.
Ben deposits $1,750 into each of two savings accounts.

Account I earns 2.75% annual simple interest
Account II earns 2.75% interest compounded annually
Ben does not make any additional deposits or withdrawals. Which amount is closest to the difference between the interest Ben will earn in Account I and the interest Ben will earn in Account II at the end of 2 years?

Answer:

[tex]x=6-\sqrt{ -100}/2=3-5i=3.0000-5.0000i\\x=6+\sqrt{-100} )/2=3+5i=3.0000+5.0000i[/tex]

Step-by-step explanation:

Step 1: Trying to factor by splitting the middle term

The first term is,  x²  its coefficient is  1 .

The middle term is,  -6x  its coefficient is  -6 .

The last term, "the constant", is  +34

Step-1 : Multiply the coefficient of the first term by the constant   1 • 34 = 34

Step-2 : Find two factors of  34  whose sum equals the coefficient of the middle term, which is   -6 .

     -34    +    -1    =    -35

     -17    +    -2    =    -19

     -2    +    -17    =    -19

     -1    +    -34    =    -35

     1    +    34    =    35

     2    +    17    =    19

     17    +    2    =    19

     34    +    1    =    35

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 1:

 x² - 6x + 34  = 0

Parabola, Finding the Vertex:

 Find the Vertex of   y = x^2-6x+34

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   3.0000  

Plugging into the parabola formula   3.0000  for  x  we can calculate the  y -coordinate :

 y = 1.0 * 3.00 * 3.00 - 6.0 * 3.00 + 34.0

or   y = 25.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-6x+34

Axis of Symmetry (dashed)  {x}={ 3.00}

Vertex at  {x,y} = { 3.00,25.00}

Function has no real roots

Solve Quadratic Equation by Completing The Square

Solving   x2-6x+34 = 0 by Completing The Square .

Subtract  34  from both side of the equation :

  x2-6x = -34

Now the clever bit: Take the coefficient of  x , which is  6 , divide by two, giving  3 , and finally square it giving  9

Add  9  to both sides of the equation :

 On the right hand side we have :

  -34  +  9    or,  (-34/1)+(9/1)

 The common denominator of the two fractions is  1   Adding  (-34/1)+(9/1)  gives  -25/1

 So adding to both sides we finally get :

  x2-6x+9 = -25

Adding  9  has completed the left hand side into a perfect square :

  x2-6x+9  =

  (x-3) • (x-3)  =

 (x-3)2

Things which are equal to the same thing are also equal to one another. Since

  x2-6x+9 = -25 and

  x2-6x+9 = (x-3)2

then, according to the law of transitivity,

  (x-3)2 = -25

We'll refer to this Equation as  Eq. #2.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-3)2   is

  (x-3)2/2 =

 (x-3)1 =

  x-3

Now, applying the Square Root Principle to  Eq. #2.2.1  we get:

  x-3 = √ -25

Add  3  to both sides to obtain:

  x = 3 + √ -25

In Math,  i  is called the imaginary unit. It satisfies   i2  =-1. Both   i   and   -i   are the square roots of   -1

Since a square root has two values, one positive and the other negative

  x2 - 6x + 34 = 0

  has two solutions:

 x = 3 + √ 25 •  i

  or

 x = 3 - √ 25 •  i

Solve Quadratic Equation using the Quadratic Formula

2.3     Solving    x2-6x+34 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     1

                     B   =    -6

                     C   =   34

Accordingly,  B2  -  4AC   =

                    36 - 136 =

                    -100

Applying the quadratic formula :

x = 6 ± √ -100/2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -100  =

                   √ 100 • (-1)  =

                   √ 100  • √ -1   =

                   ±  √ 100  • i

Can  √ 100 be simplified ?

Yes!   The prime factorization of  100   is

  2•2•5•5

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 100   =  √ 2•2•5•5   =2•5•√ 1   =

               ±  10 • √ 1   =

               ±  10

So now we are looking at:

          x  =  ( 6 ± 10i ) / 2

Two imaginary solutions :

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

 or:

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

Two solutions were found :

x =(6-√-100)/2=3-5i= 3.0000-5.0000i

x =(6+√-100)/2=3+5i= 3.0000+5.0000i

Answer:

1. 3.33

2. 8.75

3. 4.8

4. 2.5

Step-by-step explanation:

divide the numbers.

Answer:

volume is 20^3 inches i hope i helped

(mark brainliest)

45-12=33

then divide 33 by 9: 33÷9=3.66666666 repeating forever. you can round up to 3.7.

Answer:

10 x 0.007 = 0.07

Step-by-step explanation:

im not sure if thats what you meant

Answer:

Angle u is 52

Step-by-step explanation:

I only know this

52 because internal angle of triangle is 180 subtract 90 and 38 from 180 and you will get 52

Answer:

5x(squared)-4x+1

2x(squared)+11xy+14

7x(squared)+7xy+3x-17

Step-by-step explanation:

Answer:

[tex]3z {}^{3} \times 12[/tex]

[tex]36z {}^{3} [/tex]

Answer:

Pls try to send ur questions the right way and ask again attaching the picture of the figure. Otherwise, there is no way to solve

Answer:

y=1/4x+3

Step-by-step explanation:

You can find the slope by starting at the point (4,2), then using "rise over run" you can count up(rise) 1, then side(run) 4. So the slope, or "m" would be 1/4x. The B value is the y Intercept, and the y Intercept is (0,3) so you would write it as 3 in the equation.

Answer: 4n-7

Step-by-step explanation:

A graph that shows a function must pass the vertical line test

The true statement is (b) No; the graph fails the vertical line test.

For a graph to show a function, the graph must pass the vertical line test

The given graph do not pass the vertical line test;

This is so because, a line drawn from the x-axis would touch the graph at at least two different points

Hence, the true statement is (b) No; the graph fails the vertical line test.

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Step-by-step explanation:

[tex] \frac{19695}{x - 15605} = 100[/tex]

[tex]19695 = 100(x - 15605)[/tex]

[tex]19695 = 100x - 1560500[/tex]

[tex]19695 + 1560500 = 100x[/tex]

[tex]15801 95 = 100x[/tex]

[tex] \frac{1580195}{100} = x[/tex]

[tex]x = 15801.95[/tex]

Look at the diagram for the answer

Hope that helps!

Answer:

B  Angle obtuse Since 126o 32 ' is bigger  90o but  smaller than 180o.

Step-by-step explanation:

Acute: An angle that measures < 90o.

Right: An angle that measures 90o.

Obtuse : An angle that is > 90o but < 180o.

Straight: An angle that measures 180o.

Answer:

the answer is 56in2

Step-by-step explanation:

[tex]b = 14in \\ h = 8in \\ area \: of \: triangle = \frac{1}{2} b \times h \\ = \frac{1}{2} \times 14 \times 8 \\ = 56inches[/tex]

Answer:

iam thinking the answer is ""-262,5ft""

The height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

The height is a vertical distance between two points. It is given that A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h² where h and d are measured in feet.

The height will be calculated by forming the two equations from the given data in the question.

25  =  625  +  h²

100  =  4  (  625   +  h² )

100  =  ( 2500   +  4h²  )

By solving both the equations:

100  -  25  =  2500  -  625  +  4h²   -   h²

3h²   =  1800

h   =   √600

h   =   24.49 feet

Therefore the height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.

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Answer:

x=6

Step-by-step explanation:

Rearrange terms:

8+x=14

x+8=14

Subtract 8 from both sides and simplify.

Given :-

To find :-

Solution :-

8+x = 14

x = 14-8 (Signs change when transferred to opposite side)

x = 6

Answer:

56 Chickens

36 Cows

Step-by-step explanation:

You can set this up as a system of equations:

(x=chickens, y=cows)

[tex]\left \{ {{92 = x+y} \atop {256=2x+4y}} \right. \\[/tex]

To solve this system, first we can solve for x in the top equation:

[tex]x=92-y[/tex]

Next, we can plug in x to the second equation and solve for y:

[tex]256=2(92-y)+4y\\256=184+2y\\2y=72\\y=36[/tex]

And now that we have y, we can plug it into the first equation and solve for x:

[tex]92=x+36\\x=56[/tex]

Answer:

600in³

Step-by-step explanation:

the equation for volume is:

V=s*3

(s is a varible which means LengthxHeightxWidth)

step 1

V= (10")(5")(12")

then it equals your answer

up above is the answer.

Hope it help you out.

Don't forget to label.

Answer:

Step-by-step explanation:

This is a proportion question which is 2 ratios which are equal to one another. If 3 of the 4 parts are known, the 4th part can be calculated.

36 liters.

36 km/3 Liters = x / 36             multiply both sides by 36

36*36 / 3 =  x

1296/3 = x

x = 432 km

So on 36 L he can go 432 km

3 liters

Given as 36 km

48 liters

36km/3 liters = x / 48 liters         Multiply both sides by 48

48*36/3 = x

576 km = x

So on 48 liters, he can go 576 km

132 liters

36 km/ 3 liters = x/132

x = 1564 km

On 132 liters Pat can go 1564 km

Answer:

65%

Step-by-step explanation:

We need to divide to solve this :)

13/20 = 0.65

Now we multiply :)

0.65 x 100 = 65%

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

D. 65%

Step-by-step explanation:

the Number of red marbles is 13

The total number of marbles is 13 + 7 = 20

Then

the percentage of red marbles is :

[tex]\frac{13}{20} \times 100[/tex]

[tex]=\frac{13 \times 100}{20}=13 \times 5=65 \%[/tex]

Answer:

$35

Step-by-step explanation:

7 customers - 2 who didn't tip =  5 who did tip

$7 from those who did tip * 5 ppl who tipped = $35 earned

100x³²

..................

Answer: Degenerate

Step-by-step explanation:

This conic section (intersecting lines) is a degenerate

The conic section is degenerate.

The correct option is (e).

Any curve produced by the intersection of a plane and a right circular cone.

As, the given figure shows a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve.

Hence, the conic section is degenerate.

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=10297\\ h=21 \end{cases}\implies 10297=\pi r^2(21)\implies \cfrac{10297}{21\pi }=r^2 \\\\\\ \cfrac{1471}{3\pi }=r^2\implies \sqrt{\cfrac{1471}{3\pi }}=r\implies 12\approx r[/tex]

Answer:

^EKF and^HKI

Step-by-step explanation:

Answer:

D. x>5

Step-by-step explanation:

[tex]3x + 2 < 4x - 3 \\ = 3x - 4x < - 3 - 2 \\ = - x < - 5 \\ = x > 5[/tex]

The LSRL is the Least Squares Regression Line of the new engine design performance

This is the equation of the Least Squares Regression Line.

From the calculation summary, we have the following parameters:

So, the LSRL is:

y = 11.6559 + 3.47812x

Where y represents the predicted volume and x represents the weight.

In (a), we have:

y = 11.6559 + 3.47812x

Substitute 100 for x

y = 11.6559 + 3.47812 * 100

Evaluate

y = 359.4679

Hence, the predicted top speed when the weight is 100 tons is 359.4679

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