please answer this question​

Answer:

your welcome    

Step-by-step explanation:

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The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b² + c² - a²)/2bc

cos B= (a² + c²- b²)/2ac

cos C = (a²+ b²- c²)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s² + s² - s²)/(2s×s)

cos A = (s² )/(2s²)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s² + s² - s²)/(2s×s)

cos B = (s²)/(2s²)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s² + s² - s²)/(2s×s)

cos C = (s² )/(2s²)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

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Triangle ABC is congruent to triangle DEF based on the SAS congruence theorem.

The SAS theorem is a triangle congruence theorem that states that two triangles are congruent if they have two pairs of congruent sides that are corresponding to each other, and a pair of congruent included angles.

Triangles ABC and DEF have:

Therefore, they are congruent by SAS.

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Answer:

[tex]f(x) = cos(x - \frac{\pi }{4} ) -1[/tex]

Step-by-step explanation:

In this graph, we have the coordinate point ([tex]\frac{\pi }{4} , 0[/tex]). Without translations, cos(0) = 0, which means that the graph is shifted to the right by [tex]\frac{\pi }{4}[/tex]. We also know that the graph is shifted down by 1 because we have the point

([tex]\frac{5\pi }{4} , -2[/tex]), but accounting for the right shift, this point should really by ([tex]\pi , -2[/tex]). cos([tex]\pi[/tex]) = -1, but on the graph it is -2, meaning that it is shifted down by 1.

Therefore, accounting for the right shift by [tex]\frac{\pi }{4}[/tex] and the shift down by 1, our equation is [tex]f(x) = cos(x - \frac{pi}{4} ) - 1[/tex].

Answer:

it's either 20 or 80..

Answer:

80 shoes

Step-by-step explanation:

40×2

Answer:

Steps

-x/3 >5

Multiply both sides by 3

3(-x/3)>5.3

Simplify

-X> 15

Multiply both sides by - 1 (reverse the inequality)

(-x)(-1)<15(-1)

Simplify

X< -15

so C is the answer

Answer:

decreasing and linear

Step-by-step explanation:

it just is

Answer:

Decreasing,  linear

Step-by-step explanation:

you are going -4 every time

Answer:

The equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x+y=-5 is 2x+y=4

Answer:

Step-by-step explanation:

Because a square must be positive no matter what the sign of x is.

(-2)^2 = 4

2^2 = 4

Step-by-step explanation:

hope you anderstand

if that's the answer can you brainliest me please thank you

Answer:

712

Step-by-step explanation:

2 + 3 = 5 + 5 = 10 + 7 = 17 + 11 = 28 + 13 = 41 + 17 = 58 + 19 = 77 + 23 = 100 + 29 = 129 + 31 = 160 + 37 = 197 + 41 = 238 + 43 = 281 + 47 = 328 + 53 = 381 + 59 = 450 + 61 = 511 + 67 = 578 + 71 = 649 + 73 = 712

cant delete this answer. my bad

The area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The length of the rectangle = [tex]64\dfrac{5}{7}[/tex]  m = 453/7 m

The breadth of the rectangle = [tex]23\dfrac{3}{8}[/tex] m = 187/8 m

The area of the rectangle hall:

= (453/7)(187/8)  = 1512.69 ≈ 1512.7square m

Thus, the area of the rectangle hall is 1512.7 square m if the length 64 5/7 m and breadth 23 3/8 m​

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Answer:

6 friends

Step-by-step explanation:

because 1/4 goes 4 times into a whole 1 and then 2 times into a half, equalling six

Step-by-step explanation:

[tex] = \frac{2}{9} \times \frac{3}{5} \\ [/tex]

[tex] = \frac{6}{45} \\ [/tex]

Change into lowest term...

[tex] = \frac{2}{15} \\ [/tex]

The  Indication of the position of port Q on the drawing is shown by using the example of the image attached.

To Indicate the position of port Q on the drawing (use the x tool).

12 * 5  = 60km

Note that S=  VT

Because 1cm represent 3km

1/3 =x/60

3x = 60

x= 60/3

x= 20

So therefore, 60km needs 20cm.

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Answer:

21.5 to 1 decimal place.

Step-by-step explanation:

The total number of marks for all the boys = 28*28 = 784 marks.

The total number of marks for all the girls   = 24*14  = 336 marks.

So the mean mark for the whole group  

= (784+336) / (28+24)

= 1120 / 52

= 21.538

Answer:

180

Step-by-step explanation:

bcoz it's a straight angle

Answer:

The fourth option shows how Bruno is incorrect

Step-by-step explanation:

Multiplication does not always result in a number greater than the initial value. If n can be any value, then Bruno's claim is false. For instance, multiplying a value greater than one by a decimal will perform the inverse operation (division):

3 × 0.87 = 2.61

When multiplying fractions of 1, this occurs when the multiplied number is greater than the multiplier:

0.55 × 0.21 = 0.1155

If decimals are not allowed, multiplying positive and negative values will give the positive result but with the inverse sign, which is less than the initial one since the result is less than 0:

12 × -2 = -24

Now back to the example. If we let n = 0.75 (3/4);

0.8 × 0.75 = 0.6

Hope that clears things up.

Ajay wraps a gift box in the shape of a triangular pyramid. The amount

of wrapping paper he uses is 173.2 square inches.

The formula for calculating the total surface area is expressed as:

Area = 4(area of triangle)

The area of the triangle

A = 0.5(8.66)(10)

A = 43.3 square inches

The total surface area will be

TSA = 4(43.3)

TSA = 173.2 square inches

Hence the amount of wrapping paper Ajay uses is 173.2 square inches

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Answer:

The y-intercept is 4

Step-by-step explanation:

You find the y-intercept by finding where x is zero. In the table, when x=0 the y=4. The y-intercept is 4. The graph of the function crosses the x-axis at the point (0,4).

Answer:

4

Step-by-step explanation:

the y-intercept is the y-coordinate where the line intersects the facis.So if we want to figure out the intercept,we're going to set x=0 and sdue for Y.

Answer:

The third box model

Step-by-step explanation:

Since she earns 162 from babysitting and got a total of $810, it would eman that (x represents the amount of money she got from mowing lawns) 810-162=x

x=648 so the third box model is correct

Answer:

The angles are vertical, and the value of x is 128 degrees

Step-by-step explanation:

You can tell vertical angles apart from adjacent by looking at their position. Adjacent angles are side by side, right next to each other. Vertical angles are directly across from each other, with their points touching.

Since the angle measures of vertical angles are equal, the value of x is 128

i hope this helps

Using the given information, Aina's net income is for the month is 35,834 PHP

From the question, we are to determine the net Aina's net income

Aina's net income is the value of her total income minus all other expenses

From the given information,

Aina's monthly salary is 35,000 PHP per month and also receives 3,500 PHP for a monthly allowance

∴ Aina's total income = 35,000 PHP + 3,500 PHP

Aina's total income = 38,500 PHP

Sum of her other expenses = 1,466 PHP + 300 PHP + 800 PHP + 100 PHP

Sum of her other expenses = 2,666 PHP

∴ Aina's net income = 38,500 PHP - 2,666 PHP

Aina's net income = 35,834 PHP

Hence, Aina's net income is for the month is 35,834 PHP.

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Answer:

x = 90

Step-by-step explanation:

X is equal to 90 degrees:

As you can see it forms paralell line we know paralell line is equal to 180 degrees just divide it by 2, so 90

Answer:

One solution

Step-by-step explanation:

The only solution is x = 2/3

Answer:

y = (x + 1)(x - 2)(x -3)

Step-by-step explanation:

Looking at the graph we see our zeros which is on the x-axis is -1 , 2, 3.

Thus create an equation.

y = (x + 1)(x - 2)(x -3)

Answer:

n = 9 / 2 or 4.5

Step-by-step explanation:

2/3 = 3/N

cross multiply

2 x n = 2n

3 x 3 = 9

2n = 9

divided both sides by 2

2n / 2 = 9 / 2

n = 9 / 2

Answer:

87124 + 14997 = 102121

Hope it helpz~ uh..

Carry on learning :)

Answer:

102121

Step-by-step explanation: