What is the equation of the following line? Be sure to scroll down first to see all answer options.

A race car driver is 3.79 km away from where she started.

Assume that a race car driver turns southwest, at an angle of  45 degrees.

Also she turns East making another 45 degree angle.

So, we get a right triangle.

Let ABC be right triangle with A = 90°, B = 45° and C = 45°

For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)

Consider the sine of angle B

sin(B) = Opposite side of angle B / Hypotenuse

sin(45) = x / 2.75

x = 1.94

sin(C) = Opposite side of angle C / Hypotenuse

sin(45) = y/2.75

y = 1.94

So, the distance to north before paths crossed would be,

N = 4.69 - y

N = 3.31

And the distance after she passed her northern path.

E = 3.89 - x

E = 1.85

Let m be the distance from Starting Point to End Point.

Using Pythagoras theorem,

m² = N² + E²

m² = (3.31)² + (1.85)²

m = 3.79 km

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Answer:

20+18 = 38

or its

2838

My reasoning --> because if you add 17+14 its 31  .... look at the patterns I guess?

2838

If you like, I can give more explaintion.

The measure of the angle x would be 25.2°.

What is a circle theorem?

The circle theorem is a set of mathematical rules and relationships that apply to circles and their components, such as chords, tangents, and angles. These theorems describe how the different parts of a circle relate to each other and are used to solve geometric problems involving circles. Some common circle theorems include the inscribed angle theorem, the chord-chord theorem, and the tangent-secant theorem.

By using the circle theorem, we can write

5x-7 = 119

5x = 119 + 7

5x = 126

x = 126/5

x = 25.2°

Hence, the measure of the angle x would be 25.2°.

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Answer: rational

Step-by-step explanation:

16/5=

(160/5)/10=

32/10=3.2 ==> rational since it has a finite number of digits before and after the decimal.

1.5 x 10⁵

We use scientific notation to write huge ( or micro ) numbers as easily as possible. To do that, we use the following notation: a x 10ᵇ

Take 150,000, and put a decimal right between the 1 and 5, like so:

1.50000

Now simply count the numbers after the decimal:

1 . 5 0 0 0 0

    1  2 3 4 5

That's five places, or numbers, after the decimal, and now we can use the notion mention earlier, a x 10ᵇ

So a = 1.5 and b = 5, and now we can combine the whole thing, so 1.5 x 10⁵

We can double check if needed/desired by doing the following

10⁵ = 100,000 x 1.5 = 150,000

150000 is 1.5×10⁵ in scientific notation.

Scientific notation is a form of expressing large no. in compact form where the base (digit before the decimal) should be 1≤base<10.There after we multiply the base with powers of 10 to how much digits we have moved the decimal from rightmost side.

According to the given question

Asher is involved in a competition where the grand prize is 150000 dollars.

We have to express this in scientific notation.

150000 = 1.5×10⁵

What we did here is we placed a decimal 5 digits to the left and therefore raised it to the power of 10.

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The probability that the first is a king, the second a diamond and the third a diamond quiz let is 1/13, 1/4 and 10/52 respectively.

Now, we know that there are 52 cards in the deck of cards, and there are 13 cards of each suits i.e. diamonds, spade, heart and clubs. Also there are 12 face cards in total of the deck.

So, the probability if getting the first card is king :

King is a face card and there are 4 kings in the deck so the probability will be :

P(getting 1st card as king) = 4/52 = 1/13.

The probability of getting the second card a diamond is :

we know that there are 13 cards of the diamond in the deck so the probability will be :

P(getting the diamond card) = 13/52 = 1/4.

Now, lastly the probability if getting the diamond quiz let is :

There are 10 flashcards of the diamonds in the deck, so the probability will be :

P(getting the diamond flashcard) = 10/52.

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Answer:

16

Step-by-step explanation:

There are 2 different ways to solve this

1) The bigger triangle is 4 times bigger than the smaller one

5 x 4 = 20

3 x 4 = 12

From this method you can see they all connect so you take the smaller triangles value of 4 and multiply it by 4

4 x 4 = 16

2) Pythagorean theorem and reorganizing the formula so that the a value is found

\(a = \sqrt{c^{2} -b^{2} }\)

Based on the uninhibited growth model, we would predict that the population of Cary in 2001 would be approximately 101,656.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x.

The uninhibited growth model assumes that the population grows exponentially over time. We can use the formula for exponential growth to predict the population of Cary in 2001:

P(t) = P0*\(e^{(rt)}\)

where:

P(t) = the population at time t

P0 = the initial population

r = the growth rate

e = the mathematical constant e (approximately 2.71828)

t = the time elapsed since the initial population measurement

We can use the population measurements from 1980 and 1987 to estimate the growth rate:

P0 = 21763

P(1987) = 39387

t = 7 years

r = ln(P(1987)/P0)/t

r = ln(39387/21763)/7

r = 0.0935

Now we can use this growth rate to predict the population in 2001:

P(2001) = P0 * \(e^{(rt)}\)

P(2001) = 21763 * \(e^(0.0935*21)\)

P(2001) ≈ 101,656

Therefore, based on the uninhibited growth model, we would predict that the population of Cary in 2001 would be approximately 101,656.

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Answer:

34.40

Step-by-step explanation:

43×0.2 = 8.60

43-8.60= 34.40

the answer is -24

(-) x (+) = (-)

Glow costs 16/27 dollars, which is equal to 59.3 cents per volume unit.

Let's start by assigning variables to the unknown prices and volumes of the toothpastes. Let x be the price per unit volume of Fresh, y be the price per unit volume of Glow, and z be the price per unit volume of Bright. Let v1 be the volume of Fresh, v2 be the volume of Glow, and v3 be the volume of Bright. From the information given in the problem, we can set up the following equations:

z = 1.6y (a tube of Bright is 60% more expensive than a tube of Fresh)

v3 = 0.75v2 (a tube of Bright has 25% less volume than Glow)

y = 0.75z (a tube of Glow is 25% less expensive than a tube of Bright)

v2 = v1 + 100/3 (a tube of Glow has 100/3 more volume than Fresh)

We can substitute the first equation into the second equation to eliminate z:

v3 = 0.75v2

(substitute v2 = 0.75z and v1 = 1)

0.75v2 = 0.75(0.75z + 100/3)

0.75v2 = 0.5625z + 25

(substitute z = 1.6y and v2 = v1 + 100/3)

0.75(v1 + 100/3) = 0.5625(1.6y) + 25

0.75v1 + 25/3 = 0.9y + 25

0.75v1 = 0.9y + 50/3

We can substitute the third equation into the fourth equation to eliminate y:

v2 = v1 + 100/3

(substitute y = 0.75z)

0.75z = 0.75(0.75y) + 100/3

z = y + 16/9

(substitute z = 1.6y)

1.6y = y + 16/9

y = 16/27

Therefore, the price per unit volume of Glow is 16/27 dollars, or 59.3 cents per unit of volume.

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Answer:

v(-2) = 20

Step-by-step explanation:

The number of viewers, in t days after Jada saw the video, is given by:

\(v(t) = 320*(4)^{t}\)

Find v(−2).

This is v when \(t = -2\). So

\(v(-2) = 320*(4)^{-2} = \frac{320}{4^2} = \frac{320}{16} = 20\)

So

v(-2) = 20

Answer:

In simplest form it would \(\frac{2}{3}\) or 0.66666666 and so on.

Answer:

2/3

Step-by-step explanation:

I can add a explenation soon, I’m in class

Step-by-step explanation:

answers...................

The value we can use in the series is \($\sum_{k=0}^\infty 1/k^8\).

To check the convergence we consider two series as

Series 1: \($\sum_{k=0}^\infty \frac{k^8}{5(3-6k+3k^6)^2}$\)

Series 2: \($\sum_{k=0}^\infty \frac{k^8 + k^3 + 4k}{5(3-6k+3k^6)^2}$\)

We employ the p-test, which indicates that the series converges if the ratio of succeeding entries in a series approaches a number less than 1. The ratio of successive terms for Series 1 approaches 1, indicating that Series 1 diverges.

We can infer that Series 2 also diverges because Series 1, which is smaller than Series 2, likewise diverges.

Thus, the given series also diverges.

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Answer:

he length of the rope is approximately equal to 10.99 feet

Answer:

it is incorrect becuase 5.68 rounded is 6 ,  4.1 rounded is 4 . 4 times 6 equals 24

Step-by-step explanation:

i passed the quiz

Answer:   The $20 estimate is too low. $5.68 was incorrectly rounded down; it should have been rounded up to $6. The correct estimate should have been $24, so $20 will not be enough to buy 4.1 pounds of cherries.

