If tanA=1/7 and tanB=1/3 prove that cos2A=sin4B

AB = AD and BC = DC are given. Furthermore, we can see that AC = AC by the reflexive property. We have three pairs of congruent corresponding sides, which allows us to use the SSS congruence theorem. From that, we would use CPCTC to conclude that angle B is congruent to angle D.

CPCTC = corresponding parts of congruent triangles are congruent.

Answer:

Using a calculator;

A is approximately 51.34°

G is approximately 28.36°

Step-by-step explanation:

Part 1

The given trigonometric ratio is presented as follows;

tan A = 5/4

Therefore, the angle, A = arctan(5/4)

Using a calculator,  the value of A is found as follows;

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Entering 5/4 into the calculator, using the keypad

3 . Selecting the arctan button to give, A ≈ 51.34°

Part 2

The given trigonometric ratio is cos G = 0.88

Therefore, G = arccos(0.88)

1. Ensure the angle mode of the calculator is set to the correct value (the selected mode here is degrees)

2. Enter 0.88 into the calculator by typing

3. Select arccos from the function menu, to give

arcos(0.88) = G ≈ 28.36°.

Answer:

10100009ehsbsbb hebehe

Answer:

The game console cost $436.80

Step-by-step explanation:

546 x 0.20 = 109.20

546 - 109.20 = 436.80

Answer:

m∠1 = 103

m∠2 = 103

Step-by-step explanation:

by definition, the opposite angles of a kite are congruent.

we know that a quadrilateral's angles add up to 360.

117 º+ 37º + 2xº = 360º

2xº = 206º

xº=103º

Answer:

f(n) = f(n - 1) - 5

Step-by-step explanation:

The recursive formula allows a term in the sequence to be found by adding the constant difference to the previous term.

Here d = 1 - 6 = - 4 - 1 = - 9 - (- 4) = - 14 - (- 9) = - 5 , then

f(n) = f(n - 1) - 5 with n ≥ 1 and f(1) = 6

Answer:

11

Step-by-step explanation:

Vicky used 462 beads to make 11 necklaces, she would have left 38 beads.

Answer:

He make seven necklaces

Answer:

5

Step-by-step explanation:

A function

[tex]a \times {b}^{x} [/tex]

where a is the initial value and b is the multiplicative rate of change.

In the function,

[tex]f(x) = 2 \times {5}^{x} [/tex]

5 is the value of b so

5 is the multipicative rate of change

Answer:

6(x + 2)^2 + 8x + 2 + 1 = 0

Step-by-step explanation:

A quadratic equation has the variable with the highest power of 2

6(x + 2)^2 + 8x + 2 + 1 = 0  when foiled out it has the highest power of 2

6x4 + 7x2 – 3 = 0  power of 4

5x6 + x4 + 12 = 0 power of 6

x9 + x3 – 10 = 0  power of 9

Answer:

C (the third option)

Step-by-step explanation:

the reason that C is in quadratic form is because the first exponent is a multiple of the following exponent (s)

That is the easiest way I've learned to determine if an equation is quadratic or not. Keep in mind the equation will not always be in simples form so make sure you simplify it all the way.

Hope this Helps <3

Given:

The preimage and image of a triangle in the given figure.

To find:

The dilation scale factor.

Solution:

From the given figure it is clear that the vertices of the triangle ABC are A(-2,-2), B(-1,2) and C(2,1).

The vertices of the triangle A'B'C' are A'(-4,-4), B'(-2,4) and C'(4,2).

If a figure is dilated by factor K with (0,0) as the center of dilation, then

[tex](x,y)\to (kx,ky)[/tex]

Let the scale factor be K, then the image of point A is:

[tex]A(-2,-2)\to A'(k(-2),k(-2))[/tex]

[tex]A(-2,-2)\to A'(-2k,-2k)[/tex]

From the given figure it is clear that the image of point A is A'(-4,-4).

[tex]A'(-2k,-2k)=A'(-4,-4)[/tex]

On comparing both sides, we get

[tex]-2k=-4[/tex]

[tex]k=\dfrac{-4}{-2}[/tex]

[tex]k=2[/tex]

Therefore, the dilation scale factor is 2.

Answer:

QD = 13

Step-by-step explanation:

According to the Centroid theorem of a triangle, the Centroid is ⅔ of the distance from every vertex angle to the midpoint of the side opposite to each of them.

By this we can deduce that:

QD = ⅔(QD + DK)

Substitute

QD = ⅔(QD + 6.5)

Multiply both sides by 3

3*QD = 2(QD + 6.5)

3QD = 2QD + 13

Subtract both sides by 2QD

3QD - 2QD = 13

QD = 13

First find the gradient of L.

-6÷3=-2

gradients of perpendicular lines multiply together to give -1.

(-2)×1/2=-1

m=1/2 or 0.5

y=0.5x-1.5

Answer:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the total orders is not given.

To solve this question, I will assume a value for the total number of order.

Let

[tex]x \to 12-cup[/tex]

[tex]n_x = 18[/tex] ---- number of 12-cup

[tex]y \to 36-cup[/tex]

[tex]n_y = ??[/tex] ---- number of 36-cup

[tex]n \to[/tex] Total order

Required

Calculate [tex]n_y[/tex]

To do this, we make use of the following equation:

[tex]n_x * x + n_y * y = n[/tex]

Substitute known values

[tex]18 * 12 + n_y * 36 = n[/tex]

[tex]216 + 36n_y= n[/tex]

Collect like terms

[tex]36n_y= n - 216[/tex]

Divide both sides by 36

[tex]n_y= \frac{n - 216}{36}[/tex]

Assume the number of orders is: 540 cups

The equation becomes

[tex]n_y= \frac{540 - 216}{36}[/tex]

[tex]n_y= \frac{324}{36}[/tex]

[tex]n_y= 9[/tex]

Answer:

The angle between two nonzero vectors u and v is given by

Cos Θ=u*v/║u║║v║

1) If u*v=0, then CosΘ=0

arccos 0=90°

2) If u*v > 0, then CosΘ >0

If (cos Θ > 0, then Θ is less than 90°

3) If u*v < 0, then Cos Θ < 0

If Cos Θ < 0, then Θ is greater than 90°

OAmalOHopeO

Answer:

32.8 mi²

Step-by-step explanation:

Hi there!

Area of a triangle when given two sides, a and b, and the angle that conjoins them, C:

[tex]A=\frac{1}{2} ab*sinC[/tex]

Plug in the known information:

a=11, b=6, C=97°

[tex]A=\frac{1}{2} (11)(6)*sin(97)\\A=33sin(97)\\A=32.8[/tex]

Therefore, the area of the triangle is approximately 32.8 mi².

I hope this helps!

Answer:

B

Step-by-step explanation:

The trick here is to find the height. The answer is

height = sin(180 - 97) * 11

The height is found by finding the supplement of 97, taking the sin of that angle and multiplying by 11.

There is a drawing required. You need to extend ZY until a line from x meets ZY (extended) at right angles. When that happens you find the sine of the supplement.

height = sin(83)*11

height = 10.92

Now use the standard area formula.

Area = base (ZY) * height / 2

base = 6

height = 10.92

Area = 6 * 10.92 /2

Area = 32.75

Answer:

[tex]3\frac{5}{7}[/tex]

Step-by-step explanation:

13 ÷ 3.5

[tex]3.5=3\frac{5}{10}[/tex]

Answer:

so from looking at this we can see there is

0=5

1=5

2=3

3=2

4=4

5=1

6=2

7=2

8=1

9=1

now we have to add them up

5+6+16+5+12+14+8+9=75

and now we have to add up the total plots on the chart

5+5+3+2+4+1+2+2+1+1=26

now we divide

75 divided by 26=2.88461538462

so 2.9 is the mean

now we add up the number from least to greatest

0,0,0,0,0,1,1,1,1,1,2,2,2,4,4,4,4,5,6,6,7,7,8,9

so the medien is 4

Hope This Helps!!!

Step-by-step explanation:

Finding the median

The median is the number that is located in the middle of the set of numbers. First you count the number of X's, which is 26. This means that the median is in between number 13 and 14, which is 2 and 3 in this number set. Then you average the two numbers ([tex]\frac{2+3}{2}[/tex]) to get 2.5.

Finding the mean

The mean is the average of all of the numbers located in the set. First, you add up all of the numbers.

5(0) + 5(1) +3(2) + 2(3) +4(4) + 1(5) + 2(6) + 2(7) + 1(8) + 1(9) = 81

After, you divide by how many numbers there are in the set, which as we found earlier, is 26

[tex]\frac{81}{26}[/tex] = 3.12

9514 1404 393

Answer:

  (b) 82.9253

Step-by-step explanation:

The first attachment shows the rectangles. The second shows the sum of their areas.

The integers ranging from 5n to 5n + 10, with 5n as a positive odd integer, in each case, the range contains three even integers.

When n = 1:

The range is 5(1) to 5(1) + 10

= 5 to 15.

There are three even integers in this range: 6, 8, and 10.

When n = 3:

The range is 5(3) to 5(3) + 10

= 15 to 25.

There are three even integers in this range: 16, 18, and 20.

When n = 5:

The range is 5(5) to 5(5) + 10

= 25 to 35.

There are three even integers in this range: 26, 28, and 30.

In each case, the range contains three even integers.

Learn more on positive integers here https://brainly.com/question/1367050

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Answer:

the answer is c

Step-by-step explanation:

when solving for theta, we are given the side length adjacent to it (5) and the length of the hypotenuse ( 14).

the trigonometric function that deals with adjacent and hypotenuse values is cosine.

you can use SOH CAH TOA

stands for :

sin = opposite/hypotenuse

cos = adjacent/ hypotenuse

tan = opposite/adjacent

we dont know theta so :

cos(theta) = 5/14

cos = about 69

check :

cos(69) = 5/14

                   cos(69) = 0.35836794954

                   5/14 = 0.35714285714

Answer:

-14

Step-by-step explanation:

have a great day good luck

PT is 8 because since P is the incenter it's equidistant from all sides.

The increase in the amount of wages of Gabriela is $ 41,400

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount after increase in wages be = A

Now , the initial amount of Gabriela be = $ 36,000

And , the percentage increase in the wages = 15 %

So , the equation will be

Total amount after increase in wages A = initial amount + ( percentage increase x initial amount )

Total amount after increase in wages A = 36,000 + ( 15/100 x 36,000 )

Total amount after increase in wages A = 36000 + ( 15 x 360 )

Total amount after increase in wages A = 36000 + 5400

Total amount after increase in wages A = $ 41,400

Therefore , the value of A is $ 41,400

Hence , The increase in the amount of wages of Gabriela is $ 41,400

To learn more about equations click :

https://brainly.com/question/10413253

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Answer:

[tex]f(x) = x^4-5x^2+3[/tex] is symmetric to the y-axis

Step-by-step explanation:

Given

[tex]f(x) = x^4-5x^2+3[/tex]

Required

Determine if it is symmetric

First, we check if the function is even by calculating f(-x)

[tex]f(x) = x^4-5x^2+3[/tex]

[tex]f(-x) = (-x)^4-5*(-x)^2+3[/tex]

[tex]f(-x) = x^4-5*x^2+3[/tex]

We have:

[tex]f(x) = f(-x) = x^4-5*x^2+3[/tex]

This implies that the function is even, and even functions are symmetric to the y-axis.

Hence:

[tex]f(x) = x^4-5x^2+3[/tex] is symmetric to the y-axis

Step-by-step explanation:

in this situation

A+B =D

Answer:

[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]

Step-by-step explanation:

We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .

We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .

[tex]\sf\longrightarrow Slope =\dfrac{-3}{4}[/tex]

On using point slope form ,

[tex]\sf\longrightarrow y-y_1= m ( x - x_1) [/tex]

Substitute the respective values ,

[tex]\sf\longrightarrow y - (-1) = \dfrac{-3}{4}( x - 4 ) [/tex]

Simplify ,

[tex]\sf\longrightarrow y +1 = \dfrac{-3}{4}x + 3 [/tex]

Multiply both sides by 4 ,

[tex]\sf\longrightarrow 4y + 4 = -3x + 12 [/tex]

Put all terms on same side , i.e. on LHS ,

[tex]\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}[/tex]

Hence the equation of the line is 3x + 4y - 8 = 0.

Answer:

2.828

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(6 - 4)² + (0 - 2)²

√(2)² + (-2)²

√4 + 4

√8

2.828

Answer: QF = 5

Step-by-step explanation:

We know that if a triangle has a centroid, the ratio of the longer segment to shorter segment is 2:1. We can set up a proportion [tex]\frac{2}{1} = \frac{10}{x}[/tex], where x is the length of QF. By cross multiplying and dividing, you get x = 5 or QF = 5.

Answer:

5

Step-by-step explanation: