A certain college graduate borrows $5900 to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and th the borrower makes payments continuously at a constant annual rate k dollars per year, determine the payment rate k that is required to pay off the loan in 6 years (Round your answer to two decimal places.) k=$ per yr Determine how much interest is paid during the 6-year period. (Round your answer to two decimal places.)

A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.

The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,

[tex](2x-5)=0\\\\2x=5\\\\x=\dfrac52[/tex]

[tex]x-5=0\\\\x=5[/tex]

Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0[/tex]

Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.

[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}[/tex]

Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.

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The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

When the three sides of a triangle is known, then to find any angle, the law of cosine is used.

It can be given as,

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)[/tex]

Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.

Triangle ΔABC has side lengths of a = 18, b=18√3  and c = 36 inches.

Put the value, in the cosine law, the measure of angle A.

[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\[/tex]

Using the chart of unit circle, the value of tangent A can be found out. The tangent A is,

[tex]\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}[/tex]

Use the following formula to find area of ΔABC.,

[tex]A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2[/tex]

Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.

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Answer:

x^14 y^9

Step-by-step explanation:

Add the exponent of the x's

(x^5) + (x^9) = x^14

Add the exponent of the y's

(y^7) + (y^2) = y^9

You can't combine different varibles so your answer will be x^14 y^9

Answer:

39 units

Since two side lengths and a right angle are given, we can use pythogoras theorem to determine the missing side (c) of the triangle. It should be noted that pythgoras theorem can only be used if the triangle is a right triangle.

Pythogoras theorem formula:

[tex](\text{Side}_{1} })^{2} + (\text{Side}_{2} )^{2} = (\text{Hyptenuse})^{2}[/tex]

Substitute the legs of the triangle and the hyptenuse

[tex]\implies (36)^{2} + (15 )^{2} = (c)^{2}[/tex]

Simplify both sides of the equation

[tex]\implies 1296 + 225 = (c)^{2}\\[/tex]

[tex]\implies 1521 = (c)^{2}\\[/tex]

Take square root both sides

[tex]\implies \sqrt[2]{1521 } = \sqrt[2]{c^{2} }[/tex]

Solve for "c" by simplifying the roots

[tex]\implies \sqrt[2]{39 \times 39 } = \sqrt[2]{c \times c }[/tex]

[tex]\implies \boxed{39 = c}[/tex]

Thus, the measure of the missing side length (c) is 39 units.

Answer:

126 square units

Step-by-step explanation:

Area of section 1 is 8 square units which is triangle and,

Area of triangle is =  [tex]\frac{1}{2}\times b\times h[/tex]

b= 2 units and height =8 units

So,

Area of section 1  =  [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Same Area is of section 2 which is also a triangle and has same base and height.

So,

Area of Section 2 = [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]

Now the Area of section 3 which is square with side of 10 units

So,

Area of section 3 =  [tex]a^{2} =10\times10=100\quad \text{square units}[/tex]

Total Area of Trapezoid = [tex]8+8+100=126 \quad \text{square units}[/tex]

Answer:

2 the change in expected height for every additional centimeter of femur length

Step-by-step explanation:

1 and 4 have 55 is the starting point but is just there to throw you off and 3 has expected femur length, but the graph says expected height

3n+19

Explanation:

(1/2)(6n + 38)

Answer:

All of them but the last one

Step-by-step explanation:

Answer:

3,052.08

Step-by-step explanation:

Formula for sphere: (4/3)(pi)(r^3)

Filled in: (4/3)(3.14)(729)

Calculated: 3,052.08

Answer:

Trigonometry Examples

Since π3 is in the first quadrant, the reference angle is π3 .

Since π3 is in the first quadrant, the reference angle is 60 degrees

Step-by-step explanation:

HOPE THIS WILL HELP YOU

Answer:

25 years

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

f(x) = g(x) at x=5

means

f(5) = g(5)

Answer:

Estos pares de factores son (1, 35) y (5, 7).

espero que esto ayude.

➡ (1,35)

➡ (5,7)

Find the volume of a cylinder with a radius of 4 meters and a height of 13 meters. Use * 3.14.

radius of the cylinder = 4 m

height of the cylinder = 13 m

To find: The volume of the cylinder (where pi = 3.14)

We know that volume of cylinder

[tex] \pi {r}^{2} h[/tex]

Now by using the formula = 3.14 × (4) × (4) × 13

= 3.14 × 208

= 653.12 m³

Answer:

m<ABC = 90 degrees  m<ABD = 57 degrees

Step-by-step explanation:

OMG this is soooooo easy I love geometry.

