A car travels 21 km in 16 minutes. What is its average speed in km/h?
Give your answer rounded to 1 decimal place.

The division of the given polynomial is \(\frac{20x^3+12x^2+17x-17}{5x^2-2x}=4x+4+\frac{25x-17}{5x^2-2x}\).

What is a long division of polynomials?

A long-division polynomial is an algorithm for dividing polynomials by another polynomial of the same or a lower degree. The long division of polynomials also consists of the divisor, quotient, dividend, and the remainder as in the long division method of numbers.

The given expression is (20x³ + 12x² + 17x - 17) ÷ (5x² - 2x)

\(=\frac{20x^3+12x^2+17x-17}{5x^2-2x}\\\\=4x+\frac{20x^2+17x-17}{5x^2-2x}\\\\=4x+4+\frac{25x-17}{5x^2-2x}\\\)

Hence, the division of the given polynomial is \(\frac{20x^3+12x^2+17x-17}{5x^2-2x}=4x+4+\frac{25x-17}{5x^2-2x}\).

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The angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

We shall evaluate for the angle of elevation θ in degree, and then convert the result to radian as follows:

θ = tan⁻¹(4255/2000)

θ = 64.82482°

we multiply by π/180 to convert to radian;

θ' = 64.82482° × π/180

θ' = 1.13186 rounded to five decimal place.

Therefore, the angle of elevation θ is equal to 1.13186 in radian rounded to five decimal place.

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Answer:

x = 3, the error is that the -2x should be added.

Step-by-step explanation:

The -2x should be added to the left side.

3x - 7 = -2x + 8

3x + 2x = 8 + 7

5x = 15

x =3

Answer lest edited 3:11 PM Central, 11/24/2020

Answer:

x=5

Step-by-step explanation:

Correct way:

Add 2x to 3x ( 5x )

3x-7=8

Add 7 to 8 ( 15 )

3x=15

Divide 15/3

x= 5

What was wrong:

You need to combine like terms and put the variable on the left side of the equation and then follow the steps above. You also forgot to divide.

Hope this helped, Have a Great Day!!

The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.

A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.

As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.

Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.

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A) The total amount they ended up paying for the house is $786,685.60.

B) They paid $442,685.60 in interest on the mortgage.

A) The total amount paid for the house is the sum of the down payment and the total mortgage payments.

Down payment: $43,000

Total mortgage payments

= 3602.46 x 12

= 743,685.60

Total amount paid for the house

= Down payment + Total mortgage payments

= $43,000 + $743,685.60

= $786,685.60

Therefore, the total amount they ended up paying for the house is $786,685.60.

B) Principal amount

= Purchase price - Down payment

= $387,000 - $43,000

= $344,000

Interest paid on the mortgage

= Total amount paid for the house - Principal amount

= $786,685.60 - $344,000

= $442,685.60

Therefore, they paid $442,685.60 in interest on the mortgage.

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Step-by-step explanation:

First one is 4,713,354

And for the second one I'm just going to assume that the sum of those 2 numbers on the right side is the answer.

So 1,377,136 for bottom one.

An inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

In the given question,

cost for admission parking = $15

Tickets = $25 per person

Let x be the number of people those who go to the amusement park.

On parking and admission spent not more than $115

So we get an inequality,

15 + 25x ≤ 115

We solve above inequality.

25x ≤ 115 - 15

25x ≤ 100

25x / 25 ≤ 100/25

x ≤ 4

This means that approximately 4people can go to the amusement park.

Therefore, an inequality which can be used to determine x the number of people who can go to the amusement park is: 15 + 25x ≤ 115

Also, approximately 4 people can go to the amusement park.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Hello!

TO find the root all you gotta do is 3x3 which gives you 9

The value of m + n is given as follows:

A. 18.

The exponential expression for this problem is defined as follows:

\((x^5y^6)^{\frac{1}{5}}(x^3y^4}^{\frac{1}{4}}\)

Applying the power of power rule, we have that the exponents are given as follows:

Then the values of m and n are given as follows:

m = 7, n = 11.

Thus the sum is given as follows:

m + n = 7 + 11 = 18.

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The equation of the exponential function represented by the table will be:

\(f(x) = 2(4)^{x}\)

An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

We know the equation of exponential function such as

\(f(x) = ab^{x}\)

Put x=0, and y=2 in the function

\(2 = ab^{0} \\2 = a\)

Also x=1, and y=8 in the function

\(8 = 2b^{1} \\b = 4\)

Thus,

\(f(x) = ab^{x} \\f(x) = 2(4)^{x}\)

Therefore, the equation of the exponential function represented by the table will be:

\(f(x) = 2(4)^{x}\)

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Answer: 1/5

Step-by-step explanation:

Answer:

I'm pretty sure the answer is 48 minutes!

The doctor recommends rest if the patient has the flu. Then the correct option is A.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Read the following two statements.

Then, if possible, use the Law of Detachment to draw a conclusion.

Then the correct option is A.

The doctor recommends rest if the patient has the flu.

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Answer:

Um, hi...do you have a question at all??

Step-by-step explanation:

Answer:

The answer is 60 hours.

Step-by-step explanation:

We could use proportions to solve.

\( \frac{1 \: hour \: on \: earth}{4hours \: on \: planet \: s} = \frac{x}{240hours \: on \: planet \: s} \)

\(4 \times x = 4x \\ 1 \times 240 = 240\)

\( \frac{4x}{4} = \frac{240}{4} \\ x = 60\)

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

The correct answer is:

P(nuts)=7/9

Step-by-step explanation:

The experimental probability that the next sundae sold will have nuts is

7/9

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

\(P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}\)

where, \(P_e(E)\)  is denoting the experimental probability of occurrence of E.

We are given that At Frosty Freeze, 14 of the last 18 sundaes sold had nuts.

Therefore,

Probability that the next sundae has nuts is 14/18 = 7/9.

Thus, Probability that the next sundae does not have nuts = 2/9

P(nuts)=7/9

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Given set A={1,2,3) and a relation R ={(1,2), (2,1)), The relation R will be​ (1, 1)

Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects.

t is used to explain collections of elements such as numbers, alphabets, and variables. The notation and symbols for sets are based on the operations performed on them.

The Given set A={1,2,3) and a relation R ={(1,2), (2,1)),

Then the relation will be the transitive if (1, 1) is added

Here, (1,2) e (2,1) ∈ R, if transitive (1, 1) should belong to R

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1.5 im sorrry again if im wrong:(

Step-by-step explanation:

im sorry if i am wrong

Answer:

178.64 square cm

Step-by-step explanation:

5.8 x 8.8 x 2 = 102.08

8.8 x 8.7 = 76.56

76.56 + 102.08 =

178.64

Hope that helps!

Answer:

Step-by-step explanation:

The first thing we need to focus on is the fact the large bag (30 cups) is 2.5 larger than the small bag. So, the first we need to do is divided 30 by 2.5, which is 12. (300/25 = 30/2.5 = 12, in case you're confused.) So the small bag has 12 cups of sugar.

What that down, we need to focus how many cakes the small bag can make, which was 9. 3/4 of a cup is left over. We can create an equation from that info, that being 9x + 0.75 = 12. Now let's solve for x.

9x + 0.75 = 12

First, subtract 0.75 from both sides. With that, we can solve for x directly.

9x = 12 - 0.75

9x = 11.25

Now, divide both sides by 9.

x = 11.25/9

x = 1.25

With that, we now know that each cake needs 1.25 cups of sugar.

With that, the last thing we need to is divide 30 by 1.25. Again, I can use powers of ten, to quickly divide 3000 by 125 (10²) to get 24 cakes.

With that done, we have our answer. 24 cakes can be made with a large bag of sugar.

I hope this helps!  (⌒ω⌒)

The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer:

(xyz + 1)

Step-by-step explanation:

We can use the identity:

\(a^2 - b^2 = (a + b)(a - b)\)

to solve for the blank in this equation.

On the left side, we can identify a difference of two squares (a² - b²).

We can see that there is already an (a - b) term on the right, so in the blank, we just have to construct an (a + b) term:

(xyz + 1)

This satisfies the equation:

(xyz)² - 1 = (xyz + 1) · (xyz - 1)

The value of x = -3/2 .

An equation is a mathematical statement that relates unknown variable to constants to determine their value.

The equation given is

(2x+3 ) / 7 Divided by 1 = 0

2x +3 = 0

2x = -3

x = -3/2

Therefore the value of x = -3/2 .

The complete equation is

(2x+3)/7

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Answer:

the numbers are 7 and -3

Step-by-step explanation:

Answer:

7 and -3 are the numbers

Step-by-step explanation:

7-3= 4

7×-3= -21

Answer:

-6

Step-by-step explanation:

If ∠2=10x+7 and one angle is 67 degrees then value of x is 6.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that the triangle has two equal sides which makes the triangle as isosceles.

In an isosceles triangle the two sides will be always equal and the angles will be also equal.

One angle of the triangle is 67 degrees

We need to find the ∠2.

As we know that the equal sides make equal angles.

∠2=67 degrees

and from given ∠2=10x+7

Now equation 67 with the 10x+7 to find the value of x.

So 67=10x+7

subtract 7 from both sides

67-7=10x+7-7

60=10x

Divide both sides by 10

x=60/10

x=6

Hence, the value of x is 6.

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The accrued value of the account in 14 years is $4967.89

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Amount = P * (1 + 0.25r)ᵗ

Where

P = Principal = 4200

r = Rate = 5.2% = 0.052

t = time = 13

Substitute the known values in the above equation, so, we have the following representation

Amount = 4200 * (1 + 0.25 * 0.052)¹³

Evaluate

Amount = 4967.89

Hence, the amount is 4967.89

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