Suppose you want to buy a great pair of designer jeans that were originally priced at $95, but are now on sale for 10% off. When you buy the jeans, you need to pay sales tax of 10% on the sales price. How much will you have to pay for the jeans?
Answer:
$94.05
Step-by-step explanation:
Original price of jeans=$95
Discount=10%
New price=(100% - 10%) of $95
=90% × 95
=90/100 × 95
=0.9 × 95
=$85.5
Sales tax of 10%
10% of the new price
=10/100 × 85.5
=0.1 × 85.5
=$8.55
Sales tax =$8.55
Total amount paid for the jeans= sales tax + new tax
=$8.55 + $85.5
=$94.05
Question 10 of 25
The polynomial (x-2) is a factor of the polynomial 5x² - 6x +4.
O A. True
OB. False
Answer:
B. False
Step-by-step explanation:
5x² - 6x + 4 | 5 × 4 = 20
Can't factor it normally
√b² - 4ac
-b ± ---------------
2a
√(-6)² - 4(5)(4)
-(-6) ± ---------------
2(5)
√36 - 80
6 ± ---------------
10
6 ± √-44
---------------
10
6 ± √-4 × 11
---------------
10
6 ± 2i√11
---------------
10
The answer is actually
3 ± i√11
---------------
5
I hope this helps!
Answer:
B. False
Step-by-step explanation:
You want to know if (x -2) is a factor of 5x² -6x +4.
RemainderThere are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:
5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12
The value is not 0, so (x -2) is not a factor.
Other factorAnother way to tell is to determine what the other factor would be.
The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...
(5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial
The polynomial 5x² -6x +4 does not have a factor (x -2).
GraphThe graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.
7)
Ella started exercising. Which division expression means she lost 5 pounds every 2 weeks?
5
A)
B)
0
D)
JU
Answer:
-5/2
Step-by-step explanation:
19. A carpenter cut the top section of a window frame with a 40º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown.
Will the side pieces of the frame be parallel?_____________________
How do you know?
If a carpenter cut the top section of a window frame with a 40º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown. Yes the side pieces of the frame will be parallel. How i know is that both side are equal or parallel.
ParallelThe interior angles are the same in measure and the sum of the interior angles have to be 180°.
The two side pieces on both the right and left hand side are equal in measure. The sides can be parallel only if the sum of both side angles is equal to 180°
Hence,
One side of the interior angle=40º+50º
One side of the interior angle=90°
Both side of the interior angle=90°+90°
Both side of the interior angle=180°
Hence,
180°=180°, the sides are parallel
Therefore Yes the side pieces of the frame will be parallel. How i know is that both side are equal or parallel.
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Randy divides (2x4 – 3x3 – 3x2 7x – 3) by (x2 – 2x 1) as shown below. what error does randy make? x squared minus 2 x 1 startlongdivisionsymbol 2 x superscript 4 baseline minus 3 x cubed minus 3 x squared 7 x minus 3 endlongdivisionsymbol. minus 2 x superscript 4 baseline minus 4 x cubed 2 x squared to get a remainder of x cubed minus 5 x squared 7 x. minus x cubed minus 2 x squared x to get a remainder of negative 3 x squared 6 x minus 3. minus negative 3 x squared 6 x minus 3 to get a remainder of 0 and a quotient of 2 x squared x 3. he makes a subtraction error. he makes an error writing the constant term in the quotient. he makes an error choosing the x-term in the quotient. he makes an error rewriting the problem in long division.
By subtracting this from the dividend, the next step would be:
\((2x^4 - 3x^3 - 3x^2 + 7x - 3) - (-5x^3 + 10x^2 - 5x) = 2x^4 + 2x^3 - 13x^2 + 12x - 3\)
This error occurs because he forgets to distribute the -2 in \(-2(x^2 - 2x + 1)\)when subtracting from \(2x^4\). This leads to a mistake in the next step when he subtracts \(x^3 - 2x^2\) from \(x^3 - 5x^2\) to get \(-3x^2\)instead of \(-3x^2 + 6x\). This error then leads to the incorrect constant term in the quotient.
Therefore, the error Randy makes is a subtraction error in the first step of the long division. It is important to pay attention to signs and distribute coefficients correctly when performing long division with polynomials.
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Answer: A. x + 2
Step-by-step explanation:
Edge 2023
Find the solution to the system of equations by using either graphing and substitution y=2x-1 and y=x+3
pls explain ur answer
Answer:
x= 4 and y=7
Step-by-step explanation:
Bellow is the graph of the two systems, you can find the coordinates (4,7) were they intersect.
Because of this the two equations are true
7= 4+3 (True)
Determine Number of Solutions in System
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
As both left side is same
Slopes are equalThere is no solutions .
Answer:
no solutions
Step-by-step explanation:
Given equations:
Equation 1: \(-x+y=8\)Equation 2: \(2x-2y=-14\)Rewrite the given equations to make y the subject:
Equation 1
\(-x+y=8\)
\(\implies y=x+8\)
Equation 2
\(2x-2y=-14\)
\(\implies 2y=2x+14\)
\(\implies y=x+7\)
Slope-intercept form of a linear equation: \(y=mx+b\)
(where m is the slope and b is the y-intercept)
As both equations have the same slope, the lines are parallel and therefore there is no solution to the system of equations as the lines do not intersect.
Which of the following is an equation of the line whose graph is shown in the coordinate plane below?
Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?
Answer: In total the three teams have won
Optional working
games
Answer:
38
Step-by-step explanation:
:) hope this helps
2(4x-1) = -8x-2 no solution or infinitely many solution
Answer:
One solution only.
Step-by-step explanation:
2 ( 4x - 1 ) = -8x - 2
8x - 2 = -8x - 2
0 = 0
One solution only.
Mrs. Roxas bought 20 kilograms of sweet mangoes. She gave 5 2/3 kilograms to the frontliners assigned near their village and 3 3/8 kg to their neighbors. How many kilograms of sweet mangoes were left?
9514 1404 393
Answer:
10 23/24 kg
Step-by-step explanation:
Subtract the numbers given away from the number Mrs. Roxas bought:
20 -5 2/3 -3 3/8 = 20 -5 -3 -(2/3+3/8) = 12 -25/24 = 10 23/24
Mrs. Roxas has 10 23/24 kg of sweet mangoes left.
_____
Additional comment
Without worrying too much about "common denominator", you can always add fractions with the formula a/b +c/d = (ad +bc)/(bd). You can always reduce the sum, if necessary. Subtraction is just addition of a number that has a negative sign.
It is often convenient to deal separately with the integer and fractional parts when adding or subtracting mixed numbers.
Two buses, which are 2400 miles apart, travel towards each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours. Find their speeds.
According to the Question
Two buses started 2400 miles apart
They pass each other and they must have together to cover = 2400 miles
Now
Using Formula :-
Distance = Speed × Time
First bus ⇒ 5 × b = 5b
Second bus ⇒ 5(b + 60)
Now put in a Equation we get :-
5b + 5(b + 60) = 2400
5b + 5b + 300 = 2400
10b + 300 = 2400
10b = 2400 - 300
10b = 2100
b = 2100 / 10
b = 210
Hence :-
One bus speed is 210 miles
Another bus speed ⇒ 210 + 60 = 270 miles
\(x = 8\)I need help solving this.
Answer:
2
Step-by-step explanation:
x³ = 8
∛8 = 2
found by 2 • 2 • 2 = 4 • 2 = 8
Which of the following characteristics does not describe a stock?
O A. No guarantee you will get your money back
B. No maturity date
C. Money can be earned from capital gains
O D. No certificate of ownership
Answer:
D. No certificate of ownership
Solve the separable differential equation for u Du/dt=e^3u+10t Use the following initial condition: u(0)= 7.u = ___
The solution to the given separable differential equation for u, with the initial condition u(0) = 7.
To solve the separable differential equation for u, we start by rearranging the equation f as:
(1/u) du/dt = e^(3u)/u + 10t/u
We can now integrate both sides of the equation with respect to t and u, separately. Starting with the left-hand side, we have:
∫(1/u) du = ln|u| + C1
where C1 is the constant of integration. For the right-hand side, we can use u-substitution by letting v = 3u, dv/du = 3, and du/dv = 1/3u. Substituting these values into the equation f and simplifying, we have:
(1/3) ∫e^v dv = (1/3) e^v + C2
where C2 is another constant of integration. Substituting v = 3u back into the equation and combining the constants of integration, we get:
ln|u| = e^(3u)/3 + 10t/3 + C
where C = C1 + C2. To solve for u, we exponentiate both sides of the equation:
|u| = e^(e^(3u)/3 + 10t/3 + C)
We can drop the absolute value since u(0) = 7 > 0, and simplify the exponential expression by using the properties of exponents:
u = e^(e^(3u)/3) * e^(10t/3 + C)
Finally, we use the initial condition u(0) = 7 to solve for C:
7 = e^(e^(3(7))/3) * e^(10(0)/3 + C)
7 = e^(e^21/3) * e^C
ln(7/e^(e^21/3)) = C
Substituting this value of C back into the equation for u, we get:
u = e^(e^(3u)/3) * e^(10t/3 + ln(7/e^(e^21/3)))
This is the solution to the given separable differential equation for u, with the initial condition u(0) = 7.
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In 2010, the population of a city was 167,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 3%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
The population decreased by 5,400 people from 2015 to 2020.
By how much did the population decrease?Also known as population decline, means the reduction in a human population size
Population in 2015 = Population in 2010 + Growth from 2010 to 2015
Population in 2015 = 167,000 + (8% of 167,000)
Population in 2015 = 167,000 + 13,360
Population in 2015 = 180,360
Population in 2020 = Population in 2015 - Decrease from 2015 to 2020
Population in 2020 = 180,360 - (3% of 180,360)
Population in 2020 = 180,360 - 5,411.8
Population in 2020 = 174,948.2
The population decrease from 2015 to 2020 is:
= Population in 2015 - Population in 2020
= 180,360 - 174,948.2
= 5,411.8
= 5,400 to nearest 100 people.
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1. If Gallup, Harris and other pollsters asked people to indicate their political party affiliation as Democrat, Republican or Independent, the data gathered would be an example of which scale of measurement
Answer:
im not sure but i think its a bargraph if the answer is coreect please tell
A graph has time (years) on the x-axis and height (inches) on the y-axis. A line goes through points (2, 3) and (4, 6). The graph shows a linear relationship between the height and years of a plant’s growth. Find the rate of change. Select all that apply. The rate of change of a linear function is always the same. The rate of change of a linear function always increases as the input increases. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
The correct statement is: The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.
The rate of change in a linear function represents how the dependent variable (in this case, height) changes with respect to the independent variable (time). To find the rate of change in this scenario, we can calculate the slope of the line that goes through the given points (2, 3) and (4, 6).
The slope of a line is determined by the change in the y-values divided by the change in the x-values. In this case, the change in y is 6 - 3 = 3 inches, and the change in x is 4 - 2 = 2 years.
Therefore, the rate of change is 3 inches / 2 years = 1.5 inches per year. This means that for every additional year of growth, the plant's height increases by an average of 1.5 inches.
Now, let's analyze the given statements:
1. The rate of change of a linear function is always the same.
This statement is true. In a linear function, the rate of change (slope) remains constant throughout the entire graph.
2. The rate of change of a linear function always increases as the input increases.
This statement is not necessarily true. The rate of change can be positive or negative, depending on whether the line slopes upward or downward.
3. The rate of change from 2 years to 4 years on the graph is 1.5 inches per year.
This statement is true. We calculated the rate of change to be 1.5 inches per year.
