The minimum value of S is 10 when both x and y are equal to 5.
To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.
First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:
∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0
Solve the first two equations for λ:
λ = 1/y and λ = 1/x
Now, set these two equations equal:
1/y = 1/x
Since x and y are positive, you can safely cross-multiply:
x = y
Now, use the constraint equation (xy = 25):
x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)
Since x = y, we also have y = 5. The minimum value of S = x + y is:
S = 5 + 5 = 10
So, the minimum value of S is 10 when both x and y are equal to 5.
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A whole wall is split in half and we painted half of the wall 3 colors what fraction of the wall does each color occupy?
The total fraction of the wall that has been painted is 1/2. If a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area.
To answer your question, we need to first determine the total fraction of the wall that has been painted. Since the wall has been split in half, we can say that the painted area covers half of the wall. Therefore, the total fraction of the wall that has been painted is 1/2.
Now, we need to divide this 1/2 fraction among the three colors that were used. Let's say the three colors are red, blue, and green. We can represent the fraction of the wall occupied by each color as follows:
- Red: 1/3 x 1/2 = 1/6
- Blue: 1/3 x 1/2 = 1/6
- Green: 1/3 x 1/2 = 1/6
So each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall. This means that if the wall was not split in half and we painted the entire wall with the same 3 colors, each color would occupy 1/12 of the total wall area.
In summary, if a whole wall is split in half and we painted half of the wall 3 colors, each color occupies 1/6 of the painted area, which is equivalent to 1/12 of the whole wall.
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Find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.
Point (0, 9, 0) Perpendicular to
n = -2i ÷ 4k
To find the equation of the plane that passes through the point (0, 9, 0) and is perpendicular to the vector n = -2i ÷ 4k, we first need to find the normal vector of the plane.
Since the plane is perpendicular to the given vector, the normal vector will be parallel to it. So, we can take the given vector and multiply it by -1 to get a vector in the opposite direction, which will be normal to the plane.
n = -2i ÷ 4k = -1/2i ÷ k
Multiplying by -1 gives us:
n = 1/2i ÷ k
Now we can use the point-normal form of the equation of a plane:
r · n = d
where r is the position vector of any point on the plane, n is the normal vector, and d is the distance of the plane from the origin (since the normal vector is normalized, d will be the signed distance of the plane from the origin).
Substituting the given point (0, 9, 0) and the normal vector n = 1/2i ÷ k into the equation, we get:
(0, 9, 0) · (1/2i ÷ k) = d
0 + 9(1/2) + 0 = d
d = 4.5
So the equation of the plane is:
x/2 + z/2 = 4.5
or, multiplying by 2 to eliminate fractions:
x + z = 9
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A helicopter takes off from the roof of a building and travels at 100 mph on a bearing of 558°e. the flight takes 3. 8 hr. to the nearest mile, how far south and
how far east has the helicopter traveled?
can someone pls help me
The helicopter traveled approximately 175.5 miles east and 299.1 miles south.
How to find the helicopter traveled?Let's say the building is located at point A and the helicopter travels to point B. We know that the bearing of B from A is 558°e, which means the angle formed by the line AB and the east direction is 558°.
Next, we can use trigonometry to find the horizontal and vertical components of the distance traveled. Let x be the horizontal distance (in miles) traveled by the helicopter and y be the vertical distance (in miles) traveled. We can then use the following equations:
cos(558°) = x / d
sin(558°) = y / d
where d is the total distance traveled (in miles). We can also use the formula:
d = r * t
where r is the speed of the helicopter (100 mph) and t is the time taken for the flight (3.8 hours). Substituting this into the first two equations, we get:
x = d * cos(558°)
y = d * sin(558°)
d = r * t = 100 * 3.8 = 380 miles (rounded to the nearest mile)
Substituting the values of d and the angle into the equations for x and y, we get:
x = 380 * cos(558°) ≈ -175.5 miles
y = 380 * sin(558°) ≈ 299.1 miles
Note that the negative sign for x indicates that the helicopter traveled west, not east. We can take the absolute value of x to get the distance traveled east:
|x| ≈ 175.5 miles
Therefore, the helicopter traveled approximately 175.5 miles east and 299.1 miles south.
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Your doing practice 4
Using the compound interest formula, the amount in Russ' account after 4 years is $ 12588.15
How to find the how much will be in Russ' account after 4 years?To find how much will be in Russ' account after 4 years, we use the compound interest formula.
A = P(1 + r)ⁿ where
A = amount after n years,P = principal,r = interest rate andn = number of yearsGiven that
P = $8000r = 6 % compounded semi annually = 6% ÷ 1/2 per year = 12 % per year = 0.12n = 4 yearsSo, substituting the values of the variables into the equation, we have that
A = P(1 + r)ⁿ
A = $8000(1 + 0.12)⁴
A = $8000(1.12)⁴
A= $8000(1.5735)
A= $ 12588.15
So, the amount is $ 12588.15
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The Nielsen Company surveyed 371 owners of Android phones and found that 200
of them planned to get another Android as their next phone. What is the lower
bound for the 95% confidence interval for the proportion of Android users who plan
to get another Android?
The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .
It can be evaluated applying the formula
Lower Bound = Sample Proportion - Z-Score × Standard Error
Here
Sample Proportion
= 200/371 = 0.539
Z-Score = 1.96 (for a 95% confidence interval)
Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,
Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.
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How to find number 3?
Answer:
V=3456, SA= 1008
Step-by-step explanation:
V=b*h*L (Formula)
8*18*24=3456 (sub, alg)
SA=30*8+24*18+24*8+8*18=54*8+32*18=1008 (Formula; sub, alg)
The Yert family hires a landscaping company for 30 weeks. There are two companies to choose from. Green Lawns charges 2 for the first time they service your lawn, and the price will multiply by a factor of 0. 90 every week thereafter. Green Thumbs charges 400 for the first time they service your lawn, and then charges an additional 40 every week thereafter. At 30 weeks, if the Yert family chooses the company that is cheaper, how much money will they save?
Let's first calculate the total cost of using Green Lawns for 30 weeks. We can use the formula for the sum of a geometric series to do this:
Total cost of Green Lawns =[tex]2(1 - 0.9^30) / (1 - 0.9) + 0.9^30 * 2[/tex]
Total cost of Green Lawns = [tex]2(1.7379) / 0.1 + 0.0359[/tex]
Total cost of Green Lawns = 38.8179
Now let's calculate the total cost of using Green Thumbs for 30 weeks:
Total cost of Green Thumbs = [tex]400 + 40 * 29[/tex]
Total cost of Green Thumbs = 1160
Therefore, the Yert family would save:
$1160 - $38.8179 = $1121.18
So the Yert family would save $1,121.18 by choosing Green Lawns over Green Thumbs for 30 weeks.
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Consider a piece of wire with uniform density. It is the quarter of a circle in the first quadrant. The circle is centered at the origin and has radius 6. Find the center of GRAVITY (x¯,y¯) of the wire. x¯=
y¯=
the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
How to Find the center of GRAVITY (x¯,y¯)The center of gravity (x¯,y¯) of the wire lies on the line of symmetry, which passes through the origin and the centroid of the quarter-circle.
The centroid of a quarter-circle with radius 6 is located at (4/3, 4/3) from the origin (as derived using calculus). Thus, the line of symmetry passes through the origin and (4/3, 4/3).
The equation of the line passing through two points (x1, y1) and (x2, y2) is given by:
(y - y1) / (x - x1) = (y2 - y1) / (x2 - x1)
Substituting (x1, y1) = (0, 0) and (x2, y2) = (4/3, 4/3), we get:
(y - 0) / (x - 0) = (4/3 - 0) / (4/3 - 0)
Simplifying, we get:
y = x
Therefore, the center of gravity (x¯,y¯) is located on the line y = x.
Since the wire has uniform density, the center of gravity is located at the centroid of the quarter-circle, which is (4/3, 4/3).
Hence, x¯=y¯=4/3.
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8. If AB and BC are tangent to circle D,
AB = 15 inches, and DB = 17 inches, find
the perimeter of ABCD.
Answer:
46 inches
Step-by-step explanation:
You want the perimeter of ABCD, where AB and BC are tangent to circle D, and AB = 15 inches, BD = 17 inches.
FigureThe attachment shows the figure. Radii DA and DC are perpendicular to the tangens, so each triangle is a right triangle. The hypotenuse BD is given as 17 inches, and the leg AB is given as 15 inches. The other leg is found from the Pythagorean theorem (or from your knowledge of Pythagorean triples). It is ...
