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umka2103 [35]
3 years ago
5

Solve 9^x-10x3^x+9=0

Mathematics
1 answer:
Goshia [24]3 years ago
4 0
Let y = 3^x , then 9^x = (3^2)^x = (3^x)^2 = y^2,  so we can write the equation as

y^2 - 10y + 9 = 0

(y - 9)(y - 1) = 0

giving y = 9 or y = 1

Therefore  3^x = 9    giving x = 2

and 3^x = 1 giving x = 0


so the solution  set is {0, 2}

Note - I have assumed that the 'x' after the 10 means 'multiply'.   Is that correct?
You might be interested in
What the answer for this ? :/
goblinko [34]
Hello there! I can help you! In order to answer those questions, we need to plug in the values, based off of the variable.

g. Okay. We are solving b - 10. b = -8. When you subtract something from a negative number, the number is even lower. Let's add the numbers first and then put in the negative symbol. 8 + 10 is 18. Put the negative sign and you get -18. The difference is -18.

h. Now, we solve a - b. a = 5 and b = -8. Because we are subtracting a negative number from a positive, we have to add both numbers, which means the number gets bigger. Ignore the negative sign and add. 5 + 8 is 13. There. The sum is 13.

i. The problem is c - a. c = -9 and a = 5. So as explained on problem G, for this problem, ignore the negative symbol and add. 9 + 5 is 14. Plug in the negative sign to get -14. There. The difference is -14.
3 0
3 years ago
There are 140 legs on a planet zids have 5 legs and zods have 7 legs h=how many soulutions are there
abruzzese [7]
Number of zids=x
number of zods=y
number of zid legs=5x
number of zod legs=7y

so
5x+7y=140
try to get it into slope intercept from so you can graph is (y=mx+b)
5x+7y=140
subtract 5x from both sides
7y=140-5x
divide both sides by 7
y=20-5/7x
y=-5/7x+20

plug in numbers for x and get numbers for y (you can only plug in multiples of 7 for x so that there are a whole number of zids and since you are counting, x and y must never be negative)

lets try 0 for x

y=-5/7(0)+20
y=20
 so x=0 and y=20 is an answer (if you can have only one of that species)


lets try 7 for x
y=-5/7(7)+20
y=-5+20
y=15

so x=7 and y=15 is an answer


lets try 14 for x

y=-5/7(14)+20
y=-10+20
y=10

so x=14 and y=10 is another answer


lets try 21 for x
y=-5/7(21)+20
y=-15+20
y=5

so x=21 and y=5 is another answer


lets try 28 for x
y=-5/7(28)-20
y=-20+20
y=0

so x=28 and y=0 is an answer (if there can be only one of a species)


if we go further, then y will be negative so the answers are

(x,y)
(0,20)
(7,15)
(14,10)
(21,5)
(28,0)

if it is allowed that only one species exists then there are 5 possible answers
if both must exist simultaneously, then there are only 3 answers
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8 0
3 years ago
What values of x and y satisfy the system of equations {10x+3y=−5−5x−4y=10? (0,−53) (25,−3) (−2,0) (12,−103)
Kitty [74]

Answer:

<em>The solution of the equation </em>

<em>( 0.4 ,-3)</em>

Step-by-step explanation:

<u><em>Explanation</em></u>:-

<u><em>Step(i):</em></u>-

Given system of equations

                                  10 x+3 y = −5 ...(i)

                                 - 5 x - 4 y = 10 ...(ii)

Multiply (i) with '5'

          10 × 5 x +  3×5 y = - 25  

              50 x + 15 y = 25 ...(iii)

Multiply (ii) with '10'

        -5 × 10 x - 4×1 0 y = 100

       - 50 x - 40 y =100 ...(iv)

<u><em>Step(ii)</em></u>:-

Solving (iii) and (iv)

        50 x + 15 y =- 25

     <u>  - 50 x - 40 y =100</u>

                - 25 y = 75

Dividing ' - 25' on both sides, we get

               <em>    y = -3</em>

<em>substitute y = -3 in equation (i) , we get</em>

<em>            </em>  10 x+3 y = −5

             10 x - 9 = - 5

                10 x = -5 + 9

                    x = \frac{4}{10}

                 <em>  x =  0.4  </em>

<u><em>Final answer</em></u>:-

 <em>The solution of the equation   ( 0.4 ,-3)</em>

           

7 0
3 years ago
HELP!!!!
Lisa [10]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
70% of voters in a certain state support an increase in the minimum wage. A researcher believe that the percentage of fast food
Artist 52 [7]
<h2><u>Answer with explanation:</u></h2>

Let p be the proportion of voters in a certain state support an increase in the minimum wage.

As per given , we have

H_0: p =0.70\\\\ H_a: p >0.70

Since alternative hypothesis is right-tailed so the test is a right-tailed test.

Test statistic : z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

, where n= sample size.

p= population proportion.

\hat{p} = sample proportion.

. In a random sample of 300 fast food workers for 240 supporters increase an minimum-wage.

i.e. n= 300 and \hat{p}=\dfrac{240}{300}=0.8

Then,

z=\dfrac{0.8-0.7}{\sqrt{\dfrac{0.7(1-0.7)}{300}}}\approx3.78

For significant level α = .05 , the critical z-value is

z_{0.05}=1.645

Decision : Since calculated z-value (3.78) is greater than the critical value (1.645) , so we reject the null hypothesis.

Conclusion : We have sufficient evidence o support researcher's claim that  that the percentage of fast food workers for support and increase is higher than 70%..

4 0
3 years ago
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