Classifying Triangles Card Sort ​

Ariana is 20 years old, and Nora is 18 years old.

The word integers meaning a whole number but not fraction or decimal.

The positive whole number, zero and negative whole numbers are classified as integers.

Consecutive means following a specific sequence. Consecutive even integers mean the integers that follow a sequence and difference between each number is 2.

Ariana is older than Nora and their ages are consecutive even integers.

let Ariana is (x+2) years old and Nora is X years old.

The statement says the sum of Ariana's age and 2 times Nora's age is 56

the equation that expresses it can be written as

x+2+2x = 56

3x = 56 -2

3x = 54

x = 18

Nora is 18 years old.

Ariana is x+2 = 18+2 =20 years old.

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A fixed point in the plane around which all points are enlarged or contracted is the centre of a dilation. The centre, which may be found within, outside, or on a figure, is the only invariant (not changing) point under a dilation (k 1).

A Dilation of an image in mathematics refers to a change that results in an image with the same shape but a different size, either larger or smaller. A dilation can only be built with two bits of information.

The scale factor determines how much the dilated image is enlarged or reduced in size in relation to the original. A positive scale factor is required. When the scale factor exceeds 1, the dilation becomes an expansion. If it falls within the range of 0 and 1, the dilation is a contraction.

The point from which the image is dilated is known as the centre of dilatation (or point of dilation).

Following are some shape characteristics that aren't altered by the dilation transformations:

Horizontal Dilation

The dilation transformation of a function y=f(x) is dilated horizontally by a scale factor C is

Y = f(Cx)

This kind of transformation is called a horizontal dilation.

Vertical Dilation

The dilation transformation of a function y=f(x) is dilated vertically by a scale factor C isY = C * f(x)

This kind of transformation is called a Vertical dilation.

The ratio of matching side lengths is the scale factor of a dilatation. The origin will always be the centre of dilatation in this course. You can enlarge a polygon by connecting its vertices while multiplying each vertex's coordinates by the scale factor k.

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Andrea's distance from the base of the cliff is given as follows:

233 feet.

The three trigonometric ratios are defined as follows:

For this problem, we have a right triangle in which:

Hence the distance is obtained as follows:

tan(42º) = 209.75/d

d = 209.75/tan(42º)

d = 233 feet.

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The final purchase price would be $81.20.

Sale is an act of exchanging goods or services for money. It is a business transaction in which a seller transfers the ownership of goods or services to a buyer in exchange for money. Sale can be done in a variety of ways, such as through retail stores, online stores, auctions, or even by bartering. Sale is one of the most important aspects of any business and is the primary way businesses make money.

This includes the 30% discount, which reduces the original price of the art set from $125 to $87.50, plus the 8% sales tax,

which adds an additional $6.70 to the total.

Therefore, the final purchase price is $87.50 + $6.70 = $81.20.

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Complete questions as follows-
A $125 art set is on sale for 30% off. What is the final purchase price if there is an 8% sales tax?

Answer: 132

Step-by-step explanation:

$871 divided by 67= 13
13= how much money each person spends

so we 1716 divided by 13= 132

Answer:

132

Step-by-step explanation:

I divided $871 by 67 customers and got $13 each person . Then, I divided 1716 by 13 to find out how many people was needed to get the total number of customers needed.

Answer:

Step-by-step explanation:

Since 3 balloons can carry 24 grams of weight, you would multiply 3/24 by 3 to get 72 grams of weight with 9 balloons.

Then, you would divide 3 and 24 by 2/3 to get 16 grams of weight with 2 balloons.

Lastly, add 9/72 grams of weight with 2/16 grams of weight to get a total of "11 balloons can carry 88 grams".

If Reasoning Tommy earned ​$57.00 in interest after 5 years on a principal of ​$300.  The bank you would  rather​ use is: Jane's, because  her bank offers a better interest rate.

Interest rate can be defined as the rate or percentage that enables a borrower to know the interest they will pay on the amount loaned to them. On the other hand interest rate means the rate a person earn on their saved amount.

Based on the given scenario i would make use of Jane bank based on the fact that Jane bank offers a better interest than Tommy bank.

Therefore Jane bank is better.

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The complete question is:

Tommy earned $30.40 in interest after 4 years on a principal of $200. His simple interest rate is 3.8%. Jane earned $81.90 in interest after 3 years on a principal of $700. Her simple interest rate is 3.9%. Which bank would you rather use? Explain your reasoning.

answer choices

Jane's because her bank offer a better interest rate.

Jane's because her bank accepted a smaller principal.

Tommy's because his bank paid more interest.

Tommy's because his investment took less time.

The value of x in the given equation is 17.5

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this article, let's learn more about math equations.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

In the given equation:-

2x+20-55=0

x=35/2

x=17.5

Hence the value of x is 17.5

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Answer:

D. 1500H = 55(40)

Step-by-step explanation:

This equation represents the point where the total pay from the salaried job offer and the total pay from the hourly wage job offer are equal.

It can be read as : total pay of salaried job = total pay of hourly job.

On the left side of equation, 1500 is the weekly salary, and on the right side 55 is the hourly rate and 40 is the number of hours per week.

So on solving the provided question we can say that - the statical data will be2 ; $27  = 4; $5400 = 6; $8100 = 8; $10800

Statistics covers the gathering, organization, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Proudful Personal waste from concerts A data element is a feature (or attribute) data such as height, origin country, income, etc. that is measured or tallied. Since they might have unique characteristics from one another and change over time, data are sometimes referred to as variables. Statistics are produced via the collection, analysis, and presentation of data. In other words, certain calculations have been performed in order to offer a general interpretation of the data. Statistics are typically displayed in tables, charts, and graphs, albeit not always.

statistical data will be as follows -

2 ; $27

4; $5400

6; $8100

8; $10800

10; $135 00

12; $162 00

14; $189

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On solving the provided question we can say that value equation is y = mx => -7 = m * 4 => m = -7/4 and x² + y² = 13 => x² + (-7)² = 13 => x

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

So the equation of the tangent line is y = m(x - 0) + 0, where m = -(x+4)/(y-7)

Now we can substitute the coordinates of the center of the circle into the equation of the tangent line to get y = -(x+4)/(y-7) * x

Squaring both sides and simplifying we get:

3m² + 56m + 36 = 0

b) To find the coordinates of the points A and B, we can use the equation of the tangent line and the equation of the circle.

We know that the equation of the tangent line is y = -(x+4)/(y-7) * x and the equation of the circle is (x+4)² + (y-7)² = 13.

We can substitute y = -(x+4)/(y-7) * x into the equation of the circle and solve for x.

This equation simplifies to 3x² + 56x + 36 = 0, which factors to (x+12)(x+3) = 0

y = -(-12+4)/(y-7) * -12 = 8/(y-7) * 12 = 96/(y-7)

y = 96 + 7 = 103 and y = -96 + 7 = -89

The coordinates of the points A and B are (-12,103) and (-3,-89) respectively.

We know that the equation of the tangent line is y = mx and the equation of the circle is x² + y² = 13.

We can substitute the point (4, -7) for x and y in the equation of the tangent line and the equation of the circle and solve for m and x,y respectively.

y = mx => -7 = m * 4 => m = -7/4

x² + y² = 13 => x² + (-7)² = 13 => x

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So on solving the provided question, we can say that the triangle are similar, angles have a cosine that is equal to sin(L) are angle K and angle R

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

the triangle are similar and angle K and angle R are congruent and is a right angled triangle

so,  angles have a cosine that is equal to sin(L) are angle K and angle R

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The equation which has been given is a linear equation, therefore in order to solve the equation, simply the basic mathematical operation is to be performed. The acquired value of x is not the same as the value. So, when 12=13.x+5, the value of x=21 is not true.

Given information:

The equation given in the question is: 12 = 3x + 5

The value of x=21

Perform the basic mathematical operations and find the value of a variable.

  13x + 5 =12

⇒13x = 12 -5

⇒ 13x = 7

⇒ x = 7/13

⇒ x = 0.538

The acquired value of x is not the alike as the given value.

Hence, when 12=13.x+5 the value of x=21 is not true.

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Step-by-step explanation:

I never thought about this before, but yes, they can.

linear functions :

explicit :

y = ax + b

recursive :

xn+1 = xn + a

because

a(x + 1) + b = ax + b + a

ax + a + b = ax + a + b

exponential functions :

explicit :

y = a^x

recursive :

xn+1 = xn × a

because

a^(x + 1) = a^x × a = a^(x + 1)

remember,

a^x = a×a×a×a×a×...×a×a×a

x times a multiplied by itself.

