Using Intermediate Value Theorem determine which of the following
function has a real root on [1,2].

The expression that is equivalent to 2(3x^2-6x+4)+2(-2x+25x+100) is 2(3x² + 1x + 104)

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

This will be illustrated as:

2(3x^2-6x+4)+2(-2x+25x+100)

= 6x² - 12x + 8 - 4x + 50x + 200

= 6x² +34x + 208

= 2(3x² + 1x + 104)

The equivalent expression is 2(3x² + 1x + 104).

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Answer:

f(x)=4x^2 is facing up, it has a minimum, and it's horizontally compressed

Step-by-step explanation:

It's facing up because there's no negative sign in front of the coefficient of x.

It has a minimum because any quadratic function that faces up will have a minimum, and any quadratic function that faces down will have a maximum.

It's horizontally compressed because as can be seen in the picture below, f(x)=4x^2 (red) has more "slope," so it's condensed toward the y-axis. Hence, if the coefficient is bigger than 1, then the function will be horizontally compressed, and if the coefficient is smaller than 1, then the function will be horizontally stretched.

The number of points at least 23 he will need to score in the next game in order for Mark to average at least 15 points per game.

Mark has scored 8,14,10,20, and 5 points in the past 5 basketball games.

Let the required number of points would be x

n = 6

∑x = 8 + 14 + 10 + 20 + 5 + x = 57 + x

As per the given question, we can write the inequality as:

∑x/n ≥ average per game

(57 + x)/6 ≥ 15

57 + x ≥ 15 × 6

57 + x ≥ 80

x ≥ 80 - 57

x ≥ 23

Thus, the number of points at least 23 he will need to score in the next game in order for Mark to average at least 15 points per game.

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The rate of interest compounded continuously is 16.7%

What does the math term "rate of interest" mean?

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.

Formula: [tex]A=Pe^{rt}[/tex]

Where A = final amount

P = initial amount

e =mathematical constant approximated as 2.7183

r = rate of interest

t = time

Initially (t=0) in 1945 a famous painting was sold for $21,210

[tex]21210 = Pe^{0} \\P = 21210[/tex]

In 1987 (t=42) the painting was sold for $33.3 million

[tex]33.3 * 10^{6} = 21210 e^{42r} \\e^{42r} = \frac{33.3 * 10^{6}}{21210 } \\\\e^{42r} = 1570.014\\42r = ln( 1570.014)\\r = \frac{1}{42} ln( 1570.014)\\r = \frac{1}{42} 7.36\\r = 0.167\\r = 16.7%[/tex]

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Answer:

-243

Step-by-step explanation:

x^5 = x * x * x * x * x

( - 3 )^5 = (-3) * (-3) * (-3) * (-3) * (-3) = -243

Expansion of x(3.25y - 4.86) is 3.25xy - 4.86x and expansion of

x(-1.75y + 5y - 3.86) + x is 3.25xy - 2.86x. The expressions are not equivalent as the coefficient of x is different in the expanded form.

What are equivalent expressions?

In expanded form, the expression combines all its like terms.

Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other.

According to the given question:

The given expressions are

1. x (3.25y - 4.86)

2. x (-1.75y + 5y - 3.86) + x

Expanding each expression

1. x (3.25y - 4.86)

= 3.25*x*y - 4.86*x

= 3.25xy - 4.86x

2. x (-1.75y + 5y - 3.86) + x

= -1.75*x*y + 5*x*y - 3.86*x + x

= 3.25xy - 2.86x

Clearly coefficient of x variable is different after expansion of expressions. Therefore, the expressions are not equivalent.

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Answer:

X=5

Angle c is 42 degrees

Step-by-step explanation:

sum of all angles in a triangle equal 180 degrees so we set all these angles equal to that

(9x-3)+(22x+1)+(42-3x)=180

31x-2+42-3x=180

28x+40=180

      -40.  -40

28x=140

/28.   /28

x=5

So now to find angle c we just fill in X

9(5)-3

45-3

42

Hopes this helps please mark beainliest

The equation of the graph g(x)  is [tex]3^{x-6}[/tex]

What is a graph ?

A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;

In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.

The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

If the graph of the function  f(x) = 3^x is translated 6 units to the right , then the function becomes

g(x) = f(x - 6)

     = [tex]3^{x-6}[/tex]

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The cost per message is $0.025 and  the graph that represents the Jerry's text message plan is graph 2

The cost of every 30 messages = $0.75

To find the cost of one message we have to use the unitary method

The cost of 1 message = The cost of every 30 messages / 30

Substitute the values in the equation

The cost per message = 0.75 / 30

Divide the terms

= $0.025

Next find the cost 40 messages = The cost per message × 40

Substitute the values in the equation

The cost of 40 messages = 0.025 × 40

= 1

Using these details the graph that represents the Jerry's text message plan is graph 2

Hence, the cost per message is $0.025 and  the graph that represents the Jerry's text message plan is graph 2

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After 30 Days will they be watered together again.

The smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.

                Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.

cacti gets watered every 10 days.

ferns get watered every 3days

LCM of 3 and 10 is 30.

After 30 Days will they be watered together again.

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Guyton can make the 72,072 distinct arrangements of the flowers.

Given, that Guyton bought 13 plants to arrange along the border of his garden.

Now, we are asked that how many distinct arrangements he can make.

As, we know that to arrange 13 plants comprised of 5 tulips, 5 roses, and 3 daisies,

we need to apply Permutations over 13 objects among which 5 are tulips, 5 are roses and 3 are daisies.

Now, on applying the permutations, we get

13 plants can be arranged in 13! ways,

but as among them 5 are tulips, 5 are roses and 3 are daisies.

So, Guyton can arrange the flowers in 13!/(5!×5!×3!).

= (6,22,70,20,800)/(120×120×6)

= 72,072

So, the arrangement can be done in 72,072 ways.

Hence, he can make the 72,072 distinct arrangements.

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The number of hours it will take them to lawn is 4 / 3 hours.

It take Sam 4 hours to rake the front lawn, while his brother, Dave, can rake the lawn in 2 hours.

The number of hours it will take both of them to rake the lawn together is as follows:

Hence, recall they a doing the same work

1 / t =  1 / 4 + 1 / 2

where

t = time(hours) both of them will work together

1 / t = 1 + 2 / 4

1 / t = 3 / 4

cross multiply

4 = 3t

divide both sides by 3

t = 4 / 3

Therefore,

t = 4 / 3 hours

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Answer:

80y by 40y

Step-by-step explanation:

The area of the rectangle that maximizes the enclosed area is

80 by 40

80+80=160

40+40=80

160+80=240 yards.

The derivative of the inverse function of the differentiable and increasing function f(x), g(x) = f⁻¹(x), at x = -2, g'(-2) is [tex]\dfrac{1}{7}[/tex]

An inverse function reverse the effect of the operations of a function, such that when the output of a function is the argument of its inverse function, the input of the function is obtained.

The derivative of an inverse function is found using the formula;

[tex]\dfrac{d}{dx} f^{-1}(x) = \dfrac{1}{f'[f^{-1}(x)]}[/tex]

When x = -2, we get, from the table included in the question;

g(-2) = f⁻¹(-2) = 1

Therefore;

[tex]\dfrac{d}{dx} f^{-1}(-2) = \dfrac{1}{f'[f^{-1}(-2)]} = \dfrac{1}{f'[1]}[/tex]

[tex]g'(-2) = \dfrac{d}{dx} f^{-1}(-2) = \dfrac{1}{f'[1]}[/tex]

In the included table, f'(1) = 7, from which we get;

[tex]g'(-2) = \dfrac{1}{f'[1]}=\dfrac{1}{7}[/tex]

[tex]g'(-2) = \dfrac{1}{7}[/tex]

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The required answer is [tex](7^{\frac{1}{3}})^{3} = (7^{\frac{1}{3}*3}) = 7^1=7[/tex].

what is a power rule for exponents ?

