You are deciding between First National Bank and Liberty Bank. They both offer checking and savings accounts. First National charges a $10 fee to receive checks and charges $2.50 per ATM transaction. Liberty Bank has no check fee but charges $3.25 per ATM transaction. How many times do you need to be charged an ATM fee before you are paying the same amount of money in fees at both banks?
Step 1: Define your variables - Look at the question statement. What are you being asked to find?



Step 2: Write 2 equations that use those unknown variables



Step 3: Solve the system of equations



Step 4: State your solution. What does it mean in the context of the word problem?

This [tex]4x^2 - 12x + 9[/tex] factors into [tex](2x - 3)^2[/tex], and is thus a perfect square trinomial.

A perfect square is a number system that can be expressed as the

square of a given number from the same system.

Trinomial [tex]Ax^2 + Bx + C[/tex] is a perfect square if

A > 0

C > 0

B = ±2√A√C

1. [tex]36b^2 - 24b - 16[/tex]

C < 0

2. [tex]4a^2 - 10a + 25[/tex]

2√A√C = 2×2×5

              = 20,

B = −10

3. [tex]16x^2 + 24x - 9[/tex]

not a perfect square,

C < 0

4. [tex]4x^2- 12x + 9[/tex]

perfect square

A>0,

C>0,

2√A√C = 2×2×3

-B = 12

= [tex](2x - 3)^2[/tex]

Thus,  [tex]4x^2- 12x + 9[/tex] the polynomial is a perfect square trinomial.

Learn more about perfect square;

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DI AKO KRINUSHBAK SANA KAYO DIN

Answer:

[tex]\sqrt{53}[/tex]

Step-by-step explanation:

First, we find out the length of EH, which is 7. And then, we find the length of GH, which is 3. If we square both the numbers and add them, we get 53. And then we square root that to get [tex]\sqrt{53}[/tex]

Hope this helps <:)

Don't forget to put brainliest!

Answer:

50%

Step-by-step explanation:

Hope this helped

Maybe mark brainiest

Dime = 10 cents

Nickel = 5 cents

Total value of coins = 3(10) + 4(5) = 30 + 20 = 50

To find the percent, first create a fraction. The fraction will be the amount of money that Benjamin has over the total (one dollar).

50 / 100 = 5 / 10 = 0.5

0.5 x 100 = 50

50%

Answer: 50% of a dollar

Hope this helps!

Answer:

406.08

Step-by-step explanation:

First FInd the area of the rectangle : which is short side * long side

-> 15*12=180m

Then find the area of the half circle, the formula of the area of a circle is [tex]\pi r^2[/tex]

here it's half a circle so it's [tex]\frac{\pi r^2}{2}[/tex] where r is 12

-> [tex]3.14\cdot \frac{\left(12\right)^2}{2}=226.08 m[/tex]

Finally just add the area of the rectangle with the area of the half circle

-> [tex]180+226.08=406.08 m[/tex]

Answer:

x= -2
y=4

Step-by-step explanation:

Since we have an equation set equal to y, we can plug it in for either value of y.

I will be using y= x+6 in this case.

Plug in x+6 for the other equation, so instead of y=-x+2 it will now be that x+6 = -x+2

Now add x to both sides, and that will remove the x on the left side leaving us with 2x+6 = 2

Now, subtract 6 from both sides to get 2x isolated, and you will get 2x= -4

Divide both sides by 2 to get x= -2

Not plug x= -2 in back for the top (or bottom) equation and get that y=4

Hope this helps and isn't too complicated!

[tex]\frac{1}{2a}[/tex]

Simplify or expand

[tex](2a)^{-1}[/tex]

Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]

[tex]\frac{1}{2a}[/tex]

I hope this helps you

:)

Answer:

200/7

Step-by-step explanation:

(2 meters)/(7 centimeters) or (2m/7cm)

1 meter = 100 cm

(2m/7cm)*(100cm/1m) = 200/7 (or   28.57) scale factor.

Answer:

483

Step-by-step explanation:

I really really pray and hope this helpss.

Answer:

X=3(7+23)

Step-by-step explanation:

Given a graph with a line running through coordinates (0,0) and coordinates (40,12), the unit rate of the relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes (x) is given by the slope of the line.

Step-by-step explanation:

Given:-

To Find:-

Solution:-

SP = MP - Discount.

Discount = (Discount %) of MP

Discount = (5/100) 54p

Discount = 27 Rs

Subtract discount from MP to get SP

SP = MP - Discount

SP = 540 - 27 Rs

SP = 513 Rs

Answer;

soln;

MP= Rs 540

discount = 5%

now,

SP = MP - D% of MP

    = 540 - 5/100 * 540

    =Rs 513

Answer:

14,464

Step-by-step explanation:

16,000 - 20% = 12,800

12,800 + 13% = 14,464

I hoope this is correct. Have a wonderful day and dream a good dream of good people. :)

Answer:

x coordinate is +3 and y coordinate is +1

Step-by-step explanation:

just count three squares right and one square down from D

Answer:

angle 1=angle 4 ( vertical opposite angle)

Answer:

[tex]\boxed{\sf{(x-4)(x-6)}}[/tex]

Step-by-step explanation:

In order to solve this problem, all you have to do is multiply their expressions by their factors.

To begin, you must group these expressions.

[tex]\sf{x^2-10x+24=\left(x^2-4x\right)+\left(-6x+24\right)}[/tex]

After that, you factor.

Solve.

[tex]\sf{x^2-4=x(x-4)}[/tex]

-6x+24=-6(x-4)

Then rewrite the problem down.

x(x-4)-6(x-4)

Factor by the common term.

(x-4)(x-6)

Therefore, the final answer is (x-4)(x-6).

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

  (b)  65/27

Step-by-step explanation:

Here, we notice the index for the summation runs from 0 to 3, so there are a total of 4 terms.

The sum represented by the summation symbol is ...

  5(-2/3)^0 +5(-2/3)^1 +5(-2/3)^2 +5(-2/3)^3

  = 5(1 -2/3 +4/9 -8/27)

  = 5/27(27 -18 +12 -8)

  = 5(13/27) = 65/27

__

There is a formula for the sum of a geometric series:

  Sn = a1×(1 -r^n)/(1 -r)

Here, the first term is a1 = 5(-2/3)^0 = 5. The common ratio is the base of the exponential, r = -2/3. So, the sum of n=4 terms is ...

  S4 = 5×(1 -(-2/3)^4)/(1 -(-2/3)) = 5×(1 -16/81)/(5/3) = 65/27

Answer:

it'sssssss 2.51

Step-by-step explanation:

========≈==================

Answer:

1.451 seconds.  Hurry.

Step-by-step explanation:

The position(height, h) of the foot ball will be given by the equation:

h = -32.2t^2 + 45t + 2.5

The term -32.2t^2 consists of the acceleration caused by gravity at Earth's surface ( -32 ft/sec^2) and the term +45t accounts for the initial velocity.  The + is assigned since the ball is moving vertically from ground.  The negative sign in -32t^2 is due to the acceleration being towards ground.  The term 2.5 accounts for the fact that the initial height of the ball is 2.5 feet above ground.

We can either calculate or graph with this function to find the time the ball spends in the air:

Calculate:

h = -32.2t^2 + 45t + 2.5

We need a value of t that would cause h to be 5.5 feet, the level it was caught:

5.5 = -32.2t^2 + 45t + 2.5

-32.2t^2 + 45t + 2.5 = 5.5

-32.2t^2 + 45t -3.0  = 0

Solve for t using the quadratic formula.  I get a value of 1.33 seconds.

Graph:

See the attached graph.  It confirms the 1.33 second value

Answer:

27=mean. 30=Median

Step-by-step explanation:

trust me I know what I'm doing

Answer: 12.16

Step-by-step explanation:

Answer:

If it is a conjunction that uses the word and, the solution must work in both inequalities and the solution is in the overlap region of the graph. If it is a disjunction that uses the word or, the solution must work in either one of the equations.

Step-by-step explanation:

Parallelogram is a quadrilateral with equal diagonals. The statement BO = 7.8 cm is the only false statement

From the given diagram, the opposite sides and angle of the figure are the same but the diagonals are not equal. This shows that:

m<B = m<D

m<A = m<C

Since the diagonals are not equal that is BD is not equal to AC, hence:

OB ≠ OC

Hence the statement BO = 7.8 cm is the only false statement

Learn more on parallelogram here: https://brainly.com/question/970600

Answer:BO = 7.8 cm

Step-by-step explanation: just did the quiz

Answer: (All below)

Step-by-step explanation:

1. 2x + y = 10

2(3) + 4) = 10

6 + 4 = 10

2. 3x + 2y =

3(3) = 2(4) =

9 + 8 = 17

3. 3y + 2x = 18

3(4) + 2(3) = 18

12 + 6 = 18

4. 10x + 4y + 2x = 52

10(3) + 4(4) + 2(3) = 52

30 + 16 +6 = 52

46 + 6 = 52

5. 6y + 5x =39

6(4) + 5(3) = 39

24 + 15 = 39

6. 7x + 4y = 37

7(3) + 4(4) = 37

21 + 16 = 37

7. 2(x+4) + 10 = 28

2( 5 + 4) + 10 = 28

2(9) + 10 = 28

18 + 10 = 28

8. 3(4x) + 4 = 64

3(4(5)) + 4 = 64

3(20) + 4 = 64

60 + 4 = 64

9. 10(xy) = 300

10(5(6)) = 300

10(30) = 300

10. 2(x + y) = 22

2(5 + 6) = 22

2(11) = 22

11. 3(rs) + 4(x)

3(2(3)) + 4(5) =

3(6) + 20 =

18 + 20 = 38

12. 2(q) + 2(x + t) = 20

2(1) + 2(5 + 4) =  20

2 + 2(9) = 20

2 + 18 = 20

13. 6(3t + 4s) = 84

6(3(1) + 4(3)) = 84  

6(2 + 12) = 84

6(14) = 84

14. 10(10x) + 10y = 560

10(10(5)) + 10(6) = 560

10(50) + 60 = 560

500 + 60 = 560

15. x(xy) = 150

5(5(6)) = 150

5(30) = 150

16. r(s)(t) = 24

2(3(4)) = 24

2(12) = 24

17. (r)(s)(t)(x)(y) =720

(2)(3)(4)(5)(6)= 720

6(20)(6) = 720

120(6) = 720

18. 6(2x + 3Y) = 1080

6(2(5) + 3(6)) = 1080

6(10 + 18) = 1080

6(180) = 1080

Hey there!

Answer:

336.84%

3200 out of 950 is 336.84%

Solution:

3200 out of 950 is what %?

3200 out of 950 is P%

Equation: Y/X = P%

Solving our equation for P

P% = Y/X

P% = 3200/950

p = 3.3684

Convert decimal to percent:

P% = 3.3684 * 100 = 336.84%

well, if we take 3200 to be the 100%, what is 950 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3200 & 100\\ 950& x \end{array} \implies \cfrac{3200}{950}=\cfrac{100}{x}\implies \cfrac{64}{19}=\cfrac{100}{x} \\\\\\ 64x=1900\implies x=\cfrac{1900}{64}\implies x = 29.6875[/tex]

Answer:

B

Step-by-step explanation:

4(-2)-8 = -16, so not C
4(-1)-8 = -12, so not A or D
4(0)-8 = -8, so not D
4(1)-8 = -4, so not A or D
4(2)-8 = 0, so not D

Answer:

$1.66 or $1.70 if you round up

Step-by-step explanation:

Answer: amplitude is 5 and Period is pi/2

Step-by-step explanation:

yes ‍♀️

Answer:

40" by 50"

Step-by-step explanation:

From inspection of the diagram,

height of 2 squares of the quilt ≈ height of doll plus a little bit

⇒ height of 2 squares of the quilt ≈ 18 + 2 = 20 in

⇒ height of 1 square of the quilt ≈ 20 ÷ 2 = 10 in

As the height of a square = width of a square

⇒ width of 1 square of the quilt ≈ 10 in

Dimensions of the quilt

width = 4 squares = 4 × 10 = 40 in

height = 5 squares = 5 × 10 = 50 in

Ratios

We can also work out the width and height by using ratios.

The ratio of width to height of the quilt = 4 squares : 5 squares

If we multiply by 10, the ratio becomes 40 : 50

Final Solution

40" by 50"

Answer:

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).