Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.

Part A: Find the average rate of change of each section. (4 points)

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)

(10 points)

Answer:

b)−1×2×−3×4×−5 has a negative value.

Step-by-step explanation:

Given expressions are a)−1×−2  b)−1×2×−3×4×−5 C) 1×−2×−3×−4×−5 d)1×−2×3×−4×5

Firstly we have to multiply the digits with digit then after minus sign.

So for a)−1×−2

Solution, [tex]1\times2\ =2[/tex]

When two negative signs are multiplied with each other it gives a positive sign.

Both digits have a negative sign that means it gives a positive sign.

So the solution for 1st expression is [tex]2.[/tex]

b)−1×2×−3×4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here three digits have negative sign, two negative gives positive and then multiplied by negative gives negative.

So the solution for 2nd expression is [tex]-120[/tex].

C) 1×−2×−3×−4×−5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Here four digits have negative sign, two negative gives positive and again two negative gives positive means positive multiplied with positive gives positive.

So the solution for 3rd expression is [tex]120[/tex].

d)1×−2×3×−4×5

Solution,[tex]1\times2\times3\times4\times5\ =120[/tex]

Two digits have a negative sign that means it gives a positive sign.

So the solution for 4th expression is [tex]120[/tex].

Hence the correct option is b.

Answer:

B

Step-by-step explanation:

Answer:

15 shelves

Step-by-step explanation:

6 dvds = 1 shelf

89/6= 14.8333333333 shelves

But you cannot have 0.8333333333 shelves so you would round  0.8333333333 to 1

Answer:

I think it was warmer

Answer:

[tex]\dfrac{4}{27}[/tex]

Step-by-step explanation:

A bag contains 8 blue marbles 6 red marbles and 4 green marbles, 8 + 6 + 4 = 18 marbles in total.

The probability of selecting a blue marble is

[tex]P(\text{blue marble})=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}=\dfrac{8}{18}=\dfrac{4}{9}[/tex]

Then the blue marble was replaced in the bag.

The probability of selecting a red marble is

[tex]P(\text{red marble})=\dfrac{\text{Number of red marbles}}{\text{Total number of marbles}}=\dfrac{6}{18}=\dfrac{1}{3}[/tex]

The probability of selecting a blue marble replaced it in the bag and then selecting a red marble is

[tex]P=\dfrac{4}{9}\cdot \dfrac{1}{3}=\dfrac{4}{27}[/tex]

Answer:

w ≥ 141/2

Step-by-step explanation:

12 − 4/6 w ≤ 2/8 − 3/6 w

First, combine like terms.  Add 4/6 w to both sides, and subtract 2/8 from both sides.

12 − 2/8 ≤ 4/6 w − 3/6 w

12 − 2/8 ≤ 1/6 w

Reduce 2/8 to 1/4:

12 − 1/4 ≤ 1/6 w

To get rid of the fractions, multiply both sides by 12 (the LCM of 4 and 6):

12 (12 − 1/4) ≤ 12 (1/6 w)

144 − 3 ≤ 2w

141 ≤ 2w

Divide by 2:

141/2 ≤ w

If you'd like, flip the equation:

w ≥ 141/2

Answer:

y=-3/4x-5/4

Step-by-step explanation:

use the formula y-y1=m(x-x1)

y-4=-3/4(x-(-7))

Answer: 240 km

Step-by-step explanation:

From the graph :

50 miles = 80km

1 miles = 80/50 km

Therefore :

150 miles = 80/50 x 150

150 miles = 240 km

Answer:

16 is x<3

Step-by-step explanation:

4x-10<2

Add 10 to both sides

4x<12

Divide 4 from both sides and you get x<3

Answer:

Standard Form : 3x+1y=35

Step-by-step explanation:

The equation of the line will be 3x+y-35=0

The equation of the line in standard form will be expressed by using the coefficient of x and coeficient of y which is given

ax+by+c=0

The equation of line which passes through two points will be

(y-y₁)/(x-x₁)=(y₂-y₁)/(x₂-x₁)

So according to asked question,

x₁=10,y₁=5

x₂=13,y₂=-4

the equation of line will be

(y-5)/(x-10)=(-4-5)/(13-10)

⇒(y-5)/(x-10)=-9/3

⇒(y-5)/(x-10)=-3

⇒y-5=-3(x-10)

⇒y-5=-3x+30

⇒y+3x-5-30=0

⇒3x+y-35=0

Therefore the equation of the line will be 3x+y-35=0

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Answer:

If I'm correct it is 10.

Step-by-step explanation:

The distance was 10 ;-;.

Tip: use desmos for this

Answer:$728

Step-by-step explanation:

Final answer:

To provide Noreen with her new monthly mortgage payment, the cost of 2 mortgage points is added to the original 20% down payment, resulting in a decreased loan amount. A mortgage calculator or formula is then used to determine the monthly payment at a 5.15% interest rate for the new loan amount over 30 years, which would be higher than with the points purchased. Answer : 725$

Explanation:

To calculate Noreen's monthly mortgage payment, we need to first understand the impact of her decision to apply the price of 2 points to her down payment instead of purchasing points. Points are upfront fees paid to the lender at closing in exchange for a reduced interest rate. One point is equal to 1% of the loan amount. However, since Noreen is opting to add the cost of these points to her down payment, we'll calculate her down payment and loan amount without considering a reduction in interest rate.

1. Calculate the down payment:

Noreen's home costs $170,000, and she is required to make a 20% down payment.

Down payment = 20% of $170,000 = 0.20 * $170,000 = $34,000

2. Calculate the cost of 2 points:

Since Noreen is not buying points and instead adding this cost to her down payment, we calculate the initial loan amount to find out how much 2 points would cost.

Initial loan amount without points = $170,000 - $34,000 = $136,000

Cost of 2 points = 2% of $136,000 = 0.02 * $136,000 = $2,720

3. Adjust the down payment:

Noreen decides to add the $2,720 (cost of 2 points) to her down payment.

New down payment = $34,000 + $2,720 = $36,720

4. Calculate the new loan amount:

New loan amount = Home price - New down payment = $170,000 - $36,720 = $133,280

Now, we use the loan amount of $133,280 and the original interest rate of 5.15% to calculate the monthly mortgage payment over a 30-year term.

The formula for monthly mortgage payments is:

[tex]\[M = P\frac{r(1+r)^n}{(1+r)^n - 1}\][/tex]

First, calculate the monthly interest rate:

[tex]\[r = \frac{0.0515}{12} = 0.00429167\][/tex]

Then, plug in the values into the formula:

[tex]\[M = 133,280\frac{0.00429167(1+0.00429167)^{360}}{(1+0.00429167)^{360} - 1}\][/tex]

This calculation can be complex, so it's often easiest to use a mortgage calculator or financial calculator to compute \(M\).

When you perform this calculation, you should get:

[tex]\[M \approx 725\][/tex]

Thus, Noreen's monthly mortgage payment would be approximately $725 when rounded to the nearest dollar. Please note, the exact payment can slightly vary based on the precision of the interest rate conversion and the calculation method.

Answer:

[tex]\displaystyle 3 = m[/tex]

Step-by-step explanation:

2 = −7 + 3m

+ 7 + 7

__________

[tex]\displaystyle \frac{9}{3} = \frac{3m}{3} \\ \\ 3 = m[/tex]

I am joyous to assist you anytime.

Answer: 200cm long

Step-by-step explanation:

Let the length of the rod be x

red = 1/4 of the rod , which means 1/4 of x

orange = 2/5 of x

The remainder = x - ([tex]\frac{x}{4}[/tex] +[tex]\frac{2x}{5}[/tex])

= x - ([tex]\frac{13x}{20}[/tex])

= [tex]\frac{7x}{20}[/tex]

yellow = 2/7 of the remainder , that is

yellow = 2/7 of [tex]\frac{7x}{20}[/tex]

yellow = [tex]\frac{x}{10}[/tex]

and it was given that the yellow section was 20cm long , that is

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

x = 20 x10

x = 200

Therefore the rod was 200cm long

To determine the length of a rod based on fractions of it being painted different colors, with the yellow section known to be 20cm, we set up a proportion based on the fractions of the rod painted and use this to solve for the total length of the rod, which is 200cm.

