The number of lines of symmetry of an equilateral triangle is _______.

Question 5 options:

A: 4


B: 1


C: 2


D: 3

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

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:

32.61° is the answer

Step-by-step explanation:

Tanx=17.6/27.5

Answer:

The correct answer is (-6, 10).

Step-by-step explanation:

You can find the equation of the blue line and then find out which point is on the perpendicular line to that blue line but you also can figure this out visually by looking at where the points are.

Feel free to message me if you still have questions :)

Answer:

(–6, 10)

Step-by-step explanation:

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:

126

Step-by-step explanation:

54 + x = 180

x = 180 - 54

x = 126

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:

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]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

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

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

Answer:

y = 3

Step-by-step explanation:

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

Step-by-step explanation:

in this situation

A+B =D

Given:

Melinda walked to the mall at 4 miles per hour and then rode back home in a bus at 24 miles per hour.

Total traveling time was 14 hours.

To find:

The distance between Melinda's house and mall.

Solution:

Formula used:

[tex]Time=\dfrac{Distance}{Speed}[/tex]

Let x miles be the distance between Melinda's house and mall.

Melinda walked to the mall at 4 miles per hour. So, the time taken by Melinda is [tex]\dfrac{x}{4}[/tex] hours.

Speed of bus is 24 miles per hour. So, the time taken by bus is [tex]\dfrac{x}{24}[/tex] hours.

Total traveling time was 14 hours.

[tex]\dfrac{x}{4}+\dfrac{x}{24}=14[/tex]

[tex]\dfrac{6x+x}{24}=14[/tex]

[tex]7x=14\times 24[/tex]

Divide both sides by 7.

[tex]\dfrac{7x}{7}=\dfrac{14\times 24}{7}[/tex]

[tex]x=2\times 24[/tex]

[tex]x=48[/tex]

Therefore, the mall is 48 miles far from Melinda's house.

Answer:

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

Step-by-step explanation:

13 ÷ 3.5

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

Answer:

(x-8)²+20  vertex=(8,20)

Step-by-step explanation:

(x-8)² = -20

Graphing Form: y = 1(x-8)²+20    

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:

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:

Your correct answer is 1514.27

Step-by-step explanation:

Here is my step by step for you!

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:

D. Negative slope

Step-by-step explanation:

The slope goes down from left to right, so it is a negative slope

Up from left to right is a positive slope

A vertical line is undefined

A horizontal line is zero slope

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.

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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.

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:

im not sure but i think it might be 10??

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:

Answer:

x = 30

Step-by-step explanation:

If A and B were parallel, then 2x + 50 and 5x - 80 are same- side interior angles and sum to 180° , then

2x + 50 + 5x - 80 = 180

7x - 30 = 180 ( add 30 to both sides )

7x = 210 ( divide both sides by 7 )

x = 30