The dimensions of the rectangular poster are 9 inches by 22 inches.
Let's assume the width of the rectangular poster is x inches.
According to the given information, the length of the poster is 4 more inches than two times its width. So, the length can be expressed as 2x + 4 inches.
The formula for the area of a rectangle is length × width. In this case, the area is given as 198 square inches.
Therefore, we have the equation:
(2x + 4) × x = 198
Expanding the equation:
\(2x^2 + 4x = 198\)
Rearranging the equation to standard quadratic form:
\(2x^2 + 4x - 198 = 0\)
To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± √\((b^2 - 4ac\))) / (2a)
Plugging in the values:
x = (-4 ± √\((4^2 - 4(2)(-198)))\) / (2(2))
x = (-4 ± √(16 + 1584)) / 4
x = (-4 ± √1600) / 4
x = (-4 ± 40) / 4
Simplifying:
x = (-4 + 40) / 4 = 9
x = (-4 - 40) / 4 = -11
Since we are dealing with dimensions, the width cannot be negative. Therefore, the width of the poster is 9 inches.
Substituting the value of x back into the length equation:
Length = 2x + 4 = 2(9) + 4 = 18 + 4 = 22 inches
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You’ve decided to give your best friend a bag of marbles for his birthday. Since you know that your friend likes green marbles better than red ones, the bag has twice as many green marbles as red. The label on the bag says it contains a total of 84 marbles.
How many green marbles are in the bag? Write an equation (or system of equations) for this problem. Then solve the problem using any method you choose. Be sure to check your answer when you are finished.
Step-by-step explanation:i went on half of 84 wich was 42 so i found another problem that can equal into 84 wich was 63 green marbles 21 red
Select all of the following functions that are quadratic.
y = 2x2
3 = 2x2 – 8
y = –2 + 2x – 8
y + 3x = 2x2 – 8
y +3x2 = 2x + 3x2 – 8
Answer:
y = 2x2
y + 3x = 2x2 – 8
Step-by-step explanation:
The equations that are quadratic in nature are -
y = 2x²2x² - 8 - 3 = 0y = 2x² - 3x - 8What is a quadratic equation?A quadratic equation is a equation that is of the form -
y = f{x} = ax² + bx + c.
Given are the set of equations.
A quadratic equation is a equation of degree 2. The equation with degree 2 are -
y = 2x²2x² - 8 - 3 = 0y = 2x² - 3x - 8Therefore, the equations that are quadratic in nature are -
y = 2x²2x² - 8 - 3 = 0y = 2x² - 3x - 8To solve more questions on quadratic equations, visit the link below -
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What are the zeros of the polynomial function f(x) = x(x + 5)(x – 8)?
–5, 8
0, –5, 8
5, –8
0, 5, –8
Answer:
Option B is answer.
Step-by-step explanation:
Hey there!
Given;
f(X) = X(X+5)(x-8)
According to the factor theorem, f(X) = 0;
Or, X(X+5)(x-8) = 0
Either;
x = 0
Or;
(x+5)= 0
X = -5
Or;
(x-8)= 0
x = 8.
Therefore, the zeros of the polynomial are: 0,-5,8.
Hope it helps!
6th grade math , help me pleasee :)
Answer: A) 18x +15
Step-by-step explanation:
First distribute
20x + 15 - 2x
Then combine like terms
18x + 15
Answer:
A. 18x + 15
Step-by-step explanation:
5(4x + 3) - 2x
20x + 15 - 2x --> Distributive Property
18x + 15 --> Combine Like Terms (C.L.T)
(a) Use six rectangles to find estimates of each type for the area under the given graph of f from x
We have to find the area under the graph but since we are not given the graph ,So let's learn how it is done. To estimate the area under the graph of function f from x, you can use rectangles. Here's how you can do it:
Step 1: Divide the interval [a, b] into six equal subintervals.
Step 2: Calculate the width of each rectangle by dividing the total width of the interval [a, b] by the number of rectangles (in this case, 6).
Step 3: For each subinterval, find the value of the function f at the right endpoint of the subinterval.
Step 4: Multiply the width of the rectangle by the value of the function at the right endpoint to find the area of each rectangle.
Step 5: Add up the areas of all six rectangles to estimate the total area under the graph of f from x.
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Consider the initial value problem y’ = ty^3, y(0) = 1/5.
(a) Solve. (Using separation of variables).
(b) Does your solution make sense at t=6?
(c) If this equation was describing something like the energy of a system, what happens at t=5?
(a)the solution to the initial value problem is:
y =\(\frac{1}{\sqrt{\frac{1}{25}-\frac{t^{2} }{2}} }\)
(b) Since the argument of the square root is negative, y(6) is not defined. Therefore, the solution does not make sense at t=6.
(c)This means that the inverse of the energy of the system becomes infinite at t=5, which indicates a singularity or a breakdown of the model at that point. This could imply a physical phenomenon such as a phase transition or an instability in the system.
(a) We have the differential equation:
\(\frac{dy}{dt}\) = t\(y^{3}\)
Separating the variables, we get:
\(\frac{1}{y^{3} }\) dy = t dt
Integrating both sides, we get:
\(\frac{-1}{2y^{2} }\)= \(\frac{1}{2t^{2} }\) + C
where C is the constant of integration. To find C, we use the initial condition y(0) = \(\frac{1}{5}\):
\(\frac{-1}{2(\frac{1}{5} )^{2} }\)= \(\frac{1}{2(0)^{2} }\) + C
C = \(\frac{-1}{50}\)
Thus, the solution to the initial value problem is:
\(\frac{-1}{2y^{2} }\) =\(\frac{1}{2t^{2} }\) - \(\frac{1}{50}\)
Solving for y, we get:
y =\(\frac{1}{\sqrt{\frac{1}{25}-\frac{t^{2} }{2}} }\)
We need to check if y(6) is defined or not. We have:
y(6) = \(\frac{1}{\sqrt{\frac{1}{25}-\frac{6^{2} }{2} } }\) = \(\frac{1}{\sqrt{\frac{-34}{25} } }\)
Since the argument of the square root is negative, y(6) is not defined. Therefore, the solution does not make sense at t=6.
(c) If the equation was describing something like the energy of a system, the quantity y^2 would represent the inverse of the energy of the system. At t=5, we have:
y(5) = \(\frac{1}{\sqrt{\frac{1}{25}-\frac{5^{2} }{2} } }\) = 0
This means that the inverse of the energy of the system becomes infinite at t=5, which indicates a singularity or a breakdown of the model at that point. This could imply a physical phenomenon such as a phase transition or an instability in the system.
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The equation of the line in this graph is y=____ x + ____
determine the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2.
the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>
A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.
To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.
To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.
To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:
d\vec r/dt = <1, -2t^-3, -4e^-t^-4>
So the tangent to the curve at t = 2 is:
d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>
Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.
The cross product of the tangent and the unit vector i is given by:
\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>
Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:
\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>
So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:
\vec n = <0,0,-1>
This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.
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NEED HELP ASAP ON TIMER 30 MINUTES LEFT
find the least common multiple (lcm) of:
25y^5 and 5xy and 2x^3y
Answer:
50 x^3 y^2
Step-by-step explanation:
25y^5 = 5*5 * y*y
5xy = 5*x*y
2x^3y = 2*x*x*x*y
The least common multiply is found by taking the least number of times each appears
5 appears 2 times
2 appears 1 time
x appears 3 times
y appears 2 times
5*5*2 * x*x*x * y*y
50 x^3 y^2
Answer:
50 x^3 y^2
Step-by-step explanation:
25y^5 = 5*5 * y*y
5xy = 5*x*y
2x^3y = 2*x*x*x*y
The least common multiply is found by taking the least number of times each appears
5 appears 2 times
2 appears 1 time
x appears 3 times
y appears 2 times
5*5*2 * x*x*x * y*y
50 x^3 y^2
please...............
Answer: A and D
Step-by-step explanation:
Graph the line that represents a proportional relationship between ddd and ttt with the property that an increase of 555 units in ttt corresponds to an increase of 222 units in ddd. What is the unit rate of change of ddd with respect to ttt
a) The unit rate of change of d with respect to t is equal to 1.6
b) the graph of the line in the attached figure.
Given: A proportionate relationship between d and t with the characteristic that a rise in t of 5 units causes a rise in d of 8 units.
To locate: A rise of 5 units in t causes a rise of 8 units in d, according to the line's unit rate of change with respect to t.
=> Slope = Δd/Δt = 8/5 = 1.6
the proportional relationship between d and t
=> d ∝ t
=> d = 1.6t
t d=1.6t
0 0
1 1.6
2 3.2
3 4.8
Plot the points and draw a line passing through points.
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Gerry borrowed $7500 at a simple interest rate of 9% for 4 1/2 years to buy a car. How much simple interest did Gerry pay?
Answer:
the answer is $3037.50
Step-by-step explanation:
%9 = 0.9
by multiplying 0.9 to 7500 we get 675
once we get this we must multiply it by the number of years
4 and 1 half or 4.5 times 675 gives us our answer my friend ;)
Pls help me pls please please
Answer:
do you need help with all ?
Step-by-step explanation:
Answer:
1. 3:5
2. 1:6
3. 1:2
4a. 2:3
b. 2:1
c. 1:3
5. 2:1
Which statement is true about the parentheses in this expression? 10 ÷ (8 − 6) − 2 A) The parentheses indicate that 6 − 2 should be evaluated first. B) The parentheses indicate that 8 − 6 should be evaluated first. C) The parentheses indicate that 10 − 2 should be evaluated first. D) The parentheses indicate that 10 ÷ 8 should be evaluated first.
Answer:B
Step-by-step explanation: When solving expressions with parentheses it’s important to always solve what’s in parentheses first. And when there’s parentheses in parentheses, solve the parentheses that are in the parenthesis. Whew...I hope this helps :)
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Lines CD and DE are tangent to circle A, as shown below:
CE is 105°, what is the measure of angle CDE?
52.5°
62.5
75°
255°
Answer:
The correct answer is 75 dgrees
Step-by-step explanation:
<CDE = arcCBE - arcCE / 2
arcCE = 105°
arcCBE = 360° - 105° =255°
<CDE = 255° - 105°
<CDE = 150 / 2
<CDE = 75°
Therefore the measure of < CDE is 75°
Which is a component of cell theory?
Cells come from bacteria.
Cells come from cells.
Cells come from nonliving matter.
Cells come from non-cells.
Answer:
A. Cells come from bacteria
Step-by-step explanation:
I did the test in edge
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The lenght is (x+2) and the width is (x+4). Find the Area if
the Perimeter is 44.
O 140
O 180
O 160
O 120
Answer:
correct answer is option (d)
120
Step-by-step explanation:
Tip:
The area of a rectangle is the region occupied by a rectangle within its four sides or boundaries.
given length l = (x+2)
given width b= (x+4)
perimeter =44
2(l+b) =44
2[x+2+x+4]=44
4x +12 =44
4x = 32
x= 8
now length = x+2 =8+2 = 10
width = x+4 = 8+4 = 12
area of rectangle = l x b = 10 x 12
=120
Find JH if I is the midpoint.
Answer:
158
Step-by-step explanation:
If I is the midpoint of JH, JI= IH
JH= JI +IH
JH= JI +JI (subst. IH= JI)
JH= 2(JI)
Since JI= 79,
JH= 2(79)
JH= 158
Integrate the ODE
dy/dx = x² √y, 0 < x < 2, y(0) = 1
using Euler's method (Δx = 0, 2) to compute y(2). Obtain analytical solution to the ODE and compare y(2) obtained using Euler's method with that obtained analytically.
we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.
Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:
Step 1: For x = 0, y = 1 (initial condition).
Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.
Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.
Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.
Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.
Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.
Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.
Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.
Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.
Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.
Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.
Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.
To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:
∫(1/√y) dy = ∫x² dx
Integrating both sides gives:
2√y = (1/3)x³ + C
Solving for y:
y = (1/4)(x³ + C)²
Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:
1 = (1/4)(0³ + C)²
1 = (1/4)C²
4 = C²
C = ±2
Since C can be either 2 or -2, the general solution to the ODE is:
y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²
Now, let's evaluate y(2) using the analytical solution:
y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5
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at the town flea market, monica purchases a big box of used tennis balls to throw to her dog. she scoops some tennis balls out of the box at random. here are the colors of the balls: yellow, blue, yellow, red, green, blue, yellow, red, yellow, green, yellow, red, green based on the data, what is the probability of choosing a yellow tennis ball from the box? write your answer as a fraction or whole number. submit
Answer: 5/13
Step-by-step explanation: i did this IXL and got it right
if you run 4 1/2 miles in three quarter of an hour, how many miles would you run in two thirds
Answer:4
Step-by-step explanation: each quarter of an hour is 1.5 miles they both can go into 12 so if you multiply 2*4 and 3*4 you get 8/12 and if you multiply 3*3 and 4*3 you get 9/12 then you subtract 9/12 by 8/12 to get so 1/12=1/2 miles so you would subtract 4 1/2 by 1/2 to get 4
Please help me out!!! :)
How can you look at the equation of two lines and determine if they will be parallel?
Answer:
fafg and then do the 2a ab 2b
Step-by-step explanation:
An expression is given (3^2)^3•3^6/3^4 the rest of the question is in the picture
Answer:
3⁷
Step-by-step explanation:
it's kinda messy but my step by step is in the picture. practically when you "multiply" an exponent (as long as they have the same base number) with another like 3⁴×3⁵ or (3⁴)⁵ you add the exponents together so you'd get 3⁴×3⁵=3⁹
when dividing an exponent by another exponent (with again, the same base number) you subtract the exponents like this: 3⁶÷3² or 3⁶/3² would equal 3⁴
37) If cashews cost $6.59 a pound, how much would it cost to buy two
and a quarter pounds of cashews? Round your answer to the nearest cent.
Answer:
1,318
Step-by-step explanation:
you will multiple 6.59 by 2
Answer:
22.40 pounds
Step-by-step explanation:
2 cashews =13.18 pounds
A quarter of cashew =1/4*6.59
=9.226 pounds
Total amount =22.406 pounds
Nearest cent=22.40 pounds
the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square
The ratio of the area of the smaller square to the area of the larger square, that have a perimeter ratio of 2:7 is 4:49
What is the ratio of the area given the ratio of the perimeters of the squares?The ratio of the perimeter of the squares = 2 : 7
Required: The ratio of the area of the smaller square to the larger square.
Solution: The perimeter of a square of side x is 4•x
The comparative length of the side of each square are therefore;
2/4 and 7/4
The comparative area are therefore;
(2/4)² and (7/4)²The ratio of the areas of the square is therefore;
(2/4)² : (7/4)² = 1/4 : 49/16
Multiplying both sides of the ratio by 16 gives;
16×1/4 : 16×49/16
4:49
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Consider the DNA sequence: CAT TAGA, which belongs to a penguin. A different fossilized species is found which contains the sequence GATTAGA. Which organism does it most likely belong to? A.Dog b.Bird c.Snake d.Horse
This sequence likely belongs to a bird rather than to a dog, snake, or horse.
What is DNA?DNA stands for deoxyribonucleic acid and it is essential in genetics and biology because it composes genes. Moreover, DNA is expressed as a sequence of four bases:
Thymine (T).Adenine (A).Cytosine (C).Guanine (G).What does the similarity between DNA sequences reveal?Considering all living organisms share a common ancestor and modern species evolved from older species, a similarity in DNA shows organisms are genetically and phenotypically similar.
In the case of the penguin and the fossilized species, the DNA sequence is almost identical. Due to this, this organism should be very similar to the penguin, and therefore, the most likely organism is another bird.
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Please help me solve this. warning: an equation may have no solution, one solution or more than one solution.
5x-13=2x-9-4+3x
I got the answer and steps for this math problem,
Answer:
\(5 \times - 13 = 2 \times - 9 - 4 + 3 \times \\\)
= 1 5/9 or 1 .5555556.
Step-by-step explanation:
Please comment if I'm
wrong...
Determinan las siguientes tablas muestran magnitudes directamente correlaciones o directamente proporcionales
Responder:
Los cuadros 89 y 91 presentan proporcionalidad directa
El cuadro 90 muestra una correlación directa.
Explicación paso a paso:
De la imagen adjunta:
Cuadro 89:
Para mostrar proporcionalidad directa:
y α x
y = kx; k = constante de proporcionalidad
Comprobando las tablas:
Cuadro 89:
A = 1,5; B = 3
B = kA; 3 = 1.5k
k = B / A
k = 3 / 1,5 = 2
Usando k = 2;
demuestre que B = 4 cuando A = 2; para establecer proporcionalidad directa.
B = 2 * 2 = 4
Por tanto, el cuadro 89 exhibe proporcionalidad directa
Comprobando las tablas:
Cuadro 90:
C = 2; D = 8
D = kC; 8 = 2k
k = 8/2 = 4
Usando k = 4;
demuestre que D = 9 cuando C = 3; para establecer proporcionalidad directa.
B
D = 4 * 3 = 12
De la tabla, D = 9;
Por tanto, el cuadro 90 presenta una correlación directa pero no una proporcionalidad directa.
Comprobando las tablas:
Cuadro 91:
E = 1; F = 1/2
F = kE; 1/2 = k
k = 1/2
Usando k = 1/2;
demuestre que F = 3/2 cuando E = 3; para establecer proporcionalidad directa.
F = 1/2 * 3 = 3/2
Por tanto, el cuadro 91 presenta proporcionalidad directa.
Find b given that A (-6, 2), B (b, 0), and C (3,-4) are collinear.
Answer:
b = -3.
Step-by-step explanation:
If the 3 points are collinear then:
Slope of AB = Slope of BC and so
(0-2)/(b + 6) = (-4-0)/( 3 - b)
-4(b + 6) = -2(3 - b)
-4b - 24 = -6 + 2b
-24 + 6 = 2b + 4b
6b = -18
b = -3.
The interior angle of a regular pentagon has a measure of:
A) 72°.
B) 108°.
C) 120°.
D) 144°.
Answer:
B) 108°
Step-by-step explanation:
You want the interior angle measure for a regular pentagon.
Interior anglesThe interior angles of a regular n-gon will have measure ...
180° -360°/n
When n = 5, the interior angles have measure ...
180° -360*/5 = 180° -72° = 108°
The interior angles of a regular pentagon are 108°.
__
Additional comment
The 360°/n comes from the fact that the sum of exterior angles for any convex polygon is 360°. For a regular n-gon, those exterior angles are congruent, so each is 360°/n. The interior angle is its supplement.
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