Write the sum as a product:
sin(13.2u) sin(6.8u) =

The definition of a rate of change is a rate that expresses how one quantity changes in relation to another quantity. When d(t)=2t is stated, the average speed from t=5 to t=9 is 28 feet or 2 feet per second.

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

d(t)=2t² is given, we need to find the average speed in feet per second from t=5 to t=9.

d(t)=2t².

The average rate of change is calculated by the formula:

d(t₂) - d(t₁) / t₂ - t₁

So plug in 5 as t₁ and 9 as t₂.

=> d(9) - d(5) / 9 - 5

=> (2×81) - (2×25) / 9 - 5

=> 162 - 50 / 4

=> 112 / 4 = 28

Therefore the average speed is 28 feet.

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Answer:30

Step-by-step explanation:

30*30=900

Answer: 30

Step-by-step explanation:

Okay so first you have 30mm right but in total you need 900 so here is a shortcut you just have to multiply 30 x 30 and you get 900 so the answer is 900 (I would know because I am learning about this)

(a) The net change is -1

(b) The average rate of change is -1/5.

Net change of a function is the difference of the output values corresponding to two input values.

Consider the function y = f(x).

Net change from a point x = a to x = b is,

Net change = f(b) - f(a)

Average rate of change of a function from x = a to x = b is,

Average rate of change = [f(b) - f(a)] / [b - a]

The points are (0, 5) and (5, 4).

Here, the value of x on the indicated points are x = 0 and x = 5.

The value of y are f(0) = 5 and f(5) = 4.

Net change = f(5) - f(0) = 4 - 5 = -1

Average rate of change = [f(5) - f(0)] / [5 - 0] = (4 - 5) / 5 = -1/5

Hence the net change is -1 and the average rate of change is -1/5.

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Answer:

0.413333333

Step-by-step explanation:

hope this helps

Answer:

0,39 because if you do 0.496÷1.2=0,3908333333 and If you round up is 0,39

Answer:

after 42 months he has $2,696 in interest

compound quarterly is equivalent to annual rate of 4.835%

Part b

after 42 months he has $2,713 compound continuously

the diffrence is $17  

15000 + 4.75% · 42  compound quarterly is $2,696

15000 + 4.75% · 42 compound continuously is $2,696

Answer:

Step-by-step explanation:

Stop posting FLVS questions on this website. It is illegal, and you can be expelled from the program. :)

The required graph of the inequality  |x| + 1 < 3  is shown in the image.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given inequality,
|x| + 1 < 3

|x| < 2
-2 < x < 2

So the graph of the given inequality is the region between -2 < x < 2.

Thus, the required graph of the inequality   |x| + 1 < 3 is shown in the image.

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The next step on solving completing square is  5(x² + 4x)=7 and

5 (x² + 4x + 4 )=7 + 20

Quadratic equation is the equation of the 2nd degree. One of the standard formulas for solving quadratic equations is 'ax² + bx + c = 0' here a, b, and c are constants or numerical coefficients. 'X' here is an unknown variable.

Case (I).

Given equation is

5x² + 20x- 7 =0

Firstly, we will add of 7 in both sides

5x² + 20x- 7 +7 = 7

Now, same variable of opposite sign is cancelled

5x² + 20x=7

Now, taking 5 common from left side

5(x² + 4x)=7

Case (II).

Given equation

5x² + 20x- 7 =0

Firstly, we will add of 7 in both sides

5x² + 20x= 7

Now, we will add of 20 in both sides

5x² + 20x + 20= 7 + 20

Now, taking common of 5 from left side

5 (x² + 4x + 4 )=7 + 20

So, The next step on solving completing square is  5(x² + 4x)=7 and

5 (x² + 4x + 4 )=7 + 20

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Answer:

The final answer is 7.