Answer:

Tom sits in the middle and he is 18

Step-by-step explanation:

On the table you will first mark off Tom from being in the rear, as well as being 19

You will mark off Tom and Roy from the 1st, which places Davis as 1st, you also know that Tom is neither 1st nor last, so he is in the middle.

Now you see that Roy is neither in the 1st nor middle, so he is last.

Last is also the 20 yr old, so Roy is 20yrs and last seat.

Tom is neither 19 or 20.

So Tom is in the middle and 18yrs old

Answer:

$114.19

Step-by-step explanation:

7.25*15 = 108.75

108.75*1.05 = 114.1875

You can't have less than a cent, so it is $114.19

Answer: $114.19

Step-by-step explanation:

Answer:

root 7

Step-by-step explanation:

apply tan60=p/b=root 21/ x

Answer:

1: 3

Step-by-step explanation:

2 triangles : 6 circles

Divide each side by 2

2/2 : 6/2

1 :3

1 triangle : 3 circles

The probability of getting exactly 8 hits in his next 20 at-bats is 0.153 (Round off to the nearest thousandth.).

The correct option is (c)

Binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

where, n= number of trial,

r= number of success desire,

p= probability of success,

q= probability of Failure

probability of success = 0.34

To find the probability of winning exactly 8 hits in next 20 at-bats we find

dbinom (8, 20, 0.34)

Since p= 0.34

q= 1-p

 = 1-0.34

 = 0.66

n= 20, r=8

Using Binomial Distribution, we get

Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]

                 =[tex]\frac{n!}{r!(n-r)!} p^{r}\; q^{(n-r)}[/tex]

                 = [tex]\frac{20!}{8!(20-8)!} (0.34)^{8}\; (0.66)^{(20-8)}[/tex]

                = 125970 x 0.0001785794 x 0.00683168

                = 0.1536830

                ≈ 0.153 (Round off to the nearest thousandth.)

Hence, the probability of getting exactly 8 hits in his next 20 at-bats is 0.153.

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Answer:

48.2 feet

or

578.4 inches

Step-by-step explanation:

Perimeter is the distance around the shape or in this case the room. Assuming the room is a rectangle you would have two walls of the same length totaling 4 walls.

To find the perimeter add up 14.5 + 14.5 + 9.6 + 9.6 = 48.2 feet

Since it askes for the answer in inches you have to convert from feet to inches by multiplying your answer by twelve.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ M(\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 0}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\textit{\Large Q}}{(4~~,~~10)}\implies \begin{cases} \cfrac{x+0}{2}=4\\[1em] \boxed{x=8}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=10\\[1em] y+8=20\\ \boxed{y=12} \end{cases}[/tex]

Answer:

I hope dis helps

Step-by-step explanation:

Simplify  

           x2 + 5x + 4

Trying to factor by splitting the middle term

1.1     Factoring  x2 - x - 2

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -2

Step-1 : Multiply the coefficient of the first term by the constant   1 • -2 = -2

Step-2 : Find two factors of  -2  whose sum equals the coefficient of the middle term, which is   -1 .

     -2    +    1    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  1

                    x2 - 2x + 1x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-2)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-2)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-2)

            Which is the desired factorization

Trying to factor by splitting the middle term

1.2     Factoring  x2+5x+4

The first term is,  x2  its coefficient is  1 .

The middle term is,  +5x  its coefficient is  5 .

The last term, "the constant", is  +4

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   5 .

     -4    +    -1    =    -5

     -2    +    -2    =    -4

     -1    +    -4    =    -5

     1    +    4    =    5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  4

                    x2 + 1x + 4x + 4

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x+1)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x+1)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x+1)

            Which is the desired factorization

Canceling Out :

1.3    Cancel out  (x+1)  which appears on both sides of the fraction line.

Final result :

 x - 2

 —————

 x + 4

Answer:

[tex] \dfrac{1}{9^6} [/tex]

Step-by-step explanation:

[tex] \dfrac{9^3}{9^9} = 9^{3 - 9} = 9^{-6} = \dfrac{1}{9^6} [/tex]

Answer:

B

Step-by-step explanation:

Out of all the answers given as a choice B makes the most sense because the triangle AB and point of intersection of the two circles form an equilateral triangle.

In general to construct a perpendicular bisector after we drew the two circles we have to ...draw a straight line trough the points where the two circles intersect and that is our perpendicular bisector of AB.

Answer:

1) 108 A+    2) 98 B+

Step-by-step explanation: