A business is operating with a monthly debt for its account balance. In January, the account had a balance of $-\$1,350$ . In February, the account had a balance of $-\$725$ .

Part A
Write two different expressions that correctly represent the change in the account balance, in dollars, from January to February.

The equation of line with slope 3 and y-intercept 6 is y = 3x + 6.

In the given question, we have to find the equation of the line with slope 3 and y-intercept 6.

The slope-intercept version of the line's equation is what we need. In other words, we want y=mx+b in the form of ax+by=c. M is the slope and b is the y-intercept in the slope-intercept form.

From the given question, m = 3 and c = 6.

Now putting the value in the equation y = mx +c

y = 3x + 6

Hence, the equation of the line with slope 3 and y-intercept 6 is y = 3x + 6.

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Dividend ÷ Divisor = Quotient and Remainder

When a dividend is divided by a divisor, we get the value of the quotient in the result.

The result of dividing one integer by another is the quotient. For example, in 8 ÷4 = 2, the division result is 2, hence the quotient is 2. The dividend is eight, while the divisor is four.

The derivative of a quotient is the denominator times the numerator's derivative minus the numerator times the denominator's derivative, all divided by the denominator's square, according to the Quotient Rule.

When dividing one exponential equation by another, we use this rule. We must subtract the exponent in the denominator from the exponent in the numerator using the quotient formula, but the bases must be the same.

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The value of log7 base 10 is 0.84509804.The logarithm of a number is the exponent to which another fixed number (in this case 10) must be raised to produce that number.

The logarithm of a number is the exponent to which another fixed number (in this case 10) must be raised to produce that number. So to find the logarithm of 7 base 10, we must find the exponent to which 10 must be raised to produce 7. This can be solved using a calculator by taking the logarithm of 7 (log 7) and setting the base to 10 (log 10). The answer is 0.84509804. This means that 10 must be raised to the power of 0.84509804 to produce 7.

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The Ying-yang symbol has rotational symmetry, the flag has radial symmetry, and the three-leg figure has radial symmetry.

The word symmetry refers to the characteristic of figures being the same in terms of proportion and shape.

Bilateral symmetry: This means the two sides of a shape are the same.

Radial symmetry:  This implies that there are symmetric sections if lines are drawn from the radius or center.

Rotational symmetry: This implies two sides are the same but they are rotated.

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Answer:

3

Step-by-step explanation:

y=7x

x+y=24

x+7x=24

8x=24

x=3

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200 decreased by 30% is 140 for the given question.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted using the percent sign, "%". For example, 45% can be written as 0.45 or 45/100. Percentage is used to express how large or small one quantity is relative to another quantity. For example, if a student scores 45 out of 50 on a test, the student's score can be expressed as a percentage by dividing 45 by 50 and then multiplying by 100, which equals 90%.

Given data,

200

It decreased the price the price by 30%.

=30/100*200

=0.3*200

=60

= 200-60

=140.

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Derivative of given logarithmic function [tex]log_7x[/tex] is [tex]\frac{1}{xlog(7)}[/tex].

Logarithmic differentiation is a method for figuring out the derivatives of some difficult functions. In some cases, it is simpler to distinguish between a function's logarithm and function itself. The derivatives are made simple with the right application of logarithm characteristics and chain rule discovery. Nearly any non-zero functions with differentiable nature can be applied with this approach.

Thus, in calculus, some complex functions are differentiated by calculating logarithms, and these complex functions are subsequently solved using the logarithmic derivative.

[tex]y=log_7x[/tex]

[tex]y'=\frac{1}{xlog(7)}[/tex]

Here, differentiation of logarithmic function for different base is different.

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The solutions to both simultaneous equations are;

1) x = -2 and y = -13

2) x = -1 and y = -6

Simultaneous equations are defined as two or more algebraic equations that share variables e.g. x and y

1) The simultaneous equations we have are;

7x - y = -1

-7x + 3y = -25

Using elimination method, add both equations to get;

2y = -26

divide both sides by 2 to get;

y = -13

7x - (-13) = -1

7x + 13 = -1

7x = -14

x = -2

2) The simultaneous equations we have are;

7x - y = -1

7x + 3y = -25

Using elimination method, subtract eq 1 from eq 2 to get;

4y = -24

divide both sides by 4 to get;

y = -6

7x - (-6) = -1

7x + 6 = -1

7x = -7

x = -1

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The measure of arc or the angle indicated in the following questions where lines that appears are tangents is given by :

a. Measure of the external angle is equal to 60°.

b. The angle subtended by the given arc VS is equal to 121°.

As given in the question,

Diagram is attached.

In the given arc and tangents formed by the circle ,

Half of the difference of the angle subtended by the arc of a circle is equal to the measure of the external angle.

a. Measure of external angle ∠C = x°

Measure of the angles subtended by the arc are :

Major arc angle = 161° and Minor arc angle =  41°

x° = ( 161° - 41° ) / 2

⇒ x° = 60°

Measure of ∠C = 60°

b. Measure of external angle =31°

Measure of the angles subtended by the minor arc = 59°

Measure of the angles subtended by the  major arc = y°

( y° - 59° ) / 2 = 31°

⇒ y° =( 62 + 59 )°

⇒ y° = 121°

Therefore, the measure of the arc or the angle indicated is given by :

a. Measure of the external angle is equal to 60°.

b. The angle subtended by the given arc VS is equal to 121°.

The above question is incomplete , the complete question is:

Find the measure of the arc or angle indicated. Assume that lines which

appear tangent are tangent.

Diagram is attached.

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The number of inches in 134 miles is 8,490,240.

Inches and miles are the units that can be used for calculating the length and distance respectively. Generally inches are used to represent small lengths while miles represents long distances. If we relate the two units, the relationship will be -

1 mile = 63,360 inches

So, calculating inches in mentioned number of miles.

134 miles = 63,360 × 134

Performing multiplication on Right Hand Side of the equation

134 miles = 8,490,240 inches

Thus, the representation in inches will be 8,490,240 inches.

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Froude numbers are used to compare the inertial force to the gravitational force, allowing for dimensionless analysis.

Froude numbers are used to compare the inertial force to the gravitational force, allowing for dimensionless analysis. In this way, the same model can be used to represent different real-world systems, as the parameters that affect the performance of the model can be scaled up or down. This type of analysis allows for the study of a wide range of physical phenomena, from the motion of ships and aircraft to the flow of fluids through pipes and valves.

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The standard deviation of d is 1.27, which is the measure of the variability of a set of data. It tells us how much variation or dispersion exists from the average or mean value.

In other words, it reveals the degree to which the data points deviate from the mean. In this instance, the standard deviation of 1.27 means that, on average, the number of puzzles solved in a 5-minute period by two randomly selected participants differs by 1.27 puzzles. Accordingly, the majority of individuals ought to deviate by an amount that is within 1.27 puzzles of the mean.

Additionally, this implies that some subjects will have differences larger than 1.27 and some lower. We may quantify the level of variability in a data set using the standard deviation, which is a useful measure of variability.

Your question is incomplete but most probably your full question was A psychologist studied the number of puzzles that subjects were able to solve in a 5-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by randomly chosen subject. The psychologist found that X had the following probability distribution_ Value Probability 0.2 0.4 0.3 0.1 Let D be the difference in the number of puzzles solved by two randomly selected subjects in a 5-minute period. What is the standard deviation of D? 0.81  1.8  1.27

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Answer: 13 2/9 or 13.23

Step-by-step explanation:

5 2/3 + 7 5/9 = 119/9= 13 2/9

Answer: the plant has grown 8x inches

Step-by-step explanation:

The plant has grown 8 times more than it's height last week so,

8 x [tex]x[/tex] = 8x

Answer:

8x

Step-by-step explanation:

Plant inches: x

Amount it has grown: 8 times x (original height)

8 times x

simplify as

8x

For a book sale, you rent bookcases like the one in the picture to exhibit 943 volumes. On each shelf, you intend to place 22 books. The tops of the bookcases won't contain any books. 19 shelves, 9 bookcases, and.

It is necessary for you to borrow nine bookcases in order to display all of the books.

42.91 / 22 = 42.9 / 43 shelves.

43/5 = 8.6 + 1 = 9 bookcases.

Nineteen volumes will be on the third shelf of the final bookcase. Deductive, inductive, abductive, and analogous reasoning will be the four types of reasoning we will be concentrating on in this article.

Analytical and logical reasoning problems make up the two main categories of reasoning tests. There are two subcategories of logical reasoning: verbal and nonverbal. Fixing issues Candidates will be given a variety of questions in the logical reasoning section of the test, and they will need to conduct a variety of operations, such as addition, division, greater than, less than, etc., are interchanged or substituted to discover the right answer.

