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3 years ago

What is the midpoint of the segment shown below?

Mathematics

2 answers:

Vaselesa [24]3 years ago

5 0

B. (2, -3). The X value remains the same. -7 + 4 = -3. The Y value in the center of the existing two points is -3

ruslelena [56]3 years ago

5 0

Answer:

option A

$(2,-\frac{3}{2})$

Step-by-step explanation:

we know that

The formula to calculate the midpoint M between two points is equal to

$M (\frac{x1+x2}{2},\frac{y1+y2}{2})$

In this problem we have

$(x1,y1)=(2,-7)$

$(x2,y2)=(2,4)$

substitute the values

$M (\frac{2+2}{2},\frac{-7+4}{2})$

$M (\frac{4}{2},\frac{-3}{2})$

$M (2,-\frac{3}{2})$

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What is the value of c in the interval (5,8) guaranteed by Rolle's Theorem for the function g(x)=−7x3+91x2−280x−9? Note that g(5

jeyben [28]

Answer:

$\displaystyle c = \frac{20}{3}$

Step-by-step explanation:

According to Rolle's Theorem, if f(a) = f(b) in an interval [a, b], then there must exist at least one c within (a, b) such that f'(c) = 0.

We are given that g(5) = g(8) = -9. Then according to Rolle's Theorem, there must be a c in (5, 8) such that g'(c) = 0.

So, differentiate the function. We can take the derivative of both sides with respect to x:

$\displaystyle g'(x) = \frac{d}{dx}\left[ -7x^3 +91x^2 -280x - 9\right]$

Differentiate:

$g'(x) = -21x^2+182x-280$

Let g'(x) = 0:

$0 = -21x^2+182x-280$

Solve for x. First, divide everything by negative seven:

$0=3x^2-26x+40$

Factor:

Zero Product Property:

$x-2=0 \text{ or } 3x-20=0$

Solve for each case. Hence:

$\displaystyle x=2 \text{ or } x = \frac{20}{3}$

Since the first solution is not within our interval, we can ignore it.

Therefore:

$\displaystyle c = \frac{20}{3}$

3 0

3 years ago

The pth percentile is a value such that approximately a. p percent of the observations are less than the value and (100 - p) per

kogti [31]

Answer:

p percent of the observations are less than the value and (100 - p) percent are more than this value.

Step-by-step explanation:

Given : The pth percentile is a value such that approximately

Solution :

Definition : A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls

So, The pth percentile means p percentage of observations in a group of observations falls bellow the value

So, (100-p) percentage of observations in a group of observations falls above the value

So, Option a is true

Hence p percent of the observations are less than the value and (100 - p) percent are more than this value.

5 0

3 years ago

Please can someone help!

Rom4ik [11]

Answer:

51 mph

Step-by-step explanation:

→ The first thing we need is a formula which links speed, distance and time so,

Speed = Distance ÷ Time

Speed = mph

Distance = metres/miles

Time = hours

→ Since we want to work out the average speed of the entire journey we need to first work out the total distance and total time. Using the first sentence of the paragraph, it says that the car travels at an average speed of 45 mph for 40 minutes, we can rearrange the formula to work out the distance so,

Speed = Distance ÷ Time

→ Rearrange to get distance as subject

Distance = Speed × Time

→ Substitute in the values

Distance = 45 × 40

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

40 ÷ 60 = 0.666666667

→ Substitute in the time value multiplied by the speed

Distance = 45 × 0.666666667 = 30

⇒ 30 metres/miles is overall distance for the first part of the journey

→ Now we have to work out the distance for the second part of the journey. State the distance formula.

Distance = Speed × Time

→ Substitute in the values into the distance formula

Distance = 60 × 25

→ Remember that the time is hours but we substituted in minutes so we divide the time value by 60

25 ÷ 60 = 0.416666667

→ Substitute in the time value multiplied by the speed

Distance = 60 × 0.416666667 = 25

⇒ 25 metres/miles is overall distance for the second part of the journey

→ Now we have to add the distance of both the journeys together

25 + 30 = 55

→ Then we add the times of the journey together

40 minutes + 25 minutes = 65 minutes

→ Convert 65 minutes into hours

65 ÷ 60 = 1.08333 hours

→ Substitute both values into the speed = distance ÷ time formula

Speed = 55 ÷ 1.08333 = 50.76923077

→ The question says to round it to the nearest whole number so,

50.76923077 = 51 mph

7 0

3 years ago

What number divided by -7 is equal to -15

steposvetlana [31]

Answer:

$x = -105$

Step-by-step explanation:

What number divided by -7 is equal to -15

∨ ∨ ∨ ∨ ∨

x ÷ -7 = -15

Multiply -7 to both sides:

$\frac{x}{-7}=15$

$x = -105$

3 0

2 years ago

Explain and demonstrate the multiplication of complex conjugates using 2+3i and its complex conjugate. Be sure to discuss all st

krok68 [10]

The product of a complex number and its conjugate is (a + i b) · (a - i b), where a and b are real numbers, and the result for the complex number 2 + i 3 is 13.

<h3>What is the multiplication of a complex number and its conjugate</h3>

Let be a complex number a + i b, whose conjugate is a - i b. Where a and b are real numbers. The product of these two numbers is:

(a + i b) · (a - i b)

Then, we proceed to obtain the result by some algebraic handling:

a · (a + i b) + (- i b) · (a + i b)

a² + i a · b - i a · b - i² b²

a² - i² b²

a² + b²

If we know that a = 2 and b = 3, then the product of the complex number and its conjugate is:

$z\cdot \bar z = 2^{2} + 3^{2}$

$z\cdot \bar z = 13$

To learn more on complex numbers: brainly.com/question/10251853

#SPJ1

6 0

2 years ago