*Convert the following statements into equations.*
(a) 3 added to a number is 11
b
(b) 2 subtracted from a number is equal to 15.
(c) 3 times a number decreased by 2 is 4. (d) 2 times the sum of the number x and 7 is 13.​

Calculus is a branch of mathematics that deals with the study of rates of change and accumulation of quantities.

It has two main branches: differential calculus and integral calculus.

Differential calculus studies the rate of change of a function, also known as its derivative. It deals with concepts such as limits, derivatives and their properties and applications, such as optimization problems.

Integral calculus, on the other hand, deals with the accumulation of quantities, also known as integrals. It studies the concept of definite and indefinite integrals and their properties and applications, such as finding areas and volumes, solving differential equations and computing path length.

Calculus has a wide range of applications in various fields, such as physics, engineering, economics, and many more. It's also a fundamental tool for most mathematical modeling and scientific research.

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The mass of one molecule of methane is 2.658 × [tex] {10}^{-23} [/tex] and number of molecules of methane is 3.76.

Mass of one molecule of methane = mass of one carbon atom + 4×mass of one hydrogen atom

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 1.67 × [tex] {10}^{-24} [/tex]

Performing multiplication first

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 6 68 × [tex] {10}^{-24} [/tex]

Equating the exponents

Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 0.668 × [tex] {10}^{-23} [/tex]

Performing addition

Mass of methane = 2.658 × [tex] {10}^{-23} [/tex]

Now, 2.658 × [tex] {10}^{-23} [/tex] is the weight of molecules number = 1

1 gram will have number of molecules = 1/ 2.658 × [tex] {10}^{-23} [/tex]

Number of molecules = 3.76

Thus, mass is 2.658 × [tex] {10}^{-23} [/tex] and 3.76 molecules are there.

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A triangle is a 3 sided Polygon whose internal angle sum up to 180 degrees. It can be constructed by knowing those angles.

To construct a perfect triangle you can follow the following procedure have a brief idea on the angles of the triangle and if the angles are not available get to know about the length of each side of the triangle. If you know the each and every angle of the triangle you can proceed to the construction of triangle. Initially draw a baseline with the given dimension let us say this line is XY. Now from either left or right side of xy with the given angle draw a slanting line even if the length of the line is not known. From this from the other side draw another slanting line from the given angle and extend it up to the point where it touches the previous line. Now you have the triangle created for you. You can name the new point with the letter Z.

Now you have the triangle XYZ constructed.

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Based on the given exponential graph, the value of car will be decreased by half after 2 years.

The exponential function is a type of mathematical function that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.

Jonathan was reading a news story about the most recent bacterial growth study.

He had read that one bacteria had been used in an experiment. The bacterium doubled in size and had two by the end of the first hour. The number was four after the second hour.

he number of microorganisms was growing hourly. If this pattern holds, he wondered how many bacteria there will be in 100 hours. When he asked his teacher about the same thing, the concept of an exponential function was the response he received.

The value of y at x = 0 is 80,

So, the initial cost of car is 80 thousand dollars,

half the original value will be 40 thousand dollars,

Value with respect to 40 is 2 on the x - axis on the graph.

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Complete Question -

The amount of money that each team raised are;

Amount raised by Back Street location = $200

Amount raised by Main Street location = $250

Amount raised by Washington Street = $150

We are told that the main street location raised $50 more than the Back Street location. Thus;

m.s = b.s + 50    ------(eq 1)

The Washington Street location raised $50 more than half the amount raised at the Back Street location. Thus;

w.s = ¹/₂b.s + 50    -------(eq 2)

Total raised = $600. Thus;

m.s + b.s + ws = 600    -------(eq 3)

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

Plug in b.s + 50 for m.s and ¹/₂b.s + 50 for w.s in eq 3 to get;

(b.s + 50) + (¹/₂b.s + 50) + b.s = 600

Solve for b.s;

b.s + ¹/₂b.s + b.s + 50 + 50 = 600

(5/2)b.s + 100 = 600

(5/2)b.s = 500

b.s = $200 (amount raised by Back Street location)

m.s = b.s + 50

= 200 + 50

= $250 (amount raised by Main Street location)

w.s = (1/2)b.s + 50

w.s = 100 + 50

w.s = $150 (amount raised by Washington Street)

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If two polynomials have different degrees, the degree of the sum is the maximum of the degrees of each polynomial.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Sara have 5 cents and jon have 0.05 cents with him.

A fraction is a number that represents a part of a whole or a ratio of two numbers. It is written in the form of "a/b" where a is the numerator and b is the denominator. The numerator represents the number of parts that are being considered and the denominator represents the total number of parts in the whole. The fraction can be simplified by dividing both numerator and denominator by their greatest common factor.

Given Martin have 0.5 cents and it is mentioned that Sara have 10 times as much money as marting

so Sara have 10*0.5 cents

=> 5 cents

so sara have 5 cents

Given that jon have 1/10 fraction as much money as Martin have

so jon have 1/10 *0.5

=> 0.1*0.5

=> 0.05 cents

so Jon have 0.05 cents.

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Complete question:

Martin ha 0. 50 cent Sara ha 10 times as much as Martin and Jon has one tenth as much money as Martin . How many cents Sara and jon have

To decorate her house, Jessica buys this plant which is Boston Fern.

Sure! A plant with green leaves that Jessica can consider buying is a Boston Fern. Boston Ferns are known for their lush, bright green fronds that provide a beautiful, natural touch to any indoor space. They are popular houseplants because they are relatively easy to care for and can purify the air.

To care for a Boston Fern, place it in a location with indirect light and maintain a consistent level of moisture in the soil, avoiding letting the soil dry out completely or become waterlogged. They also benefit from regular misting to increase humidity levels.

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The figures P', P", and P"" have been drawn below in the coordinate plane. The solution has been obtained using transformation.

What is transformation?

An operation that manipulates a polygon or other two-dimensional object on a plane or coordinate system is known as a transformation.

The shape in two dimensions before any alteration is known as a pre-image or inverse image. The shape after transformation is the image.

Cyrus is planning a design to paint on his bass drum.

He starts with figure P and translates it 3 units to the right to form figure P'. This means he moves 3 units closer to the y-axis.

Then he reflects figure P' across the y-axis to form figure P".

Then he dilates figure P" using a scale factor of 2 to form figure P"". This means that the figure is twice of P".

The center of dilation is at the origin.

From this, the below figure has been obtained.

Hence, the figures of P', P", and P"" in the coordinate plane have been constructed.

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Answer:  y = 5x + 3 in standard form

Step-by-step explanation:

The solution of pair of equation 2x + y = 5 and 3x - 2y = 4 is x = 2 and y = 1.

The set of equations given is linear equations that can be solved simultaneously to find the values of variables x and y.

2x + y = 5------->(1)

3x - 2y = 4------->(2)

Multiply equation (1) by 2 and then add it to equation (2)

4x + 2y = 10

3x -  2y =   4

7x + 0  = 14

7x = 14

x = 2

Putting x = 2 in (1),

2(2) + y = 5 

y = 5 - 4 = 1

Therefore, the values of x and y obtained are 2 and 1, respectively. 

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Check the picture below.

[tex]tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

1

Step-by-step explanation:

The dependent changes because of the independent. So basically it depends on the  independent variable

Answer:

The first one

Step-by-step explanation:

s is the independent variable and f is the dependent variable.

the number of host families depends on the number of students.

According to your solution of the given system of equations, the value of y is 7.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation y = 2x + 11 and 3x + 2y = 8

From equation 1 we will substitute the value of y in the form of x in equation 2

=> 3x + 2(2x + 11) = 8

=> 3x + 4x + 22 = 8

=> 7x = 8 - 22

=> 7x = -14

=> x = -2

Substitute this value in equation 1

=> y = 2* -2 +11

=> y = -4 + 11

=> y = 7

therefore,  the value of the y is 7 from your solution of the system of equations given.

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The store that offers the better value based on the unit rate is Store A.

The unit rate is the ratio of one item to the whole item.

The unit rate represents the average of a data set.

It is computed by dividing the total value by the number of units.

