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

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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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

The unlabeled side length for this problem has the measure given as follows:

13.

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:

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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The domain and range of a function for the area of a rectangle indicates;

(a) Range; 0 ≤ y < ∞

(b) Domain; 0 ≤ x < ∞

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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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

∠b and 76° are alternate angles. They are equal.

So, m∠b = 76

That's it :)

-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.

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.

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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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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Answer: A h = - 2

Step-by-step explanation:

Substitute -2 for h

4(-2) + 3 < 10

-8 + 3 < 10

-5 < 10 true

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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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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Answer:

Step-by-step explanation:

7247.1977343

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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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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The value of the length x is 1.5

Using 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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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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Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.

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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The linear function that is modeled by the given table is:

y = -4x + 7

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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The value of x in the circle using the intersecting secants and tangents equation is 4

From 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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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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The division of the polynomial 3x³ - 2x² + x - 4 by x + 3 is:

Quotient: 3x² + 11x + 34

Remainder: -106/(x + 3)

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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The equation that can be used to calculate the base areas of the rectangular prisms is B = V/6

From 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

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}

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

using the above as a guide, we have the following:

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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.

To 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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Answer:

100

Step-by-step explanation:

square root(L^2 + W^2)

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

The value of the sides are;

c = 35. 5, y = 32. 2, <H = 65 degrees

Option D

We 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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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

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.

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.

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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The volume of cylinder B include the following: D. 80π cubic units.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

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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