answer please have no idea how to start or do it just please show the workings aswell.
Answers
The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;
(a) \(L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}\)
(b) \(L_{min}\) = 54 cm
(c) L'' at x = 3, (where \(L_{min}\) = 54 cm) is positive, therefore, x = 3 is a minimum point
P10-Focus2
The area = \(2\times x \times y+\frac{\pi\cdot x^2}{4} =4\), therefore, \(y = \frac{16- \pi \cdot x^2}{8 \cdot x}\)
The minimum point, which is an extremum point is a point where the derivative of the function is 0.
(a) The length of the cuboid = 2·x
The width of the cuboid = x
The volume of the cuboid = 81 cubic centimeters
The thickness of the cuboid is therefore;
Thickness = 81/(2·x × x) = 81/(2·x²)
The sum of the length of the twelve edges, L, is therefore;
\(L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}\)
Therefore;
\(L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}\)
The sum of the lengths of the twelve edges, L, is \(L = 12\cdot x + \frac{162}{x^2}\)
(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;
\(\frac{dL}{dx} = 12 - \frac{324}{x^3} =0\)
Therefore;
\(12-\frac{324}{x^3}=0\)
\(12 = \frac{324}{x^3}\)
x³ = 324 ÷ 12 = 27
x = ∛(27) = 3
x = 3
The minimum value of L can be obtained when x = 3 as follows;
\(L = 12\cdot x + \frac{162}{x^2}\)
\(L_{min} = 12\times 3 + \frac{162}{3^2} = 54\)
The \(L_{min}\) = 54
The minimum value of L is 54 centimeters
(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;
At the x-value of a minimum point of a function, the value of the further derivative is larger than zero
The further derivative of the specified function is found as follows;
\(L'' = \frac{dL'}{dx} =\frac{972}{x^4}\)
At the critical number, x = 3, from the first derivative, we get;
\(L'' = \frac{972}{3^4} = 12 > 0\)
The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.
(b) The radius of the quarter circle = x
The area of the figure = 4 m²
The sum of the area of the composite figures are;
\(A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4\)
Therefore;
\(y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}\)
Rearranging the right hand side expression as a fraction, we get;
\(y = \frac{16-\pi \cdot x^2}{8\cdot x}\)
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Related Questions
Kaj is flying a kite, holding her hands a distance of 3.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 33^{\circ}
∘
. If the string from the kite to her hand is 75 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Using trigonometric ratio, the height of the ground above the ground to the nearest hundredth is 44.85 ft
The situation forms a right angle triangle.
What is a right angle triangle?Right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, the length of the string is the hypotenuse side of the triangle formed . The opposite side of the triangle is the height of the kite form the ground.
Therefore, the height of the kite form the ground can be found as follows;
sin 33° = opposite / hypotenuse
sin 33° = h / 75
cross multiply
h = 75 × sin 33
h = 40.8479276261
h = 40.84
The height of kite from ground = 40.847 + 3.5 = 44.3479276261 = 44.85 ft
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Answer:
44.35
Step-by-step explanation:
i did it
Definition of a derivative (limit of the difference quotient)
Answers
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
What is derivative?
The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.
The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:
f'(a) = lim (h → 0) [f(a + h) - f(a)] / h
This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).
The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.
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In △ABC, ∠C is a right angle and sinB=725.
What is the value of cosA?
A
725
B
1725
C
1825
D
2425 giving brainliest to whoever answers correctly
Answers
9514 1404 393
Answer:
A 7/25
Step-by-step explanation:
The cosine of an angle is equal to the sine of its complement. In a right triangle, angle A is the complement of angle B. So, ...
cos(A) = sin(B)
cos(A) = 7/25
Solve the equation to find the value of x. log2(5x-4)=4
Answers
The given equation is
\(\log _2(5x-4)=4\)To solve for x, the logarithm to indices relationship will be applied
That is
\(\begin{gathered} \log _ab=x \\ \Rightarrow b=a^x \end{gathered}\)Hence
\(\begin{gathered} \log _2(5x-4)=4 \\ \Rightarrow5x-4=2^4 \end{gathered}\)This is simplified to get
\(\begin{gathered} 5x-4=16 \\ 5x=16+4 \\ 5x=20 \\ x=\frac{20}{5} \\ x=4 \end{gathered}\)Therefore, the value of x = 4
The lengths of the sides of a triangle are given. Classify each triangle as acute, right, or obtuse.
7.) 4, 5, 6
8.) 11, 12, 15
9.) 30, 40, 50
Answers
The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.
What is Triangle?Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
7.) This triangle is obtuse.
To see this, we can use the Pythagorean theorem:
4*4 + 5*5 = 16 + 25 = 41
6*6 = 36 m
Since 41 > 36, we know that the triangle is obtuse.
8.) This triangle is right.
To see this, we can again use the Pythagorean theorem:
11*11 + 12*12 = 121 + 144 = 265
15*15 = 225 m
Since 265 = 225 + 40, we know that the triangle is right.
9.) This triangle is also right.
We can use the same method as before:
30*30 + 40*40 = 900 + 1600 = 2500
50*50 = 2500 m
Since 2500 = 2500, we know that the triangle is right.
Therefore, The given triangles are obtuse , right angled and right angled.
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f(x)=2x+1/x-1 then f^-1(1)
Answers
Answer:
f⁻¹(x) = (x + 1) / (x - 2)f⁻¹(1 ) = - 2Step-by-step explanation:
Given function:
f(x) = (2x + 1) / (x - 1)Find its inverse, substitute x with y and f(x) with x, solve for y:
x = (2y + 1) / (y - 1)x(y - 1) = 2y + 1xy - x = 2y + 1xy - 2y = x + 1y(x - 2) = x + 1y = (x + 1) / (x - 2)Substitute y with f⁻¹(x):
f⁻¹(x) = (x + 1) / (x - 2)Find f⁻¹(1 ):
f⁻¹(1 ) = ( 1 + 1) / (1 - 2) = 2 / - 1 = - 2Sentence as an equation.
29 fewer than the product of t and 254 equals t reduced by 81. PLEASE HELP
Answers
Answer:
254t - 29 = t - 81
Step-by-step explanation:
The word "product" means to multiply.
Therefore, the "product of t and 254" means to multiply t by 254:
254tThe term "fewer than" means to subtract.
Therefore, "29 fewer than" means to subtract 29 from what comes after the word "than".
The term "reduced by" also means to subtract.
Therefore, "reduced by 81" means to subtract 81 from what came before the word "reduced".
Therefore:
"29 fewer than the product of t and 254 equals t reduced by 81":
254t - 29 = t - 81Which of the following is the solution of the quadratic equation xଶ 3x − 10 0?
Answers
The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.
The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where (a, b, and c) are 1, 3, and -10
So, the solutions of the equation x^2 + 3x - 10 = 0 are:
x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)
x = (-3 ± √(9 + 40)) / 2
x = (-3 ± √49) / 2
x = (-3 ± 7) / 2
x = (4, -1)
Complete question:
Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?
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Which best describes the range of the function f x 2 3 x?.
Answers
The range of the function f(x) = 2(3)x is best described by y > 0. Particularly the function when the constant is e, a function whose value is a constant raised to the power of the argument.
What is range of function?The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response. The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
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If f(1)= 1, f(2)=3, and f(n) =2f (n-1) -f (n-2) then find the value of f (5).
Answers
9514 1404 393
Answer:
f[5] = 9
Step-by-step explanation:
We can work this one term at a time.
f[3] = 2f[2] -f[1] = 2(3) -(1) = 5
f[4] = 2f[3] -f[2] = 2(5) -3 = 7
f[5] = 2f[4] -f[3] = 2(7) -5 = 9
_____
Additional comment
The terms known to this point seem to indicate f[n] = 2n -1 is a workable simplification. Or, recursively, f[n] = f[n-1] +2.
Maddy received $60 for her birthday and decided to go shopping. She bought 2 shirts priced at $12.25 each, a necklace for $8.50, and a pair of shoes for $22.75. If all the prices included tax, and she gave the cashier all of her birthday money, how much change did she get back?
Answers
Answer:
$3.75
Step-by-step explanation:
Cost of one shirt = $12.25
cost of two shirt = 2*Cost of one shirt= 2*$12.25 = $25
cost of necklace = $8.50
cost of pair of shoes = $22.75
Total cost for the shopping = cost of two shirt+cost of necklace+ cost of pair of shoes
Total cost for the shopping = $25 + $8.50+ $22.75 = $56.25
Given that Maddy had done total shopping worth $56.25 but she gave cashier all her birthday money which is equal to $60.
Then , cashier will return all the money from $60 exceeding $56.25
change returned to money = money given to cashier - total cost for shopping
change returned to Maddy = $60 - $56.25 = $3.75
Thus, Maddy got Back $3.75
5. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture?
Answers
The picture represents isosceles triangle theorem.
From the figure :
It is represented that two sides are equal.
And the angles opposite to this two equal sides are equal.
So it is a isosceles triangle.
Isosceles triangle:
If two sides of a triangle are congruent , then the angles opposite to these sides are congruent.
Therefore the picture represents isosceles triangle theorem.
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Would like the answer and an explanation.
Answers
Answer:
Step-by-step explanation:
triangles are similar so:
\(\frac{10}{10+14} = \frac{x}{36}\)
24x=360
x=15
Mrs Ong bought some fruits. 3 fewer than 1/2 of the fruits were oranges. 2 fewer than 1/2 of the remaining fruits were pears. 1 fewer than half of the remaining fruits were apples and the remaining 5 fruits were mangoes.
(a) How many fruits did Mrs Ong buy altogether?
(b) What fraction of the fruits were pears? Give your answer in the simplest form.
Answers
The number of fruits that Mrs Ong bought is 40.
The fraction of the fruits that are pears are 1/4.
How many fruits did Mrs Ong buy?The expression that represents the number of oranges is: 1/2f - 3
Where f is the number of fruits
The expression that represents the number of pears is: (1/2 x 1/2)f - 2
1/4f - 2
The expression that represents the number of apples is: 1/2[1 - (1/2 + 1/4)]f - 1
1/8f - 1
Fraction of mangoes remaining = 1 - (1/4 + 1/2 + 1/8)
1 - 7/8 = 1/8
Number of fruits bought altogether = 1/8f = 5
f = 5 x 8 = 40
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2/3 - 1/5
answer pls
Answers
(3 points) how many bit strings of length 7 are there? 128 how many different bit strings are there of length 7 that start with 0110? 8 how many different bit strings are there of length 7 that contain the string 0000?
Answers
there are 128 different bit strings of length 7. To calculate the number of bit strings of length 7, we need to consider that each position in the bit string can either be 0 or 1.
Since there are 7 positions in the string, we have 2 options (0 or 1) for each position. Therefore, the total number of bit strings of length 7 is 2^7 = 128.To calculate the number of bit strings of length 7 that start with 0110, we need to fix the first four positions as 0110. The remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that start with 0110 is 2^3 = 8.
To calculate the number of bit strings of length 7 that contain the string 0000, we need to consider the possible positions for the string 0000. It can occur in five different positions: at the beginning, at the end, or in any of the three middle positions. For each position, the remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that contain the string 0000 is 5 * 2^3 = 40. However, we need to subtract the cases where the string 0000 occurs in both the beginning and end positions, as they were counted twice. So, the final answer is 40 - 24 = 16.
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NEED ANSWER QUICK WILL MARK BRAINLYEST!
Felicia wanted to find the number of boys in the school band if 30% of the 50 students are boys. Is her answer correct? Explain why or why not.
(help me plz and if you answer thx!)
Answers
Answer:
No
Step-by-step explanation:
You cant have a fraction amount of people
Answer:
No her answer is no correct
No, Felicia’s answer is not correct. She should have divided by 2, not multiplied. 30 divided by 2 is 15. So 15 of the 50 students in the band are boys.
What is the area of the shaded region if r=4 ?
A. 64 - 16 π B. 16 - 16 π C. 16 - 8 π D. 64 - 8 π E. 64π - 16
Answers
To find the area of the shaded region when r = 4, we need to determine the area of the circle with radius r and subtract the area of the square with side length 2r. The area of a circle is given by the formula A = πr², where r is the radius. Substituting r = 4 into the formula, we have A = π(4)² = 16π.
The area of a square is calculated by multiplying the length of one side by itself. In this case, the side length is 2r, so the area of the square is (2r)² = (2 * 4)² = 8² = 64. Finally, to find the area of the shaded region, we subtract the area of the square from the area of the circle: 16π - 64. Therefore, the correct answer is A. 64 - 16π, which represents the area of the shaded region when r = 4.
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Parkers distance from home over time
Answers
help pleaseeeeeeeeee
Answers
Answer:
Hello,
Answer D
Step-by-step explanation:
I suppose that i is the imaginary (i²=-1)
i^4=1
i^99=i^(4*24+3)=i^3
i^3-i^3=0
Answer D
Answer: D) 0
======================================================
Explanation:
Take note of this pattern
i^0 = 1i^1 = ii^2 = -1i^3 = -ii^4 = 1After this point, we repeat the cycle. The cycle is 4 units long. This means we can divide the exponent over 4 and look at the remainder
99/4 = 24 remainder 3
So i^99 = i^3
which means i^99 - i^3 = i^3 - i^3 = 0
Solve please and SHOW UR WORK
Answers
x+2 x 2x+3
2x+x= 3x
2+3=5
So final answer is 3x+5
15. Apply Mathematics (1)(A) Suppose you have a box with a 4 X 4-in.
square base and variable height h. The surface area of this box is a
function of its height. Write a function to represent the surface area.
Evaluate the function for h=6.5 in.
Answers
Answer:
Step-by-step explanation:
Formula for calculating the surface area of the box S = 2(LW+LH+WH) where
L is the length of the box
W is the width of the box
H is the height of the box
If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;
S = 2(4(4)+4H + 4H)
S = 2(16+8H)
S = 32+16H
Hence, The function that represents the surface area of this box as a
function of its height is S = 32+16H where H is the height of the box
Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;
S = 32+16H
S = 32+16(6.5)
S = 32+106
S = 138in²
Hence the total surface area of the box is 138in²
an architect designs a theater with 17 seats in the first row, 21 in the second, 25 in the third, and so on. if the theater is to have a seating capacity of 1197, how many rows must the architect use in his design?
Answers
The number of rows needed to reach a seating capacity of 1197 are 14.
1st row = 17 seats
2nd row = 17 + 4 = 21 seats
3rd row = 21 + 4 = 25 seats
4th row = 25 + 4 = 29 seats
The total number of seats in the first n rows, we can use the arithmetic series formula:
Sum = (n/2) × (first term + last term)
where n is the number of terms (rows),
The first term is 17,
The last term is 17 + (n-1) × 4
We need to find the number of rows (n) such that the sum of seats is equal to 1197
(n/2) × (17 + 17 + (n-1) × 4) = 1197
Simplifying the equation
(n/2) × (34 + 4n - 4) = 1197
(n/2) × (4n + 30) = 1197
2n² + 15n - 1197 = 0
n = \(\frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)
b = 15, c = -1197, a = 2
n = -15 ± √5013/4
n = 13.9
n = 14
Therefore, the architect must use 14 rows in the theater design to achieve a seating capacity of 1197.
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a company is developing a new drug for reducing the symptoms of pollen allergies. they have developed two forms of the drug: a and b. the company wants to find out which form is most effective and to determine whether the amount to be taken each day should be split into one, two, or three doses. a set of volunteers who suffer from pollen allergies is randomly split into groups to receive treatments. a) how many factors are there? what are they? b) how many levels of the factors are there? what are they? c) how many treatments are there? what are they? d) referring to the experiment above, identify the following: response variable experimental units e) how might you incorporate a control group? why might a control group be beneficial?
Answers
The experiment involves two factors, six treatments, and the response variable is the reduction in pollen allergy symptoms among the experimental units.
The experiment being conducted by the company involves two forms of a drug, namely A and B, and aims to determine which form is more effective in reducing pollen allergy symptoms, and whether the daily amount should be split into one, two, or three doses. There are two factors involved in the experiment: the form of the drug (A and B) and the number of doses (one, two, or three). The drug form factor has two levels (A and B), while the dose factor has three levels. Therefore, there are a total of six treatments in the experiment, which are as follows: A1, A2, A3, B1, B2, and B3. The response variable in the experiment is the reduction in pollen allergy symptoms, and the experimental units are the volunteers who suffer from pollen allergies. A control group can be incorporated into the experiment by randomly assigning some volunteers to receive a placebo or an existing allergy medication, instead of the new drug. A control group would be beneficial in order to compare the effectiveness of the new drug with the existing treatment, and to ensure that any observed effects are not due to chance or other factors.
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1) Identify the property of equality that justifies the statement If AB=CD, then CD=AB. Io a to suben (57
a) Transitive
b) Substitution
c) Symmetric
d) Reflexive
2) In the figure to the right, lines m and n are parallel. One pair of corresponding angles is
-
a) <1 and <3
c) <1 and <8
3) The slope of the line that passes through (2, 3) and (-2,-5) is 4
a) —-—-/22
b)
c) -2
4) Find the value of x.
a) 21
b) < 1 and <4
d) < 1 and < 6
b) 55
c) 84
6) In circle C, mAB = 72. Find m
a) 72
b) 108
d) 2
18 (6
c) 144
d) 86
2
이호
d) 180
7) Find the sum of the measures of the interior angles of an 18-gon.
a) 2520
c) 2880
d) 3600
b) 2700
7 Of
8) A tree casts a shadow of 48 ft.
a) 86. 4 ft
b) 44 ft
31°
9) Find m
a) 5
b) 67
c) 90
d) 23
D
88 to
5) AABC-ALMN, AB = 18, BC = 12, LN = 9 and LM = 6. What is the scale factor of AABC to ALMN?
3
9
A
1
(4x + 2)°
A
5
12
55°
B (#6)
2
13
6
12
m
Nancy, who is 5 ft tall, casts a shadow of 9 ft. About how tall is the tree?
c) 36 ft
d) ) 26/3/2
(#4)
B
A
5
C
3
7
(#9)
10) The measure of an interior angle in a regular polygon is 108. How many sides does the polygon have?
a) 8
b) 7
c) 6
d) 5
m 87
4
n
8
Give
Procedure Part 1. Comparing
Answers
1) The property of equality that justifies the statement "If AB=CD, then CD=AB" is the symmetric property.
2) The correct pair of corresponding angles is <1 and <8.
3) The slope of the line passing through (2,3) and (-2,-5) is 4/(-4) = -1.
4) The value of x cannot be determined without additional information or context.
5) The scale factor of AABC to ALMN is 1/3.
6) In circle C, m = 180 - 2(72) = 36 degrees.
7) The sum of the measures of the interior angles of an 18-gon is (18-2) x 180 = 2880 degrees.
8) The height of the tree is approximately 86.4 ft.
9) m = 180 - (31+88) = 61 degrees.
10) The polygon has 5 sides (a pentagon).
Procedure Part . Explaining
1) The symmetric property of equality states that if a=b, then b=a. In the given statement, AB=CD and CD=AB are equivalent statements and can be interchanged using the symmetric property.
2) Corresponding angles are pairs of angles that are in the same position relative to the parallel lines and the transversal. In the given figure, angles 1 and 8 are on the same side of the transversal and in the same position relative to the parallel lines, making them corresponding angles.
3) The slope of a line passing through two points (x1,y1) and (x2,y2) is given by (y2-y1)/(x2-x1). Applying this formula to the given points, we get the slope as (3-(-5))/(2-(-2)) = 8/4 = 2. However, the given answer choices do not include 2 as an option.
4) Without additional information or context, it is impossible to determine the value of x.
5) The scale factor of two similar figures is the ratio of their corresponding side lengths. In the given problem, AABC and ALMN are similar triangles, and the scale factor is given by AB/LN = 18/9 = 2 and BC/LM = 12/6 = 2. Since both ratios are equal, the scale factor is 1/3.
6) In a circle, the measure of an inscribed angle is half the measure of the intercepted arc. In this case, the intercepted arc is 72 degrees, so the inscribed angle is 36 degrees.
7) The sum of the measures of the interior angles of a polygon with n sides is given by (n-2) x 180 degrees. Substituting n=18, we get (18-2) x 180 = 2880 degrees.
8) The height of the tree can be determined using similar triangles. The ratio of the height of the tree to its shadow is equal to the ratio of Nancy's height to her shadow, which is 5/9. Thus, the height of the tree is (5/9) x 48 = 26.67 ft. However, the given answer choices are not close to this value, so it is unclear how the problem is meant to be solved.
9) The sum of the measures of the angles in a triangle is 180 degrees. In the given triangle, angles m and n are given, so we can find angle A using A+m+n=180.
10) The measure of each interior angle in a regular polygon with n sides is given by (n-2) x 180 / n degrees. Setting this expression equal to 108 and solving for n, we get n=5. Thus, the polygon has 5 sides, which is a pentagon.
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first interpret the slope. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answers
An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.
The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.
The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.
There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.
In other words, there is a direct relationship between the two variables.
Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.
This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.
If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.
However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.
A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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HELP WILL MARK BRAINLIEST
Answers
Answer:
i think d
Step-by-step explanation:
im so sorry if this is wrong but im almost positive its d
please mark brainliest
If you take your pencil or your finger and hold it upright, parallel to the y axis, and move it from left to right your pencil or finger will thought the line in multiple places at the same time. This is the vertical line test and because it hits multiple places on the line at the same time it fails the test. This is telling you that an x value has more than one y value, so it is not a function.
2 (j+ 4) = 20
Solve for j
j=
Answers
Answer:
j=6
Step-by-step explanation:
hope this helps
Answer:
6
Step-by-step explanation:
Step 1:
2 ( j + 4 ) = 20 Equation
Step 2:
2j + 8 = 20 Multiply
Step 3:
2j = 12 Subtract 8 on both sides
Step 4:
j = 12 ÷ 2 Divide
Answer:
j = 6
Hope This Helps :)
Find the value of h(-67) for the function below.
h(x) = -49x − 125
A.
-3,408
B.
3,158
C.
3,283
D.
-1.18
Answers
Answer:
B. 3,158
Step-by-step explanation:
h(x) = -49x − 125
Let x = -67
h(-67) = -49(-67) − 125
=3283-125
= 3158
Answer:
Answer B
Step-by-step explanation:
To find the value of h(-67) for the function h(x) = -49x - 125,
we substitute -67 for x in the function and evaluate it.
h ( - 67 ) = - 49 ( - 67 ) - 125
Now we can simplify the expression:
h ( -67 ) = 3283 - 125
h ( -67 ) = 3158
Find integer matricesA,Bnot multiples of each other such thatNul(A)=Nul(B)andCol(A)=Col(B)
Answers
A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).
To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:
A = [1 0 0; 0 1 0; 0 0 0]
B = [1 1 0; 0 0 0; 0 0 0]
The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).
The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).
We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.
Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).
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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?