Find the average rate of change of g(x)=3x^2 ver the interval [-5, -3].

Answer:

1-x-2+2x = 10x-25-x

Step-by-step explanation:

The given equation is as follows :

1-(x+2)+2x=5(2x-5)-x

We need to solve the above equation.

Firstly opening bracket off LHS and applying distributive property at RHS.

1-x-2+2x=5(2x)-5(5)-x    (Distributive property :a(b+c) = ab+ac)

1-x-2+2x = 10x-25-x

So, the correct option is (B) i.e. 1 minus x minus 2 + 2 x = 10 x minus 25 minus x.

Answer:

It's b

Step-by-step explanation:

I got it right on edge

Answer:

No solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

5(3x+5)=3(5x+1)

Step 1: Simplify both sides of the equation.

5(3x+5)=3(5x+1)

(5)(3x)+(5)(5)=(3)(5x)+(3)(1)(Distribute)

15x+25=15x+3

Step 2: Subtract 15x from both sides.

15x+25−15x=15x+3−15x

25=3

Step 3: Subtract 25 from both sides.

25−25=3−25

0=−22

Answer:

There are no solutions.

Complete Question:

A function is expressed by the equation y = 0.3x − 6. For what value of the independent variable will the value of the function be equal to −6; −3; 0?

Answer:

If the value of the function is equal to −6, the value of the independent variable is equal to 0. If the value of the function is equal to −3, the value of the independent variable is equal to 10. If the value of the function is equal to 0, the value of the independent variable is equal to 20.

Step-by-step explanation:

Given:

[tex] y = 0.3x - 6 [/tex]

Required:

Find x, if y = -6; -3; and 0.

SOLUTION:

x = the independent variable

y = dependent variable

To find x (independent variable), when the value of the function (y) is -6, substitute y = -6 into the equation of the function:

[tex] y = 0.3x - 6 [/tex]

[tex] -6 = 0.3x - 6 [/tex]

[tex] -6 + 6 = 0.3x [/tex] (addition property of equality)

[tex] 0 = 0.3x [/tex]

[tex] \frac{0}{0.3} = \frac{0.3x}{0.3} [/tex]

[tex] 0 = x [/tex]

[tex] x = 0 [/tex]

To find x (independent variable), when the value of the function (y) is -3, substitute y = -3 into the equation of the function:

[tex] y = 0.3x - 6 [/tex]

[tex] -3 = 0.3x - 6 [/tex]

[tex] -3 + 6 = 0.3x [/tex] (addition property of equality)

[tex] 3 = 0.3x [/tex]

[tex] \frac{3}{0.3} = \frac{0.3x}{0.3} [/tex]

[tex] 10 = x [/tex]

[tex] x = 10 [/tex]

To find x (independent variable), when the value of the function (y) is 0, substitute y = 0 into the equation of the function:

[tex] y = 0.3x - 6 [/tex]

[tex] 0 = 0.3x - 6 [/tex]

[tex] 0 + 6 = 0.3x [/tex] (addition property of equality)

[tex] 6 = 0.3x [/tex]

[tex] \frac{6}{0.3} = \frac{0.3x}{0.3} [/tex]

[tex] 20 = x [/tex]

[tex] x = 20 [/tex]

Answer:

21

Step-by-step explanation:

The rule for a right triangle is (x^2)x(y^2)=(z^2)

so 20 squared is 400 and 29 squared is 841.

And since the side with the length 29 is the hypotenuse.

It is 400 + [tex]\sqrt{x}[/tex] = 841

841-400=441

the square root of 441 is 21

Answer:

I think that the answer is D

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 times 2 1/2 equals 10

5 gallons times 2 1/2 equals 12.5

The boat will use 12.5 gallons in 10 hrs

Hope this helped!

The number of gallons of gasoline the boat uses in 10 hours will be 12.5 gallons.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Dedra’s boat used 5 gallons of gasoline in 4 hours.

Then the rate will be

Rate = 5 / 4

Rate = 1.25 gallons per hour

At this rate, then the number of gallons of gasoline the boat uses in 10 hours will be

⇒ 1.25 x 10

⇒ 12.5 gallons

The number of gallons of gasoline the boat uses in 10 hours will be 12.5 gallons.

More about the ratio and the proportion link is given below.

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Answer:

a) Two thorough rinses gives;

1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The water should be divided into two quantities of 10 liters each

Step-by-step explanation:

The given parameters are;

The initial volume of strong bleach solution in the nappies = 1/2 Liters

The volume of water first used to rinse = 12 liters

The volume of water used in the second rinse = 8 liters

Therefore, we have;

The total volume of the water and the concentrated bleach in the first rinse = 1/2 + 12 = 12.5 Liters

The new concentration of the bleach in the first rinse water = (1/2 strong bleach)/12.5 L = (1/2 strong bleach)/25/2 L = 1/2×2/25 = 1/25 strong bleach/L

The volume of the first rinse introduced in the second rinse = 1/2 Liters

The concentration of the bleach introduced in the second rinse = The new concentration of the bleach in the first rinse water = 1/25 strong bleach/L

The volume of water added in the second rinse = 8 liters

The total volume of the water and the bleach in the second rinse = (8 + 1/2) liters = 8.5 liters

The concentration of bleach in the second rinse = (The concentration of the bleach introduced in the second rinse × (Volume of bleach solution introduced in the second rinse))/(The total volume of the water and the bleach in the second rinse)

The concentration of bleach in the second rinse = (1/25 strong bleach/L × 1/2 L)/(8.5 Liters)

The concentration of bleach in the second rinse = (1/25 strong bleach/L × 1/2 L)/(17/2 Liters) = 1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The the quantity of water in the first rinse = x

The amount of water in the second rinse = 20 - x

The concentration of bleach in the first rinse = 1/2/(x + 1/2) = 1/(2·x + 1)

The concentration introduced in the second rinse = 1/2 × 1/(2·x + 1) = 1/(4·x + 2)

The total volume of water and bleach introduced in the second rinse = (20 - x + 1/2) = 20.5 - x

The concentration of bleach in the second rinse = 1/(4·x + 2)/(20.5 - x)

The minimum value for the concentration can be found from taking the derivative of the function for the concentration and equation to zero as follows;

[tex]\dfrac{\mathrm{d} \dfrac{1}{\left ( 4\cdot x + 2 \right )\cdot \left ( 20.5 - x \right )}}{\mathrm{d} x} = \dfrac{2\cdot \left ( x - 10 \right )}{\left ( 2\cdot x + 1 \right )^{2}\cdot \left ( 20.5 - x \right )^{2}} = 0[/tex]

2·(x - 10) = 0

x = 0/2 + 10 = 10

x = 10

The the quantity of water in the first rinse = x = 10 liters

The the quantity of water in the first rinse = 10 liters

The amount of water in the second rinse = 20 - x = 20 - x = 20 - 10 = 10 liters

The amount of water in the second rinse = 10 liters

The water should be divided into two quantities of 10 liters each

Therefore, the water should be divided into two quantities of 10 liters each to give a final bleach solution concentration of 1/(4·x + 2)/(20.5 - x) = 1/(4×10 + 2)/(20.5 - 10) = 1/42 × 1/10.5 = 1/441 concentration/liter.

Answer: a) Two thorough rinses gives;

1/25 × 1/2 × 2/17 strong bleach/L = 1/425 strong bleach/L

b) The water should be divided into two quantities of 10 liters each

Answer:

Lin walks 500 feet and Elena walks 500 yards

Step-by-step explanation:

First of all, 1 yard is greater than 1 feet, there relation is given by:

1 yard = 1 feet

From the image attached, we can see that Lin's house is closer to the school than Elena house, therefore we can come to the conclusion that Lin walks 500 feet and Elena walks 500 yards because Elena house is farther away from the school. The distance from Elena house to the school is about 3 times the distance from Lin house to the school.

Answer: lin walks 500 feet and elena walks 500 yards

Step-by-step explanation:

1 foot is smaller then one yard

Answer:

BD= 12

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

The slope represents how much it will cost per customer

Step-by-step explanation:

btw im not fully sure so correct me if im wrong plz

Answer:

A. 2x-5

Step-by-step explanation:

(2x-5)(3x+5)

Hope this helps!

Answer:

A. 2x-5

Step-by-step explanation:

Answer:

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

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 )

Here m = [tex]\frac{1}{2}[/tex] and c = 1 , thus

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

Answer:

$57.84

Step-by-step explanation:

Balloons needed = 168

Cost of 36 balloons per pack = $11.88

Cost of 12 balloons per pack = $5.16

cost per balloon

36 per pack = $11.88 / 36

= $0.33

12 per pack = $5.16 / 12

= $0.43

In order to minimize cost, she should buy as many packs of 36 per pack balloon

36 per pack × 1 pack = 36

36 per pack × 2 packs = 72

36 per pack × 3 packs = 108

36 per pack × 4 packs = 144

36 per pack × 5 packs = 180

The required number of balloons is 168

So, the number of possible 36 packs to buy is 4, that is, 144 balloons

Balloons remaining = 168 - 144

= 24

Possible packs of 12 balloons per pack possible is

12 per pack × 1 pack = 12

12 per pack × 2 packs = 24

Therefore, Megan needs to buy 4 packs of 36 balloons per pack and 2 packs of 12 balloons per pack

Cost of 4 packs of 36 balloons per pack = 4 × $11.88

= $47.52

Cost of 2 packs of 12 balloons per pack = 2 × $5.16

= $10.32

Total cost = $47.52 + $10.32

= $57.84

Answer:

2.5 cups

Step-by-step explanation:

Answer: x-int: (-4, 0), y-int: (0, 1/2)

Step-by-step explanation:

x-int: when y = 0

-x + 8*0 = 4

-x = 4

x = -4

(-4, 0)

y-int: when x = 0

0 + 8y = 4

8y = 4

y = 1/2

(0, 1/2)

Answer: The initial value of the function is 625. This means that the first child costs $625 to send to camp.

Step-by-step explanation: I took the quiz

Answer:

x^2 - 7 x + 10

Step-by-step explanation:

use the foil method to multiply the terms.

Also - you can just plug these types of equations into WolframAlpha...

in this case you are looking for "expanded form"

Answer:

17

Step-by-step explanation:

purple triangle= 10

circle=5

square=4

pink triangle=2

Answer:

The missing number would be 17.

Step-by-step explanation:

1 equilateral triangle = 10

1 circle = 5

1 isosceles triangle = 2

When you add one of each of those together; 10+5+2, you get 17.

Answer:

Dylan can plant maximum 8 plants.

Number of marigolds in each flower box  [tex]=8[/tex]

Number of periwinkles in each flower box  [tex]=9[/tex]

Step-by-step explanation:

Number of marigolds = 64

Number of periwinkles = 72

To find the maximum number of flower boxes Dylan can plant, find H.C.F of 64 and 72.

[tex]64=2^6\\72=2^3\,\,3^2[/tex]

So,

H.C.F(64, 72) = [tex]2^3=8[/tex]

That is Dylan can plant maximum 8 plants.

Number of marigolds in each flower box = [tex]\frac{64}{8}=8[/tex]

Number of periwinkles in each flower box = [tex]\frac{72}{8}=9[/tex]

Answer:

2 : 3

Step-by-step explanation:

We have 4 squares and 6 circles. We would like the ratio of squares to circles, so we divide 4 by 6:

4 / 6  ⇒  the ratio here would be 4 : 6

We need to simplify this. Notice that both 4 and 6 are divisible by 2. So, we can divide both by 2:

4/2 : 6/2  ⇒  2 : 3

2 and 3 don't share any factors other than 1, so we leave the ratio like this.

The answer is thus 2 : 3.

~ an aesthetics lover

Answer:

Victor runs 0.6 of a lap in 1 minute

Step-by-step explanation:

From the question;

3 laps = 5 minutes

x laps = 1 minute

3 * 1 = 5 * x

3 = 5x

x = 3/5

x = 0.6

Victor runs 0.6 of a lap in a minute

Answer:

p is 2.

Step-by-step explanation:

Answer:

35.65 feet

Step-by-step explanation:

Melanie connected a brown garden hose , a green garden hose and a black garden hose to make one long hose

The brown hose is 10.75 feet

The green hose is 16.4 feet

The black hose is 8.5 feet

Therefore the farthest distance that the one hose can reach can be calculated as follows

= 10.75 + 16.4 + 8.5

= 35.65 feet

Hence the farthest distance that one hose can reach is 35.65 feet

Answer:

Answer is 120

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Let's solve y for x + 2y = 8.

x + 2y = 8

2y = -x + 8

y = [tex]-\frac{1}{2}[/tex]x + 4.

Let's solve y for x - y = 5.

x - y = 5

y = x - 5

Since both equations have been solved for y, we can combine them together into one!

x - 5 = [tex]-\frac{1}{2}[/tex]x + 4

x [tex]+ \frac{1}{2}[/tex]x = 4 + 5

1.5x = 9

x = 6

Hope this helped! If not, please let me know!

Answer:

All of the points would be eight places lower in the y value

Step-by-step explanation:

Lets check by putting 8 in the place of x y= 8^2  which equals 64, that means that y equals 64, then do the second equation y = 8^2 - 8 which equals 56, which means y equals 56, 64 minus 56 equals 8 so they have a difference of 8.

Answer:

The statement is;

A number is a prime number if and only if it has 1 and itself as factors

The truth value of this statement is true T

Step-by-step explanation:

The biconditional statement will use the statements if and only if.

Thus, we have;

A number is a prime number if and only if it has only 1 and itself as factors

The truth value of the biconditional statement is T ( true)

Answer:

99%

Step-by-step explanation:

The percentage increase of the given item is 55.56%.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Misha obtained a score of 67% on her exam, that corresponds to 67 out of 100. It is expressed as 67/100 in fractional form and as 67:100 in ratio form.

The price of an item has increased to $279 today yesterday it was $180

The percentage increase can be calculated by:

(Current price - Original price) / Original price x 100 = Percentage increase

As per the question, we have to substitute the values to get:

⇒ (279 - 180) / 180 x 100 = 55.56%

Therefore the percentage increase is 55.56%.

Learn more about the percentages here:

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