Which equation can be used to solve for b?
B
30°
8ft
G
C
b
A

Answer: -39.57

Step-by-step explanation:

The type of function that represents the bank account as a function of time is: this is an exponential function because there is a common ratio in the balance between the months.

In order to determine the type of function that models or represents the bank account as a function of time, we would check whether or not there is a common difference or common ratio.

In Mathematics, a linear function is used to model a situation when there exist a constant or common difference between its consecutive terms. On the other hand, an exponential function there is used to model a situation when there exist a constant or common ratio between its consecutive terms.

For the common difference, we have:

d = 1,474.56 - 1,843.20 = -368.64

d = 1,843.20 - 2,304.00 = -460.8

Therefore, the bank account as a function of time is not a linear function.

For the common ratio, we have:

r = 1,474.56/1,843.20 = 0.8

r = 1,843.20/2,304.00 = 0.8

Therefore, the bank account as a function of time is an exponential function.

Read more on exponential function here: https://brainly.com/question/28873368

#SPJ1

Answer:

the bank account as a function of time is an exponential function.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The solution to the system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).

A system of equations is a collection of two or more equations with a same set of unknowns.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

The given system of linear equations are :

y = 1/3x - 10 and 2x + y = 4

On solving two equations by using substitution method, It is given that

[tex]y = \frac{1}{3}x-10[/tex]    … (1)

2x + y = 4       … (2)

Substituting (1) in (2)

⇒ [tex]2x + (\frac{1}{3}x-10) = 4[/tex]

By further calculation

⇒ [tex]2x + \frac{1}{3}x - 10 = 4[/tex]

⇒ [tex]2x + \frac{1}{3} x = 4 + 10[/tex]

⇒ [tex]2x + \frac{1}{3} x = 14[/tex]

Taking LCM

⇒ [tex]\frac{(6+1)}{3}x = 14[/tex]

⇒ [tex]\frac{7}{3}x = 14[/tex]

By cross multiplication

⇒ 7x = 14 × 3

⇒ 7x = 42

Divide both sides by 7

⇒ x = 6

Substitute the value of x in equation (1)

[tex]\Rightarrow\ y = (\frac{1}{3} \times (6) - 10)[/tex]

So we get

⇒ y = (2-10)

⇒ y = -8

Therefore, the solution to the system of equations is (6, -8).

Learn more about Linear Equation by: https://brainly.com/question/2030026

#SPJ4

Answer:

y = 9, y = - 3 and y = - 6

Step-by-step explanation:

a line with equation y = c is a horizontal line parallel to the x- axis.

c is the value of the y- coordinates the line passes through.

Thus parallel lines must also be horizontal with equation y = c

a line parallel to y = 4 passing through (1, 9 ) with y- coordinate 9 is

y = 9

a line parallel to y = 2 passing through (- 1, - 3 ) with y- coordinate - 3 is

y = - 3

a line parallel to y = - 5 passing through (4, - 6 ) with y- coordinate - 6 is

y = - 6

Using the z table, the critical value [tex]z_{a/2}[/tex] needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value [tex]z_{a/2}[/tex] needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

[tex]\alpha[/tex]=1−0.82

[tex]\alpha[/tex]=0.18

Now finding the value of [tex]\alpha[/tex]/2

[tex]\alpha[/tex]/2=0.18/2

[tex]\alpha[/tex]/2=0.09

Now finding the value of [tex]z_{a/2}[/tex].

[tex]z_{0.82}[/tex] = 1.34

Hence, the critical value [tex]z_{a/2}[/tex] needed to construct a confidence interval with level 82% is 1.34.

To learn more about standard normal random variable link is here

brainly.com/question/14782203

#SPJ4

The fourth term a₄ of the sequence aₙ is 15

The definition of the function is given as

a(1)=-11

a(n)=a(n-1)x10

When this definition is rewritten properly, we have the following representation

a₁= 11

aₙ = aₙ₋₁ * 10

The above definitions imply that we simply multiply 10 and the previous term to get the current term

Using the above as a guide,

So, we have the following representation

a₂ = 11 * 10

Evaluate the products

So, we have

a₂ = 110

Also, we have

a₃ = 110 * 10

Evaluate the products

So, we have

a₃ = 1100

Lastly, we have

a₄ = 1100 * 10

Evaluate the products

So, we have

a₄ = 11000

This represents the 4th term of the sequence

Hence, the value of a₄ is 11000

Read more about sequence at

brainly.com/question/7882626

#SPJ1

Answer: [tex]x = 34[/tex]

Step-by-step explanation:

Let x be the original amount of Pokémon cards Tommy had, we know that he sold half of them; this can be express as:

                                                              [tex]\frac{x}{2}[/tex]

After this he changed his mind and bought 17 cards, then he has:

                                                         [tex]\frac{x}{2} + 17\\[/tex]

We know that he has 34, then we have the equation:

                                                       [tex]\frac{x}{2} + 17 = 34[/tex]

Solving for x we have:

                                                        [tex]\frac{x}{2} + 17 = 34[/tex]

                                                        [tex]\frac{x}{2} = 34 - 17[/tex]

                                                            [tex]\frac{x}{2} = 17[/tex]

                                                         [tex]x = (2)(17)[/tex]

                                                            [tex]x = 34[/tex]

The unit rate of kilo per pound = 0.4545

And the unit rate of pound per kilo = 2.2

Meredith's new scale measures in both pounds and kilograms.

The information on the box says the scale has a weight limit of 200 kilograms or 440 pounds.

We have a weight limit of 200 kilograms or 440 pounds.

We need to find the unit rate of kilo per pound and pound per kilo

The unit rate of kilo per pound would be,

r1 = 200/440

r1 = 0.4545

and a unit rate of pound per kilo would be,

r2 = 440/200

r2 = 2.2

Therefore, The unit rate of kilo per pound = 0.4545

And the unit rate of pound per kilo = 2.2

Learn more about the unit rate here:

https://brainly.com/question/22233867

#SPJ9

Answer:

{-4,-2,4}

Step-by-step explanation:

range are y values so we just look at the y values of the coordinates plotted on the graph

Hopes this helps

The range of the relation that is graphed above is: {-4, -2, 4}.

All values of x that are plotted on a graph of a relation is the domain, while the corresponding y-values on the graph is the range of the relation.

Given the graph of the relation above, the x-values of each of the points make up the domain of the relation, while the corresponding y-values of each point make up the range of the relation.

The y-values of each of the points are: -4, -2, and 4

Therefore, the range is: {-4, -2, 4}.

Learn more about the range of the relation on:

https://brainly.com/question/1579288

#SPJ1

Answer:

Step-by-step explanation:

$1.65

Answer:

m∠G = 118°

Step-by-step explanation:

The congruence statement that says:

△CAT ≅ △DOG,

says not only that the triangles are the same shape and size, it also says //which// angles (and sides) are conguent.

Angle C and Angle D are the same. Angle A and Angle O are the same. And Angle T and Angle G are the same.

So in △CAT, Angle C is 25° and Angle A (same as O) is 37°.

Also, all the angles in a triangle add up to 180°.

25° + 37° + T = 180°

62° + T = 180°

T = 118°

And T corresponds to G, so AngleG is also 118°.

The simplification of the given expression would be = 9^-¹⁶

Simplification is defined as editing of a given mathematical expression in a more easy to under form or less complex form.

To simplify the given expression such as 9^-53·9^37 the law of exponents should be observed.

According to the law of exponents, a^m * a^n = a^m + n

9^-53·9^37

= 9^ -53+37

= 9^-16

Therefore, the simplification of the expression above would be = 9^-¹⁶.

Learn more about exponents here:

https://brainly.com/question/27385740

#SPJ1

Answer:

Step-by-step explanation:

0.875/2.5 = 6.25/x

0.875x=15.625

x=$17.85

The height of a building is 7 m that casts a shadow of 11.3 m

The ratio between height to shadow length of man will be equal to the ratio of building. So, equating these two to find the height of building.

Height : Shadow length (man) = Height : shadow length (Building)

Keep the values as fraction

1.8/2.9 = Height/11.3

Height of building = (1.8 × 11.3) ÷ 2.9

Performing multiplication in numerator on Right Hand Side of the equation

Height of building = 20.34 ÷ 2.9

Performing division on Right Hand Side of the equation

Height of building = 7 m

Thus, the height of building is 7 m.

Learn more about shadow length -

https://brainly.com/question/14613383

#SPJ4

Answer:

Lily is correct.

Step-by-step explanation:

Because 0.3 is out of a part that is split into 10 parts.

Answer:

This is a incomplete questions.

Step-by-step explanation:

So, is there options or do you do a graph.

Feel free to ask

Answer:

B, C, and E for Edge

Step-by-step explanation:

did it and got it right lol :)

Answer:

Step-by-step explanation:

We'll look for an equation in the format y = mx + b where m is the slope and b the y-intercept.    A characteristic of parallel lines is that they have the same slope.  That means the same value of m for both equations.  

The reference equation is y = 1/3x + 5,  It has a slope of (1/3).  This means the new line will also have a slope of (1/3), and so we can write:

   y = (1/3)x + b

Any value of b will result in a parallel line to y = 1/3x + 5.  But the new line comes with the requirement that it go through point (3,5).  That's easily done if we choose the correct value for b, the y-intercept.  We could graph the line to visually determine what value of b will make the line go through this point, or we can simply enter the given point in the above equation and solve for b:

    y = (1/3)x + b  (for point (3,5)

    5 = (1/3)(3) + b

    5 = 1 + b

     b = 4

A b value of four will shift the line so that it intersects (3,5).  See the attached graph.

The regular price for the cell phone is $210

From the information given, the cell phone is on sale at $35 more than half of the regular price and the sale price is $140.

Let the regular price be represented as x.

This will be illustrated as:

1/2x + 35 = 140

0.5x + 35 = 140

Collect like terms

0.5x = 140 - 35

0.5x = 105

Divide

x = 105 / 0.5

x = 210

The regular price is $210.

Learn more about price on:

brainly.com/question/1153322

#SPJ1

Answer:volume of pyramid is equal to the volume of prism

Step-by-step explanation:

The probability that both selected pairs of socks are white is 1/3.

We have a drawer. The drawer contains 10 pairs of socks. Six out of ten pairs of socks are white. We randomly selected two pairs of socks. We need to find the probability that both selected pairs of socks are white. Let the probability be represented by the variable "P". To select the first pair of white socks, the chances are six out of ten. Once the first pair is selected, the chances of selecting the second white pair of socks are five out of nine.

P = (6/10)*(5/9) = 1/3

To learn more about probability, visit :

https://brainly.com/question/11234923

#SPJ1

Answer:

523

Step-by-step explanation:

the game

D. No, because it is possible that the student gets lower test grades because of another factor, such as not studying.

When two variables behave in unison, rising or falling in lockstep with one another, there is a positive correlation.

When two variables move in opposition to one another—that is, when one rises, the other falls, this is known as a negative correlation.

Given, A student noticed that when she gets less than 8 hours of sleep at night, she scores lower on her test grades.

No, Because it is possible that the student gets lower test grades because of another factor, such as not studying.

learn more about correlations here :

https://brainly.com/question/13503439

#SPJ1

A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 35 books.

The system of equation will be x+y = 7 and 20x+35y = 225.

Let x be the no of small boxes and y be the no. of large boxes.

Given here each small box can hold 20 books and each large box can hold 35 books.

A total of 7 boxes were sent.

So, x+y = 7.......equation 1

Also given that 7 boxes can hold 225 books altogether.

So, 20x+35y = 225.....equation 2

Hence the system of equation will be x+y = 7 and 20x+35y = 225.

To learn more combinations click here https://brainly.com/question/11732255

#SPJ4

The given expression in monomial. 2+3 is a monomial as it will give 5 which has only one degree. Layla is correct

What is monomial?

When an expression has only one similar like term of all the terms are of same degree then it is known as Monomial. When there are two distinct terms then it is said to be binomial.

We Are given an expression 2+3

Now both the number 2 and 3 have degree 0

Hence we can add them directly hence it become 5 which again has a degree 0 only

Hence it is a monomial term

Therefore Layla is correct

TO learn more about binomial please refer the following link

https://brainly.com/question/15246027

#SPJ13

Answer:1. m=1    3. m=1/3

Step-by-step explanation: your slope on number one was wrong it is 1. the slope on question 3 is 1/3. subtract two of the x-values. then subtract two y-values. they do not have to correspond with the x-values. the x will be your numerator the y your denominator. simplify the fraction

84.4 liters were consumed.

211 x 400 = 84400

In total 84400 milliliters were consumed

1000 milliliters are in one liter

So that means 84.4 liters were consumed.