This square pyramid has a volume of 48 cm³.

The term "square pyramid" refers to a three-dimensional geometric form with a square base and four faces or sides that are triangular and meet at a single point (called the vertex). Its five faces give it the name "pentahedron."

The five faces of a square pyramid, four of which are triangles, are square in shape. An upright pyramid's base is also square-shaped.

Although the square pyramid and square prism both have a square base, the four lateral faces of the former are triangular and the latter are rectangular.

V=13s2h, where s is the length of the square base's sides, is a formula that may be used to calculate the volume of a pyramid whose base is square.

           v = 1/3 * b² *h

           v = 1/3 * 6² *4

           v = 1/3 *36 *4

           V = 48cm³

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Answer: 300 tires < x < 450 tires

Step-by-step explanation:

The first store sells between 100-200 tires. This means that the number it sells is greater than 100, but less than 200. This can be represented in this inequality:

100 < x < 200

The second store sells between 200-250 tires. This means that the number it sells is greater than 200, but less than 250. This can be represented in this inequality:

200 < x < 250

The total number of tires sold can be found by adding these two inequalities:

100 < x < 200

200 < x < 250

The following inequality represents the total amount of tires sold:

300 < x < 450

Answer:

b = 5

Step-by-step explanation:

  10(b+2) + 3 = 73

10b + 20 + 3 = 73

              10b = 50

               ∴ b = 5

Using the Pythagoras theorem, the height of the tree from the reflection pond is obtained as 27.3 m.

We know that the height of the tree can be obtained from the formula for the Pythagoras's theorem and looking at the theorem, we are going to have that;

C^2 = A^2 + B^2

Where A is the  height, in meters, of the tree.

Then we have that;

30.24^ = A^2 + 12.96^2

A^2 = 30.24^2 - 12.96^2

A =27.3 m

This is the length of the tree that have been measured from the ground to the given height as we have bene shown in the question above.

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Yes , 0 can have exponent of 2 , it is represented as 0² , and the value of 0 to exponent of 2 is 0 .

What is Exponent ?

The Exponent form form of numbers represents ,  how many times a number multiplied by itself .

For Example : if the number 3 is multiplied by 5 times by itself , then in the exponent form it can be written as : 3⁵ .

we have to check whether can 0 have an exponent of 2 ;

So, the representation of 0 to exponent of 2 is ⇒ 0² ,

that means 0 is multiplied by itself 2 times , and we know that if a number is multiplied by 0 , then the value of that number is 0 .

Therefore , 0 can have an exponent of 2 and it's value is 0 .

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The solution is Option B.

The total amount of the jet ski worth after 7/4 years is given by the equation A = $ 4,784

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the total amount of the jet ski after 7/4 years be A

Now , the equation will be

Let the number of years be x

The The value of that jet ski depreciates by function f ( x ) = 8,500 ( 0.72 )ˣ

So , the equation is f ( x ) = 8,500 ( 0.72 )ˣ

Now , when x = 7/4 years

Substitute the value of x in the equation , we get

f ( 7/4 ) = 8,500 ( 0.72 ) ^ ( 7/4 )

f ( 7/4 ) = 8,500 ( 0.72 ) ^ ( 1.75 )

f ( 7/4 ) = 8,500 x 0.5627712059

f ( 7/4 ) = $ 4,783.555

Now , rounding to the nearest dollar , we get

f ( 7/4 ) = $ 4,784

Hence , the amount after 7/4 years is $ 4,784

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Answer:

1) The standard form of a circle's equation is (x - h)² + (y - k)² = r². (h,k) is the center and r is the radius.

2) The vertex is the midpoint of the directrix and the focus. It involves the parabola changing directions, and at any point the directrix and the focus will be equidistant from the parabola. The focus is a single point inside the curve of the parabola, and the directrix is a line outside the parabola.

3) The standard form of an equation of an ellipse is:

(x − h)2a 2 +( y − k) 2 b 2 = 1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1. (h,k) is the center, a is the distance from the center to the horizontal vertices and b is the distance from the center to the vertical vertices.

4) The foci are (−c,0) and (c,0). The ellipse is the set of all points (x,y) which are the sum of the distances from (x,y) to the foci is constant.  (a,0) is a vertex of the ellipse. Finally, the endpoints of the minor axis is a co-vertex of the ellipse.

5) A hyperbola has two standard equations. These equations of a hyperbola are based on its transverse axis and conjugate axis. The standard equation of the hyperbola is [(x² / a²) – (y² / b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.

6) The foci are located on the line that where the transverse axis is. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints. The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect.

Let me know if I didn't answer all of your questions, I hope this helps! :)

Step-by-step explanation:

a) Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

b) Tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

c) The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.

The equation of a circle of center  and radius r is given by:

(x-x₀) +(y-y₀) = r²

For Tunnel A, the equation is given by:

x² + y² + 28x + 52 = 0

Completing the squares:

(x + 14)² + y² = -52 + 14²

(x + 14)² + y² = 144.

Tunnel A is a circle with center (-14, 0) and radius 12, meaning that both the width and the height are of 12.

A quadratic equation is modeled by:

y = ax^2 + bx + c

For Tunnel B, the equation is given as follows:

x² - 36x + 16y + 68 = 0.

16y = -x² + 36x - 68.

Simplifying by 16:

y = -0.0625x² + 2.25x - 4.25.

Hence the coefficients are a = -0.0625, b = 2.25, c = -4.25, and the maximum height is:

y₀=(2.25)²-49-0.0625)(-1.25)/4(-0.0625) = 16

The width is the difference between the roots, which, using a calculator, are: 2 and 34, hence the width is of 32 feet.

This implies that the tunnel B is a parabola that has a width of 32 feet and a height of 16 feet.

For item c, we have that:

The maximum height of Tunnel A is of 12 feet and of Tunnel B is of 16 feet, hence, since the height of the truck is of 13.5 feet, it can pass through Tunnel B without damage, as it's height is greater than 13.5 feet.  

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Correct question:

An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 28x + 52 = 0, and tunnel B is modeled by x2 – 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels.

Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points)

Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points)

Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. (7 points)

Answer: Angle C for AAS, Side AC for SAS

Step-by-step explanation:

Your instructions were confusing since in the text it asks for SAS and in the image it asks for AAS so I just gave both.

The Probability of P(at least 3 tails) is 0.3125.

The correct option is (D).

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Total outcome= 16

Now, P( less than 3 tails)= 11 /16

So, P(at least 3 tails) = P( x ≥ 3)

= 1 - P(x < 3)

= 1- 11/ 16

=  5/16

= 0.3125

Hence, the Probability is 0.3125

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Answer:

Step-by-step explanation:

The proposed rule would prohibit motor vehicle dealers from ... Used vehicles sold by new-vehicle dealerships cost $24,542 on average. Sorry I don't know the rest.

Answer:

The answer is:

8x-29y

Step-by-step explanation:

4(2x-8y)+3y

8x-32y+3y

8x-29y

On solving the provided question, we can say that equation 6+6=4+1 has 1 solution that is x= -1.

In mathematics, an equation is a formula that uses the equals sign to connect two expressions and express their equivalence. We can solve equations to find the value of unknown variable given in the equation and the number of values that variable takes is called the solution of equation.

We have to find the no. of solution of 6+6=4+4.

To solve this, we bring all the variables to one side of equality and al the numbers on the other side. So we get,

6-4=4-6

2= -2

Dividing both sides by 2,

x= -1.

Hence, the equation 6+6=4+4 has only 1 solution. Correct option is D.

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Answer: 1 is 15 and 2 is 10.

Step-by-step explanation:

15/3=5

5+2 equals 7

10/2=5

5+6=11

m=15

x=10

The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.

The formula for calculating the sum of interior angles is (n-2)×180° where is the number of sides. All the interior angles in a regular polygon are equal. The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides.

2) The sum of the interior angles of a nonagon

Here, n=9

(9-2)×180°

= 1,260°

3) Here, ∠3+∠4=180°

∠3=101°

101°+∠4=180°

∠4=79°

So, option A is the correct answer.

4) Given that, a regular polygon with 12 sides.

Now, sum of the interior angles = (12-2)×180°

= 1800°

Measure of each angle = 1800/12

= 150°

5) Four of the angles of a pentagon measure 85°, 110°, 135°, and 95°.

Let the measure of fifth angle be x°

85°+110°+135°+95°+x°=540°

425°+x°=540°

x°=115°

So, option A is the correct answer.

The measure of the missing angle in a given pentagon is 115°. Therefore, option A is the correct answer.

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Answer:

Step-by-step explanation:

its closed to 1/2 as 12/24