Which expression would be easier to simplify if you used the associative
property to change the grouping?

Question 2.1.1

Reason:

Use the distance formula to find the distance from the origin (0,0) to the terminal point (-3, 4)

[tex](x_1,y_1) = (0,0) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(0-(-3))^2 + (0-4)^2}\\\\d = \sqrt{(0+3)^2 + (0-4)^2}\\\\d = \sqrt{(3)^2 + (-4)^2}\\\\d = \sqrt{9 + 16}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

The pythagorean theorem is a similarly related alternative path you can take.

This triangle is a 3-4-5 right triangle.

====================================================

Question 2.1.2

Reason:

r = distance from origin to terminal point

r = 5, calculated back in the previous problem above.

sin(alpha) = y/r = 4/5

cos(alpha) = x/r = -3/5

sin(alpha)+cos(alpha) = (4/5)+(-3/5) = 1/5

====================================================

Question 2.1.3

Reason:

Recall that tangent is the ratio of sine over cosine

tan = sin/cos

Therefore,

[tex]\tan(\alpha) *\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)}{\cos(\alpha)}*\frac{\cos(\alpha)}{\sin(\alpha)}\\\\\frac{\sin(\alpha)*\cos(\alpha)}{\cos(\alpha)*\sin(\alpha)}\\\\1[/tex]

This assumes that neither sin(alpha) nor cos(alpha) are zero. Otherwise, we have a division by zero error.

Answer:

16'

Step-by-step explanation:

4'

4 equal sides

4+4+4+4=16

Answer: Permimeter of a 4’ square is 16.

Step-by-step explanation:

given that:

• length = 4

∴ Perimeter of Square = 4 x length

⇒ P = 4 × 4

⇒ P = 16 units ...answer...

hope that helps...

The statement correctly describes the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.

The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right

if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.

Given graph : y = ln(x), has a vertical and horizontal translation.

As we know, y = ln(x - h) + k | where h is the vertical shift, and k is the horizontal shift.

Therefore, comparing y = ln(x - 7) + 3 it with different function we can write the graph of y = ln(x - 7) + 3 is translated 3 units up as well as 7 units to the right.

Learn more about this concept here:

https://brainly.com/question/9832306

#SPJ1

Answer:

the correct answer is B

Step-by-step explanation:

A function g is the inverse for the function f if for y-f(x), x-g(y)

y=7x-6

Replace x with y

x=7y-6

Solve for y in x=7y-6

Switch sides

7y-6=x

Add 6 to both sides

7y-6+6=x+6

Simplify

7y=x+6

Divide both sides by the coefficient of y, which is 7. We have:

7y/7 = x/7+6/7

7y & 7 are cancelled out and we're left with: x/7 & 6/7

Now we find the LCM of the denominators which is 7.

7 divide the denominators equal 1, we use the to multiply the numerators, x & 6

our final answer= x+6/7

I hope this helps.

Answer:

₹66,000

Step-by-step explanation:

If 5/6 is 55,000 then just multiply 55,000 by the reciprocal  6/5 to get 66,000

Another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]

Given the rational function expressed as:

x = √rs

We can reconstruct the expression by writing it using exponents as shown;

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

Separate to have:

[tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]

Hence another expression for the given rational function is [tex]x =r^\frac{1}{2}s^\frac{1}{2}[/tex]

learn more on rational function here: https://brainly.com/question/1851758

#SPJ1

The volume of the given rectangular pyramid.

[tex]\large\boxed{Formula:V=\frac{1}{3}lbh}[/tex]

First, multiply the length (5), breadth (4) and height (3).

[tex]5×4×3[/tex]

[tex]= 60 \: cm [/tex]

Now, divide 60 by 3.

[tex]\frac{60}{3}[/tex]

[tex]\large\boxed{V= 20 \: {m}^{3}}[/tex]

Therefore, the volume of the given rectangular pyramid is 20 cubic meters.

[tex] - 50m + 10 - 3m + ( - 13) \\ - 50m + 10 - 3m - 13 \\ - 53m - 3[/tex]

Hope it helps

please give brainliest

Answer:

0, 2, 4, 6, 8

Step-by-step explanation:

substitute 1 for n in first term, 2 for n in second term, 3 for n in third term, 4 for n in fourth term, 5 for n in fifth term

2 (1) -2 = 0 first term

2 (2)-2 = 2 second

2 (3)-2 = 4 third

2 (4)-2 =6 fourth

2 (5)-2 =8 fifth

Answer:

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y).

Step-by-step explanation:

The rotation of angle 180 degree about origin is described below.

Rotation 180° about the origin is a geometric transformation that involves rotating a figure or shape around the point (0,0),

Also known as the origin, by an angle of 180 degrees.

This means that every point on the shape is moved to an equal distance away from the origin but on the opposite side of the origin.

This transformation is a reflection where the shape is flipped along,

the x-axis or y-axis or both, depending on the shape's orientation.

The rotation 180° about the origin is a common transformation in various geometrical applications, such as computer graphics, engineering, and physics.

It is a simple transformation that can be easily represented and performed using matrices or complex numbers.

Therefore,

rotation 180° about the origin is a geometric transformation that is important in various applications and involves rotating a shape around the origin by an angle of 180 degrees, resulting in a reflection of the shape across the x or y-axis.

Learn more about the angle visit:;

https://brainly.com/question/25716982d

#SPJ6

Answer:

Factory A = 1200

Factory B= 1350

Factory C= 1050

Factory D = 1100

Step-by-step explanation:

Factory B as the fastest rate of production

Given that ABCD is a parallelogram, the sum of its interior angles is:
360°

A parallelogram is a rectilinear two-dimensional figure with four sides whose opposite sides are parallel. See the image attached.

The sum of the exterior angles of any Triangle or any polygon is 360°. Hence, the sum of the exterior angles of CHFE (a polygon) is 360°.

The sides that are parallel to CE are:

FH

AD and

The side that are perpendicular to CE is side side HH, hence we can state that:

CE ⊥ EH, because both lines intersect each other at right angles.

Because the sum of angles in a triangle is 180° and we already have ∠CEH to be equal to ∠90° hence,

∠C + ∠H? = 180° - 90°

= 90°

The measure of the exterior angles of a regular pentagon is 72°

Learn more about Parallelograms at:
https://brainly.com/question/970600
#SPJ1

Answer:

Step-by-step explanation:

Solution

The distributive property is one of the handiest tools when factoring. You can't use it all the time, but it makes this problem so much easier. Use the distributive property to factor out the 2 from all three terms.

2(x^2 - 4x - 5)

Notice how much easier the problem got. There are only 2 integers that divide into 5. One of them is 5 and the other is one. So the solution is going to look like this

2(x    5) (x    1)

But what do you put in the space? Your choice is between a plus or a minus. Look to the middle term to find out. It is a minus 4. That means that the 5 must be minus because 5 is bigger than 1.

2(x - 5)(x     1 )

So what about the second bracket? It has to be plus. An odd number of minus signs always gives a minus. We used up the one minus we had so the one must have a plus in front of it.

2(x - 5)(x  +   1 )

The quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.

It is defined as the four-sided polygon in geometry having four edges and four corners.

We have:

The angle measures of quadrilateral RSTU are shown.

m∠R = (2x)°

m∠S = (3x – 35)°

m∠T = (x + 35)°

If R and T are congruent:

2x = x + 35

x = 35 degree

Opposite angles R and T are congruent to each other if x = 35.

Thus, the quadrilateral RSTU be a parallelogram if opposite angles R and T are congruent to each other if x = 35 option first is correct.

Learn more about the quadrilateral here:

brainly.com/question/6321910

#SPJ1

Answer:

It's c

Step-by-step explanation:

On edge 2023

Answer: this is the wrong answer

Step-by-step explanation:

Answer:

what does this mean. oh wAit iM dematerializinG mvxhkgd

hdgxmgxmgxkgzkgsktxktdktdktdktdtdkgd

IT doesn't make any sense

Step-by-step explanation:

please mark me as brainlest

Answer:

Option C

Step-by-step explanation:

A clock shows the hour hand slightly past 11 and the minute hand at two marks past the 4.

The matching of each transformed function is as follows;

g(x) = 2f(x) → y-intercept at (0,2)

h(x) = f(x) + 2 → asymptote of y=2

j(x) = f(x + 2) → y-intercept at (0,4)

m(x) = function decreases as x increases

A function is simply defined as a relationship between the inputs and the outputs. Now, we want to map each transformed function.

From the graph of this question as shown in the attached brainly link, the correct matching of each transformation of function f(x) = In x with a feature of the transformed function are as follows;

g(x) = 2f(x) → y-intercept at (0,2)

h(x) = f(x) + 2 → asymptote of y=2

j(x) = f(x + 2) → y-intercept at (0,4)

m(x) = function decreases as x increases

Read more about Transformations at; https://brainly.com/question/21515360

#SPJ1

Answer:

235500m3

Step-by-step explanation:

Volume of Cylinder= πr^2h

π=3.14, D=100m, r=D/2, r=100/2, r=50m, h=30m

πr^2h= 3.14×50×50×30

=3.14×75000

=235500m3

Answer:

B. x-2y=6

Step-by-step explanation:

Taking into account the definition of ratio and proportion, the airline should sell 440 tickets.

The ratio is the comparison of two quantities and is measured from the division of two values.

The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if [tex]\frac{a}{b}[/tex] corresponds to the ratio, then [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] equals a proportion.

An airplane flight has 374 seats. The probability that a person who buys a ticket actually goes on that flight is about 85%. The airline wants to fill all the seats (100%) on the flight.

This can be represented by the proportion:

[tex]\frac{374}{85}[/tex] = [tex]\frac{amount of tickets}{100}[/tex]

Solving:

amount of tickets= 100×[tex]\frac{374}{85}[/tex]

amount of tickets= 440

Finally, the airline should sell 440 tickets.

Learn more about proportion:

https://brainly.com/question/18437927

https://brainly.com/question/26485348

#SPJ1

The domain of the graph is x ≥ -4

From the given graph, we have the following highlights:

Greater than and equal to are represented by ≥.

This means that the symbol that completes the domain of the graph is ≥

Hence, the domain of the graph is x ≥ -4

Read more about domain at:

https://brainly.com/question/1770447

#SPJ1

Answer:

the first choice is not a polynomial because you can't divide by a variable.

Answer:

The answer is below :

Answer:

$2142.86

Step-by-step explanation:

The remaining part of her money, after spending 3/5 of it and depositing 1/8 of it is equal to $750.

===============================================================

Retracing the steps :

⇒ She put 1/8 of the remainder in the bank, which gives $750

⇒ R - R/8 = 750

⇒ 7R/8 = 750

⇒ R = 750/7 × 8

⇒ R = 107.142857 × 8

⇒ R = 857.142856

* Don't worry, we'll simplify at the end of the answer *

=============================================================

Now, this remainder is what was left after spending 3/5 of it.

⇒ T - 3/5T = 857.142856

⇒ 2/5T = 857.142856

⇒ T = 857.142856/2 × 5

⇒ T = 428.571428 × 5

⇒ T = $2142.86 (nearest cent)