1. suppose you purchased a new car for
$30,000 in 2015. if the value of the car
decreased by 8% each year, during what year
will the car be worth $10,000

a) Recall the integration by parts formula:

[tex]\displaystyle \int u \, dw = uw - \int w \, du[/tex]

Then with [tex]u = x[/tex] and [tex]dw = e^x\,dx[/tex] we have

[tex]\displaystyle v = \int e^x x \, dx = xe^x - \int e^x \, dx[/tex]

[tex]\implies \boxed{v = xe^x - e^x + C}[/tex]

since [tex]w=\int e^x\,dx=e^x[/tex] and [tex]du=dx[/tex]. (C is of course an arbitrary constant that can be determined exactly if you know the velocity at some given value of x.)

b) No?

[tex]\displaystyle \int e^xx\,dx = \int xe^x\,dx[/tex]

because multiplication is commutative. I get the feeling I'm missing something here...

Answer:

slope = 1/3

Step-by-step explanation:

slope,m = vertical change/ horizotal change

that means (-3)-2/(-5)-10 or 2-(-3)/10-(-5)

and we got -5/-15 or 5/15.

So the answer is 1/3.

1 year or less is at the first quartile mark in the box plot, therefore, the number of schools that participated for a year and less is: A. 6 schools.

The data point at the beginning of the edge of the rectangular box in a box plot is the first quartile mark of the data, which is 1/4 or 25% of the data.

1 year or less is at the first quartile mark in the box plot. That is 1/4 of the total number of schools.

Therefore, schools that participated for a year and less = 1/4(24) = 6 schools.

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Step-by-step explanation:

un is the balance of the loan after n years.

so,

u12 is the balance of the loan after 12 years.

Answer:

x = (y - b)/m.

Step-by-step explanation:

y=mx+b      

Subtract b from both sides :-

y - b = mx

Divide both sides by m:-

(y - b) /m = x.

Answer:

(2,-4)

Step-by-step explanation:

Here, h=2 and k=-4, so the center is (2,-4)

Step-by-step explanation:

Solve the following equation for x.

10 = 2 – 4(ar – 3)

OA. -

a

OB.

Oc.

OD.

5

a

The equation for the (x-4)²2 is  5. x=4± √5. Hence, option D is correct.

Due to the fact that they contain two or more algebraic terms, quadratic equations fall within the category of polynomial equations. It must equal 0 in order to solve a quadratic equation. There can be zero, one, or two (true) solutions to a quadratic equation.

To solve the equation (x - 4)² = 5, we can start by taking the square root of both sides:

√[(x - 4)²] = ±√5

This gives us two possible equations:

x - 4 = √5 or x - 4 = -√5

Now it can add 4 to both sides of each equation:

x = 4 + √5 or x = 4 - √5

So the solutions to the equation (x - 4)² = 5 are x = 4 + √5 and x = 4 - √5.

Thus, option D is correct.

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The given equation is wrong, the correct equation is given below-

(x-4)²2 = 5.

Based on the table, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

In the first week, there's 9.5 pounds. This can be illustrated using the arithmetic progression. The formula will be:

= a + (n - 1)d

where,

a = first term

d = common difference

3rd term = a + 2d

13 = 9.5 + 2d

2d = 13 - 9.5

2d = 3.5

d = 3.5/2

d = 1.75

Therefore, the rate of change of the weight of the rabbit in pounds per week will be 1.75 pounds.

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Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

Answer:

Triangle ABC is not a Right Triangle

Step-by-step explanation:

The perimeter of a triangle is all of the sides added together so we can model our equation like so:

AB + BC + CA = P

or

8 + 5 + CA = 22

We first combine like terms

13 + CA = 22

Then make the variable have no numbers on its side

13 + CA = 22

-13          -13

CA = 9

So now that we know what CA is, we can determine whether or not its a right triangle

We can use the Pythagorean Theorem for this:

a^2 + b^2 = c^2   (the '^' symbol means 'to the power of')

or

5^2 + 8^2 = 9^2

Now we Solve

5^2 = 25

8^2 = 64

9^2 = 81

25 + 64 =? 81

89 does not equal 81

So Triangle ABC is not a Right Triangle

Answer:

  x ≈ 95.6

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between trig functions and sides of a right triangle. Here, the hypotenuse of the triangle and the side adjacent to the given angle are marked, so the relationship of choice is ...

  Cos = Adjacent/Hypotenuse

__

Using the values shown, we have ...

  cos(15°) = x/99

Solving for x gives ...

  x = 99·cos(15°) ≈ 95.6

The length of the side marked x is about 95.6 units.

Answer:

If I am not mistaken the number is 54,810.

Hope I helped.

[tex]2x^6y^2[/tex]The equivalent expression to the given expression is [tex]2x^6y^2[/tex] (option D)

An expression in mathematics is a fusion of numbers, variables, and operators that embodies a mathematical entity. Expressions possess the ability to symbolize magnitudes, functions, and connections, exhibiting versatility and finesse.

Expressions are used in many different areas of mathematics. They are used to represent quantities, functions, and relationships.

To determine the given expression, lets start:

[tex](12x^9y^4)/(6x^3y^2)[/tex]

= [tex](12/6) x^(^9^-^3^) y^(^4^-^2^)[/tex]

= [tex]2x^6y^2[/tex]

Therefore, the equivalent expression to [tex](12x^9y^4)/(6x^3y^2)[/tex] is [tex]2x^6y^2[/tex]

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Answer:

see explanation

Step-by-step explanation:

to find the first 4 terms substitute n = 1, 2, 3, 4 into the sequence rule

to find the 10th term substitute n = 10 into the rule

(a)

a₁ = 1² + 3 = 1 + 3 = 4

a₂ = 2² + 3 = 4 + 3 = 7

a₃ = 3² + 3 = 9 + 3 = 12

a₄ = 4² + 3 = 16 + 3 = 19

a₁₀ = 10² + 3 = 100 + 3 = 103

(b)

a₁ = 2(1)² = 2(1) = 2

a₂ = 2(2)² = 2(4) = 8

a₃ = 2(3)² = 2(9) = 18

a₄ = 2(4)² = 2(16) = 32

a₁₀ = 2(10)² = 2(100) = 200

The system of equations of two unknowns is formulated and solved.

      [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ x\times y = 4 \\ x^2+y^2 = 17 \end{matrix}\right. \ \Longrightarrow \ y=\dfrac{4}{x}} \end{gathered}$}[/tex]

        [tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x^2+\left (\dfrac{4}{x} \right )^2=17\ \Longrightarrow\ x^4+16=17x^2 } \end{gathered}$}[/tex]

                                                       [tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{align*} 0&=(x^2)^2-17(x^2)+16\\ =(x^2-16)(x^2-1) \\ \ \ \ \ \ \ \ \ \ \ =(x+4)(x-4)(x+1)(x-1) \end{gathered}$}[/tex]

Possible number pairs are 4, 1 and -4, -1 .

speed = distance/time

speed = 180/2

speed = 60km/hr

hope it helps...!!!

Answer:

see the attachment photo!

Answer:

time=t= 9.36 months.........

The money was in the SACCO for a time of 0.78125 years.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Given that,

Amount of money deposited or principal amount = 56,800

Rate of interest = 12% = 12/100 = 0.12

Final amount = 62,125

The formula for simple interest is,

A = P(1 + rt), where A is the final amount, P is the principal amount, r is the interest rate and t is the time.

Substituting,

56800 (1 + 0.12t) = 62125

1 + 0.12t = 1.09375

0.12t = 0.09375

t = 0.78125 years

Hence the time that the money kept for is 0.78125 years.

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For pumpkins

Total 12mins sets

earnings

For apples

Total 12 mins

Earnings

Total earnings

Answer:

$37.60

Step-by-step explanation:

Eve earns:

Money earned from picking pumpkins:

1 hour = 60 minutes

[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 60\:minutes\\\\& = \sf \$4.00\:per\:12\:minutes \times 60\:minutes\\\\& =\sf \dfrac{\$4.00}{12\:minutes} \times 60\:minutes\\\\ & = \sf \$4.00 \times \dfrac{60\:minutes}{12\:minutes}\\\\ & = \sf \$4.00 \times 5\\\\ & = \sf\$20.00\end{aligned}[/tex]

Money earned from picking apples:

[tex]\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 48\:minutes\\\\& = \sf \$4.40\:per\:12\:minutes \times 48\:minutes\\\\& =\sf \dfrac{\$4.40}{12\:minutes} \times 48\:minutes\\\\ & = \sf \$4.40 \times \dfrac{48\:minutes}{12\:minutes}\\\\ & = \sf \$4.40 \times 4\\\\ & = \sf\$17.60\end{aligned}[/tex]

Total earned:

= money earned from picking pumpkins + money earned from picking apples

= $20.00 + $17.60

= $37.60

The axis of symmetry of h(x) = 5x2 + 40x + 64 = -4

The formula for calculating the axis of symmetry is expressed as:

Axis of symmetry x = -b/2a

h(x) = 5x^2 + 40x + 64

a = 5 and b = 40

Answer:

11 hope this helps you and write

Answer:

-17.25

Step-by-step explanation:

The number of grams of canned apple that Chantel needs for her apple-cinnamon cake is about 1400 grams.

To know the amount of canned apple that Chantel needs for her apple and cinnamon cake recipe, we must review the amount of apple that she needs for the filling of her cake.

According to the basic recipe to make this cake, we need 6 to 8 apples. Taking into account that each apple weighs about 200g, we can infer that Chantel is going to use about 1400g of canned apple as shown below.

On average we need 7 apples.

Each apple weighs 200g, so 7 apples would be 1400g.

Based on the above, Chantel needs 1400g of canned apple.

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Answer:

y = -2x - 6

Step-by-step explanation:

We know that the slopes of the lines are equal when the lines are parallel to each other.

So, the equation of the given line is y = -2x + 2.

Here,

y = mx + c

y = -2x + 2

slope ⇒ m ⇒ -2

Therefore, the slope of the new line will be ( - 2 ).

And now we have to find the y-intercept ( c ).

For that let us use the given coordinate.

( -6 , 6 ) ⇒ ( x , y )

To find the y-intercept we have to make c the subject of the equation y mx + c.

Also, we have to replace m with ( - 2 ) as the slope of the new line is -2.

Let us solve it now.

y = m x + c

6 = -2 × -6 + c

6 = 12 + c

6 - 12 = c

-6 = c

Now we have found that,

m ⇒ - 2

c ⇒ -6

And now let us write the equation of the line.

y = m x + c

y = -2x - 6

The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7​ is given in the image attached.

This is known to be that which is created by two part that are known to give the latitude and longitude position of a person or place.

Therefore, The solution to the coordinates of A,B,C as (6,3),(-3,5),(4,-2) and the prove that ∆PBC/∆ABC=x+y-2/7​ is given in the image attached.

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Answer:

h=70°

Step-by-step explanation:

h + 110° = 180° {linear pair angles}

h = 180° - 110°

h = 70°

Answer:

h=70

pa brainliest po kuya/ate

Step-by-step explanation:

pa brainliest po

Answer:

first one

Step-by-step explanation:

because its cheap as for 1 NM it would be 10$ which is 2.5 AED so yehh

The probability that a randomly selected makeup item from her bag will be an eye shadow is 1/5 or 20%.

The probability of selecting an eye shadow from Gabby's bag can be calculated by dividing the number of eye shadows in the bag by the total number of cosmetics in the bag.

There are 4 eye shadows in Gabby's bag, and a total of 20 cosmetics. Therefore, the probability of selecting an eye shadow is:

P(eye shadow) = 4/20 = 1/5

This means that there is a 1 in 5 chance, or a 20% chance, that a randomly selected makeup item from Gabby's bag will be an eye shadow.

The probability can be expressed as a fraction or a whole number, depending on the context of the problem. In this case, we can express the probability as the fraction 1/5, which means that out of 20 possible cosmetics, only 4 are eye shadows.

We can also express the probability as the whole number 0.2 or 20%, which represents the proportion of eye shadows in Gabby's bag.

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Answer:

the missing angle is 30 and the missing exterior angle is 150

Step-by-step explanation:

180-90=90-60=30

180-30=150

Answer: Exterior angle = 150 degrees

Step-by-step explanation:

Hope that helps!

:)