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The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?

Replace the values of h and k in the equation.

Step-by-step explanation:

2 things to remember :

1. the sum of all angles in a triangle is always 180°.

2. the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

triangle 1 :

angle B = 180 - 62.2 - 43.8 = 74°.

a/sin(62.2) = 15.8/sin(74)

a = 15.8 × sin(62.2)/sin(74) = 14.53961961... in

c/sin(43.8) = 15.8/sin(74)

c = 15.8 × sin(43.8)/sin(74) = 11.37657122... in

triangle 2 :

14.9/sin(49) = 11.6/sin(A)

sin(A) = 11.6 × sin(49)/14.9 = 0.587559136...

angle A = 35.98398776...° ≈ 36°

angle C = 180 - 49 - 35.98398776... = 95.01601224...° ≈

≈ 95°

c/sin(95) = 14.9/sin(49)

c = 14.9 × sin(95)/sin(49) = 19.66708505...

newly weds triangle :

let's call the 2 sides a and b (25 m and 30 m).

the angle between them is 60°.

here we should use the extended Pythagoras for general triangles :

c² = a² + b² - 2×a×b×cos(C)

with c being the side opposite to the angle C.

so, we have in our case

c² = 25² + 30² - 2×25×30×cos(60) = 625 + 900 - 750 =

= 775

c = sqrt(775) = sqrt(25×31) = 5×sqrt(31) = 27.83882181... m

the area of the triangle we get via Heron's formula :

s = (a+b+c)/2 = (25+30+c)/2 = 41.41941091...

area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(s(s-25)(s-30)(s-c)) =

= sqrt(105,468.75) = 324.7595264... m²

with Php 2000 per m² this would cost

324.7595264... × 2000 = Php 649,519.0528...

Answer:

except c all

Step-by-step explanation:

because

5(2+4)=10+20

30=30

9(3+2)=27+18

45=45

2(5+6)=10+12

22=22

Answer:

except c all

Step-by-step explanation:

because

5(2+4)=10+20

30=30

9(3+2)=27+18

45=45

2(5+6)=10+12

22=22

Answer:  See the table below

========================================================

Explanation:

The first task is to sort the values from largest to smallest.

Doing so gets us this list

57, 51, 48, 46, 45, 44, 43, 41, 40, 39, 39, 38, 37, 36, 36, 35, 35, 34, 33, 32, 31, 29, 29, 28, 24, 21, 19, 18, 13, 8

Next, we look for values that are between 56 and 60. That would be the single value of 57. This means we have 1 tally mark for the first row and the frequency is 1.

After that, we look for values between 51 and 55. That would be the single value of 51. Like the previous row, we'll have a single tally and a frequency of 1.

The 46-50 group will have the values 48 and 46 in it, so we have two tally marks and a frequency of 2 for this row.

This process is continued until all the values are accounted for. Effectively you are sorting the values into the proper bins.

You should end up with the table below. The fourth column is optional. It helps show where all of the values are sorted (to help confirm we have the correct tallies and frequencies).

Using a system of equations, it is found that they expect to sell 175 adult tickets and 350 student tickets.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

They expect that twice as many students as adults will attend, hence:

s = 2a.

Their goal is to earn $1,500 from ticket sales, hence:

10a + 5s = 1500.

10a + 5(2a) = 1500.

20a = 1500.

a = 1500/20.

a = 175.

s = 2a = 2 x 175 = 350.

They expect to sell 175 adult tickets and 350 student tickets.

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Answer:

Step-by-step explanation:

[tex]f(x) = \dfrac{2}{3}x-4\\[/tex]

When x = 0  ;   f(x) = 0-4 = -4

When x = 3  ;

       [tex]\sf f(3) =\dfrac{2}{3}*3-4\\\\ = 2-4\\\\ f(3) = -2[/tex]

When x = 6,

           [tex]\sf f(6) = \dfrac{2}{3}*6-4\\\\ f(6) =2*2-4 = 4-4\\\\ f(6)= 0[/tex]

When x = -6;

         [tex]\sf f(-6) =\dfrac{2}{3}*(-6)-4\\\\[/tex]

                   = 2*(-2)-4

                   = -4 - 4

          f(-6) = -8

Answer:

[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]

Step-by-step explanation:

the slope of the line AC :

[tex]\frac{6-1}{1-2} = \frac{5}{-1} =-5[/tex]

Let y : mx + p be the equation of the line D passing through B and perpendicular to AC.

Where m is the slope and p is the y value of the y intercept point.

The line D is perpendicular to AC means the product of their slopes is −1

Therefore

(−5) × m = −1

Then

[tex]m=\frac{-1}{-5} =\frac{1}{5}[/tex]

We obtain, the equation of D is :

[tex]y : \frac{1}{5} x + p[/tex]

At this point ,we still need the value of p to get the full equation of D.

B(3, 3)∈ D

[tex]3=\frac{1}{5} \left( 3\right) +p[/tex]

[tex]\Longleftrightarrow p=3-\frac{3}{5} =\frac{12}{5} =2.4[/tex]

thus , the equation of D is :

[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]

Yes it's possible through matrix

Let's find out the area formula for our vertices

That's

[tex]\\ \rm\Rrightarrow \left|\begin{array}{ccc}\rm 2&\rm 1&\rm 1\\ \rm 3&\rm 3&\rm 1\\ \rm 1&\rm 6&\rm 1\end{array}\right|[/tex]

The determinant values modulus is the area

Slope of AC

Perpendicular lines have slopes negative reciprocal to each other

So

Equation in point slope

Answer:

y=4

Step-by-step explanation:

steps

3×9+4y=43

4y=43-27

4y=16

Divide both side by 4

4y/4=16/4

y=4

A triangle is a fundamental form in geometry. The AAA property can not be used to prove if the triangles are congruent.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

The property angle-angle-angle (AAA), is used for similar triangles. It can not be used to prove that two triangles are congruent triangles. Therefore, it is not a valid criterion.

Now, this can be proved using two triangles having the same angle measurement as 60°. The two triangles given below has the same angle measurement although, their sides have different measurement, thus, the two triangles are not equal.

Hence, the AAA property can not be used to prove if the triangles are congruent.

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Answer: A triangle is a basic geometric shape. Triangle congruence cannot be established using the AAA property. A triangle is a polygon having three vertices and three edges. It is a fundamental geometric figure. For comparable triangles, the property angle-angle-angle (AAA) is employed. It cannot be used to establish the congruence of two triangles. As a result, it is an invalid standard. Now, this may be demonstrated using two triangles with angles equal to or greater than 60°. The two triangles shown below are not equal because they have different side measurements despite having the same angle measurement. The triangles' congruence cannot therefore be established using the AAA property.

Step-by-step explanation:

Answer:

8 and 48

Step-by-step explanation:

Here is how to find it mathematically

x = one number     6x = other number    ( because 3x is 1/2 of x)

(x + 6x) /2 = 28

7x = 56

x = 8     then 6x = 48

Answer:

See below ....none of your answer choices  'fit'

Step-by-step explanation:

Break it into two pieces....a triangular prism and a square pyramid

prism volume = (area) * length

                      ( 1/2 base * height)     *  length  

     Use pythagorean theorem to find height of triangular prism = 12

                            1/2 * 12 * 9   * 21 = 1134 km^3

Pyramid volume = 1/3 base * height =

               =   1/3  *   (9*21)    *    7 = 441 km^3

Summed = 1575 km ^3          

Answer:

-6/5 = x

Step-by-step explanation:

Multiply by 5 to get rid of fractions:
-40 = 35x + 2

Subtract by 2 to get all terms on one side:

-42 = 35x
Divide by 35 to get x term:

-42/35 = x

-6/5 = x

Answer:

Two equal sides: 15 centimeters, Third side: 21 centimeters

Step-by-step explanation:

Sorry If I'm late, so how I solved this was by using variables and algebra. The perimeter of a triangle is the sum of all three sides. Let's now break down the problem and use the useful information, we know that the perimeter is 51 centimeters, and that there are two equal sides and the third side is 6 inches longer than the two equal sides. So it is pretty much an isosceles triangle since it has two sides of equal length and the third side is not equal to the others. So we can make an equation with variables. 51(Perimeter)=x(first equal side)+x(second equal side)+x(third side)+6(The third side is 6 centimeters longer than the two other sides), now we simplify the equation just like we do with most algebraic equations. x+x+x can be turned into 3x. This now makes the equation 51=3x+6, we can subtract 6 from both sides to just have the variable on one side, 3x+6-6, both sixes cross out making it 3x, 51-6 is equal to 45. Now we divide by three on both sides to give just x and find out what x is. 3x/3=x and 45/3=15. x=15, x is the equal side length, so the two equal sides are 15 centimeters and the third one is 21 centimeters. The reason for this is because 15+6=21. I hope this helped with your learning, if I am wrong please tell me :)

Answer:

25

Step-by-step explanation:

[2 x (10+5)] - 5

[2 x (15)] - 5

[30] - 5

25

Answer:

D. reference a question in well-known literature and provide an answer.

Step-by-step explanation:

Answer:

d.  0.71 percentage points

Step-by-step explanation:

13.62 % is .1362 in decimal

  quarterly period compounding makes periodic (quarterly) interes rate

         = .1362/4 = .03405 per period

  FOUR periods in a year

    (1+ .03405)^4 = 1.1433  

            which means effective interest is .1433  or 14.33 %

14.33 - 13.62 = .7115 percentage points difference

Answer:

2 inches is the height of the box.

Step-by-step explanation:

Answer:

Checking your credit history and credit scores can help you better understand your current credit position. Regularly checking your credit reports can help you be more aware of what lenders may see. Checking your credit reports can also help you detect any inaccurate or incomplete information.

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Answer:

73.40°

Given a right angle triangle.

Solve the missing angle using cosine rule.

[tex]\sf cos(x) = \dfrac{adjacent}{hypotenuse}[/tex]

Here given:

adjacent: 2

hypotenuse: 7

angle: x

Solve:

[tex]\rightarrow \sf cos(x) = \dfrac{2}{7}[/tex]

[tex]\rightarrow \sf x = cos^{-1}(\dfrac{2}{7})[/tex]

[tex]\rightarrow \sf x =73 .40^ \circ \:[/tex]

Answer:

108π

Step-by-step explanation:

volume of a cylinder = πr²h , where r = radius and h = height

given values

==> plugging in given values into formula

V = πr²h

r = 3 , h = 12

V = π(3²)(12)

==> evaluate exponent

V = π(9)(12)

==> multiply 9 and 12

V = 108π

Answer:

I think its c but not really sure but ill calculate it if I ever had the chance

Answer:

B

Step-by-step explanation:

B is the answer to your question

Answer:

Step-by-step explanation:

lim         1 / (x + h +1) - 1 (x + 1)

x--> 0

lim         -h/ (x + h +1)(x + 1)

x--> 0

lim         -h/ (x^2 + 2x + hx + h + 1)

x--> 0

-1/ (x^2 + 2x + 1)

Answer:

Step-by-step explanation:

The radius of the is extended to 2*3 = 6 cm.

The measure of the central angle is unchanged.

Answer:

A^d

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

Volume of Rectangular Prism: Volume = Length*Width*Height

300 = x * x * 12

300 = x^2 * 12

25 = x^2

x = 5

All of these can be samples but the best example is 6th grade students whose last name begins with "T"; all students in 6th grade

A sample refers to a small portion of a population. Most samples are selected randomly to make sure the sample represents all the population but they can also be selected based on a specific criterium.

One example of this concept is 6th grade students whose last name begins with "T"; all students in 6th grade because the student whose last name begins with "T" are a fraction of all the population. Moreover, they are more likely to represent all the population.

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Answer:

252

Step-by-step explanation:

Hope this helped you, and have a good day! (Please tell me if the answer is incorrect and I will try and correct it as soon as possible)