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2 years ago

What must be added to 3x -7 to make x 2 + 4x -1?

Mathematics

1 answer:

Elanso [62]2 years ago

6 0

There is the answer!

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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

2 years ago

Read 2 more answers

Julie has 5 cherry lollipops,1 lime lollipops, and 2 grape lollipops in a bag. She is going to select one lollipop, replace the

Georgia [21]

Answer: $\dfrac{15}{32}$

Step-by-step explanation:

Given : The number of cherry lollipop = 5

The total number of lollipop = 8

the number of lollipops other than grape =6

The probability of selecting a cherry lollipop is given by :_

$\text{P(Cherry)}=\dfrac{5}{8}$

The probability of selecting a lollipop other than grape is given by :_

$\text{P(Other than grape)}=\dfrac{6}{8}$

Since, there is replacement , then the events are independent of each other.

Now, the probability that Julie will select a cherry lollipop and then a lollipop other than grape is given by :-

$\text{P(Cherry and other than grape)}=\dfrac{5}{8}\times\dfrac{6}{8}=\dfrac{15}{32}$

Hence, the required probability = $\dfrac{15}{32}$

3 0

3 years ago

A survey asked people to name their favorite season. The results of the survey showed that 34% said spring and 15% said fall. Wh

max2010maxim [7]

Answer:

D. 29% and 22%

Step-by-step explanation:

The known percentages are 34% and 15%. Add these two together to get 49%. All four choices should add up to 100%. So subtract to find what remains:

100% - 49%

= 51%

We don't actually have enough information to determine the percents for summer and winter. BUT the only answer that adds up to 51% is answer D. 29% and 22%.

8 0

2 years ago

Question 2

Dima020 [189]

Answer:

1 is answer

Step-by-step explanation:

2*3/5*3___6/5

7 0

1 year ago

Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zea

lidiya [134]

<h2>Answer with explanation:</h2>

Given : The proportion of New Zealanders consume five or more servings of soft drinks per week : $\hat{p}= 0.16$

a) The number of survey respondents reported that they consume five or more servings of soft drinks per week = 2006

b) Confidence interval for population proportion (p) :

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = Sample proportion.

n= Sample size.

z* = Critical value.

For n= 2006 , $\hat{p}= 0.16$ and critical value for 95% confidence interval : z* = 1.96

Then , the required confidence interval will be :

$0.16\pm (1.96)\sqrt{\dfrac{ 0.16(1- 0.16)}{2006}}$

$0.16\pm (1.96)\sqrt{ 0.000066999002991}$

$0.16\pm (1.96)(0.00818529186963)$

$0.16\pm 0.0160431720645$

$(0.16-0.0160431720645,\ 0.16+0.0160431720645)$

$(0.143956827935,\ 0.176043172064)\approx(0.144,\ 0.176)$

i.e. A 95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. = $(0.144,\ 0.176)$

c) $(0.144,\ 0.176)=(0.144\times100\%,\ 0.176\times100\%)$

$=(14.4\%,\ 17.6\%)$ 176\times100\%)[/tex]

d) The estimate might be biased because the survey is taken online that means offline New Zealanders are out of consideration.

6 0

2 years ago