All categories

3 years ago

4. Explain and correct the error made by a student who simplified this expression.

Mathematics

1 answer:

Fiesta28 [93]3 years ago

3 0

Answer:

I notice that the first equation has a 7x, term and the second equation has a -7x term. These terms will cancel if we add the equations together—that is, we'll eliminate the the x terms:

Step-by-step explanation:

2y+7x= -5 + 5y-7x=12

You might be interested in

For a science project, 3/4 of the students chose to make a poster and 0.25 of the students wrote a report. Rosa said that more s

Viktor [21]

She’s right because .25 converted into a fraction is 1/4 and 3/4 is greater than 1/4

3 0

3 years ago

Save me the headache

maxonik [38]

$(9\sin2x+9\cos2x)^2=81$

Taking the square root of both sides gives two possible cases,

$9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1$

$9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1$

Recall that

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

If $\alpha=2x$ and $\beta=\dfrac\pi4$ , we have

$\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}$

so in the equations above, we can write

$\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1$

Then in the first case,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi$

(where $n$ is any integer)

$\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi$

$\implies x=n\pi\text{ or }\dfrac\pi4+n\pi$

and in the second,

$\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}$

$\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi$

$\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi$

$\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi$

Then the solutions that fall in the interval $[0,2\pi)$ are

$x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4$

5 0

3 years ago

Read 2 more answers

How many 3 digit numbers can you make using these numbers: 4,2,9 (numbers can be reapeated)

bogdanovich [222]

Answer:

You can make 27 different 3 digit numbers

Step-by-step explanation:

Since we can use 3 different numbers this means that each of the 3 digits can be one of the 3 numbers (4,2,9). This means that there are 3 different values for the first digit, 3 different values for the second digit, and 3 different values for the third digit, which mean that we can make 3 x 3 x 3 different 3 digit numbers (we took the number of possible values for each digit and multiplied them together.

3 x 3 x 3 = 27

8 0

3 years ago

For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you subs

tatiyna

$-x-2y=-4 \\ 3x+y=12 \\ \\ \hbox{the first equation:} \\ -x-2y=-4 \ \ \ \ \ \ |+2y \\ -x=2y-4 \ \ \ \ \ \ \ \ |\times (-1) \\ x=-2y+4$

The expression you would substitute for x is -2y+4. The answer is d.

4 0

4 years ago

Jacob is a plumber. Due to increased material costs, he puts all his prices up by 7%. He now chargers R320 per hour for her serv

Lorico [155]

Answer:

R290.1

Step-by-step explanation:

Let

x = charge before he put his prices up

New charge = R320

Percentage increase in price = 7%

x + 7% of x = 320

x + 0.07 * x = 320

x + 0.07x = 320

1.07x = 320

x = 320/1.07

x = 299.06542056074

Approximately

x = R290.1

Charge before he put his prices up = R290.1

4 0

3 years ago