Find the amplitude of the sine curve shown below. a. 3 b. p c. 1.5 d. 6

Answer:

x = 4√3

y = 8√3

Step-by-step explanation:

This is a special 30° 60° 90° right triangle

In this special triangle if the side length that sees 30° is represented by x and the side length that sees 90° is represented by 2x and the side length that sees 60° x√3

Here, the side length that sees 60° is given as 12

12 = x√3 and x = 4√3 therefore y is 8√3

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

[tex]\angle AED = \angel BEC[/tex] ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

[tex]\angle ABC = 90^{\circ}[/tex]

In ΔDBC

BC=DC (Given)

So,[tex]\angle CDB=\angle DBC[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle CDB=\angle DBC=x[/tex]

So,[tex]\angle CDB+\angle DBC+\angle BCD = 180^{\circ}[/tex] (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,[tex]\angle CDB=\angle DBC=x = 65^{\circ}[/tex]

Now,

[tex]\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90[/tex]

So,[tex]\angle ABD=90-x=90-65=25^{\circ}[/tex]

In ΔABD

AB = BD (Given)

So,[tex]\angle BAD=\angle BDA[/tex](Opposite angles of equal sides are equal)

So,[tex]\angle BAD=\angle BDA=y[/tex]

So,[tex]\angle BAD+\angle BDA+\angle ABD = 180^{\circ}[/tex](Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively

Question:

Which of the following expressions represents the distance between 1.7 and −1/2 on a number line?

Choose 1 answer: 

[tex]A.\ |1.7 - 1/2|[/tex]

[tex]B.\ |1.7 -(-1/2)|[/tex]

C. None of the above

Answer:

[tex]B.\ |1.7 -(-1/2)|[/tex]

Step-by-step explanation:

Given

Numbers: 1.7 and -1/2

Required

Determine the distance

To calculate the distance, we start by calculating the difference between the given numbers;

[tex]Difference = 1.7 - (-1/2)[/tex]

Then, we calculate the distance;

In this case, the distance is meant to be positive; So, we'll introduce the symbol for absolute value;

Hence,

[tex]Distance = |Difference|[/tex]

Substitute [tex]1.7 - (-1/2)[/tex] for Difference;

[tex]Distance = |1.7 - (-1/2)|[/tex]

Hence, the correct option is B

The expression that represents the distance between 1.7 and -0.5 is given by |1.7 - (-0.5)| and this can be determined by using the arithmetic operations.

Given :

Numbers  --  1.7 and -0.5

The distance between two points 1.7 and -0.5 is given by:

Distance = 1.7 + |-0.5|

               = 2.2

Now, check all the options in order to determine the correct option:

A) |1.7 - 0.5|

Simplify the above expression.

|1.7 - 0.5| = 1.2

B) |1.7 - (-0.5)|

Simplify the above expression.

|1.7 - (-0.5)| = |1.7 + 0.5| = 2.2

Therefore, the correct option is B).

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Answer:

y + 5 = (1/3)(x - 6)

Step-by-step explanation:

Line p is perpendicular to line q, and therefore the slope of line p is the negative reciprocal of the slope of line q:  -1/3.

Starting with the point-slope formula y - k = m(x - h), we get

y + 5 = (1/3)(x - 6)

Answer:

the third one is correct

Answer:

Using the Pythagorean theorem we can know from the first triangle that the height of the two triangles are 12. So, we then know that a = 20.

(Root 15^2-9^2=12) (Root 12^2+16^2=20)

Another way is using the whole triangle. The step above used two triangles. The two triangles together makes a big right triangle, so we can again use the Pythagorean theorem. So, the answer again is 20.

(Root 25^2-15^2=20)

Step-by-step explanation:

Using the Pythagorean theorem we can know from the first triangle that the height of the two triangles is 12. So, we then know that a = 20.

We have to find the value of ‘a’ using two different ways.

By the Pythagorean theorem,

By cross multiplication,

16(25) = a2

a2 = 400

Taking square root,

a = 20

Therefore, the length of the other side a = 20.

You can calculate the mean value by adding up the numbers and then dividing the result by the number of numbers. For instance, to find the mean value of 4, 1, 3, and 8, first, add up the numbers: 4+1+3+8=16 4 + 1 + 3 + 8 = 16.

Therfore=a2−b2.

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Answer:

3 or 3/1

Step-by-step explanation:

Slope is also known as rise/run.

The formula used to find slope is y^2-y^1/x^2-x^1.

The work is below:

-1-5/0-2

-6/-2

3/1

m=3

When we calculate the slope using the formula, we find that the slope(m) equals to 3/1 or 3 which means that you rise up by 3 and run to the right 1.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The slope of the line through (0, 5) and (-2, -1) will be 3 or 3/1.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same). A measure of steepness is a slope. When building roads, one must determine how steep the road will be. These are some examples of slopes in real life.

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given the line is passed through the following points,

(x₁,y₁)=(0, 5)

(x₂,y₂)=(-2, -1)

The slope of the line is found as,

m=(y₂-y₁) / (x₂-x₁)

Substitute the given values,

m=-(1-5)/(0-2)

m=(-6)/(-2)

m=3/1

The slope(m) equals 3/1, or 3 when we compute the slope using the formula, meaning that you rise up by 3 and move to the right by 1.

Thus, the slope of the line through (0, 5) and (-2, -1) will be 3 or 3/1.

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Answer:

12 units

Step-by-step explanation:

Notice that as we go from Q to R, x (the horizontal distance) increases by 12 and y (the vertical distance) does not change.  Thus, the distance between the two points is merely the horizontal distance, 12 units.

Answer:

  6 < x < 8

Step-by-step explanation:

The compound inequality in this instance represent the "and" condition, not the "or" condition.* We might solve it like this.

  -47 > 1 -8x > -63 . . . . given

Multiply by -1:

  47 < -1 +8x < 63

Add 1:

  48 < 8x < 64

Divide by 8:

  6 < x < 8

______

* You can tell this is the case by looking at the ends of the given statement:

  -47 > -63 . . . . a true statement, so the solution set will be an intersection, not a union.

Answer:

B is the correct answer.

Step-by-step explanation: If tanx=1, then cosx=√2/2. Use your half angle formulas to plug cosx in, and you should get B as your answer.

Answer:

16.7 Units

Step-by-step explanation:

To find the length of r, you set up the equation as sin(45)= 4.9/r. Then you get r by itself changing it to r = 4.9/sin(45). Then you can find that r = 6.9. Since this is an isosceles triangle, n^1 has to be equal to 4.9. Then you add all the side lengths together. 4.9 + 4.9 + 6.9 = 16.7 units

Answer:

it is b

Step-by-step explanation:

just because it is ...

Answer:gjcnlfjdk

Step-by-step explanation:

Answer:Such sequences can be expressed in terms of the nth term of the sequence. In this case, the nth term = 2n. To find the 1st term, put n = 1 into the formula, to find the 4th term, replace the n's by 4's: 4th term = 2 × 4 = 8

Answer:

[tex]\boxed{p=\sqrt[3]{8}}[/tex]

Step-by-step explanation:

p³ = 8

Take the cube root on both sides.

[tex]\sqrt[3]{p^3 } =\sqrt[3]{8}[/tex]

[tex]p=\sqrt[3]{8}[/tex]

Answer:

[tex]\boxed{Option \ A}[/tex]

Step-by-step explanation:

[tex]p^3 = 8[/tex]

Taking cube root on both sides

[tex]\sqrt[3]{p^3} = \sqrt[3]{8}[/tex]

=> p = [tex]\sqrt[3]{8}[/tex]

Answer:

it is D. 5

Step-by-step explanation:

The long side (B) will always be (A root 3) meaning, if you just take away the square root of 3, then you get the short side A

Answer:

[tex]\boxed{Shortest\ Leg = 5}[/tex]

Step-by-step explanation:

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Where θ = 60 , opposite = [tex]5\sqrt{3}[/tex] and adjacent = shortest leg

=> Tan 60 = [tex]5\sqrt{3}[/tex] / shortest leg  (Tan 60 = √3)

=> Shortest Leg = [tex]\frac{5\sqrt{3} }{\sqrt{3} }[/tex]

=> Shortest Leg = 5

Answer:

a = 16

Step-by-step explanation:

To solve your question all you have to do is subtract 15 on both sides so,

15 - 15 + a = 31 - 15

Which will give you,

15 - 15 = 0

31 - 15 = 16

So,

a = 16

Hope this helps!!

Answer:

Step-by-step explanation:

[tex]15 + a = 31[/tex]

Move constant to R.H.S and change its sign

[tex]a = 31 - 15[/tex]

Subtract the numbers

[tex]a = 16[/tex]

Hope this helps..

Best regards!!

Answer:

C

Step-by-step explanation:

CB is congruent to AB because the both are 30 degrees

Answer:

a) 28

b) 56

Step-by-step explanation:

A cube is a three dimensional shape gotten from a square. It has 6 faces, and an equal line segment that form its sides.

A vertex is the edge of a figure.

In the given cube ABCDEFGH, since the vertices to be considered are not only the adjacent vertices, then;

a) By connecting the vertices of the cube, 28 different segments can be obtained.

b) The number of triangles that can be formed by connecting 3 of the vertices of the cube is 56.

Answer: C

Step-by-step explanation:

I hope it right :)

Answer:

She can expect 400 tails.

Step-by-step explanation:

When doing a coin toss, the theoretical probability of getting either heads or tails is 1/2. If we apply this fraction to the 800 total simulated tosses, she should get about 400, more or less.

Answer:

400

verified on a p e x

Answer:

n=4

Step-by-step explanation:

-28 divided by -7 is 4

Answer:

4

Step-by-step explanation:

divide -7 on both sides

-28/-7=4

Answer:

Step-by-step explanation:

Let the equation of the exponential function is f(x) = a(b)ˣ

Two points (-2, 4) and (-1, 2) lie on the graph,

For (-2, 4),

By substituting the values in the given function,

[tex]4=a(b)^{(-2)}[/tex]

[tex]4=\frac{a}{b^{2} }[/tex] ------(1)

For second point (-1, 2),

[tex]2=a(b)^{-1}[/tex]

[tex]2=\frac{a}{b}[/tex] -----(2)

Dividing equation (1) by equation (2),

[tex]\frac{4}{2}=\frac{\frac{a}{b^2}}{\frac{a}{b} }[/tex]

[tex]2=\frac{a}{b^{2}}\times \frac{b}{a}[/tex]

[tex]2=\frac{1}{b}[/tex]

b = [tex]\frac{1}{2}[/tex]

From equation (1),

[tex]4=\frac{a}{(\frac{1}{2} )^2}[/tex]

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) = [tex]1.(\frac{1}{2})^{x}[/tex]

[tex]f(x)=(\frac{1}{2})^x[/tex]

Option (A) will be the answer.

Answer:Answer:

Option (A)

Step-by-step explanation:

Let the equation of the exponential function is f(x) = a(b)ˣ

Two points (-2, 4) and (-1, 2) lie on the graph,

For (-2, 4),

By substituting the values in the given function,

------(1)

For second point (-1, 2),

-----(2)

Dividing equation (1) by equation (2),

b =

From equation (1),

4 = 4a

a = 1

Therefore, equation of the exponential function will be,

f(x) =

Option (A) will be the answer.

Step-by-step explanation:

Answer:

6 combinations

Step-by-step explanation:

There are 6 combinations because:

1.) Red coat, black scarf, white gloves.

2.) White coat, grey scarf, white gloves.

3.) Pink coat, black scarf, white gloves.

4.) Red coat, grey scarf, white gloves.

5.) White coat, black scarf, white gloves.

6.) Pink coat, grey scarf, white gloves.

Answer: {-7, 2}

Step-by-step explanation: This type of equation is called a polynomial equation and in order to solve for x, we would first factor the left side.

Notice that the left side of the equation is a trinomial in a special

form that can be factored as he product of two binomials.

As our first term for each binomial, we have the factors of x², x · x

and as the second term, we have the factors of -14 that add to 5.

In this case, the factors are +7 and -2.

So we have (x + 7)(x - 2) = 0.

If (x + 7)(x - 2) = 0, that means that either x + 7 = 0 or x - 2 = 0.

Solving for x in each equation, we have x = -7 or x = 2.

We can write our answer as the solution set {-7, 2}.

The solution of quadratic equation is,

⇒ x = - 7, 2

We have to given that,

An equation is,

⇒ x² + 5x - 14 = 0

We can factorized the above quadratic equation as,

⇒ x² + 5x - 14 = 0

⇒ x² + (7 - 2)x - 14 = 0

⇒ x² + 7x - 2x - 14 = 0

⇒ x (x + 7) - 2 (x + 7) = 0

⇒ (x + 7) (x - 2) = 0

This gives,

x + 7 = 0

x = - 7

x - 2 = 0

x = 2

Therefore, The solution of quadratic equation is,

⇒ x = - 7, 2

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Simplify and write answer in standard form, a + bi

Answer: -54-54i

Answer:

84.78cm^2

Step-by-step explanation:

first we do pi*r^2.

3.14*6^2=113.04

Then, because we know that 1/4 of the circle is missing, just multiply 113.04 by .75.

113.04*.75=84.78cm^2

Answer:

84.78cm^2

Step-by-step explanation:

Answer: A) g(x) is shrunk horizontally by a factor of 1∕3 compared to ƒ(x).

Step-by-step explanation:

Given: f(x) 10x

g(x) =10(3x)

= f(3x)

Since, f(ax) is a horizontal compression when a> 1 by the factor of [tex]\dfrac{1}{a}.[/tex]

That means g(x) is shrunk horizontally by a factor of [tex]\dfrac{1}{3}[/tex] compared to ƒ(x).

So, the correct option is A) g(x) is shrunk horizontally by a factor of 1∕3 compared to ƒ(x).

Answer:

Step-by-step explanation:

Answer: A) g(x) is shrunk horizontally by a factor of 1∕3 compared to ƒ(x).

Answer:

c

Step-by-step explanation:

combine like terms:

5/7a^2+-5/7a+10

HOPE THIS HELPS!!!!!!:)

Answer:

add pic

Step-by-step explanation:

Answer:

m=6.5

Step-by-step explanation:

thats what you type in

Answer:

Yes she has enough money. She would have $3.42 left over.