The domain of the function f(x) = 4[(x-2)^(1/2)]-8 is the set of all real numbers x such that x ≥ 2.
This is because the expression (x-2)^(1/2) is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)^(1/2)]-8 is always greater than or equal to -8 for all values of x in the domain.
So, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)
In conclusion, the domain and range of the function f(x) = 4[(x-2)^(1/2)]-8 are [2, ∞), [-8, ∞).
The domain of the function f(x) = 4[(x-2)1/2]-8 is the set of all real numbers x such that x ≥ 2. This is because the expression (x-2)1/2 is only defined for x ≥ 2. The range of the function is the set of all real numbers y such that y ≥ -8. This is because the expression 4[(x-2)1/2]-8 is always greater than or equal to -8 for all values of x in the domain.
So, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are:
Domain: [2, ∞)
Range: [-8, ∞)
In conclusion, the domain and range of the function f(x) = 4[(x-2)1/2]-8 are [2, ∞), [-8, ∞).
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Multiply Binomials Feb 19, 7:13:44 PM Express as a trinomial. (2x-1)(2x+2) Answer: Submit Answer
The expression [tex](2x-1)(2x+2)[/tex] can be expressed as the trinomial [tex]4x^2 + 2x - 2[/tex].
To express the given expression as a trinomial, we need to use the distributive property to multiply the two binomials.
1. Multiply the first term of the first binomial by the first term of the second binomial:
[tex](2x) * (2x) = 4x^2[/tex]
2. Multiply the first term of the first binomial by the second term of the second binomial:
[tex](2x) * (2) = 4x[/tex]
3. Multiply the second term of the first binomial by the first term of the second binomial:
[tex](-1) * (2x) = -2x[/tex]
4. Multiply the second term of the first binomial by the second term of the second binomial:
[tex](-1) * (2) = -2[/tex]
5. Add the four products together:
[tex]4x^2 + 4x + (-2x) + (-2) = 4x^2 + 2x - 2[/tex]
So, the expression [tex](2x-1)(2x+2)[/tex] can be expressed as the trinomial [tex]4x^2 + 2x - 2[/tex].
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Please help!! Anything is fine
The missing angle is 90°. So, to obtain the values of the sides given the lengths we will have:
8. PT = 1
PV = 2
9. VT = 0.76
PV = 0.66
10. PT = 3
PV = 6
11. PV =0.58
PT =1.154
12. PT = 1.73
VT = 3
13. VT = 3
PV = 3.5
How to find the missing sidesThe given triangle is a scalene triangle because of the three different angles it has which sum up to 180 degrees. The sides will also be different.
For the first triangle whose known side is √3, the missing values can be obtained this way:
sin 60°/ √3 = sin 90/PV
PV = √3 Sin 90/ sin 60
PV = 1.732/0.866
= 2
PT = sin 60/ √3 = sin 30/ PT
PT = √3 sin 30/sin 60
PT = 1
Using this same pattern, the values for the other figures can be obtained.
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Us the point slope formula to write an equation of the line that
passes through (2/7,7/3) and has an undefined slope. Write the
answer in slope-intercept form.
The equation of the line is
The equation of the line passing through (2/7,7/3) and having idenfinite slope is x = 2/7.
A straight line is a geometric figure that extends infinitely in both directions.
The point slope formula is:
y - y₁ = m(x - x₁)
Where m is the slope of the line, and (x₁, y₁) is a point on the line.
In this case, the slope of the line is undefined, which means that the line is a vertical line. Therefore, the equation of the line is x = 2/7, and there is no slope-intercept form of the equation.
So, the answer is: The equation of the line is x = 2/7.
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(-18xu+9x^(7)u^(5)+24x^(7)u^(4))-:(3x^(3)u^(2)) Simplify your answer as much as possible.
The division of these expressions "(-18xu+9x^(7)u^(5)+24x^(7)u^(4))-:(3x^(3)u^(2))" gives the simplified expression "3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u)":
To simplify the given expression, we need to divide each term by the divisor 3x^(3)u^(2):(-18xu)/(3x^(3)u^(2)) + (9x^(7)u^(5))/(3x^(3)u^(2)) + (24x^(7)u^(4))/(3x^(3)u^(2))
Simplifying each term by canceling out common factors gives us:
-6/(x^(2)u) + 3x^(4)u^(3) + 8x^(4)u^(2)
Combining like terms gives us the final simplified expression:
3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).
Therefore, the simplified expression is 3x^(4)u^(3) + 8x^(4)u^(2) - 6/(x^(2)u).
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After tasneens birthday half of the cake was left over tasneens and his 4 friends are only allowed to 1/5 of the half cake what fraction of the whole cake will tasneens and his friends have eaten after had birthday party
The fraction of the whole cake they eat is 1/10
How to determine the fraction of the whole cake?A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.
From the question, we have the following information:
Left over = 1/2
Fraction of left over cake eaten = 1/5
Using the above as a guide, we have the following:
Fraction eaten = 1/2 * 1/5
Evaluate
Fraction eaten = 1/10
Therefore, the fraction is 1/10
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You have $300,000 saved for retirement. Your account earns 10% interest. How much will you be able to pull out each month if you want to be able to make withdrawals for 25 years?
You will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.
To find out how much you will be able to pull out each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest, we can use the formula:
Monthly withdrawal = (Starting balance * Interest rate) / (1 - (1 + Interest rate)^(-Number of withdrawals))
In this case, the starting balance is $300,000, the interest rate is 10% or 0.10, and the number of withdrawals is 25 years * 12 months = 300 withdrawals.
Plugging in the numbers, we get:
Monthly withdrawal = ($300,000 * 0.10) / (1 - (1 + 0.10)^(-300))
Monthly withdrawal = $30,000 / (1 - 0.031)
Monthly withdrawal = $30,000 / 0.969
Monthly withdrawal = $30,956.52
Therefore, you will be able to pull out $30,956.52 each month if you want to make withdrawals for 25 years with $300,000 saved for retirement and 10% interest.
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Over the interval from [0, 1], which of the two functions shown here is increasing at a faster rate? f(x) shown in red or g(x) shown in green?
The function that is increasing at a faster rate, given the graph shown, is D. g ( x ) increases at a faster rate.
How to find the faster increasing function ?You can find which function is increasing faster by looking at the steepness of the line.
When the slope of a line is positive, it means that as we move from left to right along the line, the y-coordinate of a point on the line increases. This indicates that the line is moving upward and becoming steeper. The steeper the line, the larger the magnitude of the slope.
g ( x ) was more steep in the interval [ 0, 1 ] and so was increasing at a faster rate.
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The height (feet) of a ball launched in the air t seconds after it is launched is given by
F(t) = 16t^2 – 220t + 19 Alter how many seconds is the ball falling at 130 feet per second? _____sec
The ball is falling at 130 feet per second after 10.9375 seconds.
The height of the ball launched in the air t seconds after it is launched is given by the equation F(t) = 16t^2 – 220t + 19. We need to find the time t when the ball is falling at 130 feet per second. To do this, we need to find the derivative of the function F(t) with respect to time t, which represents the velocity of the ball at any given time t.
The derivative of F(t) with respect to t is F'(t) = 32t - 220. We can set this equal to 130 to find the time when the ball is falling at 130 feet per second:
32t - 220 = 130
32t = 350
t = 350/32
t = 10.9375 seconds
Therefore, the ball is falling at 130 feet per second after 10.9375 seconds.
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Calculate the surface area of each pyramid with the following values. (P = perimeter, b = one side of the base, s=side, h=height). Number of sides is given in each problem. The first two have hints to let you know what the shape of the base is. 1. P = 12 ft, s = 4 ft, b = 4 ft, h=2 ft, 3 sides (base is a triangle)
2. B = 4 in, P = 16 in, s = 12, 4sides (base is a square)
3. P = 48 m, b = 12 m, s=12, 4sides
4. P = 45 yds, b = 15 yds, s=15, h=12, 3 sides
5. B = 6 ft, P = 24 ft, s=6, 4sides
6. P = 15 ft, b = 5 ft, s=5 ft, h= 4, 3 sides
7. B = 4 in, P = 16 in, s=11, 4sides
8. P = 40 m, b = 10 m, s=10, 4sides
9. P = 45 yds, b = 15 yds, s=10, h=8, 3 sides
10. B = 16 ft, P = 64 ft, s=8, 4sides
11. B = 5 ft, P = 20 ft, s=7, 4sides
12. P = 45 ft, b = 15 ft, s=10, h=8, 3 sides
13. B = 13 in, P = 52 in, s=11, 4sides
14. P = 28 m, b = 7 m, s=8, 4sides
15. P = 27 yds, b = 9 yds, s=30, h=25, 3 sides
1. Surface area of the pyramid is 24.36 [tex]ft^2[/tex]
2. Surface area is 259.2 [tex]in^2[/tex]
3. Surface area is 912 [tex]m^2[/tex]
4. Surface area is 1226.08 [tex]yd^2[/tex]
5. Surface area is 204 [tex]ft^2[/tex]
6. Surface area is 67.49 [tex]ft^2[/tex]
7. Surface area is 334.2 [tex]in^2[/tex]
8. Total surface area of the pyramid is 300 [tex]m^2[/tex]
9. Total surface area of the pyramid is 257.43 [tex]yd^2[/tex]
10. Total surface area of the pyramid is 80 [tex]ft^2[/tex]
11. Total surface area is 77.96 ft²
12. Total surface area is 292.55 ft²
13. Total surface area is 429 in²
14. Total surface area is 129 m²
15. Total surface area is 1256.4 yd²
1. The following formula is used to get the surface area of a pyramid having a triangle base:
Surface area = (1/2)P x s + B
where
P is the perimeter of the base,
s is the slant height, and
B is the area of the base.
By using the given values, we have:
B = (1/2) x b x h = (1/2) x 4 x 2 = 4 [tex]ft^2[/tex]
s = [tex]\sqrt{(1/2\times4)^2 + 2^2)} = \sqrt{17}[/tex] ft
P = 12 ft
Surface area = (1/2) x 12 x [tex]\sqrt{17}[/tex]+ 4 = 24.36 [tex]ft^2[/tex]
2.The following formula is used to get the surface area of a pyramid having a square base:
Surface area = (1/2)P x s + B
By using the given values, we have:
B = [tex]s^2 = 12^2 = 144 \:in^2[/tex]
s = [tex]sqrt{(1/2\times16)^2 + 12^2}[/tex] = 14.4 in
P = 16 in
Surface area = (1/2) 1614.4 + 144 = 259.2 [tex]in^2[/tex]
3. By using the same formula as above, we have:
B = [tex]s^2 = 12^2 = 144\: m^2[/tex]
s =[tex]\sqrt{(1/2\times48)^2 + 12^2}[/tex] = 24 m
P = 48 m
Surface area = (1/2)4824 + 144 = 912 [tex]m^2[/tex]
4. By using the same formula as above, we have:
B = (1/2) x b x h = 90 [tex]yd^2[/tex]
s = [tex]\sqrt{(1/2*15)^2 + 12^2} = \sqrt{369}[/tex] yd
P = 45 yd
Surface area = (1/2)45 [tex]\sqrt{369}[/tex] + 90 = 1226.08 [tex]yd^2[/tex]
5. By using the same formula as above, we have:
B = [tex]s^2 = 6^2 = 36 ft^2[/tex]
s = [tex]\sqrt{(1/2\times24)^2 + 6^2}[/tex]= 12 ft
P = 24 ft
Surface area = (1/2)2412 + 36 = 204 [tex]ft^2[/tex]
6. By Using the same formula as problem 1, we have:
B = (1/2) x b x h = 10 [tex]ft^2[/tex]
s = [tex]\sqrt{(1/2\times5)^2 + 4^2} = \sqrt{41}[/tex] ft
P = 15 ft
Surface area = (1/2) 15 [tex]\sqrt{41}[/tex] + 10 = 67.49 [tex]ft^2[/tex]
7. By using the same formula as problem 2, we have:
B = [tex]s^2 = 121 in^2[/tex]
s =[tex]\sqrt{(1/2\times16)^2 + 11^2} = \sqrt{185}[/tex] in
P = 16 in
Surface area = (1/2) x 16 x [tex]\sqrt{185}[/tex] + 121 = 334.2 [tex]in^2[/tex]
8. The pyramid's base is a square with long sides. b = 10 m,
