The ratio of the given expression is equal to 1:16.
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Sometimes, pupils struggle to understand the relationship between ratio and proportion.
We have x=1 and y=2, and we have to find the ratio of x4:y4,
x=1 and y=2 (given)
[tex]x^4:y^4=(1)^4:(2)^4\\\\x^4:y^4=1:16=1/16[/tex]
the ratio of the given expression is equal to 1:16.
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help me please :(.......
Answer:
a) $2125
b) $2000
Step-by-step explanation:
In this problem, we are asked to solve for the manufacturing price of different printers if the printer company sells their printers at a price that makes them 25% profit, assuming there are no extra expenses.
We can solve this type of problem by manipulating ratios, like for example:
manufacturing price : sale price
100 : 125
This ratio represents the the sale price being 25% more than the manufacturing price.
a) We can equate the above ratio to the ratio of the manufacturing price (in this problem, $1700) to the sale price of the printer (represented by x).
100 : 125 = 1700 : x
This can be solved for x when the ratios are represented as fractions.
[tex]\dfrac{100}{125} = \dfrac{1700}{x}[/tex]
↓ simplify the fraction on the left side
[tex]\dfrac{4}{5} = \dfrac{1700}{x}[/tex]
↓ cross multiply
[tex]4x = 1700 \cdot 5[/tex]
↓ divide both sides by 4
[tex]x=\$ \, 2125[/tex]
So, the price that the customer would pay for a printer that the company bought for $1700 is $2125.
b) We can solve in the same way that we did for section a.
However, this time, the variable (y) represents the manufacturing price, NOT the sale price.
100 : 125 = y : 2500
↓ rewrite with fractions
[tex]\dfrac{100}{125} = \dfrac{y}{2500}[/tex]
↓ simplify the fraction on the left side
[tex]\dfrac{4}{5} = \dfrac{y}{2500}[/tex]
↓ cross multiply
[tex]5y = 2500 \cdot 4[/tex]
↓ divide both sides by 5
[tex]y = \$ \, 2000[/tex]
So, the price that the company would pay for a printer that a customer buys for $2500 is $2000.
Use the drop-down menus to compare −2. 25 and −3.
please i need help!!!
-2.25 is larger when it compares to -3, because when you order negative numbers, the larger the number after the negative sign, the smaller the number actually is. This means -2.25 > -3
What is negative numbers?
On a number line, numbers always move from right to left and grow (become "more positive") in that direction. The numbers to the right are bigger than the numbers to the left, while the numbers to the left are smaller. Numbers with a minus sign before them are considered negative numbers. They could be fractions, decimals, or integers. Negative numbers include, for instance, -4, -15, -4/5, and -0.5. A negative number in mathematics represents the reverse. A negative number is one that is less than zero in the real number system. Negative numbers are frequently used to indicate how great a loss or a shortage is.
-2.5>-3 because the bigger a negative number is like -15,-18, etc the smaller it’s value actually gets so -2.5 is greater because it is closer to 0 on a number line.
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I need the second answer please.
Answer: 40.75
Step-by-step explanation:
Which graph do you create if you plot the function on a coordinate plane?
Answer:
B
Step-by-step explanation:
B..................
please help!
A gumball machine contains 200 gumballs. A random sample of 25 gumballs was collected from the machine. The results from the random sample are shown.
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
Based on the random sample results, complete the prediction statements for the entire machine of 200 gumballs.
Move the answers to the correct boxes.
There are
red gumballs in the machine.
There are
more green gumballs than white gumballs in the machine.
There are
gumballs that are either blue or green in the machine.
Based on the random sample results, the prediction statements for the entire machine of 200 gumballs is completed below;
There are 10 red gumballs in the machine.There are 3 more green gumballs than white gumballs in the machine.There are 13 gumballs that are either blue or green in the machine.Complete the prediction statement using the random sample?Total gumballs in the gumball machine= 200 gumballs
Result from the random sample= 25 gumballs
From the random sample selected:
10 gumballs are red
8 gumballs are blue
5 gumballs are green
2 gumballs are white
There are 10 red gumballs in the machine.
There are 3 more green gumballs than white gumballs in the machine.
= Green gumballs - red gumballs
= 5 - 2
= 3 gumballs
There are 13 gumballs that are either blue or green in the machine.
= Blue gumballs + green gumballs
= 8 + 5
= 13 gumballs
Ultimately, the prediction statement is completed using 10, 3 and 13 respectively.
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Could the lengths 6 8 and 15 represent the sides of the triangle?
The lengths 6, 8 and 15 cannot represent the sides of the triangle. The solution has been obtained by using the triangle inequality theorem.
What is the triangle inequality theorem?
The triangle inequality theorem outlines the relationships between a triangle's three sides. According to this theorem, the lengths of any triangle's two shorter sides add up to be longer than the triangle's third side. In other terms, this theorem states that the shortest path between any two places is always a straight line.
We are given the lengths to be 6, 8 and 15.
Using the triangle inequality theorem,
⇒ 6 + 15 > 8
⇒ 21 > 8
Also,
⇒ 8 + 15 > 6
⇒ 23 > 8
Also,
⇒ 6 + 8 > 15
But,
⇒ 14 < 15
Hence, the lengths 6, 8 and 15 cannot represent the sides of the triangle.
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The Johnsons set aside money in their budget for food for their anniversary party. They spent $320 but had set aside 25% more than that. How much money did the Johnsons set aside in their budget for food for the party?
Answer:
$400
Step-by-step explanation:
25% = 0.25
320 times 0.25 = $80
$320 + $80 = $400
So, the Johnsons set aside $400 in their budget for food for the party.
find the value of the integral ∫ (∇ × a® ).® if the vector a® = eˆ eˆ eˆ and is the surface defined by the paraboloid = 1 − 2 − 2 , where ≥ 0.
The integral is equal to zero, since the divergence of a constant vector is always zero.
The integral ∫ (∇ × a® ).® is equal to zero. This is due to the fact that the curl of a constant vector is always zero. The vector a® is given to be eˆ eˆ eˆ, therefore it is a constant vector. Since the divergence of a constant vector is always zero, the integral is equal to zero.
To further illustrate this point, we can expand the integral in terms of its components. ∇ × a® is equal to 0 as it is the curl of a constant vector. Similarly, a® .® is equal to 0 since the inner product of two constant vectors is always zero. Therefore, the integral is equal to 0.
The surface defined by the paraboloid is not used in this calculation, as the surface does not affect the value of the integral. The surface is used to define the range of the integral, but not to calculate the value of the integral itself.
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Six Republicans and six Democrats orally cast their vote in the U.S. Senate. In how many orders can they vote they must alternate Republican, Democrat, Republican, Democrat, and so on, and if a Republican must always be the first to vote?
If Six Republicans and six Democrats orally cast their vote in the U.S. Senate , if they are alternate Republican, Democrat, Republican, Democrat, and so on, and if a Republican must always be the first to vote then the number of ways in which they can vote is 518400 ways .
the number of Republicans for voting is = 6 ;
the number of Democrats for voting is = 6 ;
so , total number of voters is = 12 ,
they have to vote alternately starting with a Republicans .
the first republican has to choose from = ⁶C₁ = 6 ;
the second republicans has to choose from the remaining 5 republicans , = ⁵C₁ = 5 ;
Similarly following the pattern ,
we get ;
Total chances of required way of casting votes ;
= 6×6×5×5×4×4×3×3×2×2×1×1
= (1×2×3×4×5×6)²
= (6!)² = (720)² = 518400 ways .
Therefore , the number of ways of voting is 518400 ways .
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Rectangle PQRS is dilated by a scale factor of 5 to form rectangle '. Side QR measures 5. What is the measure of Q'R'?
The length of Q'R' is 5 * 5 = 25.
Dilating Rectangle MeasurementThe steps to find the measure of Q'R' are:
Start with the length of QR, which is given as 5.Apply the dilation factor of 5 to find the length of Q'R'.The length of Q'R' is obtained by multiplying the length of QR by the scale factor: 5 * 5 = 25.So, the measure of Q'R' is 25.
This method is applicable for finding the length or width of a dilated figure when the original length or width and the scale factor are given. The formula to find the length (or width) of a dilated figure is: length (or width) of dilated figure = scale factor * length (or width) of original figure. The formula for finding the length or width of a dilated figure is a basic concept in geometry and is widely used in solving related problems.
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While playing a game of chance, Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times. What could Tarik conclude about the die?
A: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this includes 0.5, the die appears to be fair.
B: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.422 and 0.618. Since this is much greater than 1 out of 6, the die appears to be unfair.
C: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.
D: We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this is much greater than 1 out of 6, the die appears to be unfair.
We are 90% confident that the true proportion of times the die would land on the number 1 is between 0.438 and 0.602. Since this includes 0.5, the die appears to be fair.
The correct option is C.
What is the probability?The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.
Given:
While playing a game of chance,
Tarik rolled a regular six-sided die 100 times and noticed that it landed on the number 1 exactly 52 times.
The probability P is = 52/100 = 0.52.
The lower limit = P - z√(P(1 - P)/n
The lower limit = 0.52 - 1.645√(0.52 x 0.48)/100
The lower limit ≈ 0.438.
The upper limit = P + z√(P(1 - P)/n
The upper limit = 0.52 + 1.645√(0.52 x 0.48)/100
The upper limit ≈ 0.602.
Therefore, the die would land on the number 1 is between 0.438 and 0.602.
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22 miles in 20 minutes A < B > C = 38 miles in 30 minutes
It is found that 22 miles in 20 minutes is LESS
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We have to compare the two rates:
=> 22 miles in 20 minutes
=> 38 miles in 30 minutes
Let's simplify each rate by finding the speed, which is distance divided by time.
That is:
Speed = distance/time
For the first one:
s = 22/20 = 1.1 milesl/min
For the second one:
s = 38/30 = 1.27 milesl/min
Since 1.1 is less than 1.27, so, 22 miles in 20 minutes is less than 38 miles in 30 minutes.
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The complete question is;
Is 22 miles in 20 minutes greater than, equal to or less than 38 miles in 30 minutes?
determine the new limits of integration after the given substitution is made.
[tex]$\int_{-2}^{4} f(x)dx$[/tex] with the substitution [tex]$u = x^2$[/tex] . The new limits of integration are 0 and 8.
The substitution [tex]$u = x^2$[/tex] implies that [tex]$du = 2x dx$[/tex], so when [tex]x = -2$, $u = (-2)^2 = 4$[/tex]. Similarly, when [tex]x = 4$, $u = 4^2 = 16$[/tex]. Thus, the new limits of integration are 0 and 8.
To determine the new limits of integration, we must first find the values of u for the original limits of integration. Since we have [tex]$u = x^2$[/tex], when x = -2, we have [tex]$u = (-2)^2 = 4$[/tex]. Similarly, when x = 4, we have [tex]u = 4^2 = 16$.[/tex]Therefore, the new limits of integration are 0 and 8.
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a faucet is turned on at 9:00am and water starts to flow into a tank at the rate of r(t)=7t√, where t is time in hours after 9:00am and the rate r(t) is in cubic feet per hour.
7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
The equation r(t) = 7t √ represents the rate at which water is flowing into the tank, measured in cubic feet per hour, at time t after 9:00am. The expression 7t √ means that the rate of flow increases over time, starting at 0 cubic feet per hour at t = 0 and increasing as t increases.
To find the volume of water in the tank at a specific time t after 9:00am, we can integrate the rate of flow over the time interval from 9:00am to t. The volume of water in the tank at time t can be expressed as:
V(t) = ∫ r(t) dt from 9:00am to t
= ∫ 7t √ dt from 0 to t
= 7/3 t^(3/2) + C
where C is an arbitrary constant of integration. This equation represents the volume of water in the tank as a function of time t.
Therefore, 7/3 t^(3/2) + C This equation represents the volume of water in the tank as a function of time t.
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carbon-14 has a half-life of 5,730 years. if a sample contains 80 mg originally, how much is left after 17,190 years?
Answer:
After 17,190 years, the amount of carbon-14 left would be approximately 5 mg.
The half-life of carbon-14 is 5,730 years, which means that every 5,730 years, half of the remaining carbon-14 decays. To calculate the amount of carbon-14 remaining after 17,190 years, we can use the formula:
A = A0 * (1/2)^(t/T)
where:
A0 is the initial amount (80 mg)
t is the time elapsed (17,190 years)
T is the half-life (5,730 years)
A = 80 * (1/2)^(17,190/5,730)
A = 80 * (1/2)^3
A = 80 * (1/8)
A = 10 mg * 1/2
A = 5 mg
Question 1 (2 points)
Kala is financing a house for $123,500. She has to pay $300 plus 1. 05% for a brokerage fee.
How much are the mortgage brokerage fees? (2 points)
a$429. 68
b$1,296. 75
c$1,596. 75
d$2,152. 50
Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.
What is the math formula for mortgage?These factors include the total amount you're borrowing from a bank, the interest rate for the loan, and the amount of time you have to pay back your mortgage in full. For your mortgage calc, you'll use the following equation: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1].
Calculate H = P*J, this is your current monthly interest.
Calculate C = M - H, this is your monthly payment minus your monthly interest, so it is the amount of principal you pay for the month.
Calculate Q = P - C, this is the new balance of your principal of your loan.
P = the payment.
L = the loan value.
c = the period interest rate, which consits of dividing the APR as a decimal by the frequency of payments. ...
n = the total number of payments in the life of the loan (for monthly loan payments this is the loan term in years times twelve)
With given data:
123,500 x 1.05% =$1,296.75 percentage of the fee.
Total mortgage brokerage fees
$1,296.75 + $300 =$1,596.75
Thus, Total mortgage brokerage fees is $1,596.75. Thus, option c is correct.
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determine if the subset of consisting of vectors of the form , where is a subspace.
The subset of consisting of vectors of the form is indeed a subspace.
A subspace is a special type of set within a vector space that has the same properties as the larger vector space.
In order to determine if a subset of a vector space is a subspace, we must check if it satisfies certain conditions.
The first condition is that the subset must contain the zero vector.
The second condition is that the subset must be closed under addition.
The third condition is that the subset must be closed under scalar multiplication.
Now, let's apply these conditions to the subset of consisting of vectors of the form . It is clear that the zero vector satisfies this condition, as.
The subset is also closed under addition, as adding two vectors of the form and will result in a vector of the form.
Finally, the subset is closed under scalar multiplication, as multiplying a vector of the form by a scalar will result in a vector of the form .
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a team played 7 games. In those games the team won by 7points,lostby10,won by 8, won by 11,lostby2 and won by 10. What was the mean difference in game scores in the six games
The mean difference in game scores over the six games is 12
What is mean difference?The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.
Given the points by which a basketball team either won or lost 6 games.
- Won by 7 points = +7
- Lost by 10 points = -10
- Won by 8 points = +8
- Won by 11 points = +11
- Lost by 2 points = -2
- Won by 10 points = +10
Thus;
Mean difference of the 6 games is;
= (+7 - 10 + 8 + 11 - 2 + 10)/6
= 24/6
= 12
Hence, the mean difference in game scores over the six games is 12
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It costs $12. 50 to enter an amusement park and $1. 50 to play each game. Solve an inequality to find the number of games, g, Cole can play if he has $35 to spend at the park
The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games.
The total money cole have is $35
To enter an amusement parks it costs around $12.5
so, remaining money by subtracting = 35-12.5 = $22.5
so, by dividing the remaining money with $1.5 paid per each game gives how many games does cole can play.The number of games cole can play $12.5 to enter and $1.5 to play each game by subtracting and dividing with $35 is 15 games. By dividing the remaining money with $1.5 paid per each game gives how many games does cole can play. Total number of games does cole can play is 22.5/1.5 = 14 games.
Therefore , the number of games cole can play are 14 games exactly.
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Stuck on homework please help
The circumference of a circular garden is 75.36 feet. What is the diameter of the garden?
Answer:
24.12 feet.
Step-by-step explanation:
The formula to find the diameter of a circle from its circumference is:
diameter = circumference / π
Plugging in the given values:
diameter = 75.36 feet / π
diameter = 75.36 / 3.14
diameter ≈ 24.12 feet
So, the diameter of the circular garden is approximately 24.12 feet.
Which sequence of transformations produces A’B’C’ from ABC? a translation up 3 and then a 90 degree counterclockwise rotation about the origin a 90 degree counterclockwise rotation about the origin and then a translation up 3 a reflection over the x-axis and then a translation left 2 and down 1 a translation left 5 and down 2 and then a reflection over the x-axis
A reflection over the x-axis changes the signs of the y-coordinates of the points, and a translation left 2 and down 1 changes the position of the figure, but it does not change the orientation of the figure.
A 90 degree counterclockwise rotation about the origin followed by a translation up 3 produces A’B’C’ from ABC. A 90 degree counterclockwise rotation about the origin changes the coordinates of the points, but it does not change the relative positions of the points. The translation then moves the entire figure up 3 units along the y-axis. A reflection over the x-axis changes the signs of the y-coordinates of the points, and a translation left 2 and down 1 changes the position of the figure, but it does not change the orientation of the figure.
A translation left 5 and down 2 followed by a reflection over the x-axis changes the position and orientation of the figure, but it does not produce the same result as a 90 degree counterclockwise rotation about the origin followed by a translation up 3.
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The lateral height of a cone is 8 inches and the area of the base of the cone is 49π in². It requires 2.5 minutes to paint the cone. The area of the base is doubled. How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14. Enter your answer, rounded to the nearest tenth, in the box.
___ Min
(GIVEING BRAINLEST)
The time it take to paint this cone if it can be painted at the same rate is 4.21 minutes.
What is Total Surface area?The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.
Given:
Base area = 49π in²
h= 8 inches
So, area of a circle, A = πr^2
r = √(A/π).
r = √(49π/π)
r = 7 in.
Now, they doubled cone has a base area
= 2 x 49 in²
= 98 π in²
Then, r = √(98π/π)
r = 7√2 inch
Thus, the time taken
= TSA (R= 7) / TSA (r= 7√2) x2.5
= πR(l+ R) / πr(l+r)
= 14(4√2+7)π/105π x 2.5
= 4.21 min
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Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x))
The x-intercept of the composition is x = -1/2.
How to find the x-intercept of the composition?Remember that a linear function can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If a liear function passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For g(x) we can use (-1, 2) and (1, 6), the slope is:
a = (6 - 2)/(1 + 1) = 2
Then the function is something like:
g(x)= 2x + b
To find the value of b, we use again the point (1, 6)
g(1) = 6 = 2*1 + b
6 - 2 = b
4 = b
So:
g(x) = 2x + 4
Now the same for h(x), we can use the points (-1, -1) and (1, 7), we will get:
a = (7 + 1)/(1 + 1) = 4
h(x) = 4x + b
Using the point (1, 7)
h(1) = 7 = 4*1 + b
7 - 4 = b
3 = b
h(x) = 4x + 3
The composition is:
g( h(x)) = 2*h(x) + 4
= 2*(4x + 3) + 4
= 8x + 10
The x-intercept is the value of x such that:
0 = 8x + 4
-4 = 8x
-4/8 = x
-1/2 = x
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Given the following exponential function,
identify whether the change represents
growth or decay, and determine the
percentage rate of increase or decrease.
y = 25(1.071)^x
Answer:
Step-by-step explanation:
The given exponential function will grow at 6.1%
Given,
y =
To find,
identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Solution,
We have,
y =
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is:
y(x)= a(1-r)^x such that r is the growth percent.
==> 1+r = 1.061
==> r = 0.061 = 6.1%
A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 2 comma 6
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The meaning of the slope and of the intercept of the linear function are given as follows:
The slope is negative -3/2, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases 3/2 of an inch every hour.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the value of y when the graph of the function touches of crosses the y-axis.The two points for the function in this problem are given as follows:
(0,9) and (2,6).
When x = 0, y = 9, hence the intercept b is given as follows:
b = 9.
Meaning that the initial value of the problem is of 9.
The slope is given as the change in y divided by the change in x, hence:
m = (6 - 9)/(2 - 0)
m = -3/2.
Meaning that the rate of change is a decrease of 3/2 units for each unit of the input.
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Write the product using exponents.
(-4) x (-4) x (-4) x Y x Y
Using exponents, the product is _.
The product of the expression (-4) x (-4) x (-4) x y x y is -64y²
What are expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression, (-4) x (-4) x (-4) x y x y
We need to find its product,
(-4) x (-4) x (-4) x y x y
= -4³ × y²
= -64 × y²
= -64y²
Hence, the product of the expression (-4) x (-4) x (-4) x y x y is -64y²
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when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin. true or fal
When u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin, this statement is false.
The span of two nonzero vectors, u and v, is the set of all linear combinations of u and v. This can be a line, a plane, or even the entire space, depending on the vectors u and v. In general, the span of two nonzero vectors does not contain the line through each vector and the origin, unless the two vectors are collinear (i.e. they lie on the same line).
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Find the slope and the -intercept of the line y=5/2x-9
Answer:
The slope is 5/2 and the y-intercept is -9.
Step-by-step explanation:
You do not have to graph anything for this problem, as the slope and y-intercept are already in the problem.
1 x 103 + 3 x 102 + 9 x 101 + 2
Answer:
1320
MDAS Method
Answer:
Your answer is 1320
Step-by-step explanation:
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