You start with $575 in your bank account and deposit $60 each month. Write a linear or exponential equation

Answer:

6x - 9

Step-by-step explanation:

18x -11 - (12x - 2)   Can be written

18x -11 -1(12x -2)  Distribute the -1

18x - 11 -1(12x) + (-1)(-2)

18x - 11 -12x +2  Combine like terms

6x -9

$93.60

Simple interest shows the amount of money an account earns based on the initial deposit.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this equation, I is the total interest earned, P is the principal or the initial deposit, r is the interest rate as a decimal, and t is the time in years.

To find the total balance of the account just add the interest amount to the principal. So, A = I + P, where A is the total balance.

Solving for Simple Interest

For this question, the variables are:

Now, we can plug these values into our formula.

After 4 years, the account will earn $93.60 in simple interest.

Our Pythagorean triplets will be (6,8,10), (5,12,13), and (3,4,5).

So what is the Pythagorean triplet?

The square of the greatest number in a Pythagorean triplet equals the sum of the squares of the other two numbers.

The greatest side in a right-angled triangle is called the hypotenuse.

So, in our first triplet A(6,8,10) the greatest side is 10. So, hypotenuse = 10.

= [tex]hypotenuse^{2}[/tex] = [tex]10^{2}[/tex] = 100.

Now, [tex]6^{2}[/tex] + [tex]8^{2}[/tex] = 36 + 64 = 100.

[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]8^{2}[/tex]

Thus A(6,8,10) is a Pythagorean triplet.

In the second case B(5,12,13) hypotenuse = 13.

= [tex]hypotenuse^{2}[/tex] = [tex]13^{2}[/tex] = 169.

Now, [tex]12^{2}[/tex] + [tex]5^{2}[/tex] = 144 + 25 = 169.

[tex]13^{2}[/tex] = [tex]12^{2}[/tex] + [tex]5^{2}[/tex]

Thus B(5,12,13) is a Pythagorean triplet.

In the Third case C(7,13,15) Hypotenuse = 15.

= [tex]hypotenuse^{2}[/tex] = [tex]15^{2}[/tex] = 225.

Now, [tex]7^{2}[/tex] + [tex]13^{2}[/tex] = 49 + 169 = 218.

[tex]15^{2}[/tex] [tex]\neq[/tex] [tex]7^{2}[/tex] + [tex]13^{2}[/tex]

Thus C(7,13,15) is not a Pythagorean Triplet.

In the last case D(3,4,5) Hypotenuse = 5.

= [tex]hypotenuse^{2}[/tex] = [tex]5^{2}[/tex] = 25.

Now, [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16 = 25.

[tex]5^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

Thus D(3,4,5) is a Pythagorean triplet.

Therefore our three results A(6,8,10) B(5,12,13) and D(3,4,5) are Pythagorean triplets.

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No, 1234 is not an arithmetic sequence. A sequence is a list of numbers, arranged in a specific order.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. It is also known as an arithmetic progression.

The sequence 1234 does not have a common difference between its terms. It's just a set of numbers arranged in a specific order, but the difference between the terms is not always the same.

Arithmetic sequence has the general formula of a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the number of the term. The sequence 1234 doesn't follow this formula.

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The thermometer functions because of temperature-related expansion and contraction. Conduction is the process by which heat moves from one item to another.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The thermometer will display a greater temperature as the liquid expands and rises as it gets hotter.

The thermometer functions because of temperature-related expansion and contraction.

Conduction is the process by which heat moves from one item to another.

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Answer:

[tex](x+1)(x-2)(x-4)[/tex]

Step-by-step explanation:

By the Rational Root Theorem, possible rational solutions for the given polynomial are [tex]\pm1,\pm2,\pm4,\text{ and}\pm8[/tex], so we can test each one:

1 |  1  -5   2   8

____ 1_-4_-2

    1  -4  -2 | 6 <-- (x-1) IS NOT a root

-1 |  1  -5   2    8

____-1_ 6_ -8

     1  -6   8  | 0 <-- (x+1) IS a root

So, [tex]x^3-5x^2+2x+8=(x+1)(x^2-6x+8)=(x+1)(x-2)(x-4)[/tex]

The rate of change of f on the interval [2, 4] is 6.

The rate of change of a function f on the interval [a,x] is the slope of the corresponding secant line m(sec), which is given by the following formula:

m(sec)=(f(x)-f(a))/(x-a)

To calculate the rate of change, we can take an example function f(x) = x^2. Let's say we want to find the rate of change of f on the interval [2, 4]. Using the formula from above, we get:

m(sec)=(f(4)-f(2))/(4-2)

= (4^2 - 2^2)/(4-2)

= (16 - 4)/2

= 12/2

= 6

Therefore, the rate of change of f on the interval [2, 4] is 6.

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Answer:

180 cm

Step-by-step explanation:

I had to look up some of these equations

Central angle  'a' = 2 arcsin ( c/(2R) = 2 arcsin (120/(2*100) ) = 73.74°

d= R cos ( a/2) = 100 cos ( 73.74/2) = 80 cm

So from the cutout to the bottom will be   80 + 100 = 180 cm

Graph 1 has n<14 inequalities, and graph 2 has n>14 inequalities.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.

The two rules of inequality :

Rule 1: Adding or subtracting the same amount from both sides of an inequality does not change the inequality symbol. Rule 2: Multiplying or dividing both sides by a positive number does not change the inequality symbol.

Here graph 1 depicts

The line is extending to the left of the number 14, excluding 14.

So, the inequality will be;

n < 14.

The graph 2 depicts

The line, which includes the number 14, is moving to the right.

So, the inequality will be ;

n≥14

As a result, the inequalities are n14 and n14 of graphs 1 and 2, respectively.

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On solving the question, the answer of given trigonometric question  is tanx-sinx.

This is due to the fact that trigonometry is still regarded as a very challenging and abstract branch of mathematics in comparison to other branches. When learning trigonometry, students frequently run into mistakes, misunderstandings, and barriers. A subfield of mathematics known as trigonometry studies how angles and length ratios relate to one another. Applications of geometry to astronomical research led to the field's emergence in the Hellenistic civilization during the third century BC.

cosecx(secx−1)−cotx(1−cosx)

= 1/sinx*1(1-cosx)/sinxcosx−cosx(1−cosx)/sinx

=((1−cosx)−sinxcosx(1−cosx))/sinxcosx

=sinxcosx(1−cosx)−cos^2x(1−cosx)​

=(1−cosx)(1−cos2x)/sinxcosx

=(1−cosx)×sin2^x/sinxcosx

=tanx(1−cosx)

=tanx−tanxcosx

=tanx−sinx/cosx×cosx

=tanx−sinx

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Answer:

Undefined

Step-by-step explanation:

[tex]f(x)=2+|x-3|\\f'(x)=\frac{x-3}{|x-3|}\\f'(3)=\frac{3-3}{|3-3|}=\frac{0}{0}[/tex]

Therefore, the function is not differentiable at x=3

When the inequality is solved, we have r-2. Each side can be multiplied or divided by the identical positive value, added to or subtracted from by the same amount, and more.

Using inequality characters like "," ">," "," or "," expressions using linear inequalities compare exactly two values. Such values could be algebraic, numerical, or both.

Here,

Linear inequalities: How are they solved

In the first step, solve the equality for y.

Step 2: Sketch the boundaries of the inequality on a graph.

The region that addresses the inequality should be shaded. Step 3. Step four requires you to solve the third inequality for y. In step 5, the boundary line of the second inequality must be graphed. Cover the region that fulfills the second condition.

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In the function f(x) = a(b^x), the initial value is always a because a is independent on x. So, when x changes, b^x will change as well but a will remain the same.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. A function is an equation with a single solution for y for each value of x. A function pairs each input of a particular type with exactly one output.

For example, let a = 2, b = 3, and x = 0: f(0) = 2 3^0 = 2 1. If x = 1, then f(1) = 2 3^1 = 2 3. If x = 2, then f(2) = 2 3^2 = 2 9, etc. As you can notice a = 2 remain unchanged as the initial value, because a is independent on x change.

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The distance from Point B to Point C of the triangle will be 45 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Triangle ABC is similar to Triangle ADE. Then the equation is given as,

x / 15 = (40 + 20) / 20

x / 15 = 60 / 20

x / 15 = 3

x = 45 feet

The distance from Point B to Point C of the triangle will be 45 feet.

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The complete question is given below.

Answer:

216.7 m/min

Step-by-step explanation:

1 km = 1000 m

1 hour = 60 min

13km/h = 13 (1000 m) / (60 min) = 216.7 m/min

Answer:216.6667

Step-by-step explanation:

kph × 16.66667

m/min =13 × 16.66667

m/min =216.6667

Answer:

This is a simple algebraic equation, it can be solved by isolating the variable on one side of the equation.

-2.75x + 7 = -26

Add 26 to both sides of the equation:

-2.75x + 33 = 0

Divide both sides by -2.75:

x = -12

So the solution of the equation is x = -12.

Note that x = -12 is the value of x that makes the equation true

Answer:

x = 12

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 12

So, 30 and 5 are the values that are missing is calculated by ratio and proportion.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

If both the antecedent and the consequent are multiplied or divided by the same non-zero number, the ratio remains the same.

i.e.,

We can see from the provided table that:

In the second column,

Since, 6x0.5=3

Thus, multiply 10 by the same number.

10x0.5=5

For the third column,

since,

50=10x5

multiply by the same number, then

6x5=30

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Answer:

47,174,400 possible number plates

See important note at the bottom of the explanation

Step-by-step explanation:

The easiest way to handle a problem of this type is to note the following

There are 9 digits 1-9 that we can use for the first four characters of the license plate

So the number of ways to arrange the first 4 digits without repetition is
9  x 8 x 7 x 6 = 3024 possible ways

For the letters, assuming that we are using the English alphabet, the 5th spot where the first letter after the numbers is can be done in 26 possible ways since there are 26 alphabets.

For the second letter that will leave us with 25 possibilities

For the third and final spot there are 24 possibilities

This means that, without repetition, the letters can be arranged in 26 x 25 x 24 ways = 15,600 ways

Together we can arrange the digits and letters in 3024 x 15600 ways which works out to
3024 x 15600 = 47,174,400 ways or possible number  plates

Or we could simply write this in one step as

9 x 8 x 7 x 6 x 26 x 25 x 24 = 47,174,400 ways or possible number  plates

Note

Even though there are 10 digits 0 - 9, the question clearly states that we should choose from digits 1 through 9 only.

If we are allowed to use all 10 digits the first 4 digits can be put together in 10 x 9 x 8 x 7 = 78,624,000 ways

You should clarify this with your teacher.

One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m.

You can find the slope of the line by determining the rise and run of two locations on the line. The rise is the vertical change between two places, while the run is the horizontal change. The slope is calculated by dividing the climb by the run: Riserun = Slope Slope = rise and run.

Depending on the form of the equation in front of you, the procedure for calculating the slope will differ. If the equation is written as y = mx + c, the slope (or gradient) is simply m. If the equation is not in this form, attempt rearrangement. You will need to do the following to determine the gradient of additional polynomials:

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The amount that her clothes weigh more than her books would be

= 57kg

The amount for the shipping cost for her school would be

= 5600+25400 = $31000

Postal Service:

The Postal Service is an American indie pop supergroup from Seattle, Washington, consisting of singer Ben Gibber, producer Jimmy Tamborello, and backing vocalist Jenny Lewis.

The band released her only album Give Up in 2003 on her Sub Pop Records to mostly positive reviews. The album reached his number 114 spot on the US Billboard 200 album chart and was certified platinum by the Recording Industry Association of America.  Laura Bergen joined the line-up for the entire tour, providing additional vocals and instruments, while Jen Wood and Jenny Lewis filled in for some shows.

According to the Question:

The mass of Moya's books = 70 kilograms

The mass of Moya's clothing = 127 kg

The difference between the both masses = 127 - 70 = 57kg

The cost per kg for books = $80 per kg

The cost per kg of clothing = $200

Therefore, the amount for the shipping cost for her school would be = (70×80) + (127 ×200)

= 5600+25400 = $31,000.

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The value of the ratio OC'' : OC' is given as follows:

OC'' : OC' = 1 : 4.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For point C', the scale factor is given as follows:

k = 2.

For point C'', the scale factor is given as follows:

k = 1/2.

The ratio between two amounts a and b is given by the division of a and b, as follows:

a : b.

Hence the ratio between the distances OC'' and OC' is given as follows:

(1/2)/2 = 1/2 x 1/2 = 1/4.

(division of fractions, we multiply the first fraction, of 1/2, by the inverse of the second fraction 2/1, which is of 1/2).

In ratio notation, we have that:

OC'' : OC' = 1 : 4.

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a) To determine the distance covered by a bus in a given number of minutes, we can use the formula: distance = speed x time. Since the speed of the bus is given in miles per hour (mph) and we want to know the distance covered in minutes, we need to convert the time to minutes. Therefore, distance = speed x (time in minutes / 60).

b) To determine the distance covered by a bus traveling at sodi mph for 3 hours, we can use the formula: distance = speed x time.

distance = sodi x 3

c) To determine the distance covered by a bus traveling at sodi mph for 30 minutes, we need to convert 30 minutes to hours. Therefore, time = 30/60 = 0.5 hours.

distance = sodi x 0.5

It's important to note that I'm not able to understand the value of "sodi" as it is not a valid unit for speed or distance. Please provide the correct value for sodi.

