if x=10^a , y=10^b and x^b.y^a=100.prove that xy=1​

Same as my answer last time:

Answer:

NO solution

Step-by-step explanation:

log(16x+2) - log(4x+2) = log((16x+2)/(4x+2)).

remove log

(16x+2)/(4x+2) = 2x + 4

multiply both sides by 2x + 1

8x + 1 = (2x + 4)(2x + 1)

distribute

8x + 1 = 4x^2 + 10x + 4

move to one side

4x^2 + 2x + 3 = 0

factor

but you can't

so you try to use quadratic formula, but you find that the discriminate is less than zero.

So there is no solution when x is a real number.

gcd  =  6  ⋅  d

Step-by-step explanation:

We have that  

6 d ^2  =  6  ⋅  d  ⋅  d and  18 d  =  3  ⋅  6  ⋅  d  hence the  gcd  =  6  ⋅  d

(Hope this helps <3)

Answer:

(a) the new angle the ladder makes with the ground is [tex]32.7^o[/tex]

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

[tex]sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m[/tex]

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

[tex]sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o[/tex]

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

[tex]cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m[/tex]

Now fro the new position of the bottom of the ladder relative to the wall:

[tex]cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m[/tex]

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

Step-by-step explanation:

Hey, there!!

a. (-12)×(-11)×10

Here, (-)×(-)=(+)

(-12)×(-11)=132

so,

=132×10

=1320.

For b.

(-25)×(-8)×(-2)

(-)×(-)=(+)

(-25)×(-8)=200

so,

=200×(-2) { (+)×(-)=(-)}.

= -400.

Therefore, the answer of a. no. is 1320, and no. b is (-400).

Hope it helps....

Answer:

[tex]\frac{1}{16}[/tex] x [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]

multiply 16 by 4 to get the denominator

The fraction 1/16 times 1/4 is equal to 1/64.

To find the product of 1/16 and 1/4, we can multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

1/16 x 1/4

= (1 x 1) / (16 x 4)

The product of the numerators is 1 x 1 = 1, and the product of the denominators is 16 x 4 = 64.

So, the result is:

1/16 x 1/4 = 1/64

Therefore, 1/16 times 1/4 is equal to 1/64.

Learn more about fraction here:

https://brainly.com/question/29019463

#SPJ6

Answer:

No solution

Step-by-step explanation:

I hope it helps

Answer:

You'll find out once you go through the steps below.

Step-by-step explanation:

First look at x and y being multiplied. You'll get an idea of what are the possible pair of numbers that multiply together. So in this case they could be 6 and 4 but it cant be possible since they will add and become 10 but we need eight. We now know that the answer is in a decimal. I hope these steps were helpful. Have a nice day. :)

Answer:

Please see steps below

Step-by-step explanation:

Start by writing all trig functions in the equation in terms of their simplest forms using the two basic trig functions: [tex]sin(\alpha) \,\,and\,\,cos(\alpha)[/tex]:

[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)} = \frac{1}{sin(\alpha)}[/tex]

Now work on the left side (which is the most complicated one), trying to simplify it using the properties for adding fractions with different denominators:

[tex]sin(\alpha)+ cos(\alpha)\,\frac{cos(\alpha)}{sin(\alpha)}=sin(\alpha)+\frac{cos^2(\alpha)}{sin(\alpha)} =\frac{sin^2(\alpha)}{sin(\alpha)} +\frac{cos^2(\alpha)}{sin(\alpha)}=\frac{sin^2(\alpha)+cos^2(\alpha)}{sin(\alpha)}=\frac{1}{sin(\alpha)}[/tex]

where in the last step we have used that the Pythagorean identity for:

[tex]sin^2(\alpha)+cos^2{\alpha)=1[/tex]

Notice that we arrived at the expression: [tex]\frac{1}{sin(\alpha)}[/tex], which is exactly what appears on the other side of the initial equation/identity we needed to prove, so the prove has been completed.

Hey There!!

The answer to this is: 25 times larger. The scale factor is 5, so each side length of the polygon was multiplied by 5.

Key Idea

If the length of a figure scales by x, then area of the figure scales by x^{2}

The Polygon B is created with a scale factor of 5. So, the area of Polygon B scales by 5^{2}

5^{2} = 5 × 5=25

The area of Polygon B is 25 times larger than the area of Polygon A

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

3s = 5s - 10

Step-by-step explanation:

Answer:

width = 12.5

Step-by-step explanation:

rectangular volume = height * width * length

1200 = 4 * w * (20 + 4)

1200 = 4 * w * 24

1200 = 96w

12.5=w

Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).

FOR EXAMPLE

5/10 = 1/2

HERE 1/2 IS THE SIMPLEST FRACTION

Answer:

3.5

Step-by-step explanation:

I recommend using a calculator. Divide 7/2.

Answer:

x = -3

Step-by-step explanation:

expand -23x + 36 = 105

subtract 36 from both sides -23x +36 -36 = 105 - 36

Simplify -23x = 69

Divid both sides by -23: -23x / - 23 = 69 / -23

x = -3

Answer:

y = - 0.681 % ≈ -0.7 %

Step-by-step explanation:

Given:

                                                               April 19,1998            October 30, 1998

Value immediately prior to deposit                95                               105

                     Deposit                                       2X                                 X

amount in the account on January 1, 1999 = 115

effective dollar weighted yield = 0%

annual effective time weighted yield = y

To find:

Calculate y

Solution:

Given that the dollar weighted return is 0%

100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X

100 + 2x + x = 115

3x = 115 - 100

3x = 15

x = 15/3

x = 5

Compute y

1 + y = (95/100)(105/105)(115/110)

1 + y = 0.95 * 1 * 1.045

1 + y = 0.99318

y = 0.99318 - 1

y = - 0.0068 * 100

y = - 0.681 % ≈ -0.7 %

y = -0.7 %

To find the slope of this line, let's use the slope formula.

m = y2 - y1 / x2 - x1

m = 4 - 2 / 8 - 0 ⇒ 2/8 ⇒ 1/4

So m = 1/4.

To solve this equation, let's factor the left side.

Although you can factor it in different ways, I will show you a trick.

First, forget about the 3 and we have x² - 8x + 5.

Now, multiply the 3 by the constant to get 15.

So we have x² - 8x + 15.

Now factor to get (x - 5)(x - 3).

Now divide each of the constants in the

binomials by the leading coefficient, 3.

So we have (x - 5/3)(x - 3/3).

Simplify to get (x - 5/3)(x - 1).

Now move any denominators in front of the x in the binomial.

Moving the 3 in front of the x, we have 3x.

So our answer is (3x - 5)(x - 1) = 0.

So either 3x - 5 = 0 or x - 1 = 0.

Solving from here, we get x = 5/3 or x = 1.

Answer: Testing the effectiveness of a mouthwash by allowing one group to use it and comparing the results with those of a group that doesn't use it.

Step-by-step explanation: It's the most effective

Answer:

14 is less than 21

Answer:

If the value of our test statistics is less than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

If the value of our test statistics is more than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Step-by-step explanation:

We are given that the population mean equals 500 and we use a 0.10 level of significance in a two-tail hypothesis test.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 500

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 500

Here, the null hypothesis states that the population mean is equal to 500.

On the other hand, the alternate hypothesis states the population mean is different from 500.

Now, firstly we should note that for the two-tailed test, the level of significance to be taken is ([tex]\frac{\alpha}{2}=\frac{0.10}{2}[/tex]) = 0.05 or 5%.

So, the decision rule for rejecting a null hypothesis is given by;

Answer: $180

Step-by-step explanation:

If she purchased 20 shares of ad stock for $43 per share then multiply 20 by 43 to find the total amount of money.

20 * 43 = $860   which means that she spent a total of $860  for the 20 shares.

If she then sold the 20 stocks for $52 each then you will multiply 20 by 52 and subtract 860 from it to find the total amount she made.

20 * 52 = 1040    

$ 1040 - $860 = $180

Answer:

The Alpha Level

Step-by-step explanation:

The critical value is obtained by applying the alpha value to an area. For example if we choose the alpha level of 0.05 the critical value would be 1.96 for a two tailed test. But if the alpha is 0.1 the critical value would be 1.645 and similarly the critical value would be 2.58 for 0.01 alpha level.

The critcal value depends on the alpha level and is set accordingly depending on one tailed or tailed test. It does not involve the use of The Obtained Statistic  or The Population Mean.

Complete Question

Two different red-light-running signal systems were installed at various intersection locations with the goal of reducing angle-type crashes. Red-Light-Running System A resulted in 60% angle crashes over a sample of 720 total crashes. Red-Light-Running System B resulted in 52% angle crashes over a sample of 680 total crashes. Was there a difference between the proportions of angle crashes between the two red-light-running systems installed? Use an alpha of 0.10.

Answer:

Yes there is a difference between the proportions of angle crashes between the two red-light-running systems installed

Step-by-step explanation:

From the question we are told that

   The first sample  proportion  is  [tex]\r p_ 1 = 0.60[/tex]

   The  second sample proportion is  [tex]p_2 = 0.52[/tex]

    The first sample size is  [tex]n_1 = 720[/tex]

     The second sample size is  [tex]n_2 = 680[/tex]

     The  level of significance is  [tex]\alpha = 0.10[/tex]

The null hypothesis is [tex]H_o : \r p_1 - \r p_2 = 0[/tex]

The  alternative hypothesis is  [tex]H_a : \r p_1 - \r p_2 \ne 0[/tex]

Generally the pooled proportion is mathematically represented as

       [tex]p_p = \frac{(\r p_1 * n_1 ) + (\r p_2 * n_2)}{n_1 + n_2 }[/tex]

=>     [tex]p_p = \frac{(0.6 * 720) + ( 0.52 * 680)}{720 +680 }[/tex]

=>    [tex]p_p = 0.56[/tex]

 Generally the test statistics is evaluated as        

       [tex]t = \frac{ ( \r p_1 - \r p_2 ) - 0 }{ \sqrt{ (p_p (1- p_p) * [ \frac{1}{n_1 } + \frac{1}{n_2 } ])} }[/tex]

        [tex]t = \frac{ (0.60 - 0.52 ) - 0 }{ \sqrt{ (0.56 (1- 0.56) * [ \frac{1}{720} + \frac{1}{680 } ])} }[/tex]    

       [tex]t = 3.0[/tex]

The  p-value obtained from the z-table is  

      [tex]p-value = P(Z> t ) = 0.0013499[/tex]

From the question we see that [tex]p-value < \alpha[/tex] so the null hypothesis is rejected

 Hence we can conclude that there is a difference between the proportions

Re-writing question 5:

5. Determine if the statement below is true or false. If it is false, rewrite it so it is true. Rewriting √-10 in terms of i results in −10i.

A. This statement is true.

B. This statement is false. Rewriting √-10 in terms of i results in (√10)i.

C. This statement is false. Rewriting √-10 in terms of i results in −10√i.

D. This statement is false. Rewriting √-10 in terms of i results in 10√i.

Answer:

1) C. an imaginary number

2) A. In order for a + bi to be a complex number, b must be nonzero

3) 4

4) -6

5) B. The statement is false. Rewriting √-10 in terms of i results in (√10)i

Step-by-step explanation:

1. When a number can be expressed in the form a+bi where a and b are real numbers, then the number is said to be a complex number.

For example, the following are complex numbers where i = √-1 ;

i. 3 + 5i

ii. 4 - 7i

iii. -3 - 9i

Well, even real numbers are a subset of complex numbers. For example,

=> 5 can be written as 5 + 0i

=> -12 can be written as -12 + 0i

-- But when a and b are non-zero real numbers or at least b is a non-zero real number, then the number is said to be an imaginary number.

-- If a is zero, then the number is a purely imaginary number

-- If b is zero, then the number is a purely real number

2. For a number to be called a complex number;

i. it can be written in the form a + bi where a and b are real numbers,

ii. either a or b, or both, may be zero,

iii. a is the real part of the complex number,

iv. b is the imaginary part of the complex number.

v. it could also be a real number since every real number is also a complex number.

3. Given 4 - 5i

The real part is 4

and the imaginary part is -5

4. Given 7 - 6i

The real part is 7

and the imaginary part is -6

5. Rewrite √-10 in terms of i

Remember that i = √-1

Therefore,

√-10 = √(-1 x 10) = √-1 x √10

=> √-10 = √-1 x √10

=> √-10 = i x √10

=> √-10  = (√10)i

Answer:

x= -35 because you have tk get x alone. so you subtract 20 from -15

Answer:

x = -35

Step-by-step explanation:

20 + x = -15

(20 + x) - 20 = -15 - 20

x = -35

Store A: 1 foot= 42.50÷5 = $8.50

Store B= 1 foot= 49.50÷6 = $8.25

Answer:

Store B has a better buy because the price for 1 foot sandwich is cheaper than Store A.

Answer:

Following are the answer to this question:

Step-by-step explanation:

Given value:

[tex]\to x > 0[/tex]

[tex]\to S= { n\varepsilon N : x^n \leq 0 } \\\\ s \neq \phi \\\\ \to x^n \leq 0\\[/tex]

[tex]\to x^{n-1} x\leq 0\\\\ \to x>0 = x^{n-1} \leq 0 \\\\\to n-1 \varepsilon s \\ \ \ _{where} \ \ n-1 < n \\\\\to s= \phi \\\\\to \hence x^n > 0 \\[/tex]

Answer:

D

Step-by-step explanation:

7^2 + 4^2 = [tex]\sqrt{65\\[/tex]

assume it is a triangle and x is the hypotenuse and use Pythagorean theorem

Answer:

D

Step-by-step explanation:

7^2 + 4^2 =

assume it is a triangle and x is the hypotenuse and use Pythagorean theorem

Answer:

8

Step-by-step explanation:

n×8=8n

8n+136=144n

144n÷8=18n

18n-n = 18

Answer:

Amount after 4 years = $3274.125

Step-by-step explanation:

Time t= 4 years

Principal amount p= $2500

Interest rate R= 6.75%

Number of times compounded n= 4*12

Number of times compounded n= 48

Amount A = p(1+r/n)^(nt)

A= 2500(1+0.0675/48)^(48*4)

A= 2500(1+0.001406)^(192)

A= 2500(1.001406)^192

A= 2500(1.30965)

A= 3274.125

Amount after 4 years = $3274.125

Hi

add "x" with "x" and numbers with numbers

5x+3x+2+4 = 8x+6

Answer: [tex]8x+6[/tex]

Add

[tex]5x+3x=8x\\2+4=6\\8x+6[/tex]