020 ;)
Step-by-step explanation:
The right rectangular prisms are similar. Which statements are correct? Check all that apply. The angles in the smaller prism measure 90 degrees. The perimeter of the rectangular bases changes by a factor of 2. The surface area changes by a factor of 8. The larger prism has twice the volume of the smaller prism. The area of the rectangular bases changes by a factor of 4. PLEASE HURRRYYYYY!!!!!
Answer:
- the angles in the smaller prism measure 90 degrees
- the perimeter of the rectangular bases changes by a factor of 2
-the area of the rectangular bases changes by a factor of 4
Step-by-step explanation:
I just got it right
Answer:
the angles in the smaller prism measure 90 degrees
the perimeter of the rectangular bases changes by a factor of 2
the area of the rectangular bases changes by a factor of 4
Step-by-step explanation:
A particular type of Gasoline is suppose to have a mean octane rating greater than 90%. Five measureaments are taken of the octane rating, as follow:
90.1 88.8 89.5 91.0 92.1
Can you conclude that the mean octane rating is great er than 90%?
Answer:
Yes
Step-by-step explanation:
The mean octane rating will be 90.3
Hope this helps!
Answer:
Yes
Step-by-step explanation:
The mean is just the average, and it's calculated by adding up all the data set numbers and dividing that sum by the number of numbers:
(90.1 + 88.8 + 89.5 + 91.0 + 92.1) / 5 = 451.5 / 5 = 90.3
Our average/mean is 90.3%, which is clearly greater than 90%. So, yes, we can conclude that the mean octane rating is greater than 90%.
Hope this helps!
The answer the book gave was (1/2, -2)
I was getting close answers as I work it differently but can't seem to work it out to become the answer above...
Answer:
(x, y) = (1/2, -2)
Step-by-step explanation:
Many people find it convenient to work these problems by eliminating fractions as a first step.
Here, you can do that by multiplying the first equation by 4
4(1/2x +2y) = 4(-15/4)
2x +8y = -15
From here, there are a number of possibilities for arriving at a solution.
__
Multiply the first equation by 2 and you have ...
4x +16y = -30
The second equation says you can replace the first term with -y:
-y +16y = -30
15y = -30
y = -30/15 = -2
Substituting this value into the second equation gives ...
4x = -(-2) = 2
x = 2/4 = 1/2
The solution is (x, y) = (1/2, -2).
__
Alternate solution
You can rearrange the second equation to give an expression for y:
y = -4x
Then, substitute this into the first equation:
(1/2)x +2(-4x) = -15/4
(-15/2)x = -15/4
x = (-15/4)/(-15/2) = 2/4 . . . . . . divide by the coefficient of x
x = 1/2
4(1/2) = -y = 2 . . . . . substitute for x in the second equation
y = -2 . . . . . . . . . . . . multiply by -1
_____
Additional comments on problem solving
I find the key to working troubling problems is to be very meticulous. Make certain you follow the rules of algebra: anything you do to one side of the equation must also be done to the other side. I find it easier to think in those terms when moving stuff around.
Some folks would say, "move this term over there and ...". I like to think of it as "subtract this term from both sides of the equation."
It also helps to be careful when dealing with fractions. Make sure you know how to add, subtract, multiply, and divide fractions. You should be just as able to handle that arithmetic as with integers or decimals. Use a calculator if your skills are shaky.
As you may notice, a graphing calculator can help you verify your answer.
Will give brainliest!!! Determine the answer to (−5) + 4 and explain.
Answer:
The answer is -1 because adding onto a negitive number makes the number go towards 0
Step-by-step explanation:
Answer:
-1
Step-by-step explanation:
So, if you have 5 negatives (A) and 4 positives (B) and pair them together:
A B A B A B A B A
You'll see that you have one extra A or -1 leftover.
So, -5 + 4 = -1
3x+6y=12
x +5y=10
x = 10 – 5y
3(10 – 5y)+6y=12
30–15y+6y=12
30-9y= 12
-9y=-18
y=2
Joey has to solve the system of equations using substitution. He had completed the work shown. What should be his next step
the point (-3,6) is located in which quadrant
Answer:
Quadrant 2
Step-by-step explanation:
Here's how you distinguish which points are in which quadrants.
Quadrant 1: (+x, +y)
Quadrant 2: (-x, +y)
Quadrant 3: (-x, -y)
Quadrant 4: (+x, -y)
(-3,6) has a negative x and a positive y. All the points in Quadrant 2 have a negative x and positive y.
Someone Please help
I’ll give brainliest x
Answer:
7)
a. a=5
b. b=7
c. y=10
d. z=6
Step-by-step explanation:
hope this helps:)
4. You are reading a book that is 268 pages. You have already read 112 pages. You read 39
pages each day. How long will it take you to finish the whole book?
Answer:
4 days
Step-by-step explanation:
268-112= 156
156 divided by 39 = 4
Answer:
i think it is 4
Step-by-step explanation:
bc you do 268-112=156 then you take 156 and divide it by 39 and you end up getting 4.
for desert you can choose apple cherry blueberry or peach pie to eat and milk or juice to drink how many different possibilities of one pie and one beverage are possible
Answer:
8 possibilities
Step-by-step explanation:
The pies we have to choose from are 1)Apple 2)Cherry 3)Blueberry or 4)Peach.
The beverages we have to choose from are 1)Milk and 2)Juice.
Here are the possibilities:
Apple + Juice
Apple + Milk
Cherry + Juice
Cherry + Milk
Blueberry + Juice
Blueberry + Milk
Peach + Juice
Peach + Milk
So we have a total of 8 possibilities for one pie and one beverage.
Answer:
8 outcomes
Step-by-step explanation:
Given the function g(x) = -x^2+ 2x + 8, determine the average rate of change of
the function over the interval -3 < x < 2.
Answer:
3
Step-by-step explanation:
The average rate of change of g(x) in the closed interval [ a, b ] is
[tex]\frac{g(b)-g(a)}{b-a}[/tex]
Here [ a, b ] = [ - 3, 2 ], thus
g(b) = g(2) = - 2² + 2(2) + 8 = - 4 + 4 + 8 = 8
g(a) = g(- 3) = - (- 3)² + 2(- 3) + 8 = - 9 - 6 + 8 = - 7
average rate of change = [tex]\frac{8-(-7)}{2-(-3)}[/tex] = [tex]\frac{15}{5}[/tex] = 3
Someone please help, it's important!!
Step-by-step explanation:
BC is tangent to the circle with center A at point C and AC is radius.
[tex] \therefore AC \perp BC\\
\therefore \angle ACB =90°\\[/tex]
Now by Pythagorean theorem:
[tex] AB^2 = AC^2 + BC^2 \\
\therefore AC^2 = AB^2-BC^2\\
\therefore x^2 = 17^2-14^2\\
\therefore x^2 =289-196\\
\therefore x^2 =93\\
\therefore x =\sqrt{93}\\
\therefore x =9.64365076\\
\huge \purple {\boxed {\therefore x = 9.64\: units}} [/tex]
message me! i have made an edited file of it finished <3
Mrs. Hendricks used gallons of gas on a business trip. Her averages 25miles per gallon. How may miles did she travel?
Answer:
625 miles
Step-by-step explanation:
This is because, since each 25 miles takes one gallon 25 gallons would mean you would go 25 times 25 miles which is 625 miles in all.
. Two pentagons are similar. Their sides are in a ratio of 7:2. If the larger pentagon has a perimeter of 28 in., find the perimeter of the smaller pentagon.
Answer:
8 in
Step-by-step explanation:
The ratio of sides and perimeter in similar figures are equal.
let x be the perimeter of the smaller figure, then by proportion
[tex]\frac{7}{28}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )
7x = 56 ( divide both sides by 7 )
x = 8
The perimeter of the smaller pentagon is 8 in
Relative to the circle with the equation x^2 + y^2 = 4 how has the circle with the equation (x+5)^2 + (y-6)^2 = 4 been shifted, what is the radius of the circle
Answer:
the circle is shifted -5 on the x and +6 on the y. Center is (-5,6). Radius = 2.
Step-by-step explanation:
*WILL MAKE BRAINLIEST*
What is the scale factor of this dilation?
a) 1/5
b) 1/2
c)1
d) 2
Answer: 1/2
Step-by-step explanation: The scale factor of the dilation is 1/2 because it's 1/2 of the other triangle. As you can see it used to be 10, but now it's 5.
Have a good day :D
Answer:
From Triangle ABC to Triangle A'B'C', the scale factor is 1/2
b) 1/2
Step-by-step explanation:
Side Length of Line Segment AC is 8 units
Side Length of Line Segment AB is 6 units
Side Length of Line Segment of BC is 10 units
Side Length of Line Segment A'C' is 4 units
Side Length of Line Segment A'B' is 3 units
Side Length of Line Segment B'C' is 5 units
Checking:
A'C'/AC=4/8=1/2 simplified
Hence, the answer is 1/2 as the scale factor for the dilation.
15grams of powder to make a 22oz shake.i make skakes for the week and plans to make 198oz. how many grams of protein will I use for the entire week?
Answer:
135 grams
Step-by-step explanation:
Since there are 15 grams of powder in a 22oz serving, if you divide 198 by 22 you will get 9 total servings. If you multiply 15 by 9 you will get 135 total grams.
Determine which numbers are solutions for x>7 from the solution set
of { 7,8,9}
Answer:
8, 9
Step-by-step explanation:
Since x > 7
This means that x cannot equal 7 but must be greater values than 7.
Thus 8 and 9 are solutions
Which set of side lengths forms a right triangle?
2, 3,13
4, 6, 10
9, 12, 18
15, 36, 39
PLEASE HELP, DUE TODAY!!! Whoever answers first I will mark as brainliest.
The volume of a large aquarium is 525 yd3. It is 16 2/3 yd wide and 2 4/5 yd high. What is the length of the aquarium?
Answer:
45/4
Step-by-step explanation:
Volume = h x w x l
First multiply the numbers you have
16 2/3 x 2 4/5= 140/3
Then divide the volume.
525 ÷ 140/3 = 45/4
45/4
A stack of 10 quarters is a cylinder. If the diameter of a single quarter is 2.2 cm and the approximate height is 0.17 cm, what is the surface area of a 10-quarter stack?
To find the surface area of a 10-quarter stack, calculate the surface area of each quarter and then multiply by the number of quarters.
Explanation:To find the surface area of a 10-quarter stack, we need to calculate the surface area of each quarter and then multiply it by the number of quarters in the stack. The surface area of a quarter can be calculated using the formula for the surface area of a cylinder: SA = 2πr^2 + 2πrh.
Since the diameter of a quarter is 2.2 cm, the radius (r) is half of that, which is 1.1 cm. The approximate height (h) of a quarter is 0.17 cm.
Substituting these values into the formula, we get: SA = 2π(1.1 cm)^2 + 2π(1.1 cm)(0.17 cm). Calculating this gives us the surface area of a single quarter. Then, multiplying it by 10 gives us the surface area of a 10-quarter stack.
40. A car stereo originally cost $268. It is now being sold for 85% of its original price. How much does
the car stereo cost now?
Answer:
The stereo is now being sold for $227.80.
Step-by-step explanation:
To calculate percentage discounts, multiply the original price (268) by the discount percentage (.85). Make sure to put move the percentage value two places to the right before multiplying, as percentages are percentages of a whole.
268 * .85 = 227.8
The constants a,b,c are positive. Solve the inequality for x.
a>-bx+c
Answer:
x > (c - a)/b
Step-by-step explanation:
a > -bx + c
We need to make x the subject of the inequality so, first remove c from the right hand side of the inequality by adding -c to both sides. So,
a - c > -bx
Now, we need to remove -b from the right hand side. So, we will divide both sides of the inequality with -b. Multiplying the inequality with a negative number will also change the sign of the inequality. So,
-(a-c)/b < x
x > (c - a)/b
Answer:
C on edge
Step-by-step explanation:
Please Help!!!
The Barber family just left the local pet store with Lucky, their new family dog. The pet store owner told the Barber family that for the next six months, Lucky will grow at an average rate of four pounds per month. Currently, Lucky is three months old and weighs five pounds.
Age, in months 3 4 5 6 7 8 9
Weight, in pounds 5
Part A: Complete the given table that represents Lucky's current weight, in pounds, as a function of his age, in months.
Part B: If Lucky continues to grow at the rate of 4 pounds per month beyond the expected six months, how much will Lucky weight by time he is one year old?
Answer:
Part A
Months, Pounds
3,5
4,9
5,13
6,17
7,21
8,25
9,29
Part B
1 year = 12 months
If we continue the chart it would look like this:
10,33
11,37
12,41
Lucky will weigh 41 pounds by 1 year.
Hope this helps!
Final answer:
Lucky will weigh 41 pounds by the time he is one year old.
Explanation:
To complete the table representing Lucky’s current weight as a function of his age, we'll calculate Lucky's expected weight at each month by using the growth rate of four pounds per month. Starting with Lucky's current weight at three months old, which is five pounds:
Age 4 months: 5 pounds + (1 month * 4 pounds/month) = 9 pounds
Age 5 months: 5 pounds + (2 months * 4 pounds/month) = 13 pounds
Age 6 months: 5 pounds + (3 months * 4 pounds/month) = 17 pounds
Age 7 months: 5 pounds + (4 months * 4 pounds/month) = 21 pounds
Age 8 months: 5 pounds + (5 months * 4 pounds/month) = 25 pounds
Age 9 months: 5 pounds + (6 months * 4 pounds/month) = 29 pounds
Continuing with the growth rate of four pounds per month, by the time Lucky is one year old, which is 12 months, the calculation would be:
Lucky's weight at one year old = initial weight + (growth over months)
12 months old: 5 pounds + (9 months * 4 pounds/month) = 41 pounds.
JUst please help fast because this a quizziz
Answer:
b
Step-by-step explanation:
use slope intercept form
Answer:
2
Step-by-step explanation:
Since you need it fast, I am not going to explain.
(2, 4) - (6, 12) = (-4, -8)
-8/-4 = 2
What type of decimal is the following number?
0.1313
Answer:
it is repeating decimal.
Answer: repeating
Step-by-step explanation: