Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high school in five years. Roughly how much more will Martha need to save for one-year's tuition to account for an annual rate of inflation of 3%?

Answer:

The total number of marbles in the set is 107 marbles

Step-by-step explanation:

The parameters given are;

Let the size of the marbles be 1 unit

The marbles are arranged to form the equilateral triangle as follows;

1st row = 1 marble

2nd row = 2 marbles and so on so that the total number of marbles for an arithmetic series as follows;

Total number of marbles, t = 1 + 2 + 3 + ... + n

Therefore;

[tex]t = \dfrac{1 + n}{2} \times n[/tex]

Since there are 2 marbles left in forming the first equilateral triangle, we have the total number of marbles in the set, t₁, is given as follows;

[tex]t_1 = \dfrac{1 + n}{2} \times n + 2[/tex]

When the same marble set are arranged into a triangle in which each side has one more marble than in the first arrangement, there where 13 marble shortage, hence, the total number of marbles is given as follows;

[tex]t_1 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]

We therefore have;

[tex]t_1 = \dfrac{1 + n}{2} \times n + 2 = \dfrac{1 + (n+1)}{2} \times (n+1) -13[/tex]

Which gives;

[tex]\dfrac{n^{2}+n+4}{2}=\dfrac{n^{2}+3\cdot n-24}{2}[/tex]

Therefore;

n² + n + 4 = n² + 3·n - 24

2·n = 24 + 4 = 28

n = 14

From which we have;

[tex]t_1 = \dfrac{1 + 14}{2} \times 14 + 2 = 107[/tex]

Therefore, the total number of marbles in the set, t₁ = 107 marbles.

The number of marbles in the set would be as follows:

[tex]107[/tex] marbles

Arrangement

Given that,

After arranging the marbles in an equilateral Δ, 2 marbles would be left

The size of marble being 1 unit,

So,

The first row of the equilateral Δ will consist of 1 marble,

while

The second row comprises of 2 marbles.

The process goes so on and on.

Therefore,

Total marbles [tex]t = 1 + 2 + 3 + ... + n[/tex]

Hence,

[tex]t = (1 + n)/2[/tex] × n

Because 2 marbles are extra,

[tex]t = (1 + n)/2[/tex] × n [tex]+ 2[/tex]

In case,

The same marble set are framed into a triangle, every side would contain 1 marble exceeding the previous one where 13 marbles would be felt short.

Thus,

Total marbles = [tex]\frac{1 + (n + 1)}{2}[/tex] × [tex](n + 1) - 13[/tex]

by putting the values, we get

[tex]n^2 + n + 4 = n^2 + 3n - 24\\2n = 24 + 4 = 28\\n = 14[/tex]

∵ Total marbles [tex]= (1+ 14)/2[/tex] × [tex]14 + 2[/tex]

[tex]= 107[/tex]

Thus, 107 marbles are the correct answer.

Learn more about "Probability" here:

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Answer:

Step-by-step explanation:

There are infinitely many rational numbers between any two rational numbers.

Answer:

x = ± ( 5√5 - 3 ) / 2

Step-by-step explanation:

We are given the equation ( 2x + 3 )² = 125;

[tex]( 2x + 3 )^{ 2 } = 125 - Take Square Root on Either Side,\\| 2x + 3 | = \sqrt{ 125 } - Simplify Square Root of 125,\\\\| 2x + 3 | = \sqrt{ 5 * 25 } - Simplify Further,\\| 2x + 3 | = 5\sqrt{ 5 } - Take | |,\\\\2x + 3 = 5\sqrt{ 5 } , and , 2x + 5 = - 5\sqrt{ 5 } - Algebra, \\2x = 5\sqrt{ 5 } - 3 , and , 2x = - 5\sqrt{ 5 } - 3 - Divide Either Side by 2\\\\x = ( 5\sqrt{ 5 } - 3 ) / 2, and , x = ( - 5\sqrt{ 5 } - 3 ) / 2\\Conclusion ; x = ( + / - 5\sqrt{ 5 } - 3 ) / 2[/tex]

Solution ; x = ± ( 5√5 - 3 ) / 2

Answer:

Ava is 10 years old

Step-by-step explanation:

Sara is 8

Sara=$8 per week for 12 weeks

$8×12 weeks=$96

Ava has $24 more than Sara

x*12=96$+$24

12x=120

x=120/12

x=10

Ava's age is 10

Answer:

142 pages

Step-by-step explanation:

The parameters given are

First page of part of the book available = 143

The last is numbered with the digits 143

Since the book is said to have been split into two parts with, we have that one part of the book starts from the beginning, while the other part continue from the first part stops

Number on the pages on the first part = from 1 to number on the first page on the second part - 1

Hence, the part of the book available is the second part and the number of pages in the first part = 1 to 142 or 142 pages.

Answer:

37

Step-by-step explanation:

If this is a regular hexagon, the sides have the same length

3y +19 = 6y+1

Subtract 3y from each side

3y+19-3y = 6y-3y+1

19 = 3y+1

Subtract 1 from each side

19-1 = 3y+1-1

18 = 3y

Divide each side by 3

18/3 = 3y/3

6 =y

ST = 6y+1

     =6*6+1

     =36+1

     = 37

Answer:

37 units

Step-by-step explanation:

sides are equal

3y+19=6y+1

3y= 18

y= 6

3y+19= 3*6+19= 37

QR=ST= 37 units

Answer:

Step-by-step explanation:

The solution is Option D.

The figure represents a construction of congruent segments

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first line segment be represented as P

Let the second line segment be represented as Q

Now , the equation will be

The length of the line segment P is congruent to the line segment Q

Therefore , the line segments P and Q are congruent to each other

Hence , the figure represents a construction of congruent segments

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Answer: C

Step-by-step explanation:

If you look at the patterns in the table, you will notice that y is always the square of x. So y = x^2 (C)

Answer:

c

Step-by-step explanation:

When you multiply any negative number by any power the answer is the same as the positive of that number.Just make sure you put it in like this into the calculator:

[tex](-4)^{2}[/tex]

The Answer:

2 is an integer.

Answer:

c

Step-by-step explanation:

edgeinuity

Answer:

x=-12        x =2

Step-by-step explanation:

-x^2-10x+24=0

Divide by -1

x^2 +10x -24 = 0

Factor

What 2 terms multiply to -24 and add to 10

12 * -2 = -24

12 -2 = 10

(x+12) ( x-2) = 0

Using the zero product property

x+12 =0    x-2 =0

x=-12        x =2

Answer:

7 inches

Step-by-step explanation:

formula for a trepezoid is 1/2(a+b)*h

1/2(5+x)X3=18 (now make x the subject)

(5+x)X3=36

5+x=12

x=7

so the other base is 7in

Answer:

| 4x - 6 | = - 6

Step-by-step explanation:

The absolute value function always produces a positive value.

| 4x - 6 | = - 6 ← negative value is not possible

Answer:

The first one

Step-by-step explanation:

For the second one x is equal to 11 bc -2 minus 11 is 9 which is a solution

The third one x is equal to 0 which is a solution

The last one x is equal to 4 which is a solution

There are no solution for the first on bc it does not equal to -6

Correct me if this is wrong

Answer:

reflect over line b

counterclockwise rotation about P by 180 degrees

Step-by-step explanation:

reflecting over b will put it in the same place bc b goes down the middle of the rectangle

if you rotate it counterclockwise around p by 180 degrees it would flip it upside down but that doesn't really matter because the length on the top and bottom are equal

Answer:

I would check:

reflect over line b  and check

counterclockwise rotation about P by 180 degrees

Step-by-step explanation:

First of all, b is a horizontal line going through the middle. If you reflect across it you will get the same rectangle just backwards but exactly the same position.

If you rotate 180, then you will get the exact same shape just upsides down.

Thanks and please give brainliest have a nice day :)

There is no picture ; - ;

Answer:

its C

Step-by-step explanation:

Answer:

The volume of the solid is the volume of the prism minus the volume of the cylinder.

For the cylinder, diameter = d = 4 cm

radius = d/2 = (4 cm)/2 = 2 cm

V = volume of prism - volume of cylinder

The volume of a prism is length times width times height.

The volume of a cylinder is pi times the square of the radius times the height.

V = LWH - (pi)r^2h

V = 6 cm * 6 cm * 15 cm - (pi)(2 cm)^2(15 cm)

V = 540 cm^3 - 60pi cm^3

V = (540 - 60pi) cm^3

Answer:

6 divided by 4=6/4 (bottom left)

Step-by-step explanation:

You're dividing a 6 meter area into 4 parts, so you're dividing 6 by 4 (6/4 m)

Answer:

6/4 m or 1.5 m

Step-by-step explanation:

Given 6 meter divided by 4 = 6/4

Answer:

Step-by-step explanation:

The length of each side corresponds to the sizes of each angle respectively.

To determine the length of each side, we would apply sine rule which is expressed as

a/sinA = b/SinB = c/SinC

The diagram of the triangle is shown in the attached photo. The longest side is c. If the shortest side is 10 cm less than the longest side, it means that the length of the shortest side is c - 10

Therefore,

c/Sin75 = (c - 10)/Sin45

c/0.966 = (c - 10)/0.707

Cross multiplying, it becomes

c × 0.707 = 0.966(c - 10)

0.707c = 0.966c - 9.66

0.966c - 0.707c = 9.66

0.259c = 9.66

c = 9.66/0.259

c = 37.3 cm

The shortest side is

37.3 - 10 = 27.3 cm

Applying the sine rule again,

b/Sin60 = 37.3/Sin75

b/0.866 = 37.3/0.966

Cross multiplying, it becomes

0.966b = 0.866 × 37.3

b = 32.3018/0.966

b = 33.4 cm

The perimeter is

27.3 + 33.4 + 37.3 = 98 cm

Answer: find the answer in the explanation

Step-by-step explanation:

Two times a number, n that is, 2n

and four less than three times the same number, that is, 3n - 4

Cole is wrong for not interpreting the two statement differently into two separate expression.

