Next → The Unit Circle: Mastery Test
The measure of angle 0 is 7pi/4. The measure of its reference angle is and tan 0 is

The percentage of total variation in the dependent variable that is described by the independent variable is expressed by coefficient of determination . So, correct answer is option (a).

The coefficient of determination R² is equal to the square of the correlation coefficient, r² expressed as a percentage, represents the percentage of variation in the dependent variable y that can be explained by variation in the independent variable x using the regression line. Coefficient of determination is a statistical measure that examines how differences in one variable can be explained by differences in her second variable. In other words, this coefficient, commonly known as R-squared (or R²), measures how strong the linear relationship between two variables is. This coefficient is commonly known as the R-square (or R²) and is sometimes called the "goodness of fit". This measurement is expressed as a value between 0.0 and 1.0..

To learn more about Cofficient of determination, refer:

https://brainly.com/question/17237825

#SPJ4

Answer:

120 Degrees

Step-by-step explanation:

(6-2)*180 = 720

720/6 = 120

So the answer is 120

Hope this helps!

The degree will carry the regular hexagon onto itself is 60 degrees.

"A regular hexagon is a closed shape polygon which has six equal sides and six equal angles. In case of any regular polygon, all its sides and angles are equal. When we arrange six equilateral triangles side by side, then a regular hexagon is composed. Then, the area of the regular hexagon becomes equal to six times the area of the same triangle."

Regular Hexagon Properties

1. It has 6 equal sides and 6 equal angles.

2. It has 6 vertices.

3. Sum of interior angles equals 720°.

4. Interior angle is 120° and exterior angle is 60°.

5. It is made up of six equilateral triangles.

6. 9 diagonals can be drawn inside a regular hexagon.

7. All the sides opposite to each other are parallel.

We know

There are 6 sides to a hexagon

360 degrees in a hexagon

The degree will carry the regular hexagon onto itself

= \(\frac{360}{6}\)

= \(60^{0}\)

Thus, The degree will carry the regular hexagon onto itself is 60 degrees.

Learn more about regular hexagon here

https://brainly.com/question/1694257

#SPJ2

Answer:

y = x - 2

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Slope m = 1

y-intercept b = -2

Step 2: Write linear function

y = x - 2

Answer: B, y=x-2

Step-by-step explanation:

The slope-intercept form is y=mx+b where m=slope and b=y intercept

therfore, subtituting 1 for m and -2 for b

y=x-2

You have the following expression:

To verify the identity, you have that the left side of the equation becomes:

(1 + cosx)(1 - cosx) = (1 - cos^2 x)

because of the product of an expression by its conjugate result in a difference of squares. Or simplfy by expanding the factors and simplying.

Next, you have:

1 - cos^2 x = sin^2 x

because the Pythagorean identity.

Then, the identity is verified.

Answer:

The sum of the first ten terms is -35.

Step-by-step explanation:

The first term of an arithmetic sequence is 10, and its common difference is -3.

We want to find the sum of the first 10 terms of this sequence.

Remember that the sum for an arithmetic sequence is given by:

\(\displaystyle S=\frac{k}{2}\left(a+x_k\right)\)

Where k is the number of terms, a is the initial/first term, and x_k is the last term.

Since our initial term is 10, a = 10.

And since we want to find the sum of the first ten terms, k = 10.

So, we will need to find the last or tenth term. We can write an explicit formula. The standard explicit formula for an arithmetic sequence is:

\(x_n=a+d(n-1)\)

Where a is the initial term and d is the common difference.

So, by substituting, we acquire:

\(x_n=10-3(n-1)\)

Then the tenth or last term is:

\(x_{10}=10-3(10-1)=10-3(9)=10-27= -17\)

Then the sum of the first ten terms will be:  

\(\displaystyle S_{10}=\frac{10}{2}(10+(-17))=5(-7)=-35\)

Answer:

-35

Step-by-step explanation:

\(a_{1}\) = 10+(-3)(0) = 10

\(a_{10}\) = 10+(-3)(9) = -17

\(S_{10}\) = 10[(10 -17)/2] = 10(-7/2) = -70/2

Answer:

C.) <-11, -10>

Step-by-step explanation:

Let's define how to work with vectors.

For two vectors:

V = <a, b>

W = <c, d>

The product of a scalar k and a vector is given by:

k*V = k*<a, b> = <k*a, k*b>

And the sum (or difference) of two vectors is given by:

V ± W  = <a, b> ± <c, d> = <a ± c, b ± d>

Now that we know this, we can solve the problem.

Here we have the vectors:

u = <2, 1>

v = <5, 4>

then:

2u - 3*v = 2*<2, 1> - 3*<5, 4>

             = <2*2, 2*1> - <3*5, 3*4>

             = <4, 2> - <15, 12>

             = <4 - 15, 2 - 12>

             = < -11, -10>

Then the correct option is C.

Answer:

i dont understand what you want us to do lol?

Step-by-step explanation:

Answer:

Step-by-step explanation:

do u have an actual pictrue of problem 8 & 10 ?

The 3rd graph (bottom left)

2.58

Answer:

Step-by-step explanation:

Answer:

0.003

Step-by-step explanation:

(30%)/100

Result

0.003

Decimal approximation

0.003

Rational approximation

3/1000

Answer:

1 or more than 1

Step-by-step explanation:

This is your answer

Answer:

23.9425 (Round if needed)

Step-by-step explanation:

This is 2 half circles so you can find the area of a circle and divide it by 2.

First circle has a diameter of 6 cm

6/2=3 cm

So, circle has radius of 3.

Area of circle= 3.14(pi) radius^2

3.14 x 3^2= 28.26

28.26/2=14.13 cm

Area of first half circle= 14.13

Repeat that process for the second circle.

3.14 x 2.5^2=19.625

19.625/2=9.8125

14.13+9.8215=23.9425

Area=23.9425

Answer:

The quen is as following:

ABC is a right triangle at C,

Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

If CH is an altitude to AB and CL is an angle bisector of ∠ACB, find m∠HCL.

The solution is:  m∠HCL = 30°

Step-by-step explanation:

See the attached figure.

∵The triangle is right at C   ∴∠C = 90°

∴∠A + ∠B = 90° ⇒(1)

∵ Acute angles are in the ratio 5:1, i.e. ∠BAC : ∠ABC = 5:1

∴∠A = 5 times ∠B

Substitute at (1)

∴ 5 ∠B + ∠B = 90° ⇒⇒⇒ ∴∠B = 15°  and ∠A = 75°

∵CL is an angle bisector of ∠ACB

∴ ∠ACL = 90°/2 = 45°

∵ CH is an altitude to AB ⇒ ∠CHA = 90°

At the triangle AHC:

∠ACH = 180° - (∠CHA + ∠CAH) = 180° - (90° + 75°) = 15°

∴ ∠HCL = ∠ACL - ∠ACH = 45° - 15° = 30°

Answer:

Solution for Find the exact value of the expression cos 11π/6. ... Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!* ... Q: The pair of equations x+2y+5 = 0 and -3x-6y+1=0 have how many ... of the tangent line to the graph of f(æ) = (e¯")² at a = - In 2 is Select one: O a. y + . ... All Rights Reserved.

Answer:

B: (2,-4)

Step-by-step explanation:

x-2=0

x=2

y+4=0

y=-4

Answer:

hyee

Step-by-step explanation:

hope this helps :)

Options: A. The equation -3|2x + 1.2| = -1 has no solution

B. The equation 3.5|6x - 2| = 3.5 has one solution

C. The equation 5|-3.1x + 6.9| = -3.5 has two solutions

D. The equation -0.3|3 + 8x| = 0.9 has no solution

The correct answer is D. The equation -0.3|3 + 8x| = 0.9 has no solution

Step-by-step explanation:

I just took the test and got 100%

The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

For such more questions on probability

https://brainly.com/question/25839839

#SPJ8

The midline equation of the function is y = 1.5.

The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.

Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.

Using the definition of the amplitude the midline is the given amplitude.

Hence, the midline equation of the function is y = 1.5.

Learn more about amplitude here:

https://brainly.com/question/9124856

#SPJ1

Answer:

3

Step-by-step explanation:

Khan Academy

Answer:

If \(g(x) = f(x+5)\), then horizontal asymptote is the same.

Step-by-step explanation:

The graph represented in the figure is a hyperbola of the form:

\(y = \frac{A}{(x-k)} + B\) (1)

Where:

\(x\) - Indendent variable.

\(y\) - Dependent variable.

\(k\) - Horizontal coordinate where vertical asymtote goes through.

\(A, B\) - Coefficients.

When \(x = k\), the equation becomes undefined and vertical asymptote passes through \((x, y) = (k, 0)\). If \(x \to \pm \infty\), then \(y \to B\), coinciding with the horizontal asymptote.

The graph have the following parameters: \(k = 2\), \(B = 3\). If \(g(x) = f(x+5)\), then horizontal asymptote is the same.

Answer:

The graph of h(x) = g(x + 5) has

the same horizontal asymptote as function g

and

a vertical asymptote at x = -7

Step-by-step explanation:

Given the Initial principal and interest rate, the time taken for the value of the investment to reach $20,000 is 14.1 Years.

An Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is  number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

A = P(1 + r/n)^(n*t)

We make t the subject of the formula

t = In(A/P) / n[In(1 + r/n)]

t = In(20000/8000) / 365[In( 1 + 0.065/365 )]

t = In(2.5) / 365[In( 1 + 1.78×10⁻⁴ )]

t = In(2.5) / 365[In( 1.000178 )]

t = In(2.5) / 365[In( 1.000178 )]

t = 0.91629 / ( 365 × 0.00017798 )

t = 14.1 years

Given the Initial principal and interest rate, the time taken for the value of the investment to reach $20,000 is 14.1 Years.

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1

Answer:

8p+16q

hope this helps

4x2p=8p

4x4q=16q

Answer:

r = 1

Step-by-step explanation:

Step 1: Write equation

-3r + 18 = 15r

Step 2: Solve for r

Step 3: Check

Plug in r to verify it's a solution.

-3(1) + 18 = 15(1)

-3 + 18 = 15

15 = 15

Step-by-step explanation:

- 3r - 15r = -18 .... Moved variables to one side and constants to the other

- 18r = - 18 ..... Simplified

r = 1 ..... Divided to isolate the r

Check:

Plug in 1 for r

-3(1) +18 = 15(1)

- 3+18 = 15

15 = 15 .... Therefore 1 is correct

Answer is 1

Hope this helps!

By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

For more such questions on triangle

https://brainly.com/question/2773823

#SPJ8

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

Learn more about Circumference here

https://brainly.com/question/16125353

#SPJ1

Answer:

Shifts 4 units down ---> \(g(x)=2x-10\)

Stretches f(x) by a factor of 4 away from x-axis--->\(g(x)=8x-6\)

Shifts f(x) 4 units right---> \(g(x)=2x-14\)

Compress f(x) by a factor of 1/4 toward the y-axis ---> \(g(x)=1/2x-3/2\)

Step-by-step explanation:

We are given \(f(x)=2x-6\)

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

\(g(x)=2x-6-4\\g(x)=2x-10\)

So, Shifts 4 units down ---> \(g(x)=2x-10\)

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

\(g(x)=2(4x)-6\\g(x)=8x-6\)

So, Stretches f(x) by a factor of 4 away from x-axis--->\(g(x)=8x-6\)

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

\(g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14\)

So,  Shifts f(x) 4 units right---> \(g(x)=2x-14\)

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

\(g(x)=1/4(2x-6)\\g(x)=1/2x-3/2\)

Compress f(x) by a factor of 1/4 toward the y-axis ---> \(g(x)=1/2x-3/2\)

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)

Answer:

r= -0.1

Step-by-step explanation:

Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

Learn more about distance at:

https://brainly.com/question/7243416

#SPJ1