What is the length of X

Answer:

y = -2x - 5

Step-by-step explanation:

y = -2x + b

- To find the y-intercept, plug the values of the variables.

5 = -2(-5) + b

5 = 10 + b

- Subtract 10 from both sides.

-5 = b

A statement that best explains whether the data in this table represents a linear or nonlinear function include the following: A. the table represents a linear function because the graph shows a constant rate of change.

In Mathematics and Geometry, the rate of change (slope) of any straight line can be determined by using this mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the rate of change (slope) of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (1.5 - 3)/(-1 + 4) = (1 - 1.5)/(0 - 1)

Rate of change (slope) = -1.5/3 = -0.5/1

Rate of change (slope) = -0.5

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The value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.

Mean value theorem is the theorem which is used to find the behavior of a function.

The function given as,

\(f(x) = 6x^2 - 4x + 2\)

The value of function at 0,

\(f(0) = 6(0)^2 - 4(0) + 2\\f(0)=2\)

Differentiate the given equation,

\(f(x)' = 6\times2x - 4\times1 + 0\\f(x)' = 12x - 4\\f(x)' = 12x -4\)

If the constant c between 1 and 9 such that the average value of the function f(x) on the interval (1,9], then,

\(f(c)'=12c-4\)

Using Lagrange's mean value theorem,

\(f(c)'=\dfrac{f(9)-f(1)}{9-1}\\12c-4=\dfrac{452-4}{9-1}\\12c=54+4\\c=\dfrac{60}{12}\\c=5\)

Thus, the value of constant c between 1 and 9 such that the average value of the function f(x) on the interval [1,9] is equal to is 5.

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Answer:

5.5402

Step-by-step explanation:

First you need to find the average value of the function, you can use a calculator to do that, which you will find is 164.

The questions asks you to find a number between 1 and 9 so that f(c) (which is just f(x)) equals the average value of the function.

Since you already know the average value (164), you can set the equation equal to 164 and solve for x, which should give you 5.5402.

If you want more information: the function equals the average value, which is 164=6x^2-4x+2, is the equation you want to set up and solve for x.

You may get two answers and I can't explain why because I don't understand it that well, just use the one that is in the 1 to 9 range.

The second answer should be negative which is out of the 1 to 9 range, which leaves you with the other number that rounds up to 5.5402

I hope this helps any other struggling students

9514 1404 393

Answer:

  $6190.48

Step-by-step explanation:

The price is now 1 -16% = 84% of the original price (p).

 $5200 = 0.84p

  p = $5200/0.84 = $6190.48

The price before the discount was $6190.48.

The cosine components to discover the aspect of the triangle is given by: c = √[a2 + b2 – 2ab cos C] .

Where a,b and c are the edges of the triangle. The L is a remodel-pair courting among a DT sign and its continuous-frequency remodel this is used notably withinside the evaluation and layout of DT systems. So lifestyles method really that the sum that defines a does now no longer blow up.

This is simple to show for certainly summable sequences. If you are taking the value of the at any factor omega, that is identical to the sum for n that is going from minus infinity to plus infinity of x[n] instances e to the- j omega n in value.Therefore, the Fourier remodel of cosine wave characteristic is, F[cosω0t]=π[δ(ω−ω0)+δ(ω+ω0)].

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If I'm not wrong, then the answer will be:-

Given

• centers A, B, C

• three congruent sides

• have no common points

So, the result is:-

| PQ | + | RS | + | TU | = | QR | + | ST | + | UP |

I hope this answer is correct and helps you.

✍️ By Benjemin ☺️

Using the point-slope form:

⇒ \((y-y0) = m(x-x0)\)

Which require one point (x0,y0) on the line and the slope (m)

Thus let us plug int the value

\((y + 2) = 0(x + 4)\\y + 2 = 0\\y = -2\)

Thus the equation of the line is y = -2

Hope that helps!

Answer:

-20

Step-by-step explanation:

=(9+5-(-6)) (5+(-6))

=(20) (-1)

=-20

Answer:

Step-by-step explanation:

3x+2

i) the original distance when the lighthouse is due West of the ship is 7 km

ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes

iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km

To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:

i) Finding the original distance when the lighthouse is due West of the ship:

The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.

To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:

Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).

ii) Finding the time in minutes when the lighthouse is due West of the ship:

To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:

Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).

To find the time, we can use the formula:

Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).

iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:

We can use the formula for relative velocity to find the distance:

Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)

Using the values we calculated earlier, we have:

Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).

Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.

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Answer: 71 inches

Step-by-step explanation: minus five from 137, which is 132. The divide 132 by2 which is 66. This is Tamika's height. then add 5 inches on to get Lucas' height, wich is 71 inches.

Answer:

The average rate of change of the function over the interval –3 ≤ x ≤ 4 is 2.

Answer:

21.748 mph

Step-by-step explanation:

Answer:

a. 5.53

b. 1.078

c. 0.126

d. 0.109

e. 0.549

f. 0.834

g.  0.451

Step-by-step explanation:

The percentage of the flights that arrive on time, P(x) = 79%

The number of flights in the sample, n = 7 flights

a. The mean of the probability distribution, μ = ∑x·P(x)

Therefore, we have; μₓ = n·p

μₓ = 7 × 79/100 = 5.53

b. The standard deviation, σₓ = √(n·p·(1 - p))

∴ σₓ = √(7 × 0.79 × (1 - 0.79)) ≈ 1.078

c. We have;

p = 0.79

q = 1 - p = 1 - 0.79 = 0.21

By binomial probability distribution formula, we have;

The probability of exactly four, P(Exactly 4) = ₇C₄·p⁴·q³

P(Exactly 4) = 35 × 0.79⁴×0.21³ ≈ 0.12625

d. The probability of less than 4 is given as follows;

P(Less than 4) = ₇C₀·p⁰·q⁷ + ₇C₁·p¹·q⁶ + ₇C₂·p²·q⁵ + ₇C₃·p³·q⁴

∴ P(Less than 4) = 1×0.79^0 * 0.21^7 + 7 * 0.79^1 × 0.21^6 + 21*0.79^2*0.29^5+ 85×0.79^3*0.21^4 ≈ 0.109

The probability of less than 4 is ≈ 0.109

e. The probability that more than 5 is given as follows;

P(More than 5) = ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.549

f. The probability that at least 5 of the flight were on time is given as follows;

P(At least 5) = ₇C₅·p⁵·q² + ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

∴ P(At least 5) = 21×0.79^5 * 0.21^2 + 7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.834

g.  For the probability that no more than 5 of the flights were on time, e have;

P(At most 5) = 1 - P(More than 5)

∴ P(At most 5) = 1 - 0.549 ≈ 0.451.

Answer:

f(g(- 3) ) = - 5115

Step-by-step explanation:

Evaluate g(- 3) then substitute the value obtained into f(x)

g(- 3) = (- 3)² + 6(- 3) - 7 = 9 - 18 - 7 = - 16 , then

f(- 16) = (- 16)³ - 4(- 16)² + 5

        = - 4096 - 4(256) + 5

        = - 4096 - 1024 + 5

        = - 5115

Answer:

See Below

Step-by-step explanation:

The boundary line follows the graph of y = 2x - 4 because it represents the line of maximum or minimum values the graph could take. y = 2x - 4 has a y-intercept of -4 because it is in slope-intercept form. It also has a slope of 2, so to find another point on the line, you can go up two and right one. Also, this inequality has a solid line because it is "less than or equal to" and a solid line represents the values that equal.

Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Explanation:

The graph of y = 5 is the horizontal line through 5 on the y axis. Two points on this line are (0,5) and (1,5).

Similarly, the graph of y = -3 is the same idea, but the horizontal line goes through -3 this time. Two points on this line are (0,-3) and (1,-3)

Let's say we're at (0,5). Directly below this point, on the other line, is (0,-3). The midpoint of (0,5) and (0,-3) is (0,1)

The midpoint of (1,5) and (1,-3) is (1,1)

We form a horizontal line through (0,1) and (1,1). This is the locus of points equidistant from the lines y = 5 and y = -3. It's the middle line halfway between the two given lines. Think of it as the median of the highway (the two shoulders of the highway being y = 5 and y = -3).

So that's why the answer is A) 1 line

------------

Side note: any time we have parallel lines like this, the locus of points equidistant from the two lines is always one single line, and it's the median/middle line as described above. This applies to diagonal parallel lines as well, and vertical parallel lines.

The predicted population in the year 2030 is 10 people

From the question, we have the following parameters that can be used in our computation:

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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Answer:

9.95h + 5  ≤ 125

Step-by-step explanation:

let 'h' = number of hats

The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is

                       multiply \(2\frac{1}{2} * 3\) and then add 3/4.

According to the question we have been given that

The height of the small plant = \(2\frac{1}{2}\) inch

In  1 week the plant grows = \(\frac{3}{4}\) inch

We need to find the height of the small plant after 3 weeks.

For that we will first find how much tall it will be in 3 weeks using unitary method that is,

                              1 week = \(\frac{3}{4}\) inch

                               3 week = \(\frac{3}{4}\)  * 3 inch

                                          = 9/4 inch

Therefore the height of the small plant after 3 weeks will be

                         \(=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}\)

hence the height is 19/4 inch

And the method which will not give the correct number of inches is the first option which is

               multiply \(2\frac{1}{2} * 3\) and then add 3/4.

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The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Answer:

5/11

Step-by-step explanation:

6 × 5

11 × 6

=

30/66

To simplify, do

30 divided by 6 = 5

66 divided by 6 = 11

Giving you the answer, 5/11.

Answer:

Step-by-step explanation:

A graph of the exponential function \(f(n)=37000(1.06)^n\) is shown in the image attached below.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

\(f(x)=a(b)^x\)

Where:

Based on the information provided above, your salary can be modeled or represented by the following exponential function;

\(f(n)=37000(1.06)^n\)

Lastly, we would use an online graphing calculator to plot the given exponential function as shown in the graph attached below.

In conclusion, the rate of change of this exponential function is equal to 1.06.

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Answer:

-136

Step-by-step explanation:

Given :

-17(|8|)

Mod of positive number is positive

So, |8|=8

-17(8)

=-136

Therefore,-17 mod 8 is -136

Answer:

B. v

Step-by-step explanation:

I calculated it logically

Answer:B

Step-by-step explanation:

Answer:

-y= -4x -4

y= 4x +4

slope is 4

Step-by-step explanation: