Dan believes he can use the information given in the diagram and the SAS rule to prove the two triangles are congruent. Is he correct? Explain.

Answer:

Infinite solutions

Step-by-step explanation:

2x-3y=10

-4x+6y=-20

Turn them into point-slope form.

y = 2/3x - 10/3

y = 2/3x - 10/3

They are the same equation, so they will have infinite solutions.

Answer:

infinite solutions i did the quiz and got a 100 pls give brainliest

Step-by-step explanation:

Answer:

1) Is 180

2) Is 5

Step-by-step explanation:

Answer:

g(n)=80×3^(n-1)

Step-by-step explanation:

First term (a)=80

The ant population tripled every week.

So, the population of ant after 1st week will be (80 × 3) = 240

After 2 weeks, the population triples again.

We have, (240 × 3) = 720

Common ratio (r)=720/240

=3

r=3

The ants population is increasing in a geometric progression

A geometric progression is given by

g(n)=a × r^(n-1)

Substitute values of a and r to get the explicit formula

g(n)=a × r^(n-1)

g(n)=80×3^(n-1)

Answer:

Angle 1= 180 - 110 = 70 (straight angle)

Angle 2 = 180 - 115 =65 (straight angle)

Angle 3= angle 2 =65 (corresponding alternating angles)

Angle 4 =180 - angle3 = 180 - 65 = 115 (straight angle)

Angle 5 = 180 - angle 1 - angle 3= 180 - 70 - 65 = 45 (sum of triangle angles is equal to 180)

Angle 6 = angle 5= 45 ( interior alternating angles)

Angle 7 = angle 6= 45 (vertical opposite angles)

Angle 1= 180 - 110 = 70

Angle 2 = 180 - 115 =65

Angle 3= angle 2 =65

Angle 4 =180 - angle3 = 180 - 65 = 115 (straight angle)

Angle 5 = 180 - angle 1 - angle 3= 180 - 70 - 65 = 45

Angle 6 = angle 5= 45

Angle 7 = angle 6= 45

Not to sound like the other person but yeah,these are the answers.

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Explanation:

Let's say this is a 1 by 1 square. The area is 1*1 = 1 square unit. Whatever the area of the triangle is, we divide it over 1 and it will yield the same value as the area of the triangle. In other words, the area of the triangle will be the answer.

Along the top we have 3 ticks to indicate the top segment has been cut into 3+1 = 4 equal parts. The horizontal distance from the the vertical side of the triangle to the peak of the triangle is 3/4 units. This is because we travel 3 ticks out of 4 total. So this is the height when we consider the vertical segment of the triangle to be the base.

The base is 1 unit as it spans the original square's side length

base = 1

height = 3/4

area of triangle = (1/2)*(base*height)

area of triangle = (1/2)*(1*3/4)

area of triangle = 3/8

ratio of triangle area to square area = (triangle area)/(square area)

ratio of triangle area to square area = (3/8)/1

Answer:

3/8

Step-by-step explanation:

let side of square=x

Area of a square =x^2

height of a triangle= 3x/4  ( 4/4=1/4) since height is only 3x/4 from the square)

( base =x same side as a square)

Area of a triangle=1/2 bh=1/2(x*3x/4)= 3x^2/8

the ratio of shaded triangle to the area= (3x^2/8)/x^2=3x^2/8x^2=3/8

Answer:

14.3

Step-by-step explanation:

first find length of VW

10/sin 119 = VW/ sin 26

VW = 5

angle V = 180 - 119 - 26 = 35

then area = 1/2 ab sin C

1/2 (10)(5) sin 35 = 14.33941.....

Answer:

Third option is the right choice.

Step-by-step explanation:

[tex]y=a(b)^x[/tex]   where "b", is the common ratio.

The common ratio for third table is constant for all the terms.

Best Regards!

Answer:

14 paychecks

Step-by-step explanation:

$495 + $65 = $560

$560 / 40 = 14

Therefore , he must save for 14 paychecks

Hope this helps and pls mark as brainliest :)

Answer:

14

Step-by-step explanation:

$495 + $65 = $560

$560 / 40 = 14

He must save for 14 paychecks.

Hope this help

Mark me BRAINLIEST

Tysm

Answer:

166.07

Step-by-step explanation:

since the domain is [0,89] means the maximum amount is when x=89

vertex is where it reached the maximum amount:(44.512,166.07)

Answer:

$122.1

Step-by-step explanation:

We are given the following data in the question

$124, ​$256 ​, $118, ​$441, ​$122, ​$335, ​$340, ​$191

Step 1

Find the mean

Mean = Sum of Terms / Number of Terms

Number of Terms = 8

Mean = ($124 + $256 ​+ $118 + ​$441 + $122 + ​$335 + ​$340 + ​$191 )/ 8

Mean = $1927/8

= $240.875

Approximately to 1 decimal place

$240.9

Step 2

Standard deviation formula

S = √( x - μ)²/ N - 1),

N = Number of terms

μ = Mean

S = √[($124 - $240.9)² + ($256 - $240.9)² + ($118 - $240.9)² + (​$441 - $240.9)² + ($122 - $240.9)² + ​($335 - $240.9)² + ​($340 - $240.9)²+ ​($191 -$240.9)²/ 8 - 1]

S = $122.0895

Approximately to 1 decimal place

S = $122.1

Therefore, the standard deviation for the given data is $122.1

a) The population is all of the flights belonging to the particular airline. It's not all flights in general because the airline does not have control over a rival company's flight schedule.

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b) The sample is the 5 airlines the company selected. Ideally the sample should represent the population as much as possible. The larger the sample, the more representative the sample is.

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c) No, the sample is likely not representative because one day of flight does not represent the entire lifetime of all flights done so far for that company. This particular day could have been a very good day with good weather, which may explain why the 5 flights were all on time.

------------------

d) It would be better for the company to select the days at random and sample all of the flights for those particular days chosen. This is a cluster sample. Each cluster is a day. Also, I think more flights should be sampled. Five flights does not seem like enough.

Answer:

37

Step-by-step explanation:

Answer:

Hey there!

60=0.5(55+5x+15)

120=5x+70

50=5x

x=10

Hope this helps :)

Answer:

Answer is 8

Step-by-step explanation:

Answer:

1020

Step-by-step explanation:

well, the first three significant figures stops at the 102, so round the 1023.4567 to a whole number which just becomes 1023

then, round the answer so you only have the 102, so you would round down since 4 or less, which 3 is less than 4, you round down, and you would get 1020

that last 0 is not a significant figure because it does not have a decimal point or any other number following after it--any 0s at the end of a number are not significant if there is no decimal point or other number after them.

Answer:

63.4°

Step-by-step explanation:

The following data were obtained from the question:

Opposite = 6 cm

Adjacent = 3 cm

Angle x =?

The value of angle x can be obtained as follow:

Tan x = Opposite/Adjacent

Tan x = 6/3

Tan x = 2

Take the inverse of Tan.

x = Tan¯¹ 2

x = 63.4°

Therefore, the value of angle x is 63.4°

Answer:

63.4°

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

First you need to factor the equation. You can do this by multiplying the numbers by eachother so they have a denominatior of 12.

You would come out to have this...

((x+2)*4)/12 + ((2x-4)*3)/4=3

At this point you can combine the numerators over the common denominator.

((x+2)*4+(2x-4)*3)/12=3

You can now rewrite the equation into factored form.

5x-2/6=3

Multiply both sides of the equation by 6.

5x-2=18

move the terms not containing x to the right

5x=20

and divide by 5

x=4

You use Pythagoras' Theorem and the theorem of 30-60-90 triangle

करना चाहिए। वे तुम्हें नष्ट कर देंगे।

आप कोई मौका नहीं खड़े हैं। तुम

उसके हाथ पर मर जाओगे। पछताना

When you reflect a diagonal over a line of symmetry, the diagonal will land perfectly on the other diagonal (and vice versa). This suggests that one diagonal is a mirror copy of the other.

Another way to put it: The vertex points of the rectangle will swap when we reflect over a line of symmetry. A diagonal is simply the opposite vertex points joined together. So this is why the diagonals swap places (because the vertices line up perfectly when you apply the reflection).

A shape with a line of symmetry will land on itself, when reflected across the line of symmetry. The true statements are:

From the question, we understand that; the rectangle is reflected across the line of symmetry

When this is done, the half of the rectangle will land directly on the other half.

This means that, the diagonal of the rectangle will land perfectly on the other diagonal

The statement above suggests that, the diagonal of a rectangle is also a line of symmetry of the rectangle.

Read more about lines of symmetry and diagonals at:

https://brainly.com/question/1045307

Answer:

4 adults

Step-by-step explanation:

There will be 3 people handling eight children each and one person handling 6 children in a total of 30 children

Answer:

-5

Step-by-step explanation:

2^2*(3-8)÷5-1

4*(-5)÷4

-20÷4

=-5

Answer:

-5

Step-by-step explanation:

Firstly 2^2=4, 4(3-8)=4*(-5)= -20, -20/5 -1= -4-1= -5

Answer:

60n seconds

Step-by-step explanation:

In 1 min, there are 60 seconds

So,

1 min = 60 secs

For n minutes, it becomes:

=> 60n seconds

Answer:

Step-by-step explanation:

x² + 2x + 1 = 0

Using the quadratic formula

[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

a = 1 , b = 2 , c = 1

We have

[tex]x = \frac{ - 2± \sqrt{ {2}^{2} - 4(1)(1)} }{2(1)} \\ \\ x = \frac{ - 2 ± \sqrt{4 - 4} }{2} \\ \\ x = \frac{ - 2 ± \sqrt{0} }{2} \\ \\ x = - \frac{2}{2} \\ \\ x = - 1[/tex]

Hope this helps you

Answer:

Step-by-step explanation:

common denominator

[tex](\sqrt(2)+1)(\sqrt(2)-1) = (\sqrt{2})^2-1^{2}=2-1 = 1[/tex]

Add with common denominator

[tex]\dfrac{1}{\sqrt2+1}+\dfrac{1}{\sqrt2-1}.[/tex]

[tex]= \frac{{\sqrt2-1}}{1} + \frac{\sqrt2+1}{1}[/tex]

[tex]=2* (\sqrt2)[/tex]

Answer:

Step-by-step explanation:

Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.

If the weight of an alloy = x kgs

Then weight of copper = [tex]\frac{9}{7+9}\times (x)[/tex]

                                      = [tex]\frac{9}{16}\times (x)[/tex]

And the weight of zinc = [tex]\frac{7}{7+9}\times (x)[/tex]

                                      = [tex]\frac{7}{16}\times (x)[/tex]

If the weight of zinc = 31.5 kg

31.5 = [tex]\frac{7}{16}\times (x)[/tex]

x = [tex]\frac{16\times 31.5}{7}[/tex]

x = 72 kgs

Therefore, weight of copper = [tex]\frac{9}{16}\times (72)[/tex]

                                               = 40.5 kgs

2). i). 2 : 3 = [tex]\frac{2}{3}[/tex]

        4 : 5 = [tex]\frac{4}{5}[/tex]

Now we will equalize the denominators of each fraction to compare the ratios.

[tex]\frac{2}{3}\times \frac{5}{5}[/tex] = [tex]\frac{10}{15}[/tex]

[tex]\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}[/tex]

Since, [tex]\frac{12}{15}>\frac{10}{15}[/tex]

Therefore, 4 : 5 > 2 : 3

ii). 11 : 19 = [tex]\frac{11}{19}[/tex]

    19 : 21 = [tex]\frac{19}{21}[/tex]

By equalizing denominators of the given fractions,

[tex]\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}[/tex]

And [tex]\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}[/tex]

Since, [tex]\frac{361}{399}>\frac{231}{399}[/tex]

Therefore, 19 : 21 > 11 : 19

iii). [tex]\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}[/tex]

             [tex]=\frac{3}{2}[/tex]

     [tex]\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}[/tex]

              = [tex]\frac{4}{3}[/tex]

Now we equalize the denominators of the fractions,

[tex]\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}[/tex]

And [tex]\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}[/tex]

Since [tex]\frac{9}{6}>\frac{8}{6}[/tex]

Therefore, [tex]\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}[/tex] will be the answer.

IV). [tex]1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}[/tex]

                  [tex]=\frac{6}{5}\times \frac{3}{4}[/tex]

                  [tex]=\frac{18}{20}[/tex]

                  [tex]=\frac{9}{10}[/tex]

Similarly, [tex]\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}[/tex]

                       [tex]=\frac{4}{15}[/tex]                  

By equalizing the denominators,

[tex]\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}[/tex]

Similarly, [tex]\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}[/tex]

Since [tex]\frac{270}{300}>\frac{80}{300}[/tex]

Therefore, [tex]1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}[/tex]

V). If a : b = 6 : 5

     [tex]\frac{a}{b}=\frac{6}{5}[/tex]

        [tex]=\frac{6}{5}\times \frac{2}{2}[/tex]

        [tex]=\frac{12}{10}[/tex]

  And b : c = 10 : 9

  [tex]\frac{b}{c}=\frac{10}{9}[/tex]

 Since a : b = 12 : 10

 And b : c = 10 : 9

 Since b = 10 is common in both the ratios,

 Therefore, combined form of the ratios will be,

 a : b : c = 12 : 10 : 9

Answer:

N = 14348907

Step-by-step explanation:

81^5 = 3486784401

3486784401/243 = 14348907

Double Check

3486784401 / 14348907=243

So N = 14348907.

Answer:

D. [tex] \frac{{7}^{11} }{ {4}^{11} } [/tex]

Step-by-step explanation:

[tex]( \frac{7}{4}) {}^{11} = \frac{7 {}^{11} }{4 {}^{11} }[/tex]

Since we are multiplying an exponential number to a fraction the answer is going to be

[tex] \frac{7 {}^{11} }{4 {}^{11} } [/tex]

Hope this helps ❤❤❤ ;)

Answer:

[tex]D. \frac{7^{11} }{4^{11} } \\[/tex]

Step-by-step explanation:

Hello, I can help you with this

Let's remmber some propiertis of the fraction numbers and the potenciation

Let

[tex]a^{m} * a^{n}=a^{m+n}\\(a^{m})^{n}=a^{m*n}\\(\frac{a}{b})^{m}=\frac{a^{m} }{b^{m}}[/tex]

Step 1

All you have to do is identify and use the formula

let

[tex](\frac{7}{4})^{11}\\ a=7\\b=4\\m=11\\so\\(\frac{7}{4})^{11}=\frac{7^{11} }{4^{11} } \\[/tex]

so, the answer is D.

I hope it helps, have a nice day

Answer:

The correct option is;

f(x) = 3·sin x/8·π + 2

Step-by-step explanation:

The given parameters for the sinusoidal function are;

Amplitude of oscillation = 3

Frequency of oscillation = 1/8·π

Midline of oscillation= 2

The general form of sinusoidal equation is y = A·sin(B(x - C)) + D

Where;

A = The amplitude

B = The frequency

C = The horizontal shift

D = The midline or vertical shift

Substituting the given values into the general form of sinusoidal equation, we have;

f(x) = y =  3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2

Which gives;

f(x) = 3·sin(x/8·π) + 2.

C.

Because the marble is not replaced and that affects the next event where another marble is chosen.

Dependent events:

It is the event where one event outcome is dependent on the other event outcome.

Independent events:

It is the event where one event outcome is not dependent on the other event outcome.

You choose a marble from a bag, don't replace it, and then choose another marble.

This is a dependent event.

Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.

Option C is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Dependent events:

It is the event where one event outcome is dependent on the other event outcome.

Independent events:

It is the event where one event outcome is not dependent on the other event outcome.

Now,

A. Rolling an odd number, and then rolling an even number.

This is an independent event.

B. You choose a number from 1 to 50 from a hat, replace it, and then draw a second number.

This is an independent event.

C. You choose a marble from a bag, don't replace it, and then choose another marble.

This is a dependent event.

Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.

D. You roll a 4 and then spin yellow on a spinner.

This is an independent event.

Thus,

You choose a marble from a bag, don't replace it, and then choose another marble.

This is a dependent event.

Since we are not replacing the first marble outcome that is chosen, the next marble outcome is dependent on the first outcome.

Option C is the correct answer.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ6

Answer:

The statement, one fifth of the square of a number is written as

[tex] \frac{1}{5} {x}^{2} [/tex]

Hope this helps you