Answer:

Takes maria

Step-by-step explanation

Maria's rate of speed is 46.5 kilometers per hour.

What is the distance?

Distance is defined as the product of speed and time.

Since there are 3600 seconds in an hour, we can divide the time it takes Gretchen to travel 4400 meters by 3600 to find the number of hours it takes her:

⇒ 340 seconds / 3600 seconds/hour = 0.09444444 hours.

Next, we need to convert the distance she travels to kilometers. Since there are 1000 meters in a kilometer, we can divide the distance Maria travels by 1000 to find the number of kilometers she travels:

⇒ 4400 meters / 1000 meters/kilometer = 4.4 kilometers.

Now that we have the distance Maria travels and the time it takes her to travel that distance in the appropriate units, we can divide the distance by the time to find her rate of speed in kilometers per hour:

⇒ 4.4 kilometers / 0.09444 hours = 46.5882375  kilometers/hour.

Thus, Maria's rate of speed is 46.6 kilometers per hour.

The selling price of the washer/dryer is $1,137.86. Thus, the correct answer is option b.

To find the cost of the washer/dryer, we need to reverse the markup percentage. We can do this by dividing the markup by 100 and then multiplying by the selling price.

Markup = (Markup Percentage) x (Cost)

So, if we rearrange this equation and solve for cost:

Cost = (Markup) / (Markup Percentage)

Plugging in the given information:

Cost = $295.00 / 0.35

Cost = $842.86

To find the selling price, we add the markup to the cost:

Selling Price = Cost + Markup

Selling Price = $842.86 + $295.00

Selling Price = $1,137.86

The selling price of the washer/dryer is $1,137.86.

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The complete question- Appliance World places a markup on a washer/dryer combination of $295.00, which is 35%based on cost. Find the cost, then the selling price. What is the selling price of the washer/dryer? a)$1,098.74. b) $1,137.86 c)$1,032.19. d)$1,059.43

Answer: 23

Step-by-step explanation:

Answer:23

Step-by-step explanation:

A sentence must have a singular or plural subject and verb in order to be grammatically correct. To put it another way, the tenses of the subject and verb must match.

According to their structure and function, sentences can be divided into eight categories: declarative, interrogative, exclamatory, imperative, simple, compound, complex, and compound-complex sentences.

You must look at what a grammatical name accomplishes in an English sentence in order to recognise it. Consider: At this morning's assembly, Susan performed a song. You must take into account the work each unit performs in the sentence in order to identify the various units' grammatical names.

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On solving the provided question, we can say that volume of the toy = volume of cylinder + volume of hemi-sphere Volume, V = [tex]\pi r^2 + 2/3\pi r^3[/tex] V = [tex]3.14*2*2*3 + 2/3*3.14*2*2*2[/tex] = 54.4266666667 = 54 cubic in.

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

volume of the toy = volume of cylinder + volume of hemi-sphere

Volume, V = [tex]\pi r^2 + 2/3\pi r^3[/tex]

V = [tex]3.14*2*2*3 + 2/3*3.14*2*2*2[/tex] = 54.4266666667 = 54 cubic in.

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The inverse additive of 2 3 is -2 3.. This means that when you add the two numbers together, the result is 0.

2 3 + (-2 3)

= (2 x -1) + (3 x -1)

= -2 + (-3)

= -5

= 0

The additive inverse of 2 3 is -2 3. In mathematics, an additive inverse is a number that when added to another number will produce a result of zero. This means that when you add 2 3 and -2 3 together, the result will be 0. To calculate this, we first start by multiplying each number by its opposite sign. So,

2 x -1 = -2 and

3 x -1 = -3.

Then, we add the two numbers together

: -2 + (-3) = -5.

Finally, we simplify the equation to 0. The additive inverse of 2 3 is -2 3, meaning that when added together, the result will be 0.

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The value of 3/x-1 - 4/x+3 is (13-x)/(x-1)(x+3)

Algebraic fractions are fractions using a variable in the numerator or denominator, such as . Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0.

The numerator and denominator are called the terms of the algebraic fraction.

We simplify the expression by finding the LCM of the denominator.

therefore 3( x+3) - 4(x-1))/(x-1)(x+3)

opening the parentheses

(3x+9-4x+4)/(x-1)(x+3)

= (13-x)/(x-1)(x+3)

Therefore the value of 3/x-1 - 4/x+3 is (13-x)/(x-1)(x+3)

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