AD = √(DB² -AB²)
AD = √(17² -15²) = √(289 -225) = √64
AD = 8
PerimeterThe perimeter is the sum of side lengths. The kite shape is symmetrical, so the perimeter is ...
P = 2(AD +AB) = 2(8 +15) = 46 . . . . inches
The perimeter of ABCD is 46 inches.
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Ginny made a cylindrical clay vase for her art project. If the vase has a
volume of 672 cubic inches and a diameter of 10 inches, which is closest to
the height of the vase?
If the vase has a volume of 672 cubic inches and a diameter of 10 inches, the height of the cylindrical clay vase is closest to 8.56 inches.
To find the height of the cylindrical vase, we'll use the formula for the volume of a cylinder: V = πr²h, where V is the volume, r is the radius, and h is the height. Given the diameter is 10 inches, the radius (r) is half of that, which is 5 inches. The volume (V) is 672 cubic inches.
Now, we can solve for the height (h) using the formula:
672 = π(5²)h
First, calculate the area of the base (πr²):
π(5²) = 25π
Now, divide the volume by the area of the base to find the height:
h = 672 / 25π
h ≈ 8.56 inches
So, the height of the cylindrical clay vase is closest to 8.56 inches.
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How many 1/4 cm cubes fit inside the prism below
55 cubes I think because in the end you have to like divide it 2 times.
Answer: 110 cubes
Step-by-step explanation:
First, we will find the volume of this prism.
V = LWH
V = (2.75 cm)(0.5 cm)(1.25 cm)
V = 1.71875 cm³
Next, we will find the volume of the cube.
V = L³
V = (0.25 cm)³
V = 0.015625 cm³
Next, we will divide the prism's volume by the cube's volume.
1.71875 cm³ / 0.015625 cm³ = 110 cubes
Using the substitution method, find the solution to this system of equations. -2x+2y=7 -x+y=4 Be sure to show your work!
Based on your results in Problem 1, what do you know about the two lines in that system (graphically)?
There is no solution to the given system of equations and the lines are parallel which has been obtained by using the substitution method.
What is the substitution method?
When solving simultaneous linear equations in algebra, the substitution approach is a common technique. As the name of the procedure suggests, one variable's value from one equation is switched in the second equation.
We are given equations as -2x + 2y = 7 and -x + y = 4.
Now, using the second equation, we get
⇒ -x + y = 4
⇒ y = 4 + x
Now, on substituting this in the first equation, we get
⇒ -2x + 2y = 7
⇒ -2x + 2 (4 + x) = 7
⇒ -2x + 8 + 2x = 7
⇒ 8 ≠ 7
So, there is no solution to the given system.
This means that the two lines in the system are parallel which means they will never meet.
A graph depicting the same has been attached below.
Hence, there is no solution to the given system.
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2. A triangle has one side that is 5 units long and an adjacent angle that measures 25 The two other angles in the triangle measure 90° and 65°. Complete the two diagrams to create two different triangles with these measurements. 25° 5 25° 5
The diagram to create a similar triangle has been attached.
How to create a similar triangles?Similar triangles are defined as triangles that possess the same shape, but then their sizes will likely vary. We can also say that two triangles are referred to as similar if they possess the same ratio of its' corresponding sides and also an equal pair of corresponding angles
The two different triangles can be formed by placing the 90° angle adjacent to, or opposite the given side.
In the diagram below attached, we see that the two triangles are ABC and ABD. Thus, the right angles are located at vertex C and vertex B, respectively.
Thus, it has been created with the given measurements
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La rueda de una bicicleta mide 62.2 cm de diámetro, ¿cuál es el perímetro de la rueda?
Answer:
"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:
Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.
Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.
Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.
Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.
Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.
Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.
Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.
Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.
Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.
Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.
Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.
Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.
Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.
Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.
Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.
Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.
Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.
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Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is C(x) = 2300 + 5x + 0.01x2 + 0.0002x? (a) Find the marginal cost function 5 + 0.02x + 0.0006r2 (b) Find C'(100) C'(100) = 11 What does this predict? The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans. (c) Find the difference between C'(100) and the actual cost of manufacturing the 101st pair of jeans (Round your answer to two decimal places.) $ 3100
The exact cost of the 100th pair of jeans. The approximate cost of the 101st pair of jeans. The approximate cost of the 100th pair of jeans. The exact cost of the 101st pair of jeans The exact cost of the 99th pair of jeans.
