All categories

4 years ago

Simplify the expression.

Mathematics

1 answer:

Yuri [45]4 years ago

3 0

Answer:

The answer to your question is letter A) cot x

Step-by-step explanation:

$\frac{1 - cot x}{tan x - 1}$

Remember that cot x = $\frac{1}{tan x}$

Then

$\frac{1 - \frac{1}{tan x} }{tanx -1}$

Simplify

$\frac{\frac{tan x - 1}{tan x} }{tan x - 1}$

$\frac{tan x - 1}{tan x (tan x - 1)}$

$\frac{1}{tan x}$

Result

$\frac{1}{tan x} = cot x$

You might be interested in

Solve −5x = 30 I need help ASAP

liq [111]

Answer:

x = -6

Step-by-step explanation:

−5x = 30

Divide each side by -5

-5x/-5 = 30/-5

x = -6

6 0

3 years ago

Read 2 more answers

Complete the number sentence to solve. Three students share 5 feet of ribbon equally. How many feet of ribbon does each student

AlladinOne [14]

Answer:

The answer is that each student gets 1.666667 feet of ribbon

Step-by-step explanation:

8 0

4 years ago

A devastating freeze in California’s Central Valley in January 2007 wiped out approximately 75% of the state’s citrus crop. It t

inna [77]

The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

The linear equation of the function is: $g(P) =22.9P +7$ , while its inverse is: $g^{-1}(c) = \frac{c - 7}{22.9}$ .
The domain is from 0% to 100%, while the range is from 7 to 29.9

Given that:

$c = g(P)$

Input and Output quantity

The input quantity is the percentage of frozen citrus crop, while the output quantity is the cost of box of oranges

Linear Function

The given parameters can be written as:

$(P_1,c_1) = (20\%, 11.58)$

$(P_2,c_2) = (80\%, 25.32)$

Calculate the slope (m)

$m = \frac{c_2 - c_1}{P_2 - P_1}$

So, we have:

$m = \frac{25.32 - 11.58}{80\% - 20\%}$

$m = \frac{13.74}{60\%}$

$m = 22.9$

The equation is then calculated using:

$c =m(P - p_1) + c_1$

So, we have:

$c =22.9(P - 20\%) + 11.58$

$c =22.9P - 4.58 + 11.58$

$c =22.9P +7$

So, the function is:

$g(P) =22.9P +7$

The domain and the range

The domain is the possible input value (i.e. possible values of P).

Because P is a percentage, its possible values are 0% to 100%.

Hence, the domain of the function is: $[0\%,100\%]$

The range is the possible output value (i.e. possible values of c).

When P = 0% and 100%

$c = 22.9 \times 0\% + 7 = 7$

$c = 22.9 \times 100\% + 7 = 29.9$

Hence, the range of the function is: $[7,29.9]$

The meaning of $g^{-1}(12)$

$g^{-1}(12)$ is an inverse equation, where 12 represents the cost of box of oranges.

So, $g^{-1}(12)$ represents the percentage of frozen citrus crop, when the cost is $12.

The inverse formula

We have:

$c =22.9P +7$

Make P the subject

$22.9P = c - 7$

Divide by 22.9

$P = \frac{c - 7}{22.9}$

So, the inverse function is:

$g^{-1}(c) = \frac{c - 7}{22.9}$

This is used to calculate the percentage of frozen citrus crop, when the cost is known.

$g^{-1}(c) = \frac{c - 7}{22.9}$

Substitute 12 for c

$g^{-1}(12) = \frac{12 - 7}{22.9}$

$g^{-1}(12) = \frac{5}{22.9}$

$g^{-1}(12) = 22\%$

Read more about linear equations at:

brainly.com/question/19770987

4 0

3 years ago

Find the distance between P(2, 5 ) and Q( 7 , 3)

Sloan [31]

Answer:

PQ = √(7-2)²+(3-5)²

= √ 5²+(-2)²

= √ 25+4

=√29 units

Hope it helps !

Don't forget to mark me as brainliests.

5 0

2 years ago

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respect

AysviL [449]

Answer:

<NPM + <NZM = 146°

Step-by-step explanation:

Given:

In triangle STU: M, N and P are the midpoints of the line TU, US and ST respectively.

Line UZ is the altitude of the triangle STU

<TSU =71°, <TSU = 36°, <TUS = 73°

From the diagram:

N is the midpoint of line SU and M is the mid point of line UT.

∴ Line NM is parallel to line ST

P is the mid point of line ST and M is the mid point of line UT

∴Line PM is parallel to line SU

N is the mid point of line SU and P is the mid point of line ST

∴Line NP is parallel to line UT

Δ SPN = Δ STU = 36°

<SPN + <NPM + <MPT (Sum of angles in a triangle = 180°)

<UST = <MPT = 71°

36° + <NPM + 71° = 180°

<NPM + 107° = 180°

<NPM= 180°-107°

<NPM= 73°

In ΔSNZ, line SN = line NZ

∴ side SN = side NZ

< NSZ = <NZS = 71°

<MTZ = <MZT = 36°

<NZS + <NZM <MZT = 180° (Sum of angles in a triangle = 180°)

71° + <NZM + 36° = 180°

107° + <NZM = 180°

<NZM = 180° - 107°

<NZM = 73°

<NPM + <NZM =73° + 73°

<NPM + <NZM = 146°

5 0

3 years ago