Pls help asap, 35 POINTS
The smaller triangle is dilated to create the larger triangle. The center of datio. Is plotted but not labeled.
Describe this dilation. Be sure to include all of the information someone would need to perform the dilation.

Answer:

m∠1 = 30°

m∠2 = 120°

m∠3 = 30°

w = 52

x = 104 (approximately)

y = 156 (approximately)

z = 180

Step-by-step explanation:

Step 1: Label your diagram with variables to make solving easier

Step 2: Solve for the missing degrees

Step 3: Solve for the missing side lengths

Answer:

(3, 2)

Step-by-step explanation:

4x + 5y = 22

2x + 3y = 12

4x + 5y = 22

-4x - 6y = -24

-y = -2

y = 2

4x + 5(2) = 22

4x = 12

x = 3

Answer: (3, 2)

The actual width of dining room is 6m, if Tristan drew a scale drawing of an apartment. He used the scale 1 millimeter = 2 meters. In the drawing, the dining room is 3 millimeters wide.

The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world. A measurement on a model and its matching measurement on the real item are referred to as being on the same scale in mathematics. An organized system of numbering or indexing that serves as a measurement reference standard and in which each number is associated with a specific physical quantity.

Given,

Tristan drew a scale drawing of an apartment. He used the scale 1 millimeter = 2 meters. In the drawing, the dining room is 3 millimeters wide.

The actual width of dining room is 6m.

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Answer: No, only Alex's solution is correct.

Step-by-step explanation:

Morgan's solution is incorrect because he subtracted 3 from the parentheses, which is illegal (in math, of course). This means that his answer is incorrect.

Answer: Alex is correct.

Step-by-step explanation:

Alex's steps are correct and are used properly, unlike Morgan, which did steps that aren't allowed and don't make sense. Alex's answer is correct.

The cost of another 2 panes of glass cost = $5.90.

A nurery owner buy 7 pane of glass to fix some damage to his greenhoue.

The 7 pane cost = ​$20. 65

First find the cost of one pane of glass (the "unit cost")

7 panes of glass cost $20.65, so one pane of glass costs

= 20.65 ÷ 7

= $2.95 ← cost of one pane of glass

Then use that answer to find the cost of two panes of glass

If one pane of glass costs $2.95, then 2 panes cost

= 2 × $2.95

= $5.90 ← cost of two panes of glass

Hence the answer is the cost of another 2 panes of glass cost = $5.90.

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Answer:

12x² + 6xy - 30x

Step-by-step explanation:

Given expression,

→ 6x(2x + y - 5)

Simplifying the given expression,

→ 6x(2x + y - 5)

→ (6x × 2x) + (6x × y) - (6x × 5)

→ 12x² + 6xy - 30x

Thus, answer is 12x² + 6xy - 30x.

The distance between the base to the summit of the mountain is 300 meters.

Here Given that,

Person climbs a mountain road from the bas to the summit at a speed of 45 m/min.

And

descends the same road from top to bottom at a speed of 60 m/min

Now,

The time difference between the climbing and descending is 20 min.

So, we can say that

Velocity v₁=45 m/min

Velocity v₂=60 m/min

Time difference ∆t=20 min

We have to find the distance between the base to the summit.

As we know,

The formula for average velocity is

∆v=∆x/∆t

v₂-v₁=∆x/∆t

60-45=∆x/20

∆x=15×20

∆x=300 meter

Hence,

it is 300 meters from the base to the summit of the mountain.

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Answer:

120 ft²

Step-by-step explanation:

The length of each of the congruent sides is (50-16)/2 = 17 ft.

So, using the Pythagorean theorem, the altitude drawn from the vertex angle to the base has a length of 15 ft.

Thus, the area is (1/2)(15)(16) = 120 ft².

The correct graph of the given information is given by (A).

Let the number of pounds is = x

Given that, Shipping company A charges a flat fee of $7 plus $0.50 for each pound.

So the suitable equation of the shipping A is when the total charge is y, is given by,

y = 7 + 0.50x

Again it is given that Shipping company B charges a flat fee of $11 plus $0.25 for each pound.

So the suitable equation of the Shipping B is when the total charge is y, is given by,

y = 11 + 0.25x

Hence the correct graph is (A).

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The values of x and y are 44.8 & 19.2 respectively.

What is the similarity theorem of the triangle?

According to the fundamental theorem of similarity, a line segment can divide two triangle sides into proportionate segments if and only if it is parallel to the third side of the triangle.

We have,

ΔABC ~ ΔAVW

We know the similarity theorem of triangle,

[tex]\frac{AC}{AW} = \frac{CB}{VW}[/tex]  

28/ x = 16/10

x = 1.6 * 28

x = 44.8

[tex]\frac{AB}{AV} = \frac{CB}{VW}[/tex]

y/12 = 16/10

y =  1.6 * 12

y = 19.2

The values of x and y are 44.8 & 19.2 respectively.

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The number of people that would have become sick in total over an indefinite period of time is of:

7500.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, meaning that each term is obtained by the multiplication of the previous term by the common ratio q.

The nth term of a geometric sequence is given by the rule presented as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of an infinite sequence, as long as |q| < 1, is given by:

[tex]S = \frac{a_1}{1 - q}[/tex]

The first term and the common ratio in this problem are given as follows:

Hence the total number of people who got sick is obtained as follows:

S = 3000/0.4 = 7500.

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Using the Pythagorean Theorem, 12² + 5² = 169 = ✓169 = 13

This is simply the way that one can find the missing length of a right angled triangle.

In this case, it should be noted that the theorem is in the form of:

a² + b² = c²

c = hypothenuse

a and b are the other sides

Based on the information given, this will be:

5² + 12²

= 25 + 144

= 169

Now the square root of 169 is ✓169 = 13.

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The length of the side AD is 24 inches

Consider the triangle ABC

The area of the triangle = 288 square inches

The length of the side CD = 9 inches

The length of the side DB = 15 inches

The length of the the base = The length of the side CD + The length of the side DB

Substitute the values in the equation

The length of the the base  = 9 + 15

= 24 inches

The area of the triangle = (1/2) × Base × Height

Substitute the values in the equation

288 = (1/2) × 24 × AD

288 = 12 × AD

AD = 288 / 12

AD = 24 inches

Hence, the length of the side AD is 24 inches

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Answer: 201

Step-by-step explanation: Ok this is very simple for those of you who are stuck on this. First you divide 12 by 268. You would get 22 with a remainder of 4. This in fractions would be 22 1/3. So he would be driving 22 1/3 miles with 1 galloon of gas. If you multiply this by 9 you would get 201 miles which is how much he can drive in 9 gallons of gas.

Hoped this helped!

Answer:

Point Slope Form:  y - 0=2 (x - 0)

Simplified Form:  y=2x

Step-by-step explanation:

The point-slope form of line is given by:

y - y1=m(x - x1)

Where

m is the slope

 is the first x-coordinate

 is the first y-coordinate

Given slope is 2, thus we can say:

m = 2

Also, it says the line goes through the point (0,0), so:

and

Now, substituting, we get the point slope form to be:

y-y1=m(x - x1)

y-0=2(r-0)

y=2(x)

y=2x

The equation of line will be y = 2x

The slope of the equation m = 2 and the point P ( x₁ , y₁ ) = P ( 0 , 0 )

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let the point be represented as P

The value of P = P ( 0 , 0 )

The slope of the equation m = 2

Slope m = 2

Now , the equation of line in the slope intercept form is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = 2 ( x - 0 )

On simplifying the equation , we get

y = 2x

Therefore , the value of A is y = 2x

Hence , the equation of line is y = 2x

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Answer:

560 children tickets

540 adult

Step-by-step explanation:

560x6=3360

540x11=5940  

3360+5940 = 9300

Answer:

72.3

Step-by-step explanation:

72.381% as a recurring decimal using dot notation is 0.72381.

To express 72.381% as a recurring decimal using dot notation, we can follow these steps:

Convert the percentage to a decimal by dividing it by 100:

72.381% = 72.381 / 100 = 0.72381

Write the decimal part without the leading zero:

Decimal part: 0.72381

Place a dot above the repeating part of the decimal, which is the entire decimal in this case:

Decimal part with dot notation: 0.72381

Thus, 72.381% as a recurring decimal using dot notation is 0.72381.

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The number of pieces of tiles that are needed to pave a path 5 m long and 1 m wide is; 20 tiles

We are told that the size of each piece of tile is 50 cm by 50 cm.

Now, we are told that the area that needs to be paved with tiles measures 5 m by 1m. Thus;

Converting the area that needs to be tiles to cm, we have;

5m = 500 cm

1m = 100 cm

Thus;

Area to be tiled = 500 * 100 = 50000 cm²

Area of each tile = 50 cm * 50 cm = 2500 cm²

Thus;

Number of tiles that are required to pave the given path = 50000/2500 =20 tiles

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Answer:If Giulio chooses the first option he will pay about 4,500

If he chooses the second option with the lower rate and compound interest, he will pay a total of about 3,000.

Step-by-step explanation: I dont have an explanation but I think I'm right

The expression <√2 / 10, 7√2 / 10> is the unit vector of the vector <1, 7>.

Vectors are characterized by two features: Magnitude and direction. The magnitude represents the "quantity" contained by the vector and the direction indicates the distribution of the "quantity" along the orthogonal axes of the vector, that is, the x and y axes.

We can obtain the unit vector of any non-zero vector by dividing it by its magnitude. The magnitude can be found by using Pythagorean theorem. Now we proceed to determine the unit vector associated with vector <1, 7>.

First, determine the magnitude of the vector:

||[tex]\vec v[/tex]|| = √(1² + 7²)

||[tex]\vec v[/tex]|| = √50

||[tex]\vec v[/tex]|| = 5√2

Second, calculate the unit vector:

||[tex]\vec u[/tex]|| = (1 / 5√2) · <1, 7>

||[tex]\vec u[/tex]|| = <1 / 5√2, 7 / 5√2>

||[tex]\vec u[/tex]|| = <√2 / 10, 7√2 / 10>

The unit vector is <√2 / 10, 7√2 / 10>.

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The volume increase when the radius changes from 7 to 7.1 ft is 62.45 ft³ i.e. 4.34%. of the previous volume.

We know that the volume of the sphere is 4/3πr³.

So, here the radius of the sphere is 7 ft,

Therefore the volume of the sphere will be = 4/3π(7)³.

so, V1 = 4/3*3.14*(7)³.

V1 = 1436.76  ft³.

When the radius of the sphere will increase tp 7.1 feet then the volume will also increase which will be :

V2 = 4/3*3.14*(7.1)³.

V2 = 1499.21 ft³.

Now the increase in volume is V2- V1 .

which is , 1499.21 ft³ -  1436.76  ft³

i.e. 62.45 ft³ is the increase of the volume of the sphere.

This increased volume is the 4.34% of the previous volume of the sphere.

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The required price of one battery from the pack is   £0.465.

When we given a pack of objects with some cost, then to calculate the price of one object, divide the amount of pack by number of objects in the pack.

we have, price of 6 battery = £2.79

Then, the price of one battery = £2.79/6 = £0.465

Thus, the the price per battery is £0.465.

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The solution of the system of equations y = -x + 6 and y = (1/2)x - 6 be

(8 , -2)

Given, two linear equations

y = -x + 6

y = (1/2)x - 6

Now, to plot the first equation i.e. y = -x + 6

first plot two points

(0 , 6) and (6 , 0)

Now, pass a straight line through these two points and we get the graph of the given equation.

Now, to plot the second equation i.e. y = (1/2)x - 6

first plot two points

(0 , -6) and (12 , 0)

Now, pass a straight line through these two points and we get the graph of the given equation.

Now, to get the solution Plot the point of intersection of these two lines i.e. (8 , -2)

Hence, the solution of the system of equations be (8 , -2).

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The 90th percentile with a mean of 392 hours and a standard deviation of 9 hours is  403.538.

Given:

The lifetimes of light bulbs of a particular type are normally distributed with a mean of 392 hours and a standard deviation of 9 hours.

P(z<=?) = 0.90

z = 1.282

1.282 = x - mean / standard deviation

1.282 = x - 392 / 9

1.282 * 9 = x - 392

11.538 = x - 392

x = 392 + 11.538

x = 403.538.

Therefore the 90th percentile with a mean of 392 hours and a standard deviation of 9 hours is 403.538.

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0.68 is the variable is normally distributed when standard deviation is r29. 44.

What is standard deviation in math?

μ = 146.21   σ = 23.44         x ~ n

P{ x < 160 } = ρ{ x - μ/σ < 160 - 146.21/29.44 }

                   = ρ{ z < 0.47 }

                    = 0.6808

                    ≈ 0.68

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Step-by-step explanation:

we have to mark the angles in the point denoted in the graph and connect it

The illustration of the dilated triangle has been shown.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The vertices of a triangle are A(-4, 6), B(6.4), and C(6. - 2).
The scale factor of 1/2.​,

Coordinates of the vertices of the triangle with scale factor,
A' = (-4 × 1/2 , 6 × 1/ 2)
A' = (-2, 3)

Similarly,
B' = (3, 2)
C' = (3, -1)

Thus, the illustration of the dilated triangle has been shown.

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The estimate should be 24 within a margin of error -4% with 90% confidence level.

In statistics, the margin of error is the degree of error in results from random sampling surveys. A wider margin of error in statistics suggests a reduced likelihood of relying on the results of a survey or poll, i.e. less trust in the results to represent a population.

A margin of error is a statistical parameter that compensates for the gap between actual and projected findings in a random survey sample. In layman's words, the margin of error measures the degree of unpredictability in data and research conclusions.

Given,

Confidence level=90%=0.90

Margin of error= -4%

α=1-0.9

α=0.1

α/2=0.05

P(z>[tex]z_{0.05}[/tex])=0.05

P(z>[tex]z_{0.05}[/tex])=1-0.05

P(z>[tex]z_{0.05}[/tex])=0.95

[tex]z_{0.05}[/tex])=1.96

Approximating P=0.5 and using E=0.2,

n=((1.96)²(0.5)(0.5))/(0.2)²

n=24.01

n=24

Therefore, the estimate should be 24 within a margin of error -4% with 90% confidence level.

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