[tex](a^m)^n=a^{mn}[/tex] is known as the power rule for exponents. Exponent times power is how you raise a number with an exponent to a power.

A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. It could be an integer, a fraction, a negative integer, or a decimal.

[tex](7^{\frac{1}{3}})^{3} = (7^{\frac{1}{3}*3}) = 7^1=7[/tex]

Here, we have used the rule [tex](a^m)^n=a^{mn}[/tex]

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Try this option ↓

Step-by-step explanation:

1) if to evaluate the given limits using math methods, then:

[tex]\lim_{h \to 0} \frac{2.7^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.7^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.7^h*ln2.7}{1} =ln2.7;[/tex]

and

[tex]\lim_{h \to 0} \frac{2.8^h-1}{h}=[\frac{0}{0}]= \lim_{h \to 0} \frac{(2.8^h-1)'}{(h)'}= \lim_{h \to 0} \frac{2.8^h*ln2.8}{1} =ln2.8;[/tex]

2) for more info see the attached graphs; note, ln2.7≈0.993252, ln2.8≈1.029619 and the function is undefined in the points where x=0.

If Jerry currently has 20 points and likes to pick up the pink sticks, earning 4 points every turn, and his cousin has a strategy to catch up to jerry from 0, by getting all the red ones, earning 6 points per turn, then their scores will be tied after 10 turns from now on, and their points then will be 60.

As per the question statement, Jerry and his cousin are playing a game where they pick up colored sticks and Jerry currently has 20 points picking up the pink sticks which earn him 4 points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by picking all the red ones, which can earn 6 points per turn.

Then we are required to calculate the number of turns from now on, after which, their scores will be tied, and the magnitude of their points at that instant.

Let us assume that, their scores will be tied after "x" turns from now on.

Then, [{20 + (4 * x) = (6 * x)]

Or, [(20 + 4x) = 6x]

Or, [20 = (6x - 4x)]

Or, (2x = 20)

Or, [x = (20/2)]

Or, (x = 10)

That is, their scores will be tied after 10 turns from now on, and their points then will be [(20 + 4x) = (20 + 40) = 60].

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Answer: 4

Step-by-step explanation:

$7969.24 invested at 8% and $3930.76 invested at 5%

From given information,

Amount invested = $11,900

Rate of interest for first part = 8%

Rate of interest for second part = 5%

Let the amount invested for 8% be 'x'.

Let the amount invested for 5% be 'y'

According to question, we get an equation,

0.08x - 0.05y = 441

x + y = 11,900

x = 11,900 - y

0.08(11,900 - y) - 0.05y = 441

952 - 0.08y - 0.05y = 441

-0.13y = -511

y = (-511)/(-0.13)

y = 3930.76

so, x = 11,900 - 3930.77

x = 7969.23

Therefore, $7969.24 invested at 8% and $3930.76 invested at 5%

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The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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The number of beads that are in each group when Jade divides the beads is 30.

From the information, Jade has 72 unopened package of beads and she also has 8 beads in a package that is already open. Jade puts all the beads together.

The addition will be:

= 72 + 8

= 80

She then divides then into 4 groups, the number in each group will be:

= Total beads / Number of group

= 80 / 4

= 20 beads

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Complete question

Jade has 72 unopened package of beads. she also has 8 beads in a package that is already open. Jade puts all the beads together and divides then into 4 equal groups to share with her friends. how many beads are in each group?

260 occurrences of the letter e we can expect to find.

Frequency = 13%

Total letters = 2000

E letters = 13% of 2000

              = (13/100)*2000

              = 13*20

              = 260

Hence, there are 260 e letters in 2000 of total letters.

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Answer:

20%.