The marginal cost function of C(x) = 2300 + 5x + 0.01x2 + 0.0002x is $3100
Process of finding marginal cost:
(a) To find the marginal cost function, we need to take the derivative of the cost function C(x) with respect to x. This gives us:
C'(x) = 5 + 0.02x + 0.0006x^2
So the marginal cost function is:
MC(x) = 5 + 0.02x + 0.0006x^2
(b) To find C'(100), we simply plug in x = 100 into the marginal cost function we just found:
C'(100) = 5 + 0.02(100) + 0.0006(100)^2 = 11
This predicts the exact cost of manufacturing the 101st pair of jeans.
The approximate cost of the 101st pair of jeans can be found by plugging in x = 101 into the original cost function C(x):
C(101) = 2300 + 5(101) + 0.01(101)^2 + 0.0002(101) ≈ $3120.02
The approximate cost of the 101st pair of jeans.
The exact cost of the 100th pair of jeans can be found by plugging in x = 100 into the original cost function C(x):
C(100) = 2300 + 5(100) + 0.01(100)^2 + 0.0002(100) = $3100
Hence the marginal cost is $3100
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Solve for the indicated variable. X/y=z-8 for x
Answer: To solve for x in the equation X/y=z-8, we need to isolate x on one side of the equation.
Multiplying both sides by y, we get:
X = y(z-8)
Therefore, the solution for x is:
X = y(z-8)
Step-by-step explanation:
The attendance for a week at a local theatre is normally distributed, with a mean of 4000 and a standard
deviation of 500. Draw the normal curve to represent the normally distributed attendance for the week.
What percentage of the attendance figures would be less than 3500? What percentage of the attendance
figures would be greater than
5000? What percentage of the attendance figures would be between 3700
and 4300 each week?
About 15.87% of the attendance figures would be less than 3500.
About 0.62% of the attendance figures would be greater than 5000.
About 34.13% of the attendance figures would be between 3700 and 4300 each week.
The mean is the average of a set of numbers, while the standard deviation measures the spread of the data around the mean. The normal distribution is fully characterized by its mean and standard deviation. In this case, the mean attendance is 4000, and the standard deviation is 500.
To answer the first question, "What percentage of the attendance figures would be less than 3500?" we need to calculate the area under the curve to the left of 3500. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 15.87%.
To answer the second question, "What percentage of the attendance figures would be greater than 5000?" we need to calculate the area under the curve to the right of 5000. Again, we can use a standard normal distribution table or a calculator to find this area. The result is approximately 0.62%.
To answer the third question, "What percentage of the attendance figures would be between 3700 and 4300 each week?" we need to calculate the area under the curve between 3700 and 4300. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 34.13%.
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If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3 find the value of x.
If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3, then the value of x is 4 or 4.5
To solve this problem, we'll need to use some geometry and algebra.
Using the Pythagorean theorem, we can set up two equations:
OA² + AD² = OD² (for right triangle OAD)
OB² + BD² = OD² (for right triangle OBD)
In these equations, "OD" is the radius of the circle. We don't know this value yet, but we can express it in terms of "x" using the fact that "BD" = 4x-3.
Now, we can simplify these equations by substituting in the values we know. We get:
OA² + 13² = OD²
OB² + (4x-3)² = OD²
This means we can set up the equation:
OA = OB
Now we can substitute in the expressions we found for "OA" and "OB" earlier:
√(OD² - 13²) = √(OD² - (4x-3)²)
We can then square both sides to eliminate the square roots:
OD² - 13² = OD² - (4x-3)²
Simplifying this equation, we get:
169 = (4x-3)²
Taking the square root of both sides (and remembering to include the positive and negative solutions), we get:
4x-3 = ±13
Solving for "x," we get two possible values:
x = 4
x = 4.5
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Help!! Will give out brainliest answer :)
Leslie paid $13 for 4 children’s tickets and 1 adult ticket.
Antonio paid $14 for 3 adult’s tickets and 2 children’s tickets.
Write and solve a system of equations to find the unit price for a child ticket and an adult ticket. Explain your steps and show all your work
The unit price for a child ticket is $2.50 and the unit price for an adult ticket is $3.
To find the unit price for a child ticket and an adult ticket, we can set up a system of equations based on the given information. Let x be the unit price for a child ticket and y be the unit price for an adult ticket.
From the first sentence, we know that:
4x + y = 13 ...(1)
From the second sentence, we know that:
3y + 2x = 14 ...(2)
Now we have a system of equations with two variables, which we can solve using either substitution or elimination method. For simplicity, we will use the elimination method.
Multiplying equation (1) by 3, we get:
12x + 3y = 39 ...(3)
Subtracting equation (2) from equation (3), we get:
10x = 25
x = 2.50
Substituting x = 2.50 into equation (1), we get:
4(2.50) + y = 13
y = 3
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Your local high school is putting on a musical. They have sold 1000 tickets. Adult tickets
were sold for $8. 50, while child tickets were sold for $4. 50. A total of $7100 was
collected from ticket sells. How many tickets of each kind were sold?
650 adult tickets were sold.
Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.
From the problem, we know that:
A + C = 1000 (the total number of tickets sold is 1000)
8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)
We can use the first equation to solve for A in terms of C:
A = 1000 - C
Substituting this expression for A into the second equation, we get:
8.50(1000 - C) + 4.50C = 7100
Expanding and simplifying:
8500 - 8.50C + 4.50C = 7100
4C = 1400
C = 350
So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:
A + 350 = 1000
A = 650
Therefore, 650 adult tickets were sold.
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An ant travels 33cm in walking completely around the edges of a rectangle. If the rectangle is twice as long as it is wide, how long is the shortest side?
Rectangle: w = 5.5cm, l = 11cm. Shortest side is width.
Q11
A ball is thrown vertically upward. After t seconds, its height, h (in feet), is given by the function h left parenthesis t right parenthesis equals 76 t minus 16 t squared. After how long will it reach its maximum height?
Round your answer to the nearest hundredth.
Group of answer choices
90 seconds
1.2 seconds
0.17 seconds
2.38 seconds
Answer:
Step-by-step explanation:
To find when the ball reaches its maximum height, we need to find the vertex of the quadratic function h(t) = 76t - 16t^2.
The vertex of a quadratic function of the form y = ax^2 + bx + c is at the point (-b/2a, f(-b/2a)), where f(x) = ax^2 + bx + c.
In this case, a = -16 and b = 76, so the time at which the ball reaches its maximum height is given by:
t = -b/2a = -76/(2*(-16)) = 2.375
Rounded to the nearest hundredth, the ball reaches its maximum height after 2.38 seconds (Option D).
The domain of the function is the set of all real numbers, and the range of the function is the set of all real numbers greater than or equal to ------.
The range of the function is the set of all real numbers greater than or equal to -4.
What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function, that is, all the values assumed by the independent variable x in the function.The range of a function is the set that contains all possible output values of the function, that is, all the values assumed by the dependent variable y in the function.The function assumes values of y = -4 or greater, which represent the range of the graphed function.
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Insert a monomial so that the trinomial may be represented by the square of a
binomial.
0.0152 +.... +100c2
The trinomial can now be represented by the square of the binomial (0.123 + 10c)²
To insert a monomial so that the trinomial may be represented by the square of a binomial, consider the trinomial 0.0152 + ... + 100c².
1: Identify the square root of the first and last terms, which are √0.0152 and √100c². The square roots are 0.123 and 10c, respectively.
2: Determine the middle term by multiplying the square roots together and doubling the result. (0.123)(10c)(2) = 2.46c.
3: Insert the middle term into the trinomial, forming the complete trinomial: 0.0152 + 2.46c + 100c².
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in the figure below, AC and BD are diameters of the circle P what is the arc measure of minor BC
The arc measure of minor BC is 155°
How to determine the arc measure of minor BC?An arc is a segment of a circle is defined by two endpoints and the set of points on the curve between them.
The length of an arc is a fraction of the circumference of the circle, and can be calculated using the angle between the two endpoints and the radius of the circle.
We can say that measure of arc BC is m∠ BPC. Also, arc AD is m∠ APD
By Vertical Angles Theorem. That is:
Provided AC and BD are diameters,
m∠ BPC = m∠ APD
m∠ BPC = 155°
Since m∠ BPC = 155°
Therefore, the arc measure of minor BC is 155°
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Complete Question
See attached image
Solve this system.
Select one:
a.
No solution
b.
(4,-2)
c.
(5,10)
d.
Infinite solutions
The solution to this system of equations are x =5 and y =10
Calculating the x and y coordinates of the solution to this system of equations.From the question, we have the following parameters that can be used in our computation:
5x - 2y = 5 2x + 2y = 30
Express properly
So, we have
5x - 2y = 5
2x + 2y = 30
Add the equations to eliminate y
7x = 35
Divide both sides by 7
x = 5
Next, we have
2(5) + 2y = 30
So, we have
2y = 20
y = 10
Hence, the value of y is 10
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Robert takes out a loan for $7200 at a 4. 3% rate for 2 years. What is the loan future value?
(Round to the nearest cent)
The loan future value is $7726.73.
To find the loan future value, we need to calculate the total amount that Robert will owe at the end of the 2-year loan term, including both the principal (initial loan amount) and the interest.
To begin, we can use the formula for calculating compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
In this case, we know that the principal is $7200, the interest rate is 4.3% (or 0.043 as a decimal), the loan term is 2 years, and the interest is compounded once per year (n = 1).
Substituting these values into the formula, we get:
A = 7200(1 + 0.043/1)²
A = 7200(1.043)²
A = 7726.73
Therefore, the loan future value is $7726.73. This means that at the end of the 2-year loan term, Robert will owe a total of $7726.73, which includes the original $7200 loan amount and $526.73 in interest.
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Belmont is a growing industrial town. Every year, the level of CO2 emissions from the town increases by 10%. If the town produced 330,000 metric tons of CO2 this year, how much will be produced 6 years in the future?
The required answer is CO2 emissions in 6 years = 583,500 metric tons.
Based on the information given, we know that Belmont is a growing industrial town and that every year the level of CO2 emissions from the town increases by 10%. If the town produced 330,000 metric tons of CO2 this year, we can use this information to calculate how much CO2 will be produced in 6 years.
To do this, we can use the formula:
CO2 emissions in 6 years = CO2 emissions this year x (1 + growth rate)^number of years
Compound interest means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e. In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate.
The rate of interest is equal to the interest amount paid or received over a particular period divided by the principal sum borrowed or lent.
In this case, the growth rate is 10% per year and the number of years is 6. So, plugging in the numbers we get:
CO2 emissions in 6 years = 330,000 x (1 + 0.1)^6
CO2 emissions in 6 years = 330,000 x 1.77
CO2 emissions in 6 years = 583,500 metric tons
Therefore, if the town continues to grow at the same rate, it will produce 583,500 metric tons of CO2 in 6 years. This is an increase of 253,500 metric tons from the current level of emissions.
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Simplify each of the following and leave answer in standard form to 3 decimal places.
(3. 05 x 10 ^ -7) (8. 67×10 ^ 4)
The simplified standard form of (3.05 x 10⁻⁷) (8.67 x 10⁴) is 2.642 x 10⁻¹.
To simplify (3.05 x 10⁻⁷) (8.67 x 10⁴) and leave the answer in standard form to 3 decimal places:
1: Multiply the decimal numbers:
3.05 * 8.67 = 26.4245
2: Add the exponents:
-7 + 4 = -3
3: Combine the result and exponent in standard form:
26.4245 x 10⁻³
4: Adjust the decimal to have only one non-zero digit to the left of the decimal point and adjust the exponent accordingly:
2.64245 x 10² x 10⁻³
5: Simplify by combining exponents:
2.64245 x 10⁻¹
6: Round to 3 decimal places:
2.642 x 10⁻¹
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(a) Find the size of angle PQR. Reason (b) Find the size of angle PRQ. Reason (c) Find the size of angle POQ.. Reason
Answer:
a) Angle PQR=90 degrees
b) Angle PRQ=56 degrees
c) Angle POQ=112 degrees
Step-by-step explanation:
a) Angle PQR=90 degrees
reason: the angle in a semicircle is 90°
b) Angle PRQ=56 degrees
reason: angles in same segment of a circle are equal, so far, the segment PQ is common for angles PSQ and PRQ. Therefore, PRQ is 56 degrees.
c) Angle POQ=112 degrees
Reason: isosceles triangle