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Answer:

System A to System B

Option 3 and the answer in the box is [tex]\boxed{-2}[/tex]

System B to System C

Option 4 and the answer in the box is [tex]\boxed{-2}[/tex]

Step-by-step explanation:

Only showing work for correct options:

System A to System B

Correct choice: Option 3  with -2 as multiplier

[tex]\bold{-2}[/tex]  x Equation [A1] :

[tex]\implies -2(-7x + 2y = 13)\\\\\implies 14x - 4y = -26\\[/tex]

[tex]\bold{-2}[/tex] x Equation [A1] + Equation [A2]

[tex]14x - 4y = -26 + (-8x +5y = 4)\\\\14x -8x -4y +5y = -26 + 4\\\\6x + y = -22\\\\\textrm{This is equation B2}[/tex]

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

System B to System A

Correct choice: Option 4 with [tex]\boxed{-2}[/tex] as multiplier

[tex]\bold{-2}[/tex] x Equation [B2]:
[tex]\implies -2(6x + y = -22)\\\\\implies -12x -2y = 44\\\\[/tex]

[tex]\bold{-2}[/tex] x Equation [B2] + Equation [B1]:

[tex]-12x -2y = 44 + (-7x + 2y = 13)\\\\\implies -12x -7x -2y + 2y = 44 + 13\\\\-19x = 57\\\\[/tex]

The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally.

Generally speaking, the formula logbn = an is equal to the formula ba = n. In other words, the result you get when you raise b to the power of an is n, where the base is b, the exponent is a, and the exponent is the exponent. You'll see that an expression highlights its power when written in exponential form, whereas it emphasises its exponent when written in logarithmic form.

Any function's inverse function graph is a mirror of the function's graph around the line y=x.

The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally.

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Hi!  This looks like homework...

so I can help!

What you would need to do first is find the height of the triangle, you know, the dashed line.  15 is the hypotenuse side length.  Now we need to solve for a^2 + b^2 = c^2 (hypotenuse formula)  a^2 = 10^2, and c^2 = 15^2.   So now..

if a^2 + b^2 = c^2, then c^2 - a^2 = b^2.  Just moving stuff around. :D

That would be 15^2 - 10^2 = b^2, which is 225 - 100 = b^2.  The result is 125 = b^2.  

ehaggghh it's a decimal

b^2 is 125... and b is 11.1803398875.  So I can see a snippet of your paper that says round to the nearest tenth.  Yay.

that would be 11.2.  :>

The height is 11.2!! So now... oh noes you have to do it again.

Except this time, you're solving for a^2!

Switch the formula like this: c^2 - b^2 = a^2

13^2 - 11.2^2 = a^2 (base)

43.56 = a^2

6.6 = a

So now, the base is 6.6 + 10, which is 16.6 in total.  13 and 15 are the two side lengths.  But you don't need those.  You only need the height, 11.2.  So multiply 16.6 x 11.2, and you get 185.92, or 185.9.  Then divide that by two, since it's a triangle, not a square.  That's 92.96.  Yay you have the area!  

Hypotenuse formula: a^2 + b^2 = c^2
Use this if you don't have the given height, so you can solve for it.  The dashed line separated the triangle into two parts, so you could find the needed sides of both triangles.  Later, when you get into triangle proofs, you could use the "by construction" postulate to be able to find the similarity or congruence done here.

Have a good day!

Answer:

2.475

Step-by-step explanation:

12 divide into 29.7 goes 2.475 times

use the illustration from the other example and you should be able to do it

12 into 29 goes twice

subtract 29-24 to get 5

bring down the 7 to get 57

12 into 57 goes four times

57-48 = 9

bring down a zero to get 90

12 into 90 goes seven times

90-84 = 6

12 into 60 is 5

18÷29.70= 0.40

that should be right

The circumference of the grain bin with radius 20 feet is 125.6ft.

The distance around the boundary of a circular object is referred to as a circumference.

The formula for calculating circumference is expressed as;

C = 2 × π × r

Given the data in the question;

Plug in the given values into the above formula

C = 2 × π × r

C = 2 × 3.14 × 20ft

C = 125.6ft

Therefore, the circumference is 125.6ft.

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Answer:

40 units

Step-by-step explanation:

AB = AC as the opposite angles are equal.

4x + 4 = 6x - 14

2x = 18

x = 9 units

Therfore, AC = 6 x 9 - 14 = 54 - 14 = 40 units

In ΔACE, BG = 7, GE = 14 is the centroid theorem and BE = 21 then BG = 7, GE = 14.

The method for determining a triangle's centroid is called the centroid formula. Any object's centroid is its geometric center. The point that divides the medians in half by two is referred to as a triangle's centroid. The geometric center of any geometric object, whether it be a one-dimensional curve, a two-dimensional region, or a three-dimensional volume, is called the centroid. Centroids can very handy for a variety of tasks in Statics and later courses, such as the study of distributed forces, beam bending, and shaft torsion.

The place where the triangle's three medians intersect is known as the centroid (each median connecting a vertex with the midpoint of the opposite side).

According to the centroid theorem, the centroid is located 2/3 of the way between each vertex and the middle of the opposing side.

Point G is 2/3 of the way from point E, and BE is the median:

GE = 2/3BE = 2/3(21) = 14

BG = BE - GE = 21 - 14 = 7

BG = 7, GE = 14

Therefore, the correct answer is option c) BG = 7, GE = 14.

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Yes, the height of the tree is a function of the number of months and it is a linear function x = 5 + n.

In Mathematics, a linear function is described as a function that has either one or two variables without exponents. It is a function that has a graph in a straight line. In case, if the function includes more variables, then the variables should be constant, or it might be the known variables for the function to remain in the same linear function condition.

Height of tree = 5 ft

Grow per month = 1 ft

Assume;

The new height of the tree = x

Number of months = n

x = 5 + 1(n)

x = 5 + n

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The maximum number of interior angles of a convex n-gon that can have measure 131° is equals to the seven.

A polygon is said to be convex n-gon when no line segments between the points, goes inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°. Sum of interior angles of n sided polygon

= 180(n- 2) degrees

We have, Alex assume that one of interior angle of convex n-gon is 131° . Let total maximum number of interior angles of a convex n-gon or polygon that can have measure 131° be "x".

Total measures of all remaining interior angles, (n - x) of this polygon

= 180(n- 2) - 131x

But for a convex n-gon, interior angles of a convex polygon are less than 180°. So,

180(n- 2) - 131x < (n - x) 180

Now, solve this Inequality,

=> 180n - 360 - 131x < 180n - 180x

=> -360 + 180x - 131x < - 180x + 180x

=> - 360 + 49x < 0

=> 49x < 360

=> x < 360/49

=> x < 7.34 ~ 7

So, the required value of x is 7 .

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She can save $432 each year.

Now, According to the question:

Li-Mei thinks she can save money on electricity by changing all her bulbs from incandescent bulbs to fluorescent bulbs.

Incandescent bulb - 150 hours monthly use $.05 per hour Fluorescent bulb - 150 hours monthly use $.02 per hour.

We have to following statement.

Incandescent: 0.05 × 150 × 12 × 8=720

Fluorescent: .02 × 150 × 12 × 8=288

720-288=$432 less per year

Hence, She can save $432 each year.

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The complete question is this:

Li-Mei thinks she can save money on electricity by changing all her bulbs from incandescent bulbs to fluorescent bulbs. Based on the following energy cost table, how much can she save each year if she replaces 8 bulbs? Incandescent bulb - 150 hours monthly use $.05 per hour Fluorescent bulb - 150 hours monthly use $.02 per hour

Answer:

1/7

Step-by-step explanation:

The expression to represent the total cost of joining the gym using m as a variable is 100 + 30m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Local gym:

one time fee = $100

Monthly fee = $30

The total cost for m months.

= 100 + 30m

Thus,

The total cost for m months is 100 + 30m.

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Given points for a line two points j and k

Point j=(-3,7) and point k=(4,-2)

For find the mid point between two points

Formula for midpoint m(X,Y)= [tex](\frac{x_{1} +x_{2} }2,\frac{y_{1} +y_{2}}2)[/tex]

  m=[tex](\frac{-3+4}{2} ,\frac{7-2}{2} )[/tex]

  m=[tex](\frac{1}{2} ,\frac{5}{2} )[/tex]

Therefore ,the mid point of j and k points are    m=[tex](\frac{1}{2} ,\frac{5}{2} )[/tex]

For find the distance between two points

Formula distance=[tex]\sqrt{( y_{2}-y_{1})^{2}+ ( x_{2}-x_{1})^{2} }[/tex]

Distance of jk=[tex]\sqrt{( -2-7)^{2}+ ( 4-(-3))^{2} }[/tex]

Distance of jk =[tex]\sqrt{( -2-7)^{2}+ ( 4+3))^{2} }[/tex]

Distance of jk=[tex]\sqrt{( -9)^{2}+ ( 7))^{2} }[/tex]

Distance of jk =[tex]\sqrt{81+ 49 }[/tex]

Distance of jk=[tex]\sqrt{130\\}[/tex]

Therefore, the distance between the endpoints of jk is [tex]\sqrt{130}[/tex]

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If the system is consistent, then the equations must be simultaneously solvable, meaning that there is at least one solution. However, it is possible that there are multiple solutions.

If the system is consistent, then there must be an infinite number of solutions. This is because if a system is consistent, then any values that satisfy the equations can be a valid solution. Therefore, if there is at least one solution, then there must be an infinite number of solutions since there are an infinite number of values that can satisfy the equations.

Furthermore, if the system is consistent, then the equations do not contradict each other and therefore can be solved with any combination of values. Therefore, the system must have an infinite number of solutions.

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Answer: 1/3

Step-by-step explanation: In order to find the slope, you need two points.

(0, 2) and (3, 3). To find the slope, you need to use

Difference of Y values

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

Difference of X values

3 - 2 / 3 - 0

1/3

Answer: Slope = 1/3 or .333

Step-by-step explanation:

Resources:

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