Module 1: directions: respond to this question to demonstrate your understanding of the topic/content. be sure to provide adequate and relevant details learned in the module to support your response. pay close attention to organizing your response so it makes sense and uses correct grammar. your response should be at least 5-7 sentences at a minimum. question: given the two points (1,5) and (-2, -4), write a set of instructions for your younger cousin that determines the equation of the line in slope-intercept form (y=mx+b). be sure to write the equation.

Answer:

  2

Step-by-step explanation:

You want the count of negative terms in the simplified form of -3x² + 2y² + 5xy - 2y + 5x² - 3y².

The expression is simplified by combining like terms.

  -3x² + 2y² + 5xy - 2y + 5x² - 3y² = (-3+5)x² +5xy +(2-3)y² -2y

  = 2x² +5xy -y² -2y

There are two negative terms in the simplified expression.

For the given expression 300 - 5x , Diana's saving after five weeks is equal to 275 dollars.

As given in the question,

Given expression to represent the Diana's saving is written as:

300 - 5x

Where 'x' represents the number of weeks.

Now the Diana's savings after five weeks is given by :

Here x = 5

Substitute the value of x in the given expression 300 - 5x we get,

300 - 5x

= 300 - 5( 5 )

= 300 - 25

= 275 dollars

Therefore, the Diana's savings as per the given expression 300 - 5x after five weeks is equal to 275 dollars.

The above question is incomplete, the complete question is:

Diana's savings at the end of each week can be described by the expression (300-5x) dollars where x represents the number of the week.

What is her savings after five weeks in dollars?

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The linear, quadratic and exponential functions form a set because they differ only in the values of exponents.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Choose a set among the 4 sets.

Let us choose set 2.

Linear Function :

Linear functions are functions whose variable has the highest degree equal to 1. The graph of the linear function is a line.

Standard form of linear equation is y = mx + c.

For example, let f(x) = 5x + 2.

Quadratic Function :

Quadratic functions are functions whose variable has the highest degree of 2. The graph of quadratic function is a parabola.

Standard form of quadratic function is y = [tex]ax^{2} +bx+c[/tex]

For example, let f(x) = [tex]2x^{2} +4x-5[/tex]

Exponential function :

Exponential functions are functions where the variable lies in the exponent. The graph of exponential functions makes a curve which grows steeper over time.

Standard form of exponential function is y = [tex]e^{x}[/tex]

For example, let f(x) = [tex]2^x[/tex]

Hence these formed into a group because of they are different type of functions which differ in the exponents.

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The common ratio of the given geometric sequence is 0.5

We know that for any geometric sequence,

aₙ = arⁿ⁻¹

where aₙ is the nth term of the sequence

a is the first term of the sequence

r is the common ratio.

Hence when we say that the third term is 100 we can conclude that for the series

ar³⁻¹ = 100

or, ar² = 100                                                                                      [1]

Also, we have been given that the eight-term is 3.125

Hence we can say that,

ar⁷ = 3.125                                                                                        [2]

By dividing equation 1 by equation 2 we get

ar⁷/ar² = 3.125/100

or, r⁵ = 3125/100000

or,  r⁵ =  5⁵/ 10⁵

Since the powers are the same, the bases can be equated to get

r = 0.5

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Complete Question

A geometric sequence has only positive terms. The third term is 100 and the eighth term is 3.125. Find the common ratio.

Irene's measuring error is 12.5% when she believes she has space for a 45-inch-wide bookcase but only has enough for a 40-inch-wide bookcase.

A data value's approximation error is the difference between an exact value and some approximation to it. This inaccuracy can be stated as either an absolute or relative error. A computing machine accuracy or measurement mistake can generate an approximation error. The difference between the estimated and real values in relation to the actual value is indicated as a percentage. In other words, the relative error multiplied by 100 equals the percent error. The percentage error compares an estimate to the true amount and expresses the difference as a percentage. This statistic enables analysts to determine the magnitude of the inaccuracy in relation to the real value.

Here,

percent error,

=(45-40)/40*100

=5/40*100

=12.5%

The percent error in irene's measurement is 12.5% when she thinks she has space for a 45-inch-wide bookcase but turns out that she only has space for a 40-inch-wide bookcase.

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Answer:  Arc EG/GE = 135°

Step-by-step explanation:

Given:

∠EGF = 80°

Arc FG = 65°

Since ∠EGF = 80°, the value of Arc EF = 2(∠EGF)

Therefore, Arc EF = 2(80°) = 160°

The arc measure of an entire circle is 360°.

Therefore,

360° = EF + FG + GE

360° = 160° + 65° + GE

GE/EG = 135°

The measure of the angle m<ROS = 14°.

What is the angle?

An angle is a geometric figure that is defined by two rays that have the same endpoint. The rays are called the sides of the angle and the common endpoint is called the vertex of the angle. The angle is the amount of rotation between the two rays, measured in degrees or radians.

In the given figure,

m<QOS = 46, m<POR = 58 and m<POQ = 26

m<POR = m<POQ + m<QOR

58 = 26 + m<QOR

m<QOR = 32

m<QOS = m<QOR + m<ROS

46 = 32 + m<ROS

m<ROS = 14

Hence, the measure of the angle m<ROS = 14°.

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Figure A is replicated in scale in Figure B. A figure that is geometrically identical to the original figure is called a scale copy.

Given are two triangular figures, Figure A and Figure B.

The scale factor from figure A to figure B is requested of us.

As a result, Figure B is the last figure and Figure A is the first figure.

Any figure's scale factor is described as stated in equation (1)

[tex]Scale Factor =\frac{\text { Final Dimension }}{\text { Initial Dimension }} \ldots \ldots . . .(1)$[/tex]

We can see from the preceding figures that while figure A uses 4 squares to represent the length of a pair of one parallel sides, figure B only needs 2 squares to represent the same length.

As a result, we can write that using equation (1).

[tex]Scale factor =\frac{\text { Dimension of figure } \mathrm{B}}{\text { Dimension of figure } \mathrm{A}}=\frac{2}{4}=\frac{1}{2}=0.5$[/tex]

Since the scale factor is smaller than 1, the figure is contracted, and the scale factor from Figure A to Figure B is therefore 0. 5.

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The length of the ribbon that Regina needed is 38.10 inches

The measurement of the circle's boundaries is known as the circumference or perimeter of the circle. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it.

The formula for the Circumference of the circle is given by

where 'r' is the radius of the circle.

Here we have

Regina is tying a bow around a soccer ball to give to her sister.

The ribbon must be 10 inches longer than the circumference of the ball

Length of the ribbon = Circumference of ball + 10 inches

Given the radius of the ball, r = 4.5 inches  

Circumference of ball = 2(3.14)(4.5) = 28.26 inches

So, Length of the ribbon = 28.26 inches + 10 inches = 38.10 inches

Therefore,

The length of the ribbon that Regina needed is 38.10 inches.

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The value of x in the triangle is 110 degrees.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, the sum of the two opposite interior angle is equals to the exterior angle x.

Hence, using exterior angle theorem,

x = 45 + 65

x = 110 degrees

Therefore, the most efficient way to measure the angle x is by summing the opposite interior angles.

The value of x is 110 degrees.

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The probability that at least 2 people believe that they have seen a UFO is 0.264.

Here, n = 10, p = 0.1, (1 - p) = 0.9 and x = 2

As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 2).

P(X >= 2) = (10C2 * 0.1^2 * 0.9^8) + (10C3 * 0.1^3 * 0.9^7) + (10C4 * 0.1^4 * 0.9^6) + (10C5 * 0.1^5 * 0.9^5) + (10C6 * 0.1^6 * 0.9^4) + (10C7 * 0.1^7 * 0.9^3) + (10C8 * 0.1^8 * 0.9^2) + (10C9 * 0.1^9 * 0.9^1) + (10C10 * 0.1^10 * 0.9^0)

P(X >= 2) = 0.194 + 0.057 + 0.011 + 0.001 + 0 + 0 + 0 + 0 + 0

P(X >= 2) = 0.264

The probability is 0.264.

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Randomly surveyed 50 seventh-grade students at Pablo's school.

What is confidence in statistics?

In statistics, confidence refers to the level of certainty or trust in the accuracy of a statistical estimate. A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence. The level of confidence is usually expressed as a percentage, such as 95% or 99%.

In this experiment, the focus is on seventh graders, and therefore a more representative sample of the population will be selected 50 seventh-grade students from Pablo's school. Selecting this category of the sample will increase confidence in the result of the statistical experiment.

Hence, randomly surveyed 50 seventh-grade students at Pablo's school.

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Area of the enclosed figure is, 8√ 5 (5 + 2√5) units².

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Maria plots the following points on a coordinate grid.

Here, Points are,

⇒ (1, 3) (5, 7) (5, 5) (8, 9) (8, 3 ) (1, 3)

Clearly, It make pentagon.

And, Area of pentagon = 1/4 √5 (5 + 2√5) a²

Here, The side of pentagon = √ (7 - 3)² + (5 - 1)²

                                           = √4² + 4²

                                           = √32

                                           = 4√2

Thus, Area of figure = 1/4 √5 (5 + 2√5) a²

                               = 1/4 √5 (5 + 2√5) (4√2)²

                               = 8√ 5 (5 + 2√5)

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Answer:

b

Step-by-step explanation:

hopefully this helps

Answer:-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

When you are dividing negative numbers, it's going to stay negative:

[tex]= > -21/3=\\\\= > -7[/tex]

Therefore, the correct answer is -7

Option A) 59.6 is correct.

How to calculate Distance?

Using the distance formula: This method is also used to find the distance between two points in a plane. The formula is: distance = √((x2 - x1)² + (y2 - y1)²)

To find the distance between the man and the cliff, we can use trigonometry. We know that the angle of elevation is 40° and the height of the cliff is 50 m. We can use the tangent function to find the distance.

distance = (height of cliff) / (tangent of angle of elevation)

distance = 50 m / (tan 40°)

distance = 50 m / 0.8391

distance = 59.6 m

So, the distance between the man and the cliff is approximately 59.6 meters.

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The number line that represents the solutions that is n > 3 is number line 1.

Any real number can be represented in two dimensions using a number line. Any number on the number line with a solid circle next to it means to include that number followed by the rest of the values, and any number with a hollow circle means to exclude that value from the list before the rest of the values.

The solutions represented by number line 1 are those where n>3. By using special representational techniques, number lines are used to represent real numbers. This was Illustrated in number line 1.

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We can summarize the relationships among these shapes as:

Quadrilaterals --> Parallelograms --> Rhombuses

--> Trapezoids --> Isosceles Trapezoids

--> Rectangles --> Squares

--> Kites

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Answer:

the probability of landing on a number less than seven is 2/3 which is five and six

the probability of landing on a factor of forty- two is the same which is 2/3 because it is 6 and 7

The answer(s) to the initial equation is/are  -5 - √21/2 , -5 + √21/2.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign. 

According to our question-

Use the substitution u = x + 4 to solve the problem

(x + 4)2 - 3(x + 4) - 3 = 0 The equation will then look at that.

further solving gives,

x1 = -5 - √21/2 , x2 = -5 + √21/2.

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The value of f(7.5) of the exponential function is 86.84

The general form of an exponential function is given by:

f(x) = abˣ

Since f(x) is an exponential function, and f(4)=21 and f(4.5)=47. We can write that:

21 = ab⁴   --- (1)

47 = ab⁴°⁵  --- (2)

Divide (2) by (1):

47/21 = b⁴°⁵⁻⁴

47/21 = b⁰°⁵

b =√(47/21)

b = 1.50

Put b = 1.5 into (1):

21 = ab⁴

21 = a(1.5)⁴

a = 21/(1.5)⁴

a = 4.15

So the exponential function f(x) = 4.15(1.50)ˣ

To find the value of f(7.5), put  x = 7.5 into the exponential function:

f(x) = 4.15(1.50)ˣ

f(7.5) = 4.15(1.50)⁷°⁵

f(7.5) = 86.84

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So, the indicated value of the subject using direct capitalization is $995,909.09.

To find the indicated value of the subject property using direct capitalization, you need to use the following formula:

NOI / Cap Rate = Indicated Value

The overall capitalization rate is 6.00% and the projected first-year NOI is $247,000.

Therefore, Indicated value can be calculated as:

Indicated Value = $247,000 / 0.06 = $4,116,666.67

Another way to find the indicated value is using the Going-out cap rate, which is 22.0% and fifth-year NOI $218,300.

Indicated Value = $218,300 / 0.22 = $995,909.09

It's important to note that a pro forma is a projection and not a guarantee of future results. Also, the value obtained from using direct capitalization method is an indication, not the actual value, as it's based on certain assumptions and it may not reflect the current market conditions.

Therefore, the indicated value of the subject using direct capitalization is $995,909.09

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The percent change in the blu-ray player decreased by 20%.

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given the cost price of a Blu-Ray player = $300

the selling price of a Blu-Ray player = $240

loss = $300 - $240

loss = $60

Decrease in percent  = 100*(loss)/cost price

Decrease in percent  = 100*(60)/300

Decrease in percent  = 20%

Hence there is a decrease of 20%.

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The building have to rent 14 offices with area 500 ft² each so that the total acquired space is  7000 ft².

What is division?

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

The area of one office is 500 ft².

The total space acquired by the office building is 7000 ft².

To find the number of offices the building is renting, use the formula of division -

Number of office = Total space rented / Area of one office

Let the value of number of office rented be x.

Substituting the values in the equation -

x = 7000/500

x = 14

Therefore, the number of offices being rented is 14.

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Answer:

Step-by-step explanation:

I had to do this like 3 times; hope this helps!! Remember both parts are 3d spaces.

Basically I did whole box - part of the box

Remember your formulas !! <3

Answer:

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

According to the given information in the question the water level drop -0.15 each​ hour.

You must add "an" before words that begin with any of the five vowels, a, e, I, o, or u. However, how you say it is more important than how you spell it. Examples are "a history" and "an hour" (both of which begin with a vowel sound) (because history begins with a consonant sound).

Hipparchus recommended splitting the day into 24 require longer hours depending on the 12 days of daylight and 12 hours or darkness observed on solstice days. Hipparchus' work mostly occurred between 147 and 127 B.C.

rate = (change in water level) / (time elapsed)

rate = (4/25) / (-2.64)

rate = -0.15

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Answer:

5h - 2(2j+k)

Step-by-step explanation:

Best we can do here is 5h - 2(2j-k) but there's no simplifying further

Answer:

the answer is A. 64:343.

Step-by-step explanation:

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding side lengths. Since the scale factor of the two cylinders is 4:7, the ratio of their corresponding radii is 4:7 and the ratio of their heights is also 4:7.

So, the ratio of their volumes is (4/7)^3 = (64/ 343) = 64:343

So, the answer is A. 64:343.