Solve each equation.
3⁻²x⁺²=81

After evaluating the expression x³ . x⁵, we get the result as 256.

We are given an expression:

x³ . x⁵

We can use the properties of exponents that if the base is same and two numbers are multiplied, then the powers get added.

So, the expression will become:

= x ³⁺⁵

Simplifying the expression, we get that:

= x⁸

Now, we need to evaluate the expression at x = 2

Put x = 2 in the expression, we get that:

= 2⁸

Evaluating it, we get that:

= 256

Therefore, after evaluating the expression x³ . x⁵, we get the result as 256.

Learn more about expressions here:

https://brainly.com/question/723406

#SPJ4

Since both terms are perfect squares, factor using the difference of squares formula, ( [tex]a^{2}-b^{2} =(a+b)(a-b)[/tex] )

Answer:

(2)(6)+3

?

=

15

15=15

True

Step-by-step explanation:

help

The mean of of −26,39,−10,−16,12,31 is 5 which is determined by summing up the numbers and dividing by 6

What is the mean?

The mean is the sum of the integers divided by the number of integers therein, in other words, the mean is determined sum , having computed the sum we divide by 6 since there are six numbers in the distribution

sum=-26+39-10-16+12+31

sum=30

mean=sum/n

n=6(there are six numbers)

mean=30/6

mean=5

Find out more about mean on:https://brainly.com/question/11051787

#SPJ1

Answer:

Hello,

Step-by-step explanation:

[tex]n=\overline{EDCBA}\\\\A=3*B\ My\ ones\ digit\ is\ three\ times\ greater\ than\ my\ tens\ digit.\\E=3+B\ My\ ten\ thousands\ digit\ is\ 3\ more\ than\ my\ tens\ digit.\\C=2*E\ My\ hundreds\ digit\ is\ twice\ my\ ten\ thousands\ digit. \\D=C-1\ My\ thousand\ digit\ is\ one\ less\ than\ my\ hundreds\ digit.\\\\A=3*B\\E=3+B\\C=2*E\\D=C-1\\\\\begin{array}{|c|c|c|c|c|}A&B&C&D&E\\--&--&--&--&--\\0&0&6&5&3\\3&1&8&7&4\\6&2&X&X&5\\9&3&X&X&6\\X&4&X&X&X\\--&--&--&--&--\\\end{array}\\[/tex]

[tex]\\\\Numbers\ are\ 35600\ or\ 47813.[/tex]

Answer:

B/a

Step-by-step explanation:

Because 1/a is still the same as a to power negative one and so 1/b. 1/a divided by 1/b is b/a

In 12144 ways the students can get first, second, or third place.

The permutation system is used to locate the special range of preparations that may be shaped through taking r matters from the n to be had matters. Permutations are beneficial to shape distinctive words, quantity preparations, seating preparations, and for al. of the conditions related to special preparations. As consistent with the permutation formula, the permutation of 'r' items taken from 'n' items is identical to the factorial of n divided through the factorial of distinction of n and r.

The formula for permutations is

nPr= n!/(n-r)!

From the given question let us consider,

n= 24    r=3

Now let us solve using formula

24P3= 24!/(24-3)!

=24*23*22*21......*2*1

=12144

Therefore there are 12144 ways.

To know more about Permutations visit:

brainly.com/question/1216161

#SPJ1

The simplified form of trigonometric expression, cosec θ / sin θ + cos θ cot θ is 1.

Given,

The trigonometric expression = cosec θ / sin θ + cos θ cot θ

We have  to simplify this expression.

For that we can use trigonometric identities.

cosec θ = 1 / sin θ

cot θ = cos θ / sin θ

We can substitute the above given identities in the expression.

Then we get,

cosec θ / sin θ + cos θ cot θ = (1 / sin θ) / (sin θ + cos θ x (cos θ/sin θ))

= (1 / sin θ) / ((sin²θ + cos²θ) / sin θ)

Cancel sin θ from both numerator and denominator.

= 1 / sin² θ + cos² θ

We know that sin² θ + cos² θ = 1

So, we get,

1 / sin² θ + cos² θ = 1 / 1 = 1

Therefore, the simplified form of  cosec θ / sin θ + cos θ cot θ is 1.

Learn more about trigonometric identities here:

https://brainly.com/question/20896895

#SPJ1

A composite function exists as a function that depends on another function. A composite function exists formed when one function exists substituted into another function.

The value of g(3x) = 9x.

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = 3x and g(x) = x²

f(g(x)) = f(x²)

f(x²)  =  3x²

simplifying the above equation, we get

g(f(x)) = g(3x)

g(3x) = (3x)²

g(3x) = 9x

Therefore, the value of g(3x) = 9x.

To learn more about composition function refer to:

brainly.com/question/10687170

#SPJ4

The percentage of scores will fall between 85 and 115 is 68.26%

Given,

Scores on the Wechsler Adult Intelligence Scale (WAIS) are normally distributed with,

Mean = 100

Standard deviation = 15

We have to find the percentage of scores fall between 85 and 115.

That is,

P(85 < X < 115) = \ [tex]P[/tex] [tex](\frac{85-100}{15}[/tex]  <  [tex]\frac{x-mean}{standard deviation}[/tex]  < [tex]\frac{115-100}{15}[/tex][tex])[/tex]

= P(-1 < Z < 1)

= \P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

\P(85 < X < 115) = 0.6826

The probability that a person would score between 85 and 115 is 0.6826

And, the percentage of scores will fall between 85 and 115 is 68.26%

Learn more about percentage of scores here: https://brainly.com/question/10672120

#SPJ1

We need to know about logarithm to solve this problem. The value of the given logarithm is 1.

Logarithm is an exponent that the base is raised to inorder to get a certain number. There are few rules of logarithm, log a +log b can be written as log ab, log a -log b can be written as log a/b, when the number whose logarithm is calculated has been raised to a power then the power can be multiplied to the log itself. When logarithm is written as log with no mentioned base then the base is 10. The log of a number same as the base is always 1 and the log of 1 is always zero because a nonzero number raised to zero is always 1. We will be using these rules to find the value of the given logarithm.

[tex]log_{9}9[/tex]=1 since [tex]9^{1} =9[/tex]

Therefore we found the value of the given logarithm to be 1.

Learn more about logarithm here:

https://brainly.com/question/14393032

#SPJ9

For the given statement conclusion it was drawn using the law of syllogism.

Option A is our correct answer

The Law of Syllogism states that,

If the following two statements are true:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

We have,

p - If you do the unit review, q - you will do well on the test.

q - If you do well on the test, r - then you will do well in the course.

Therefore, p - if you do the unit review, r - then you will do well in the course.

This is in the form of:

- If p, then q.

- If q, then r.

Then the third statement is true:

- If p, then r.

Thus this conclusion was drawn using the law of syllogism.

Learn more about the law of syllogism here:

https://brainly.com/question/24760664

#SPJ1

Answer:

∠ 10 = 86°

Step-by-step explanation:

∠ 7 and ∠ 10 are same- side interior angles and sum to 180° , that is

∠ 7 + ∠ 10 = 180°

94° + ∠ 10 = 180° ( subtract 94° from both sides )

∠ 10 = 86°

The zeros of p(x)=x2-1 is:

1,-1

Answer:

529

Step-by-step explanation:

Answer: 1185

Step-by-step explanation: add 328 and 857

Answer: yes, because you can't score negative numbers in a game and the absolute value is really just making all numbers positive unless there is a negative variable outside of the absolute value symbols

Step-by-step explanation: brainliest?

According to the solving equation  the ball will be in the air for:

5.3 seconds

A linear equation is an algebraic equation of the form y=mx+b, including only a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. The preceding is sometimes referred to as a "linear equation with two variables," where y and x are the variables.

y = ax2 + bx + c

When:

x = 0 , y = 6

y = a(0)2 + b(0) + c = 6

c = 6

When x = 2, y = 22

a(2)2 + b(2) + 6 = 22

4a + 2b = 16

On dividing the entire equation by 2,

2a + b = 8 → (1)

When x = 4, y = 22

a(4)2 + b(4) + 6 = 22

16a + 4b + 6 = 22

16a + 4b = 16

On dividing the entire equation by 4,

4a + b = 4 → (2)

Subtracting (1) from (2)

2a = -4

a = -2

b = 4 - 4(-2) = 4 + 8

b = 12

y = -2x2 + 12x + 6

y = -2x + 12x + 6

Solve the equation.

On solving using quadratic formula,

x = (-12 ± √(144 - 4*-2*6) ) / -4

x = (-12 ± 13.8564) / -4

x ≈ -0.46 and x ≈ 6.46

The ball is above seconds

-2x2 + 12x + 6 = 10

2x2 - 12x + 4 = 0

On solving the above equation using quadratic formula,

x ≈ 0.354 and x ≈ 5.646

So, the ball is above 10 feet for about,

5.646 - 0.354 = 5.3 seconds

5.3 seconds

According to the solving the ball will be in the air for:

5.3 seconds

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ9

Answer:

45°

Step-by-step explanation:

AB and BC are congruent which mean ∠BAC and ∠BCA are congruent.

We already know ∠ABC is 90°.

We cans set up the equation with what is given.

180 = 90 + 2c

Subtract 90 from both sides.

90 = 2c

Divide both sides by 2

45 = C

So angle C is 45°

Answer: (A) -24x1/4  (B) Negative multiplied by a positive equals a negative

Step-by-step explanation:

The question says below sea level, so the whole number is negative. we don't need city A its a distraction so city C is multiple by city D. why do we multiply because the word of means multiple there for the expression is

write the product into one single fraction

-24x1

   4        canceled the 4 in the fraction -24x1

                                                                      4

-6x1    any expression divided by one remains the same -6x1

  1

solution

x1=0

The lower and upper bounds for the following to the given degrees of accuracy are: a- 64 mins (63.5 ≤ 64 < 64.5) c- 30m/s (27.5 ≤ 30 < 32.5) b- 20g (15 ≤ 20 < 25) d-7500mm (7450 ≤ 7500 < 7550)

The upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.

For a- 64 mins (nearest 1 min)

As the degree of accuracy is to the nearest 1 min;

1 min ÷ 2 = 0.5 min

Upper bound = 64 + 0.5 = 64.5 min

Lower bound = 64 - 0.5 = 63.5 min

For c- 30m/s (nearest 5m/s)

5m/s ÷ 2 = 2.5 m/s

Upper bound = 30 + 2.5 = 32.5 m/s

Lower bound = 30 - 2.5 = 27.5 m/s

For b- 20g (nearest 10g)

10g ÷ 2 = 5

Upper bound = 20 + 5 = 25g

Lower bound = 20 - 5 = 20g

For d- 7500(nearest 100mm)

100mm ÷ 2 = 50mm

Upper bound = 7500 + 50 = 7550mm

Lower bound = 7500 - 50 = 7450mm

To learn more about upper and lower bounds, click here:

https://brainly.com/question/1089252

#SPJ4

Answer: A and B

-3^4 = -3 × -3 × -3 × -3 = 81

When dealing with multiplying all negative numbers, the result is going to be positive.

-3^2 = -3 × -3 = 9

Step-by-step explanation:

Divide

81/9 = 9

Find an equivalent expression whose product is |+9|

(-3)^2 = -3 × -3 = 9

(-3)^4 = -3 × -3 × -3 × -3 = 81

81/9 = 9

A is correct, so we must find the next correct answer.

(-3)^6 = -3 × -3 × -3 × -3 × -3 × -3 = 729

(-3)^4 = -3 × -3 × -3 × -3 = 81

729/81 = 9

B is correct. Thus,

[tex]\frac{(-3)^4}{(-3)^2} = B)\frac{(-3)^6}{(-3)^4} = A)\frac{(-3)^2}{(-3)^4}[/tex]

Hope this helps, and have a great day.

The probability that a randomly selection of 20 toasters for testing, no more than one is defective is: 0.9401

To solve this exercise the formula and the procedure that we have to use for binomial distribution is:

Where:

Information about the problem:

Applying the binomial distribution formula, we get:

P(x) = n! /[x! *(n-x)!] * pˣ * (1 - p)ⁿ⁻ˣ

P(x) = 20! /[x! *(20-x)!] * 0.02ˣ * (1 - 0.02)²⁰⁻ˣ

Using the P formula to calculate the probability that no more than one of these toasters is defective, we have:

P = P(0) + P(1)

P(0) = 20! /[0! *(20-0)!] * 0.02⁰ * (1 - 0.02)²⁰⁻⁰

P(0) = 20! /(0!*20!) * 0.02⁰ * (0.98)²⁰

P(0) = 1/0! * 1 * 0.6676

P(0) = 1/1 * 1 * 0.6676

P(0) = 0.6676

P(1) = 20! /[1! *(20-1)!] * 0.02¹ * (1 - 0.02)²⁰⁻¹

P(1) = 20! /(1!*19!) * 0.02¹ * (0.98)¹⁹

P(1) = (20*19!) / (1!*19!) * 0.02¹ * (0.98)¹⁹

P(1) = 20/1! * 0.02 * 0.6812

P(1) = 20 * 0.02 * 0.6812

P(1) = 0.2725

P = P(0) + P(1)

P =  0.6676 + 0.2725

P =  0.9401

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Learn more about probability at: brainly.com/question/251701

#SPJ4

Answer:

X = -1

Step-by-step explanation:

1. expand the right side of the equation

8x + 6

7x + 5 = 8x + 6 should look like this

2. minus 7x on both sides

5 = 1x + 6 should look like this

3. minus 6 on both sides

-1 = 1x should look like this

4. divide by 1 from the x on both sides

-1 = x this is the only answer for this equation

[tex]\displaystyle\\Answer:\ C. \ f=\sqrt{\frac{B}{4} }[/tex]

Step-by-step explanation:

The possible two-course meals that could be ordered assuming diners must order one meal from each category are;

It follows from the task content that the categories are as indicated below;

Starters Mains

Garlic Bread

Prawns Soup

Chicken Risotto

The condition that diners must order one meal from each category simply leaves the diners with;

Consequently, the expected number of possible two-course meal combination is; 3 × 3 = 9.

Ultimately, the possible two-course meals that could be ordered assuming diners must order one meal from each category are as listed above.

Read more on possible combinations;

https://brainly.com/question/28370067

#SPJ1

An elevator descends at a constant speed, the change in elevation after 19 seconds will be an elevation of distance

d= 19v where acceleration remains constant

Generally, An angle is created when a horizontal line and a line of sight are placed side by side.

In conclusion, This angle is known as the angle of elevation. If the line of sight rises above the horizontal line, the angle that is generated is known as an angle of elevation.

Read more about elevation

https://brainly.com/question/481548

#SPJ1

Answer:

51

Step-by-step explanation: