A person invests 7000 dollars in a bank. The bank pays 7% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 12400 dollars?

Answer:

(a) the law of cosines

(b) approximately 6

Step-by-step explanation:

Check out the attached photo.

The answers are presented below:

The quadratic function can be represented by a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

The vertex of an up-down facing parabola of the form ax²+bx+c is [tex]x_v=\frac{-b}{2a}[/tex]  . Knowing the x-coordinate of vertex, you can find the y-coordinate of vertex. When a vertical line passes through the vertex of the parabola, it  is called the axis of symmetry.

The y-intercept is the point where the function crosses the y-axis. And, the x-intercept is the point where the function crosses the x-axis, in other words, when y=0.

First, you should convert the given equation to Standard form.

f(x) = -(c+7)² + 4

f(x)= - (c²+14c+49)+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-49+4

f(x)= -c²-14c-45

After that, you should check each option of the question.

Correct because present a degree 2 -- f(x)= -c²-14c-45

Incorrect because it is a quadratic function and this function is represented by a parabola.

The coefficients are: a=-1, b=-14, c=-45. Therefore,

[tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]

Incorrect because x-coordinate of vertex is -7

Correct because  [tex]c_v=\frac{-b}{2a}=-\frac{-14}{2*(-1)} =-\frac{-14}{-2}=-(7)=-7[/tex]

You can find the y-intercept using c=0, then f(x)= -c²-14c-45 will be:

f(x)=-45.

Incorrect because the y-intercept is (0,-45).

The coefficient a of a quadratic function is negative, thus the function has a point maximum. A relative maximum point is defined as the point where the function changes your direction. In other words, the values of the function increase before the relative maximum and the values decrease after the relative maximum.

Correct, see the attached image.

It is possible to find the number of roots or solutions from discriminant.

For quadratic equation the discriminant is determined by D=b²-4ac, where: a, b and c are coefficients.

If D > 0 - the function will have two real solutions;

If D = 0 - the function will have one real solution;

If D < 0 - the function will have imaginary solutions;

For given equation, the coefficients are: a=-1, b=-14, c=-45. Thus, D=(-14)²-4*(-1)*(-45)

D=196-180=16

D=16 thus D > 0

Incorrect because the D>0.

Read more about the quadratic function here:

brainly.com/question/1497716

Answer:

39364.

Step-by-step explanation:

I guess its an = 4*(3)^(n-1)

r = 3, a1 = 4 and n = 9

Sum of n terms = a1 * (r^n - 1) / (r - 1)

so S9 = 4 *(3^9 - 1) / (3 - 1)

= 4 * (19683  - 1) / 2

= 78728/2

= 39364.

Answer:

x = 142°

Step-by-step explanation:

The first thing you need to figure out is the missing interior angle of the triangle.

There is 180 degrees in a triangle, there is a 90° and 52° angle listed, so subtract that from 180° to get the missing angle.

180° - 90° - 52° = 38°

Now we want the exterior angle x. Angle x and the interior angle form a straight line when combined which will also be a 180° angle. You can picture this as a half circle (a full circle is 360°).

So subtract the interior angle 38° from 180°

180° - 38° = 142°

Answer:

Step-by-step explanation:

The property of rhombus that can be used to proof that a triangle is an equilateral triangle is that when it is split into two equal parts, an equilateral triangle is formed.

A rhombus is defined as a quadrilateral that has four equal straight sides with opposite sides parallel and equal opposite angles.

A rhombus with two 60 degree angles and two 120 degree angles can be split by one of its diagonals (the one that bisects the 120 degree angles) into two congruent, equilateral triangles.

Therefore, the property of rhombus that can be used to proof that a triangle is an equilateral triangle is that when it is split into two equal parts, an equilateral triangle is formed.

Learn more about quadrilaterals here:

https://brainly.com/question/26690979

#SPJ2

Answer:

I am pretty sure it is the second option

Step-by-step explanation:

Hope this helps

Answer:

4 mm

Step-by-step explanation: The height is the same length of the length

Have a good day!

The volume of a rectangular prism is given by V = l×w×h

48 = 3×4×n

48 = 12n

n = 4

Answer:

n = 4

Step-by-step explanation:

The volume of a rectangular prism is given by

V = l×w×h

Subbing in known variables and solving

48 = 3×4×n

48 = 12n

n = 4

Answer:

Option C

Step-by-step explanation:

Attached photo might help you out

Answer:

16

Step-by-step explanation:

2 pounds = 32 ounces

32 ounces / 2 ounces = 16 ounces

Answer:

Step-by-step explanation:

an = (an-1)2 + 5. a1 = 4. Then: a1 = 4. a2 = (4)2 + 5 = 16 + 5 = 21. a3 = (21)2 + 5 = 441 + 5 = 446. a4 = (446)2 + 5 = 198916

Answer:

In March the baker will sell 34 chocolate chip cookies. In April he will sell 74 cookies.

Step-by-step explanation:

So first, we end up doubling the original amount of cookies from January for February which gets us 20 cookies, he takes 6 homes leaving us with 14. He continues to double the FULL amount so he doubles 20 for March which gets us 40, then we again take 6 away leaving us with 34. We do the same thing for April. Double 40 getting 80, take away 6 you get 74. Done.

[tex]5x^2-14x+8\\\\=5x^2-10x-4x +8\\\\=5x(x-2) -4(x-2)\\\\=(x-2)(5x-4)[/tex]

Answer:

use can FOIL method or grid method

Answer:

91

Step-by-step explanation:

If we add all of the student's scores we get 273. Because there are 3 students we divide 273 by 3 and we get 91 as the average.

Answer:

-2, 10

Step-by-step explanation:

From the image, I'm pretty sure it's asking you to find where the line can be "cut" into to make it symmetrical. If this is true, you would need to find a half way mark in the graph, or try and plot this on the graph.

Answer:

*** "and" means multiply

2/9

Step-by-step explanation:

*** "and" means multiply

spinning a vowel is 1/3

not spinning a 1 is 2/3

1/3 times 2/3 is 2/9

Answer:

30 days

Step-by-step explanation:

1.5 Kg = 1500 g

Using 50 g a day

Number of days

= 1500 / 50

= 30 days.

Answer:

6a²

Step-by-step explanation:

6×5² = 6×25 = 150cm²

thank you

Answer:

150 centimeters cubed

Step-by-step explanation:

[tex]6x2^2= 150[/tex]

Answer:

First one.

Step-by-step explanation:

Quantity is usually the best way to know people's preference, that's why Family Feud asks 100 people for their question's answers. This answer may be wrong, since this question is a bit due to opinion. Hope this helps! <3

Answer:

64 cm^2

Step-by-step explanation:

Split the figure into two parts (top and bottom rectangle)

TR : 2 x (12-5)*

   2 x 7 = 14

*= Since there are a few ways to split it up but I chose to make the top one shorter so you have to subtract 5 from 12

BR : 10x5 = 50

Add together

14 + 50 =

64 cm^2

Hope this helps :)

Answer:

18

Step-by-step explanation:
given that the eggs cost 16ct in 1990 and 22ct in 1992 you can calculate

16ct+2ct=18ct and 22ct-4ct=18ct

see this vid for full explanation

Answer:

b. The new maen age is less than 33.4 years.

Answer:

6.14

Step-by-step explanation:

The required area would be 6.14 m²

I hope I helped you

Answer:

6.14m^2

Step-by-step explanation:

Maybe this will help you..

Answer:

Step-by-step explanation:

2.25m + 2(2.25m) + 90 cm =

2.25m + 4.50m + 90 cm

6.75m + 90 cm

1 cm = 0.01m...so 90 cm = 90 * 0.01 = 0.9m

6.75m + 0.9m = 7.65m <===

2.25m + 2(2.25m) + 90 cm =

2.25m + 4.50m + 90 cm

6.75m + 90 cm

1 cm = 0.01m...so 90 cm = 90 * 0.01 = 0.9m

6.75m + 0.9m = 7.65m

OR../=-

1m = 100 cm....so 7.65m = 7.65 * 100 = 765 cm

Answer:

a. 4x = 332

b. 83 students

Step-by-step explanation:

Write equation:

4x = 332

Since we know that each ticket per student is $4, we can use "x" as our variable for the number of students

_________________________________________-

Solve

4x = 332

/4       /4

____________

x = 83 students

Hope this helps :)

Answer:

Angle I = 44

Measure GH=7.64

Measure GI=7.91

Step-by-step explanation:

Since we know that m∠H = 46 and m∠G=90, we can find measure angle I by subtracting from 180.

[tex]180=46+90+x\\44=x[/tex]

Since we are given that m∠H = 46, and the triangle is right, we can use trigonometric functions to find the two sides.

First is GH, since it's adjacent to the angle, we will use cosine.

[tex]cos(x)=\frac{adjacent}{hypotenuse} \\cos(46)=\frac{adjacent}{11}\\ 11*cos(46)=adjacent\\7.64=adjacent[/tex]

The same idea as previous, only instead we will use sine since we need to find the opposite.

[tex]sin(x) = \frac{opposite}{hypotenuse}\\ sin(46)=\frac{opposite}{11}\\ 11*sin(46)=opposite\\7.91 = opposite[/tex]

Answer:

180 angles usually up and down from each other

Step-by-step explanation:

85.2

94.8