The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 16 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

To convert miles to feet, we need to multiply the number of miles by the number of feet in one mile. There are 5,280 feet in one mile. So, to find out how many feet Rachel ran, we can multiply 3 miles by 5,280 feet/mile:

3 miles x 5,280 feet/mile = 15,840 feet

Therefore, Rachel ran 15,840 feet. Answer: 15,840 feet.

Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

Answer:

The discount is $8.55, which is option C.

Step-by-step explanation:

To find the discount, we need to calculate 20% of the original price:

Discount = 20% x $42.75

Discount = $8.55

Therefore, the discount is $8.55, which is option C.

The fourth term of the sequence with the definition of functions a₁ = 5 and aₙ = 2aₙ₋₁ + 3 is 61.

Given the following definition of functions

a₁ = 5

aₙ = 2aₙ₋₁ + 3

To find the fourth term of the sequence defined by a₁ = 5aₙ = 2aₙ₋₁ + 3, we can use the recursive formula to generate each term one by one:

a₂ = 2a₁ + 3 = 2(5) + 3 = 13

a₃ = 2a₂ + 3 = 2(13) + 3 = 29

a₄ = 2a₃ + 3 = 2(29) + 3 = 61

Therefore, the fourth term of the sequence is 61.

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Answer:

If you deposit $1000 each year into an account earning 8% compounded annually, you will have $13,366.37 in the account in 10 years. Using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years, we can calculate the amount. Plugging in the values, we get A = 1000(1 + 0.08/1)^(1*10) = $2,159.15. Therefore, the total amount after 10 years will be $13,366.37, which is the sum of the principal and the interest earned.

Given,

Annual deposit = $1000

Rate = 8% compounded annually

Time(n) = 10 year

Amount = ?

As we know the formula ,

Amount = P(1+r/100)ⁿ

Amount = 1000(1+8/100)¹⁰

Amount = 1000(1+0.08)¹⁰

Amount =1000(1.08)¹⁰

Amount = 1000 × 2.15892

Amount = $2158.92

Hence, amount in 10year will be $2158.92

The graph of f(x) is a parabola that opens downward and has a vertex at (-3/2, 3/4), while the graph of g(x) is a parabola that opens upwards and has a vertex at (-1/2, 7/4). They both intersect at the point (-3/2, -5/4).

Vertex is a mathematical term used to describe the point where two lines or line segments meet. It is the point of intersection for two or more lines. In a two-dimensional plane, a vertex is the point that marks the beginning and end of a line segment. In a three-dimensional plane, a vertex is the point of intersection of three or more lines. A vertex can also refer to a corner, such as the vertex of a triangle or a cube. In graph theory, a vertex is a node, or point, in a graph. Vertex can also refer to the highest point of a graph, such as the vertex of a parabola.

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Answer:

Step-by-step explanation:

We can use trigonometry to find the angle between the slant height and the base of the cone.

The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).

Using the Pythagorean theorem, we can find the height of the cone:

height^2 = (slant height)^2 - (radius)^2

height^2 = (4.70 cm)^2 - (1.65 cm)^2

height^2 = 19.96 cm^2 - 2.72 cm^2

height^2 = 17.24 cm^2

height = sqrt(17.24) cm

height = 4.15 cm (rounded to two decimal places)

Now we can use trigonometry to find the angle between the slant height and the base of the cone.

tan(angle) = opposite / adjacent

tan(angle) = height / radius

tan(angle) = 4.15 cm / 1.65 cm

tan(angle) = 2.515

Taking the inverse tangent (or arctan) of both sides, we get:

angle = arctan(2.515)

angle = 70.32 degrees (rounded to two decimal places)

Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.

It switches between negative and positive every 40 seconds.  it switches between positive and negative every 80 seconds. So correct statements are B and E.

Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.

Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.

As a result, every 40 seconds it alternates between negative and positive.

B is accurate.

We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.

As a result, every 80 seconds it alternates between positive and negative.

E is accurate.

The complete question is:

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The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:

Balance of the first account with simple interest:

FV = P(1 + rt)

FV = $600(1 + 0.075 x 5)

FV = $825

Balance of the second account with compounded interest:

FV = P(1 + r)^n

FV = $900(1 + 0.06)^5

FV = $1,286.87

Total balance = $825 + $1,286.87

Total balance = $2,111.87

The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.

The sum of the two functions  f(x) + g(x)  is  (x+2)/(x^2 - 9) + 11/(x^2 + 3x)

(a) To find f(x) + g(x), we simply add the two functions together:

f(x) + g(x) = (x+2)/(x^2 - 9) + 11/(x^2 + 3x)

(b) To determine the excluded values, we need to look for values of x that make the denominators of the two functions equal to zero. The denominators are:

x^2 - 9 and x^2 + 3x

Setting these equal to zero and solving for x, we get:

x^2 - 9 = 0 => x = ±3

x^2 + 3x = 0 => x(x+3) = 0 => x = 0 or x = -3

Therefore, the excluded values are x = ±3 and x = 0.

(c) To classify the type of discontinuity at each of the excluded values, we need to examine the behavior of the function as x approaches these values.

At x = ±3, the denominators of both functions become zero, which means that the function is undefined at these values. This creates a vertical asymptote, which is a type of infinite discontinuity.

At x = 0, the denominator of g(x) becomes zero, but the denominator of f(x) does not. This creates a removable discontinuity, because we can define f(0) separately to make the function continuous at this point. Specifically, we can set f(0) = 2/(-9) = -2/9 to remove the discontinuity.

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Answer:

Starting with:

-15 > -11 + w

Add 11 to both sides:

-15 + 11 > w

Simplifying:

-4 > w

Therefore, the solution for the inequality -15 > -11 + w, when solved for w, is:

w < -4

Answer: 82y

Step-by-step explanation:

147y - 65y = 82y

Just perform simple subtraction

Answer:

0.33

Step-by-step explanation:

There are a total of 5 + 15 + 10 + 15 = 45 people in the restaurant.

The probability of selecting a manager or a cook is the sum of the probabilities of selecting a manager and selecting a cook, since these events are mutually exclusive (a person cannot be both a manager and a cook at the same time).

The probability of selecting a manager is 5/45, since there are 5 managers out of 45 people in total.

The probability of selecting a cook is 10/45, since there are 10 cooks out of 45 people in total.

Therefore, the probability of selecting either a manager or a cook is:

P(manager or cook) = P(manager) + P(cook)

P(manager or cook) = 5/45 + 10/45

P(manager or cook) = 15/45

P(manager or cook) = 1/3

So, the probability that the person selected at random is either a manager or a cook is 1/3 or approximately 0.333

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Therefore , the solution of the given problem of angles comes out to be  the engraved angle ACB is 16 degrees in size.

Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.

Here,

A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:

=> Angle ACB = 32 / (1/2)

=> ACB = 16 degree angle

As a result, the engraved angle ACB is 16 degrees in size.

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Answer: 1050$

Step-by-step explanation:

im a math teacher

Answer:

Step-by-step explanation:

I'm sorry, but there seems to be some information missing from your question. Specifically, it is unclear what quantity or angle you want to determine the cosine of.

If you meant to ask for the value of the cosine of an angle given that its sine is 3/4, then we can use the Pythagorean identity to determine the cosine:

sin^2(x) + cos^2(x) = 1

Plugging in sin(x) = 3/4, we get:

(3/4)^2 + cos^2(x) = 1

Simplifying, we have:

9/16 + cos^2(x) = 1

Subtracting 9/16 from both sides, we get:

cos^2(x) = 7/16

Taking the square root of both sides, we get:

cos(x) = ±sqrt(7)/4

Since the sine is positive (3/4 is in the first quadrant), we know that the cosine must also be positive. Therefore:

cos(x) = sqrt(7)/4

I hope this helps! Let me know if you have any further questions.

Let x be the number of pounds needed for 6035 square feet.

We can set up a proportion between the pounds of grass seed and the square feet covered:

5 pounds / 355 square feet = x pounds / 6035 square feet

To solve for x, we can cross-multiply and simplify:

5 pounds * 6035 square feet = 355 square feet * x pounds

30175 = 355x

x = 30175 / 355

x ≈ 85.07

Therefore, approximately 85.07 pounds of grass seed are needed for 6035 square feet

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

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Answer:

[tex] \rm \: f(x) = \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } [/tex]

Differentiating both sides with respect to x

[tex] \rm \dfrac{d}{dx} ( {f}( x) = \dfrac{d}{dx} \bigg( \dfrac{5}{x} + \dfrac{7}{ {x}^{2} } \bigg)[/tex]

Using u + v rule

[tex] \rm \: {f}^{ \prime} x = \dfrac{d}{dx} \bigg( \dfrac{5}{x} \bigg) + \dfrac{d}{dx} \bigg( \dfrac{7}{ {x}^{2} } \bigg)[/tex]

[tex] \rm \: {f}^{ \prime} x = 5. \dfrac{d}{dx} ( {x}^{ - 1} ) + 7. \dfrac{d}{dx} ( {x}^{ - 2} )[/tex]

[tex] \rm \: {f}^{ \prime} x = 5.( - 1. {x})^{ (- 1 - 1)} + 7.( - 2. {x})^{ - 2 - 1} [/tex]

[tex] \rm \: {f}^{ \prime} x = { - 5x}^{ - 2} { - 14x}^{ - 3} [/tex]

[tex] \rm \: {f}^{ \prime} x = - \dfrac{5}{ {x}^{2} } - \dfrac{14}{ {x}^{3} } [/tex]

[tex] \rm \: {f}^{ \prime} x = - \bigg(\dfrac{5}{ {x}^{2} } + \dfrac{14}{ {x}^{3} } \bigg)[/tex]

Hense The required Derivative is answered.

