Find three consecutive odd integers such that
the sum of four times the first, three times the
second, and two times the third is 167.

Answer:

Step-by-step explanation:

it is A/ this relationship is not a function because only one amount of plant food remains each day.

Answer:

it is A/ this relationship is not a function because only one amount of plant food remains each day.

Step-by-step explanation:

Answer:

the answer to that question is A:3

Answer:

\(4 \frac{1}{4} \)

Step-by-step explanation:

\(5 \frac{2}{3} \times \frac{3}{4} \\ \frac{17}{3} \times \frac{3}{4} \\ 17 \times \frac{1}{4} \)

\( \boxed{Answer{\boxed{\green{= \frac{17}{4} = 4 \frac{1}{4} }}}}\)

Answer:

3.24/2.4=c

Step-by-step explanation:

division

The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).

Harmonic motion is a motion that repeats itself after a certain period of time.

Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.

The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.

Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.

Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.

A simple harmonic motion is a projection of uniform circular motion in a straight line.

The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.

Let's now calculate the values of displacement, velocity, and acceleration.

Displacement, s = A sin (ωt)

Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)

So, s = 3 sin (8 x 1) = 2.68 m (approx)

Velocity, v = Aω cos(ωt)

Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)

Acceleration, a = -Aω2 sin(ωt)

Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)

Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.

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Answer:

Its A

Step-by-step explanation:

common sence

Answer:

DB...hope I helped!

Step-by-step explanation:

Since m1+m2=180 and m1=76, then m2=104

m2=m4, so m4 is also 104

m3=m1, so it is 76

Hope I helped!

Answer:

J.) (-2,-4)

Step-by-step explanation:

It is divided into two sections, a 57-inch piece. The length of one component is double that of the other. The length of the shortest piece wound be 29.

Given that,

It is divided into two sections, a 57-inch pipe. The length of one component is double that of the other.

We have to calculate the shorter piece's length.

Let us take the length of shortest piece as x

The length of longest piece wound be 2x

We can write as,

x+2x=57

3x=57

x=57/3

x=29

The length of largest piece will be 2×29=58

Therefore, The length of the shortest piece wound be 29.

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The situations that best represent the scenario shown in the graph of the quadratic functions, y = x² and y = x² + 3 include the following:

B. "From x = -2 to x = 0, the average rate of change for both functions is negative."

C. "For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function."

D. "The quadratic function, y = x², has an x-intercept at the origin."

In Mathematics, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).

In this context, we can logically deduce that the x-intercepts of the graph of the given equation y = x² is at the origin:

x = (0, 0)

For the the coordinate (2, 7), we would evaluate the quadratic function, y = x² + 3 as follows;

7 = 2² + 3

7 = 4 + 3

7 = 7 (True).

By critically observing the graph of both functions, we can logically deduce that their average rate of change is negative from x = -2 to x = 0.

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The publisher must produce and sell at least 120 books to cover the production costs.

Let's denote the number of books the publisher must produce and sell as 'x'.

The fixed costs per book are $12. Therefore, the total fixed costs for 'x' books will be 12x.

The selling price per book is $18.50. Therefore, the total revenue from selling 'x' books will be 18.50x.

To break even, the production costs must equal the revenue, so we can set up the equation:

12x = 18.50x

Simplifying the equation, we have:

18.50x - 12x = 0

6.50x = 0

Dividing both sides of the equation by 6.50, we get:

x = 0/6.50

x = 0

This implies that the publisher needs to produce and sell at least 0 books to cover the production costs. However, this is not a realistic solution as the publisher must sell some books to generate revenue.

Therefore, we need to consider the next possible integer value for 'x', which is 1. Calculating the costs and revenue for 1 book:

Fixed costs = $12 * 1 = $12

Revenue = $18.50 * 1 = $18.50

Since the revenue ($18.50) is greater than the fixed costs ($12), the publisher would make a profit by selling 1 book.

Hence, the publisher must produce and sell at least 1 book to cover the production costs.

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The measure of an angle if the measures of its two adjacent supplementary angles at up to 100 is 130.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given,

The measures of its two adjacent supplementary angles at up to 100.

We are aware of:

x + y = 180°

x + z = 180°

y + z = 100°

Combining the first two equations:

2x + y + z + 360° For the product of y + Z, substitute 100°.

Since 2x + 100° = 360°, both sides must be reduced by 100°.

Divide both sides by 2 to get 2x = 260°.

x = 130° .

The measure of an angle if the measures of its two adjacent supplementary angles at up to 100 is 130.

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The answer is the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x). The upper bound theorem does not specify any upper bound for the real zeros of (x)

The Lower bound theorem states that "If the terms of a polynomial are arranged in descending order of their degrees, then the absolute value of the quotient of the constant term and the coefficient of the term of the highest degree gives a lower bound for the absolute value of its zeros." Let's examine whether the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x) and whether 3 is an upper bound for the real zeros of (x).

As f(x) = 56 = x + 17x² + 11x + 23Since f(x) is not arranged in descending order of their degrees, we have to rearrange it as follows. 17x² + 11x + x + 23 + 56 = 17x² + 12x + 79 on rearranging the equation we have: 17x² + 12x + 79 = 0Hence the constant term is 79 and the coefficient of the term of the highest degree is 17. Thus, using the lower bound theorem, we can evaluate that a lower bound for the absolute value of the zeros of the polynomial is 79/17 ≈ 4.65 Since -2 is less than the calculated lower bound of 4.65, it is indeed a lower bound for the real zeros of f(x). Now, for (x), the constant term is 0, and the coefficient of the term of the highest degree is 1. Thus, using the upper bound theorem, we can evaluate that an upper bound for the absolute value of the zeros of the polynomial is 1/0, which is equal to infinity. Since infinity is not a number, 3 cannot be an upper bound for the real zeros of (x).

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The surface area of the triangular prism is 152 sq, ft.

A triangular prism is a three-dimensional (3D) object having two identical triangle-shaped faces joined by three rectangular faces. The bases are the triangle faces, while the lateral faces are the rectangular faces. The top and bottom (faces) of the prism are other names for the bases.

The surface area of the triangular prism is given as:

SA = bh + (b1 + b2 + b3)l

Here, b = 6, h = 4, b1 = b2 = 5, b3 = 6 and l = 8.

Substituting the values we have:

SA = (6)(4) + (5 + 5 + 6) (8)

SA = 24 + (16)(8)

SA = 152 sq. ft.

Hence, the surface area of the triangular prism is 152 sq, ft.

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The possible values for the number of tables that the store must sell in order to meet the requirements are 9 and 10.

Let's solve the problem step by step:

The price of each chair is $200, and if 6 chairs were sold, the total value of chairs sold is 6 \(\times\) $200 = $1200.

The store must sell at least $7600 worth of chairs and tables combined. Since we have already sold $1200 worth of chairs, the remaining amount to be sold is $7600 - $1200 = $6400.

The price of each table is $700. To find the possible values for the number of tables, we divide the remaining amount by the price of each table: $6400 / $700 ≈ 9.1428.

Since the number of tables must be a whole number, the possible values for the number of tables are 9 and 10.

Therefore, the possible values for the number of tables that the store must sell in order to meet the requirements are 9 and 10.

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Answer:

72π

Step-by-step explanation:

The computation of the volume of the cone is shown below:

Here The radius of the base is one of the legs, therefore it is 6.

And, The height of the cone represent the other leg, therefore it is also 6.

Now as we know that

The volume of the cone is

= 1 ÷ 3 πr^2h

= 1 ÷ 3π 6^2 6

= π × 36 × 2

= 72π

2.492 is the critical t-value used for calculating a 98% confidence interval with 24 degrees of freedom.

