what does the denominator of a rational exponent represent? 15 POINTS

To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can use the expression 9(8 - x), where x represents 'a number'.

To represent the sentence 'Nine times the difference of 8 and a number.' as an algebraic expression, we can start by assigning the letter x to represent a number. Then, we can write the expression as 9(8 - x), where 8 - x represents the difference of 8 and the number x.

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The given sentence 'Nine times the difference of 8 and a number' can be translated into the algebraic expression 9(8 - x).

The given sentence, 'Nine times the difference of 8 and a number' can be represented as an algebraic expression as follows: First, identify the operation for 'difference' which is subtraction. Then, identify the 'number', which is given as x. So, 'the difference of 8 and a number' would be 8 - x. 'Nine times the difference' implies multiplication, so the entire expression would be 9(8 - x). Therefore, the algebraic expression to represent the sentence in question is 9(8 - x).

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The division between two numbers is positive if and only if they have the same sign. So, this fraction is positive if numerator and denominator are either both positive or both negative.

For this reason, you want to study the sign of numerator and denominator separately first.

As for the numerator, you have

[tex] 3x+8 \geq 0 \iff 3x \geq -8 \iff x \geq -\dfrac{8}{3} [/tex]

Similarly, for the denominator you have

[tex] x-4 > 0 \iff x > 4 [/tex]

(note that we used strict inequality for the denominator, since it can't be zero).

So, the sign of the fraction works like this:

Answer:

A. x ≤ −8/3 or x>4

Step-by-step explanation:

Edge 2020 answer is A

Answer:

Independent.

Step-by-step explanation:

Answer: Picture

Step-by-step explanation:

Using the exponential decay formula, the resale value of a car initially purchased at $29,500 and depreciating at 35% per year will be approximately $5,266.08 after 4 years.

To calculate the resale value of a car after depreciation, we can use the formula for exponential decay, which is [tex]V = P (1 - r)^t[/tex], where V is the future value of the car, P is the initial purchase price, r is the rate of depreciation, and t is the time in years. In this case, P = $29,500, r = 35% or 0.35, and t = 4 years.

Following the formula, the resale value after 4 years would be:

V = $29,500 (1 - 0.35)⁴

V = $29,500 (0.65)⁴

V = $29,500 (0.17850625)

V = $5,266.08 approximately

Therefore, the resale value of the car after 4 years will be around $5,266.08.

"how long..." is asking for time (t).  "The amount of time spent in the air" is the time from when the ball was kicked (0 seconds) to the time it landed on the ground.  Need to find the x-intercepts (one will be negative which will be invalid). You can do this by factoring ... or by using the quadratic formula. With the equation you provided, it is not factorable, so you must use the quadratic formula.

h = -16t² + 60t + 3

   a=-16   b=60  c=3

[tex]t = \frac{-b +/- \sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]t = \frac{-60 +/- \sqrt{60^{2}-4(-16)(3) } }{2(-16)}[/tex]

[tex]t = \frac{-60 +/- \sqrt{3600 + 192} }{-32}[/tex]

[tex]t = \frac{-60 +/- \sqrt{3792} }{-32}[/tex]

[tex]t = \frac{-60 +/- 61.6}{-32}[/tex]

[tex]t = \frac{-60 + 61.6}{-32}[/tex]   or   [tex]t = \frac{-60 - 61.6}{-32}[/tex]

[tex]t = \frac{1.6}{-32}[/tex]        or     [tex]t = \frac{-121.6}{-32}[/tex]

   t = -0.05            or     t = 3.8           disregard the negative

Answer: 3.8 seconds

f(x)=-3x^2-1

f(-2)= -3(-2)²-1=-3·4-1= - 13

Final answer:

To simplify 4m - 3 - 9m + 8, combine like terms to get -5m + 5, which is the simplified expression.

Explanation:

To perform the indicated operation and simplify 4m - 3 - 9m + 8, we need to combine like terms. The terms 4m and -9m are like terms, as are the constants -3 and +8. So, let's combine them.

First, combine the m terms:

4m - 9m = -5m

Next, combine the constant terms:

-3 + 8 = 5

Putting it all together, we have:

-5m + 5

This is the simplified form of the original expression.

3/100, 5/100, 5/100 75/100

Answer:

The width of the room is 20 feet.

The Length of the room is  [tex]46[/tex] feet.

Step-by-step explanation:

Lets take the width of the room as [tex]x[/tex] feet

Then the length of the room will be [tex]2x+6[/tex] feet

Perimeter of a room is the addition of all the walls making the boundary of the room.

Perimeter of the rectangular room = 2 * Width + 2 * Length

⇒[tex]132=2*x+2*(2x+6)[/tex]

⇒[tex]132=2x+4x+12[/tex]

⇒[tex]132=6x+12[/tex]

⇒[tex]132-12=6x[/tex]

⇒[tex]120=6x[/tex]

⇒[tex]20=x[/tex]

Therefore,

The width of the room is 20 feet.

The Length of the room is,

[tex]2x+6[/tex] = [tex]2*20+6[/tex] = [tex]46[/tex] feet

5,254,071,926

Is the standard form

The number 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six' can be written in standard form as 5,254,071,926.

The number 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six' is written in words. In standard form, we write it as a numeric value instead. So,

5,254,071,926

is the standard form of 'five billion two hundred fifty four million seventy one thousand nine hundred twenty six'. The standard form simply means writing the number as we typically would in mathematics or everyday usage.

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To find the length of the hypotenuse in a right-angled triangle with sides measuring 7ft and 4ft, use the Pythagorean Theorem: 7² + 4²= c², which gives us the hypotenuse length of approximately 8.06 feet.

The question is asking for the length of the hypotenuse of a right-angled triangle when the lengths of the other two sides are known (7ft and 4ft).

To find the hypotenuse, we use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as a² + b² = c².

By applying the Pythagorean Theorem:

72 + 42 = c²
49 + 16 = c²
65 = c²
c = √65 ≈ 8.06 ft

Therefore, the length of the hypotenuse is approximately 8.06 feet.

To find the total amount of snow accumulated after one month, simply add in the inches recorded.

9.2 in. + 0.5 in. + 6 in. + 5.9 in. = 21.6 total inches of snow fell over the one month period

We are given

a cubic polynomial function has the same zeroes

Let's assume that zeros as 'a'

so, we can write it as

[tex]f(x)=(x-a)^3[/tex]

now, we are given y-intercept

(0,-5)

at x=0 , y=-5

we can use it and then find 'a'

[tex]-5=(0-a)^3[/tex]

[tex]a=\sqrt[3]{5}[/tex]

now, we can plug it

and we get

[tex]f(x)=(x-\sqrt[3]{5})^3[/tex]..................Answer

Answer:

Use the zeroes to determine the roots.

Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.

Use the y-intercept (0, –5) to solve for the leading coefficient.

Substitute the leading coefficient into the polynomial function for a and simplify.

Step-by-step explanation:

Binomial: A polynomial that is the sum of two terms, each of which are monomials. The answer here would be A. b² - 14, because it is comprised of two terms. Answer B is a monomial because it only has ONE term, C is a trinomial because it has three terms, and D. is a multinomial, or a polynomial because it has more than three terms. Hope that helps!

ANSWER

[tex]S_5=91\frac{10}{81}[/tex]

EXPLANATION

The sum of the first [tex]n[/tex] terms of a geometric sequence is given by;

[tex]S_n=\frac{a_1(1-r^n)}{1-r} ,-1<\:r<\:1[/tex]

Where [tex]n[/tex], is the number of terms and [tex]a_1[/tex] is the first term.

When [tex]n=5[/tex], we have [tex]a_1=81[/tex], we get;

[tex]S_5=\frac{81(1-(\frac{1}{9})^5)}{1-\frac{1}{9}}[/tex]

[tex]S_5=\frac{81(1-\frac{1}{59049})}{1-\frac{1}{9}}[/tex]

[tex]S_5=\frac{81(\frac{59048}{59049})}{\frac{8}{9}}[/tex]

[tex]S_5=\frac{7381}{81}[/tex]

[tex]S_5=91\frac{10}{81}[/tex]

Answer:

y = 3x - 17

Step-by-step explanation:

Here is the point-slope form of the equation of a line.

