7.4x+3-9= 6 + 7.4x

with solution please

Using the Newton law of cooling;

a) 78

b) 4.4 min

c) 8.2 min

We know that;

T(t) = T(s)  + (To - Ts)e^-kt

T(t) = Temperature at time t

T(s) = Temperature of the surroundings

k = Rate of cooling

t = time taken

108 = 65 + (207 - 65)e^-2k

108 - 65 = (207 - 65)e^-2k

43 = 142e^-2k

43/142 = e^-2k

-2k = ln(0.3)

k = ln(0.3)/-2

k = 0.6

Thus;

At t = 4

T(t) = 65 + (207 -65)e^-4 *0.6

T(t) = 78

For T(t) = 75℉

75 = 65 + (207 -65)e^-t *0.6

75 - 65 = 142e^-t *0.6

10/142 = e^-t *0.6

-t *0.6 = ln(0.07)

t =  ln(0.07)/-0.6

t = 4.4 min

For T(t) = 64℉

64 = 65 + (207 -65)e^-t *0.6

-1 = 142e^-t *0.6

-1/142 = e^-t *0.6

t = ln(-0.007)/-0.6

t = 8.2 min

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The graph has a y-intercept at (0, 1) and is decreasing over the interval. Then the correct option is C.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The exponential function is given below.

f(x) = (1/3)ˣ

The value of the function at x = 0 will be given as,

f(0) = (1/3)⁰

f(0) = 1

As the value of the variable 'x' increases, then the value of the variable 'y' decreases. Then the function is a decreasing function.

Then the correct option is C.

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Two-and-four-fifths is less than three-and-one-half.

The correct option is B.

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

Comparing two-and-four-fifths and three-and-one-half.

two-and-four-fifths = [tex]2\frac{4}{5}[/tex]

three-and-one-half = [tex]3\frac{1}{2}[/tex]

Changing them from mixed fractions to improper fractions

[tex]2\frac{4}{5} = \frac{14}{5} \\\\3\frac{1}{2} = \frac{7}{2}[/tex]

We can deduce that [tex]\frac{14}{5}[/tex] < [tex]\frac{7}{2}[/tex]

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The value of  y and x intercepts are 1 and -5/2

We should know that the x-intercept is the point where the x line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis respectively

The equation of the graph is give as follows

m=(y-y₁)/(x-x₊)

Taking the points (0,1) and (5,3)

We can use them to find the slope

3-1/5-0

m=2/5

Applying this to the equation of the line to get

2/5 = y-1/x-0

2/5=y-1/x

Cross and multiply to get

2x=5y-5

Rewrite the equation and make y the subject of the relation

y=2/5x+1

When y=0 2/5x=-1

This implies that x= -5/2

Also, when x=0

y=0+1 = 1

The y intercept is 1 and the x intercept is -5/2

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Answer:

x = 0, y = 1

Step-by-step explanation:

This is a system of simultaneous equations in two variables

One method of solving is to get the coefficients of one of the variables same, add or subtract to eliminate that variable and solve for the other variable.

We have

x + 3y = 3 ...............[1]
3x +5y = 5................[2]

If we multiply Equation [1] by 3 we can get the x coefficients the same

[1] x 3 :

3x + 9y = 9..............[3]

Subtract equation [2] from equation [3]

[3] - [2]

(3x + 9y) - (3x + 5y) = 9-5

3x - 3x + 9y - 5y = 4

4y = 4

y = 1

Substitute for y = 1 in equation [1] to get

x + 3(1) = 3

x + 3 = 3

x = 0

So answer is

x = 0, y = 1

Answer:

x=3-3y------eq_i

3x=5-5y

x=5-5y--------eq_ii

3

equating eq i and ii

x=x

3-3y=5-5y

3

3(3-3y)=5-5y

9-9y=5-5y

-9y+5y=5-9

-4y= -4

y=1

now, subsituting the value of y in eq i

x=3-3y

x=3-3×1

x=3-3

x=0

Answer:

y = -1x + 4

Step-by-step explanation:

First find the slope (m):

m = (0-6)/(4-(-2)) = -6/6 = -1

y = mx + b

Plug one of the points into the equation: (pick (4,0))

0 = -1(4) + b

b = 4

Now you have the complete equation:

y = -1x + 4

Answer: I am confused by this can you explain further

Step-by-step explanation:

Answer:

Step-by-step explanation:

All of the other answers except for PQY are lines. You can assume that the answer is PQY.

Answer:

1 mile to 0.033333333333 repentant

Step-by-step explanation:

The category of the numbers are

From the question, we have the following parameters that can be used in our computation:

50 1/3 divided 50 1/4

This means that the individual numbers are

50 1/3 and 50 1/4

From the above numbers, we have

The greater the denominator, the smaller the number

This means that:

The greater number is 50 1/3, the smaller number is 50 1/4 and the numbers are close to one another

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Consequently, y=90/x serves as the equation illustrating the connection between the two variables.

An equation is a mathematical formula that joins two statements and uses the equal symbol (=) to indicate equivalence. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign divides the variables 3x + 5 and 14. The relationship between the two sentences on either side of a letter is explained by a mathematical formula. There is frequently only one variable, which also serves as the symbol. for instance, 2x - 4 = 2.

given

We can express this relationship as y1x if the variable y varies inversely as the variable x.

Y=k/x is the result of taking away the proportionality sign and adding a proportionality constant.

If y is equal to 18 when x is equal to 5, then 18=k/5 k=185=90.

Consequently, y=90/x serves as the equation illustrating the connection between the two variables.

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Answer:

y - 9 = 3(x - 4)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (4, 9 ) , then

y - 9 = 3(x - 4) ← equation of line

Answer: y - 9 = 3(x - 4)

Step-by-step explanation: The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = 3 and (a, b ) = (4, 9 ) , then

y - 9 = 3(x - 4) ← equation of line

The proof to show that ΔTSV ≅ ΔRSV, given that V is the midpoint of TR.

Two right angled triangles are said to be congruent if they have the same corresponding properties when compared.

A midpoint is said to divide a given line into two equal parts. So that the measure of length of the two parts are exactly the same. It may be determined by bisecting the line.

The following is the proof that ΔTSV ≅ ΔRSV;

<RSV ≅ <TSV                                   (definition of an angle bisector)

<RVS ≅ <TVS                                   (definition of right angle)

RS ≅ TV                                            (sides of congruent triangles)

RT = RV + VT                                    (addition property of a line bisector)

RV ≅ VT                                            (definition of a midpoint)

Therefore it can be deduced that;

ΔTSV ≅ ΔRSV                              (Side-Angle-Angle congruency theorem)

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Answer: 1.15

Step-by-step explanation:

2/5+3/4=1.15

Answer:

1.8 × 10-6.

Step-by-step explanation:

Answer: A: S = {1, 2, 3, 4, 5, 6, 7}

Step-by-step explanation:

"If a fair seven-sided die is rolled, the sample space, or S = {1, 2, 3, 4, 5, 6, 7} will be the numbers from 1 to 7.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.A sample space is a set of potential results from a random experiment. The letter ""S"" is used to denote the sample space.

Events are a subset of an experiment's potential outcomes.Hence if a fair seven-sided die is rolled, the sample space will be the numbers from 1 to 7 that is S = {1, 2, 3, 4, 5, 6, 7}.

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Answer:

A -1/4

B 1/6

Step-by-step explanation:

To find the slope from (-7, 5) to (-3, 4), we can use the slope formula:

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

Substituting in the coordinates of the two points, we get:

slope = (4 - 5) / (-3 - (-7))

= (-1) / 4

= -1/4

Therefore, the slope from (-7, 5) to (-3, 4) is -1/4.

To find the slope from (-3, 4) to 3,5, we can use the slope formula again:

slope = (5 - 4) / (3 - (-3))

= 1 / 6

= 1/6

Therefore, the slope from (-3, 4) to 3,5 is 1/6.

The slopes from Parts A and B tell us that the relationship between all the points in the table is that the y-values are increasing as the x-values increase, but the rate of change is different between the two pairs of points. Specifically, the y-values are increasing more quickly (at a slope of 1/6) as the x-values increase from (-3, 4) to 3,5 than they are (at a slope of -1/4) as the x-values increase from (-7, 5) to (-3, 4).

Sales increased until 2000 and then generally decreased. Hence, option C is the most appropriate answer to this question.

From the given graph,

The 0 on the x-axis denotes the year 1997, the 1 on the x-axis denotes 1998, and so on.

We can clearly see that the graph is neither steadily increasing nor steadily decreasing. Hence, options A and B are ruled out.

Sales never remained steady from 1997 to 2009 since the graph showed upward and downward movements. Hence, option D is wrong.

We can see the Graph is moving up from 1997 to 2000 and then moving down from 2000 to 2009.

Thus, sales increased from 1997 to 2000 and decreased from 2000 to 2009, so we can say they generally decreased after 2000.

Hence, option C is the correct answer.

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The complete question is -

Based on the graph, which of the following best describes the general trend in music album sales from 1997 through 2009?

A) Sales generally increased each year since 1997.

B) Sales generally decreased each year since 1997.

C) Sales increased until 2000 and then generally decreased.

D) Sales generally remained steady from 1997 through 2009.

The quocient rule can not be used in option C.

We know that in dealing with exponents there are certain laws that come into play and a few among these are;

a) Multiplication law

b) quotient law

c) Power law etc

The quotient law states that;

If a^m ÷ a^n

Then;

a^ m - n

This would only hold where there is a division thus it doesn't hold for the expression in option C. In this case, we would have to use the multiplication rule  of exponents.

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Answer:

c

Step-by-step explanation:

The value of x in the diagram is x = 5

The steps for this process are as follows

Step 1: Since MNP = AXYZ, we can set up an equation to solve for x.

Step 2: We can use the information from the diagram to form the equation.

Step 3: 3x + 4 = 6x - 11

Step 4: Subtract 3x from both sides of the equation.

Step 5: 4 = 3x - 11

Step 6: Add 11 to both sides of the equation.

Step 7: 15 = 3x

Step 8: Divide both sides of the equation by 3.

Step 9: 5 = x

The theory used in this question is algebra. Algebra is used to solve equations and determine values for variables. In this case, algebra was used to solve for the value of x.

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The number of people who receive a share of 2/5 from the given amount is 16 people.

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Given that the amount of share is GHc 40.00 and each individual person receives [tex]\frac{2}{5}[/tex] of the cedi.

The number of people who received the share can be calculated as:

[tex]n = 40 * \frac{2}{5}\\ \\n=16[/tex]

Hence, the number of people who receive a share of 2/5 from the given amount is 16 people.

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The probability the second card drawn is also a heart is 12/51.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

1) The probability the first card drawn is a heart is 13/52= 1/4. Since that heart is NOT returned to the deck, there are now 51 cards, 12 of them hearts. The probability the second card drawn is also a heart is 12/51. Since that heart is NOT returned to the deck there are now 50 cards, 11 of them hearts.

2) You draw cards with replacement from a standard deck until you have drawn 4 black cards.

Here, 22/48

= 11/24

4) The probability that the kth face card is drawn on the xth turn

Probability =k/x

Therefore, the probability the second card drawn is also a heart is 12/51.

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It is true the historical setting is important because due to this historical setting and the fact women were not allowed to vote politics were affected.

The historical setting refers to the conditions that affect a specific year, decade or historial moment. For example, in 1944 in you lived in Europe the most important factor of the historical setting was the Second War World.

It is true the historial settign greatly affected politics. Indeed historical conditions such as the fact women could not vote or were limited to do so affected not only those that were choosen as politicians but also the laws and policies created. For example, as there were not women in the government there were not laws to protect women.

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x+y≥9, 5x+10y≤70 and x≥0 and y ≥ 0 are the required system of linear inequalities that shows all possible combinations of the plants Emma could purchase.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Emma is buying new herbs for her garden

Basil plants cost $5 each and mint plants cost $10 each.

She wants to buy at least 9 plants but cannot spend more than $70.

Let x represents the number of Basil plants

y represents the number of mint plants

x+y≥9

5x+10y≤70

x≥0 and y ≥ 0

Now x=9-y

5x+10y≤70

5(9-y)+10y=70

45-5y+10y=70

45+5y=70

Subtract 45 on both sides

5y=70-45

5y=25

Divide both sides by 5

y=5

x+5=9

x=4

Hence, x+y≥9, 5x+10y≤70 and x≥0 and y ≥ 0 are the required system of linear inequalities that shows all possible combinations of the plants Emma could purchase.

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The dimensions of the deck should be increased by 5 feet each

From the question, we have the following parameters that can be used in our computation:

Length = 20 feet

Width = 25 feet

So, the area is

Area = 20 * 25

Evaluate

Area = 500

When increased by 50%, we have

(20 + x) *(25 + x) = 500 * 1.50

Evaluate

(20 + x) * (25 + x) = 750

Express 750 as 25 * 30

So, we have

(20 + x) * (25 + x) = 25 * 30

This means that

20 + x = 25

25 + x = 30

Solve for x

x = 5 and x = 5

This means that

Increment = 5

Hence, the lengths should be increased by 5 feet

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When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

The spikes that go through the middle of a cycle's wheel from one end to the other are an illustration of diameter. Since the diameter is the line segment that begins at one end of a circle and finishes at the other end of the circle, passing through the center, we can compare this to the diameter of a circle. The diameter of a circle cuts through the center, whereas the radius circumscribes the circle from edge to edge. The size of a circle essentially divides it in two. the distance in a straight line going from one edge of a tumor or other item, through the middle, and out the other edge.

given

d = 20 m

r = 10 m

θ = θ1 + 90°

tan θ1 = 5 /10

θ1 = 26°

θ = 26° + 90°

= 116°

that wheel was rotated 116° for you to be at 15 m elevation .

wheel rotates 360° in 4 min

time taken for the wheel to rotate 116° will be

time taken = (116° / 360°) * 4 min

1.29 min = 77.4 sec

When the ferris wheel rotates once every four minutes, your seat will be above 15 meters for 77.4 seconds of each revolution.

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Anna moves 100 jellybeans from bottle a to bottle b, changing the number of red jellybeans in bottle a to 80% and the number of yellow jellybeans in bottle b to 40 percentage

Let x be the number of jellybeans Anna moves from bottle a to bottle b

Original:

Bottle a: 400 jellybeans, 75% red, 25% yellow

Bottle b: 300 jellybeans, 50% red, 50% yellow

After:

Bottle a: 400 jellybeans, 80% red, 20% yellow

Bottle b: 300 + x jellybeans, 40% yellow, 60% red

Equations:

75% of 400 = 300 red jellybeans in bottle a

50% of 300 = 150 red jellybeans in bottle b

80% of 400 = 320 red jellybeans in bottle a

60% of (300 + x) = 180 red jellybeans in bottle b

320 red jellybeans in bottle a - 300 red jellybeans in bottle b = 20 red jellybeans

180 red jellybeans in bottle b - 150 red jellybeans in bottle b = 30 red jellybeans

20 red jellybeans in bottle a = 30 red jellybeans in bottle b

x = 100 jellybeans

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The area of the shaded regions is 4π - 8

From the question, we have the following parameters that can be used in our computation:

We start by calculating the area of the triangle using

Area of triangle = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area of triangle = 1/2 * 4 * 4 * sin(90 degrees)

Evaluate

Area of triangle = 8

Next, we calculate the area of the semicircle using

Area = 0.125πd²

Where

d² = (4² + 4²) = 32

So, we have

Area semicircle = 0.125π * 32 = 4π

The area of the circle is

Area circle = 0.25πd²

This gives

Area circle = 0.25π * 32 = 8π

The area of the shaded regions is

Shaded region = circle - semicircle - triangle

Substitute the known values in the above equation, so, we have the following representation

Shaded region =  8π - 4π - 8

Evaluate

Shaded region =  4π - 8

Hence, the shaded region is 4π - 8

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Answer:6.5

Step-by-step explanation:

it cant be 2 ft or 72 feet so it leaves us with the other two opsitions