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3 years ago

Describe linear equation

Mathematics

1 answer:

Ymorist [56]3 years ago

5 0

Answer:

an equation between two variables that gives a straight line when plotted on a graph.

Step-by-step explanation:

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Ms.Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms.Kitts sold

Murrr4er [49]

Answer: $\left \{ {{l=3t+6} \atop {l+t=110}} \right.$

Step-by-step explanation:

Let be "l" the number of CDs Ms.Kitts sold last week, and "t" the number of CDs she sold this week.

You need to remember that:

1. The word "times" indicates a multiplication.

2. The word "more" indicates addition.

Then, the sentence "Last week she sold 6 more than 3 times the number of CDs that she sold this week" can be represented with equation:

$l=3t+6$

According to the information given in the exercise, the sum of the number of CDs Ms. Kitts sold last week and this week is: 110 CDs.

Since a sum is the result an Addition, you can write the following equation:

$l+t=110$

Therefore, the System of equations that can be used to find the number of CDs she sold last week and the number of CDs she sold this week, is:

$\left \{ {{l=3t+6} \atop {l+t=110}} \right.$

7 0

3 years ago

I need help with number 7, and the second part of number 8. Thank you!

tangare [24]

Answer:

7. $\dfrac{\pi }{3},\ \pi ,\ \dfrac{5\pi }{3}$

8. b. $0,\ \dfrac{2\pi }{3},\ \pi,\ \dfrac{4\pi }{3}$

Step-by-step explanation:

7. Solve the equation

$\cos x+\cos 2x=0$

First, note that

$\cos 2x=2\cos^2x-1$

Hence,

$\cos x+2\cos ^2x-1=0$

Use substitution

$t=\cos x,$

then

$2t^2+t-1=0\\ \\D=1^2-4\cdot 2\cdot (-1)=1+8=9\\ \\\sqrt{D}=\sqrt{9}=3\\ \\t_{1,2}=\dfrac{-1\pm 3}{2\cdot 2}=-1,\ \dfrac{1}{2}$

Now,

$\cos x=-1\ \text{or}\ \cos x=\dfrac{1}{2}$

Solve each equation separately for $0\le x$

$\cos x=-1\\ \\x=\pi+2\pi k, \in Z\\ \\\text{only } x=\pi \in [0,2\pi)$

$\cos x=\dfrac{1}{2}\\ \\x=\pm\arccos \dfrac{1}{2}+2\pi k,\ k\in Z\\ \\x=\dfrac{\pi }{3}\ \text{and}\ x=\dfrac{5\pi }{3}$

8. b. Solve the equation

$\sin x+2\sin x\cos x=0$

Rewrite it:

$\sin x(1+2\cos x)=0$

By zero product property,

$\sin x=0\ \text{or}\ 1+2\cos x=0$

Solve each equation separately.

$\sin x=0\\ \\x=\pi k,\ k\in Z\\ \\\text{for}\ x\in [0,2\pi),\ \ \ \ x_1=0\ \ x_2=\pi$

$1+2\cos x=0\\ \\\cos x=-\dfrac{1}{2}\\ \\x=\pm \arccos \left(- \dfrac{1}{2}\right)+2\pi k,\ k\in Z\\ \\x=\dfrac{2\pi }{3}\ \text{and}\ x=\dfrac{4\pi }{3}$

5 0

4 years ago

What's is the square root of -1 -i i -1 1

tankabanditka [31]

Answer:

see explanation

Step-by-step explanation:

The $\sqrt{-1}$ = i

7 0

3 years ago

Read 2 more answers

HELP needed urgently cause this is a huge grade for my school

Annette [7]

Answer:

1.72 2.128 3.8 4.15

Step-by-step explanation:

3 0

3 years ago

HeELPPPPP! Breana is selling tickets to a choral performance. On the first day of ticket sales, she sold 3 senior citizen ticket

Lena [83]

Let S = senior citizen and c = child:

Day 1: 3S + 1C = $38

Day 2: 3S + 2C = $52

Difference between day 1 and 2 in money = 52 - 38 = 14

The only difference in ticket amounts was 1 child ticket, so 1 child ticket cost $14.

Using Day 1, subtract 14 from the total and then divide by 3 to find the price of a senior ticket:

38 - 14 = 24

24 / 3 = 8

A senior citizen ticket cost $8

4 0

3 years ago

Describe linear equation​

Describe linear equation