Determine whether the pair of polygons is similar using properties of similar polygons. Explain your reasoning.​

Answer:

[tex]y=\frac{-1}{3}x+5[/tex]

Answers being -1/3 and 5

Step-by-step explanation:

In slope-intercept form, you seem to be missing your slope and intercept.  Luckily, the graph has everything you need.

Recall slope is rise over run or y over x.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

The slope of this line can be determined by counting the x and y movements of the line between two intersections where it evenly collides.  For instance, between (0,5) and (3,4), the line moves right three and down one.  

This would give you a slope of -1/3.

Another way to find the slope is to choose any two points and use the slope formula above.  Using those same two points:

[tex]m=\frac{4-5}{3-0}[/tex]

[tex]m=\frac{-1}{3}[/tex]

Now you have the first part of your answer.  The slope is -1/3.

The second part is the y coordinate of the y-intercept.  In this case, the graph includes the intercept, which we can clearly determine is (0,5).  Therefore, your second answer would be 5.

The full answer being [tex]y=\frac{-1}{3}x+5[/tex].

Answer:

y = 3(e)^(-0.69x)

Explanation:

Taking into account the following property

We can replace (0.5)^x by

So, now we can rewrite the function as

Therefore, the answer is

y = 3(e)^(-0.69x)

Answer:

y=3e^(ln0.5)x

Step-by-step explanation:

Answer:

Sale Price = $490

Explanation:

After 30% off, the sale price is 100% - 30% = 70% the original price.

70% of the original price is

which is our answer!

Hence, the sale price of the wool suit is $490.

Answer:

k = 4

Explanation:

1) The triangles in example 1 are similar triangles but differs in size

We are to calculate the scale factor k

Using the formula

Scale factor k = size of the larger triangle/size of the smaller trinagle

Since they are similar triangles;

k = DF/AB

Given

DF = 48

AB = 12

Substitute the given values into the expression for k above to have;

k = 48/12

k = 4

Hence the scale factor from triangle ABC to DEF is 4

Answer: 1 3/4

1/4= 15 minutes

1/2 = 30 minutes

add 1/2 to 1/4 and you get 3/4 because 1/2 is equal to 2/4 if you add the 1/4 to it

heres the actual math:

1/2 = 2/4

2/4 + 1/4 = 3/4

slap that one in front of it so its 1 3/4 and therea your answer

    A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed. We find it easier to graph linear equations when we consider intercepts.

    Where a line on a graph crosses the x-axis is known as the x-intercept. At that time, the y coordinate's value is zero. For instance, the x-intercept would be where the equation y = x + 5 crosses the x-axis at the location (-5, 0).

      We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

        This is an illustration of a y-intercept. Think about the line y = x + 3. The point where this graph crosses the y-axis is (0,3). Therefore, the y-intercept of the line y = x+ 3 is (0,3).

       If you can locate the x-intercept of a linear function, finding the zero should be simple. The x-coordinate of the x-intercept is zero.

Summary

         Consider the numbers as being on the x-axis to help you remember this. The positive values are located to the right of the origin, and the negative values are located to the left of the origin.

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Proportionately, the total number of registered doctors, based on the ratio of female doctors, is 150,637.

Proportion refers to the quantity relationship of a variable contained in another.

Using proportion, two values are equated to each other.

For instance, we equate the percentage of registered female doctors to the number of registered female doctors.

Proportions, like ratios, are stated as fractions, decimals, or percentages because they depict the portion of a variable in another.

The ratio of registered female doctors = 31.4%

The number of registered female doctors = 47,300

31.4% = 47,300

100% = 47,300/31.4% x 100

The total number of registered doctors = 150,637  (47,300/31.4%)

Thus, the total number of registered doctors is 150,637, given that 47,300 female registered doctors proportionately represent 31.4% of the population.

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The formula for radius is

radius = diameter/2

If diameter = 5, then

radius = 5/2

radius = 2.5

Answer:

have you heard of the genger bread man

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

(40-32 / 32) × 100% = 25%

The numbers are:

1. The value of x = 5

2. The value of x = 15 or 8 and y = 8 or 15

What is Square?

The word Square means a number multiplied by itself.

The above answers were gotten in the following way:

1. Let the unknown negative number be x

The square of the negative number: x² is

Sixteen more than six times of negative x: 6x+16

It is written as: (x)²=6x+16

Equating to zero, we have:

x²-6x-16=0

Factorizing, we have:

x²-8x+2x-16=0

x(x-8)+2(x-8)=0

x+2=0 and x-8=0

x=-2 and 8

Since the number is negative, x = -2

Therefore, the value of the negative number is -2

2. Given:

Sum of two numbers = 23

Product of two numbers = 120

Calculation:

Let the two numbers be x and y

x+y=23...............equation 1

xy=120..................equation 2

From equation 1, x=23-y

Substitute the value of x in equation 2, we have:

(23-y)y=120

Opening the brackets, we have:

23y-y²=120

Rearranging the equation, we have:

-y²+23y=120

Equating to zero, we have:

-y²+23y-120=0

Multiplying both sides by (-1), we have:

y²-23y+120 = 0

Factorizing, we have:

y²-15y-8y+120=0

y(y-15)-8(y-15)=0

(y-8)(y-15)=0

y=8 or 15

Substituting the values of y in any of the equation. Choosing equation 1, we have:

From Equation 1: x+y=23

When y=8,

x+8=23

x=23-8

x=15

When y=15

x+15=23

x=23-15

x=8

Therefore the values of the two numbers are 15 and 8

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The length of the three sides of the triangle are 11 feet, 12 feet and 15 feet.

A triangle is a polygon with three sides.

The perimeter of a triangle is 38 feet.

The perimeter of the triangle is the sum of the whole three sides.

One side of the triangle is one foot longer than the second side.

let

the second side = x

longer side = x + 1

The third side is four feet longer than the second side.

Hence,

Third side = 4 + x

Therefore,

38 = x + x + 1 + x + 4

38 = 3x + 5

3x = 38 - 5

3x = 33

x = 33 / 3

x = 11

Therefore, the sides of the triangle are 11 ft, 12 feet and 15 ft.

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3) Store A sells 36 pack box of chocolates for $54. Store B sells 6-pack boxes of the same size chocolates for $12. Which store offers a better deal? (Organize your information in the tables given below) Store A Store B # of Chocolates Price $ Price $ # of Chocolates.​

________________________________

# of Chocolates​ Price Ratio (Price per chocloate)

Store A 36 pack box 54 54/ 36 = 3/2 = 1.5

Sotre B 6-pack boxes 12 12/ 6 = 2

_____________________________

Store A 1.5

______________________________

Answer

Store A offers a better deal

The types of transformations that occur as a result of the motion on the ball are;

A) Rotation

B) Translation

Transformation is a method required to resize or change the orientation of a given shape or figure. The types of transformation are translation, reflection, rotation, and dilation.

Translation is a method of transformation that involves moving an object or shape from one point to another without changing any dimension.

Reflection is a method of transformation that involves flipping a given figure about a given reference point or line. In order words, a mirror image of the original object.

Rotation is a method of transformation that involves  turning a given figure at an angle about a reference point.

Dilation is a method of transformation whereby the length of the sides of the figure is either increased or decreased.

A) When James spins a basketball on his finger, it is clear that this transformation is rotation because it involves turning the ball at an  angle about a given point.

B) When James passes the basketball, the transformation would be translation because it involves moving the ball from one point to another without changing the dimension of the ball.

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slope=1.43

y-intercept=1

x-intercept=-1.43

Explanation

Step 1

get the slope intercept form of the equation

where

m is the slope and b is the y-intercept

to do this, isolate y

so,

Step 2

to find the x-intercept replace the y value with zero in the equation

so, the x intercept is

I hope this helps you

A motion sensor, sometimes known as a motion detector, is a piece of technology that use a sensor to find nearby individuals or objects. Any security system needs motion sensors as a crucial part. A sensor will alert your security system and, with newer systems, your cell phone when it senses motion.

How does a motion sensor function?

Active ultrasonic motion detectors emit ultrasonic sound waves, which bounce off surrounding objects and return to the source of emission. The sensor initiates and completes the required action, whether it be turning on a light or sounding an alert, when a moving object interferes with the waves.

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You have the following data set:

x 1 0 -3

y 5 4 1

Where y is a function of x. In order to translate the previous function 2 unitd downward, you take into account that you subtract 2 units to the given values for y. Then, you have:

y (5-2) (4-2) (1-2)

which becomes:

y 3 2 -1

Finally, the given table becomes:

x 1 0 -3

y 2 2 -1

Given that

The population of a certain city is 1.50 million initially and it gets increased by 6.5% exponentially. And we have to find the number of years in which the population becomes 2.31 million.

Explanation -

The formula for the exponential growth is given as

Here we have f(x) = 2.31 million, a = 1.50 million , r = 6.5% and x = ?

So let the time be t.

Then, on substituting the values we have

We must solve the following quadratic equation by completing squares:

1) First, we rewrite the equation in the following way:

2) We sum to both sides of the equation (5/2)², get:

3) Expressing the first term as a square, we have:

4) Passing the +6 at the left as -6 at the right:

5) By taking the square root on both sides, we get two solutions:

1) Re-writing the equation:

2) Summing (5/2)² on both sides:

3) Expressing the first term as a square:

4) Simplifying:

5) Taking the square root:

Answer: 105

Step-by-step explanation:

Angles in a triangle add up to 180 degrees always, you already have two angles. Subtract those two angles from 180 then you have 75. A straight line always equals 180, and since we just found one angle on that line which is 75, just subtract 75 from 180 to get the answer.

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

We solve and reduce like terms, just like this:

Brief history of triangle numbers

What is Triangle Number?

An equilateral triangle-shaped group of objects is counted using a triangular number or triangle number. Square and cube numbers are two further examples of figurate numbers, which also include triangle numbers.

Students are typically introduced to triangular numbers through the account of Carl Gauss, a well-known mathematician who used the concept of the triangle number formula to aid him with summing consecutive integers as a student. This tale and its applications in many situations are discussed in the article Clever Carl.

Triangular numbers were created by the Pythagoreans, who discovered connections between geometric forms and numbers, giving rise to triangular, square, pentagonal, and other numbers.

After four or five terms, students may recognize that the answer can be discovered by adding consecutive terms, according to our research. As an illustration, you may use the formulas 1+2+3+4+5 or 10 (the preceding term) + 5 to determine the fifth term. However, when students attempt to transition from this to the general formula for triangle numbers of

n(n+1)/2

Drawing triangle numbers is an exercise that could be helpful in establishing a connection between these two concepts.

The nth term and substitution into algebraic expressions can then be discussed using this formula. Sequences, notably quadratic sequences, can also be discussed.

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The amount that needs to be deposited to have a saving of $50,000 in 30 years at the given interest rate is $8,302.10.

The compound interest formula is expressed as;

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

Where P is principal, A is amount accrued, r is interest rate is compound period and t is time elapsed.

Given the data in the question;

First, convert rate from percent to decimal.

Rate r = 6%

Rate r = 6/100

Rate r = 0.06 per year

To determine the principal, plug the given values into the formula above and solve or P

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

P = $50,000 / (1 + 0.06/12)^( 12 × 30 )

P = $50,000 / (1 + 0.05)³⁶⁰

P = $50,000 / (1.05)³⁶⁰

P = $8,302.10

Therefore, the principal investment is $8,302.10.

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If She was entitled to a personal exemption of $2900 and had deductions totaling $5090. her gross income is $36,100, adjusted gross income is  $33,400 , and taxable income is $25,410.

Gross Income:

Gross Income= Wages + Interest received

Gross Income= 34,600 + $1500

Gross Income= $36,100

Adjusted Gross Income:

Adjusted Gross Income  = Income - Tax Def Contribution

Adjusted Gross Income = $36,100- $2,700

Adjusted Gross Income = $33,400

Taxable Income :

Taxable Income = AGI - Deductions - Personal exemption

Taxable Income= $33,400- $5,090 - $2,900

Taxable Income= $25,410

Therefore her  gross income is $36,100.

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The equivalent of one square meter in square feet is  10.89 [tex]ft^{2}[/tex]  and of one cubic meter in cubic feet is  35.937 [tex]ft^{2}[/tex].

One meter is about 3.3 ft. So, we can write

1 meter = 3.3 ft

Part : A

We know, 1 meter = 3.3 ft

On squaring both sides of this equation, we will get

[tex](1 meter )^{2}[/tex]= [tex](3.3 ft )^{2}[/tex]

1 [tex]meter^{2}[/tex] = 10.89 [tex]ft^{2}[/tex]                                   equation 1

The equivalent of one square meter in square feet is  10.89 [tex]ft^{2}[/tex] .

Part : B

We know, 1 meter = 3.3 ft

On taking cube on both sides of this equation, we will get

[tex](1 meter )^{3}[/tex]= [tex](3.3 ft )^{3}[/tex]

1 [tex]meter^{3}[/tex] = 35.937 [tex]ft^{3}[/tex]                                   equation 1

The equivalent of one cubic meter in cubic feet is  35.937 [tex]ft^{2}[/tex]

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The angle m∠FCD is 56°

Here the line CF is an angle bisector of ∠GCD.

By this we have,

∠GCF = ∠FCD

It is given that

∠GCF = ∠GCB - 12°

Let ∠GCB be x.

∠GCF = x - 12° = ∠FCD

BCD is a straight line which form 180°.

∠BCG + ∠GCF + ∠FCD = 180°

x + x - 12° + x - 12° = 180°

3x = 204°

x = 68°

∠FCD = x - 12°

          = 68° - 12°

          = 56°

Therefore m ∠FCD = 56°.

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Solution

Step 1

Write the equation

Step 2

Apply the addition equality theorem

Step 3

Use the division equality theorem:

Final answer

x = 5

Answer:

2346 dl sheep

Step-by-step explanation:

all well STrxrcgvw'#'zuucrb if ivAr4w3ws4

ANSWER

The arithmetic sequences are: I and iii

EXPLANATION

The formula for the nth term of an arithmetic sequence is:

where a1 is the first term of the sequence and d is the common difference.

For the first sequence I. 2, 4, 6, 8, 10... we can find the common difference by subtracting the first term from the second:

So the nth term of this sequence is:

Each term of this sequence follows this rule. Therefore this is an arithmetic sequence.

For the second sequence II. 2, 4, 8, 16, 32... there's no common difference because between the first and second term there's a difference of 2, between the second and third there's a difference of 4, and this increases as we move through the sequence. Therefore this is not an arithmetic sequence.

For the third one, III. a, a+2, a+4, a+6, a+8... we can see that there is a common difference:

The rule for the nth term is:

Let's find the first 5 terms:

This shows that each term follows the same rule. Therefore this is an arithmetic sequence.