so the area of the base is A = [tex]b^2[/tex] = 100 [tex]m^2[/tex]
The lateral area of the pyramid is L = 4 × (1/2 × s × P/4) = 5P [tex]m^2[/tex]
Substituting the given values, we get L = 5 × 40 = 200 [tex]m^2[/tex]
So, the total surface area of the pyramid is then
A + L = 100 + 200 = 300 [tex]m^2[/tex]
9. A side-length equilateral triangle forms the pyramid's base.b = 15 yds,
so the area of the base is
A = ([tex]\sqrt(3)[/tex]/4) × [tex]b^2[/tex] = 97.43 [tex]yd^2[/tex]
The lateral area of the pyramid is L = (1/2 × s × P/3) × h = 160 [tex]yd^2[/tex]
The total surface area of the pyramid is then
A + L = 97.43 + 160 = 257.43 [tex]yd^2[/tex]
10. The base of the pyramid is a square with sides of length
b = P/4 = 16 ft/4 = 4 ft,
A = [tex]b^2[/tex] = 16 [tex]ft^2[/tex]
L = 4 × (1/2 × s × P/4) = 64 [tex]ft^2[/tex]
The total surface area of the pyramid
A + L = 16 + 64 = 80 [tex]ft^2[/tex]
11. The surface area may be computed as follows since the base is square and has sides that are each 5 feet long:
Area of each triangular face = (1/2) x s x h = (1/2) x 7 x 3.64 = 12.74 ft²
Area of the square base = b² = 5² = 25 ft²
Total surface area = 4 x (12.74) + 25 = 77.96 ft²
12. Calculate the length of the altitude by using the Pythagorean theorem:
a² + b² = c², where a = 8 ft,
b = (1/2) x b = (1/2) x 15 ft = 7.5 ft, c = h = unknown height
8² + 7.5² = c²
c ≈ 11.18 ft
Then, we can calculate the surface area as:
Area of each triangular face = (1/2) x b x h = 83.85 ft²
Area of the triangular base = (1/2) x b x h= 60 ft²
Total surface area = 3 x (83.85) + 60 = 292.55 ft²
13. Surface area can be calculated as:
Area of each triangular face = (1/2) x s x h = 55 in²
Area of the square base = b² = 13² = 169 in²
Total surface area = 4 x (55) + 169 = 429 in²
14. The surface area can be calculated as:
Area of each triangular face = (1/2) x s x h = (1/2) x 8 x 5 = 20 m²
Area of the square base = b² = 7² = 49 m²
Total surface area = 4 x (20) + 49 = 129 m²
15. By using the Pythagorean theorem:
a² + b² = c², where a = 25 yds, b = (1/2) x b = (1/2) x 9 yds = 4.5 yds, c = h = unknown height
25² + 4.5² = c²
c ≈ 25.42 yds
Then, we can calculate the surface area as:
Area of each triangular face = (1/2) x b x h = 381.3 yd²
Area of the triangular base = (1/2) x b x h =112.5 yd²
Total surface area = 3 x (381.3) + 112.5 = 1256.4 yd²
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What is the distance between each pair of numbers?
0 and 3
Answer:
It should be three units
Step-by-step explanation:
Answer:
3 units. .
Step-by-step explanation:
0,1,2,3 not counting your starting number
Suppose that the relation C is defined as follows. C={(c,h),(j,j),(j,c),(e,a)} Give the domain and range of C.
The domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}
The domain and range of a relation C are the set of all x-values and y-values in the ordered pairs of C. The domain of C is the set of all x-values, and the range of C is the set of all y-values. We can find the domain and range of C by looking at the ordered pairs in C={(c,h),(j,j),(j,c),(e,a)}.
The domain of C is {c, j, e} because these are the x-values in the ordered pairs. The range of C is {h, j, c, a} because these are the y-values in the ordered pairs.
Therefore, the domain and range of C are:
Domain of C: {c, j, e}
Range of C: {h, j, c, a}
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The expression 5x − 7 represents the time it takes a commuter to travel in the morning to work. The expression 11x – 1 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?
The expression that represents the total travel time is 16x − 8
Adding Polynomials:
To add polynomial expressions we need to add or subtract like terms and constant terms.
In the given problem to find the total travel time we need to add the time takes to travel to work and the time takes to travel from work to home.
Here we have
The expression represents the time takes to travel to work = 5x − 7
The expression represents the time takes to travel from work = 11x – 1
The total travel time = 5x − 7 + 11x – 1
=> 5x + 11x − 7 – 1
=> 16x − 8
Therefore,
The expression that represents the total travel time is 16x − 8
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Draw the line 3y-4x=12 for values of x from -3 to 3
We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12.
What is graph ?
Graphs are visual representations of data or mathematical functions that are used to help people understand and analyze the relationships between different variables. Graphs can be used to show patterns, trends, and relationships in data that might be difficult to see from a table or list of numbers.
To draw the line 3y-4x=12 on the graph, we can solve for y and plot several points for different values of x, then connect the points with a straight line.
When x = -3:
3y - 4(-3) = 12
3y + 12 = 12
3y = 0
y = 0
So one point on the line is (-3, 0).
When x = 0:
3y - 4(0) = 12
3y = 12
y = 4
So another point on the line is (0, 4).
We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12. The graph should look like this:
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The arm span and foot length were both measured (in centimeters) for each of 20 students in a biology class. The computer output displays the regression analysis.
Which of the following is the coefficient of determination?
0.63
0.65
0.79
0.81
50
45
36
35
27
44
43
32 Write next to these numbers if these numbers are composite or prime
Answer:
50: Composite
45: Composite
36: Composite
35: Composite
27: Composite
44: Composite
43: Prime
32: Composite
calculate the side of the unknown side of this right angled triangle 17cm 9cm
The side of the unknown side of this right angled triangle is 14cm
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given two sides of the triangle are 17cm and 9cm.
We have to find the unknow side of the triangle.
By Pythagoras theorem we find the length of unknown side.
The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
17²=9²+x²
289-81=x²
208=x²
Take square root on both sides
x=√208
x=14.42 cm
Hence, the side of the unknown side of this right angled triangle is 14cm
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x^(4)-4x^(3)-5x^(2)+16x+4=0 ble rational roots. c division to test several possible rati
To find the rational roots of the equation x^(4)-4x^(3)-5x^(2)+16x+4=0, we can use the Rational Roots Test. This test states that any rational root of the equation can be expressed as p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In this case, the constant term is 4 and the leading coefficient is 1. The factors of 4 are 1, 2, and 4, and the factors of 1 are 1. Therefore, the possible rational roots are 1, 2, 4, -1, -2, and -4.
We can use synthetic division to test each of these possible roots. If the remainder is 0, then the root is a rational root of the equation. For example, let's test the root 1:
1 | 1 -4 -5 16 4
| 1 -3 12 28
---------------
| 1 -3 -8 28 32
The remainder is 32, which is not 0, so 1 is not a rational root of the equation.
We can continue to test the other possible roots in the same way until we find the rational roots of the equation. Once we have found the rational roots, we can use them to factor the equation and find the remaining roots.
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SYSTEMS OF EQUATIONS AND MATRICES Linear programming Find the maximum value of the function z=8x+3y subject to the following constraints y>=0 x>=4 y<=10 5x+2y<=60
The maximum value of the function z=8x+3y subject to the constraints is 94
The maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 can be found using the method of linear programming.
Graph the constraints on a coordinate plane. The constraints y>=0 and x>=4 are vertical and horizontal lines, respectively.
The constraint y<=10 is a horizontal line at y=10, and the constraint 5x+2y<=60 can be rewritten as y<=-5/2x+30 and graphed as a line with a slope of -5/2 and a y-intercept of 30.
Identify the feasible region, which is the area of the graph that satisfies all of the constraints.
In this case, the feasible region is the quadrilateral bounded by the lines x=4, y=0, y=10, and y=-5/2x+30.
Find the vertices of the feasible region. The vertices are the points (4,0), (4,10), (8,10), and (10,5).
