use the present value formula to determine the amount to be invested now, or the present value needed.

the desire accumulated amounts is $140,000 after 2 years invested in an account with 8% interest compounded quarterly.

the amount to be invested now, or the present value needed is?

Step-by-step explanation:

Equation: y= [tex]-x^2+3x+9[/tex]

To create a parabola:

Does your parabola open up or down: If up, a>0 if down, a<0

This one opens down.

Is there a vertical strech or vertical compression:

No

What is the y-intercept: (0,9)

What strategy: Quadratic formula

Why?: You can fully factor the equation. You just get

-([tex](x^2-3x-9)[/tex]  which isn't factorable.

Use the quadratic formula, where a= -1, b= 3, and c=9 to show your work.

Quadratic formula: [tex]\frac{-b+\sqrt{b^2-4ac} }{2a} \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\frac{-(3)+\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex] and [tex]\frac{-(3)-\sqrt{(3)^2-4(-1)(9)} }{2(-1)}[/tex]

[tex]\frac{-3+\sqrt{9-4(-9)} }{-2}[/tex] and[tex]\frac{-3-\sqrt{9-4(-9)} }{-2}[/tex]

[tex]\frac{-3+\sqrt{9+36} }{-2}[/tex] and [tex]\frac{-3-\sqrt{9+36} }{-2}[/tex]

[tex]\frac{-3+\sqrt{45} }{-2}[/tex] and[tex]\frac{-3-\sqrt{45} }{-2}[/tex]

[tex]\sqrt{45}[/tex] = [tex]\sqrt{9 (5)} = 3\sqrt{5}[/tex]

[tex]\frac{-3+3\sqrt{5} }{-2}[/tex] and [tex]\frac{-3-3\sqrt{5} }{-2}[/tex]

Cancel the negatives (-3) and (-2)

[tex]\frac{3 +3\sqrt{5} }{2} or\frac{3 -3\sqrt{5} }{2}[/tex] = end result

Good luck!

I hope this helps you

Answer:  B) sin θ = 5/13    and    D) tan θ = 5/12

Step-by-step explanation:

[tex]\csc\theta=\dfrac{r}{y}=\dfrac{13}{5}[/tex]

Use Pythagorean Theorem: x² + y² = r² to calculate x = 12

[tex]\sin \theta=\dfrac{y}{r}=\dfrac{5}{13}\qquad \qquad \qquad \csc \theta=\dfrac{r}{y}=\dfrac{13}{5}\\\\\\\\\cos \theta=\dfrac{x}{r}=\dfrac{12}{13}\qquad \qquad \qquad \sec \theta=\dfrac{r}{x}=\dfrac{13}{12}\\\\\\\\\tan \theta=\dfrac{y}{x}=\dfrac{5}{12}\qquad \qquad \qquad \cot \theta=\dfrac{x}{y}=\dfrac{12}{5}[/tex]

Answer: Hope this helps <3

Step-by-step explanation:

Answer:

  y = (1/3)x +4

Step-by-step explanation:

The line intercepts the y-axis at y=4. It has a "rise" of 1 unit for each "run" of 3 units, so its slope is rise/run = 1/3.

The slope-intercept form of the equation of a line is ...

  y = mx + b . . . . . where m is the slope and b is the y-intercept.

When we put the proper numbers in the equation, we have ...

  y = (1/3)x + 4

Answer: 240 seconds OR 4 minutes

Step-by-step explanation:

Length of the train = 1 km

Length of the tunnel = 1 km

Therefore, length of the train + length of the tunnel = (1 + 1) km = 2 km

= 2000 m

Speed of the train = 30 km/hr = 8.333 metres per second

Therefore, time taken by the train to cross the tunnel = 2000 m/ 8.333 m/sec.

= 240 seconds = 4 minutes

Answer:

x=3.5

Step-by-step explanation:

Perimeter: 8.5+8.5+2x=24

Simplifying we get: 17+2x=24

Subtracting 17 we get: 2x=7

Dividing by 2 we get: x=3.5

Answer:

No

Step-by-step explanation:

For X and Y to be in proportion, The values should both be the same so if x is 10 y is 10 and so on.

Answer:

(A)Cost of Rental A, C= 15x

Cost of Rental B, C=5x+50

Cost of Rental C, C=9x+20

(B)

i. Rental C   ii. Rental A     iii. Rental B

Step-by-step explanation:

Part 1

Let x be the number of hours of the barbeque use by the club.

Rental A: $15/h

Cost of Rental A, C= 15hx

Rental B: $5/h + 50

Cost of Rental B, C=5x+50

Rental C: $9/h + 20

Cost of Rental C, C=9x+20

Part 2

The graph of the three models is attached below

Part 3(11.05-4.30)

If the barbecue's usage hour is from 11.05 to 4.30 when the football match ends.

Number of Hours between 11.05am and 4.30pm=4 hours 25 Minutes = 4.42 Hours

Cost of Rental A, C= 15x=15(4.42)=$66.30

Cost of Rental B, C=5x+50 =5(4.42)+50=$72.10

Cost of Rental C, C=9x+20=9(4.42)+20=$59.78

Rental C should be chosen as it offers the lowest cost.

Part 4 (11.05-12.30)

Number of Hours = 12.30 -11.05 =1 hour 25 Minutes = 1.42 Hours

Rental A should be chosen since it offers the lowest cost.

Part 5

If the barbecue is returned the next day, say after 24 hours

Rental B should be chosen as it offers the lowest cost.

Answer:

2133 bricks

Step-by-step explanation:

a27=1

a4=139

  a27=a4+23r

   1=139+23r

  23r=1-139

23r=-138

r=-138/23=-6

a4=a1+3r

139=a1-18

a1=139+18

a1=157

n=a1+......+a1+26*r=a1+a1+r+......+a1+26r=27*a1+r(1+2+...+26)

=27*157-6*26*27/2=4239-3*26*27=4239-2106=2133

Answer:

6 km

Step-by-step explanation:

40 min = 40/60 h = 4/6 h = 2/3 h

1 h ................. 9 km

2/3 h ..............x km

x = 2/3×9km = 18/3 km = 6 km

Answer:

The answer would be f(a)=-1

-AC I hope this helps<3

Answer:

[tex]\boxed{\sf \ \ \ x=-9 \ \ or \ \ x=2 \ \ \ }[/tex]

Step-by-step explanation:

hello,

[tex]2x^2+7x-14=x^2+4\\<=> 2x^2+7x-14-x^2-4=0\\<=> x^2+7x-18=0\\<=>x^2-2x+9x-18=0\\<=> x(x-2)+9(x-2)=0\\<=> (x+9)(x-2)=0\\<=> x+9 = 0 \ \text{or} \ x-2=0\\<=> x = -9 \ \text{or} \ x=2[/tex]

hope this helps

Answer:

[tex]\left[\begin{array}{ccc}-5\\-5\\\end{array}\right][/tex]

Step-by-step explanation:

Consider any one of the vertices of A

To translate to the corresponding vertex in B , the requirement is

shift 5 to the left, that is negative 5

shift 5 units down that is negative 5

The single translation is [tex]\left[\begin{array}{ccc}-5\\-5\\\end{array}\right][/tex]

Answer:

Step-by-step explanation:

quotient of a number and -5 is written as

[tex] \frac{x}{ - 5} [/tex]

Equate it to 2

We have

[tex] \frac{x}{ - 5} = 2[/tex]

Cross multiply

That's

x = 2 × - 5

x = - 10

Hope this helps you

Answer: -10

Step-by-step explanation:

So to set up the equation, it will be x/-5 = 2.

Then, you multiply (because it is the inverse of dividing) 2 by -5, and you get -10.

Answer:

k-4.7

Step-by-step explanation:

It is k minus 4.7 because when it says less than it means the number that is stated before the phrase is being subtracted :)

Answer:

k-4.7

Step-by-step explanation:

For writing algebraic expressions, we have translate the words to math.

