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fenix001 [56]
3 years ago
14

Today 4 friends went out for lunch. Their total bill was $24.80, including tax and gratuity. They decided to split the bill equa

lly and each paid with a $10 bill. How much money will each person get back
Mathematics
1 answer:
Advocard [28]3 years ago
6 0

Answer:

each person would getb3 dollars back

Step-by-step explanation:

since each friend pays $10 and there are 4 friends the total is 40 but now you have to do $40.00 minus $25.00 because of tax and gratuity so when you do that you get $15.00 now you have to do 15 ÷ 4 and that equals $3.75 and since you cant divide 75 coins to 4 people we dont add that but now you have your answer each friend gets $3.00

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Verify the identity (tan x + 1)^2 + (tan x-1)^2= 2 sec^2 x
Elina [12.6K]

(\tan x+1)^2+(\tan x-1)^2=2\sec^2x\\\\\text{use}\ \tan x=\dfrac{\sin x}{\cos x}\\\\L_s=\left(\dfrac{\sin x}{\cos x}+\dfrac{\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x}{\cos x}-\dfrac{\cos x}{\cos x}\right)^2\\\\=\left(\dfrac{\sin x+\cos x}{\cos x}\right)^2+\left(\dfrac{\sin x-\cos x}{\cos x}\right)^2\\\\=\dfrac{(\sin x+\cos x)^2}{\cos^2x}+\dfrac{(\sin x-\cos x)^2}{\cos^2x}\\\\\text{use}\ (a\pm b)^2=a^2\pm2ab+b^2

=\dfrac{\sin^2x+2\sin x\cos x+\cos^2}{\cos^2x}+\dfrac{\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{\sin^2x+2\sin x\cos x+\cos^2+\sin^2x-2\sin x\cos x+\cos^2}{\cos^2x}\\\\=\dfrac{2\sin^2x+2\cos^2x}{\cos^2x}=\dfrac{2(\sin^2x+\cos^2x)}{\cos^2x}\\\\\text{use}\ \sin^2x+\cos^2x=1\\\\=\dfrac{2(1)}{\cos^2x}=2\cdot\dfrac{1}{\cos^2x}=2\left(\dfrac{1}{\cos x}\right)^2\\\\\text{use}\ \sec x=\dfrac{1}{\cos x}\\\\=2(\sec^2x)=2\sec^2x=R_s\\\\L_s=R_s\Rightarrow The\ identity

4 0
3 years ago
2,76<br> 5. Rationalize the denominator of the following: 2 root 6 divided by root 2 + root 3
rewona [7]

Answer:

6 √2 -4 √3

Step-by-step explanation:

Here, we want to rationalize the denominator of the following surdic fraction;

2√6/(√2 + √3)

To rationalize this, we have to multiply the numerator and the denominator by the conjugate of the denominator

The conjugate of the denominator is √2 - √3

So, we have the rationalization as follows;

2 √6(√2-√3)/(√2 + √3)(√2-√3)

Thus, we have

(4√3-6 √2)/(-1)

= 6 √2 -4 √3

8 0
2 years ago
What is an equivalent expression to q(2a+1)
kvasek [131]

You can distribute the q to both terms to get

q(2a+1) = q\cdot 2a + q\cdot 1 = 2aq+q

7 0
3 years ago
Read 2 more answers
yolanda makes 3 sweaters a day. she sews 6 buttons onto each sweaters she makes. how many buttons will she sew in 3 day​
KengaRu [80]
Yolanda will sew 54 buttons in 3 days.

If she sews 3 sweaters a day then, by the end of each day she will have 18. After three days she will have 54.

hope this helps and have an awesome day !
4 0
3 years ago
The linear equation y = mx + b contains the point (4, -2) and is perpendicular to the
xenn [34]

A linear equation is represented as: y = mx + b.

The equation of the line is: y =3x - 14

First, we calculate the slope (m) of 6x + 18y = 11

Make y the subject

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Divide by 18

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In y = mx + b

m \to slope

So, the slope of y = -\frac{1}{3}x + \frac{11}{18} is:

m = -\frac 13

Since, the line is perpendicular to 6x + 18y = 11

The slope of the line is:

m_1 = -\frac{1}{m}

So, we have:

m_1 = -\frac{1}{-1/3}

m_1 = 3

The line passes through (4,-2).

So, the equation is:

y =m(x - x_1) + y_1

This gives:

y =3(x - 4) -2

y =3x - 12 -2

y =3x - 14

Hence, the linear equation is:

y =3x - 14

Read more about  at:

brainly.com/question/11897796

7 0
3 years ago
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