Suppose the area of a rectangle is represented by the expression 100 – 49. When the expression is fully factored, the factors represent the dimensions of the rectangle. What expressions represent the dimensions of the rectangle?
Answers
Answer:
a - b and a + b.
Step-by-step explanation:
Let's say the area of a rectangle is represented by the expression 100a^2 - 49b^2.
According to an algebraic formula, a^2 - b^2 = (a - b) * (a + b) = a^2 - ab + ab - b^2.
In this case, the square root of 100 is 10, and the square root of 49 is 7. That means that we have (10a - 7b) * (10a + 7b).
We can check that by doing... (10a - 7b)(10a + 7b) = 100a^2 - 70ab + 70ab - 49b^2 = 100a^2 - 49b^2.
Since it matches to the expression given, the expressions that represent the dimensions of the rectangle are (a - b) and (a + b).
Hope this helps!
Related Questions
How many cubic centimetres would you place in a tub of water to displace 1 L of water?
Answers
1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water
What is conversion of units?Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.
From the information given, we have that;
Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water
So, we have that there is 1 liter of water in the tub
In order to displace, you need to put something in that is the same amount
Now, let's convert the units
1 liter = 1000 cubic cm
Hence, you need 1000 cubic cm to displace 1 liter
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given f(x)=3/4x and f(x) = 75 solve for x
Answers
Answer:
x=100
Step-by-step explanation:
75=3/4x
4/3 × 75 = x
4 × 75 = 300
300/3= 100
100(3/4) = 75
x = 100
A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
Answers
Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.
Pythagoras theorem, \(x^{2} + y^{2} = (12)^{2}\) --->(1)
Given,\(\frac{dx}{dt}= 2feet/second\) at x=3
Put x=3 in Pythagoras theorem equation (1)
\((3)^{2} + y^{2} = 144\)
\(y^{2} = 144 - 9\)
\(y^{2}\) = 135
y = 11.61
Derive equation (1) w.r.t to 't'
\(2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\) ---->(2)
substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
\(2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0\)
12 + 23.22 \(\frac{dy}{dt}\) = 0
\(\frac{dy}{dt}= \frac{-12}{23.22}\)
\(\frac{dy}{dt} = -0.518\)
Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
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The manager of a popular restaurant wants to know what types of vegetarian dishes people prefer to eat. Which sample would provide the most accurate data? 10 friends at a cookout the first 30 people leaving the local hamburger stand a random group of 40 people on the street a random group of 5 people at a grocery store.
Answers
Answer:
a random group of 40 people on the street.
Step-by-step explanation:
It's random people and also has the most people.
Answer:
C:a random group of 40 people on the street.
Step-by-step explanation:
cuz its random and unbiast
£4500 is shared between 4 charities.
the donation to charity b is 5/6 of the donation to charity d
charity d's donation is twice the donation to charity c.
the ratio of donations for charity c to charity a is 3:4.
work out the donation to charity b.
Answers
If the donation to charity b is 5/6 of the donation to charity d, charity d's donation is twice the donation to charity c and the ratio of donations for charity c to charity a is 3:4 then the donation to charity b is £1250.
Let's denote the donation to charity a as x. Then the donation to charity c is (3/4)x, and the donation to charity d is 2(3/4)x = (3/2)x.
We know that the donation to charity b is 5/6 of the donation to charity d, so:
donation to charity b = (5/6)(3/2)x = (5/4)x
We also know that the total donation is £4500, so we can set up an equation:
x + (3/4)x + (3/2)x + (5/4)x = £4500
Multiplying through by 4 to get rid of the fractions, we have:
4x + 3x + 6x + 5x = £18,000
18x = £18,000
x = £1000
So the donation to charity b is: (5/4)x = (5/4)(£1000) = £1250
Therefore, the donation to charity b is £1250.
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A rectangle and a square have the same area. The length of the rectangle is seventy feet more than two times its width. The length of a side of the square is thirty feet. What equation would help you solve for the dimensions of the rectangle? What are the dimensions of the rectangle?
Answers
Using the side of the square find the area:
Area = 30^2 = 900 square feet.
The rectangles area is the same, 900 square feet.
Let the width = X
The length would be 2X + 70
Area = length x width
X * 2x+ 70 = 900
This expands to 2x^2 * 70x = 900
Use the quadratic formula to solve for x:
-70 +/- sqrt(70^2-4*2(-900))/2*2
X = 10
Width = x = 10 feet
Length = 2x + 70 = 90 feet
What is the value of x - 9 = - 13?
