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3 years ago

13

the coordinates of the endpoints of BC are B(3,2) and C(8,17). Point D is on BC and divides it such that BD:CD is 3:2. What are

the coordinates of D

1 answer:

eduard3 years ago

3 0

Snsjdnsndnxnendndnfbdnxndjdnxjxhsbsbshxhxhdhd

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If f(x) = 4x-3, which of the following is the inverse of f(x)?

GalinKa [24]

Answer:

$\huge\boxed{f^{-1}(x)=\dfrac{x+3}{4}=\dfrac{1}{4}x+\dfrac{3}{4}}$

Step-by-step explanation:

$f(x)=4x-3\to y=4x-3\\\\\text{exchange}\ x\ \text{to}\ y\ \text{and vice versa}\\\\x=4y-3\\\\\text{solve for}\ y\\\\4y-3=x\qquad|\text{add 3 to both sides}\\\\4y-3+3=x+3\\\\4y=x+3\qquad|\text{divide both sides by 4}\\\\\dfrac{4y}{4}=\dfrac{x+3}{4}\\\\y=\dfrac{x+3}{4}\to y=\dfrac{1}{4}x+\dfrac{3}{4}$

5 0

2 years ago

A Survey of 85 company employees shows that the mean length of the Christmas vacation was 4.5 days, with a standard deviation of

GenaCL600 [577]

Answer:

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

Step-by-step explanation:

We have the standard deviations for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 85 - 1 = 84

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 84 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.989.

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.989\frac{1.2}{\sqrt{85}} = 0.26$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.26 = 4.24 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.26 = 4.76 days

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

92% confidence interval:

Following the sample logic, the critical value is 1.772. So

$M = T\frac{s}{\sqrt{n}} = 1.772\frac{1.2}{\sqrt{85}} = 0.23$

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.23 = 4.27 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.23 = 4.73 days

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

8 0

3 years ago

Data show that men who are married, and also divorced or widowed men, earn quite a bit more than men the same age who have never

lozanna [386]

Answer:

Work ethic, is a lurking variable, because the work ethic i.e the number of hours worked overtime of single men is often less, while the length of breaks is often more compared to married, divorced or widowed men.

Step-by-step explanation:

In to gain a better understanding of the above answer we need to known that

Men who are married, widowed, or divorced are usually more committed both in their personal and professional lives because of the responsibility of not only taking care of them self but their family, enabling them to succeed in their careers.

4 0

3 years ago

What does the dotted line in the diagram imply about the number of triangles you can construct from the given information

nekit [7.7K]

Answer:

Step-by-step explanation:A triangle is aptly named: it is composed of three (tri) angles formed by three non-coincident, non-parallel lines. That the lines are non-coincident means they do not overlap, and that they are non-parallel means that each line intersects with every other line. Correspondingly, a triangle also has three sides.

3 0

3 years ago

Can someone answer question 2a and b only please

Mice21 [21]

Answer:

2a) -2

b) 8

Step-by-step explanation:

<u>Equation of a parabola in vertex form</u>

f(x) = a(x - h)² + k

where (h, k) is the vertex and the axis of symmetry is x = h

2 a)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is 6, then

f(6) = 0

⇒ a(6 - 2)² - 6 = 0

⇒ 16a - 6 = 0

⇒ 16a = 6

⇒ a = 6/16 = 3/8

So f(x) = 3/8(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

f(x) = 0

⇒ 3/8(x - 2)² - 6 = 0

⇒ 3/8(x - 2)² = 6

⇒ (x - 2)² = 16

⇒ x - 2 = ±4

⇒ x = 6, -2

Therefore, the other x-axis intercept is -2

b)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is -4, then

f(-4) = 0

⇒ a(-4 - 2)² - 6 = 0

⇒ 36a - 6 = 0

⇒ 36a = 6

⇒ a = 6/36 = 1/6

So f(x) = 1/6(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

f(x) = 0

⇒ 1/6(x - 2)² - 6 = 0

⇒ 1/6(x - 2)² = 6

⇒ (x - 2)² = 36

⇒ x - 2 = ±6

⇒ x = 8, -4

Therefore, the other x-axis intercept is 8

8 0

2 years ago