4.7 less than a number k, means subtraction (notice the word- less)

Thus, we have k-4.7

Hope this helps :)

Answer:

a. 6.75 ft

b. Exponent on w is w^4

Step-by-step explanation:

a. The best thing here is to work with decimals

each piece was 3/4 foot tall which means each piece is 0.75 ft tall

Now since he staked 9, the height of the wood pile would be 9 * 0.75 = 6.75 ft

b. Firstly let’s evaluate the denominator

That becomes; 2v^-3w^8 * v^4w = 2v^(-3+4)w^(8+1) = 2vw^9

So let’s now divide this by the numerator

Since we are concerned with only the exponent on w, we place w^13 over w^9 = w^(13-9) = w^4

Answer:

Oregon:

Median: 467.5

Mean: 451.33

Standard Deviation: 113.6

Washington:

median: 380

Mean: 396.6

Standard deviation: 56.3

Step-by-step explanation:

To calculate the median, we need to organize the price and select the value that is in the middle position.

To calculate the mean, we need to sum all the values and divide them by the number of values

To calculate the standard deviation, we need to square the distances between every price and the mean, sum it all and divide them by the number of values less 1 and finally calculate the square root.

So, for Oregon, the organized values are:

$295, $345, $460, $475, $538, $595

The median is a value between $460 and $475. it is calculated as:

[tex]\frac{460+475}{2}=467.5[/tex]

The mean is:

[tex]\frac{295+475+345+595+538+460}{6}=451.33[/tex]

The standard deviation is:

[tex]\sqrt{\frac{(295-451.3)^2+(475-451.3)^2+(345-451.3)^2+(595-451.3)^2+(538-451.3)^2+(460-451.3)^2}{6-1}}=113.6[/tex]

At the same way, we can calculate the median, mean, and standard deviation for Washington and get:

median: 380

Mean: 396.6

Standard deviation: 56.3

Answer:

f(4) = 24

Step-by-step explanation:

Plug in 4 for x in the equation:

f(x) = x² + 3x - 4

f(4) = (4)² + 3(4) - 4

Remember to follow PEMDAS. PEMDAS =

Parenthesis

Exponents (&  Roots)

Multiplication

Division

Addition

Subtraction

and is the order of operation.

First, solve the power:

(4)² = 4 * 4 = 16

Next, multiply 3 with 4:

3 * 4 = 12

Next, combine the terms:

f(4) = 16 + 12 - 4

f(4) = (16 + 12) - 4

f(4) = 28 - 4

f(4) = 24

f(4) = 24 is your answer.

~

Answer:

24

Step-by-step explanation:

Plug x as 4.

(4)² + 3(4) - 4

16 + 12 - 4

= 24

Answer:

false

Step-by-step explanation:

its false I think

Answer:

GY = 10 cm

YX = 16 cm

A = πr²

A = π (26cm)²

A = 676cm² π

Step-by-step explanation:

The area of Marco's new circle is A = 676π cm²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be represented as r

Now , the value of r = 26 cm

And , area of the circle = πr²

On simplifying , we get

A = π ( 26 )²

A = 676π cm²

Hence , the area of the circle is 676π cm²

To learn more about circle click :

https://brainly.com/question/28391204

#SPJ3

The complete question is attached below :

Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX.

Marco wants to create a new circle using GX as a radius. What will be the area of Marco’s new circle?

10Pi centimeters squared

16Pi centimeters squared

356Pi centimeters squared

676Pi centimeters squared

Answer:

x=-1, y=2, z=3

Step-by-step explanation:

First at all, you can divide these equations into two group. It is easier to you.

4x-2y+3z=1

3x+y+2z=5

x+3y-4z=-7

3x+y+2z=5

Then, you can simplify these group of equation that you divided.

So, we have to simplify these step by step.

First, we can simplify the first group of equation.

4x-2y+3z=1

3x+y+2z=5

We have to find which variable you want to eliminate. I choose y.

You can multiply the second equation of first group by 2 and eliminate them.

4x-2y+3z=1

6x+2y+4z=10

As the variable of y is same and we can eliminate y by addition.

4x-2y+3z=1

6x+2y+4z=10

become

10x+0+7z=11

10x+7z=11

10x+7z=11 as the third equation.

Next, simplify the second group of equation.

x+3y-4z=-7

3x+y+2z=5

Same way as the previous one. We need to find which variable that you want to eliminate. I choose y.

We need to balance for the first equation x+3y-4z=-7 at least one variable.

We need to multiply this equation by -3 below to get the same value of y to eliminate the above equation.

3x+y+2z=5 (multiply by -3)

-9x-3y-6z=-15

x+3y-4z= -7

-9x-3y-6z= -15

Here we go! Now these group has same value and variable to eliminate.

We can eliminate these equations by addition method.

x+3y-4z= -7

-9x-3y-6z= -15

-8x+0+10z= -22

-8x+10z= -22

Furthermore, we have to combine these equations that we have simplified from the previous groups.

10x+7z=11

-8x+10z= -22

10x+7z=11 and -8x+10z= -22 as a new group.

Finally, it is time to solve these equations!!

10x+7z=11

-8x+10z= -22

First equation of the above group, we can multiply by 10. Like this:

100x+70z=110

Second equation of the above group, we can multiply by 7. Like this:

-56x+70z=-154

So, we can see there are same value from these equation which are +70z and -70z.

Now, we can eliminate this variable by sum these equations.

100x+70z=110

-56x+70z=-154

44x= -44

x= -1

When we get x= -1 , we can use this value to any equation that you want. You can get the same answer as well.

When x= -1,

substitute into 100x+70z=110

100(-1)+70z=110

-100+70z=110

70z=110+100

70z=210

z=3

When z=3 and x= -1, we can substitute into x+3y-4z= -7

-1+3y-4(3)= -7

-1+3y-12= -7

3y=6

y=2

So, the answer is x= -1 , y=2 , z=3

I hope you will understand my solution and explanation. Bye!!

Answer:

The answer is option C.

Step-by-step explanation:

h(x) = 2(3x – 5) = 6x - 10

k(x) = –2x + 1

h • k (x) = (6x - 10) ( - 2x + 1)

= - 12x² + 6x + 20x - 10

The final answer is

= - 12x² + 26x - 10

Hope this helps you

Answer:

C)  h · k(x) = –12x2 + 26x – 10

Step-by-step explanation:

Answer:

Lateral surface area of cuboid = 448 ft²

Step-by-step explanation:

Given:

Height of cuboid(h) = 14 ft

Length of cuboid(l) = 9 ft

width of cuboid(b) = 7 ft

Find:

Lateral surface area of cuboid

Computation:

Lateral surface area of cuboid = 2 h(l + b)

Lateral surface area of cuboid = 2(14)(9 + 7)

Lateral surface area of cuboid = 28(16)

Lateral surface area of cuboid = 448 ft²

Answer:

reflection and rotation

Step-by-step explanation:

Answer:

x=42

Step-by-step explanation:

The tens digit of a two-digit number is twice the units digits. put it in an equation:

10(2x)+x = 10x+2x+18

21x=12x+18

21x-12x=18

x=18/9=2

substitute x:

10(2x)+x = 10x+2x+18

10(2*2)+2=10(2)+2(2)+18

42=24+18

Answer:

x^2-4x-4

Step-by-step explanation:

Dimension of the painting=x

Frame=2in wide is. Each side of the square painting

Length of the painting= x-2

Area of a square=lenght^2

=(x-2)^2

Multiply

=(x-2)(x-2)

=x^2-2x-2x+4

Combine like terms

Area of the square painting=x^2-4x-4

Answer:

the value of x_y is 1.

hope u get it.....

Answer:

The correct answer is B

Answer:

0 < x < 25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given figure : Trapezium

Upper base of trapezium ( b1 ) = 7

Lower base ( b2 ) = 3

Height ( h ) = 3

Now, finding the area of trapezium:

[tex] \frac{1}{2} (b1 + b2)h[/tex]

Plugging the values

[tex] \frac{1}{2} \times (7 + 3) \times 3[/tex]

Calculate the sum

[tex] \frac{1}{2} \times 10 \times 3[/tex]

Reduce the numbers with G.C.F 2

[tex]5 \times 3[/tex]

Calculate the product

[tex] = 15 \: {units}^{2} [/tex]

Hope this helps..

Best regards!

Answer:

x = 5

Step-by-step explanation:

Here, we want to use Crammer’s rule to find the value of x

Please check attachment for complete solution