Step-by-step explanation:

A sum of money will triple itself in ten years at an annual interest rate of 20%.

Answer:

∴ x = 4.5, y = 5.5

Step-by-step explanation:

x + y = 10 ------ equation (1)

x - y = -1 ------ equation (2)

Add equations (1) and (2):

(x + y) + (x - y) = 10 + (-1)

   x + y + x - y = 10 - 1

                  2x = 9

                 ∴ x = 4.5

Substitute x = 4.5 into equation (1):

4.5 + y = 10

     ∴ y = 5.5  

The number of machines must be made to minimize the unit cost is 280

What is second order derivative test?

A real-valued function formed on a closed or bounded interval can have its absolute maximum and lowest values determined systematically using the second derivative test. In physics, economics, and engineering, the second derivative test can be used to solve optimization problems.

We are given a function

C(x)=0.7x²-392x+60,983.

We first find the first derivative of the function we get

C'(x) = 1.4x-392

We now equate the first derivative to zero

we get

1.4x= 392

x= 280

Now we derivate the function again we get

C"(x)= 1.4

Now this value is greater than zero hence here is the greatest minimum

Hence the company must produce 280 units to minimize the cost

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The function that models the distance in miles is f(x) = 20 + 50x

The domain of the function is 0 ≤ x ≤ 2

Information given in the question include

Ali and Kris are driving to a city that is 120 miles from their house

They have already traveled 20 miles

they are driving at a constant rate of 50 mi/h

The function can be modeled as a linear function

A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = c + mx

Definition of variables to suit the problem to be solved

y = total mileage covered = f(x)

m = mileage covered per hour = 50 mph

x = number of hours

c = miles already covered = 20 miles

The function is substituted to the equation as below

y = c + mx

f(x) = 20 + 50x

The domain refers to the reasonable time spent during the journey

this is time at minimum distance = 0 to time at maximum distance = 120

f(x) = 20 + 50x

0 = 20 + 50x

-20 = 50x

x = -2/5

since there is no negative time, it is more reasonable to start with zero

120 = 20 + 50x

120 - 20 = 50x

50x = 100

x = 100 / 50

x = 2 hours

A reasonable domain is 0 ≤ x ≤ 2

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Answer:

it's correct

Step-by-step explanation:

17+2.6b=30

2.6b=30-17

2.6b=13

b=13÷2.6

b=5

Answer:

ima need a complete question

Step-by-step explanation:

Given O is the midpoint of PT and RS

Therefore, In triangles POR and TOS, we have

PO = TO (O, the midpoint of PT);

∠POR=∠TOS, (vertically opposite angles);

RO=OS, (O, the midpoint of RS)

So by SAS postulate, we have

△POR = △TOS    Hence proved

What is the midpoint?

The midpoint is a line segment's center point in geometry. The midpoint is also the centroid of the segment and the endpoints are equally spaced from both endpoints. The midpoint can also be described as a point that divides a segment in half or as one that is equally spaced from both ends of a line.

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The equation that represents the total cost of electric service using Zap Electric company is y = $0.06r + $6.55

The equation that represents the total cost of electric service using Bolt Electric Company is y = $0.12r + $2.83

The equation that can be used to determine the total cost of electric service is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is usually a straight line.

The total cost is the sum of the monthly service fee and the total cost of the kilowatt used.

Total cost = service fee + (charge per kilowatt x number of kilowatts used)

Zap Electric company : $0.06r + $6.55

Bolt Electric Company : y = $0.12r + $2.83

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The temperature of the solution is -7.6°F.

Temperature simply means the degree of hotness and coldness in a body.

In this case, the temperature of a solution increases by 1.7° F each minute for 2 minutes and the solution is then placed in an ice bath, and its temperature decreases by 11°F over the next minute.

The current temperature will be:

= (1.7 × 2) - 11

= 3.4° - 11°

= 7.6°F

The temperature is -7.6°F.

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