The function g(x) is defined as shown.
x-1, -2 g(x) = 2x+3, -1 6-X, X23

Answer:

32028.8 ounces

Step-by-step explanation:

We are given that there are 908 kilograms of of trial mix are in a bag and we are to find the number of ounces of the same amout of mix in the bag.

For that, we will use the ratio method.

We know that, 1 kg = 35.274, so:

[tex] \frac { 1 k g }{908kg} =\frac{35.274 oz}{x}[/tex]

[tex]x=32028.8[/tex]

Therefore, there are 32028.8 ounces of mix in the bag.

Final answer:

To find the amount of trail mix in ounces from 0.908 kilograms, convert the weight to grams and then to ounces using the conversion of 1 oz = 28.35 g, resulting in approximately 32.012 ounces of trail mix.

Explanation:

To convert the weight of the trail mix from kilograms to ounces, we need to use the conversion factor: 1 oz is produced by a mass of 28.35 g. First, convert the kilograms to grams by multiplying by 1000, because there are 1000 grams in a kilogram. Then, once we have the weight in grams, we can convert grams to ounces using the provided conversion rate.

Here's the calculation step by step:

Convert kilograms to grams: 0.908 kg × 1000 = 908 grams.

Convert grams to ounces: 908 g ÷ 28.35 g/oz = 32.012 ounces (rounded to three decimal places).

Thus, a bag that weighs 0.908 kilograms contains approximately 32.012 ounces of trail mix.

Answer:A

Step-by-step explanation:

Edge 21’

The true statement comparing the graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 is: The foci of both graphs are the same points.

When we look at graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 we would tend to see that the focus or foci of this two graph are the same point.

In order to know or determine that both graph are the same point or in order to determine each conic you have to focus on where the point crosses the axes.

Therefore the true statement comparing the graphs of x^2/6^2-Y^2/8^2 = 1 and x^2/8^2-y^2/6^2 = 1 is: The foci of both graphs are the same points.

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Answer:

L = 4d + 54

when d = 31 days

L = 4(31) + 54

L = 124 + 54

L = 178 miles

Step-by-step explanation:

The length of the road after 35 days of construction is 76 miles.

The length of the road after 35 days can be calculated using the given function L(d) = 41 + d, where L represents the length in miles and d represents the number of days of construction. To find the length after 35 days, we substitute d = 35 into the function.

L(35) = 41 + 35

L(35) = 76

Therefore, the length of the road after 35 days of construction is 76 miles.

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Answer:

Option C.

[tex]a=6\sqrt{3}[/tex]

[tex]b=12[/tex]

[tex]c=6\sqrt{2}[/tex]

Step-by-step explanation:

step 1

Find the value of a

we know that

[tex]tan(60\°)=a/6[/tex]

Remember that

[tex]tan(60\°)=\sqrt{3}[/tex]

so

[tex]a/6=\sqrt{3}[/tex]

[tex]a=6\sqrt{3}[/tex]

step 2

Find the value of b

we know that

[tex]cos(60\°)=6/b[/tex]

Remember that

[tex]cos(60\°)=1/2[/tex]

so

[tex]6/b=1/2[/tex]

[tex]b=12[/tex]

step 3

Find the value of c

we know that

[tex]cos(45\°)=c/b[/tex]

[tex]cos(45\°)=c/12[/tex]

Remember that

[tex]cos(45\°)=\sqrt{2}/2[/tex]

[tex]c/12=\sqrt{2}/2[/tex]

[tex]c=6\sqrt{2}[/tex]

Answer:

C.

Step-by-step explanation:

Answer:

Does it say a standard 6 sided die because if so then it would be 6/6 probability because the number can only go up to 6 an so there is no probability of getting anything more then 6

Step-by-step explanation:

Answer:

x = -13

Step-by-step explanation:

Distribute:

8 - 6x + 10x - 15 = 20 - 5x

Combine like terms:

4x - 7 = 20 - 5x

Isolate Variable

-x = 13

-1(-x) = -1(13)

x = -13

Answer: [tex]x=3[/tex]

Step-by-step explanation:

You need to apply Distributive property on the left side of the equation:

[tex]2(4-3x)+5(2x-3)=20-5x\\\\8-6x+10x-15=20-5x[/tex]

Now you must add the like terms on the left side of the equation:

[tex]-7+4x=20-5x[/tex]

Add [tex]5x[/tex] to both sides:

[tex]-7+4x+5x=20-5x+5x\\\\-7+9x=20[/tex]

Add 7 to boht sides of the equation:

[tex]-7+9x+7=20+7\\\\9x=27[/tex]

And finally, divide both sides by 9:

[tex]\frac{9x}{9}=\frac{27}{9}\\\\x=3[/tex]

Answer:

6x^3-3x^3y^2

Step-by-step explanation:

6x^3+\left(-3x^3y^2\right)

6x^3+\left(-3x^3y^2\right)=6x^3-3x^3y^2

=6x^3-3x^3y^2

the answer is 3x^3(2-y^2).

6x^3 + (-3x^3y^2) =

6x^3 - 3x^3y^2 =

3x^3(2-y^2)

bAnswer:

B)

Step-by-step explanation:

Answer:

g^5h^2

Step-by-step explanation:

12g^5h^4, g^5h^2

This is one way of doing it. Break down every number and every variable into a product of the simplest factors. Then see how many of each factor appear in both monomials.

12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h

g^5h^2 = g * g * g * g * g * h * h

So far you see every single prime factor of each monomial.

Now I will mark the ones that are present in both. Those are the common factors.

12g^5h^4 = 2 * 2 * 3 * g * g * g * g * g * h * h * h * h

g^5h^2 = g * g * g * g * g * h * h

The greatest common factor is the product of all the factors that appear in both monomials.

GCF = g * g * g * g * g * h * h = g^5h^2

Answer:

Step-by-step explanation:

To build the equation we need to get  the value.

120,000

Lets add the percent which is 1.055 since it is 5.5% added to nothing increasing

120,000(1.055)x

Answer:

120000(1.055)x

Step-by-step explanation

Answer:

[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]

Initial value: 250

Decay

Decay rate: 11%

[tex] y = 4 0 ( 1.11 ) ^ x [/tex]

Initial value: 40

Growth

Growth rate: 11%

Step-by-step explanation:

The function we have on the left of the table is:

[tex] y = 2 5 0 ( 0 . 8 9 ) ^ x [/tex]

Initial value (when x = 0): [tex] y = 2 5 0 ( 0 . 8 9 ) ^ 0 [/tex]

y = 250 (initial value)

Growth or Decay: 0.89 < 1 so decay

Decay rate: (1 - 0.89) * 100 = 11%

Function on right side:

[tex] y = 4 0 ( 1.11 ) ^ x [/tex]

Initial value (when x = 0): [tex] y = 4 0 ( 1 . 1 1 ) ^ 0 [/tex]

y = 40 (initial value)

Growth or decay: 1.11 > 1 so growth

Growth rate: (1.11 - 1) * 100 = 11%

i took the test 100%

Answer:

1) the factored form is  y= ( x-5 ) ( x+4 )

2) the vertex is (4.5, -0.25)

3) the y intercept is when x equals 0 so it is at (0,20)

4) it opens upward and the vertex is (4.5, -0.25) the x intercepts are (4,0) and (5,0) and the y intercept is  (0,20)

5)

a. it dips  between 4 seconds and 5 seconds so the x intercepts are (4,0) and (5,0)

b. it is taken at the vertex aka the lowest point so the height is -0.25

Answer:

Part 1:

[tex]y= (x-4)(x-5)[/tex]

Part 2:

[tex](\frac{9}{2}, - \frac{1}{4})[/tex]

Part 3:

[tex]Y=20[/tex]

Part 5:

The height:

[tex]-\frac{1}{4}[/tex]

The time:

[tex]\frac{9}{2}[/tex]s

Step-by-step explanation:

[tex]y = x^{2}  -9x+20[/tex] Is a quadratic equation.

Part 1:

We use [tex]x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex] to factor quadratic equations

[tex]y = x^{2}  -9x+20[/tex]

a=1 b=-9 c=20

[tex]x = \frac {-(-9) \pm \sqrt {(-9)^2 - 4(1)(20)}}{2(1)}[/tex]

[tex]x = \frac {9 \pm \sqrt {81 -80}}{2}[/tex]

[tex]x = \frac {9 \pm {1}}{2}[/tex]

we solve both possibilities

[tex]x = \frac {9 + {1}}{2}=5[/tex]

[tex]x = 5[/tex]  

[tex]x = \frac {9 -{1}}{2}=4[/tex]

[tex]x=4[/tex]

The factored form would be

[tex]y= (x-4)(x-5)[/tex]

Part 2:

We use the formula to find the x coordinate of the vertex of a parabola

[tex]V_{x}=\frac{-b}{2a}[/tex]

