Let f and g be differentiable functions. If g and f are inverses of each other,
g(-4)= 7, and f'(7) = 2, then g'(-4) =

Select one answer
A -2
B -1/2
C 1/2
D 2

A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).

In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.

By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).

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Complete Question:

The graph below shows distance over time. Which of these situations could be represented by this graph?

answer choices

A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.

A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.

A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.

La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.

Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.

Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:

6m/8m = 0.75

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The simplest form of the given expression is -19x + 10.

The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.

Given that

(-10x+2) + (-9x+8)

We have to simplify the given expression

= -10x + 2 - 9x + 8

= (-10x - 9x) + (2 + 8)

= -19x + 10

Therefore the simplest form of the given expression is -19x + 10

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Answer:

125 in simplest form is 1/8.

Step-by-step explanation:

Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​ in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality is true.

In this case, you know that:

Being "x" the number of folders, the inequality that expresses the previous relationship is

45 + 0.45x > 50.40 + 0.15x

Solving:

0.45x - 0.15x > 50.40 -45

0.30x> 5.4

x> 5.4÷ 0.3

x> 18

Finally, the number of folders Jan would need to buy is more than 18.

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The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:

= 3.6 x 10^7 + 2.1 x 10.^7

= 5.7 × 10^7

Therefore, the correct option is D.

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Answer:

43446

Step-by-step explanation:

52 weeks in an year

835.5 × 52 = 43446

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

Given that

form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice

let's consider that letter a is not there in the string

each letter is repetitive then it is [tex]4^{5}[/tex]

now letter a is considered once

5c1 ×[tex]4^{4}[/tex]

now letter a is repetitive twice

5c2 × [tex]4^{3}[/tex]

[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]

1024+ 1280 + 640 = 2944

2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice

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Answer:

$134.86

Step-by-step explanation:

Let the original price before tax be x.

A whole amount is 100% of the amount, so x is 100% of the original price without tax.

The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.

106% of x = $142.95

106/100 × x = 142.95

1.06x = 142.95

x = 142.95/1.06

x = $134.86

Answer: $134.86

Answer: (p/6 + q) + 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

105 min

60 min in a hour and then 3/4 of a hour is 45 min.

Total: 105 minutes

Answer:

[tex]12x -6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

As a fraction in simplest form it SHOULD be 24 over 25.

Step-by-step explanation:

"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)

Answer:

24/25

Step-by-step explanation:

0.96

By counting the numbers after the decimal point which is two.

so we will write: 96/100, since hundred has to two zero.

Then we will divide 96/100 to it simplest form which is 24/25

Answer:

64000

Step-by-step explanation:

When you are rounder you must look at the last number to determine if you are rounding up or down.

The line equation passing through the given points and parallel to the given lines are:

Line 1: y=-4x+13...(i)

Line 2: y=2x-12...(ii)

Line 1

The first line is passing through point (1,9) and parallel to the y=4x+2 line.

Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=4x+2 has:

ay = bx + c, m= -b/a

y=4x+2, m=-4

We could use the line equation formula, where:

y-y1 = m (x-x1)

we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:

y-9 = -4(x-1)

y-9=-4x+4

y=-4x+13...(i)

Line 2

The first line is passing through point (5,2) and parallel to the y=-2x+7 line.

Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).

Using the standard formula of line equation, we could identify that line y=-2x+7 has:

ay = bx + c, m= -b/a

y=-2x+7, m=-2

We could use the line equation formula, where:

y-y2 = m (x-x2)

we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:

y-2 = 2(x-5)

y-2 = 2x-10

y=2x-12...(ii)

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Answer:

Step-by-step explanation:

x=26

Answer:

1.209  <  1.29  <  1.9  <  3.76

Step-by-step explanation:

The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is

option B.

B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.

Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.

The reason for arriving at the above selection is as follows:

According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.

                        ∠ONP ≅ ∠LNM

The required parameters are:

To find the additional information that would prove ΔONP and ΔMNL by

AA (Angle-Angle) similarity postulate.

Given from the drawing,

One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.

Prove that:

either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:

Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.

Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.

Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.

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Answer:

b

Step-by-step explanation:

Answer:

10 + 5i

Step-by-step explanation:

[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]

Answer: C

Step-by-step explanation:

Answer:

perimeter = 22 km and area = 18 km^2

Step-by-step explanation:

First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.

Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.

To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)

let me know if anything is confusing :-))

Andre used 2983 gallons of liquid all through this month.

Given;

Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.

To get the measurement that is closest to the number of liters Andre used during this month;

The total gallons of water used in a month = 785 gallons

The quantity of water in a single gallon = 3.8 liters

Therefore, the number of liters Andre used during this month;

U = total gallons of water used in a month * quantity of water in a single gallon

U = 785 * 3.8

U = 2983

Hence, the number of liters Andre used during this month is 2983 gallons.

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From the calculation, the original number is obtained as 84.

We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.

Let the tens digit be T and let the units digit be U

We can then write

10U+T = 10T+U-36

Since the reversed number is 36 less than the original number.

Then;

9U = 9T -36

Dividing both sides of the equation by  9

U = T -4

U=2U-4

U=4

T = 8

It then follows that the original number is 84.

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Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping

Step-by-step explanation:

i personally used a guess and check method.

i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39

i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39

39 + 39 = $78

Answer:

second number = (x + 7.5)

Since the product of the two numbers is double of their sum,

             x(x + 7.5) = 2(x + x + 7.5)

             x² + 7.5x = 2(2x + 7.5)

             x² + 7.5x = 4x + 15

x² + 7.5x - 4x - 15 = 0

      x² + 3.5x - 15 = 0

                      ∴ x = -6 or 2.5

∴ second number

= -6 + 7.5 or 2.5 + 7.5

= 1.5 or 10

∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.

The value of x will be 24.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

For a given right triangle, the expression is,

⇒ sin (3x - 7) = cos (x + 1)

Now,

Solve for x as;

The expression is,

⇒ sin (3x - 7) = cos (x + 1)

Since, sin x= cos (90 - x)

So, We get;

⇒ sin (3x - 7) = cos (x + 1)

⇒ cos (90 - (3x - 7)) = cos (x + 1)

⇒ 90 - (3x - 7) =  (x + 1)

⇒ 90 - 3x + 7 = x + 1

⇒ 97 - 3x = x + 1

⇒ 97 - 1 = x + 3x

⇒ 96 = 4x

⇒ 4x = 96

⇒ x = 96/4

⇒ x = 24

Thus, The value of x will be 24.

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Answer:

Hi

Step-by-step explanation:

so the question is asking what is 2/5  of  150

if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.  

does 150 split up into 5 even parts??

hmmm  you probably are thinking,  15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30  :)

2 time 30 = 60

so there is how to figure out the answer and , the answer 60 :)

The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23

The equation is linear equation in the slope intercept form as

y = mx + c

where

m = slope = -8

c = intercept = 184

x = input variables = m

y = output variables = A(m)

The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0

0 = 184 - 8m

8m = 184

m = 23

The maximum value of m is 23 hence the domain is m ≤ 23

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