The subject of this question is Mathematics, and it is typically encountered at the Middle School level. To find the length of the entire rod when 1/4 is painted red, 2/5 is painted orange, and 2/7 of the remainder is painted yellow with the yellow section being 20cm, we need to set up an equation and solve for the total length of the rod.

First, we determine the fraction of the rod that remains after painting 1/4 red and 2/5 orange:

Let's start the calculations:

1. (1/4) + (2/5) = 5/20 + 8/20 = 13/20.

2. The remaining fraction = 1 - 13/20 = 7/20.

3. Let x be the total length of the rod. Since 2/7 of the remainder is 20cm, we can write the equation (2/7) * (7/20) * x = 20cm.

4. Simplify and solve for x:

(2/7) * (7/20) * x = 20cm,

(1/10) * x = 20cm,

x = 20cm * 10,

x = 200cm.

Therefore, the total length of the rod is 200cm.

Answer:

No Solution.

Step-by-step explanation:

2(x-1)-y=-8

y=2x+8

----------------

2x-2-(2x+8)=-8

2x-2-2x-8=-8

2x-2x-2-8=-8

0-2-8=-8

-2-8=-8

-10=-8

no solution

value of x is: [tex]x=\frac{-31}{12}[/tex]

Step-by-step explanation:

We need to solve the equation f(x)=g(x)

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

and [tex]g(x) = 3x + 5[/tex]

Solving to find f(x)=g(x)

Putting values of f(x) and g(x)

[tex]f(x)=g(x)\\(\frac{1}{2})^2-3=3x + 5\\\frac{1}{4}-3=3x + 5\\Subtarct\,\,5\,\,on\,\,both\,\,sides:\\\frac{1}{4}-3-5=3x + 5-5\\\frac{1}{4}-8=3x\\Taking\,\,LCm\,\,on\,\,left\,\,side\\\frac{1-8*4}{4}=3x\\\frac{-31}{4}=3x\\Divide\,\,both\,\,sides\,\,by\,\,3\\x=\frac{-31}{4*3}\\x=\frac{-31}{12}[/tex]

So, value of x is: [tex]x=\frac{-31}{12}[/tex]

The graph will be a straight line x= -2.58 or x = -31/12

Keywords: Composition of Functions

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Answer:

100 seconds

Erica and Amy are at distance of 1 km in 100 seconds

Step-by-step explanation:

They both are travelling in opposite directions so the sum of the distances they travel is the distance between them.

Let's take t as the total time taken to achieve a seperation of 1km

Distance traveled by Erica , (Speed of Erica - v1)

x1 = v1 * t

Distance travelled by Amy , (Speed of Amy - v2)

x2 = v2*t

Therefore sum of the distances they traveled is x1+x2 = x

x = v1*t + v2*t

x = t*(v1 + v2)

Here it is given that final seperation between Amy and Erica is 1km or 1000 m

Therefore x = 1000 m

Thus t = [tex]\frac{x}{v1+v2}[/tex]

Substituting given values v1 = 6 m/s v2 = 4 m/s

Therefore,

They are apart by exactly 1km in a time of 100 sec

Answer:

11

Step-by-step explanation:

because that are 11 pencils that are 6 inches or longer, that's what the picture says.

Answer:

Helpful piece of information - each x = 1 pencil

Step-by-step explanation:

If each x = 1 pencil, and their are 6 x's over the 6 inch mark, 2 x's over the 7 inch mark, and 3 x's over the 8 inch mark, how many pencils measure 6 inches or more?

11 pencils measure 6, 7, and 8 inches.

I hope this helps!

Answer: 15

Step-by-step explanation: Linear equations can be written in the form

y = mx + b where the base "b" represents the y-intercept of the line.

So in this case, the y-intercept of the line would positive 15.

The equation can written as y = 4x + 15.

This equation is written in slope-intercept. y = mx + b

m = slope

b = y-intercept

In this equation the y-intercept (b) is 15.

_______

Best Regards,

Wolfyy :)

Answer:

[tex]x=-\frac{88}{3}[/tex]

Step-by-step explanation:

When a quantity "A" varies DIRECTLY with another quantity "B", we can write the proportionality equation as:

A = kB

Where k is the proportionality constant (to be found)

In this problem, it is given x varies DIRECTLY with y, so we can write:

x = ky

Also, given, x = 11, y = -3, so we plug these into the equation and first find k:

x = ky

11 = k(-3)

k = -11/3

Now, we need to find x when y = 8, so we substitute and find x:

[tex]x=ky\\x=(-\frac{11}{3})(8)\\x=-\frac{88}{3}[/tex]

To find x for a given value of y when x varies directly as y, determine the constant of proportionality using the provided pair of values. Then use this constant to calculate x for the new value of y.

Since x varies directly as y, we can write this as x = ky, where k is the constant of proportionality. To find the value of k, we use the given values: x=11 when y=-3. Substituting these values into the equation gives us 11 = k(-3), or k = -11/3.

To find x when y=8, we substitute y=8 and the value of k into the direct variation equation: x = (-11/3)(8) = -88/3 = -29.33. Therefore, x is approximately -29.33 when y=8.

Answer: No

Step-by-step explanation: because

1/2 +1/4 +1/3 is larger than one bowl.

6+3+4/12 = 13/12

;. 1 ¹/12.

Therefore, 1 bowl can not carry it

No, One bowl can not carry all of the ingredients at one time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad made a snack by combining 1/3 of a bowl of granola with ¼ of a bowl of chopped banana and ½ of a bowl of yogurt.

The total amount 1/2 +1/4 +1/3 is larger than one bowl.

6 + 3 + 4/12 = 13/12

also 1 ¹/12.

Therefore, No 1 bowl can not carry it.

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8 minutes is 2/15 of an hour when simplified, which is obtained by dividing both the numerator and denominator of the fraction 8/60 by the greatest common divisor of 8 and 60, which is 4.

To convert 8 minutes into a fraction of an hour, first understand that 1 hour is equivalent to 60 minutes. Therefore, to find what fraction 8 minutes is of an hour, you can create the ratio of 8 minutes to 60 minutes, which simplifies to:

8 minutes / 60 minutes = 8/60

This fraction can then be simplified by dividing both the numerator and the denominator by the greatest common divisor (GCD) of 8 and 60, which is 4, to obtain:

8/60 ÷ 4/4 = 2/15

Thus, 8 minutes is 2/15 of an hour in simplest form.

The system that will be used to find the numbers

x+y=142

x-y = 14

Step-by-step explanation:

The linear equations are used for representing real life situations

Let x be the first number

and

y be the second number

Then

According to given statement,

"The sum of two numbers, x and y, is 142."

[tex]x+y=142[/tex]

And

"Their difference is 14."

[tex]x-y=14[/tex]

Hence

The system that will be used to find the numbers

x+y=142

x-y = 14

Keywords: Linear Equations

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The price of house is $185000.

Step-by-step explanation:

The percentage formula will be used for finding the price of the house

Given

Down payment = $25900

Percentage = 14%

Let x be the price of the home

Then

[tex]Down\ payment=14\%\ of\ x\\\\25900=0.14 * x\\\\x = \frac{25900}{0.14}\\\\x =185000[/tex]

Hence,

The price of house is $185000.

Keywords: Down payment, percentage

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Answer:

A. $3,150

B. $2,100

Step-by-step explanation:

A. Given,

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 10 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/10

Depreciation Expense = $31,500/10

Depreciation Expense = $3,150

Therefore, under the straight-line method, the depreciation expense will be = $3,150.

B. Given, (When the useful year is 15)

Trucks cost price = $40,000

Salvage Value = $8,500

Useful life = 15 years

Since there is no requirement, I am using straight-line depreciation method to calculate the depreciation expense.

We Know,

Depreciation Expenses = (Cost price - Salvage Value) / Useful Life

Therefore,

Depreciation expense = ($40,000 - $8,500)/15

Depreciation Expense = $31,500/15

Depreciation Expense = $2,100

Therefore, under the straight-line method, the depreciation expense will be = $2,100

Answer:

Part 1) The equation in slope intercept form is [tex]y=4x-8[/tex]

Step-by-step explanation:

Part 1) Write an equation in slope-intercept form for a line that passes through (3,4) (and has a y intercept of -8)

we know that

The equation of a line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have

[tex]b=-8[/tex]

[tex]point\ (3,4)[/tex]

substitute

[tex]4=m(3)-8[/tex]

solve for m

[tex]4+8=3m[/tex]

[tex]3m=12[/tex]

[tex]m=4[/tex]

therefore

[tex]y=4x-8[/tex]

Answer: X = 4.33

Step-by-step explanation:

cos angle = hypotenuse / opposite side

cos 30° = X/5

0.866 = X/5

X = 4.33

1) The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 ,

c = 0

2) The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 ,

c = -15

3) The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4) The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5) The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

Step-by-step explanation:

The standard form of a quadratic equation is ax² + bx + c = 0, where

1)

∵ 2x² = 3x

- Subtract 3x from both sides

∴ 2x² - 3x = 0

∵ The coefficient of x² = 2

∴ a = 2

∵ The coefficient of x = -3

∴ b = -3

∵ There is no numerical term

∴ c = 0

The standard form of the equation is 2x² - 3x = 0, a = 2 , b = -3 , c = 0

2)

∵ 4x² - 10 = 5

- Subtract 5 from both sides

∴ 4x² - 10 - 5 = 0

- Add like terms

∴ 4x² - 15 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ There is no x term

∴ b = 0

∵ The numerical term = -15

∴ c = -15

The standard form of the equation is 4x² - 15 = 0, a = 4 , b = 0 , c = -15

3)

∵ 3(x² - 4x) = 2(x + 2)

- Simplify each side

∴ 3x² - 12x = 2x + 4

- Subtract 2x from both sides

∴ 3x² - 12x - 2x = 4

- Subtract 4 from both sides

∴ 3x² - 12x - 2x - 4 = 0

- Add like terms

∴ 3x² - 14x - 4 = 0

∵ The coefficient of x² = 3

∴ a = 3

∵ The coefficient of x = -14

∴ b = -14

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 3x² - 14x - 4 = 0, a = 3 , b = -14 ,

c = -4

4)

∵ 3x(x + 2x) = 11

- Add the terms in the bracket

∴ 3x(3x) = 11

- Simplify the left hand side

∴ 9x² = 11

- Subtract 11 from both sides

∴ 9x² - 11 = 0

∵ The coefficient of x² = 9

∴ a = 9

∵ There is no x term

∴ b = 0

∵ The numerical term = -11

∴ c = -11

The standard form of the equation is 9x² - 11 = 0, a = 9 , b = 0 ,

c = -11

5)

∵ 6x(x - 8) = 2x² + 4

- Simplify the left hand side

∴ 6x² - 48x = 2x² + 4

- Subtract 2x² from both sides

∴ 4x² - 48x = 4

- Subtract 4 from both sides

∴ 4x² - 48x - 4 = 0

∵ The coefficient of x² = 4

∴ a = 4

∵ The coefficient of x = -48

∴ b = -48

∵ The numerical term = -4

∴ c = -4

The standard form of the equation is 4x² - 48x - 4 = 0, a = 4 , b = -48 ,

c = -4

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Answer:

160 ounces

Step-by-step explanation:

1 pound=16 ounces

so,

10 pounds=16 multiplied by 10= 160 ounces

Fun fact u spelled ounces at the very last.

pls can I have five star

The weight of the 10-pound package is 160 ounces.

There are 16 ounces in 1 pound. Juan is mailing a packet that weighs 10 pounds. To find the weight of the package in ounces, multiply the number of pounds (10) by the unit equivalence (16).

Therefore, the weight of the package is 160 ounces.

Answer:

m=-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3-9)/(1-(-5))

m=-6/(1+5)

m=-6/6

m=-1

Answer:

0/36

Step-by-step explanation:

Answer:

0/36

Step-by-step explanation:

It is impossible to roll two dice and get a sum less than 2.

(I'm assuming this is a 6 sided die, but either way if you have more than one die this is impossible.

The lowest you can roll would be 1+1 therefore adding up to a 2.