Step-by-step explanation:

Since the question states that Little's law can be applied to any single part of the store (for example, just the checkout line), then the average number of shoppers,

�

, in the checkout line at any time is

�

=

�

�

, where

�

is the number of shoppers entering the checkout line per minute and

�

is the average number of minutes each shopper spends in the checkout line.

Since 84 shoppers per hour make a purchase, 84 shoppers per hour enter the checkout line. However, this needs to be converted to the number of shoppers per minute (in order to be used with

�

=

5

). Since there are 60 minutes in one hour, the rate is

84

shoppers

per

hour

60

minutes

=

1.4

shoppers per minute. Using the given formula with

�

=

1.4

and

�

=

5

yields

�

=

�

�

=

(

1.4

)

(

5

)

=

7

Therefore, the average number of shoppers,

�

, in the checkout line at any time during business hours is 7.

The variable equation is  z=262+387 and the solution being z=649

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: z minus 387 is equal to 262 write in variable equation

we can construct an equation z-387=262

Simplifying we get  z=262+387

                                z=649

Hence, The variable equation is  z=262+387 and the solution being z=649

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Answer: Justin is 9 years old, Peyton is 6 years old and Matt is 24 years old

Step-by-step explanation: Let the age of Justin be x years .

And Peyton is three years younger than Justin, therefore Peyton age is

(x-3) years

And Matt is four times as old as Peyton, therefore Matt age is

4(x-3) years

And it is given that

x + x - 3 + 4 (x - 3) = 39

x + x - 3 + 4x - 12 = 39

6x - 15 = 39

6x = 54

x = 9

Therefore , Justin is 9 years old, Peyton is 6 years old and Matt is 24 years old .

The complete proof by giving the correct reasons is explained below.

A segment is a drawn straight line which has two end points. It may be divided into a number of sub-segments.

The complete proof which explains the correct reasons are given as:

                  STATEMENT                     REASON

1. AC = AB + BC                                   Addition property of a segment

2. DE = DB + BE                                   Addition property of a segment

3. AC = DE                                           Equality property of line segments

4. AB + BC = DB + BE                        Congruent parts of equal line segments

5. AB = BE                                           Given

6. BE + BC = DB + BE                         Substitution property

7. BC = DB                                          Congruent parts of equal line segments

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need more info. add the question in but try the whole question.

When Δ BCF is congruent to Δ BDE, then the value of x is obtained as 10.

What is congruence?

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.

It is given that Δ BCF ~ Δ BDE.

Since the triangles are congruent so, it can be written that -

BC/BD = BF/BE

Substituting the values in the equation -

52/(52 + 39) = 56/[(56) + (5x-8)]

Simplifying the equation -

52/91 = 56/[(56) + (5x-8)]

4/7 = 56/(48+5x)

4(48+5x) = 56 × 7

192 + 20x = 392

20x = 392 - 192

20x = 200

x = 200/20

x = 10

Therefore, the value of x is obtained as 10.

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Answer: To calculate the final value of an investment with compound interest, you can use the formula:

A = P(1 + r/n)^(nt)

where:

A = final amount

P = initial investment (principal)

r = annual interest rate (expressed as a decimal)

n = number of times interest is compounded per year

t = number of years the investment is held

In this case, we have:

P = 170000

r = 0.04 (4% expressed as a decimal)

n = 2 (semiannually)

t = 7

So plugging these values into the formula:

A = 170000(1 + 0.04/2)^(2*7)

A = 170000(1.02)^14

A = 170000(1.286816)

A = 217,912.72

The final value of the investment after 7 years is 217,912.72 baht.

Please note that this is a simple interest calculation, and in real world some other factors like taxes, fees, etc should be taken into account.

Step-by-step explanation:

The length of EF is 10.63 units.

The formula to find the distance between the two points is usually given by d=√((c – a)² + (d– b)²).

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Given:

From the graph the coordinates of E( -3, -4) and F(4, 4).

Using Distance Formula

EF = √ (4 - (-3))² + ( 4 -(-4))²

EF = √ (4+ 3)² + (4+4)²

EF = √ 7² + 8²

EF = √ 49 + 64

EF = √113

EF = 10.63 units

Hence, the length of EF = 10.63 units

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The function that represents the point (x, y) being reflected across the y-axis is F(x, y) = F(-x, y)

A point (x, y) can be reflected across the y-axis by multiplying the x-coordinate by -1.

This is because the y-axis is a vertical line running through the center of a coordinate plane, and reflecting a point across this line means reversing its position along the horizontal (x) axis.

So, to reflect a point (x, y) across the y-axis, the function can be represented as:

f(x, y) = (-x, y)

This function takes in the coordinates (x, y) of a point and returns the new coordinates (-x, y) after reflecting it across the y-axis.

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Answer: So in the image here, you are able to use the point thingamajig so here are the coordinates you would graph

(-2,-1)

(2 , 1 )

(4 , 2 )

(6 , 3 )

but after that i have no idea on what the inverse and direct operations are!

but i hope ^ that helps!!!

Their ages Mario is four years old, while Martina is five.

If a person is "x" years old now, then "n" years from now, that person will be "x + n" years old. The age of this would be equal to x - n years n years ago.

Mario is four years old, while Martina is five.

Explanation:

2x -y = 6 adding two to the number 4x -2y = 12

3x + 2y = 23

The sum of the two figures

4x - 2y = 12

3x + 2y = 23

7x = 35 by 7 multiply both sides.

Marina is x years old.

2x - y = 6 Put 5 in place of x, then figure out y.

2(5) -y = 6

10 -y = 6 From both sides, deduct 10

-y = -4 Divide the two sides by -1.

Mario has a value of 4.  

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The solution to the algebra word roblem is; After 1 months, there will be 10 of each on staff.

We are given;

Initial number of junior residents = 9

Initial number of senior residents = 6

Rate of hiring  junior residents = 1 per month

Rate of hiring  senior residents = 4 per month

If number of months is x, then we have that;

9 + x = 6 + 4 x

Rearranging, we have;

4x - x = 9 - 6

3x = 3

x = 3/3

x = 1 months

Thus;

9 + x = 9 + 1

= 10 staff

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the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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Answer:

I think 0.15b would be a no because that is just what a customer would tip.

15b is also a no because that is 15 times the price of the bill.

b + 0.15b is a yes because you are adding the bill and 15% of the bill as a tip.

1.15b is a no because you are multiplying the bill by 1.15.

1.015 is a no because you're multiplying the bill by 1.015.

b + (15/100)b is a yes because you are adding the bill and 15% out of 100% of the bill as a tip.

b + 0.15 is a no because you would be tipping them 15 cents, not 15% of the bill.

The explicit Sequence is [tex]a_n = 3. 6^{n-1[/tex].

The 10 term of the sequence is 3,023,308.

A series of terms is referred to as a geometric progression if each next term is produced by multiplying each previous term by a fixed amount. (GP), whereas the common ratio is the name given to the constant value.

Given:

3, 18, 108, 648, ...

First term, a= 3

common ratio, r= 18/3

                          = 6

Now, using geometric sequence

[tex]a_n = a. r^{n-1[/tex]

So, the explicit function is

[tex]a_n = 3. 6^{n-1[/tex]

let us find the fifth term

[tex]a_5[/tex] = 3. [tex]6^4[/tex]

    = 3888

and, the 10 term of the sequence is

[tex]a_5[/tex] = 3. [tex]6^9[/tex]

    = 3,023,308

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Answer:

x−y=−2

4x−y=4

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

x−y=−2,4x−y=4

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

x−y=−2

Add y to both sides of the equation.

x=y−2

Substitute y−2 for x in the other equation, 4x−y=4.

4(y−2)−y=4

Multiply 4 times y−2.

4y−8−y=4

Add 4y to −y.

3y−8=4

Add 8 to both sides of the equation.

3y=12

Divide both sides by 3.

y=4

Substitute 4 for y in x=y−2. Because the resulting equation contains only one variable, you can solve for x directly.

x=4−2

Add −2 to 4.

x=2

The system is now solved

The value of x is 25.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The given figure is an equilateral triangle.

AB = BC = AC

Now,

3x - 5 = 2x + 20 = 4x - 30

Take any two sides.

Now,

Solve for x.

3x - 5 = 2x + 20

3x - 2x = 20 + 5

x = 25

or

Solve for x.

2x + 20 = 4x - 30

20 + 30 = 4x - 2x

50 = 2x

x = 25

or

Solve for x.

3x - 5 = 4x - 30

30 - 5 = 4x - 3x

25 = x

x = 25

Thus,

The value of x is 25.

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Answer:

1/24

Step-by-step explanation:

[tex]a^{-1} =\frac{1}{a} \\24^{-1} =\frac{1}{24}[/tex]

A negative exponent is converted to a fraction while the power goes to the base which is at the denominator.

Evaluation of the  amount is 42.78.

Evaluated; assessing Identify or set the value of anything by using a transitive verb to determine its importance, value, or condition, generally by meticulous analysis and research.

The act of evaluating or determining the standard, significance, quantity, or worth of something: It will be necessary to wait until all the data has been gathered before evaluating this new medicine.

Process, impact, result, and summative assessment are the four primary forms of evaluation.

$32.01

$0.76

$10.00

Evaluation of the  amount is

32.01 + 0.76 + 10.00 = 42.78.

Evaluation of the  amount is 42.78.

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For the given similar triangles ΔBCF ~ΔBDE, the value of x is, 10

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔBCF

one segment CF which is intersecting sides BD & BE

ΔBDE has one similar triangle inside, which is ΔBCF

Triangles ΔBDEand ΔBCF similar,

So, we can say ΔBCF ~ΔBDE

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, BD/BE = BC/BF

⇒ 91/(56+ 5X-8) = 52/56

⇒ 65X + 624 = 1274

⇒ 1274-624 = 65X

⇒ X = 10

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Answer: I'm sorry, I am a text-based user and do not have the capability to drag tiles. However, I can provide you with a written proof of the statement "ABCD is a parallelogram" given the given information "AD = BC and AD || BC":

Statements:

AD = BC

AD || BC

Angles A and C are congruent

Angles B and D are congruent

Opposite sides are equal in length

Reasons:

Given

Given

If two lines are parallel, then the corresponding angles are congruent

If two lines are parallel, then the corresponding angles are congruent

If opposite angles of a quadrilateral are congruent, then the opposite sides are equal in length

Therefore, ABCD is a parallelogram.

Step-by-step explanation:

Answer: x is equal to 0.88

Step-by-step explanation:

To solve for x, we can start by simplifying both sides of the equation:

89(54x - 36) + 2 = -34(-40 + 16x) + 90x

First we can simplify the left side of the equation:

89(54x - 36) + 2 = 4846x - 3204 + 2 = 4846x - 3202

Now we can simplify the right side of the equation:

-34(-40 + 16x) + 90x = -34(16x - 40) + 90x = -544x + 1360 + 90x = -454x + 1360

Now we can set the left side of the equation equal to the right side and solve for x:

4846x - 3202 = -454x + 1360

Now we can add 454x to both sides and subtract 1360 from both sides

5,300x = 4660

x = 4660/5300

x = 0.88

Therefore, x is equal to 0.88

Answer:

0.86

Step-by-step explanation:

89(54x-36)+2=-34(-40+16x)+90x

4806x-3204+2=1360-544x+90x

4806x+500x-90x=3204-2+1360

5260x=4562

x= 4562/5260

x=0.86

Answer:

below

Step-by-step explanation:

(8)(-2)(-1)   =   8 * -2 * -1 = 8 * 2 = 16