the numbers being multiplied in a product are called

(a) The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) The slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec². The slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Both are walking at a velocity of 7.2 ft/sec at t=8 sec.

What is velocity?

(a) For Alicia,

m=(Δv/Δt)=(8-4)/(10-0)=4/10=0.4

f(t)=0.4t+4

for Damon,

m=(Δv/Δt)=(9-0)/(10-0)=9/10=0.9

g(t)=0.9t

The formula for velocity functions is:

f(t)=0.4t+4

g(t)=0.9t

(b) Value and meaning of the slope is

m for Alicia =0.4

Slope is determined (Δv/Δt)=(8-4)/(10-0)=4/10=0.4 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.4 ft/sec².

m for Damon=0.9

Slope is determined (Δv/Δt)=(9-0)/(10-0)=9/10=0.9 ft/sec².

So, the slope of the v-t graph gives us the acceleration which as found above is 0.9 ft/sec².

(c) Value and meaning of the average rate of change on the interval:

the average rate of change of Δ on the interval [4,8] =

[tex]\frac{Velocity\ at\ 8\ sec - Velocity\ at\ 4\ sec}{Time\ interval\ (8-4)\ sec}[/tex]

=(7.2-3.6)/(8-4)=(3.6/4)=0.9 ft/sec²

So, Damon is accelerating with 0.9 ft/sec² in intervals [4,8].

(d) Let both are walking with the same velocity at t sec.

So, Let's equate their velocities

0.4t+4=0.9t

t=4/0.5 = 8 sec

The velocity of Alicia at 8 sec = 0.4(8)+4 = 7.2 ft/sec

The velocity of Damon at 8 sec = 0.9(8) = 7.2 ft/sec

So, both are walking at a velocity of 7.2 ft/sec at t=8 sec.

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The polynomial function is V(x) = x^3 - 7x^2 + 10x and domain of x is (5,6]

Here we are given that the length of the box is x

Also, the width of the box should be 5 feet shorter than the length

Thus, width = x - 5

and the height should be 3 feet longer than the width

Thus, height = x - 5 + 3

= x - 2

Now the volume of the box = length × width × height

Volume = x (x-5) (x-2)

V(x) = (x^2 - 5x) (x-2)

V(x) = x^3 - 2x^2 - 5x^2 + 10x

V(x) = x^3 - 7x^2 + 10x

Now, looking at the options, we see that option C is eliminated.

Now, let us look at the domain of x

Since width cannot be negative (x-5) > 0

⇒ x > 5

Now in option A domain is (0, 6], but x cannot take values from (0,5). Thus, option A is eliminated.

Similarly, we can eliminate option B also since x cannot take values from (0, 2)

Thus, option 4 is the correct answer.

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Your question was incomplete. Check for the missing options below, in the figure attached.

Answer:

its 1/3

Step-by-step explanation:

see picture for referance

Answer:

The figure is reflected over y = -2

Step-by-step explanation:

If you draw a horizontal line through y = -2, so will see that every point is the same distance from y = -2 but in the opposite direction.  For example, Point w is 3 units above  y= -2 and w' is three units below y = -2. That is true for every point on original to the image.

By decomposing the figure into simpler ones, we conclude that the area of the irregular figure is 108 square inches.

Here we have an irregular figure that can be decomposed into 3 simpler figures, these are:

Remember that the area of a rectangle is the product between the two dimensions, so the areas of these 3 rectangles are:

a = 6in*8in = 48in^2

a' = 10in*4in = 40in^2

a'' = 5in*4in = 20in^2

Adding these areas we get:

48in^2 + 40in^2 + 20in^2 = 108 in^2

The area of the irregular figure is 108 square inches.

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Explanation:

A = last year's value = 290,700

B = this year's value = 312,000

C = change in values

C = B - A

C = 312,000 - 290,700 = 21,300

The positive result shows the increase of 21,300 more motorcycles made this year, compared to last year. A negative C value would represent a percent decrease.

