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lakkis [162]
3 years ago
14

X+y=5 x^y+y^x=17 solve for the value of y and x

Mathematics
1 answer:
pentagon [3]3 years ago
7 0
X = 2 
<span>y = 3 </span>

<span>2 + 3 = 5 </span>
<span>2³ + 3² = 17 </span>

<span>------------------- </span>

<span>BUT: </span>

<span>x + y = 5 </span>
<span>x^y + y^ x = 17 </span>

<span>y = 5 - x</span>
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Help please i dont get it
ale4655 [162]

Answer:

  (c)  x = 2 and x = -8

Step-by-step explanation:

The rules of logarithms let you rewrite this as a quadratic equation. That equation will have two (2) potential solutions. We know from the domain of the log function that any negative value of x will be an extraneous solution.

__

The rules of logarithms that apply are ...

  \log(a)+\log(b)=\log(ab)\qquad\text{all logarithms to the same base}\\\\\log_b(a)=c\ \Longleftrightarrow\ b^c=a\\\\

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<h3>take antilogs</h3>

We can rewrite the equation so that only one logarithm is involved. Then we can take antilogs.

  \log_4(x)+\log_4(x+6)=2\\\\\log_4(x(x+6))=2\qquad\text{using the first rule}\\\\4^2=x(x+6)\qquad\text{using the second rule}

__

<h3>solve the quadratic</h3>

Adding (6/2)² = 9 to both sides will "complete the square."

  16 +9 = x² +6x +9 . . . . . . . add 9

  25 = (x +3)²

  ±√25 = x +3 = ±5 . . . . . take the square root(s)

  x = -3 ±5 = {-8, +2}

The two potential solutions are x = 2 and x = -8.

8 0
2 years ago
Read 2 more answers
Please help. Also show how you got it thanks!
Blababa [14]
There are 12 inches in a foot so we can work this problem out in inches 3/5 is 80%......80% of 12 inches is 9.6 inches ....1/4 is 3 inches and 2/3 is 8 inches so we have 9.6,3,and8 now we multiply 9.6*3*8 for the answer to be 230.4 inches squared
8 0
2 years ago
The local farmers market has oranges on sale for 5 for 1.80 <br><br>What is the cost of one orange ?
lara [203]

Answer:.36 cent

1Step-by-step explanation:1.80 divided by 5

5 0
2 years ago
An auto company claims that the fuel efficiency of its sedan has been substantially improved. A consumer advocate organization w
zzz [600]

Answer:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

df=n-1=12-1=11

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

Step-by-step explanation:

Previous concepts

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation :

x=test value 2017 , y = test value 2019

x: 28.7 32.1 29.6 30.5 31.9 30.9 32.3 33.1 29.6 30.8 31.1 31.6

y: 31.1 32.4 31.3 33.5 31.7 32.0 31.8 29.9 31.0 32.8 32.7 33.8

Solution to the problem

The system of hypothesis for this case are:

Null hypothesis: \mu_y- \mu_x \leq 0

Alternative hypothesis: \mu_y -\mu_x >0

Because if we have an improvement we expect that the values for 2019 would be higher compared with the values for 2017

The first step is calculate the difference d_i=y_i-x_i and we obtain this:

d: 2.4, 0.3, 1.7,3,-0.2, 1.1, -0.5, -3.2, 1.4, 2, 1.6, 2.2

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}= \frac{11.8}{12}=0.983

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.685

We assume that the true difference follows a normal distribution. The 4th step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.983 -0}{\frac{1.685}{\sqrt{12}}}=2.021

The next step is calculate the degrees of freedom given by:

df=n-1=12-1=11

Now we can calculate the p value, since we have a right tailed test the p value is given by:

p_v =P(t_{(11)}>2.021) =0.0342

If we compare the the p value with the significance level provided \alpha=0.1, we see that p_v < \alpha, so then we can reject the null hypothesis. and there is a significant increase in the miles per gallon from 2017 to 2019 at 10% of significance.

4 0
3 years ago
a game consists of randomly choosing a bag (labelled 1, 2 or 3) out of a choice of 100, and then again randomly, picking a ball
Anton [14]

Answer:

hello your question has some missing information attached below is the missing information

answer :  112 black balls

Step-by-step explanation:

Given data:

Each bag contains ; 10 balls

Total number of ball = 100 balls

<u>first: calculate the number of Black balls to be picked from the three bags</u>

From bag 1 = 0.4 * 0.35 * 10 = 1.4 balls

From bag 2 =  0.8 * 0.45 * 10 = 3.6 balls

From bag 3 = 0.3 * 0.2 * 10 = 0.6 ball

Total black balls picked = 5.6

∴ percentage of black balls picked given that each bag contains 10

5.6 / 10 * Total balls available  =  56 balls = 56% of 100 balls

Hence If the player plays this game 200 times the number of black balls he will pick = 56% * 200 =  112 balls

4 0
3 years ago
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