4. The rate of change from 0 years to 6 years on the graph is 1.5 inches per year.
This statement is not necessarily true. The rate of change may vary depending on the specific section of the graph being considered. However, we only calculated the rate of change between 2 and 4 years, so we cannot determine the rate of change over a larger time frame based on this information.
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She counted the money and found out she has $14.90 in the jar. How many dimes and quarters does she have?
Answer:
There're too much possibilities of the answer.
Describe fully the single transformation that takes shape A to shape B.
It is a ......
angle ...... degress clockwise
about the point.....
Answer: It is a Rotation Angle 90 Degrees clockwise about the point (3,4)
Step-by-step explanation:
Mark the point (3,4) with your finger and turn your phone once to the right Your old shape is where your new shape your be now. That’s rotation.
a group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream how far did they walk alltogether? thank u for helping !!
Answer:
13.9 miles
Step-by-step explanation:
We know
A group of hikers walked 8 7/10 miles to caribou cave and then 5 1/5 miles to silver stream. How far did they walk altogether
8 7/10 = 87/10
5 1/5 = 26/5
87/10 + 26/5 = 87/10 + 52/10 = 139/10 = 13.9 miles
So, they walked 13.9 miles.
determine the probability that all the molecules of a gas will be found in one half of a container when the gas consists of 1 molecule.
The probability that all the molecules of a gas consisting of 1 molecule will be found in one half of a container is 1 or 100%.
If a gas consists of only one molecule, then it will always be found in one half of the container. This is because there is no other molecule to interact with and no other half of the container to occupy. Therefore, the probability that all the molecules of a gas consisting of 1 molecule will be found in one half of a container is 1 or 100%.
However, this is not the case for gases consisting of more than one molecule. In fact, the probability of all the molecules being found in one half of a container is extremely low and depends on the number of molecules, the volume of the container, and the temperature and pressure of the gas.
This phenomenon is related to the concept of entropy and the tendency of systems to move towards a state of higher disorder. As the number of molecules in a gas increases, the probability of all the molecules being found in one half of a container decreases exponentially.
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Jacob drives 8km in 12 minutes. What is his average speed (km/h) ?
Answer:
40 km/h
Step-by-step explanation:
PLz mark brainliest
16km:24mins
24km:36mins
32km:48mins
40km:60mins
Answer:
Step-by-step explanation:
8km per 12 min would be 40km/hr :)
Helen had $330 in her savings account when Vince opened a savings account with zero dollars. Helen deposited $30 into her account each week for x weeks. Vince deposited $50 into his account each week for x weeks. The accounts did not earn interest. Which inequality represents this situation when the amount of money in Helen's account was greater than the amount of money in Vince's account? A. 30x < 330 + 50x A. , 30x < 330 + 50x B. 50x > 330 + 30x B. , 50x > 330 + 30x C. 30x > 330 + 50x C. , 30x > 330 + 50x D. 50x < 330 + 30x
Answer:
\(50x < 330 + 30x\)
Step-by-step explanation:
Given
Helen:
\(Base\ Amount = \$330\)
\(Weekly = \$30\)
Vince:
\(Base\ Amount = \$0\)
\(Weekly = \$50\)
First, we need to determine Helen's and Vince's balance at x weeks.
\(Balance = Base\ Amount + Weekly\ Earnings * x\)
For Helen:
\(Balance = 330 + 30 * x\)
\(Balance = 330 + 30x\)
For Vince:
\(Balance = 0 + 50 * x\)
\(Balance = 50x\)
As an inequality, we have:
\(Helen > Vince\)
\(330 + 30x > 50x\)
Reorder
\(50x < 330 + 30x\)
determine whether the random variable x is discrete or continuous. explain. let x represent the amount of rain that fell in spring
The random variable x, which represents the amount of rain (in inches) that fell this spring, is a continuous random variable.
In this context, a continuous random variable is one that can take on any value within a certain range. The amount of rain can be measured with different levels of precision, such as 2.5 inches or 2.5342 inches, indicating that there is an infinite number of possible values between any two given points.
On the other hand, a discrete random variable would involve countable outcomes or a finite number of possible values. For example, if we were counting the number of rainy days during the spring, the random variable would be discrete since it can only take whole number values.
In the case of measuring the amount of rain, there can be infinitely many possible values within any given range, and therefore, it is considered a continuous random variable. So, the correct answer is option A.
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The complete question is:
Decide whether the random variable x is discrete or continuous. Explain your reasoning Let x represent the amount of rain (in inches) that fell this spring. Is the random variable x discrete or continuous? Choose the correct answer below.
A. Continuous, because x is a random variable that cannot be counted.
B. Discrete, because x is a random variable that can be counted.
In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was 1300 grams and mass was decreasing by 6% per day. Determine the mass of the radioactive sample at the beginning of the 8th day of the experiment. Round to the nearest tenth (if necessary).
The mass of the radioactive sample at the beginning of the 8th day of the experiment a_13=310.7.
In a lab experiment, the decay of a radioactive isotope is being observed.
At the beginning of the first day of the experiment, the mass of the substance was 1300 grams and the mass decreased by 6% per day.
What is the formula of the nth term?
\(a_n=a_1r^{n-1}\)
Use the given value in the formula so we get,
\(a_{13}=1100(0.9)^{13-1}\)
Simplify the given term
\(a_{13}=310.7\)
Therefore, The mass of the radioactive sample at the beginning of the 8th day of the experiment a_13=310.7.
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Answer:
389
Step-by-step explanation:
What is the formula for varies inversely?
Inverse variation is the relationships between variables that are represented in the form of \(y=\frac{k}{x}\), where \(x\) and \(y\) are two variables and \(k\) is the constant value. It states that if one quantity's value rises, the other quantity's value falls.
We notice that the variation in values of one quantity depends on the variation in values of another quantity in our day-to-day lives. A variable's inverse variation in relation to another variable is known as inverse variation. It exemplifies the opposite relationship that exists between two quantities. As a result, a variable and another variable are inversely proportional.
In everyday life, there are numerous real-world examples of inverse variation. For instance: If a train travels at a constant speed for a greater distance, it takes longer to complete the journey, and vice versa. On the other hand, if more people are assigned to a job, it takes less time to complete it.
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The area of Kylie's room is 400 square feet. The width of her room is 20 feet. What is the length of her room?
Answer and Step-by-step explanation:
Assuming the room is a type of rectangle, we need to divide the area by the width to get the length.
So, do 400 divided by 20 to get the length, as length times width equals the area.
400 divided by 20 = 20.
The length of the room is 20 ft. (meaning the room is a perfect square.
#teamtrees #PAW (Plant And Water)
the last choice says x=4 . but pls help asap
Answer:
x = 6
Step-by-step explanation:
6x + 27 = 12x - 9
6x -12x = -9 -27
-6x = -36 /: (-6)
x = 6
The tenth through thirteenth terms of an arithmetic sequence are given by a 10 = 47,aji = 53,a12 = 59, and a3 = 65.
Which formula can be used to find ?
O A. An = 6 - 13
OB. An = 67 + 37
OC. An = 6n +41
O D. An = 6 - 47
O E. An = 6 - 7
Your question involves the terms of an arithmetic sequence. The general formula for the nth term in an arithmetic sequence is An = A1 + (n - 1) * d, where An is the nth term, A1 is the first term, n is the term number, and d is the common difference between the terms.
You've provided the 10th through 13th terms of the sequence: a10 = 47, a11 = 53, a12 = 59, and a13 = 65. We can observe that the common difference (d) between consecutive terms is 6.
Now, we can use this information to find the formula for the nth term. We know that a10 = 47, so we can write:
47 = A1 + (10 - 1) * 6
47 = A1 + 54
Solving for A1, we get:
A1 = -7
So the formula for the nth term of the arithmetic sequence is:
An = -7 + (n - 1) * 6
This simplifies to:
An = 6n - 13
Hence, the correct answer is:
O A. An = 6n - 13
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