The cost of 5 notebooks at Store A = $6.75

The unit rate of notebooks at Store A = $1.35 ($6.75/5)

The cost of 3 notebooks at Store B = $4.50

The unit rate of notebooks at Store B = $1.50 ($4.50/3)

Thus, using the unit rate as the basis of consideration, we can conclude that Store A offers Ben a better value than Store B.

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The answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

When two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given are some questions regarding production of glucose molecules during aerobic metabolism.

1) 1 glucose molecules produces 30 ATP molecules, how many for 50 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 50 ATP molecules,

1 / 30 = x / 50

x = 5/3

x = 1.67

Therefore, there are 1.67 glucose molecules required to produce 50 ATP molecules.

2) 1 glucose molecules produces 6 ATP molecules, how many for 216 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 216 ATP molecules,

1 / 6 = x / 216

x = 36

Therefore, there are 36 glucose molecules required to produce 216 ATP molecules.

3) 1 glucose molecules produces 30 ATP molecules, how many for 450 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 450 ATP molecules,

1 / 30 = x / 450

x = 15

Therefore, there are 15 glucose molecules required to produce 450 ATP molecules.

4) Since, in one day it's 1200 times an ATP molecule is reused in a human body,

We need to find for a week, there are 7 days in a week,

Therefore, an ATP molecule is reused in a human body for a week = 1200 x 7 = 8400 times.

Hence, the answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

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Answer:

On a logarithmic scale, numbers on the Y-axis don't move up in equal increments but instead each interval increases by a set factor – it's often 10 but could be a factor of 3 or 350 or 3,500, anything at all.

Step-by-step explanation:

Answer:

30 seconds.

Step-by-step explanation:

Think of it this way:

20 seconds has a two and 2/3 has a two.

1/3 must be 10 seconds.

0/3 is 0 seconds.

Which means 3/3, the full length, will take 30 seconds.

side of image = 3.5 inch and 5 Inch

Area = 3.5 × 5 = 17.5 inch²

Now length is Enlarge by x

new length and Breadth are (3.5+x) and (5+x)

Area of new Image =(x+3.5)(x+5)

Area of new Image = x² + 5x + 3.5x + 17.5

Area of new Image = x² + 8.5x + 17.5

i hope it's helpful

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

The area of hexagon is 20 square units.

polygon, in geometry, any closed curve consisting of a set of line segments connected such that no two segments cross

Hexagon is a six-sided polygon or 6-gon creating the outline of a cube.

Each square in the grid below has area 1 unit.

The total number of grids are 8×8=64 grids.

1 grid of area 1 unit.

As 20 grids are used to form the hexagon.

So the area of hexagon is 20 square units.

Hence,  the area of hexagon is 20 square units.

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Answer: 20

Step-by-step explanation:

No, â =1 is not equals to ¾. Since ¾ is written as 0.75 in fractional notation.

The fraction ¾, which is equivalent to 0.75, is shown by the fractional notation "â...". The bottom number, or denominator, must be multiplied by the top number in order to comprehend this fraction (top number). 4 times 3 in this instance equals 12, which is true. Find the fractional value by first dividing the numerator by the denominator. In this case, the result of 3 divided by 4 is 0.75, or 3/4.

To calculate a fractional value, use the following formula:

Fractional Value: Numerator / Denominator

The numerator is multiplied by the denominator to arrive at 12 when calculating the fractional value of 3/4. Following that, the fractional value is obtained by dividing the numerator by the denominator:

Fractional value equals 3 / 4 = 0.75

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A reasonable prediction for the number of times a green or red bead will be drawn from the container of beads, after being replaced 60 times, would be 42.

A reasonable prediction for the number of times a green or red bead will be drawn from the container of beads, after being replaced 60 times, would be close to the proportion of green or red beads in the container. The container has 8 red beads and 6 green beads out of a total of 8 + 7 + 6 = 21 beads. The proportion of green or red beads is (8 + 6) / 21 = 14/21.

We can use this proportion to predict the number of times a green or red bead will be drawn from the container. By multiplying the proportion of green or red beads by the number of times the bead is replaced, we get (14/21) * 60 = 42.

In this scenario, we are using the concept of probability and proportion. The probability of drawing a green or red bead is 14/21, and by multiplying it by the number of trials (60), we get the expected number of times the green or red bead will be drawn. This concept is used in statistics and probability to make predictions based on the available data. It is important to note that this is only a prediction and actual results may vary.

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Answer: IQR=32

Step-by-step explanation:IQR=Q3-Q1

Answer:

700 meters.

Step-by-step explanation:

The actual distance between the two points can be determined by using the scale of the map. If the scale of the map is 1:10,000, it means that one unit of measurement on the map represents 10,000 units of the same measurement in reality.

Therefore, if the distance between the two points on the map is 7cm, the actual distance is 7cm * 10,000 = 70,000cm or 700 meters.

So, the actual distance between the two points is 700 meters.

Hey there!

Answer:

[tex]Given[/tex] → [tex]\sqrt{18x^5*y}[/tex]

[tex]Solution[/tex] → [tex]3x^2\sqrt{2x*y}[/tex]

Hope this helps! If you mark Brainliest, TYSM! :D

The turning point of the function in this problem is given as follows:

(-5,2).

The function for this problem is defined as follows:

[tex]f(x) = 2\sqrt[3]{x + 5} + 1[/tex]

The parent function is the cube root function, which has a turning point at (0,0).

The transformations are given as follows:

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Percentage of unemployment is 58.33 % in the total household of 60,000.

Although the abbreviations "pct.", "pct.", and "pct." are also used, the percent symbol, "%," is most commonly used. A percentage is a number with no dimensions and no standard measurement.

The English word "percentage" is derived from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a numerator of 100. In other words, it is a relationship in which the total value is always assumed to be one hundred.

Percentage calculation is the process of determining a percentage of a whole in terms of 100. There are two ways to calculate a percentage:

Using the unitary approach

by adjusting fraction's denominator to 100.

It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation isn't applied. In these situations, we employ the unitary technique.

Total number of household is 60000

Total number of household which is unemployed is 35000

Percentage of unemployment = (35000/60000) * 100 = 58.33 %

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The 2x²- 4, expression is equivalent to 2(x²-2) with the same variable and exponent we multiply with their constant value.

Distribution property: Multiplying numbers by the sum or difference is the same as multiplying each number in the sum or difference and then adding or subtracting. Example: 6(2+4)= 6(2) + 6(4)

Equivalent Expressions: Expressions are equivalent if they are equal to each other when contracted or expanded. Steps to write equivalent expression using distributive Property,

Step 1 : A list of all the elements with coefficient a

Step 2: List all the factors of constant b.

Step 3: Compare the factors identified in a and b and identify the factors they have in common.

Step 4: Choose one of the factors f such that f(ax/f + b/f). We have, f(x) = 2x² - 4 . Using the above steps,

=> 2x² - 4 = 2 × x × x - 2× 2

As we see, 2 is common factor in both

=> 2( x² - 2)

So, required expression is 2( x² - 2) .

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Complete question:

What is the equivalent of 2x² - 4?.

The required values of a and b are approximately 15.4 and 14.6, respectively, and Michael's speed is approximately 14.6 meters per second.

Following the given condition
Race 1: Michael wins by 1 second, so time is given as:
[tex](50/b)=(50/a)+1[/tex]

Race 2: Michael wins by 0.1 seconds over 47 meters, so time is given as:
[tex]47/a+0.1=50/b[/tex]

From Race 1, we get [tex]a=b+50/b-50.[/tex]

Substitute the value of a in terms of b into the Race 2 equation:
[tex]\dfrac{47}{b+50/b-50}+0.1-\dfrac{50}{b}[/tex]

Now, solve for b:

[tex]b\approx14.6\\[/tex]   (discard the negative solution as speed cannot be negative)

Now, calculate the value of a using the equation from Race 1:
[tex]a=b+50/b-50 \approx15.4[/tex]

Therefore, the values of a and b are approximately 15.4 and 14.6, respectively, and Michael's speed is approximately 14.6 meters per second.

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