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3 years ago

Solve for x with steps.

Mathematics

1 answer:

kiruha [24]3 years ago

8 0

Answer:

no real solution is the answer

If you have to list your extraneous solutions somewhere, that would be x=0.

Step-by-step explanation:

Cool thing here is the radical, the thing with the square root, is already isolate.

So we need to square both sides as a first step. (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)

So upon squaring both sides I get:

x^4+16=(x^2-4)^2

Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it! This gives me:

x^4+16=x^4-8x^2+16

Subtract x^4 and 16 on both sides:

0=-8x^2

Divide both sides by -8

0=x^2

Therefore x=0.

0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.

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You are going to buy doughnuts for your coworkers. You buy 2 boxes of glazed doughnuts for $3.99 each, 3 boxes of chocolate-cove

Georgia [21]

2 x 3.99 = 7.98
3 x 4.49 = 13.47
1 x 4.99 = 4.99
Total: 26.44

50.00 - 26.44 = 23.56

6 0

3 years ago

Read 2 more answers

A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name br

natima [27]

Answer:

Step-by-step explanation:

Given that:

A study is conducted and the study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands.

Thus; we formulate the null and the alternative hypotheses as follows:

The proportion is ; $\frac{64}{100}$ = 0.64

Null hypothesis: ${H_0}:p = 0.64$

The Null hypothesis states that there is no evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

Alternative hypothesis: ${H_a}:p \ne 0.64H$

The Alternative hypothesis states that there is evidence that “the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%”.

The proportion of the population = 0.64

The sample size n = 100

The number of shoppers = 52 stating that the supermarket brand was as good as the national brand

The sample proportion $\hat p = \frac{52}{100}$

$\hat p = 0.52$

The z - value is calculated by the formula:

$z = \dfrac{\hat p-p}{\frac{\sqrt{ p(1-p)}}{100 }}$

$z = \dfrac{0.52-0.64}{\frac{\sqrt{ 0.64(1-0.64)}}{100 }}$

$z = \dfrac{-0.12}{0.048 }}$

z = -2.50

Since z = -2.50

the p-value = 2P(Z ≤ -2.50)

p-value = 2 × 0.0062

The p-value = 0.0124

At significance level, ∝ = 0.05 ; The p-value = 0.0124

According to the rejection rule, if p-value is less than 0.05 then we will reject null hypothesis at ∝ = 0.05

Hence, the p-value =0.0124 < ∝ (=0.05)

According to the reject rule; reject null hypothesis.

Conclusion: There is no evidence at all that the percentage of supermarket shoppers believes that the supermarket ketchup is good as the national brand ketchup differ form 64%.

d) we know that the significance level of ∝ = 0.05

The value ${z__{0.05}}$ is obtained as:

$P\left( {\left| Z \right| \le z} \right) = 0.05$

Now; to determine Z ; we locate the probability value of 0.05 form the table of standard normal distribution. Then we proceed to the left until the first column is reached and the value is 1.90. Also , we move upward until we reach the top and the value is 0.06. Now; the intersection of the row and column results the area to the left of z

This implies that : $P(Z \leq -1.96)=0.05$

The critical value for left tail is -1.96 and the critical value for right tail is 1.96.

Conclusion:

The critical value is -1.96 and the value of test statistic is - 2.50. Here, we can see that the value of test statistic is lesser than the critical value. Hence, we can be concluded that there is evidence that reject the null hypothesis.

Therefore, Yes, the national brand ketchup manufacturer is pleased with the conclusion.

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2 years ago

Use the Chain Rule (Calculus 2)

atroni [7]

1. By the chain rule,

$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}$

I'm going to switch up the notation to save space, so for example, $z_x$ is shorthand for $\frac{\partial z}{\partial x}$ .

$z_t=z_xx_t+z_yy_t$

We have

$x=e^{-t}\implies x_t=-e^{-t}$

$y=e^t\implies y_t=e^t$

$z=\tan(xy)\implies\begin{cases}z_x=y\sec^2(xy)=e^t\sec^2(1)\\z_y=x\sec^2(xy)=e^{-t}\sec^2(1)\end{cases}$

$\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0$

Similarly,

$w_t=w_xx_t+w_yy_t+w_zz_t$

where

$x=\cosh^2t\implies x_t=2\cosh t\sinh t$

$y=\sinh^2t\implies y_t=2\cosh t\sinh t$

$z=t\implies z_t=1$

To capture all the partial derivatives of $w$ , compute its gradient:

$\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}$

$\implies w_t=\dfrac1{\sqrt{-2t-t^2}}$

2. The problem is asking for $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$ . But $z$ is already a function of $x,y$ , so the chain rule isn't needed here. I suspect it's supposed to say "find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ " instead.

If that's the case, then

$z_s=z_xx_s+z_yy_s$

$z_t=z_xx_t+z_yy_t$

as the hint suggests. We have

$z=\sin x\cos y\implies\begin{cases}z_x=\cos x\cos y=\cos(s+t)\cos(s^2t)\\z_y=-\sin x\sin y=-\sin(s+t)\sin(s^2t)\end{cases}$

$x=s+t\implies x_s=x_t=1$

$y=s^2t\implies\begin{cases}y_s=2st\\y_t=s^2\end{cases}$

Putting everything together, we get

$z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)$

$z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)$

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3 years ago

What does the remainder theorem conclude given that f(x)x+3 has a remainder of 11?

Slav-nsk [51]

By the remainder theorem of polynomial division, the complete equation is f(-3) = 11

<h3>How to complete the blanks?</h3>

The equation is given as:

f(x)/x + 3

Set the divisor to 0

x + 3 = 0

Solve for x

x = -3

Given that the quotient has a remainder of 11.

It means that:

f(-3) = 11

Hence, the complete equation is f(-3) = 11

Read more about remainder theorem at:

brainly.com/question/13328536

#SPJ1

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2 years ago

Eddie drilled into a piece of wood and I joist to attach them if he drilled 3 inches in the wood was one and 1 1/3 inches thick

NARA [144]

Let JD = Distance drilled in joist
<span>JD = 3 - 1 1/3 </span>
<span>JD = 9/3 - 4/3 </span>
<span>========================== </span>
<span>JD = 5/3 or 1 2/3 in ◄ Ans

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

</span>

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2 years ago