Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.

The equation of the straight line perpendicular to the line 3x - 6y = - 8 is y-2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y=0.

The general equation of a straight line is -

y=mx+c

where -

m is slope of line which tells the unit rate of change of y with respect to x.

c is the y - intercept i.e., the point where the graph cuts the y axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

[tex]y=\frac{-A}{B} x-\frac{C}{B}[/tex]

Given that: -

[tex]3x-6y=8\\\\6y=3x-8\\\\y=\frac{1}{2}x-\frac{4}{3}[/tex]

then,

[tex]m=\frac{1}{2}\\\\c=\frac{4}{3}[/tex]

For a parallel line,

[tex]m=\frac{1}{2}\\and,(4,2)[/tex]

[tex]y-y_{1}=m(x-x_{1})\\\\y-2=\frac{1}{2}(x-4)\\\\2y-4=x-4\\\\y=\frac{x}{2}[/tex]

The equation of parallel line is y=0.5x

For a perpendicular line

[tex]m=2\\\\y-2=2(x-4)\\\\y-2=2x-8\\y-2x=-6\\y-2x+6=0\\[/tex]

Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y -2x+6=0 and of line parallel to the line 3x - 6y = - 8 is y = 0.5x.

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Answer:

18

Step-by-step explanation:

To find a percent of a number, change the percent to a decimal by dividing the percent by 100 and multiply by the number.

25% of 72 =

= 25/100 × 72

= 0.25 × 72

= 18

Answer: it would be 18

Step-by-step explanation:

Answer: About 31%

Step-by-step explanation:

1. Divide 114 to 361

The UCL and LCL are 1.00434 and 0.99566. The process is not in control and the z-value is 2.17.

We already know that the mean, x = 1.0, and the standard deviation of the process, σ = 0.01.

We already know that according to the central limit theorem, the standard deviation of sample means is equal to the standard deviation of the population divided by the square root of the sample size.

So, it is equal to = 0.01 / √25 ⇒ 0.002

For a sample size of 25. The z value, or the z-score, is about 2.17 for a confidence level of 97 percent.

So, UCL = 1.0 + 2.17 * 0.002 = 1.00434

LCL = 1.0 - 2.17 * 0.002 = 0.99566

Lastly, the process is not in control because the sample means 1.005 and 0.995 are outside the control range.

The complete question that you must be looking for is given below.

An automatic filling machine is used to fill 1-liter bottles of cola. The machine output is approximately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.

a. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.

b. Given these sample means: 1.005, 1.001, .998, 1.002, .995, and .999, is the process in control.

c. What is the z-value we should use if the control limits will include roughly 97% of the sample means?

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The two-way frequency table to display the data will be:

                         Fishing         Not Fishing Total

Swimming        15                     30           45

Not Swimming 5                 45           50

Total                  20                 75         95

20% of 120 people is 24 people, but since 20% of the people went fishing, we know that 24 people went fishing.

75% of 24 people who went fishing is 18 people.

50% of 96 people who did not go fishing is 48 people.

Total number of people who went swimming is 45 (15+30)

Total number of people who did not go swimming is 50 (5+45)

Total number of people in the survey is 95 (24+71)

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In a survey of 120 people who visited the a lake, 20% went fishing.of those who went fishing,75% also went swimming. Of those who did not go fishing ,50% went swimming. Construct a two-way frequency table to display the data.

The frequency Asked in the problem are listed below in order:

To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

Given, a partial relative frequency distribution is given. class relative frequency a 0.22 b 0.18 c 0.40 d

Since all relative frequencies add up to be 1.

So,

0.22 + 0.18 + 0.40 + x = 1

x = 0.20

For b)

total sample size * relative frequency = frequency of a class

200*0.2 = 40

For c)

Frequency distribution is calculated as the frequency of a class = total sample size * relative freq.

A = 44

B = 36

C = 80

D = 40

TOTAL = 200

For d)

Percent frequency is calculated as Percent frequency of a class = 100 * relative freq.

A = 22

B = 18

C = 40

D = 20

TOTAL = 100

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Complete question:

The expression that represents the ratio between the total number of seagulls standing on the pier and the 51 gulls in the air is given as follows:

g/51.

The ratio between two amounts a and b is found applying a proportion, which is the division between them.

The amounts for this problem are given as follows:

Hence the ratio is given as follows:

g/51.

The problem asks for the expression for the ratio the total number of seagulls standing on the pier and the 51 gulls in the air.

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The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

AB = 6

BC = 6

CG = 6

Then the length of diagonal AC is given as,

AC² = AB² + BC²

AC² = 6² + 6²

AC = 6√2

Then the length of diagonal AG is given as,

AG² = AC² + CG²

AG² = (6√2)² + 6²

AG = 6√3

The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.

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After simplification, the value of x is 6.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3x + 30 + x = 10 + 2x + 5x + 2

Now, We can solve as;

⇒ 3x + 30 + x = 10 + 2x + 5x + 2

Combine like terms;

⇒ 4x + 30 = 12 + 7x

Subtract 4x both side,

⇒ 4x + 30 - 4x = 12 + 7x - 4x

⇒ 30 = 12 + 3x

Subtract 12 both side,

⇒ 30 - 12 = 3x

⇒ 18 = 3x

⇒ 3x = 18

Divide by 3;

⇒ x = 6

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Answer:

[tex]c = \frac{d}{a} - b[/tex]

Step-by-step explanation:

Isolate the variable, c. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, divide a from both sides of the equation:

[tex]a(c + b) = d\\\frac{a(c + b)}{a} = \frac{d}{a} \\c + b = \frac{d}{a}[/tex]

Next, isolate the variable, c, by subtracting b from both sides of the equation:

[tex]c + b = \frac{d}{a} \\c + b (-b) = \frac{d}{a} (-b)\\c = \frac{d}{a} - b[/tex]

[tex]c = \frac{d}{a} - b[/tex] is your answer.

~

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Answer:

c = (d/a) - b

Step-by-step explanation:

Now we have to,

→ Find the required value of c.

The equation is,

→ a(c + b) = d

This can be distributed as,

→ a(c + b) = d

→ a(b) + a(c) = d

→ ab + ac = d

Then the value of c will be,

→ a(c + b) = d

→ a × (c + b) = d

→ c + b = d/a

→ c = -b + (d/a)

→ [ c = (d/a) - b ]

Hence, value of c is (d/a) - b.

The probability that the sample mean would be less than 21635 dollars if a sample of 193 persons is randomly selected is 65.53%.

This can be calculated using the normal distribution. The mean of the normal distribution is the population means, which in this case is 21,604 dollars per annum. The standard deviation is 727 dollars per annum. Using this information, we can calculate the z-score of 21635 dollars per annum by subtracting the population mean from it and dividing it by the standard deviation. This gives us a z-score of 0.42.

21635-21329/727=0.42

Using a z-table, we can calculate the probability of the sample means being less than 21635 dollars to be 0.6553.

This can also be written as 65.53%. This means that there is a 65.53% probability that the sample mean of 193 persons randomly selected would be less than 21635 dollars per annum.

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Valerie's table is the table for which the y-value is given by the multiplication of the x-value by -6.

A proportional relationship is modeled as follows:

y = kx.

In which k is the constant of proportionality.

The constant for the relationship in this problem is given as follows:

k = -18/3

k = -6.

Hence the relationship is given as follows:

y = -6x.

The problem is incomplete, hence the answer was given in general terms.

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The dimension of soccer field is 4252.176 in long and 2204.832 in wide.

The power to which the fundamental quantities are elevated in order to express a physical quantity is known as its dimension.

The dimension of soccer field is 108 meters long and 56 meters wide.

The dimension of soccer field in ft is 354.348 ft long and 183.736 ft in width.

As it is given that 1 m =3.28 ft

Therefore the length of the soccer field in ft is

108*3.281 = 354.348 ft

And width of the field is

56*3.281 = 183.736 ft

We know that 1 ft =12 in

Therefore, the length of the soccer field in inches is

354.348 × 12 = 4252.176 in

And width of the field is

183.736 *12 = 2204.832 in

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The inflation rate is 16.71 %

As we know the inflation rate is given by the percentage error.

We know that the formula for the percentage error:

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100

Let us assume that A represents the inflation rate of percentage error.

Here, the cost of the Jolly Peanut butter is = $ 3.59

So , the original cost = $ 3.59

The increased cost of Jolly Peanut butter is = $ 4.19

So , the new rate = $ 4.19

Now , the inflation rate is given by the formula of percentage error,

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100

A = [ ( 4.19 - 3.59 ) / 3.59 ] x 100

A =  ( 0.6 / 3.59 ) x 100

A = 0.16713 x 100

A = 16.71 %

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The amount of type A used is A=31 lbs.

Assign variables for unknowns.

Let A be the number of pounds of Type A coffee.

Let B be the number of pounds of Type B coffee.

If one pound of Type A costs $4.10 then A pound costs 4.10A

If one pound of Type B costs $5.45 then B pounds cost 5.45B

At this point, you have two equations with A and B as variables.  You can use the substitution or elimination method to solve for A.

Equations:

B = 2A----(1)

4.10A + 5.45B = 465.00

4.10A + 5.45(2A) = 465.0

4.10A + 10.9A = 465.00

15A = 465.00

A = 31 lbs (amt. of type A coffee used)

To know the amount of type B coffee used just plug the A value in equation(1) we get:

B=2(31)

B=62.

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a. The party that won the highest percentage of votes and seats in 1982 is democrat.

b. A change between the percentage of seats won by republicans in 1982 and 2012 is 4%

c. The difference between votes percentage and seats percentage for democrat is 4% and 26% respectively. The difference between votes percentage and seats percentage for republican is 3% and 26% respectively.

The pie chart is given below:

a. We have to identify the party that won the highest percentage of votes and seats in 1982.

We can see that in diagram that gray part of circle shows the vote percentage of democrat and white part of circle shows the vote percentage of republican.

Republican gain votes in 1982 = 52%

Democrat gain votes in 1982 = 49%

So the democrats get the maximum votes in 1982.

b. We have to describe a change between the percentage of seats won by republicans in 1982 and 2012.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So the change between 1982 and 2012 = (52 - 48)% = 4%

c. We have to draw a conclusion about the difference in percentage of votes won and seats.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So, the difference between vote percentage is 4%.

In 2012 republican get seats percentage = 25%

In 1982 republican get seats percentage = 51%

So, the difference between seats percentage is 26%.

In 1982 democrat get votes percentage = 49%

In 2012 democrat get votes percentage = 52%

So, the difference between vote percentage is 3%.

In 2012 democrat get seats percentage = 75%

In 1982 democrat get seats percentage = 49%

So, the difference between seats percentage is 26%.

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Here we would like to find out the value of given trigonometric ratio . A right angled triangle is given to us with perpendicular= 8 and hypotenuse= 11 . Firstly let's calculate the base using Pythagoras theorem as ,

[tex]\longrightarrow h^2=p^2+b^2\\[/tex]

[tex]\longrightarrow 11^2 = 8^2+b^2\\ [/tex]

[tex]\longrightarrow 121 = 64 + b^2\\ [/tex]

[tex]\longrightarrow b^2=121-64=57\\ [/tex]

[tex]\longrightarrow b =\sqrt{57}=7.54 \\ [/tex]

Now we know that,

[tex]\longrightarrow \tan\theta =\dfrac{p}{b}\\ [/tex]

so substitute the respective values,

[tex]\longrightarrow \tan\theta =\dfrac{8}{7.54}\\ [/tex]

[tex]\longrightarrow\underline{\underline{ \tan\theta = 1.06 \approx \boxed{1}}} [/tex]

and we are done!

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 100000e^{0.042\cdot 6} \implies A = 100000e^{0.252}\implies A \approx 128659.60[/tex]

Click It or Ticket is a nationwide campaign to enforce seat belt laws and increase seat belt use, supported by major organizations.

Click It or Ticket is a nationwide mobilization campaign to enforce seat belt laws and increase seat belt use. It is a joint effort of state and local law enforcement, highway safety offices, and the National Highway Traffic Safety Administration and is supported by national and state-level organizations, including:

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Compared to Ann and Bob, Colin has more. Thus, Ann is not have most money.

In the given question, we have to find Ann have the most money or not.

Three people Ann, Bob and Colin have a total of $1.80 between them, each having a different amount.

Ann has $0.6 amount and Bob has $0.5 amount.

Ann + Bob + Colin = 1.80

0.6 + 0.5 + Colin = 1.80

1.1 + Colin = 1.80

Subtract 1.1 on both side, we get

Colin = 0.70

So Colin has $0.70.

So, Colin has more amount than Ann and Bob. So Ann does not have most money.

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The number of bicycles there is given as follows:

63.

The number of bicycles and tricycles is obtained using a system of equations, for which the variables are given as follows:

The number of bicycles is 1 less than 4 times the number of tricycles, hence:

x = 4y - 1.

There is a total of 174 wheels, hence:

2x + 3y = 174.

The number of tricycles is obtained as follows:

2(4y - 1) + 3y = 174

11y = 176

y = 176/11

y = 16.

Hence the number of bicycles is of:

x = 4(16) - 1

x = 63.

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At a distance of 72.5 meters above the water's surface, the anchor was let go.

It takes 29 seconds to reach the water's surface.

The anchor dropped for 45 seconds at a speed of 2.5 m/s.

112.5 metres are equal to (2.5 m/s) x (45 s).

It must have dropped if it ended up only 40 meters under the water.

(112.5 m - 40 m) equals 72.5 m

Before it ever got to the water, it was in storage on the large cruise ship.

It took longer because it was descending at a speed of 2.5 m/s.

29 seconds are equal to 72.5 m / (2.5 m/s)

it began to drop, to get down to the water's surface.

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The value of x that best represent this expression √x = 11 is 121.

The square root of a number is the part of the number that, when multiplied by itself, produces the original number. Squares and square roots are examples of special exponents. The portion of a number that yields the original number when multiplied by itself is known as the square root of the number.

Examples of special exponents include squares and square roots. Think about the number 9. Nine is the result of multiplying 3 by itself. This can be expressed as either or 3*3. We refer to this as a square since it has a 2 exponent. When the exponent is now 1/2, the integer's square root is being discussed.

An integer or number (not a fraction) multiplied by itself produces a "Square Number," which is the result. For instance, 3 x 3 = or 3 squared is the result of 3 times 3.

Given:

√x+11 = 0

√x = -11

can be written as

x = -11²

x = 121

The value of x that best represent the expression √x+11 = 0 is 121.

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Correct question:

For which values of x does the expression √x + 11 = 0 make sense? ​

There are 153 parking spaces on each level of the parking garage.

Equation

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that a parking garage has 612 parking spaces on 4 levels, and each level has about the same number of parking spaces, to determine the number of parking spaces on each level the following calculation must be performed: -

so the equation is ,

612/4 = X

153 = X

X = 153.

Thus, there are 153 parking spaces on each level of the parking garage.

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If the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2), then the values of x = -12 and y = 3.

Vector translation is a mathematical concept that describes how an object is moved in space. It involves the use of a vector, which is a quantity that has both magnitude and direction. A vector can represent a displacement, a velocity, an acceleration, or any other physical quantity that has both magnitude and direction.

When an object is translated by a vector, it moves a certain distance in a specific direction. This is usually done by adding the vector to the current position of the object. The magnitude of the vector determines the distance of the translation, while the direction of the vector determines the direction of the translation.

Additionally, the vector can be used to rotate the object. This is done by multiplying the vector by the object’s rotation matrix. The result is the object's new orientation in space, which can be used to orient the object in a different direction.

Vector translation is used in a variety of applications, including computer graphics, robotics, and navigation systems. It i also used in mathematics and physics to represent physical phenomena, such as forces, velocities, or accelerations.

Let the point P(x,5) be translated by the vector t(6,-2).

The image of point P is (x',y') = (x+6,5-2) = (-6,y)

Therefore, x+6 = -6

=> x = -6-6 = -12

Similarly, 5-2 = y

=> y = 5-2 = 3

So the value of x is -12 and y is 3.

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Answer:

Step-by-step explanation:

Answer:

7/18.

Step-by-step explanation:

We know that the result is the same because multiplication is Commutative.

The order of the operation does not matter.

For two similar triangular sculptures having leg l1 = 4.5 ft, l2 = 6 ft, and base b1 = 7.2 ft, the measurement of b2 is 9.6 ft.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

Two triangles are similar.

Let the two similar triangles sculptures be ΔABC and ΔDEF.

The length of the leg ΔABC, AB = 4.5 feet

The length of the base of ΔABC, BC = 7.2 feet

The length of the leg ΔDEF, DE = 6 feet

The length of the base of ΔDEF, EF = x feet

To find the measure of base of ΔDEF, use the formula for indirect measurement.

According to indirect measurement the formula will be -

AB/DE = BC/EF

Substitute the values in the equation -

4.5/6 = 7.2/x

4.5 × x = 7.2 × 6

4.5x = 43.2

x = 43.2/4.5

x = 9.6

Therefore, the value for x is obtained as 9.6 feet.

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Answer:

s³ - 15s² + 50s - 125

Step-by-step explanation:

yes

On Monday, for completing the daily target Philip needs to travel 9/8 more miles.

As per the question,

As Philip wants to run a total of 3 miles each day.

As on Monday morning, he ran only 1(7/8) miles.

First, we will convert the given mixed fraction in form of improper fractions.

So, converting 1(7/8),

It will become equal to (8*1+7)/8 = 15/8

From above,

We can say, out of the 3 miles he only travel 15/8 miles on Monday.

So, for calculating the required distance we need to subtract the given value 15/8 from 3

Thus we will get it as:

3-15/8 = (24-15)/8 = 9/8 miles.

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