For the upcoming parade, Lauren needed to make her school's triangular flag into a larger, similar triangular flag. Using the information given, determine which (if any) similarity postulate she used in making her school's new flag.

Answer:

EF = 22 , AB = 1

Step-by-step explanation:

the midsegment of a trapezoid is equal to half the sum of the parallel bases

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) ← substitute values

x + 6 = [tex]\frac{1}{2}[/tex] (2x - 9 + x + 5) ← multiply both sides by 2 to clear the fraction

2x + 12 = 3x - 4 ( subtract 3x from both sides )

- x + 12 = - 4 ( subtract 12 from both sides )

- x = - 16 ( multiply both sides by - 1 )

x = 16

Then

EF = x + 6 = 16 + 6 = 22

Similarly

EF = [tex]\frac{1}{2}[/tex] (AB + DC ) , that is

x + 3 = [tex]\frac{1}{2}[/tex] (4x - 3 + 2x + 5 ) ← multiply both sides by 2 to clear the fraction

2x + 6 = 6x + 2 ( subtract 6x from both sides )

- 4x + 6 = 2 ( subtract 6 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

Then

AB = 4x - 3 = 4(1) - 3 = 4 - 3 = 1

2) [tex]ABCD[/tex] is a rhombus (a parallelogram with perpendicular diagonals is a rhombus)

3) [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex] (diagonals of a rhombus bisect the angles from which they are drawn)

36 litres 180 millilitres

Hope this helps!

Answer:

60 degrees.

Step-by-step explanation:

A reflection does not alter the size of the angles of the triangle so B = 60 degrees.

Answer:

Yes, it is a function

Step-by-step explanation:

A function has only one output for each input. So a function can have the same output for different input, but one input can only have one output. In this case none of the inputs output more than one output, so it is a function.

Answer: x=-8

Step-by-step explanation:

Answer:

[tex]\frac{247}{200}[/tex]

Step-by-step explanation:

1.235

= 1 + 0.235 ( the place value of the 5 is thousandths ) , then

= [tex]\frac{1000}{1000}[/tex] + [tex]\frac{235}{1000}[/tex]

= [tex]\frac{1235}{1000}[/tex] ( divide numerator/denominator by 5 )

= [tex]\frac{247}{200}[/tex] ← in simplest form

The speed of the plane after it encounters the wind is C.285mph

Since the plane takes off from an airport on a bearing of 270° and travels at a speed of 320 mph it's velocity is v = (320cos270°)i + (320sin270°)j

= (320 × 0)i + (320 × -1)j

= 0i - 320j

= - 320j mph

Also, the plane encounters a 35 mph wind blowing directly north. The velocity of the wind is v' = 35j mph

So, the velocity of the plane after it encounters the wind is the resultant velocity, V = v + v'

= -320j mph + 35j mph

= -285j mph

So, the speed of the plane after it encounters the wind is the magnitude of V = |-285j| mph

= 285 mph

So, the speed of the plane after it encounters the wind is C.285mph

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Answer:

Step-by-step explanation

5+5

a) The growth function has the form:

where:

Considering the values we get the function:

b) Number of years between 2012 and 2018 is:

Find the population, using the above equation:

c) Find the value of x when P(x) = 10 million

d) Find the doubling time:

Answer:

[tex]\textsf{a)} \quad f(x)=6.93(1.0218)^x[/tex]

b)  7.89 million (2 d.p.)

c)  2019

d)  32.14 years (2 d.p.) after 2012

Step-by-step explanation:

Exponential Function

   [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part (a)

If the exponential growth rate was 2.18% per year, then each year there would be 102.18% of the previous year's population.

⇒ b = 1.0218

Given:

Substitute the given values into the formula to create an exponential growth function:

  [tex]f(x)=6.93(1.0218)^x[/tex]

Part (b)

To estimate the population of the city in 2018, determine the value of x:[tex]x = 2018 - 2012 = 6[/tex]

Substitute the found value of x into the found exponential function:

[tex]\implies f(6)=6.93(1.0218)^6=7.89 \: \sf million\:(2\:d.p.)[/tex]

Part (c)

To determine when the population of the city will be 10 million, set the function to 10 and solve for x:

[tex]\implies 6.93(1.0218)^x=10[/tex]

[tex]\implies (1.0218)^x=\dfrac{10}{6.93}[/tex]

[tex]\implies \ln (1.0218)^x= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x\ln (1.0218)= \ln \left(\dfrac{10}{6.93}\right)[/tex]

[tex]\implies x= \dfrac{\ln \left(\frac{10}{6.93}\right)}{\ln (1.0218)}[/tex]

[tex]\implies x=17.00496413...[/tex]

To find the year, add the found value of x to 2012:

[tex]\implies \sf 2012 + 17.00496413... = 2019[/tex]

Part (d)

To find the doubling time, set the function to double the initial population and solve for x:

[tex]\implies 6.93(1.0218)^x=6.93 \cdot 2[/tex]

[tex]\implies (1.0218)^x=2[/tex]

[tex]\implies \ln (1.0218)^x= \ln (2)[/tex]

[tex]\implies x \ln (1.0218)= \ln (2)[/tex]

[tex]\implies x = \dfrac{\ln (2)}{\ln (1.0218)}[/tex]

[tex]\implies x=32.14107014...[/tex]

Therefore, the doubling time is 32.14 years (2 d.p.) after 2012.

Answer:

um tbh me dont know

Step-by-step explanation:

The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

In this question we have a trigonometric equation and we are supposed to find an expression not equivalent to the former. Herein we have that the cosine of a double angle is equivalent to the following expressions:

cos 2θ = cos² θ - sin² θ     (1)

cos 2θ = 2 · cos² θ - 1     (2)

cos 2θ = 1 - 2 · sin² θ     (3)

The trigonometric expression cos 60° is equivalent to the expressions cos² 30° - sin² 30°, 2 · cos² 30° - 1 and 1 - 2 · sin² 30°. Then, not equivalent to 2 · sin 30° · cos 30°. (Correct choice: A)

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Answer:

D

Step-by-step explanation:

By observation we just know that one of the angles of two triangles is the same.

There are two sides that are not equal in ability to determine similarity.

Answer:

0.71

Step-by-step explanation:

- Please see the attached picture for full solution!:)

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8m and 12a

Like terms are terms that can be combined to condense a mathematical expression or equation.

Unlike Terms

Unlike terms are defined as terms that have different variables or powers.

If terms meet either of these requirements, they are unlike. On the other hand, for terms to be like they must have both the same variable and power. The coefficients for the terms are not important.

Final Answer

All of the answer choices are to the first power, so the exponents are not important for this question. However, the last 3 answer choices all share the same variable. This means that they are all like terms.

The first answer choice, 8m and 12a, have different variables. This means that they cannot be combined and are unlike terms.

Answer:

65fghxtt

Step-by-step explanation:

The expression with the same values of (1/x – y) in x and y will be 10 / 7.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression x-y equals 0.7.

x - y = 0.7    …1

If x and y have certain values.

Then the expression with the same values of (1/x – y) in x and y will be

Take the reciprocal of equation 1, then we have

1 / (x – y) = 1 / 0.7

1 / (x – y) = 10 / 7.

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Answer:

No solutions

Step-by-step explanation:

First  ADD  4 /(X+4)   to both sides of the equation to get

( x+4)/ (x+ 4)  = 3

1 = 3 ????    There are no solutions

[tex]\dfrac{x}{x+4}=3-\dfrac{4}{x+4}\qquad(x\not=-4)\\\\x=3(x+4)-4\\x=3x+12-4\\2x=-8\\x=-4[/tex]

Which contradicts initial assumption, therefore [tex]x\in\emptyset[/tex].

Answer:

A 3.5

Step-by-step explanation:

To Break it down there 1 3/4 so to put in halve it would be 1/2 1/2 1/2 1/4 so u have 3 feet because 1/2 in is 3 feet then u have a 1/4 inch so that is half of a feet 1 + 1 + 1 + 1/2 is 3 1/2 converted to decimal is 3.5.

Answer:

Thus, a golden retriever should be given 19 teaspoon of medicine.

Step-by-step explanation:

Step 1 of 3

Write the data in mathematical form and simplify.

Let x=the number of teaspoon

If 1  teaspoon medicine is 5  pounds then 85  pounds is how many teaspoon of medicine.

Translate the statement into proportion.

[tex]\begin{aligned}\frac{\text { pounds }}{\text { teaspoon }} &=\frac{\text { pounds }}{\text { teaspoon }} \\\frac{5}{1} &=\frac{85}{x}\end{aligned}[/tex]

Step 2 of 3

Multiply both sides by x and simplify

[tex]$x(5)=\frac{85}{\bcancel{x}}(\bcancel{x})[/tex]

5x=85

Divide by 5,

[tex]x=\frac{85}{5}[/tex]

Simplify, x=19

Step 3 of 3

Check the answer.

Substitute x=19  in original proportion and simplify.

[tex]$$\begin{aligned}\frac{5}{1} &=\frac{85}{x} \\5 &=\frac{85}{19}\end{aligned}$\\ \\ Hence, $5=5$, True[/tex]

Answer:

150

Step-by-step explanation:

The area of the trapezoid is (½)(14+10)(2) = 24.

The area of the rectangle is (14)(9) = 126.

Adding these together, we get 126 + 24 = 150.

There are 6! = 720 ways of arranging the lamps.

If the leftmost lamp is red, there are 3 choices of lamp in the leftmost position, and the remaining 5 can be placed in any order, so there are 3×5! = 360 ways of arranging the lamps and the leftmost is red.

Hence there is a 360/720 = 1/2 probability that the leftmost lamp is red.

Ignoring lamp color for the moment, the probability of arranging 3 lit lamps and 3 unlit lamps is the same, 1/2.

Since Ryan arranges the lamps randomly by color, then turns 3 of them on randomly, the two events are independent. So

P(leftmost red AND leftmost lit) = P(red) × P(lit) = 1/2² = 1/4

Answer:

D is the right answer.

Hope it helps!

Answer:

98/22 or 4.4545

Step-by-step explanation:

Perimeter of a rectangle: 2*width+2*length

4x*2+7x*2 = 98

8x+14x = 98

22x = 98

x = 98/22 or 4.4545

Answer:

x + y ≤ 12

Step-by-step explanation:

Inequality:

   Not more than 12 means less than or equal to 12

x + y ≤ 12

Based on the terms given on the population type and the variables, the correct matches are:

The population is total set of items that a sample is drawn from and in this case it all the restaurants. The sample would be the selected items from the population.

The control group is the group that is not manipulated by the explanatory variable which is the organic cleaner. The response variable is what changes as a result of the explanatory variable so it is bacterial growth.

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Answer:

12

Step-by-step explanation:

we can setup an equation and solve for x: 500-25x = 200, where x stands for the number of weeks she withdraws money.

subtract 500 from both sides to get -25x = -300.

multiply each side by -1 to get 25x = 300

divide each side by 25 to get that x = 12