Substitute the coordinates of the vertices into the function z=8x+3y to find the maximum value. The maximum value occurs at the vertex (8,10), where z=8(8)+3(10)=94.
Therefore, the maximum value of the function z=8x+3y subject to the constraints y>=0, x>=4, y<=10, and 5x+2y<=60 is 94.
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Find the exact value of each of the remaining trigonometric functions of e. sin 0 3 and tan 0 0 4 cos 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expre tan 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expres csc = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the express sec 0 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expressic cote = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression Find the lengths and area A 80 15 yd 2 com The longth of the artis yards (Round to three decimal places as needed.) The area of the sector square yards Round to three decimal places as needed.) 1 of 2 comples Find the distance from A to C across the gorge illustrated in the figure. 170 n The distance from A to C's foot. (Do not round until the final answer. Then round to two decimal places as needed.) Name the quadrant in which the angle o lies. sin 0 <0, coto > 0 The angle o lies in which quadrant? IV 11 =
The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.
Part 1: Find the exact value of each of the remaining trigonometric functions of e.
sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3
Part 2: Find the lengths and area A.
The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.
Part 3: Find the distance from A to C across the gorge illustrated in the figure.
The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.
Part 4: Name the quadrant in which the angle o lies.
The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.
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I’ll give you brainly
Answer:
x = 1
y = 1
Step-by-step explanation:
rewrite the expression in the form
3^4*3^2
Answer: 3x3x3x3+3x3
Step-by-step explanation:
In 8 years, Claire will be three times her current age. In how many years will she be 20 years old?
Claire will be 20 years old in 16 years. To solve this problem, we use algebra.
Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:
x + 8 = 3x
Next, we can rearrange the equation to solve for x:
8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:
20 - 4 = 16
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Farmer wants to decide 8085 hacters of grazing land into 9 or 15 camps of equal size. How did he know without doing a division calculation ,that the 5 camp division is an easier practical solution than the 9 camp division?
The farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.
What is the fractions and decimals?Both fractions and decimals are just two ways to represent numbers. Fractions are written in the form of p/q, where q≠0, while in decimals, the whole number part and fractional part are connected through a decimal point.
To understand why the 5 camp division is an easier practical solution than the 9 camp division, we need to consider the common factors of 8,085 and the numbers 9 and 15.
The prime factorization of 8,085 is:
8,085 = 3 x 3 x 3 x 5 x 5 x 6
The prime factorization of 9 is:
9 = 3 x 3
The prime factorization of 15 is:
15 = 3 x 5
From the prime factorizations, we can see that 9 has a common factor of 3 with 8,085, while 15 has two common factors of 3 and 5 with 8,085. This means that dividing 8,085 into 9 or 15 camps of equal size would require dealing with fractions or decimals, which can be impractical in a farming context.
On the other hand, the prime factorization of 5 is:
5 = 5
Since 5 is a prime number, it does not have any common factors with 8,085. This means that dividing 8,085 into 5 camps of equal size would not require dealing with fractions or decimals. The farmer can simply divide the grazing land into 5 equal parts, each with an area of 1,617 hectares, without needing to perform any division calculations or deal with any fractions or decimals.
Therefore, the farmer knows that the 5 camp division is an easier practical solution than the 9 camp division because it does not require dealing with fractions or decimals.
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A 6-foot person standing 18 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
what is triangle ?A triangle is a polygon with three vertices and three angles that has three sides. It is one of the fundamental geometric shapes and has numerous uses in fields like engineering, physics, architecture, and more. The lengths of a triangle's sides and angles can be calculated using a variety of geometric formulas. Triangles come in a variety of shapes, including equilateral, isosceles, scalene, right-angled, acute-angled, and obtuse-angled triangles, each of which has unique attributes.
given
Let x represent the person's height.
Let x represent the streetlight's height.
Let d represent the distance between an individual and a streetlight.
Let s be the size of the shade cast by the subject.
According to the facts provided, x equals 6 feet (height of the person)
d Equals 15 feet (distance from the person to the streetlight)
The shadow's extent, s, is 15 feet.
Finding y's number, or the streetlight's height, is necessary.
The following ratios can be written using the comparable triangles property:
y / (d + s) Equals x / s
Inputting the numbers provided yields:
By condensing and figuring out x, we arrive at:
y = 12 feet
Consequently, the streetlight has a 12 foot height.
We can divide the streetlight's height by the person's height to determine how many times higher the streetlight is:
y / x = 12 / 6 = 2
Due to the formation of two identical rectangles, the streetlight is consequently twice as large as the individual.
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Using long division to find each quotient.
(X^2-5x-6) divided by (x+1)
hope helpful! :)
1) A 20 lb. BAG OF GRASS SEED WILL COVER AN AREA OF 10,000 ft2 . HOW MANY POUNDS WILL YOU NEED TO COVER AN AREA OF 140,000 ft2 . HOW MANY WHOLE BAGS OF SEED WILL YOU NEED TO BUY? WRITE THE EQUATION FOR A PROPORTION AND SOLVE IT.
2) SOLVE THE FORMULA FOR T2. ???????????????? ???????? = ???????????????? ????????
3) THE GILBERTS PURCHASED A CAR. IF THE TOTAL COST, INCLUDING A 5% SALES TAX, WAS $14,512, FIND THE COST OF THE CAR BEFORE TAX.
4) JIM MEYERS BOUGHT A NEW LAPTOP COMPUTER AT A 15% OFF SALE. IF THE SALE PRICE WAS $722.50, WHAT WAS THE LIST PRICE OF THE COMPUTER?
5) FIND THE x AND y INTERCEPTS FOR THE EQUATION 3x + 6y = 9.
1) 140
2) T2 = ?
3) $13,786.40
4) $835.88
5) x = 3, y=(0, 1.5)
1) To find the number of pounds of grass seed needed to cover an area of 140,000 ft2, you need to write a proportion and solve it. Set up the proportion using the given information:
20 lb/10,000 ft2 = x lb/140,000 ft2
To solve for x, multiply both sides of the equation by 140000:
20 lb * 140000/10,000 ft2 = x lb
x = 2800 lb
You will need 2800 lbs of grass seed to cover an area of 140,000 ft2. To find out how many whole bags of seed you will need to buy, divide the total number of pounds by the number of pounds in a bag, which is 20 lbs. You will need to buy 140 whole bags of seed.
2) To solve for T2 in the equation ???????????????? ???????? = ???????????????? ????????, divide both sides of the equation by ???????????????? :
T2 = ???????????????? ????????/????????????????
3) To find the cost of the car before the sales tax, subtract the 5% sales tax from the total cost. The formula is:
Cost before tax = Total Cost - (Total Cost * Sales Tax %)
Cost before tax = $14,512 - ($14,512 * 0.05) = $13,786.40
4) To find the list price of the laptop computer, add the 15% off sale to the sale price. The formula is:
List Price = Sale Price + (Sale Price * Discount %)
List Price = $722.50 + ($722.50 * 0.15) = $835.88
5) The x and y intercepts for the equation 3x + 6y = 9 can be found by setting x or y equal to 0 and solving for the other. To find the x intercept, set y = 0:
3x + 6(0) = 9
3x = 9
x = 3
The x intercept is (3, 0). To find the y intercept, set x = 0:
3(0) + 6y = 9
6y = 9
y = 1.5
The y intercept is (0, 1.5).
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5−8=State the property of real numbers being used. 5.3+2x=2x+36.(a+b)(a−b)=(a−b)(a+b)7.A(x+y)=Ax+Ay8.(A+1)(x+y)=(A+1)x+(A+1)y
The properties of real numbers being used in the equations you provided are as follows:
1. 5−8: This equation does not use any specific property of real numbers. It is simply subtraction of two real numbers.
2. 5.3+2x=2x+36: This equation uses the Commutative Property of Addition, which states that the order in which real numbers are added does not affect the sum. This is why 5.3+2x is equal to 2x+5.3.
3. (a+b)(a−b)=(a−b)(a+b): This equation also uses the Commutative Property of Multiplication, which states that the order in which real numbers are multiplied does not affect the product. This is why (a+b)(a−b) is equal to (a−b)(a+b).
4. 7.A(x+y)=Ax+Ay: This equation uses the Distributive Property, which states that multiplying a real number by a sum is the same as multiplying each term in the sum by the real number and then adding the products. This is why A(x+y) is equal to Ax+Ay.
5. (A+1)(x+y)=(A+1)x+(A+1)y: This equation also uses the Distributive Property, as explained in the previous example.
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Alex has 1400 ft of irrigation pipping. He wants to use it to irrigate his back lawn. He wants to lay the pipping in such a manner as to cut off 3 equal size rectangle regions in the yard. What are the dimensions that would produce the maximum enclosed area.
The dimensions that would produce the maximum enclosed area are 350ft x 350ft, which will cut off 3 equal size rectangle regions in the yard.
To understand why this is the case, let's consider the problem step-by-step. If Alex wants to cut off three equal size rectangle regions in the yard, he will need to divide the lawn into four equal size rectangles. Let's call the dimensions of two of these rectangles "x" and "y".
To maximize the enclosed area, we want to maximize the area of the lawn that is left over after the three rectangles are cut out. This area can be represented by the equation A = (350-x)(350-y). We know that the total length of the piping is 1400 ft, so the perimeter of the enclosed area (the sum of all four sides) is 1400 ft. This means that 2x + 2y + 1400 = 1400, or 2x + 2y = 0.
Solving for y, we get y = -x + 700. Substituting this equation into the area equation, we get A = (350-x)(350-(-x+700)), which simplifies to A = x(350-x). To find the maximum area, we can take the derivative of this equation with respect to x, set it equal to 0, and solve for x. Doing this, we find that x = 175, which means that y = 525 - x = 350. Therefore, the dimensions that would produce the maximum enclosed area are 350ft x 350ft.
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A gas station has a steady annual demand for 22,032 gallons of
diesel. It costs $9 to store 1 gallon for 1 year, $34 to ship
each order of diesel, and $19 to purchase each gallon. Quest
The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.
The gas station has a steady annual demand for 22,032 gallons of diesel. The cost to store 1 gallon for 1 year is $9, the cost to ship each order of diesel is $34, and the cost to purchase each gallon is $19. To calculate the total cost of storing, shipping, and purchasing the diesel for one year, we can use the following formula:
Total cost = (storage cost per gallon x annual demand) + (shipping cost per order x number of orders) + (purchase cost per gallon x annual demand)
To find the number of orders, we can divide the annual demand by the number of gallons per order. In this case, the number of gallons per order is not given, so we will use the variable "x" to represent it:
Number of orders = 22,032 / x
Plugging this back into the formula, we get:
Total cost = (9 x 22,032) + (34 x 22,032 / x) + (19 x 22,032)
Simplifying, we get:
Total cost = 198,288 + (748,288 / x)
To minimize the total cost, we can take the derivative of the total cost with respect to x and set it equal to zero:
d(Total cost) / dx = -748,288 / x^2 = 0
Solving for x, we get:
x = sqrt(748,288 / 0) = 865.12
Therefore, the gas station should order 865.12 gallons of diesel per order to minimize the total cost. The minimum total cost is:
Total cost = 198,288 + (748,288 / 865.12) = $198,288 + $864.87 = $199,152.87
The minimum total cost for the gas station to store, ship, and purchase 22,032 gallons of diesel for one year is $199,152.87.
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Find the 9th term of the geometric sequence
3
,
−
15
,
75
,. . . 3,−15,75,
The 9th term of the geometric sequence 3, -15, 75, ... is 1171875.
The given sequence is 3, -15, 75, ... We can see that each term is obtained by multiplying the previous term by -5. Therefore, the common ratio is -5.
We can use the formula for the nth term of a geometric sequence to find the 9th term. The formula is given by:
aₙ = a₁ x rⁿ⁻¹
where,
aₙ = nth term of the sequence
a₁ = first term of the sequence
r = common ratio of the sequence
n = index of the term we want to find
Using the given sequence, we have:
a₁ = 3 (first term)
r = -5 (common ratio)
To find the 9th term, we substitute n=9 into the formula:
a₉ = a₁ x r⁹⁻¹
a₉ = 3 x (-5)⁸
a₉ = 3 x 390625
a₉ = 1171875
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