Step-by-step explanation:

i took the quiz

Answer:

B and D

Step-by-step explanation:

7z -1 = 27 46 - 8z = 14

+1 +1 -46 -46

7z = 28 -8z = -32

/7 /7 /-8 /-8

z = 4 z = 4

Answer:

$8,720

Step-by-step explanation:

SI = PRT where;

SI = simple interest

P = principal amount/starting amount

R = rate as a decimal/fraction

T = time in years

I = 8000 . 5 . 0.018

I = 720

8000 + 720 = 8720

Answer:

the answer is 41

Step-by-step explanation:

C. 41

Step-by-step explanation:

Yes, the Mean Value Theorem can be applied to f on the closed interval [1,9]. To determine if the Mean Value Theorem can be applied to the function f(x) = (x - 10)/x on the closed interval [a, b] = [1, 9], we need to check if the function is continuous on the interval and differentiable on the open interval (a, b) = (1, 9).

1. Continuity: The function f(x) = (x - 10)/x is continuous for all x ≠ 0. Since the interval [1, 9] does not include x = 0, the function is continuous on this interval.

2. Differentiability: To check differentiability, we need to find the derivative of f(x). The derivative of f(x) = (x - 10)/x can be found using the Quotient Rule:

f'(x) = [(1)(x) - (x - 10)(1)]/(x^2) = [x - (x - 10)]/(x^2) = 10/x^2

Since the derivative exists for all x ≠ 0 and the interval (1, 9) does not include x = 0, the function is differentiable on this open interval.

Therefore, the Mean Value Theorem can be applied to the function f(x) = (x - 10)/x on the closed interval [1, 9].

Your answer: Yes, the Mean Value Theorem can be applied.

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Answer:

40% (decrease)

Step-by-step explanation:

150 - 250

|250|

× 100% =

You will have approximately $1929.29 available to spend in 6 years.

To calculate the future value of your deposit after 6 years, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)^Time

Plugging in the values:

Present Value (PV) = $1491

Interest Rate = 5.07% = 0.0507

Time = 6 years

Future Value = $1491 * (1 + 0.0507)^6

Calculating the expression:

Future Value = $1491 * (1.0507)^6

Future Value ≈ $1929.29

Therefore, you will have approximately $1929.29 available to spend in 6 years.

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Answer:

Yes

Step-by-step explanation:

Answer:

yes you can make an isosceles triangle

The mean absolute deviation, mad, of the given data, 21, 25, 16, 8, 16, 10, is 4.83

From the question, we are to calculate the mean absolute deviation, mad, of the given data

First, we will calculate the mean of the data

21, 25, 16, 8, 16, 10

Mean = (21 + 25 + 16 + 8 + 16 + 10)/6

Mean = 96/6

Mean = 16

Now, we will determine the positive differences of each number from the mean

         Positive differences

21        5

25       10

16        0

8         8

16        0

10        6

Now, we will find the mean of the positive differences

Mean absolute deviation =(5 + 10 + 0 + 8 + 0 + 6)/6

Mean absolute deviation = 29/6

Mean absolute deviation = 4.83

Hence, the mad is 4.83

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In total Julian buys about 11.4 pounds of potatoes by spending $5.58 on red potatoes and $4.68 on yellow potatoes.

To find the total amount of potatoes that Julian buys,  divide the total cost of each type of potato by the cost per pound.

Red potatoes cost $5.58 and cost $0.90 per pound, so in total Julien buys the next few pounds of red potatoes.

5.58 ÷ 0.90 ≈ 6.2 pounds (rounded to one decimal place)

Similarly, yellow potatoes cost him $4.68 and cost $0.90 per pound, so the total pounds of yellow potatoes that Julian buys would be:

4.68 ÷ 0.90 ≈ 5.2 pounds (rounded to one decimal place)

To find the total amount of potatoes that Julian bought, add the pounds of red potatoes and the pounds of yellow potatoes.

6.2 + 5.2 ≈ 11.4 pounds (rounded to one decimal place)

So in total Julian buys about 11.4 pounds of potatoes. 

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Answer:

158.94

Step-by-step explanation:

round if needed

Answer:

158.940366972

Step-by-step explanation:

calculator. pretty random question tho.