[tex]y = x^{2}  -9x+20[/tex]

a=1 b=-9 c=20

[tex]V_{x}=\frac{9}{2}[/tex]

Now we substitute the value of x in [tex]y = x^{2}  -9x+20[/tex] to find the value of the coordinate y of the vertex

[tex]y = \ (\frac{9}{2} )^{2}   -9(\frac{9}{2}) +20\\ y=  \frac{81}{4} -\frac{81}{2} +20\\ y= -\frac{1}{4}[/tex]

The vertex of the parabola is

Vertex:

[tex](\frac{9}{2}, - \frac{1}{4})[/tex]

Part 3:

the y-intercept is when the value of x = 0.

We substitute this value in [tex]y = x^{2}  -9x+20[/tex]

[tex]y = 0^{2}  -9(0)+20= 20[/tex]

The y-intercept is [tex]y=20[/tex]

Part 5:

A.

Between 4s and 5s

B and C.

Erin's photograph is taken at the lowest point of the roller coaster.

The lowest point of the parabola is the vertex.

The coordinate y of the vertex gives us the height and the coordinate x the time.

The height:

[tex]-\frac{1}{4}[/tex]

It is negative because it is below the point we take as zero.

The time:

[tex]\frac{9}{2}[/tex]s

Part 4:

The answer is the graph

C quadrant 3 because negative x value and negative y value

Answer:

x = 7

Step-by-step explanation:

angles 2 and 3 form a straight angle and are supplementary, that is they sum to 180°, hence

∠2 + ∠3 = 180 ← substitute values

20x - 1 +4x + 13 = 180

24x + 12 = 180 ( subtract 12 from both sides )

24x = 168 ( divide both sides by 24 )

x = 7

Answer:

[tex]s(x)=10(1.03)^{x}[/tex]

Step-by-step explanation:

Let

x -----> the number of weeks

S ----> the number of members in the science club

In this problem we have a exponential function of the form

[tex]s(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

we have

[tex]a=10\ membrers[/tex]

[tex]r=3\%[/tex]

[tex]b=100\%+3\% =103\%=103/100=1.03[/tex]

substitute

[tex]s(x)=10(1.03)^{x}[/tex]

Answer:

y = - [tex]\frac{1}{3}[/tex] x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 3 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], hence

y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (3, 1) into the partial equation

1 = - 1 + c ⇒ c = 1 + 1 = 2

y = - [tex]\frac{1}{3}[/tex] x + 2 ← equation of perpendicular line

Answer:

y = -1/3x + 2

got it correct on my test

Answer:

The company earned 68 billion dollars in the year 2008..

Step-by-step explanation:

This is because  the time t is the number of years since the END of 2008. The  time t = 0 at the end of 2008, so the earnings = 0^2 + 10(0) + 68 = 68 billion.

Answer:

option B

Step-by-step explanation:

A particular company's net sales is modeled by the expression (t² + 10t + 68)

Where t represents number of years since the end of year 2008.

In this expression 68 is the constant term which represents the earning of the company before 2008. or in year 2008.

The company earned 68 billion dollars in 2008.

Therefore, option B is the answer.

Answer:

3 m^2 + 4m +7

Step-by-step explanation:

3x^24 + 4x^12 + 7

Let  m =x^12

m^2 = x^12 ^2 = x^24

Substitute this into the first equation

3 m^2 + 4m +7

Answer: period

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

It is given that a driver runs over a nail, puncturing the tire without causing a leak.

Tire of a car represents a periodic function because after a particular time the tire comes its initial stage and that particular time interval is called a period.

It means period is the key feature of the function representing the nail’s travel can be used to determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire.

Therefore the correct option is A.

Answer:

Age of Jacob is 10 years.

Step-by-step explanation:

Let the age of Jacob = x years and age of Kinsley = y years

Then by first statement " Kinsley's age is 7 years less than twice of Jacob's age"

y = 2x - 7

By second statement " Kensley is 13 years old "

y = 3 years

By putting y = 13 years in the equation

13 = 2x - 7

2x = 13 + 7

2x = 20

x = [tex]\frac{20}{2}[/tex] = 10 years

Therefore, age of Jacob is 10 years.

Answer:

The Answer is B. 10

Hope This Helps!

Answer:

x=2                x=-3

Step-by-step explanation:

4x2+3x=24-x

Subtract 24 from each side

4x^2 +3x -24 = 24-24 -x

4x^2 +3x -24 = -x

Add x to each side

4x^2 +3x+x -24 = -x+x

4x^2 +4x -24 = 0

Factor out a 4

4(x^2 +x -6) = 0

Divide by 4

x^2 +x -6 =0

Factor

What 2 numbers multiply to -6 and add to 1

-2*3 = -6

-2+3 =1

(x-2) (x+3) =0

Using the zero product property

x-2 =0            x+3 =0

x-2+2=0+2    x+3-3=0-3

x=2                x=-3

Answer:x=-3 , x = 2

Step-by-step explanation:

First move the expression ( 24-x) to the left.

This gives us 4x^2+3x+24-x.

Collect the like terms which gives us 4x^2+4x+24

4x^2+4x-24 = 0.  Divide both sides by 4.

x^2 + x-6 = 0

Factorise the expression so you get (x+3)(x-2)=0

Solve the equations x+3 = 0 and x-2=0

The final solutions are x=-3 and x=2.

D

(-71+1) + 0 = (-71+1)

This is because the whole equation involves addition thus it is an example of associative property of addition

Answer:

(-71 + 1) + 0 = (-71 +1)

Step-by-step explanation:

Given 3 numbers: a,b,c

Associative property of addition: (a + b) + c = a + (b + c)

On this case: a= -71

b = 1

c = 0

(a + b) + c = (-71 + 1) + 0 = -70 + 0 = -70

(-71 + (1 + 0)) = (-71 + 1) = -70

Both the sums are equal to -70 and hence the associative property of addition for the three numbers a= -71, b = 1, c= 0 holds.

All the other options in the question contain a reference to variable i and does not have the same three values a,b,c on both sides of the equality. So they do not represent the associative property.

For this case we have that the point-slope equation of a line is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0}):[/tex] It is a point

We have as data that:

[tex](x_ {0}, y_ {0}): (- 2, -7)\\m = - \frac {3} {2}[/tex]

We replace:

[tex](y - (- 7)) = - \frac {3} {2} (x - (- 2))\\(y + 7) = - \frac {3} {2} (x + 2)[/tex]

Answer:[tex](y + 7) = - \frac {3} {2} (x + 2)[/tex]

Answer:

I just know it is 0.222222222222

Step-by-step explanation:

Answer:

± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{\frac{4}{9} }[/tex]

= [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]

Answer:

BC should be 1 unit

Step-by-step explanation:

Answer:

1 unit is your answer

For this case we must find the point that Harold used to arrive at the following equation:

[tex]y = 3 (x-7)[/tex]

Starting from the fact that the equation of the point-slope form of a line is given by:

[tex](y-y_ {1}) = m (x-x_ {1})[/tex]

If we compare the standard equation with Harold's, we see that the slope of the line is [tex]m = 3.[/tex]

In addition, it is observed that [tex]x_ {1} = 7[/tex]and [tex]y_ {1} = 0.[/tex]

Then, the correct option is: Harold used the point (7,0)

ANswer:

When Harold wrote his equation, the point was used (7,0).

Answer:

Step-by-step explanation:

its the first one in edge

The graph which shows a rate of change of 1/2 is the linear graph shown in the image attached below.

Rate of change = change in y / change in x.

The two points between -4 and 0 on the x-axis as shown in the diagram attached are, (-4, 1) and (0, 3). It is also a linear graph.

Rate of change = (3 - 1)/(0 -(-4)) = 2/4 = 1/2

The graph that shows a rate of change is the linear graph attached below.

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The inequality x - 7 > -20 is solved by adding 7 to both sides, resulting in x > -13. The graph of this inequality has an open circle at -13 with shading to the right.

To solve the inequality x - 7 > -20, you want to isolate the variable x on one side. You can do this by adding 7 to both sides of the inequality:

x - 7 + 7 > -20 + 7

x > -13

So, the solution to the inequality is x > -13. To graph this solution on a number line, you would draw an open circle at -13 and shade to the right, indicating that x can be any value greater than -13 but not including -13 itself.

Answer: C

Step-by-step explanation:

1 + 2sin(x+pi)

1 is adding to the y, so it is a vertical shift of 1 unit,

2 is a stretch because it is multiplying to the sin,

and pi is adding to the x, so it is a phase shift.

Answer:

4

Step-by-step explanation:

The median is the middle, since the amount of data is an even number we need to add up the third number and fourth number. These are 3 and 5 respectively. Adding these up gives up 8. Dividing this by 2 is 4.