The number of degrees of freedom is equal to the number of sample data that can change, and this number is used to determine the sample data mean. For instance, there are five degrees of freedom in the example presented below. This implies that each of the five data points is equally free to change.

It should be noted that a t-table must be used to look up the value in the t-distribution in order to determine the crucial t-value for a 98% confidence interval with 24 degrees of freedom.

When the sample size is small and the population standard deviation is unknown, the t-distribution is a probability distribution that can be used to calculate population parameters.

The critical t-value for a two-tailed test is the value that the test statistic exceeds with a probability of 0.02 in each tail of the distribution. The essential t-value in this case is 2.492. The right answer is C.

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Step-by-step explanation:

this is the solution of your question

a. There are 2 cycles in the graph.
b. The period of the graph is 360 degrees.
c. The amplitude of the graph is 2.


a. To determine the number of cycles in the graph, we need to count the number of complete repetitions of the pattern. In this case, there are 2 complete repetitions, so there are 2 cycles.

b. The period of a sine graph is the distance it takes to complete one full cycle. In this graph, one full cycle is completed in 360 degrees, so the period is 360 degrees.

c. The amplitude of a sine graph is the distance from the midline to the maximum or minimum point of the graph. In this case, the amplitude is 2 units. y = 2 sin θ.

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Answer:

B

Step-by-step explanation:

Answer:

x^3

Step-by-step explanation:

Answer:

(1) - C, \((3,\frac{\pi}{6})\)

(2) - B, \((0,-2)\)

Step-by-step explanation:

\(\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=\sqrt{x^2+y^2}\\\\\theta=\tan^{-1}(\frac{y}{x})\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Polar to Rect.:}}\\(r, \theta)\rightarrow(x,y)\\\\x=r\cos \theta\\\\y=r \sin\theta\end{array}\right}\)

Note that when doing these calculations, make sure your calculator is in radians mode.

Question #2:

Given:

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} ) \ \text{in} \ (x,y)\)

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} )\\\\\Rightarrow r=\sqrt{(\frac{2\sqrt{2} }{2})^2+(\frac{3}{2})^2} \\\\\Longrightarrow r=\sqrt{\frac{27}{4} +\frac{9}{4} } \\\\\Longrightarrow r=\sqrt{9}\\\\\therefore \boxed{ r=3}\\\\\Rightarrow \theta=\tan^{-1}(\frac{\frac{3}{2}}{\frac{3\sqrt{3} }{2}})\\\\\Longrightarrow \theta=\tan^{-1}(\frac{\sqrt{3} }{3})\\\therefore \boxed{\theta=\frac{\pi}{6} }\)

Thus, the correct option is C.

\(\boxed{\boxed{(3,\frac{\pi}{6})}}\)

Question #3:

Given:

\((2,\frac{3\pi}{2} ) \ \text{in} \ (r,\theta)\)

\((2,\frac{3\pi}{2} ) \\\\\Rightarrow x=(2)\cos(\frac{3\pi}{2})\\\\\Longrightarrow x=(2)(0)\\\\\therefore \boxed{x=0}\\\\\Rightarrow y=(2)\sin(\frac{3\pi}{2})\\\\Longrightarrow y=(2)(-1)\\\\\therefore \boxed{y=-2}\)

Thus, the correct option is B.

\(\boxed{\boxed{(0,-2)}}\)

Answer:

the answer is the second option

Answer:

x = 10 and

\(y = 2 \sqrt{29} \)

Step-by-step explanation:

see the explanation in attachment.

Answer:

Circle the variable.

Use the distributive property when numbers are in front of parentheses.

Combine like terms.

Same side means same operation.

Opposite side means opposite operation.

Step-by-step explanation:

yw;)

Answer

5

Explanation

Twenty divided by the difference of seven and three

In mathematical terms,

20 ÷ (7 - 3)

= 20 ÷ 4

= 5

Hope this Helps!!!