Let f(x) = 5 sin(x). Describe the graph of each of the following in terms of the graph off.
1. g(x) = 5 sin(x) + 4
2. h(x) = 5 sin(x + 1)
3. k(x) = 20 sin(x) + 10
4. m(x) = 5 sin(4x - 1)
I
Answers
The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.
To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).
1. g(x) = 5 sin(x) + 4:
The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.
2. h(x) = 5 sin(x + 1):
The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.
3. k(x) = 20 sin(x) + 10:
The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.
4. m(x) = 5 sin(4x - 1):
The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.
Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).
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Related Questions
If the piece of paper is 60 inches long and 80 inches wide, how long is the diagonal cut that Zack made?
Answers
Answer:
100
Step-by-step explanation:
square root(L^2 + W^2)
Find the value of x. If necessary, round to the nearest tenth.
5
6
x
Answers
The value of x in the circle using the intersecting secants and tangents equation is 4
How to find the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
The value of x in the circle can be calculated using the intersecting secants and tangents equation
So, we have
6² = x * (x + 5)
When expanded, we have
x² + 5x - 36 = 0
When factored, we have
(x + 9)(x - 4) = 0
Using the zero product property , we have
x = -9 or x = 4
The valiue of x cannot be negative
So, we have
x = 4
Hence, the value of x in the circle is 4
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Solid Geometry
HSG-GMD
1. Examine the 2 cylinders below and explain why the volume to the two
cylinders are the same or explain why the volume of the two cylinder are
different.
Is Sue correct? Explain why.
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___________________________________________________________________
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2. Two stacks of 23 quarters each are shown below. One stack forms a
cylinder but the other stack does not form a cylinder.
Use Cavelieri’s principle to explain why the volumes of these two stacks of
quarters are equal.
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___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Solid Geometry
HSG-GMD
The diagram below shows two figures. Figure A is a right triangular prism and
figure B is an oblique triangular prism.
Use Cavalieri's Principle to explain why the volumes of these two triangular prisms
are equal.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
Answers
1. The two cylinders have the same height and the same cross-sectional area at every point along that height, so they have the same volume. Sue is correct.
2. The two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
3. The two triangular prisms have the same height and the same cross-sectional area at every point along that height, so they have the same volume. This can also be explained using Cavalieri's principle.
How to explain the informationThe two stacks of quarters have the same height and the same cross-sectional area at every point along that height, so they have the same volume.
This can be explained using Cavalieri's principle, which states that two solids have the same volume if they have the same height and the same cross-sectional area at every point along that height.
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Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.
x= ------------
here is the picture if you need it.
Answers
The solution of the equation [tex]\rm 5^{-x/16} = 5[/tex] will be negative 16.
Given that:
Equation, [tex]\rm 5^{-x/16} = 5[/tex]
In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Take log on both sides, then we have
(-x / 16) log 5 = log 5
-x / 16 = 1
x = -16
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The probability of randomly drawing a light blue crayon from a box of crayons is 1/24.
What are the odds against drawing a light blue crayon?
Answers
The answer is 23/24
there are 23 out of the 24 crayons that arent light blue and that gives you the odds against the light blue crayon
What value for the constant C makes Z=4 PLEASE HELP
Answers
The value of c that makes z = 4 an extraneous solution is c = -1.
We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.
First, we substitute z = 4 into the equation:
√ (3/2 x + 10) = cz + 8
√ (3/2 x + 10) = c(4) + 8
√(16) = 4c + 8
4 = 4c + 8
4c = -4
c = -1
Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.
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please solve to the nearest 10th
Answers
The value of the sides are;
c = 35. 5, y = 32. 2, <H = 65 degrees
Option D
How to determine the valueWe have that the ratios of the trigonometric identities are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
From the information given, we have that;
Using sine identity
sin 25 = 15/c
cross multiply the values, we get;
c = 35. 5
Then, using tan identity;
tan 25 = 15/y
cross multiply
y = 32. 2
Sum of angles in a triangle is equal to 180 degrees.
Then, we have that;
90 + 25 + <H = 180
collect the terms
<H = 65 degrees
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Which value of h makes the inequality 4h + 3 < 10 true? A: h = -2 B: h =2 C: h = 4 D: h = 7
Answers
Answer: A h = - 2
Step-by-step explanation:
Substitute -2 for h
4(-2) + 3 < 10
-8 + 3 < 10
-5 < 10 true
6) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many total minutes did it take Stacy to run the 8 miles?
Answer Options
36 1/2
72 1/2
81
54 1/4
Answers
Answer:
72 1/2
Step-by-step explanation:
so, she ran 2 miles in 8 3/4 minutes each.
3 miles in 9 minutes each.
2 miles in 9 1/4 minutes each.
1 mile in 9 1/2 = 9 2/4 minutes.
in total that means
2×(8 3/4) + 3×9 + 2×(9 1/4) + 9 2/4 =
= 16 6/4 + 27 + 18 2/4 + 9 2/4 =
= 16 + 27 + 18 + 9 + 6/4 + 2/4 + 2/4 =
= 70 + 10/4 = 70 + 2 + 2/4 = 72 2/4 = 72 1/2 minutes
Mark was suspicious that his wife was unfaithful to him. He obtained blood samples from all family members. When the results came back, it turned out that Mark has blood type AB. His wife has blood type O. They have three children. One child has blood type A. One child has blood type B. One child has blood type O. “You cheated!” Mark yells accusingly. Is he right to make such a statement or does he owe his wife an apology? Show your work with Punnett Squares or with a written explanation
Answers
Mark's accusation is incorrect. Based on the blood type combinations, it is possible for the children to have the observed blood types without any infidelity. Mark owes his wife an apology for the false accusation.
Mark has blood type AB, which means he has one A allele and one B allele.
Mark's wife has blood type O, which means she has two O alleles.
One child has blood type A, indicating they have inherited one A allele.
One child has blood type B, indicating they have inherited one B allele.
One child has blood type O, indicating they have inherited two O alleles.
Child 1:
Mark's allele: A
Wife's allele: O
Possible combinations: AO
Child 2:
Mark's allele: B
Wife's allele: O
Possible combinations: BO
Child 3:
Mark's allele: A or B (since Mark has AB blood type)
Wife's allele: O
Possible combinations: AO or BO
From the possible combinations, we can see that it is possible for the children to have blood types A, B, and O without any issues.
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Find the unlabeled side length. If necessary, round your answer to the nearest
hundredth (two decimal places).
5
12
Answers
The unlabeled side length for this problem has the measure given as follows:
13.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side, is equals to the sum of the squares of the lengths of the other two sides.
Hence the equation for the theorem is given as follows:
c² = a² + b².
In which:
c > a and c > b is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The sides for this problem are given as follows:
5 and 12.
Hence the measure of the hypotenuse is obtained as follows:
h² = 5² + 12²
h² = 169
h = 13.
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What is the value of x?
Use the rules of special right triangles to find x.
Answers
The value of the length x is 1.5
How to determine the valueUsing the sine trigonometric identity, we have that;
sin 45 = y/6√2
cross multiply the values, we have that;
y = 1/√2 × 6/√2
Multiply the values, we get;
y = 6/2
Divide the values
y = 3
Then, using the cosine identity, we get;
cos 60 = x/3
Find the cosine value and cross multiply, we get;
x = 0.5(3)
Now, multiply the values, we get;
x = 1.5
Hence, the value of the length is 1.5
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can you help me solve this
Answers
The division of the polynomial 3x³ - 2x² + x - 4 by x + 3 is:
Quotient: 3x² + 11x + 34
Remainder: -106/(x + 3)
What is synthetic division?When dividing a polynomial by a linear binomial of the form (x - c) or (x + c), where "c" is a constant, the process is known as synthetic division. This streamlined method of polynomial long division offers a faster and clearer method for dividing polynomials by linear factors.
The process of synthetic division involves arranging the coefficients of the polynomial in descending order and performing a sequence of simple arithmetic operations.
The result of the synthetic division is:
[tex]Quotient: 3x^2 + 11x + 34[/tex]
Remainder: -106/(x + 3)
Kindly find the step by step analysis below.
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Adam wants to plant flowers in a triangular plot. He has three lengths of plastic edging that measures 8 feet, 15 feet, and 17 feet. Determine whether these pieces fit for a right triangle. Explain.
Answers
Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.
What is Pythagorean triple?Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.
In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.
In doing so, we would use the previous formula given as;
x² = y² + z²
In a Pythagorean triple, the largest side is the hypothenuse.
17² = 8² + 15²
289 = 64 + 225
289 = 289
The numbers are equal and they're Pythagorean triple.
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Write the answer to Kiran's question using mathematical notation. (the money kiran)
Answers
-12x stands for the amount Kiran takes out each month.
B. any value of x that is less than or equal to 6.25 will work for Kiran.
c. One can use x ≤ 6.25 to show all the values that would work for Kiran.
d. The answer to Kiran's question can be written using mathematical notation as:
Kiran can be able to take out a maximum of $6.25 every month to make sure that he has at least $25 in the account a year from that time now.
What is the statement about?Since the inequality is -12x + 100 ≥ 25, the term -12x stands for the amount Kiran takes out each month. It is seen as a negative value because it stands for the monthly withdrawals from the said account.
b. To find values of x that would work for Kiran, it can be done by:
-12x + 100 ≥ 25.
-12x + 100 ≥ 25
So, subtract 100 from both sides:
-12x ≥ 25 - 100
-12x ≥ -75
Then divide both sides by -12 ( dividing by a negative number changes the inequality sign) Hence it will be:
x ≤ (-75) / (-12)
x ≤ 6.25
So, any value of x that is less than or equal to 6.25.
c. One can use x ≤ 6.25 to show all the values that would work for Kiran. based on the fact that:
Kiran requires to have at least $25 in the account a year from now, he cannot withdraw more than $6.25 per month. If he withdrew more than that, he would not have more money left in the account after a single year.
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See text below
Kiran has $100 saved in a bank account. (The account doesn’t earn interest.) He asked Clare to help him figure out how much he could take out each month if he needs to have at least $25 in the account a year from now.
a. Clare wrote the inequality -12x + 100 ≥ 25, where x represents the amount Kiran takes out each month. What does -12x represent?
b. Find some values of x that would work for Kiran.
c. We could express all the values that would work using either x ≤ _ or x ≥ _. Which one should we use?
d. Write the answer to Kiran’s question using mathematical notation.
Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake. How much space does Lacey's mom cover in frosting?
Answers
Answer:
220 in.²
Step-by-step explanation:
top face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²
bottom face - rectangle: A = LW = 9 in. × 2 in. = 18 in.²
left face - rectangle: A = LW = 12 in. × 2 in. = 24 in.²
right upper face - rectangle: A = LW = 8 in. × 2 in. = 16 in.²
right lower face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²
middle horizontal face - rectangle: A = LW = (9 - 4) in. × 2 in. = 10 in.²
front L-shaped face - 2 rectangles: A = (12 × 4 + 5 × 4) in.² = 68 in.²
back L-shaped face - same as front L-shaped face: A = 68 in.²
total surface area = (8 + 18 + 24 + 16 + 8 + 10 + 68 + 68) in.²
total surface area = 220 in.²
Jenny wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.
Area
()
y12345678910x1234567890
Length ()
Write your answers as inequalities, using or as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.
look at picture
Answers
The domain and range of a function for the area of a rectangle indicates;
(a) Range; 0 ≤ y < ∞
(b) Domain; 0 ≤ x < ∞
What is a function?A function is a definition or rule that maps the values of an input unto the values of the output variables.
The area of a rectangle, A = Length, L × Width, W
Therefore;
The area of a rectangle is directly proportional to the width of a rectangle
A ∝ W
The graph of the area to the length of the width of the rectangle indicates that we get;
(a) The domain is the set of the possible x-values of the function
The proportional relationship between the area and the width of a rectangle indicates;
The domain is; 0 ≤ x < ∞
(b) The range is the set of the possible output values of the graph, which is the set of the y-values
The proportional relationship between the area, y and the width, x , the range is; 0 ≤ y < ∞
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How many faces dose a dodecahedron have
Answers
Answer:12 faces and 20 vertices
Step-by-step explanation:
Dodecahedron:- The three-dimensional geometric geometry of a dodecahedron comprises 20 vertices, 30 edges, and 12 flat faces.
Each face is a regular pentagon, with five equal-length sides and five equal-sized angles. One of the five Platonic solids, regular, convex polyhedrons with identical regular polygon faces and equal angles between them, the dodecahedron is one of these regular, convex polyhedrons. The dodecahedron is frequently utilised in architecture, design, and the arts because of its great degree of symmetry.
A dodecahedron has 12 faces.
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Find the measure of Zb.
←
Zb=
Blank 1:
76 a
104/b
Answers
∠b and 76° are alternate angles. They are equal.
So, m∠b = 76
That's it :)
mr.james is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches
Answers
The equation that can be used to calculate the base areas of the rectangular prisms is B = V/6
Calculating the equation can be used to find B, the area of the base with volume VFrom the question, we have the following parameters that can be used in our computation:
Volume of rectangular prisms
The volume of rectangular prisms is calculated as
V = Bh
Where
B = Base area
h = height
Given that
h = 6 inches,
We have
V = B * 6
Divide both sides by 6
B = V/6
This means that the the equation to calculate the base areas is B = V/6
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Complete question
Mr. James is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches
Which equation can be used to find B, the area of the base with volume V
Cylinder A has radius r, height h, and a volume of 10% cubic units.
Cylinder B has twice the radius and twice the height.
B
Choose 1 answer:
What is the volume of cylinder B?
10 cubic units
20
cubic units
40% cubic units
2r
80% cubic units
2h
Answers
The volume of cylinder B include the following: D. 80π cubic units.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius of cylinder B = 2r
Height of cylinder B = 2h
By substituting the parameters, we have the following:
Volume of cylinder B = π × (2r)² × 2h
Volume of cylinder B = π × 4r² × 2h
Volume of cylinder B = π × 8r²h
Volume of cylinder B = 8 × πr²h
Volume of cylinder B = 8 × 10π
Volume of cylinder B = 80π cubic units.
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A photographer has been commissioned to take a series of photographs of a rocket being launched from the Kennedy Space Center in Florida. They have positioned their camera at (B) and the launching pad of rocket (A) is 300 meters. The camera must keep the rocket in sight and therefore its angle of elevation t must change with the height x of the rocket.
Find angle t as a function of the height x.
Find angle t in degrees when x is equal to 150, 300, and 600 meters. (approximate your answer to 1 decimal place).
Graph t as a function of x.
Explain the steps you took to arrive at your answer with at least 3 complete sentences.
Answers
After considering the given data we conclude that angle t as a function of the height x is θ = tan⁻¹ (x/300), and angle t in degrees when x is equal to 150, 300, and 600 meters is 63.4°, the graph represent a curve when drawn.
The angle of elevation of the camera can be evaluated by
θ=tan⁻¹(x/2000)
Here, x = height of the rocket.
Hence, the angle t as a function of the height x is given by:
θ = tan⁻¹ (x/300)
To evaluate the angle t in degrees when x is equal to 150, 300, and 600 meters, we stage these values into the equation above:
θ = tan⁻¹ (150/300) = 26.6° (approximate to 1 decimal place)
θ = tan⁻¹ (300/300) = 45° (approximate to 1 decimal place)
θ = tan⁻¹ (600/300) = 63.4° (approximate to 1 decimal place)
To graph t as a function of x, we can plot the values of θ for different values of x. The graph will be a curve that starts at 0° when x=0 and increases as x increases.
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Please help as soon as possible
Answers
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
We have,
Recall the trigonometric identities:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))
Using these identities, we can find the exact values of the expressions given.
(a) Sin (α + β)
sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 - 8/25
= (-6√5 - 8)/25
(b) Cos (α + β)
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)
= -6/25 + 4√5/25
= (4√5 - 6)/25
(c) Sin (α - β)
sin(α - β) = sin(α)cos(β) - cos(α)sin(β)
= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 + 8/25
= (-6√5 + 8)/25
(d) tan (α - β)
tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))
= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)
= (9√5/5)/(1 - 4/5√5)
= (-9√5 + 45)/4
Therefore,
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
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What is the value of S?
Answers
The value of s in the circle is 11.
We have,
When two chords in a circle have the same arc length intercepted by the chords, it means that the distances from each endpoint of the chords to the center of the circle are equal.
Now,
The arc length XY and WZ are the same.
This means,
Chord XY and Chord WZ are equal.
Now,
2s = s + 11
Solve for s.
2s - s = 11
s = 11
Thus,
The value of s in the circle is 11.