Divide this change over the original.

C/A = (21,300)/(290,700) = 0.07327141382869

which is approximate. Let's say we rounded to four decimal places to get 0.0733 which then converts to the percentage 7.33%

Answer:

15.1

Step-by-step explanation:

Answer:

x<0: 0<x<1; x>1

Step-by-step explanation:

The denominator cannot be 0 (since division by 0 is undefined), meaning x cannot be 0 or 1.

So, the domain is x<0: 0<x<1; x>1.

To address the issue, we must understand what the converse of a statement implies. The statement's opposite is true if a=bc and a/b=c.

By switching the condition and the result, a conditional statement can be made into its opposite. The converse of a statement is q—->p if the statement is p—->q. In the provided question, the condition is stated as a/b=c, and the answer is a=bc if the condition holds.

We must create the result, the condition, and the condition will be the new result in order to discover the opposite of this assertion. As a result, a=bc will be the condition for converse, and a/b=c will be the outcome if the condition is satisfied.

As a result, if a=bc then a/b=c., the supplied sentence has the opposite meaning.

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-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Yes , the equation y =8ˣ  defines y as a function of x.

Yes, because to fulfill the condition of an equation to be a function, a particular value of x must produce only one value of y and y =8ˣ fulfills the condition. This can be also tested using horizontal line test, which only cuts the graph at one point only,

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The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)

Making the exponents to be similar gives:

(2.8 × 10⁻⁹) − (69 × 10⁻⁹)

Simplifying gives:

-6.62 * 10⁻⁸

The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸

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Answer:

Step-by-step explanation:

this app is helpful

Answer:

  A.  A(l) = l² -6l

Step-by-step explanation:

You want a quadratic function for the area of a rectangle whose width is 6 feet less than its length.

Let l (ell) represent the length of the rectangle in feet. Then the width will be 6 feet less, or (l -6). The area is the product of length and width:

  A = LW

  A(l) = l(l -6)

  A(l) = l² -6l . . . . . . use the distributive property to eliminate parentheses

Answer:

w≈8.33

Step-by-step explanation:

Greetings !

Firstly recall rectangle area formula

Thus,

[tex]area \: of \: rectangle \: = length \: \times \: width[/tex]

Given values:-

require value:-

solution/ work-out:-

[tex]width = \: \frac{area \: of \: rectangle}{length} [/tex]

[tex]w = \frac{125}{15} [/tex]

[tex]w = 8.333...[/tex]

Hope it helps !!!

Answer:

9 26/30 or 9 13/15

Step-by-step explanation:

20/30 6/30

Answer:

9 13/15

Step-by-step explanation:

The position of town B in cartesian plane is 6.4 cm in 1st quadrant at an angle of 70°.

As per the question statement, we are given that a diagram which shows the position of town A and the scale of 1 cm representing 10 km.

Town B is 64 km from town A on a bearing of 070°. We are supposed to tell the position of town B.

Let's assume that town A lies at origin in cartesian plane and as 1 cm represents 10 km therefore,

[tex]1cm = 10 km\\1 km = 0.1 cm\\64 km = 64*0.1=6.4 cm[/tex]

The town B is 6.4 cm from the origin and as the angle is given as  70° so the position of town B is in 1st quadrant.

Therefore the position of town B is 6.4 cm in 1st quadrant at an angle of 70° when town A lies at origin in the cartesian plane.

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Answer:

Negative

Step-by-step explanation:

x + 5 = -8

Subtract 5 from both sides to get x by itself

x = -13

Answer:

X is negative

Step-by-step explanation:

32 ounces of pure silver were used to make the silver alloy.

Here, we are given that a silversmith combines pure silver that costs $34.48 per ounce with 51 oz of a silver alloy that cost $25.35 per ounce.

