For the following exercises, find the average rate of change of the functions from x = 1 to x =2.
24. f(x) = 4x − 3

Answer:

m (slope) = -1/10; the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter; the y intercept is how tall the candle is at the beginning

Step-by-step explanation:

to find the slope of this line we can simply use the (y2 - y1) / (x2 - x1) formula

that gives us

(0 - 25) / (250 - 0)

or

-25/250

or

-1/10

the slope means that every 1/10 minute the candle goes down 1/100 centimeters OR every 10 minutes the candle goes down 1 centimeter

the y intercept is how tall the candle is at the beginning

Answer: About 29

Step-by-step explanation: First you need to add all the numbers together. Then you divide the sum, 235, by however many numbers you have (8). And BOOM: you got your answer :)

PS: If you have a decimal number, just round it up or down ( 5 and above give it a shove; 4 and below let it lie low)!

Answer:

It is nonlinear

Step-by-step explanation:

Using relations in a right triangle, the area of the triangle is given by:

B. 9tan(65º)/2.

The relations in a right triangle are given as follows:

In this problem, we have one leg(length 3) and the angle with the hypotenuse(65º), hence the other leg can be found as follows:

[tex]\tan{65^\circ} = \frac{x}{3}[/tex]

x = 3tan(65º).

The area of a right triangle is half the multiplication of it's legs, hence in this problem:

A = 1/2 x 3 x 3tan(65º) = 9tan(65º)/2.

Which means that option B is correct.

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The fraction of 1 pound to 31 penny is 31/100.

Given that, £1  and 31 p.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, 1 pound = 100 penny

Now, the fraction of £1 is 31 p is

31/100

Therefore, the fraction of 1 pound to 31 penny is 31/100.

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[tex]9 \: units \: to \: the \: right \: = x - 9[/tex]

[tex]1 \: unit \: down \: = - 1[/tex]

[tex]g(x) = 4x {}^{2} - 16 \\ h(x) = 4(x - 9) {}^{2} - 17[/tex]

Answer:

You divide 360 by 5 which is 72 & Then muiltiply that by 2.
Your answer would be 144 tho.

The equivalent is 24a + 30b +2c + 30

Given the original expression as;

30a+12b-6a+ 2(9b+c+15)

First, expand the bracket, we have

30a + 12b -6a + 18b + 2c + 30

Then, collect like terms

30a -6a + 12b + 18b + 2c + 30

24a + 30b +2c + 30

The equivalent is 24a + 30b +2c + 30

From the result, we have that Martin is correct.

Sara wrote the equivalent as 24a + 30b +2c + 15

She made a mistake in expand the bracket = 2( 9b +c +15) = 18b + 2c + 30

Ben wrote 36a - 30b + 2c + 30. He made a mistake in issuing the sign for 30b = 12b + 18b = +30b

Thus, the equivalent is 24a + 30b +2c + 30

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Answer:

11.0 cm

P=38 cm

38/3=12.67cm length of one side

Base of triangle = 12.67/2 =6.34 cm

Use formula [tex]a^2+b^2=c^2[/tex]

[tex]6.34^2+x^2=12.67^2\\\\=11.0 cm[/tex]

x = altitude of triangle

Answer:

The answer is C: 3/4

Step-by-step explanation:

Your equation is equal to (3/2)/(4/2) due to absolute value (all numbers are positive even if negative symbol is infront of it) which is equal to 3/4.

Step-by-step explanation:

what is the real problem definition ?

is there now an absolute value around the top "-2", or not ?

in any case, remember, when we divide 2 rational numbers like this :

a/b / c/d

the result is

"outer multiplication" over "inner multiplication" :

a×d / b×c

as alternative you can always also say

a/b / c/d = a/b × d/c = a×d / b×c

so,

if the problem is

3/-2 / |-4/-2|

the result is

3×2 / 4×-2 = 6/-8 = - 3/4

if the problem is

3/|-2| / |-4/-2|

the result is

3×2 / 4×2 = 6/8 = 3/4

please pick the solution based on the actual problem.

Answer:

Step-by-step explanation:

So sin is defined as [tex]\frac{opposite}{hypotenuse}[/tex]. and cosine is defined as [tex]\frac{adjacent}{hypoteunse}[/tex]. So we need the adjacent side. Since we already have the opposite, and hypotenuse, you can use the Pythagorean identity to solve for the missing side: [tex]a^2+b^2 = c^2[/tex]

[tex]15^2 + b^2 = 19^2[/tex]

[tex]225 + b^2 = 361[/tex]

[tex]b^2 = 136[/tex]

[tex]b = \sqrt{136}[/tex]

[tex]b = \sqrt{4} * \sqrt{34}[/tex]

[tex]b = 2\sqrt{34}[/tex]

This is the adjacent side, so now plug this into the cosine equation and you get: [tex]\frac{2\sqrt{34}}{19}[/tex]

It is true that Random assignment to treatments helps control for lurking variables

The main purpose for using randomization in an experiment is to create sure that the results are accurate. you wish to avoid biasis and lurking variables. Having a randomized experiment will facilitate your to create sure that your information is correct

The main purpose for using randomization in an experiment is to manage the lurking variable and establish a cause and effect relationship. Also, by randomizing an experiment the evidence is more supported

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The probability of getting tails and rolling an odd number is P = 0.25

The probability of getting tails on the coin is 0.5

On the dice, there are 6 numbers and 3 are odd, so the probability of rolling an odd number is:

p = 3/6 = 0.5

The joint probability (of getting tails and rolling an odd number) is equal to the product between the individual probabilities:

P(odd and T) = 0.5*0.5 = 0.25

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Answer: 1 : 3

Shaded area:

[tex]\Longrightarrow \sf Length \ \times \ Breadth = \dfrac{x}{4} \ \times \ x \ = \ \dfrac{1}{4}x^2[/tex]

Unshaded area:

[tex]\Longrightarrow \sf Length \ \times \ Breadth = (x - \dfrac{x}{4}) \ \times \ x \ = \ \dfrac{3}{4}x^2[/tex]

Ratio of shaded to unshaded:

[tex]\Longrightarrow \sf \dfrac{1}{4} x^2 \ : \ \dfrac{3}{4} x^2 = 1 : 3 \quad (simplified)[/tex]

A function assigns the value of each element of one set to the other specific element of another set. The correct option is A.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means that the inverse of 'f' is an undone operator, that takes back the effect of 'f'

The graph that represents the inverse of the given function is option A because graph A is showing more rapid growth as compared to the given graph.

Hence, the correct option is A.

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The resulting equation if Becca isolated x² in the first equation and then substituted it into the second equation is (9-y²) / 25 - y²/36 = 1

x² + y² = 9

x²/25 - y²/36 = 1

From (1)

x² = 9 - y²

substitute x² = 9 - y² into (2)

x²/25 - y²/36 = 1

(9-y²) / 25 - y²/36 = 1

Therefore, the resulting equation is option C; (9-y²) / 25 - y²/36 = 1

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Answer:

(9-y²) / 25 - y²/36 = 1

Step-by-step explanation:

The information given about the probability shows that the cardinality of D is 18.

From the complete information, the number of red-colored cards is 26.

Also, the number of red-colored number cards will be 18.

The cardinality of a set is a measure of a set's size, meaning the number of elements in the set.

Here, the cardinality of set D is 18.

Here is the complete question:

Take a deck of playing cards. Form following sets out of those:

A = Set of Face Cards

B = Set of Red Coloured Face cards

C = Set of Black Coloured Face Cards

D = Set of Red Coloured Number Cards

Find the Cardinality of set D

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The rate at which the gas powered pump deliver water is 160.9 litres per seconds

The gas powered water pump delivers 42.50 gallons of water per minute.

Therefore,

1 gallon = 3.78541 litres

42.50 gallons = ?

cross multiply

volume = 42.50 × 3.78541 = 160.879925 litres

Hence,

60 seconds = 1 minutes

1 second = ?

time = 1 / 60 = 0.01666666666 seconds

Hence,

rate = 160.9 litres per second

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A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is A.

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the pair of opposite sides are equal and parallel. Therefore,

1.)  For the first pair.

(x+8) = 15

x = 7

2.) For the second pair

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

x + 2 = 2x - 5

2 + 5 = 2x - x

x = 7

(x+2) = (7+2) = 9

Since the measure of the pair of opposite sides is 15 units, the pair of the other two sides measure 9 units.

Hence, the correct option is A.

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By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.

In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.

After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:

f(5) = 5 - 3

f(5) = 2

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Answer:A which is x-3

Step-by-step explanation:

The simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]

The expression is given as:

[tex]\frac{x - y}{4x^2 - 8xy + 3y^2} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{x^2 - y^2} -1[/tex]

Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions

[tex]\frac{x - y}{(2x - y)(2x - 3y)} \div \frac{2x + y}{2x - 3y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]

Rewrite the expression as products

[tex]\frac{x - y}{(2x - y)(2x - 3y)} \times \frac{2x - 3y}{2x + y} \times \frac{4x^2 - y^2}{(x - y)(x + y)} -1[/tex]

Cancel out the common factors

[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{4x^2 - y^2}{(x + y)} -1[/tex]

Express 4x^2 - y^2 as (2x - y)(2x + y)

[tex]\frac{1}{(2x - y)} \times \frac{1}{2x + y} \times \frac{(2x - y)(2x + y)}{(x + y)} -1[/tex]

Cancel out the common factors

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

Take the LCM

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

Hence, the simplified expression is [tex]\frac{1 - x - y}{x + y}[/tex]and the restriction is [tex]y \ne -x[/tex]

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Answer:

Step-by-step explanation:

UV = [tex]\frac{XY+WZ}{2}[/tex]

[tex]\frac{XY+39}{2}[/tex] = 25

XY + 39 = 50

XY = 11    

(-∞,8) is interval is the solution to set 0.35x – 4.8 < 5.2 – 0.9x.

0.35x - 4.8 < 5.2 - 0.9x

Adding 0.9x to both sides of equation.

0.35x - 4.8 + 0.9x < 5.2 - 0.9x + 0.9x

1.25x - 4.8 < 5.2

Adding 4.8 to both sides of equation.

1.25x - 4.8 + 4.8< 5.2 + 4.8

1.25x < 10

Dividing both sides of equation by 1.25

x < [tex]\frac{10}{1.25}[/tex]

Hence x < 8

Thus, (-∞,8) interval is the solution to given set 0.35x – 4.8 < 5.2 – 0.9x.

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Answer:

35

Step-by-step explanation:

Basically, since the angle HGF consists of HGE and EGF, then that means that HGF = HGE + EGF, and since EGF and HGF is given we plug this into the equation to get: 145 = HGE + 110, so HGE = 35.

Answer: 35°

Step-by-step explanation:

Hi!

The total angle is 145°

part of the angle is 110°

to find the missing angle, do 145 - 110 = 35°

Hope this helped :)

Answer:

A) -20+48i

Step-by-step explanation:

[tex](4+6i)^2\\(4+6i)(4+6i)\\16+24i+24i+36i^2\\**i^2=-1*\\16+48i+36i^2(-1)\\16+48i-36\\-20+48i[/tex]

The average rate of change of the function given is 56

The formula for calculating the rate of change of a function is expressed as;

f'(x) = f(b)-f(a)/b-a

where

b = 4

a = 2

f(4) = 2(4)^3 +1

f(4) = 129

f(2) = 2(2)^3 + 1

f(2) = 17

Substitute

f'(x) = 129-17/4-2

f'(x) = 112/2

f'(x) = 56

Hence the average rate of change of the function given is 56

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The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used is 4c + 36

The equivalent expression without parenthesis that can be used to determine the total number of flowers the florist used.

total number of flower the florist used for the bouquet = 4(c + 9)

Therefore,

total number of flower the florist used for the bouquet = 4c + 36

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There are 20 combinations of boxes that can be used for the customer's 15 chocolate pieces.

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression. When the coefficients are themselves variables, they may also be called parameters.

It is given that a customer ordered 15 pieces of gourmet chocolate. The order can be packaged in small boxes that contain 1, 2 or 4 pieces of chocolate. Any box that is used must be full.

The coefficient of [tex]x^{15}[/tex] from the steps shown in the image is 20.

Hence, there are 20 possibilities.

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Answer:

-10 and -2

Step-by-step explanation:

ONLY IF ITS two number that mutiply to equal 20 and their sum is -12

Answer:

The second choice (-6, -5 2/5, -4 1/5)

Step-by-step explanation:

1) Find the nth term by using the rule given. Foil them out.

A(n) = -6 + 1/5n - 1/5

A(n) = 1/5n - 31/5

2) Find the first term by substituting 1 into n.

a1 = 1/5(1) - 31/5

a1 = -6

3) Find the fourth term by substituting 4 into n.

a4 = 1/5(4) - 31/5

a4 = -27/5 or -5 2/5

4) Find the tenth term by substituting 10 into n.

a10 = 1/5(10) - 31/5

a10 = -21/5 or -4 1/5

Therefore, the second choice (-6, -5 2/5, -4 1/5) is correct.