2. The area of a circle of radius 1 is π units squared. Use scaling to explain
why the area of a circle of radius r is πr^2units squared.

If we divide 3 by 1/2 then we put the multiplication sign and do reciprocal of 1/2 which is 2/1 or 2.. so 3 × 2= 6

(Hope this helps you out!)

When Martina has $80 in a savings account earning 10% interest compounded annually, she will have $106.48 in three years.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 = 2. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Here,

Initial amount=$80

rate=10% compounded annually

time=3 year

A=P(1+r/n)^(nt)

Year 0 $80.00

Year 1 $88.00

Year 2 $96.80

Year 3 $106.48

Martina will have $106.48 in 3 years when she has $80 in a savings account that earns 10% interest, compounded annually.

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The expression for the number of tiles will be 27 / ( s² ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mr. Grant wants to tile a 27 - square - foot area with square tiles. let s = the side length, in feet, of a square tile.

The number of tiles will be calculated as,

Number = Total area / Area of tile

Number = 27 / s²

Hence, the number of tiles will be calculated by the formula Number = 27 / s².

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Answer:

false

Step-by-step explanation:

The solution of this mathematical expression (12 - x) . 5 when x = 2 is equal to: C. 50.

In Mathematics, a mathematical expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

In order to evaluate the given mathematical expression, we would substitute the value of x into the mathematical expression and then open the bracket as follows;

(12 - x) . 5

When the variable x = 2, the mathematical expression becomes;

Mathematical expression = (12 - 2) × 5

Mathematical expression = 10 × 5

Mathematical expression = 50

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Only, Option B: y [ n ] = x [ n ] + x [ n - 10] forms a linear system.

A linear system is a mathematical model that represents a relationship between input and output using linear equations.

A: y [ n ] = x [ n ] x x [ n - 1]: This is not a linear system because it includes a product of two input signals x[n] and x[n-1], which makes the system non-linear.

B: y [ n ] = x [ n ] + x [ n - 10]: This is a linear system because it includes only one input signal x[n] and one delayed input signal x[n-10], which are added together. It's a linear combination of input signals and it's a linear system.

C: y [ n ] = x 2 [ n ]: This is not a linear system because it includes the square of the input signal x[n] which makes the system non-linear.

D : (a) and (c): Only option B is a linear system.

It's worth noting that linear systems are characterized by the linearity property, which means that the input-output relationship is a linear combination of the inputs.

Therefore, Option B: y [ n ] = x [ n ] + x [ n - 10] forms a linear system.

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The value of y is 12 and the scale factor is 2.

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Answer: Supply

(The answer is supply because the opposite axis in a curve is supply, there's nothing other than that)

Answer: supply

Step-by-step explanation: Just took the test

Answer: A- 0.035

Step-by-step explanation:

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

The trigonometric ratios (sine, cosine, and tangent) are the same for all 30-60-90 triangles because these triangles have a unique set of properties that make them special. Specifically, all 30-60-90 triangles have a right angle, and the angle measures are in a ratio of 1:2:3. Because of these properties, the length of the hypotenuse is always twice the length of the shorter leg, and the length of the longer leg is always equal to the square root of 3 times the length of the shorter leg. This allows us to determine the exact values of the trigonometric ratios for all 30-60-90 triangles, regardless of their size.

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Answer: 6!

Step-by-step explanation: Isolate the variables. In order to do that you have to divide each side by factors that don't contain the variables.

Answer: Correct option is (D) 1.97

Step-by-step explanation:

According to question,

ln (x + 6) – ln (2x – 1) = 1.....(i)

Now by using log rule

Log(a) – Log(b)= Log(a/b)

Equation (i) becomes

Log((x + 6) / (2x - 1)) = 1

Taking anti log on both sides

((x + 6) / (2x - 1)) = e1

We know that

e1 = 2.72

Therefore,

((x + 6) / (2x - 1)) ≈ 2.72

(x + 6) = 2.72 (2x - 1)

x + 6 = 2.72 (2x) - 2.72 (1)

x + 6 = 5.44x - 2.72

8.72 = 4.44x

By cross multiplication we get,

x = 8.72 / 4.44

x = 1.97

Hence the correct value of x is 1.97

There are several different methods for factoring quadratics, including factoring by grouping, completing the square, difference of squares, sum and difference of cubes, synthetic division and quadratic formula.

Factoring by grouping: This method involves grouping the first two terms and the last two terms of the equation, and then factoring out a common factor.

Completing the square: This method involves changing the form of the equation so that the left side is a perfect square trinomial. This allows you to take the square root of both sides and solve for the roots.

Difference of squares: This method can be used when the equation is of the form a^2 - b^2 = 0. It can be factored as (a+b)(a-b) = 0.

Sum and difference of cubes: This method can be used when the equation is of the form a^3 + b^3 = 0 or a^3 - b^3 = 0. It can be factored as (a+b)(a^2-ab+b^2) = 0 or (a-b)(a^2+ab+b^2) = 0.

Synthetic division: This method can be used when the equation is in the form of a polynomial divided by a binomial. It uses division to factor the polynomial.

Quadratic Formula: This method can be used when factoring by grouping or completing the square seems difficult or impossible. This method uses the formula -b±√(b^2-4ac) /2a where a, b, c are the coefficient of x^2,x and constant term in the equation to find the roots of the quadratic equation.

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If TV and WY are parallel lines, then m∠VUX = 53°.

What are parallel lines?

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines intersect at infinity is another way to put it.

It is given that line segment TV and WY are parallel to each other.

A line ZS intersect the parallel lines.

The measure of m∠TUS = 53°.

The measure of m∠VUX = m∠TUS as they are both vertically opposite angles and hence they are same.

Therefore, m∠VUX = 53°.

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Correct option is C, Both have fixed initial rate and payment amount.

A balloon mortgage is similar to an adjustable rate mortgage (ARM) in other ways, with an initial rate period that is equal to the balloon duration. For instance, a 7-year balloon is frequently contrasted with a 7-year ARM. For 7 years, both have a set rate; after that, the rate will change.

A balloon mortgage starts off with set payments for a set amount of time and comes to a finish with a single, large payment. Because it is substantially greater than the initial instalments, the one-time payment is known as a balloon payment. According to the definition of a balloon loan, the final payment is at least twice as much as the average monthly payment on the mortgage. Balloon payments typically cost tens of thousands of dollars.

Variable-rate mortgages (VRMs), commonly referred to as adjustable-rate mortgages (ARMs), feature an interest rate that may fluctuate on a regular basis based on changes in the appropriate financial index linked to the loan. Generally speaking, if the index rate rises or falls, your monthly payment will too.

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Answer:

Both have fixed initial rate and payment amount

Step-by-step explanation:

Answer:

Step-by-step explanation:

20

Answer:

11, 11

Each shirt costs $11 and each pair of pants costs $11.

without the math explanation we know they must be equal logically and also must both be 11 lmk if youd like an explanation for that

Step-by-step explanation:

s+3p=44

3s+p=44

s=44-3p

3(44-3p)+p=44

132-9p+p=44

-8p=-88

p=11

s+3(11)=44

s+33=44

s=11

Answer:

Each shirt costs $11 and each pair of pants costs $11.

Step-by-step explanation:

If 1 shirt costs $11, & a pair of pants also costs $11, I buy 1 shirt, my total is $11. Now, I buy 3 pairs of pants, 11x3 is $33, so 33+11 is $44. My total is $44.

My friend buys the 3 shirts, $33 is my friend's total. He now buys 1 shirt, which is also $11. Again, 33+11=$44

The process of transforming the graph into the parent function is explained below.

The term function is defined as a mathematical relationship from a set of inputs to a set of outputs

Here we have to define the process of converting the given graph into parent function.

In order to find that we must know the definition of parent function,

The term parent function is defined as the most basic version of an algebraic function.

There are basically four types of transformation are used.

They are listed as follows:

1) Translation which means that the change in the  position on the coordinate plane

2) rotation defined the change in the angle of object

3) reflection refers the a mirrored preimage, and

4) enlargement refers the increment of every side proportionally

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Answer: [tex]\sqrt{41}[/tex]

Step-by-step explanation:

Using the distance formula: D = √(2 - 7)2 + (-6 - -2)2

= √(-5)2 + (-4)2

= √41

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ M(\stackrel{x_1}{7}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{2}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ MA=\sqrt{(~~2 - 7~~)^2 + (~~-6 - (-2)~~)^2} \implies MA=\sqrt{(2 -7)^2 + (-6 +2)^2} \\\\\\ MA=\sqrt{( -5 )^2 + ( -4 )^2} \implies MA=\sqrt{ 25 + 16 } \implies MA=\sqrt{ 41 }[/tex]

mind  you that the distance equation comes directly from the pythagorean theorem.

40 grams of sample would be left 5 grams after 90 years.

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

Given:

Cesium-137 has a half-life of approximately 30 years.

The amount of 40 g sample would be left after 90 years,

= 40 x (1/2[tex])^{90/30}[/tex]

= 40 x (1/2)³

= 5

Therefore, 5 grams would be left.

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The ordered exponential values, from least to greatest, are given as follows

-4², 4^(-2), 4^0, (-4)²

An exponential value is defined as follows:

y = a^x.

In which the base and the exponent are given as follows:

When two numbers have the same base, we order them according to the exponent, the lowest the exponent, the lowest the number, hence they are ordered as follows:

4^(-2), 4^0, (-4)²

As:

2 > 0 > -2.

The smallest number is -4², as the exponential has precedence over the negative, hence the value is of -4² = -(16) = -16.

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The given relation can be written as:

y = $5*x + $20

Notice that we have a constant term, thus it is not a proportional relation.

A general proportional relationship can be written as:

y = k*x

Where k is a constant of proportionality.

The given case is:

" A bike rental store charges $20 as a flat fee, plus $5 per hour."

We know that there is a flat fee of $20 plus $5 per hour, so we can write the equation:

y = $5*x + $20

Notice that we have a constant term, thus, it is not a proportional relation.

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The bicycle travels 2198 cm or about 21.98 meters for 10 complete revolutions of the tires.

What is the circumference of the circle?

The distance traveled by bicycle each time the tires make one complete revolution is equal to the circumference of the tire. The circumference is given by the formula:

C = 2 * π * r

Where C is the circumference, π is approximately 3.14, and r is the radius of the tire. Since the diameter of the tire is 70 cm, the radius is half the diameter, which is 70/2 = 35 cm. So we can substitute that value into the formula to find the circumference:

C = 2 * 3.14 * 35 = 219.8 cm

So the bicycle travels 219.8 cm each time the tire makes one complete revolution. To find out how far the bicycle travels each time the tires make 10 complete revolutions, we simply multiply the distance per revolution by 10:

distance = 219.8 cm * 10 = 2198 cm

Hence, the bicycle travels 2198 cm or about 21.98 meters for 10 complete revolutions of the tires.

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The value of this approximation will be 3.7678.

To approximate the integral of 4 1 (2x2 1) dx using a midpoint Riemann sum with 3 equal subintervals, the following calculations can be used:

Start by finding the width of each subinterval (w). Using the given bounds of integration, this can be calculated as: w = (b-a)/n, where n is the number of subintervals. In this case, w = (2-1)/3 = 0.3333.

Next, calculate the midpoint of each subinterval. This can be done by taking the average of the lower and upper bounds of each subinterval. In this case, the midpoints are 1.1667, 1.5, and 1.8333.

Finally, calculate the value of the midpoint Riemann sum by adding the product of the function evaluated at each midpoint and the width of each subinterval. This can be expressed as:

Sum = 0.3333 * [4(1.1667)2 -1] + 0.3333 * [4(1.5)2 -1] + 0.3333 * [4(1.8333)2 -1]

This gives a value for the midpoint Riemann sum of 3.7678.

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The possible results from the simulation described from the dotplots is with most of the dots at 1 and 2.

The dot plot that best represents the possible results from the simulation described would be one where the majority of the dots are clustered around 1-2 canceled flights, with some dots representing 0 canceled flights and a few dots representing 3 or more canceled flights. This is because with a probability of success (a canceled flight) of 0.015, the expected number of canceled flights in a sample of 100 would be 1.5 (0.015 x 100), and the distribution of the number of canceled flights from the 50 trials would likely be approximately normal with a mean of 1.5 and a standard deviation of 0.35 (the standard deviation for a binomial distribution with n = 100 and p = 0.015).

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In a triangle, the measures of those two angles are, 80° and 90°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

A triangle has an angle that measures 10°.

And, The other two angles are in a ratio of 8 : 9.

Since, The other two angles are in a ratio of 8:9.

So, The value of those two angles are 8x and 9x.

We know that;

The sum of all three interior angles in a triangle is 180°.

So, We can formulate;

⇒ 10° + 8x + 9x = 180°

⇒ 10° + 17x = 180°

⇒ 17x = 180 - 10

⇒ 17x = 170

⇒ x = 170 / 17

⇒ x = 10

Thus, The value of those two angles are,

⇒ 8x = 8 × x = 80°

⇒ 9x = 9 × x = 90°

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Answer:

$14.7

Step-by-step explanation:

To find the markup, you can use the following formula:

markup = (selling price - cost price) / cost price x 100

cost price = $35

selling price = $35 + markup

markup = (selling price - $35) / $35 x 100

Now you know that selling price = $35 + markup and markup = 42%, so you can use this information to find selling price:

markup = 42% = 0.42

selling price = $35 + $35*0.42 = $35+14.7 = $49.7

So the markup is $14.7

The exponential equation is [tex]y=ab^x[/tex]. Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

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The exponential equation is y = [tex]ab^{x}[/tex] . Let's look at some properties of this equation.

'b' must be greater than 0 and not equal to 1. b>0, b1.

The formula for exponential regression is y = [tex]ab^{x}[/tex] . This refers to the process of arriving at the best exponential curve equation for your dataset. This regression is very similar to linear regression and tries to find the best (straight line) line equation for a data set.

Exponential regression refers to the process of obtaining the best exponential curve equation for a data set.

A model that explains the process of doubling growth.

The exponential equation is y = [tex]ab^{x}[/tex]

Exponential functions are commonly used in life sciences and are used to represent the specific quantity that you want to model. B. Population size modeled over time. Plots of experimental data are usually plotted with time on the x-axis and quantity on the y-axis.

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The simplified expression is -7-4z/9

Answer: Nicole had 3x = 3*24 = 72 coupons in total.

Let x be the number of coupons Wong had at the beginning.

Nicole had x coupons at the beginning because they both had an equal number of coupons.

When Wong gave Nicole 24 coupons, Nicole had x+24 coupons in total.

Nicole had 3 times as many coupons as Wong, so x+24 = 3x

x = 24

Nicole had 3x = 3*24 = 72 coupons in total.

Step-by-step explanation:

hope this helps

Between men's and women's sizes, there is a roughly 1.5 size difference. Men's sizes apply to the unisex fashions. For women, go down 1.5 sizes.

( a ) By adding 33 to your current US size, you may convert a men's US shoe size to an EU size with ease. For illustration, if you are a US men's size 9, your EU size is 42. There are centimeter-based shoe sizes throughout Europe.

( b ) European Size 40.=25,3 cm. EU Size 41.=26.0 cm Size 42 in EU.

( c ) By adding 33 to your current US size, you may convert a men's US shoe size to an EU size with ease.

( d ) US to EU and EU to US shoe size conversion for Euro shoes. According to the ISO standard, an EU Size 40 is equivalent to a US women's shoe size 9.

( e ) By adding 33 to your men's US shoe size, you can convert to Euro Sizing.

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