Robbie opens an account at a local bank by depositing $100. The account pays 2.4% interest, compounded weekly. He deposits $100 every week for 3 years.
b. Write the future value function if x represents the number of weeks.
c. Use a graphing calculator to graph the future value function.
d. Using the graph, what is the approximate balance after 2 years?

Answer:

[tex]\log_556[/tex]

Step-by-step explanation:

Given:

[tex]\log_5(4 \cdot 7)+\log_52[/tex]

Multiply the 4 and 7:

[tex]\implies \log_528+\log_52[/tex]

[tex]\textsf{Apply the Log Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_5(28\cdot2)[/tex]

Multiply the 28 and 2:

[tex]\implies \log_556[/tex]

The real solution of the equation are +0.77, -0.77, +1.85, -1.85.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given:

x^4 − 4x^2 + 2 = 0

(x²)² - 4x² + 2 =0

let us consider y= x², then the above equation become

y² - 4y + 2 =0

On further solving for 'y' we have

y= -b±√(b² -4ac) / 2a

y= 4±√(16-8)/2

y=4±2√2/2

y= 2 + √2, y=2-√2

Now, y= x²

x² = (2 + √2),  x²= 2-√2

x= +1.8477, -1.8477 , +0.7653, -0.7653

x= +0.77, -0.77, +1.85, -1.85

Learn more about quadratic equation here:

https://brainly.com/question/6168075

#SPJ1

The estimate closest to the length of a pen​ is 160​mm

Estimation is when we use approximate values in a calculation to give an approximate, predicted answer rather than an exact answer.

We can estimate some lengths and distances using approximate values for measurements.

For example, 16 cm is approximately the length of a pen.

Therefore, the estimate of a pen is 16 cm.

Since the length in cm is not in the option, we have to convert.

Hence,

1 centimetres = 10 millimetres

16 centimetres = ?

cross multiply

estimated length of a pen = 160 millimetres.

Therefore, the estimate closest to the length of a pen​ is 160​mm

learn more on estimation here: https://brainly.com/question/14182214

#SPJ1

Answer:

Step-by-step explanation:

Explanation:

This can be rewritten as

−

18

<

5

x

+

7

<

2

To solve this, isolate

x

. The first step will be subtracting

7

. However, subtract

7

from all parts of the inequality.

−

18

−

7

<

5

x

+

7

−

7

<

2

−

7

Which yields

−

25

<

5

x

<

−

5

Now, divide each part by

5

.

−

5

<

x

<

−

1

wolframalpha.com

Answer:

x>3

Step-by-step explanation:

Thats all hope this helps.

Answer:

[tex]2x^2 - 12x + 1[/tex]

Step-by-step explanation:

Hello!

Given the expression: [tex]4x^2 - 8x + 3 - (2x^2 + 4x + 2)[/tex]

Simplify by combining like terms.

Like terms are terms with the same variable and raised to the same power.

The simplified form is [tex]2x^2 - 12x + 1[/tex].

The solution to the inequality is w ≥ 470 or w ≤ 530

The given parameters are:

Number of words = 500

Absolute deviation = 30

Acceptable number of words = w

The absolute value inequality is represented as

|w - Number of words| ≥ Absolute deviation

So, we have

|w - 500| ≥ 30

Remove the absolute bracket

So, we have

w - 500 ≥ -30 or w - 500 ≤ 30

Add 500 to both sides of the inequality

So, we have

w ≥ 470 or w ≤ 530

Hence, the solution to the inequality is w ≥ 470 or w ≤ 530

Read more about inequality at

https://brainly.com/question/24372553

#SPJ1

Answer:

[tex]x=25^o[/tex]

Step-by-step explanation:

Angle sum of a triangle: [tex]< A + < B+ < C=180^o\\[/tex]

Types of Triangles: Isosceles, Equilateral, Scalene

Given AB = AC are two sides of the big triangle, then ΔABC is Isosceles.

Isosceles triangles are defined to have two equal sides and two equal angles (opposite the congruent(equal) sides).

Also, since ABC is defined as a triangle, BC is a straight line, a.k.a., it is a [tex]180^o[/tex] angle. As the image shows, the line, AD creates a right angle on one side, therefore it creates a right angle([tex]90^o[/tex]) on the other side.

Back to Isosceles Triangles, AD = AE means ΔADE is isosceles and <ADE = <AED

Using the Angle sum formula of a triangle, you can fill in <A, <B, and <C with the following:

<A=[tex]50^o[/tex]

<B=<C=y [This is because <ADE = <AED]

[tex]50^o+2y=180^o\\2y=130^o\\y=65^o[/tex]

Now, this means that <ADE=[tex]65^o[/tex] and <ADC =[tex]90^o[/tex]

<x is better seen as <EDC

<EDC+<ADE=<ADC

Since we know <ADE is 65 and <ADC is 90, we can plug in these to the formula above.

[tex]x+65^o=90^o\\x=25^o[/tex]

The numbers are 24 and 33 so the smaller one is 24

Answer:

24 and 33 are the numbers among which 24 is the smallest.

Step-by-step explanation:

Let one positive integer be x, then another will be x - 9

Solve:

[tex]\sf \dfrac{x-9 }{x} = \dfrac{8}{11}[/tex]

cross multiply

[tex]\sf 11x-99= 8x[/tex]

collect like terms

[tex]\sf 11x-8x = 99[/tex]

simplify

[tex]\sf 3x = 99[/tex]

divide both sides by 3

[tex]\sf x = 33[/tex]

As the integer is positive, x = 33, then another will be 33 - 9 = 24.

One way to simplify an expression containing trigonometric functions is to first write the expression in terms of sines and cosines only.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:

C² = A² + B² - 2(A)(B)cosθ

Similarly, the law of sine can be used to determine the missing side length of a geometric figure with the opposite and hypotenuse side lengths are given:

[tex]\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}[/tex]

In this context, we can reasonably infer and logically deduce that an expression containing trigonometric functions can be simplified by first writing the expression in terms of sines and cosines only.

Read more on law of cosine here: brainly.com/question/11000638

#SPJ1

Answer:

1.Yes

2.Yes

3.No

4.Yes

5.Yes

6.No

I hope it's help

Answer:

1. yes

2.Yes

3.no

4.no

5.yes

6.yes

Step-by-step explanation:pa brainliest po thankyou

Answer:

x=8

Step-by-step explanation:

So 6^2+x^2=10^2

36+x^2=100

x^2=64

x=8

Answer:

first put name of triangle abc than

angle _abc =180degree

10+6+c=180

16+c=180

180÷16=c

c=11.25

the value of x is 11.25 ans

Answer:

See below

Step-by-step explanation:

Answer: x=32

Step-by-step explanation:

x-7+2x+1=90

x+2x-7+1=90

3x-6=90

3x=96

x=32

Answer:

slope = 6/10

Step-by-step explanation:

Point 1: (0,2)

Point 2: (10,8)

m= Slope= Rise/run = (y2-y1)/(x2-x1) = (8-2)/(10-0) = 6/10

Answer:

10 if going from the smallest to the largest or 1/10 if going from the smallest to the largest.

Step-by-step explanation:

Let s = scale factor

10s = 100  Divide both sides by 10

s = 10

6 hundred and 73 thousand and 65..

The linear equation that represents the number of pages that Lourdes still need to read will be y =  y = 30x + 3/5y.

It should be noted that an equation is used to show the relationship between the variables. It should be noted that the person is reading a biography.

It should be noted she reads 30 pages each day and after 9 days, he has read 3/5 of the pages.

Therefore, the linear equation that represents the number of pages that Lourdes still need to read will be:

y = (30 × x) + (3/5 × y

y = 30x + 3/5y.

Finally, this is the linear equation representing the pages that Lourdes read.

Learn more about equations on:

brainly.com/question/13763238

#SPJ1

The equation of the given function will be h=-0.096x+30.6. The mass will be 63.5 grams.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is y-intercept.

1.) The slope of the given function will be,

Slope = (25.8 - 30.6) / (50 - 0) = -4.8/50 = -0.096

Now, substitute the values in the general linear equation,

h = -0.096x + c

30.6 = -0.096(0) + c

c = 30.6

Therefore, the equation of the given function will be h=-0.096x+30.6.

2.) Mass when the height is given as 24.5 cm, will be,

h = -0.096x + 30.6

24.5 = -0.096x + 30.6

24.5 - 30.6 = -0.096x

-6.1 = -0.096x

x = -6.1/-0.096

x = 63.5

Hence, the mass will be 63.5 grams.

Learn more about Equation of Line here:

https://brainly.com/question/21511618

#SPJ1

Answer:

Hello,

n=6

Step-by-step explanation:

1111 in binary is 15 in décimal

(23) base n=15 ==>

2*n+3=15

2n=12

n=6

Answer:

vvvyaz

Step-by-step explanation:

szahvzlvzlz

The actual length of the river on centimetres is 97 centimetres

The scale was 5 centimetres represents 120 miles.

Therefore, on the scale

5 centimetres = 120 miles

Now, let's find the length in centimetres if the river is measured as 2320 miles.

120 miles  = 5 centimetres

2320 miles = ?

cross multiply

actual length of the river in centimetres = 2320 × 5 / 120

actual length of the river in centimetres = 11600 / 120

actual length of the river in centimetres = 96.6666666667

actual length of the river in centimetres = 97 centimetres.

learn more on length and scale here: https://brainly.com/question/16136369

#SPJ1

Answer:

y ≥ -0.65x +110  

y ≤ -x +140

45 students, 95 adults

Step-by-step explanation:

6.50x + 10y ≥ 1100 --> 10y ≥ -6.50x + 1100 --> y ≥ -0.65x +110  

x + y ≤ 140 --> y ≤ -x +140

Answer:

61/72

Step-by-step explanation:

first find the lowest common denominator - basically in this case the lowest number that goes into 8 and 9 - 8 x 9 which is 72, then

8 goes into 72 9 times so do 9 x the numerator (5)

9 x 5 = 45

Do the same for the second fraction, 9 goes into 72 8 times so do 8 x numerator (2)

8 x 2 = 16

Now add 45+ 16 = 61 ( this is your numerator)

and you keep the denominator (72) the same, so the answer is 61/72

Answer:

62.5%

Step-by-step explanation:

We only have the measurement of 2 corresponding sides AE and A'E'.  We are going from the large to the small.

Let x = the scale factor

4x = 2.5  Divide both sides by 4

x = .625   to change that to a decimal multiply by 100

.625 x 100 = 62.5%

Answer:

1

Step-by-step explanation:

3x² +24x = -48

3x² +24x + 48 = 0

x² +8x + 16 = 0

By using cross multiplication,

(x-4)² = 0

Therefore,

x-4 = 0

x = 4 (repeated)

Answer:

Only one real solution

Step-by-step explanation:

[tex]{ \tt{ {3x}^{2} + 24x = - 48}} \\ { \tt{ {3x}^{2} + 24x + 48 = 0 }} \\ { \tt{ {x}^{2} + 8x + 16 = 0}} \\ { \tt{(x + 4) = 0}}