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2 years ago

What are the domain and range of this function

Mathematics

1 answer:

belka [17]2 years ago

3 0

$f(x)=\sqrt{x-7}+9\\\\\text{the domain:}\\x-7\geq0\to x\geq7\\\\\text{the range:}\\\sqrt{x-7}\geq0\ \text{therefore}\ \sqrt{x-7}+9\geq9\\\\y\geq9$

$Answer:\\domain:\ x\geq7\\range:\ y\geq9$

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There are 2 more angles. m angle 7 and m angle 8

Licemer1 [7]

ANSWER:

A and B aren't parallel lines, as the alternate angles aren't equivalent to each other.

For m angle 1 -

Vertically opposite angles are equivalent to each other.

m angle 1 is vertically opposite m angle 4.

Therefore:

m angle 4 = 100

m angle 1 = m angle 4

m angle 1 = 100

For m angle 6 -

Co-interior angles add up to 180°.

m angle 4 and m angle 6 are co-interior angles.

Therefore:

m angle 4 = 100

m angle 4 + m angle 6 = 180

100 + m angle 6 = 180

m angle 6 = 180 - 100

m angle 6 = 80

For m angle 7 -

Vertically opposite angles are equivalent to each other.

m angle 6 is vertically opposite m angle 7.

Therefore:

m angle 6 = 80

m angle 7 = m angle 6

m angle 7 = 80

For m angle 8 -

Corresponding angles are equivalent to each other.

m angle 8 and m angle 4 are corresponding angles.

Therefore:

m angle 4 = 100

m angle 8 = m angle 4

m angle 8 = 100

Hence, the angles are as follows:

m angle 1 = 100

m angle 6 = 80

m angle 7 = 80

m angle 8 = 100

Hope this helps! <3

5 0

2 years ago

13. Find the equations of the straight lines which passes

ipn [44]

9514 1404 393

Answer:

y = 1/2x +2
y = -2x +7

Step-by-step explanation:

The slope of a line is the tangent of the angle it makes with the x-axis. The given line has a slope of -1/3, so the lines we want will have slopes of ...

m1 = tan(arctan(-1/3) +45°) = 0.5 . . . . . using a calculator

m2 = tan(arctan(-1/3) -45°) = -2

Of course, these two lines are perpendicular to each other, so their slopes will have a product of -1: (0.5)(-2) = -1.

We can use the point-slope form of the equation for a line to write the desired equations:

y = m(x -h) +k . . . . . line with slope m through point (h, k)

<u>Line 1</u>:

y = 1/2(x -2) +3

y = 1/2x +2

<u>Line 2</u>:

y = -2(x -2) +3

y = -2x +7

3 0

2 years ago

What is 5 less than the product of 5 and a number is 22 written out in an equation?

masha68 [24]

5y - 5= 22
or
5(y)-5=22

Hope that helps!

6 0

2 years ago

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is th

Sindrei [870]

Answer:

a) 0.0025

b) 0.9975

c) 23.03 minutes

d) 23.03 minutes

Step-by-step explanation:

Let X be the random variable that measures the time waited for a taxi.

If X is exponentially distributed with a mean of 10 minutes,then the probability that you have to wait more than t minutes is

$\large P(X>t) = e^{-t/10}$

1 hour = 60 minutes, so the probability that you wait longer than one hour is

$\large P(X>60)=e^{-6}=0.0025$

Due to the “memorylessness” of the exponential distribution, the probability that you have to wait 10 or less minutes after you have already waited for one hour, is the same as the probability that you have to wait 10 or less minutes

$\large P(X\leq 10)=1-e^{-6}=0.9975$

We want x so that

P(X>x)=0.1

$\large e^{-x/10}=0.1\rightarrow -x/10=ln(0.1)\rightarrow x=-10ln(0.1)=23.03\;minutes$

We want P(X<x)=0.9

$\large 1-e^{-x/10}=0.9\rightarrow e^{-x/10}=0.1\rightarrow x=-10ln(0.1)=23.03\;minutes$

4 0

2 years ago

Darian gets paid $6.35 an hour to help out at his dad's shop. He also mows his neighbor's lawn each week for $25. He earned $119

nevsk [136]

$119.85 is the total amount he earned in 2 weeks
He mows his neighbor's lawn each week for $25...So if he mows for 2 weeks it should be
$25×2=$50
Darian gets paid $6.35 an hour to help out at his dad's shop...
Let X be the number of hours Darian worked at his dad's shop in the two weeks
So we can now make an equation to find X

(X×$6.35)+($25×2)=$119.85
(X×$6.35)+$50=$119.85
X×$6.35=$119.85-$50
X×$6.35=$69.85
X=$69.85÷$6.35
X=11

Therefore the number of hours Darian worked at his dad's shop in those two weeks is 11

4 0

2 years ago

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