In this lesson, what kinds of exponents will be discussed?
zero exponents
fractional exponents
negative exponents
decimal exponents
square root exponents

The other two zeros, which are x = 5 and x = -4.

To find the zeros of the polynomial f(x) = x³ − x² − 20x, we need to set the polynomial equal to zero and solve for x. This can be done by factoring out the common term x from each term of the polynomial:

f(x) = x(x² - x - 20) = 0

The zeros of the polynomial will be the values of x for which the product is zero. Since we already have x as one factor, one zero is x = 0. We then need to factor the quadratic, which is:

x² - x - 20

We can factor this quadratic to

(x - 5)(x + 4)

Thus, the other two zeros of the polynomial are x = 5 and x = -4.

Final answer:

Tossing a dime and then tossing a quarter are independent events because one toss does not affect the other. Picking a card from a deck, keeping it, and picking another is a dependent event because the first pick changes the composition of the deck for the second pick.

Explanation:

To determine whether the two events mentioned are dependent or independent, we can use the definition of statistical independence. If the outcome of the first event does not affect the outcome of the second event, then the events are independent. If the outcome of the first event influences the outcome of the second event, then the events are dependent.

For the first scenario, tossing a dime and then tossing a quarter are independent events. This is because the result of tossing the dime has no effect on the result of tossing the quarter, much like having a nickel and a dime in your pocket and pulling one out, replacing it, and pulling one out again with probabilities being independent.

For the second scenario, when you pick a card from a deck of cards, keep the card, and then pick another one, the events are dependent. This is because the first card you draw and keep affects the composition of the deck from which the second card is drawn. It's like not replacing the first coin before pulling out the second one; your chances change based on the first outcome.

Using the concept of compound events and the law of the probability of compound events, we can see that independent events allow us to calculate the probability of any outcome when combining two independent events. Conversely, with dependent events, the probability of the subsequent event is influenced by the outcome of the preceding one.

Answer:

f(x) = sqrt(x-5) Domain: all real numbers greater or equal to 5 f(x) = 7/(x-8) Domain: all real numbers except 8 f(x) = sqrt(x) Domain: all positive real numbers and 0 f(x) = 8x Domain: all real numbers The domain of a function is the set of all numbers for which that function is valid.

Step-by-step explanation:

Answer:

it will be 4

Step-by-step explanation:

The width of the pasture is 210 feet.

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

We are given that pasture is twice as long as it is wide. its area is 88,200 ft2.

If the width is w and the length is l, then the length is 2w=l.

In addition,

The area of the rectangle = length × Width

l x w=88200

Using the area formula, Plugging 2w in for l, we get ;

2w x w = 88200

88200= 2w².

Now Dividing both sides by 2, we get;

w²=44100

w= √(44100)

w =210.

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-18 +3(5x-2)+8=46

-18 + 15x-6 +8 = 46

-18 + 15x +2 =46

-16 +15x =46

15x = 62

x = 62/15 = 4.1333

Answer:

Option C, Intellectual Response

Step-by-step explanation:

Intellectual response comes after intellectual thinking which includes deep , intensive and focused thinking in a certain direction. In this case, Jose after hearing a song on radio remembers that his brother used to play the same song on guitar. This is an intellectual response as after listening the song Jose's brain must have evaluated the past interactions associated with this song and hence after the evaluation he comes to know that he had heard the same song in past when his brother played it on his guitar.

Thus, option C is correct.

Answer:

The solution for t is  [tex]\frac{w}{(r_1+r_2)}[/tex]

Step-by-step explanation:

The given expression is [tex]w = t(r_1+r_2)[/tex]

We need to solve for the 't' ,

To solve for t, divide [tex]w = t(r_1+r_2)[/tex] by [tex](r_1+r_2)[/tex]

[tex]\frac{w}{(r_1+r_2)} = t[/tex]

Hence, The solution for t is  [tex]\frac{w}{(r_1+r_2)}[/tex]

The answer is x=7, because if you use PEMDAS you will come up with x=7.

18% + 8.5% = 26.5% which is close to 25%

 25% of 40 is 10, 40 +10 = 50

so the total bill would be just over $50

real cost:

40*0.085 = 3.40 = 40 + 3.40 = 43.40

43.40 *0.18 = 7.81, 43.40 + 7.81 = 51.21

Answer:

The gratuity is about 20% of $40, which is $8. The tax is about 10% of $40, which is $4. So, the total cost is about $40 + $8 + $4 = $52.

43 +x = 2(15+x)=

43 + x = 30 +2x

43 = 30 +x

13 =x

13 years

43+13 = 56

15 +13 = 28 ( 28*2 = 56)

It would take 90 minutes to unload a truck containing 2700 packages at a rate of 30 packages per minute.

This problem involves performing a simple division operation. Given that 30 packages are unloaded from a truck each minute and there are a total of 2700 packages on the truck, we find the time it would take to unload the truck by dividing the total number of packages by the number of packages that can be unloaded each minute.

We solve the problem as follows:

Therefore, it would take 90 minutes to unload the entire truck.

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The length of the line segment YX in rectangle YVWX is [tex]\rm 8\sqrt{3} \; units[/tex] and it can be determine by using the trignometric properties and properties of rectangle.

Given :

The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.

[tex]\rm tan \theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]\rm tan 60 = \dfrac{24}{VW}[/tex]

[tex]\rm \sqrt{3} = \dfrac{24}{VW}[/tex]

[tex]\rm VW =8\sqrt{3}\;units[/tex]

In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8\sqrt{3}\;units[/tex].

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[tex]\rm VW=YX = 8\sqrt(3)\;units.[/tex]

The length of the line segment YX in rectangle YVWX is \rm 8√(3)  \; units and it can be determine by using the trignometric properties and properties of rectangle.

Given :

YV = XW = 24 units
[tex]\rm \angle VXW = 30^\circ\\\rm \angle XWV = 90^\circ\\\rm \angle XVW = 60^\circ[/tex]
The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.

[tex]\rm tan \theta = (Perpendicular)/(Base)\rm tan 60 = (24)/(VW)\rm √(3) = (24)/(VW)\rm VW =8√(3)\;units[/tex]

In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8√(3)\;units[/tex].

The range of the composition is:

R (-∞, 3)

How to find the range?

We have the functions:

u(x) = -2x² + 3

v(x) = 1/x

The composition gives:

(u o v)(x) = -2*v(x)² + 3

(u o v)(x) = -2(1/x)² + 3

Now, as x tends to infinity, the first term tends to zero (because the denominator is to large) then the function has an upper bound at 3.

Then as x decreases, the function decreases, when x tends to zero, the function tends to negative infinity.

So the range is:

R (-∞, 3)

The vertex of the quadratic equation y = 6x^2 - 24 + 30 is (2, -6).

The given equation is y = 6x^2 - 24x + 30.

To find the vertex of this quadratic equation, we can use the formula x = -b/2a.

In this equation, a = 6 and b = -24. Plugging these values into the formula, we get x = -(-24)/(2*6) = 24/12 = 2.

Now, substitute this value of x into the equation to find the corresponding y-coordinate of the vertex.

Substituting x = 2, we get y = 6(2)^2 - 24(2) + 30 = 12 - 48 + 30 = -6.

Therefore, the vertex of the given quadratic equation is (2, -6).

Answer:

The intensity was [tex]5.02377\times 10^{18}[/tex]

Step-by-step explanation:

We are given

An earthquake registered 7.4 on the Richter scale

so, RC=7.4

the reference intensity of this quake was 2.0 × 10^11

so,

[tex]I_r=2.0\times 10^{11}[/tex]

now, we can use formula

[tex]RS=log(\frac{I}{I_r} )[/tex]

now, we can plug values

[tex]7.4=log(\frac{I}{2.0\times 10^{11}} )[/tex]

now, we can solve for I

[tex]10^{7.4}=\frac{I}{2.0\times 10^{11}}[/tex]

[tex]I=10^{7.4}\times 2.0\times 10^{11}[/tex]

[tex]I=5.02377\times 10^{18}[/tex]

To find the intensity of an earthquake registered on the Richter scale, use the formula based on the magnitude difference and energy ratio.

The intensity of the earthquake can be calculated using the Richter scale formula, which relates the magnitude difference to the energy ratio.

Answer: 134°F

Step-by-step explanation:

Given : A scientist is measuring the temperature change and a chemical compound the temperature dropped 11° Fahrenheit per hour from the original temperature .

Let x be the original temperature.

Then , the compound temperature after t hours is given by :_

[tex]y=x-11t[/tex]

At t= 4 hours and x= 90°F, we have

[tex]90=x-11(4)\\\\\Rightarrow\ x-44=90\\\\\Rightarrow\ x=90+44=134[/tex]

Hence , the  compounds original temperature = 134°F

Answer:

the answer is 1/2

i think

Step-by-step explanation: