I've experiencing for a while but this is Finding missing angles. Please help me!!​

a.

a^2 + b^2 = c^2

The legs are a and b. c is the hypotenuse.

Let a = 6x + 9y; b = 8x + 12y; c = 10x + 15y

The equation is:

(6x + 9y)^2 + (8x + 12y)^2 = (10x + 15y)^2

b.

Now we square each binomial and combine like terms on each side.

36x^2 + 108xy + 81y^2 + 64x^2 + 192 xy + 144y = 100x^2 + 300xy + 225y^2

36x^2 + 64x^2 + 108xy + 192xy + 81y^2 + 144y^2 = 100x^2 + 300xy + 225y^2

100x^2 + 300xy + 225y^2 = 100x^2 + 300xy + 225y^2

The two sides are equal, so it is an identity.

Answer:

see below

Step-by-step explanation:

a  The pythagorean theorem is a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + b^2 = c^2

(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2

b solve

(6x+9y)^2 + (8x+12y)^2 = (10x + 15y)^2

(6x+9y)(6x+9y) + (8x+12y)(8x+12y) = (10x + 15y)(10x+15y)

Factor out the common factors

3(2x+3y)3(2x+3y) + 4(2x+3y)4(2x+3y) = 5(2x+3y)5(2x+3y)

Rearrange

9 (2x+3y)^2 +16 (2x+3y)^2 = 25(2x+3y)^2

Divide each side by(2x+3y)^2

9 (2x+3y)^2/ (2x+3y)^2 +16 (2x+3y)^2/(2x+3y)^2 = 25(2x+3y)^2/(2x+3y)^2

9 + 16 = 25

25=25

This is true, so it is an identity

Answer:

Step-by-step explanation:

5/3lit

Answer:young boy

Step-by-step explanation:two two

Answer:

Initial expected value = 7.3 $

If one more $20 bill and one more $10 bill are added to the bag expected value = 8.57 $

Step-by-step explanation:

a) Total number of bills = 2 + 1 + 4 + 3 = 10

[tex]\texttt{Probability of picking 20 dollar bill}=\frac{2}{10}=0.2\\\\\texttt{Probability of picking 10 dollar bill}=\frac{1}{10}=0.1\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{10}=0.4\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{10}=0.3[/tex]

Expected value = 20 x 0.2 + 10 x 0.1 + 5 x 0.4 + 1 x 0.3 = 7.3$

b)If one more $20 bill and one more $10 bill are added to the bag

Total number of bills = 3 + 2+ 4 + 3 = 12

[tex]\texttt{Probability of picking 20 dollar bill}=\frac{3}{12}=0.25\\\\\texttt{Probability of picking 10 dollar bill}=\frac{2}{12}=0.167\\\\\texttt{Probability of picking 5 dollar bill}=\frac{4}{12}=0.333\\\\\texttt{Probability of picking 1 dollar bill}=\frac{3}{12}=0.25[/tex]

Expected value = 20 x 0.25 + 10 x 0.167 + 5 x 0.333 + 1 x 0.25 = 8.57$            

Answer:

$7.30 for the first one and $8.58 for the second one

Step-by-step explanation:

ANSWER FOR PLATO

Answer:

c. no solution

Step-by-step explanation:

6d + 3f = 12

2d = 8 ­- f

Multiply the second equation by 3

3*2d = 3(8-f)

6d = 24-3f

Substitute into the first equation for 6d

(24-3f) +3f = 12

Combine like terms

24 =12

This is never true, so there are no solutions

Answer:

c. No Solution.

Step-by-step explanation:

6d + 3f = 12

2d = 8 ­- f

Rearranging the second equation:

2d + f = 8  Multiply this equation by 3:

6d + 3f = 24

Note that the left side of this equation = the left side of the first equation but the right sides are different. So this system does not make sense and there are No Solutions.

Answer:

Total online purchase is $26.473 .

Step-by-step explanation:

As given

Natasha places an online order for plate holders to display her antique plates.

Natasha orders 3 large holders for $4.95 each, 2 medium holders for $3.25 each and 2 small holders for $1.75 each.

Thus

Total purchase of Natasha = Number of large holders × Cost of each large holder + Number of medium holders × Cost of each medium holder +  Number of small holders × Cost of each small holder .

Put all the values in the above

Total purchase of Natasha = 3 × $4.95+ 2 × $3.25 + 2 × $1.75

                                            = $14.85 + $6.5 + $3.5

                                            = $ 24.85

As given

Site has a promotional offer of 15% off on all purchases.

15% is written in the decimal form

[tex]= \frac{15}{100}[/tex]

= 0.15

Discount amount = 0.15 × Total purchase of Natasha .

                             = 0.15 × $24.85

                             = $ 3.7275

Thus

Total purchase of Natasha after discount = Total purchase of Natasha - Discount amount .

                                                                     = $24.85 - $3.7275

                                                                     = $ 21.1225

As given

Natasha must pay a flat rate of $5.35 for shipping and handling.

Thus

Total online purchase of Natasha = Total purchase of Natasha after discount + Flat rate for shipping and handling .

Total online purchase of Natasha = $21.1225 + $5.35

                                                        = $ 26.4725

                                                        = $26.473 (Approx)

Therefore the total online purchase is $26.473 .

Answer:

the order Natasha places is as follows;

3 large holders - $4.95 each - 4.95*3 = 14.85

2 medium holders - $3.25 each - 3.25*2 = 6.5 

2 small holders - $1.75 each - 1.75*2 = 3.5

Total value for purchases is - 14.85 + 6.5 + 3.5 = 24.85

she gets 15% for all purchases therefore she has to pay only 85% of the purchase value 

$24.85 * 85% = $21.1225

She has to pay an additional $5.35 for shipping and handling 

therefore the total amount she has to pay is = 21.1225 + 5.35

total amount = 26.4725 this rounded off to second decimal place,

correct answer 

C - $26.47

Answer:

Step-by-step explanation:

The graph of even function is symmetrical about the y-axis.

The graph of odd function is symmetrical about the origin.

A. even

B. odd

C. odd

D. neither

(look at the picture)

Answer:

I would be A

Step-by-step explanation:

It has symmetry across the y axis

Answer:

  A.  20,000 square feet

Step-by-step explanation:

The description is that of a rectangle 200 ft long and 100 ft wide. The area is the product of those dimensions:

  area = (200 ft)(100 ft) = 20,000 ft²

The correct option is option A.

The area of a rectangle is the region covered by the rectangle in a two-dimensional plane.

The formula to finding the area of the rectangle is,

[tex]A=l\times b[/tex]

It is given that,

Length=100 ft

Breadth=200 ft

[tex]A=l\times b[/tex]

Now, substituting the given values into the above formula we get,

[tex]A=200 \times 100\\A=20000[/tex]

The required area is 20,000 square feet.

Learn more about the topic area of the rectangle:

https://brainly.com/question/11202023

Answer:-28x^4y^2(-4x^3y^6)

Step-by-step explanation: Distribute and add exponents, put in parentheses to make it easier to understand but it's not necessary for the final answer.

Answer:

[tex]-28x^4y^6[/tex]

Step-by-step explanation:

The given expression is

[tex]-4x^3y^2(7xy^4)[/tex]

We need to place the indicated product in the proper location on the grid.

The given expression can be rewritten as

[tex](-4\times 7)(x^3x)(y^2y^4)[/tex]

[tex]-28(x^3x)(y^2y^4)[/tex]

Using the product property of exponent, we get

[tex]-28\times x^{3+1}\times y^{2+4}[/tex]          [tex][\because a^ma^n=a^{m+n}][/tex]

[tex]-28\times x^{4}\times y^{6}[/tex]

[tex]-28x^{4}y^{6}[/tex]

Therefore the answer of given product is [tex]-28x^{4}y^{6}[/tex].

Answer:

(7.5-2.1) /2

If the shortest side measures 2.1 m.

7.5-2.1 =5.4. Then divide by 2 each side is 2.7m

Answer:

The equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.

Step-by-step explanation:

Perimeter of the isosceles triangle = 7.5 m

Length of the shortest side = 2.1 m

Let the length of each of the other sides of the triangle = x meter

Then the equation for the perimeter of the triangle becomes:

Sum of 3 sides f the triangle = 7.5 m

=> 2*x + 2.1 = 7.5

=> 2*x = 7.5 - 2.1 = 5.4

=> x = 5.4/2 = 2.7 m

So the relevant equation for finding the value of x is 2x + 2.1 = 7.5 and the value of x is 2.7 m.

Answer:

The zeros of our function f is at x=-1.

The discontinuity is at x=-4.

These are correct if the function is [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] .

Please let know if I did not interpret your function correctly.

Step-by-step explanation:

I imagine you mean [tex]f(x)=\frac{x^2+5x+4}{x+4}[/tex] but please correct me if I'm wrong.

The zero's of a rational expression occur from it's numerator.

That is, in a fraction, the only thing that makes that fraction 0 is it's numerator.

So we need to solve [tex]x^2+5x+4=0[/tex] for x.

The cool thing is this one is not bad to factor since the coefficient of x^2 is 1.  When the coefficient of x^2 is 1 and you have a quadratic, all you have to do is ask yourself what multiplies to be c and adds to be b.

[tex]x^2+5x+4[/tex] comparing to [tex]ax^2+bx+c[/tex] gives you [tex]a=1,b=5,c=4[/tex].

So we are looking for two numbers that multiply to be c and add to be b.

We are looking for two numbers that multiply to be 4 and add to be 5.

Those numbers are 1 and 4 since 1(4)=4 and 1+4=5.

The factored form of [tex]x^2+5x+4[/tex] is [tex](x+1)(x+4)[/tex].

So [tex]x^2+5x+4=0[/tex] becomes  [tex](x+1)(x+4)=0[/tex].

If you have a product equals 0 then at least one of the factors is 0.

So we need to solve x+1=0  and x+4=0.

x+1=0 when x=-1 (subtracted 1 on both sides to get this).

x+4=0 when x=-4 (subtracted 4 on both sides to get this).

The zeros of our function f is at x=-1 and x=-4.

Now to find where it is discontinuous.  We have to think 'oh this is a fraction and I can't divide by 0 but when is my denominator 0'.  If the value for the variable is not obvious to you when the denominator is 0, just solve x+4=0.

x+4=0 when x=-4 (subtracted 4 on both sides).

So we have a contradiction at one of the zeros so x=-4 can't be a zero.  

The discontinuity is at x=-4.

Answer:

This function is discontinuous at x = 4, and has a zero at x = -1.

Step-by-step explanation:

If x = -4, the denominator will be zero and thus the function will be undefined.  Thus, the discontinuity is at x = -4.

To find the zero(s):  Set the numerator = to 0, obtaining

x^2+5x+4 = 0.  Factoring this, we get (x + 4)(x + 1) = 0.  Thus, we have a zero at x = -1.  

Notice that f(x) can be rewritten as

         x^2 + 5x + 4       (x+4)(x+1)

f(x) = -------------------- = ---------------- = x + 1 for all x other than x = -4.

               x + 4                 (x+4)

This function is discontinuous at x = 4, and has a zero at x = -1.

Answer:

integer  3 represents elevator final position with respect to the main floor.

Step-by-step explanation:

Given  : An elevator starts at the main floor and goes up 8 floors. It then goes back down 5 floors.

To find : What integer represents elevator final position with respect to the main floor.

Solution : We have given

Elevator starts at the main floor and goes up floors = + 8 ( for up).

Then goes back down floor  =  - 5  ( - sign for down).

Final position  :  8 - 5 = 3 .

It will reach at 3 floor from the main floor .

Therefore, integer  3 represents elevator final position with respect to the main floor.

Answer:

2.25

Step-by-step explanation:

The total frequency is:

20 + 12 + 6 + 2 = 40

Calculate the probability of each score:

P(X=3) = 20/40 = 0.50

P(X=2) = 12/40 = 0.30

P(X=1) = 6/40 = 0.15

P(X=0) = 2/40 = 0.05

So the expected value is:

E = (3)(0.50) + (2)(0.30) + (1)(0.15) + (0)(0.05)

E = 2.25

Answer:

  V = 99π in³; S = 81π in²

Step-by-step explanation:

Volume is that of a hemisphere of radius 3 in together with that of a cylinder of radius 3 in and height 9 in.

  V = (2/3)πr³ +πr²h = (πr²)(2/3r +h)

  = 9π(2 +9) = 99π . . . . in³

__

The area is that of a hemisphere, the side of the cylinder, and the circular bottom of the cylinder.

  S = 2πr² +2πrh +πr² = πr(2r +2h +r)

  S = 3π(6+18 +3) = 81π . . . . in²

AnswEr:

Add the two, to both sides. -2+2=0

So, the equation would like like this

x -2= 9

+2 +2

Then solve, the 2’s cancel out leaving you with x by itself. Finishing the equation to look like this-> x=11

Answer:

g(x) = -5x

Step-by-step explanation:

If the point from f(x) is plotted using the slope, the coordinate would be located at (1, 5) since the slope of 5x tells us we go up 5 units from the origin and over 1 unit to the right.  That point will be reflected through the x-axis to land at (1, -5).  That means that the equation of the new line would be

g(x) = -5x

A reflection across the x -axis would have the opposite value of the output.

If the value is a positive value, the mirrored value would be a negative value.

The function of g(x) would be g(x) = -5x

Answer:

(- 4, 1 )

Step-by-step explanation:

A translation (x + 1), y - 3 ) means add 1 to the original x- coordinate and subtract 3 from the original y- coordinate.

B = (- 5, 4 ), thus

B' = (- 5 + 1, 4 - 3 ) = (- 4, 1 )

[tex]B=(-5,4)\\\\B'=(-5+1,4-3)\\B'=(-4,1)[/tex]

Answer:

A.

Step-by-step explanation:

If

[tex]y=x^2+2x+7[/tex] AND

y = x + 7, then by the transitive property of equality:

[tex]x^2+2x+7=x+7[/tex]

We can solve for the values of x by getting everything on one side of the equals sign and then solving for x:

[tex]x^2+x=0[/tex]

We can factor out the common x to get:

x(x + 1) = 0

which tells us by the Zero Product Property that either

x = 0 and/or x + 1 = 0 and x = -1

We are expecting 2 solutions for x since this is a second degree polynomial.  We will sub both -1 and 0 into y = x + 7 to solve for the corresponding values of y

y = 0 + 7 so

y = 7 and the coordinate is (0, 7)

y = -1 + 7 so

y = 6 and the coordinate is (-1, 6)

Final answer:

The total number of hours worked by the person is calculated by adding the working times from two segments of the day. The morning session contributes 3 hours and 15 minutes, and the afternoon session adds 4 hours and 45 minutes. The combined total working hours are 8 hours.

Explanation:

To calculate the total number of hours worked by the person, we need to break down their workday into segments and sum up the time they spent working.

Morning session: From 8:30 AM to 11:45 AM

Afternoon session: From 12:30 PM to 5:15 PM

Calculating each session separately, we get:

Morning session: 11:45 AM - 8:30 AM = 3 hours and 15 minutes

Afternoon session: 5:15 PM - 12:30 PM = 4 hours and 45 minutes

Adding both sessions together:

3 hours and 15 minutes + 4 hours and 45 minutes = 8 hours total

Final Calculation:

3 hours 15 minutes + 4 hours 45 minutes = 7 hours 60 minutes = 8 hours

Therefore, the total number of hours worked by this person was 8 hours.

Answer:

[tex]\$105.47[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$250\\r=25\%=25/100=0.25\\x=3\ years[/tex]

substitute

[tex]V=250(1-0.25)^{3}[/tex]  

[tex]V=250(0.75)^{3}[/tex]  

[tex]V=\$105.47[/tex]  

Answer and Step-by-step explanation:

After three years the worth of it will be [tex]$105.47[/tex]

We know that each year, it's worth 75% of what it was, giving us :

[tex]=0.75*W[/tex] (Note that "W" means "Worth")

Now we calculate it in three years time so,

The first year is :[tex]250*0.75 = $187.50[/tex]

The second year is :[tex]187.5*0.75 = $140.625[/tex]

The third year is :[tex]140.625*0.75 = $105.47[/tex]

Now, we have our answer :

After three years time the worth of it is [tex]$105.47[/tex]

It takes 24 hours for the number of bacteria to increase to 300.

We have given that,

A scientist running an experiment starts with 100 bacteria cells.

These bacteria double their population every 15 hours.

Find how long it takes for the bacteria cells to increase to 300.

Use the formula, where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number.

[tex]P_0=100[/tex]

[tex]d=15[/tex]

[tex]P_t=P_02^{\frac{t}{d} }[/tex]

[tex]Pt=300=100\times2^{\frac{t}{15} }[/tex]

[tex]3=2^{\frac{t}{15}}[/tex]

[tex]\frac{t}{15} =1.6[/tex]

t=24

It takes 24 hours for the number of bacteria to increase to 300.

To learn more about the population increase visit:

https://brainly.com/question/11608113

#SPJ2

Step-by-step explanation:

[tex] { \sin(x) }^{4} { \tan(x) }^{2} [/tex]

[tex] { \sin(x) }^{4} \frac{ { \sin(x) }^{2} }{ { \cos(x) }^{2} } [/tex]

[tex] \frac{ ({ {1 - \cos(x) }^{2} })^{3} }{ { \cos(x) }^{2} } [/tex]

hopefully this helps, I'm rusty with my trig identities

Answer:

  sin⁴(x)tan²(x) = (10 -15cos(2x) +6cos(4x) -cos(6x))/(16(1 +cos(2x))

Step-by-step explanation:

The relevant identities are ...

[tex]\sin^4{x}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\\\\\tan^2{x}=\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\\cos{(a)}\cos{(b)}=\dfrac{\cos{(a+b)}+\cos{(a-b)}}{2}[/tex]

Then your product is ...

[tex]\sin^4{(x)}\tan^2{(x)}=\dfrac{3-4\cos{(2x)}+\cos{(4x)}}{8}\cdot\dfrac{1-\cos{(2x)}}{1+\cos{(2x)}}\\\\=\dfrac{3-4\cos{(2x)}+\cos{(4x)}-3\cos{(2x)}+4\cos^2{(2x)}-\cos{(4x)}\cos{(2x)}}{8(1+\cos{(2x)})}[/tex]

Collecting terms and using the identity for the product of cosines, we get ...

[tex]=\dfrac{3-7\cos{(2x)}+\cos{(4x)}+4\dfrac{1+\cos{(4x)}}{2}-\dfrac{\cos{(6x)}+\cos{(2x)}}{2}}{8(1+\cos{(2x)})}\\\\=\dfrac{10-15\cos{(2x)}+6\cos{(4x)}-\cos{(6x)}}{16(1+\cos{(2x)})}[/tex]

Answer:

Step-by-step explanation:

[tex]cosecant=\dfrac{hypotenuse}{opposite}\\\\\text{We have}\ opposite=3b,\ \text{and}\ hypotenuse=22.5,\ \text{and}\ \csc x=\dfrac{5}{4}.\\\\\text{Substitute:}\\\\\dfrac{5}{4}=\dfrac{22.5}{3b}\qquad\text{cross multiply}\\\\(5)(3b)=(4)(22.5)\\\\15b=90\qquad\text{divide both sides by 15}\\\\b=6[/tex]

Answer :

22.5 is the answer

MARK ME AS BRANILIST

Answer: 90

Step-by-step explanation:

Basically you reflect twice and then rotate it

Answer:

  FALSE

Step-by-step explanation:

Assuming ZY is a tangent, the measure of the arc will be twice the measure of the angle. If the angle ZYX is 23°, the measure of arc YX will be 46°.

Answer:

C. 3(2x2 – 4x + 3)

Step-by-step explanation:

6x^2 – 12x + 9

We can factor out a 3

3(2x^2 -4x+3)

Answer:

c. 3(2x^2-4x+3)

Step-by-step explanation:

The numbers 6, 12, and 9 are all multiples of 3. Divide everything by three, move it to the outside. There are no more common factors between all 3 terms so the trinomial is completely factored. Hope this helped, if not then I apologize.

Answer:

  not rational

Step-by-step explanation:

√2 is irrational. Any arithmetic operation (addition, subtraction, multiplication, division) performed on that number and any rational number will result in an irrational number (except for multiplication by 0).

Answer:

Step-by-step explanation:

Because of that sqrt, this expression is irrational.  A rational expression is one that can be expressed as the ratio of two integers.

Answer:

The lens is 1 inch from the mirror

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (0 , 0) and

 transverse axis parallel to the y-axis is y²/a² - x²/b² = 1

- The coordinates of the vertices are  (0 , ± a)

- The coordinates of the co-vertices are (± b , 0)  

- The coordinates of the foci are (0 , ± c) where c² = a² + b²

* Lets solve the problem

∵ The equation of the hyperbola is y²/16 - x²/9 = 1

∵ The form of the equation is y²/a² - x²/b² = 1

∴ a² = 16

∴ a = √16 = 4

∵ The coordinates of the vertices are  (0 , ± a)

∴ The coordinates of the vertices are  (0 , 4) , (0 , -4)

∴ b² = 9

∴ b = √9 = 3

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = √25 = 5

∵ The coordinates of the foci are (0 , ± c)

∴ The coordinates of the foci are (0 , 5) , (0 , -5)

∵ The camera is pointed towards the vertex of the hyperbolic mirror

   which is (0 , 4) and is positioned such that the lens is at the nearest

  focus to that vertex which is (0 , 5)

∴ The distance between the lens and the mirror equal the distance

   between the vertex and the focus

∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)

∴ The distance = 5 - 4 = 1 inch

* The lens is 1 inch from the mirror

Answer:

Rx-axis (P) is (-4 , 1)

Step-by-step explanation:

* Lets revise the reflection

- If point (x , y) reflected across the x-axis

 ∴ Its image is (x , -y)

- If point (x , y) reflected across the y-axis

 ∴ Its image is (-x , y)

- If point (x , y) reflected across the line y = x

 ∴ Its image is (y , x)

- If point (x , y) reflected across the line y = -x

 ∴ Its image is (-y , -x)

* Lets solve the problem

∵ The point P is (-4 , -1)

∵ Rx-axis (P) means reflect point P across the x-axis

∵ The reflection of a point (x , y) across the x-axis is (x , -y)

- That means we will change the sign of the y-coordinate of point P

∵ P = (-4 , -1)

∴ The y-coordinate of point P is -1 will change to 1

∴ The image of point P after reflection is (-4 , 1)

* Rx-axis (P) is (-4 , 1)

Answer:

P is -4 , 1

Step-by-step explanation:

Answer:

B) f(x)=1.74(0.81)^3x

and

D) f(x)=156(1-0.19)^x

Step-by-step explanation:

The percentage will always be where the b is, or inside the parentheses. You just have to make sure that, when not greater than 1, you must find out WHAT SUBTRACTS FROM 1 TO GET THAT RESULT. So ask yourself, what decimal number subtracts from 1 to get 0.81?

0.81 is the equivalent to (1-0.19) because (1-0.19) = 0.81.

0.19 is 19%, which is what we're looking for!

The exponential function with a percentage rate of change of 19% is option D) f(x)= 156(1-0.19)ˣ, because it reflects a 19% decrease with the base 0.81 (which is equal to 1 - 0.19).

Exponential functions have a percentage rate of change of 19%, we need to identify the function where the base of the exponent reflects this rate of change. The percentage rate of change can be represented as a decimal where a 19% increase is 1.19 and a 19% decrease is 0.81 (since 1 - 0.19 = 0.81).

Now, let's analyze the given functions:

A) f(x) = 3182(0.9)²ˣ does not represent a 19% rate of change.

B) f(x) = 1.74(0.81)³ˣ does not represent a 19% rate of change as it involves 0.81 to the power of 3x, not x.

C) f(x) = 0.2(0.38)ˣ/² does not represent a 19% rate of change.

D) f(x) = 156(1-0.19)ˣ does represent a 19% rate of change because the base is 0.81 which is equivalent to 1 - 0.19.

Therefore, the correct answer is option D).

Answer:

1/4

23in * 19 in.

Step-by-step explanation:

The scale factor is 1/4 and the channel size is  92*1/4 * 76 * 1/4

= 23 in * 19 in screen.

Answer:

Scale factor = 1/2,  New screen 46 in by 38 in.

Step-by-step explanation:

The dimensions of screen is 92 in. by 76 in.

It has a feature that splits the screen to allow you to watch 4 channels at once as shown in the below figure.

All four parts are equal.

Let the dimensions of new screen be x in. by y in.

[tex]2x=92[/tex] and [tex]2y=76[/tex]

Divide both sides by 2.

[tex]x=46[/tex] and [tex]y=38[/tex]

Scale factor is

[tex]\text{Scale factor}=\frac{\text{New dimension}}{\text{Corresponding original dimension}}[/tex]

[tex]\text{Scale factor}=\frac{46}{92}[/tex]

[tex]\text{Scale factor}=\frac{1}{2}[/tex]

Therefore, the scale factor is 1/2.