Let the amount of pure silver = x oz

Cost of pure silver = $34.48 per ounce

Thus, total cost of pure silver = $34.48x

Similarly, amount of silver alloy = 51 oz

Cost of silver alloy = $25.35 per ounce

Thus, total cost of silver alloy = 25.35 x 51 = $1292.85

Now, the total weight of the new silver allow formed = (x + 51) Oz

and the cost of this new allow = $28.87 per ounce

Thus, the total weight of the new alloy = $28.87 (x + 51)

Hence, we can form the following equation-

$34.48x + $1292.85 = $28.87 (x + 51)

34.48x + 1292.85 = 28.87x + 1472.37

34.48x - 28.87x = 1472.37- 1292.85

5.61x = 179.52

x = 179.52/ 5.61

x= 32

Hence, 32 ounces of pure silver were used to make the silver alloy.

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In linear equation, the total value of the gasoline in the filled tank = $65605290

What is a formula for linear equations?

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

Radius  = 150/2 = 75 feet

height = 180 feet

A)

lateral surface area = 2 *pi*r*h = 2*pi* 75 *180 =84823

number of gallons of paint=84823/225 = 377 gallons

B)

Volume of cylinder= pi*r²h= pi*75^2*180 =3180862.5618

total value of the gasoline in the filled tank =3180862.5618 *7.5 *2.75 =$65605290

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The statement that best interprets the quotient is "there are 6( 1/4 ) two  - third in 4( 1/6 )".

In mathematics, the sum obtained by diluting two numbers is known as a quotient. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

Any integer may be used as the larger number in a fraction, which is a number that represents a percentage of the larger number. It is shaped like a denominator and a numerator.

For step 1:

The shaded part is:

4 + 1/6 = 4(1/6) = 25/6

Now, dividing the shaded part by the unshaded part,

( 25/6 ) / ( 2/3 ) = ( 25/6 ) × ( 3/2 )

( 25/6 ) / ( 2/3 ) = 25/4

( 25/6 ) / ( 2/3 ) = 6( 1/4 )

Hence, there are 6( 1/4 ) two  - third in 4( 1/6 ).

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Answer:

Width = 15 ft

Step-by-step explanation:

Given formula,

→ A = L × W

Let us assume that,

→ Length = 4x

→ Width = x

→ Area = 900 ft²

Then the value of width will be,

→ A = L × W

→ 900 = 4x × x

→ 4x² = 900

→ x² = 900/4

→ x = √225

→ [ x = 15 ft ]

Hence, the value of width is 15 ft.

The union of the sets is { 22, 33, 44, 55, 66 }

The union of sets can be defined as the sum of the elements of two or more sets without repetition of those elements.

It is also known as the combination of the all the elements of two or more sets.

It is denoted using the symbol , ' ∪ '

Given the sets;

The union of the sets is:

{ 22, 33, 44, 55, 66 }

Thus, the union of the sets is { 22, 33, 44, 55, 66 }

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The average number of viewers over the two weeks is 3.85 x 10 ^4

The given parameters are

Week 1 = 3.6 x 10 ^4 viewers

Week 2 = 4.1 x 10 ^4 viewers

The average is calculated as

Average = (Week 1 + Week 2)/2

This gives

Average = (3.6 x 10 ^4 + 4.1 x 10 ^4)/2

Evaluate the sum

Average = (7.7 x 10 ^4)/2

Evaluate the quotient

Average = 3.85 x 10 ^4

Hence, the average number of viewers over the two weeks is 3.85 x 10 ^4

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The coordinates of the point on the directed line segment is (-2, 4)

The points are given as

(-5, 8) and (-1, -8)

The ratio is given as

m : n = 3 : 1

The coordinates of the point are calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(3+ 1) * (3 * -1 + 1 * -5, 3 * -8 + 1 * 8)

Evaluate

Point = 1/4 * (-8, 16)

So, we have

Point = (-2, 4)

Hence, the coordinates of the point on the directed line segment is (-2, 4)

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Answer:

True

Step-by-step explanation:

We use definitions to help us in this problem. The definition of an integer is a whole number that is not a fraction or has any fractional value. This definition includes all whole numbers, so we know that all whole numbers can be classified as integers. That's one condition done. The definition of a rational number is a number that can be written as a fraction. All whole numbers can be written as a fraction (i.e. 12/1, -3/1, 10000/1). This means that all whole numbers are also rational numbers, giving us our final answer of True.

FINAL ANSWER: True

Solve the homogeneous equation

[tex]y'' + 3y' + 2y = 0[/tex]

Its characteristic equation is

[tex]r^2 + 3r + 2 = (r + 1) (r + 2) = 0[/tex]

with roots at [tex]r=-1[/tex] and [tex]r=-2[/tex], hence the characteristic solution is

[tex]y_c = C_1 e^{-x} + C_2 e^{-2x}[/tex]

For the nonhomogeneous equation, I'll use variation of parameters. We're looking for a solution of the form

[tex]y = u_1 y_1 + u_2 y_2[/tex]

to the equation

[tex]y'' + a(x) y'' + b(x) y = f(x)[/tex]

such that

[tex]\displaystyle u_1 = - \int \frac{y_2f(x)}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{y_1 f(x)}{W(y_1,y_2)} \, dx[/tex]

The Wronskian [tex]W(y_1,y_2)[/tex] of the two fundamental solutions [tex]y_1=e^{-x}[/tex] and [tex]y_2=e^{-2x}[/tex] is

[tex]W(y_1,y_2) = \begin{vmatrix} y_1 & y_2 \\ {y_1}' & {y_2}' \end{vmatrix} = -e^{-3x}[/tex]

Then we have

[tex]\displaystyle u_1 = - \int \frac{e^{-2x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = 4 \int e^{2x} \cos(3x) \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{e^{-x} \cdot 4e^x \cos(3x)}{-e^{-3x}} \, dx = -4 \int e^{3x} \cos(3x) \, dx[/tex]

Recall Euler's identity,

[tex]e^{(a+bi)t} = e^{at} (\cos(bt) + i \sin(bt))[/tex]

Then we have the general antiderivative

[tex]\displaystyle \int e^{(a+bi)t} \, dt = \frac1{a+bi} e^{(a+bi)t} + C = \frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C[/tex]

Taking the real parts of both sides, we have

[tex]\displaystyle \mathrm{Re}\left\{\int e^{(a+bi)t} \, dt \right\} = \mathrm{Re}\left\{\frac{a-bi}{a^2+b^2} e^{(a+bi)t} + C\right\} \\\\ \int\,\mathrm{Re}\left\{e^{(a+bi)t}\right\} \, dt = \frac{e^{at}}{a^2+b^2} \mathrm{Re}\left\{(a-bi)(\cos(bt) + i \sin(bt))\right\} + C \\\\ \int e^{at} \cos(bt) \, dt = \frac{e^{at}}{a^2+b^2} (a\cos(bt)+b\sin(bt)) + C[/tex]

so that

[tex]\displaystyle u_1 = 4 \int e^{2x} \cos(3x) \, dx = \frac{4e^{2x}}{13} (2\cos(3x) + 3 \sin(3x))[/tex]

and

[tex]\displaystyle u_2 = -4 \int e^{3x} \cos(3x) \, dx = -\frac{2e^{3x}}3 (\cos(3x) + \sin(3x))[/tex]

We've found

[tex]y = u_1 y_1 + u_2 y_2[/tex]

[tex]\displaystyle y = \frac{4e^x}{13} (2\cos(3x) + 3 \sin(3x)) - \frac{2e^x}3 (\cos(3x) + \sin(3x))[/tex]

[tex]\displaystyle y = \frac2{39} e^x (5\sin(3x) - \cos(3x))[/tex]

Then the general solution to the differential equation is

[tex]\boxed{y(x) = C_1 e^{-x} + C_2 e^{-2x} + \frac2{39} e^x (5\sin(3x) - \cos(3x))}[/tex]