Which of the following is a fourth degree polynomial function?

Answer: B

Shape: Diamond (4 triangles)

Formula: A = 1/2bh

so...

A = 4(1/2bh) <------ Multiply by 4 because a diamond has 4 triangles)

A = 4(1/2(5)(10))

A = 4(5(5))

A = 4(25)

A = 100 in^2

Answer:

1/3 or 0.33333

Step-by-step explanation:

To find the product of two fractions, multiply numerators and denominators separately.

You get 2340/7020 which simplifies to 1/3.

Hope that helps.

Answer:

1/3

Step-by-step explanation:

Step 1) 12/13 x 12/15 = 156/195

Step 2) 156/195 x 15/36 = 2340/7020

Step 3) Simplify to get 1/3

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

================================================

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

Answer:

x = (-5,10)

Step-by-step explanation:

The trigonometric ratio of cos ∅ is given as: cos ∅ = length of leg adjacent ∅ / length of hypotenuse.

The trigonometric ratio of cosine of an angle ∅ is defined as the ratio of the adjacent side of a right triangle to its hypotenuse.

Let's assume that we have a right triangle with an acute angle ∅. In this case, the cosine of the angle ∅ is given by:

cos ∅ = adjacent side / hypotenuse

Therefore, the cosine of an angle ∅ is a ratio that depends on the length of the adjacent side and the hypotenuse of the right triangle. The trigonometric ratio of cosine of an angle ∅ is always defined in terms of the adjacent side and the hypotenuse of the right triangle.

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Answer:

1.125 or 9/8

Step-by-step explanation:

Answer:

Her brothers pulse rate is 76.

Step-by-step explanation:

95% of 80 is 76. That only means that her brother's pulse rate must be 76 beats per minute.

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Answer:

Decay, 60%

Step-by-step explanation:

Remember that the exponential function is written in the form \(y=ab^x\). In this problem, a=57 and b=0.4. A function is considered a growth function when \(b>1\). Since 0.4 not greater than 1, this is an exponential decay function.

Now, to find the rate of decrease we can use part of the form \(y=a(1-r)^x\).

\(1-r\) represents the percentage decrease, in this case, 0.4. If that entire term is 0.4, we need to solve for \(r\).

\(1-r=0.4\\r=0.6\)

So, the rate of percentage decrease is 60%.

I hope this helps!

Answer:

\(\displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

Step-by-step explanation:

We are given a function:

\(\displaystyle \large{y = t^2 \sin (2t)}\)

To differentiate a function, we are going to use the product rules since there are two functions which are t^2 and sin(2t) multiplying together.

From the product rules, \(\displaystyle \large{y = f(x)g(x) \to y\prime = f\prime (x) g(x)+f(x) g\prime (x)}\)

Therefore, \(\displaystyle \large{y = t^2 \sin (2t) \to y\prime = (t^2)\prime \sin (2t) + t^2 (\sin (2t))\prime}\)

Before we start differentiating, I’d like you to look at [sin(2t)]’. A function like this, you cannot just directly derive and answer. You need to use chain rules.

We know that, \(\displaystyle \large{y = \sin (x) \to y\prime = \cos (x)}\) but what if the “x” is another function? Like sin(3x), sin(x^2) as examples. The insides are another function, can be expressed as fog(x) or gof(x) is composite function.

Basically, chain rule is a rule or formula for composite function and it’s the most common and useful as well as being always used in differentiation.

Chain Rules

\(\displaystyle \large{\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}}\)

where u is another function in a bracket. From the formula above, it can be also written as:

\(\displaystyle \large{[f(g(x))]\prime = f(g(x))\prime \cdot g(x)\prime\)

To simply say, you differentiate the whole function first then multiply with the chain or inner derived function.

So from the function, we obtain:

\(\displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot (2t)\prime}\\ \displaystyle \large{y\prime = 2t \sin (2t) + t^2 \cos (2t) \cdot 2}\\ \displaystyle \large{y\prime = 2t \sin (2t) + 2t^2 \cos (2t)}\)

The factored form would be:

\(\displaystyle \large{y\prime = 2t ( \sin (2t) + t \cos (2t))}\)

From above, for polynomial function, to differentiate, you can do by using the power rules.

Power Rules

\(\displaystyle \large{y = ax^n \to y\prime = nax^{n-1}}\)

Answer:

25 liters of 20%

50 liters of 50%

Step-by-step explanation:

x = liters of 50%

75 - x = liters of 20%

50x + 20(75 - x) = 40(75)

50x + 1500 - 20x = 3000

30x = 1500

x = 50

75 - x = 25

Answer:

the ways customers could get in financial trouble with thier credit cards are:

The Allure of Excessive Spending Interst Makes Paying Off the Balance Difficult. There's a chance you'll end up in debt.

You run the risk of damaging your credit score.

Minimum payments can give the impression of safety.

Credit Card Terms Can Be Confusing.

It's more difficult to keep track of spending, especially 

when using multiple credit cards.

Step-by-step explanation:

-

Direct distance from the base of the Space Needle to Kasie's house = 1429 feet.

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Given,

Height of the observation deck AB = 520 feet

Angle of depression = 70°

Distance of the Space needle base to house BC = ?

By the figure,

tan70° = AB/BC

BC = tan70°(AB)

BC = 2.7475(520)

BC = 1428.7 feet

Distance of the Space needle base to house to nearest foot = 1429 feet

Hence, 1429 feet is the distance between base of the Space Needle to Kasie's house.

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Rick would need to have at least 100 cars on hand to immediately be able to deliver any car (model, option package, color).

To immediately deliver any car, Rick Rich's dealership must have all possible combinations of Mercedes models, option packages, and colors in stock.

With five models, four option packages, and five colors, there are 5 x 4 x 5 = 100 possible combinations.

Therefore, Rick would need to have at least 100 cars on hand, each representing a unique combination of model, option package, and color. It's worth noting that having exactly 100 cars on hand would only allow Rick to deliver one of each possible combination, so it may be prudent to have additional inventory on hand to meet demand for more popular combinations.

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Answer:

2/3

Step-by-step explanation:

\(6/10=3/5=0.6\)

\(2/3 \approx 0.66666667\)

\(5/8=0.625\)

\(7/12 \approx 0.583333333\)

The fraction 2/3 has the greatest value.

The greatest of the fractions will be 2/3.

What is mean by Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

All fractions are;

6/10 , 2/3, 5/8, and 7 /12

Now, Find the greatest factor in the above fractions as;

Solve the fraction by dividing.

The value of the first fraction is;

6 / 10 = 0.6

The value of the second fraction is;

2/3 = 0.667

The value of the third fraction is;

5/8 = 0.625

The value of the fourth fraction is;

7 / 12 = 0.583

Clearly, In all the fractions the fraction 2/3 has the greatest value.

Therefore, The greatest of the fractions will be 2/3.

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Answer:

pop music of 90

Answer:

C. Trimodal

Step-by-step explanation:

The mode of a data set is the value that appears most frequently.

If we list the given data set in increasing order, we get:

70, 75, 75, 75, 80, 83, 83, 83, 84, 84, 86, 86, 86, 88, 89

We can see that there are 3 values (75, 83, 86) that all have equally high levels of frequency. Therefore, this data set is trimodal, since tri- is the Latin root for 3.

Answer:

\(\frac{3}{35}\)

\(\frac{1}{5} *\frac{4}{7} = \frac{1 * 4}{5 * 7} = \frac{4}{35}\)

\(\frac{4}{35} = x\)

\(x * \frac{3}{4}\)

\(\frac{x(4) * 3}{y(35) * 4} = \frac{12}{140}\)

\(\frac{12 / 4}{140 / 4} = \frac{3}{35}\)

_______________________________________________________

And with that information, your final answer is \(\frac{3}{35}\)

_______________________________________________________

We learned how to multiply fractions using different denominators, and multiple parameters.

Questions related to this topic? Ask me in the comments box.

Answer:

Yes.

Step-by-step explanation:

Because yes.

The two trends that can be set up on the graph below are negative correlation and positive correlation.

We've a positive correlation. From January to August, there was an upward trend. This is due to the fact that the function values rise roughly in this sphere.

We've a negative association. From August to December, there was an upward trend. This is due to the fact that the function values drop mainly in this sphere.

A positive correlation exists when two variables work in tandem, similar that as one rises or falls, the other follows suit. A negative correlation occurs when two variables move in contrary directions, similar that when one rises, the other lowers.

Correlations can help marketers, force chain directors, and other professionals by detecting salutary trends, similar as client geste correlations or assiduity-specific practices.

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We're given:

Let x equal the calorie count per serving of the original popcorn.

The light popcorn has a calorie count of 120, which is 25% fewer calories than regular popcorn. This means that 75% of the calorie count of regular popcorn is equal to that of the light popcorn:

\(x*0.75=120\)

\(x*0.75=120\)

⇒ Divide both sides by 0.75:

\(\dfrac{x*0.75}{0.75}=\dfrac{120}{0.75}\\\\x=160\)

Therefore, each serving of regular popcorn has 160 calories.

The given expression represents the present value of a series of future cash flows discounted at a rate of 6.5% per year.

Each term in the expression represents a cash flow at a specific time in the future, and the denominator in each term represents the discount factor, which reflects the time value of money.

The first term, $250,000 / (1+0.065)^1, represents a cash flow of $250,000 that will be received in one year.

To determine its present value, we divide it by the discount factor (1+0.065)^1, which reflects the fact that the money will be received one year from now and is, therefore, less valuable than money received today.

Similarly, the second term, $37,500 / (1+0.065)², represents a cash flow of $37,500 that will be received in two years.

To determine its present value, we divide it by the discount factor (1+0.065)²,

which reflects the fact that the money will be received two years from now and is, therefore, less valuable than money received today.

This process is repeated for each term in the expression, representing cash flows that will be received in three, four, five, and six years, respectively.

The sum of these present values represents the total present value of the cash flows or the amount that they are worth today if they are discounted at a rate of 6.5% per year.

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Answer:

(5x-4)(x+1)

Step-by-step explanation:

Answer:

X = 7. You can confirm the answer yourself by plugging in this number. I hope I helped :)

Step-by-step explanation:

The division property of equality simply tells us that if we divide both sides of an equation by the same number, then the equation remains the same.

It should be noted that when the denominator of a fraction is equal to 1, and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Fractions simply means, numbers that are not whole.

If the numerator is nonzero, and the denominator is 1; then the fraction has a value of the numerator.

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Answer:

When the denominator of a fraction is equal to 1 and the numerator is nonzero, the value of the fraction is equal to the numerator of the fraction.

Step-by-step explanation:

I took a 2.12 math quiz in K12 and got it 100% Correct! Yes!

Answer:

Without knowing the specific translation applied to the function f(x), it is not possible to determine the function rule for g(x). However, the general form for a translation of a function is:

g(x) = f(x - h) + k

where h is the horizontal shift and k is the vertical shift. Therefore, if the horizontal and/or vertical shifts applied to f(x) to obtain g(x) are known, the function rule for g(x) can be determined using the above formula.

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Hello! (:

The value of 7 in 82.76 is:

\(\frac{1}{10}\)

Hope it helps! (:

If you have any. questions, feel free to comment! (:

~An excited gal

#StayJoyful

\(SparklingFlower (:\)