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Show all work and/or explain your reasoning. Please help:)
Answers
To make both triangles equal, their corresponding angles must be equal and when x = 106 degrees, the second angle in triangle 2 is equal to the third angle in triangle 1, which refutes Terry's claims.
What value of x will refute Terry's claims? Show all workTo determine the value of x that refutes Terry's claims, we need to examine the angles of the triangles and find a valid configuration where triangle 1 is similar to triangle 2.
In triangle 1, the given angles are 18 degrees and 96 degrees. The third angle can be found using the property that the sum of the angles in a triangle is always 180 degrees:
Third angle in triangle 1 = 180 - (18 + 96) = 180 - 114 = 66 degrees.
let's find the value of x that will make both triangles similar to one another or their corresponding angles to be equal.
Since we already know one angle in triangle 2 is 8 degrees, we can find the second angle as follows:
Second angle in triangle 2 = 180 - (8 + x) = 180 - 8 - x = 172 - x degrees.
To refute Terry's claims, we need to find a value of x such that the second angle in triangle 2 (172 - x degrees) is equal to the third angle in triangle 1 (66 degrees).
Setting up the equation:
172 - x = 66
Solving for x:
172 - 66 = x
106 = x
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Which of the following sets of ordered pairs represents a function? {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)} {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)} {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)} {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
Answers
The required set of ordered pairs that represent a function is {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}. Option A is correct.
Given functions,
A= {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}
B= {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)}
C = {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)}
D = {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
The other sets have repeated x-values with different y-values, which violates the definition of a function where each x-value can only have one corresponding y-value.
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Answer: The awnser is D
Step-by-step explanation: Hope this helps
May someone please help me find the domain and range thank you for the help
Answers
The domain and the range of the table of values are Domain = {-15, 0, 9, 33, 44, 45} and Range = {21, 33, 57, 15, 97, 46}
Calculating the domain and range of the table of values?From the question, we have the following parameters that can be used in our computation:
The table of values
The above table of values can be represented as a list of ordered pairs
The rule of a table of values is that
The domain is the x valuesThe range is the f(x) valuesusing the above as a guide, we have the following:
Domain = {-15, 0, 9, 33, 44, 45}Range = {21, 33, 57, 15, 97, 46}Read more about domain and range at
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1. What properties of quadratic functions cause this "death ray" effect?
2. Using the diagram below, what is the point called where the sun's rays are concentrated? Will the "death ray" always hit the same spot? Why?
2. Could this property of quadratic functions be helpful in a different situation? Explain
Answers
The properties of quadratic functions cause this "death ray" effect is discussed below.
The "death ray" effect refers to the phenomenon where a quadratic function appears to have a sharp point or vertex that shoots off to infinity in a graph. This effect is caused by the properties of quadratic functions, specifically:
The degree of the quadratic function: Quadratic functions have a degree of 2, which means they have a leading term that is a squared variable (x²). This leads to a graph that is a parabola.
The coefficient of the squared term: The coefficient of the squared term in the quadratic function determines the shape of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.
However, when the coefficient of the squared term is negative (a < 0), the graph of the quadratic function opens downward, and the vertex represents the maximum point of the parabola.
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What is the square root of 35*35*35?
Answers
Answer:
Step-by-step explanation:
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The square root of (35 x 35 x 35) is approximately 207.57.
The square root of (35 x 35 x 35) can be found by simplifying the expression under the radical sign:
√(35 x 35 x 35) = √(35³)
On simplifying 35³ to get:
√(35³) = √(42,875) ≈ 207.57
Therefore, the square root of (35 x 35 x 35) is approximately 207.57.
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What function represents the same relationship
H(x)=-4+7
H(x) =-22x+1.75
H(x)=4x+1.75
H(x)=1.75x-4
Answers
The linear function that is modeled by the given table is:
y = -4x + 7
How to find the linear function represented by the table?A general linear function is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-11, 51) and (-5.5, 29)
Then the slope is:
a = (29 - 51)/(-5.5 + 11)
a = -4
Then the linear function is:
y = -4x + b
We know that when x = -5.5, the value of y is 29
29 = -4*-5.5 + b
29 = 22 = b
29 - 22 = b
7 = b
The linear function is:
y = -4x + 7
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