[tex]\boxed{\begin{array}{c|c} \rm \: \underline{function}& \rm \underline{Derivative} \\ \\ \rm \dfrac{d}{dx} ({x}^{n}) \: \: \: \: \: \: \: \: \: \ & \rm nx^{n-1} \\ \\ \rm \: \dfrac{d}{dx}(constant) &0 \\ \\ \rm \dfrac{d}{dx}( \sin x )\: \: \: \: \: \: & \rm \cos x \\ \\ \rm \dfrac{d}{dx}( \cos x ) \: \: \: & \rm - \sin x \\ \\ \rm \dfrac{d}{dx}( \tan x ) & \rm \: { \sec}^{2}x \\ \\ \rm \dfrac{d}{dx}( \cot x ) & \rm- { \csc }^{2}x \\ \\ \rm \dfrac{d}{dx}( \sec x ) & \rm \sec x. \tan x \\ \\\rm \dfrac{d}{dx}( \csc x ) & \rm \: - \csc x. \cot x\\ \\ \rm \dfrac{d}{dx}(x) \: \: \: \: \: \: \: & 1 \end{array}}[/tex]

The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

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Answer:

Step-by-step explanation:

To simplify the expression, we can use the distributive property of multiplication:

(x−3)(2x^2 −5x−5) = 2x^3 −5x^2 −5x −6x^2 +15x +15

Next, we can combine like terms:

2x^3 −5x^2 −6x^2 −5x +15x +15 = 2x^3 −11x^2 +10x +15

Therefore, the simplified polynomial in standard form is 2x^3 −11x^2 +10x +15.

Answer:

A. To find the acceleration, we need to take the derivative of the velocity function with respect to time:

a(t) = v'(t) = 2(pi) - cos(t(pi))

B. To find the minimum acceleration, we need to find the critical points of the acceleration function in the interval [0, 3].

a'(t) = sin(t(pi))

The critical points occur when sin(t(pi)) = 0, which means t = 0, 1, 2, 3. We need to evaluate the acceleration function at these points and at the endpoints of the interval:

a(0) = 2(pi) - cos(0) = 2(pi)

a(1) = 2(pi) - cos(pi) = pi + 2

a(2) = 2(pi) - cos(2pi) = 2(pi)

a(3) = 2(pi) - cos(3pi) = pi - 2

The minimum acceleration occurs at t = 3, with a minimum value of pi - 2.

C. To find the maximum velocity, we need to find the critical points of the velocity function in the interval [0, 2].

v'(t) = 2(pi) - cos(t(pi)) = 0

The critical points occur when cos(t(pi)) = 2(pi). We can solve for t as follows:

cos(t(pi)) = 2(pi)

t(pi) = arccos(2(pi))

t = arccos(2(pi))/pi ≈ 1.58

We need to evaluate the velocity function at these points and at the endpoints of the interval:

v(0) = -sin(0) = 0

v(1.58) ≈ 1.69

v(2) = (2(pi) - 5)(2) - sin(2(pi)) = 4(pi) - 10

The maximum velocity occurs at t = 1.58, with a maximum value of approximately 1.69.

By using the Pythagorean theorem we know that the given triangle is not a right triangle.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2.

The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.

The smallest and most well-known triplets are (3,4,5).

So, we have the values already,

Now, calculate as follows:

3² + 4² = 6²

9 + 16 = 36

25 ≠ 36

Hence, the given triangle is not a right triangle.

Therefore, by using the Pythagorean theorem we know that the given triangle is not a right triangle.

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Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

Answer:

4

Step-by-step explanation:

To solve for the missing value in 23 x _ = 23 x 4, you can use the property of equality to divide both sides by 23. This will give you _ = 4.  Therefore the missing value will be 4.

Hope this helped :)

Answer: the answer is 4

Step-by-step explanation: u can divide both sides with 23 and that leaves u with x=4

Answer:

Step-by-step explanation:

Domain is now called the "source" which means before a change or transformation. In mathematics, the term "source" is often used to refer to the set of all possible inputs or values that can be fed into a function or transformation, before any changes or transformations take place. The set of all possible outputs or resulting values from the function or transformation is called the "range" or "codomain".

Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

The scale factor of PQRS to JKLM is 4/5.

The scale factor of JKLM to PQRS is 5/4.

The value of w, x, and y are 20, 12.5, and 20 respectively.

The perimeter ratio is 4:5.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image(actual figure)

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor of PQRS to JKLM = 15/12

Scale factor of PQRS to JKLM = 5/4 or 1.25.

Scale factor of JKLM to PQRS = 12/15

Scale factor of JKLM to PQRS = 4/5 or 0.8.

For the value of w;

15/12 = 25/w

15w = 12 × 25

w = 20

For the value of x;

15/12 = x/10.

12x = 150

x = 12.5

For the value of y:

15/12 = y/16

12y = 15 × 16

y = 20

Perimeter ratio = 12 : 15 = 4:5

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You will pay a total of $26.40 including the 20% tip.

To calculate the total amount including the 20% tip, you need to add 20% of the meal cost to the original meal cost:

A gratuity or a small amount of money given to someone for their service, such as a waiter or a hairdresser.

A piece of advice or a suggestion given to someone to help them do something better or more efficiently.

A pointed or tapered end of an object, such as the tip of a pen or a needle.

Tip amount = 20% of $22.00 = 0.2 x $22.00 = $4.40

Total amount including tip = $22.00 + $4.40 = $26.40

Therefore, you will pay a total of $26.40 including the 20% tip.

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