MATHEMATICS HIGH SCHOOL

Solve each equation (quadratic pattern)2^(2x) -2^(x) =12

3^(2x) + 3^(x+1) =4

4^(x) + 6 · 2^(x) +8 = 0

9^(x) = 3^(x) +6

Answers

Answer 1
Answer:

Answer:  x = 2

Step-by-step explanation:

2^(2x)-2^x-12=0\n\n\text{Let u = }2^x\n\nu^2-u-12=0\n(u-4)(u+3)=0\n\nu-4=0\quad and\quad u+3=0\nu=4\qquad and\quad u=-3\n\n\text{Substitute u with }2^x\n2^x=4\qquad and \quad 2^x=-3\n2^x=2^2\quad and\quad \text{not possible}\n\boxed{x=2}

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Answer:  x = 0

Step-by-step explanation:

3^(2x)+3^(x+1)-4=0\n\n3^(2x)+3^x\cdot3^1-4=0\n\n\text{Let u = }3^x\nu^2+3u-4=0\n\n(u+4)(u-1)=0\n\nu+4=0\quad and\quad u-1=0\nu=-4\qquad and\quad u=1\n\n\text{Substitute u with }3^x\n3^x=-4\qquad and\quad 3^x=1\n\text{not possible}\ and\quad 3^x=3^0\n.\qquad \qquad \qquad \qquad \boxed{x=0}

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Answer:  No Solution

Step-by-step explanation:

4^x+6\cdot 2^x+8=0\n\n2\cdot 2^x+6\cdot 2^x+8=0\n\n\text{Let u = }2^x\n2u+6u+8=0\n8u+8=0\n8u=-8\nu=-1\n\n\text{Substitute u with }2^x\n2^x=-1\n\text{not possible}

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Answer:  No Solution

Step-by-step explanation:

9^x=3^x-6\n\n3\cdot 3^x=1\cdot 3^x-6\n\n\text{Let u = }3^x\n\n3u=u-6\n2u=-6\nu=-3\n\n\text{Substitute u with }3^x\n3^x=-3\n\text{not possible}

Related Questions

Use synthetic division to check -4 is a root of the polynomial expression: x^4+2x^3-9x^2-2x+8=f(x)
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How do you solve (2z-3)(4z-7)=0

Answers


The key to this is to realize that if EITHER quantity in parentheses is zero,
then the whole left side is zero, and the equation is true.

First quantity:  (2z-3).  If this is zero, then the whole equation is true.

                                     2z - 3 = 0
Add 3 to each side:      2z       = 3
Divide each side by 2:    z      = 3/2  or  1.5

Second quantity:  (4z-7).  If this is zero, then the whole equation is true.

                                     4z - 7  =  0
Add 7 to each side:      4z        =  7
Divide each side by 4:   z         =  7/4  or  1.75

So the original equation has two solutions:

             z = 1.5
and
             z = 1.75 .
There are two values of z in this question.  (2z - 3)
-3 / 2 = -1.5
-1.5 x -1 = 1.5

(4z - 7)
-7 / 4 = -1.75
-1.75 x -1 = 1.75

z = 1.5 or 1.75

A manager of a grocery store wants to determine if consumers are spending more than the national average. The national average is $150.00 with a standard deviation of $30.20. The manager collects 40 random receipts and finds that the average is $160. Complete a hypothesis test with a significance level of 2.5% to determine if the average customer spends more in his store than the national average. Which of the following is a valid conclusion for the manager based on this test?a.The customers spend more than the national average in his store.b.The manager should decrease prices in his store.c.The customers do not spend more than the national average in his store.d.The customers in his store just come from a rich neighborhood.

Answers

Answer:

The correct answer is:

The customers spend more than the national average in his store

Step-by-step explanation:

The national average is $150.00 with a standard deviation of $30.20.

Sample size n =40

H0: x bar = mu

Ha: x bar >mu

(one tailed test for a single mean)

Sample average x bar = 160

Mean difference = 160-150 =10

std error = 30.20/sqrt 40

=4.775

Test statistic = 2.094

Z critical for 2.5% = 1.96 (one tailed)

Since test statistic > z critical we reject null hypothesis.

Hence the correct answer is:

The customers spend more than the national average in his store.

Answer:

Option A) The customers spend more than the national average in his store.        

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $150.00

Sample mean, \bar{x} = $160

Sample size, n = 40

Alpha, α = 0.025

Population standard deviation, σ = $30.20

First, we design the null and the alternate hypothesis

H_(0): \mu = 150\text{ dollars}\nH_A: \mu > 150\text{ dollars}

The null hypothesis states that the consumers are spending equal to the national average. The alternative hypothesis states that  consumers are spending more than the national average.  

We use One-tailed z test to perform this hypothesis.

Formula:

z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }

Putting all the values, we have

z_(stat) = \displaystyle(160 - 150)/((30.20)/(√(40)) ) = 2.094

Now, z_(critical) \text{ at 0.025 level of significance } = 1.96

Since,  

z_(stat) > z_(critical)

We reject the null hypothesis and accept the alternate hypothesis. Thus, the customers spend more than the national average in his store.

Thus, option A) is a valid conclusion for the manager

Write an equation of a line that is parallel to the line whose equation is 3y=x+6 and that passes through the point (-3,4).

Answers

The standard form of this equation is

y=(1)/(3)x+2

The slope of two parallel lines i the same, so the slope of the line we're looking for is also (1)/(3)

Since the line passes through (-3,4), the equation is:

(y-4)=(1)/(3)(x+3)

\boxed{y=(1)/(3)x+5}

A vendor sells hot dogs and bags of potato chips. A customer buys 5 hotdogs and 2 bags of potato chips for $11.50. Another customer buys 3 hotdogs and 5 bags of potato chips for $9.75. Find the cost of each items.

Answers

Answer:

Hotdogs cost $2 and potato crisps $0.75.

Step-by-step explanation:

Let the hotdogs cost  $h and the crisps $p

5h + 2p = 11.5

3h + 5p =  9.75

Multiply the first equation by  -5 and the second by 2:

-25h  - 10p = -57.5

6h + 10p = 19.5            Adding these 2 equations:

-19h = -38

h = $2.

Substitute h = 2 into the first equation:

5h + 2p = 11.5

10 + 2p = 11.5

2p = 1.5

p = $0.75.

Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?…, 1, 1/2, 1/4, 1/8, …

…, 1/4, 1/2, 1, 2,…

…, 1/72, 1/36,1/18, 1/9, …

…, 8, 4, 2, 1, …

Answers

the answer is 0.5. Because you have to half 1

A= 13+26+39+...+169What is the sum of the prime numbers that can divide A ?


A)16 B)18 C)20 D)22 E)24

Answers

A= 13+26+39+...+169=

= 13(1+2+3+....+13)=

=13* (13*14)/2=

=13*13*7

=> 13+7=20

So the answer is c)
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