Finding the sum of the two expression will be

2n + 3n - 4 = 5n - 4

So, if n = 2

Substitute 2 for n in the expression 5n -4

5(2) - 4

10 - 4 = 6

Answer:  c) 3.2 inches

Step-by-step explanation:

Let x represent the width of the frame

Then the area of the frame is:

(x + 12)(x + 14) = 261.44

Rewrite it in Standard form of a quadratic equation:

x² + 26x + 168 = 261.44

x² + 26x - 93.44 = 0

Use Quadratic Formula to solve for x:

[tex]x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-26+\sqrt{26^2-4(1)(-93.44)}}{2(1)}\\\\\\x=\dfrac{-26+\sqrt{1049.76}}{2}\\\\\\x=\dfrac{-26+32.4}{2}\\\\\\x=\dfrac{6.4}{2}\\\\\\x=\large\boxed{3.2}[/tex]

Answer:

14.29

Step-by-step explanation:

Let p be the price of the cd

we take the price of the cd plus the tax and it must be less than or equal to 15

the tax is the price of the cd times 5 %

p + p*.05 ≤15

Combine like terms

p*1.05 ≤15

Divide each side by 1.05

p ≤15/1.05

p  ≤14.28571429

Rounding to the nearest cent

p  ≤14.29

The maximum price is 14.29

Answer:

see below

Step-by-step explanation:

$36/4oz  = $9 per oz

24/3oz = $ 8 per oz

$20/2oz  = # 10 per oz

Answer:

256

Step-by-step explanation:

First..

8*2=16

Now

16 (squared)=256

Answer:

The answer is 32

Step-by-step explanation:

8 x 2 is 16

16 is 2 is 32

pls give me brainliest, I show work

Answer:

Okay, so, your picture kinda blurry but I'll still help you:

to find y intercepts you just see where the line crosses the y axis and write the coordinate down for each line.

To find the gradient, just pick two points on a line and do

1)the difference between both y axis points

2)the difference between the x axis points

and then divide 1) by 2) to get the gradient.

Hope this helps!!

Answer:

Either A or B, or both. They are both true

Step-by-step explanation:

The diameter of a circle is and only can be one value. As long as you start from the center of the circle and go in a straight line. All radii lengths are congruent is also true. Im unsure if you can choose more than one answer

Answer:

The answer is D.

Step-by-step explanation:

You have to divide it by 2 :

∠RST = ∠ROT ÷ 2

= 46° ÷ 2

= 23°

O represents the centre of circle.

(Correct me if I am wrong)

Answer:

D. 23°

Step-by-step explanation:

The measure of central angle is twice the angle of circumference lying on the same arc. So,

<RT = 2(<RST)

<RST = <RT/2

<RST = 46/2

<RST = 23°

Answer:

3x - 1 = 0

Step-by-step explanation:

3x + 1 = 0

The perpendicular of a line has a slope that is the negative reciprocal of that lines slope.

So the answer is 3x - 1 = 0

Answer:

Using the mid-term break formula for all of them.

a) x²+7x+12

= x²+3x+4x+12

= x(x+3)+4(x+3)

= (x+4)(x+3)

b) x²+6x+8

= x²+2x+4x+8

= x(x+2)+4(x+2)

= (x+4)(x+2)

c) x²+5x+6

= x²+2x+3x+6

= x(x+2)+3(x+2)

= (x=3)(x+2)

d) x²+8x+7

= x²+7x+x+7

= x(x+7)+1(x+7)

= (x+1)(x+7)

Answer:

a) the middle number is seven and the last number is 12

factorising means we want something like (x + ___) (x +__)

Which number go into the blanks?

we need 2 numbers that add together to get 7 multiplied together to get 12.

3 + 4 is equal to 7

3x4=12

Answer:

(x+3)(x+4)

b) the middle number is 6 and the last number is 8

Factoring means we want something like

(x+___)(x+___)

which number go to the blanks?

We need two numbers that add together to get 6 and multiply together to get 8

2+4=6

2x4=8

Answer:

(x+2)(x+4)

c) the middle number is 5 and the last number is 6

we need two numbers that add together to get 5 and multiply together to get 6

2 + 3 is 5 and 2 x 3=6

Answer:

(x+2)(x+3)

Answer:

d) (x+1)(x+7)

Answer:

4:45p.m

Step-by-step explanation:

40+40+35

divide by 60

you round to get 1hour and 50min

add it to 3:05

Answer:

5:00 PM

Step-by-step explanation:

She got home at 3:05 PM

--> played video games for 40 mins --> 3:45 PM

--> cleaned the kitchen 40 mins --> 4:25 PM

--> Actuall HW 35 ins --> 5:00 PM

5:00 PM

Answer:

-8

Step-by-step explanation:

Answer:

Let's do this step by step

Step-by-step explanation:

I hope this helps