Answers
x-9=-13
Add 9 to both sides.
x=-4
hope it helps!
Really appreciated :)))) (25 points) Reupload
Answers
help me please. I need help
Answers
The highest blank is (D)
The second highest blank is (E)
The third highest blank is (A)
The fourth highest blank is (C)
I’ll mark brainly hurry please
Answers
The equation for the given table is y = 20.5(\(19.5^{x}\)).
Hence, Option D is correct.
To find the equation
We use hit and trial method
So we pick the equation one by one
And then also pick the values of x and y from the table,
And make them satisfy.
And other appropriate method to find the equation,
Plot the graph of each equation one by one and then observe each value from the table.
So in order to this,
Pick the equation
y = 20.5(\(19.5^{x}\))
Now plot the graph of it:
After observing the data from the table
we get this equation satisfies the table
Thus,
This is the correct equation.
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Why does a plasmid that is going to be used in both yeast and bacteria need to have two different selection markers? Select ALL that apply. The same selection (e.g. presence of an antibiotic) may not work for both hosts. Having more genes makes the plasmid bigger and thus easier to work with and maintain. In cases where the same selection can be used in both hosts, two selection markers are still needed because bacteria and yeast recognize different promoters The codons used by bacteria correspond to different amino acids than they do in yeast.
Answers
A plasmid used in both yeast and bacteria requires two different selection markers because the same selection may not work for both hosts and bacteria and yeast recognize different promoters.
When using a plasmid in both yeast and bacteria, it is important to have two different selection markers for several reasons. First, the same selection, such as the presence of an antibiotic, may not be effective in both hosts. Different organisms have varying sensitivities to antibiotics, so a marker that works in bacteria may not work in yeast or vice versa. Therefore, two different selection markers are needed to ensure successful selection in both hosts.
Additionally, bacteria and yeast recognize different promoters, which are DNA sequences that control the initiation of gene expression. Promoters are specific to each organism and play a crucial role in regulating gene expression. By incorporating two different selection markers into the plasmid, each marker can be driven by a promoter recognized specifically by the corresponding host. This ensures that the selection marker is effectively expressed in the appropriate host organism, enabling accurate selection and maintenance of the plasmid.
In summary, using two different selection markers in a plasmid intended for both yeast and bacteria is necessary because the same selection may not be effective in both hosts, and different promoters are recognized by bacteria and yeast. This approach allows for successful selection and maintenance of the plasmid in both organisms.
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How much interest will you earn on $300 at 3% for 3 years?
Answers
Answer:
$327.00 (total interest)
Step-by-step explanation:
This is simple interest
Converting R percent to r a decimal
r = R/100 = 3%/100 = 0.03 per year.
A = 300[1 + (0.03 × 3)] = 327
A = $327.00
Answer: 27.82
Step-by-step explanation: Based on Principal Amount of $300, at an interest rate of 3%, over 3 year(s):
Margie received her store order on 12/3/16 at 4AM. She just opened one of the
fountain BIBs today, 12/7/16 at 12PM. The BIB has a printed expiration date of
1/17/2017 on it. Drag the options from the right to fill out the label properly.
12/3/2016 1/21/2017
12/7/2016
4:00 AM
Exp Date:
Exp Time:
Prep Date:
Prep Time:
Initials:
1/17/2017
12:00 PM
Undo
Reset
Submit
Answers
Answer:
Exp Date: 1/17/2017
Exp Time: 4:00am
Prep Date: 12/3/2016
Prep Time: 4:00am
Initials: 12/7/2016
Step-by-step explanation:
A well-detailed version of the question has been uploaded in form of an image for easier understand.
Looking at the question, it was said that she received her store order on 12/3/2016 at 4am, this implies that the prep date and time are 12/3/2016 and 4am respectively. Also, it was said that the expiration date was printed on the product and it is 1/17/2017. Obviously, the expiration time would also be 4am because it was prepared at 4am and if we calculate in. 24hours we would get 4am at the expiration date as well. Lastly, we were told she opened the product she received on 12/7/2016 which is the initial date the product was used. From all these we can deduce the following:
Exp Date: 1/17/2017
Exp Time: 4:00am
Prep Date: 12/3/2016
Prep Time: 4:00am
Initials: 12/7/2016
If the mean weight of 3 outfielders on the baseball team is 190lb and the mean weight of the 6 other players is 235lb, what is the mean weight of the 9-person team?
Answers
The mean weight of the 9-person team is 220 lb.
To find the mean weight of the 9-person team, we need to calculate the total weight of all the players and divide it by the total number of players.
Let's denote the mean weight of the outfielders as "M1" and the mean weight of the other players as "M2".
Given:
Mean weight of 3 outfielders = 190 lb
Mean weight of 6 other players = 235 lb
We know that the mean weight is calculated by dividing the total weight by the number of players. Therefore, we can set up the following equations:
M1 = Total weight of outfielders / Number of outfielders
M2 = Total weight of other players / Number of other players
To find the total weight of the outfielders, we multiply the mean weight by the number of outfielders:
Total weight of outfielders = M1 * Number of outfielders
Similarly, to find the total weight of the other players, we multiply the mean weight by the number of other players:
Total weight of other players = M2 * Number of other players
Since we want to find the mean weight of the entire 9-person team, we need to consider all players. Therefore, the total weight of all players is the sum of the total weight of outfielders and the total weight of other players:
Total weight of all players = Total weight of outfielders + Total weight of other players
Now, let's substitute the known values into the equations:
M1 = 190 lb
Number of outfielders = 3
M2 = 235 lb
Number of other players = 6
Total weight of outfielders = M1 * Number of outfielders = 190 lb * 3 = 570 lb
Total weight of other players = M2 * Number of other players = 235 lb * 6 = 1410 lb
Total weight of all players = Total weight of outfielders + Total weight of other players = 570 lb + 1410 lb = 1980 lb
Finally, to find the mean weight of the 9-person team, we divide the total weight of all players by the total number of players:
Mean weight of the 9-person team = Total weight of all players / Total number of players
= 1980 lb / 9
= 220 lb
Therefore, the mean weight of the 9-person team is 220 lb.
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4. The cafeteria manager at a middle
school asked 90 randomly selected
students to name their favorite school
dessert. The table below shows the
results of the manager's survey.
Favorite School Dessert
Dessert
Frequency
WWW
Cake
Cookies
关关关关
关关关关关」
Ice Cream
Cobbler
关 关
Fruit
送送送 |||
Q. Based on the results of the survey, how many of the school's 1,200 students
would the manager expect to choose fruit as their favorite school dessert?
Answers
Answer:130
Step-by-step explanation:
Finding the mean , helpppp
Answers
The reason is because the mean is the most repeated number
hlo preparation for exam help with this question?? °_*!
If p/q=q/r then prove that
p3+q3+r3=(1/p3+1/q3+1/r3)p2q2r2
Answers
Hope you could get an idea from here.
Doubt clarification - use comment section.
The equation \(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\) has been proved to be true
The equation is given as:
\(\frac pq = \frac qr\)
Cross multiply
\(pr = q^2\)
Rewrite as:
\(q^2 = pr\)
Also, we have:
\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^2q^2r^2\)
Substitute \(q^2 = pr\)
\(p^3+q^3+r^3=(\frac{1}{p^3}+\frac{1}{q^3}+\frac{1}{r^3})p^3r^3\)
Expand
\(p^3+q^3+r^3=\frac{1}{p^3} \times p^3r^3 +\frac{1}{q^3} \times p^3r^3 +\frac{1}{r^3} \times p^3r^3\)
Simplify
\(p3+q3+r3=r^3 +\frac{1}{q^3} \times p^3r^3 + p^3\)
Rewrite as:
\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (pr)^3 + p^3\)
Substitute \(pr = q^2\)
\(p3+q3+r3=r^3 +\frac{1}{q^3} \times (q^2)^3 + p^3\)
\(p3+q3+r3=r^3 +\frac{1}{q^3} \times q^6 + p^3\)
Divide q^6 by q^3
\(p3+q3+r3=r^3 +q^3 + p^3\)
Rewrite the equation as:
\(p3+q3+r3=p^3 +q^3 + r^3\)
Hence, the equation has been proved
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An accountant used to charge $50 per hour, but recently decided to charge $62 per hour. What was the percent of increase in the billing rate?
Answers
Answer:
24%
Step-by-step explanation:
we subtract to see how much it increased
62-50=12
Now divide 12 by 50 to get percent
12/50
0.24
0.24x100
24%
Hopes this helps please mark brainliest
a triangle has side lengths in the ratio is inscribed in a circle with radius . what is the circumference of the triangle?
Answers
Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.
To find the circumference of the triangle, we need to first find the lengths of its sides. Let the three sides be x, y, and z, such that x:y:z is the given ratio. Without loss of generality, we can assume that x is the shortest side.
Let k be a constant such that y = kx and z = lx, where k and l are constants. Then, we have:
x + kx + lx = 2r
Simplifying this equation, we get:
x(1 + k + l) = 2r
So, we have:
x = (2r)/(1 + k + l)
y = kx = k(2r)/(1 + k + l)
z = lx = l(2r)/(1 + k + l)
The circumference of the triangle is the sum of its three sides:
C = x + y + z
Substituting the expressions for x, y, and z, we get:
C = (2r)/(1 + k + l) + k(2r)/(1 + k + l) + l(2r)/(1 + k + l)
Simplifying this expression, we get:
C = (2r(1 + k + l))/(1 + k + l)
C = 2r
Therefore, the circumference of the triangle is 2r, which is equal to the diameter of the circle.
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The area of the triangle is equal to A) 8.64. The Correct option is A) 8.64.
Let the lengths of the triangle be, 3x,4x,5x
Square of largest side = \(25x^{2}\)
Sum of square of other sides = \(3x^{2} + 4x^{2} = 25x^{2}\)
It is a right-angled triangle because the square of the greatest side equals the sum of the squares of the other sides.
The circumference of a right-angled triangle has a diameter equal to its hypotenuse.
hence, 5x=6 or x= \(\frac{6}{5}\)
Now, two perpendicular sides are then, \(\frac{18 }{5} , \frac{24}{5}\)
\(Area = \frac{1}{2} \times \frac{18}{5} \times \frac{24}{5} = 8.64\)
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Question
A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle is equal to
A. 8.64
B. 12
C. 6
D. 10.5
What slope would be parallel to the following line? y=4x+3
Answers
Answer:
Anything with a 4x for slope. It could be y=4x + any number.
Step-by-step explanation:
Nico uses a uniform probability model for an experiment using a deck of 40 cards. there are 10 blue cards, 10 red cards, 10 green cards, and 10 yellow cards in the deck. cards will be drawn one at a time and then replaced in the deck before another card is drawn. he uses the probability model to determine the probability of drawing a green card or a red card. what is p(green or red)? enter your answer as a simplified fraction in the box.
Answers
Answer:
1/2
Step-by-step explanation:
Since there are 40 cards in total and 10 cards for each colour...the probability of drawing either a green card or red card will be 20/40 since there a are 20 green and red cards combined
Therefore the probability is 1/2
Answer:
1/2
Step-by-step explanation:
Le Test a MoNdoo
Use the graph to write a linear function that relates y to x.
y=?
Answers
As the line goes through the y axis
This is the equation that represents graph because slope = rise/run in this case 4/-1. The y intercept is the point were the line intercepts the y axis in this case it would be 2. Put that all together with refreance to the equation y=Mx +b it would be y=-4x-2.
Giving 20 points to the person who answers this correctly
Answers
y 1 3 5 7 9 is y your welcome
What is the value of x?
Answers
The value of x in the diagram is 9
What is an equilateral triangle?equilateral triangle is a triangle that has all its sides equal in length. Since the three sides are equal therefore the three angles, opposite to the equal sides, are equal in measure. Therefore, it is also called an equiangular triangle, where each angle measure 60 degrees. Just like other types of triangles, an equilateral triangle also has its area, perimeter and height formula
From the diagram all the sides are equal which means it is an equilateral triangle in which each angle is equal to 60°
To find x,
7x -3 = 60
7x = 60 + 3
7x = 63
x = 63/7
x = 9
In conclusion the value of x is 9
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2d²y/dx² + yd²y/dx² = 0, dy/dx at x = 0 = 0, dy/dx at x = infinite = 1, dy/dx at x = 5 = 0.99 d²z/dx² + k/2y dz/dx = 0 z(0) = 0 and z(infinite) = 1 k is just a constant. Solve the differential equations with boundary conditions. By using Runge kutta4 method with MATLAB
Answers
Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).
The resulting plot will show the solution curve.
To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.
Let's define new variables:
y = y(x)
z = dz/dx
Now, we have the following system of first-order differential equations:
dy/dx = z (1)
dz/dx = -k/(2y) (2)
To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.
The general formula for the fourth-order Runge-Kutta method is as follows:
k₁ = h f(xn, yn, zn)
k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)
k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)
k₄ = h f(xn + h, yn + k₃, zn + l₃)
yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6
zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6
where f(x, y, z) represents the right-hand side of equations (1) and (2).
We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:
function [x, y, z] = rungeKuttaMethod()
% Parameters
k = 1; % Constant k
h = 0.01; % Step size
x0 = 0; % Initial x
xn = 10; % Final x (adjust as needed)
n = (xn - x0) / h; % Number of steps
% Initialize arrays
x = zeros(1, n+1);
y = zeros(1, n+1);
z = zeros(1, n+1);
% Initial conditions
x(1) = x0;
y(1) = 0;
z(1) = 0;
% Runge-Kutta method
for i = 1:n
k1 = h * f(x(i), y(i), z(i));
l1 = h * g(x(i), y(i));
k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);
l2 = h * g(x(i) + h/2, y(i) + k1/2);
k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);
l3 = h * g(x(i) + h/2, y(i) + k2/2);
k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);
l4 = h * g(x(i) + h, y(i) + k3);
y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;
z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;
x(i+1) = x(i) + h;
end
% Plotting
plot(x, y);
xlabel('x');
ylabel('y');
title('Solution y(x)');
end
function dydx = f(x, y, z)
dydx = z;
end
function dzdx = g(x, y)
dzdx = -k / (2*y);
end
% Call the function to solve the differential equations
[x, y, z] = rungeKuttaMethod();
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Giving brainly for answer correctly uwu:)<3
Answers
Magda wants to compare the population density of the two largest countries in the world. She can use this formula. K=P 2.59 M K = population density (people per km2) P = population (millions) M = land area (million square miles) Canada has a population density of 3.57 people per km2 Russia has • a population of 143.96 million • a land area of 6.593 million square miles. Magda thinks that Russia has a greater population density than Canada. Is Magda correct? Show why you think this.
Answers
Answer:
Magda is incorrect
Step-by-step explanation:
Given
Formula:
\(K = \frac{P}{2.59M}\)
Population Density of Canada = 3.57 people per km²
Population of Russia = 143.96 million
Land Mass of Russia = 6.593 million square miles
Required
Which country has a greater population density.
First, the population density of Russia needs to be calculated using the given formula;
\(K = \frac{P}{2.59M}\)
Here, P = 143.96 million
M = 6.593 million square miles
Substitute these values in the above formula;
\(K = \frac{143.96}{2.59 * 6.593}\)
\(K = \frac{143.96}{17.07587}\)
\(K = 8.43\) people per square miles
Before we can make any comparison, we have to convert the unit of K to people per square kilometre.
From unit of standard conversion;
1 square miles = 2.58999 square kilometre
Hence;
\(K = \frac{8.43}{2.58999}\)
\(K = 3.25483882177\)
\(K = 3.25\) people per km²
Given that the Population Density of Canada = 3.57 people per km²
And We solved for the Population Density of Russia = 3.25 people per km²
By Comparison, the Population Density of Canada is greater than the Population Density of Russia;
Hence, Magda is incorrect
In 2007, the number of tickets sold was again 210.
Adult tickets were $2.60 each and student tickets were $1.40 each.
The total amount received from selling the 210 tickets was $480.
How many student tickets were sold?
Answers
Step-by-step explanation:
1.40x + 2.60x = 480
4x =480
x=480÷4
x=120
168 and 312
each of two persons tosses three fair coins. what is the probablity they obtain same number of heads
Answers
The probability of obtaining the same number of heads is 3/8 or 0.375 when each of two persons tosses three fair coins.
The probability that two persons will obtain the same number of heads depends on the number of possible combinations of heads and tails that can be obtained by each person.
Since each coin flip results in either a heads or tails, there are 2 possible outcomes for each flip. Therefore, for three coin flips,
there are 2^3 or 8 possible combinations of heads and tails.
Out of these 8 combinations, there are 3 in which both persons have the same number of heads (i.e., 0 heads, 1 head, or 3 heads).
So, the probability of obtaining the same number of heads is 3/8 or 0.375.
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Kira studied data collected on the school basketball team for 1 season she noticed that a player on the team had 13 succesful free throws out of a total of 20
Answers
Answer:
Percent of Total number of successful throw = 65%
Step-by-step explanation:
Given:
Total number of successful throw = 13
Total number of throw = 20
Find:
Percent of Total number of successful throw
Computation:
Percent of Total number of successful throw = [Total number of successful throw / Total number of throw]100
Percent of Total number of successful throw = [13/20]100
Percent of Total number of successful throw = 65%