state if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.ABC

We can solve both limits by using Riemann sums, which is represented by the following:

Then, for our function:

A CD has a diameter of 12 cm and the diameter of the hole in the middle is 1.5 cm. So the area of the CD excluding the area of the hole will be 111.27 cm².

The area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, while the area of a plane region or plane area is the area of a form or planar lamina.

According to the question, the given values are :

Diameter of CD = 12 cm.

Radius of CD, r₁= D/2 = 6 cm

Diameter of hole = 1.5 cm.

Radius of hole, r₂ = D/2 = 0.75 cm.

Area of one side of CD, A = Area of CD - Area of hole

Area of circle = πr²

A =  π(6)² - π(0.75)²

A = 36π - 0.5625π

A = 35.437π cm².

The area of CD will be, A = 35.437 × 3.14 = 111.27 cm².

Hence, the area of one side of the CD will be 111.27 cm².

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You can identify that the triangle ACD is divided into two different triangles. These triangles are ABD and BCD.

Notice that the triangle BCD has two congruent sides. Therefore, it is an Isosceles triangle.

The triangle ABD has three congruent sides. This means that it is an Equilateral triangle. The measure of each interior angle of and Equilateral triangle is:

Therefore, you can determine that:

Let's assume that ABD is a Right triangle. Then:

Since the other triangle C has twol equal angles:

Therefore:

The answer is:

The value of the length and the width of the rectangle are 29.5 and 30.5 meters respectively

From the question, the statement is given as

Length and width are consecutive odd integers

Where perimeter = 120 meters

Represent the dimensions with x and y

Where Length = x and Width = y

And also, we have

y = x + 1

The perimeter of a rectangle is

Perimeter = 2 x (Length + Width)

Mathematically, this can be represented as

Perimeter = 2 x (x + y)

So, we have

2 x (x + y) = 120

Substitute y = x + 1 in 2 x (x + y) = 120

2 x (x + x + 1) = 120

This gives

2 x (2x + 1) = 120

Divide by 2

2x + 1 = 60

So, we have

2x = 59

Divide by 2

x = 29.5

Substitute x = 29.5 in y = x + 1

So, we have

y = 29.5 + 1

Evaluate

y = 30.5

Hence, the length and the width are 29.5 and 30.5

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What each part of the expression represents in the context of the problem include the following:

In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used in showing the relationship that typically exist between two or more numerical quantities, variables, as well as in conjunction with different mathematical operations.

In this exercise, we are provided with the following algebraic expression:

0.07r + (r – 20)

In the context of fixing David’s broken watch, the expression 0.07r most likely represents the amount of money charged as tax while the variable r represents the original cost of the repair. Additionally, the expression (r – 20) is the discount David received to fix his broken watch.

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the formula is

For $10,

So when, x=6.3, y=$10,

Given:

Two given points are,

THe objective is to find the value of slope, (m).

The formula to find the slope is,

Now, substitute the given values in the above slope formula.

Hence, the slope of the line is 3.

the ratio of 3 parts of silver to 4 parts green paint is

hence, we need to find other fractions equivalent to 3/4.

We can see that:

for instance, in the first case,

and so on. Therefore, th answer is 6:8 and 9:12

Sorry, did you actually mean [tex]3(x-2)+6[/tex] × [tex]3[/tex] ?

If so, then here is the solution.

[tex]3x + 12[/tex]

Hope this helps!

The graph of the equation y = (1/4)x + 2 has x and y intercepts of (- 8, 0) and respectively (0, 2)

We know to find the x-intercept of a graph we have to substitute y = 0 in the given equation and to find the y-intercept we have to substitute x = 0 in the given equation.

Given a linear equation in two variables x and y which is,

y = (1/4)x + 2.

Now at y = 0.

0 = (1/4)x + 2.

(1/4)x = - 2.

x = - 8.

When x = 0.

y = (1/4)(0) + 2.

y = 2.

So, the x and y intercepts of the graph of the equation y = (1/4)x + 2

are (- 8, 0) and (0, 2)

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The linear equation y = -500x + 5000 that models the price-sales.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Two points for $6, 2000 sales/day and $8, 1000 sales/day which is given in the question.

The slope varies in y as x changes.

m = (2000-1000 )/(6-8) = -500

The equation of a line with slope m is:

⇒ y = -500x+ b

Solve for b using one of the points (y-intercept)

2000 = -500(6)+b

5000 = b

The other point will provide the same result. To find b, you simply need one point (either one).

The linear relationship is:

y = -500x + 5000

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Answer:

20

Step-by-step explanation:

4 x 2 x 1 = 8

8 divide by 0.4 = 20

For the first equation:

x^2 - 25 = 0...... x^2 = 25..... x = sqrt(25)..... x = 5 and x = -5.... so it has two solutions: 5 and -5

For the second euation:

(x - 2)^2 = 0.... the solution is x = 2 because when x = 2, (2 - 2)^2 = 0 ^ 2 = 0

So it only has one solution: 2

For the third equation:

(x - 3)^2 = 81.... x - 3 = sqrt(81) = -9 and +9

x - 3 = -9... x = -6

x - 3 = 9... x = 12

so it has two solutions: -6 and 12

Answer:

use this to help get your answer

Step-by-step explanation:

y=mx+b or rise over run

Solve x

The value of x is -7/3

Given the equation:

We can rewrite it in the slope - intercept form; as follows:

The graph is given by:

ANSWER

Answer:

Explanation:

a) increase 100 by 5%

b) increase your result form (a)by 5%

c) The overall percent increase of the number 100;

It is not 10% because the second 5% increase was not on the initial number 100.

increasing 105 by 5% is more than increasing 100 by 5%.

Therefore, increasing 100 by 5% followed by increasing the result by 5% is greater than increasing 100 by 10%.

We just need to multiply the fractions

Then, 11/15 of the class rated Mrs. Santiago as an excellent teacher

Answer:

3 to 1.

Step-by-step explanation:

3:1 is a ratio, which is comparing 2 different things.

Considering the definition of an inequality, the inequality that represents the situation is 2m + 8≤20 and indicates that Jason can purchase 6 or more mozzarella sticks.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "x" the number of mozzarella sticks Jason can purchase, the inequality that expresses the previous relationship is

2m + 8 ≤20

Graphing the inequality gives the accompanying graph. It can be seen that the graph tells you that Jason can purchase 6 or more mozzarella sticks.

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Explanation

Let the sales be represented by x

Since the person earns 6.5% of the sales, this becomes;

Recall that at least implies greater than or equal to in inequality. Therefore, the equation becomes;

We will then solve for x

Answer: $28461.5385

Tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -

2 x 2 x 2 x 2 x 3 x 3

Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.

Given is tony, who wants to write large numbers as the product of as many whole numbers greater than 1 as possible. So, he writes 144 as

2 x 72 but he sees he can go further and writes it as 2 x 2 x 36.

Yes we can still go further and write 144 as the product of whole numbers greater than 1. We have -

144 = 2 x 72 = 2 x 2 x 36 = 2 x 2 x 2 x 18 = 2 x 2 x 2 x 2 x 9 =  

2 x 2 x 2 x 2 x 3 x 3

Now, he cannot go on further to express 144 as the product of whole number greater than 1. The last digit 3 is a prime number and is divided by either 1 or itself. So, if the last digit in the product expansion is a prime number, than we cannot break it further into smaller whole numbers.

Therefore, tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -

2 x 2 x 2 x 2 x 3 x 3

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Answer:

  0.339 m/min

Step-by-step explanation:

You want to know the rate of change of the third side in a triangle with sides 10 m and 14 m and an angle between them of 60°. The angle is increasing at 2°/min.

The law of cosines tells you the third side (c) satisfies the relation ...

  c² = a² +b² -2ab·cos(C)

Filling in the given values, we have ...

  c² = 10² +14² -2(10)(14)cos(C) = 296 -280cos(C)

Taking the square root and differentiating with respect to time, we have ...

  c = √(296 -280cos(C))

  c' = 280sin(C)·C'/(2√(296 -280cos(C)))

We want the value of this when C=60°, and C' = 2°/min = π/90 rad/min.

  c' = 280(sin(60°))·(π/90)/(2√(296 -280cos(60°))) = (14π√3/9)/(2√156)

  c' ≈ 0.339 . . . . m/min

The third side is increasing at a rate of about 0.339 meters per minute.

The slope of the given = [tex]\frac{-1}{2}[/tex]

Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates,

The ratio of the increase in elevation between two points to the run in elevation between those same two points is referred to as the slope.

In the graph below ; the two points are A( -2 , 4) and B(2 , 2)

The slope thus is [tex]\frac{y_{2}- y_{1} }{x_{2}-x_{1} }[/tex]

m = [tex]\frac{2- 4}{2 - (-2)}[/tex]

m = [tex]\frac{-2}{4}[/tex]

m = [tex]\frac{-1}{2}[/tex]

Thus the slope of the given graph is [tex]\frac{-1}{2}[/tex]

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When the interest is compounded monthly, we have to do two things:

- Calculate the number of periods: in this case we have 8*12=96 months.

- The monthly interest rate: we have to divide the annual nominal rate by 12 (the number of periods in the year).

Then, we can calculate the future value as:

The future value when compounded monthly is $3,427.30.

General formula:

m: number of subperiods (monthly --> m=12)

Given:

Amount in the account after 29 years is $182696.80

Cuando expresas un valor decimal en fracciones lo haces utilizando al 10 como denominador de la misma, entonces

1 décimo en fracciones es:

3 décimas corresponde entonces a

Al expresar estos valores utilizando cifras, el denominador 10 de la fracción indica que el numerador se encuentra en el primer lugar detrás de la coma decimal, entonces

y

Al organizar estos valores tienes que tener en cuanta la posición decimal en la que se encuentran. Si ambos se encuentran en la misma posición, entonces no debes tomar ninguna consideración y puedes ordenarlos siguiendo la mísma lógica que cuando ordenas números enteros.

Es decir, si al ordenar los enteros obtienes que:

0, 1, 2, 3

Cuando los divides por diez, simplemente corres la coma un lugar a la izquierda pero no cambias el orden de los valores, entonces:

0.0, 0.1, 0.2, 0.3

Dónde puedes ver que 0.1 es más cercano a 0 que 0.3, en otras palabras, 0.1 (una décima) es menor que 0.3 (tres décimas)

The reflection across the y axis the x value changes sign but the y value remain the same.

The answer is C