[tex] y - y_1 = m(x - x_1) [/tex]

If you are given a slope, m, and a point on the line, (x1, y1), you just plug in the values into the equation above, and you get the equation of the line.

In your problem, you are given a point on the line, (5, -2). Now you need the slope of the line. Your line is perpendicular to the given line. The slopes of perpendicular lines are negative reciprocals. If you know the slope of a line, the slope of its perpendicular is found by flipping the fraction and changing the sign.

The given line has slope -1/3.

Flip -1/3 to get -3.

Now change the sign to get 3.

The slope of the line you need is 3. The line passes through point (5, -2).

Now we use the point-slope equation and we plug in the values we have.

[tex] y - y_1 = m(x - x_1) [/tex]

[tex] y - (-2) = 3(x - 5) [/tex]

[tex] y + 2 = 3x - 15 [/tex]

[tex] y = 3x - 17 [/tex]

Answer:

The roots are [tex]-3,-2,3[/tex]

Step-by-step explanation:

Let [tex]f(x)=x^3-2x^2+5x-6[/tex] and [tex]g(x)=-4x^2+14x+12[/tex].

The graph of the two functions are in the attachment.

The x-values of the points of intersection are the roots of the polynomial equation.

[tex]x^3-2x^2+5x-6=-4x^2+14x+12[/tex]

The roots are

[tex]-3,-2,3[/tex]

Answer:

-3,-2,3

Step-by-step explanation:

edge

The answer is (-3,0) if you plug the coordinates into the equation you will find that it satisfies it and indicates that you should shade below the line

:)

Answer:

The coefficient of the squared expression in the parabolas equation will be 5.

Step-by-step explanation:

The vertex form of parabola is:  [tex]y=a(x-h)^2 +k[/tex] , where [tex](h,k)[/tex] is the vertex point and [tex]a[/tex] is the coefficient of [tex]x^2[/tex] term.

The vertex is given as [tex](3,-2)[/tex]. That means, [tex]h=3[/tex] and [tex]k=-2[/tex]

So, the vertex form will be:  [tex]y=a(x-3)^2-2[/tex]

Given that, when the x-value is 4, the y-value is 3. So, plugging these values into the above equation, we will get.....

[tex]3=a(4-3)^2-2\\ \\ 3=a(1)^2-2\\ \\ a=3+2=5[/tex]

Thus, the coefficient of the squared expression in the parabolas equation will be 5.

Complimentary angles equal 90 degrees.  So the answer would be C because  77+13= 90.

Answer: Two angles are complementary when they add up to 90°

then, doing all the options:

A) 50° + 41° = 91°, so this angles are non complementary.

B) 100° + 80° = 180°, so this aren't complementary, but they are Supplementary (because their addition is 180°) angles.

C) 77° + 13° = 90°, si this angles are complementary

D) 35° + 10° = 45°, this pair is not complementary.

So the only correct answer is C.

You have 3 $5s and 4 $1 bills. Hope this helps :)

You have 3 $5s and 4 $1 bills.

Hope this helps you, if it does, please mark brain! <3

-SHOBE-

The values of x and y have been calculated as [tex]15[/tex] and [tex]12[/tex] respectively making option A the appropriate choice.

In the given question we can see that the angles [tex]62[/tex] degrees and [tex]4x + 2[/tex] degrees are alternate interior angles because they are alternately on the interior side of two parallel lines and transversal. hence, we can calculate x as:
[tex]62 = 4x + 2\\4x = 60\\x = 60/4 = 15[/tex]
Similarly, we can find the value of y as the angles [tex]12y[/tex] degrees and [tex]144[/tex] degrees are alternate interior angles.
[tex]12y = 144\\y = 144/12\\y = 12[/tex]

The values of x and y are [tex]15[/tex] and [tex]12[/tex] respectively.
Therefore, option A is the correct answer.

To factor 9x^4 - 64y^2, use the difference of squares formula. The factored form is (3x^2 + 8y)(3x^2 - 8y).

To factor 9x^4 - 64y^2, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b). Applying this, we get: 9x^4 - 64y^2 = (3x^2 + 8y)(3x^2 - 8y)

Therefore, the factored form of 9x^4 - 64y^2 is (3x^2 + 8y)(3x^2 - 8y).