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The width of a rectangle is 1 units less than the length. The area of the rectangle is 56
square units. What is the length, in units, of the rectangle?
Quadratic Word Problems
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The value of the x-coordinate of point W is -3.5.

Coordinate geometry is the study of geometry using the points in space.

From the graph, the location of the point W is (-3.5, 1.5).

In the coordinate plane, the x-coordinate is always given first, followed by the y-coordinate, in the form (x, y). Therefore, point W is located at -3.5 on the x-axis and 1.5 on the y-axis.

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The complete question is given below.

The Median  of the distribution above is 2.5.

The order the values of the numbers from smallest to largest are:

0, 1, 1, 2, 2, 3, 3, 4, 10, Q

To find the median of the data set, that is the middle value when the data is ordered, one need to average of the two middle values, and the middle values are 2 and 3:

Hence:

Median = (2 + 3)/2

            = 2.5

The interquartile range IQR is seen as the range in values that is obtained from the first quartile Q1 to the third quartile Q3 and it can be gotten from the IQR by removing Q1 from Q3.

IQR = Q3 - Q1

Note that the first quartile (Q1) is the median of the lower half of the data set, and the third quartile (Q3) is the median of the upper half. So the value  are:

Q1 = 1

Q3 = 4

IQR = Q3 - Q1

= 4 - 1

= 3

To get the range, it will be:

10 - 0

= 10

To explain, note that the range and IQR tells different areas of the data set. The range tells us the way that the data spread out and the IQR measures the spread of the middle 50% of the above data.

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The reason why none of the methods match the probability of landing on the B section of the spinner exactly is due to various assumptions, limitations, and uncertainties involved in the measurement and calculation process.

We have,

When Andre measures the spinner and finds that the B section takes up 1/4 of the circle, it means that the B section has an angle measure of 90 degrees out of a total of 360 degrees in a circle.

Now, if we try to calculate the probability of landing on the B section using different methods, we might get slightly different results for several reasons.

Firstly,

The probability of landing on a certain section of the spinner depends on the assumption that the spinner is perfectly balanced and that all sections have an equal chance of being landed on.

However,

In reality, the spinner might not be perfectly balanced, or there might be other factors that affect the outcome, such as air resistance or the force with which the spinner is spun.

Secondly,

Different methods of calculating the probability might make different assumptions or use different techniques that can affect the result.

For example, if we use the classical probability approach, we assume that all outcomes are equally likely, but in the case of a spinner, this might not be the case due to factors such as the weight or shape of the sections.

On the other hand, if we use the relative frequency approach, we base the probability on past data or observations, which might not necessarily reflect the current situation or the true underlying probabilities.

Therefore,

While the probability of landing on the B section might be close to 1/4, none of the methods will match this probability exactly due to various assumptions, limitations, and uncertainties involved in the measurement and calculation process.

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The graph has 14 vertices and 10 vertices and 70 edges, but this does not affect the chromatic number, which is 2.

A bipartite graph is a graph whose vertices can be divided into two disjoint and independent sets. In such a graph, it is always possible to color the vertices with two colors such that no two adjacent vertices have the same color. Therefore, the chromatic number of a bipartite graph is always 2.

In this problem, the bipartite graph has 14 vertices in one part and 10 vertices in the other part, which makes a total of 24 vertices. Since the graph has 70 edges, it means that each vertex in one part is connected to exactly 5 vertices in the other part (70/14=5). Similarly, each vertex in the other part is connected to exactly 7 vertices in the first part (70/10=7).

To color this bipartite graph with two colors, we can assign one color to the first set of vertices and the other color to the second set of vertices. This coloring satisfies the condition that no two adjacent vertices have the same color, and therefore, the chromatic number of the graph is 2.

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The measure of angle D is 48.59 degrees where angle D is acute.

For finding the measure of angle when a trigonometric ratio is given, we use inverse trigonometric functions.

For sine there lies arcsin, for cos, there lies arccos and so on.

Thus, sinD=0.75

∠D = sin⁻¹(0.75)

∠D = 48.59

But since ∠D is acute, thus we have ∠D = 48.59

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A square pyramid has a square base with four vertices, and an additional vertex at the apex of the pyramid, for a total of five vertices or zero-dimensional objects.

Answer:

A.) 5

Points are 0 dimensional objects.

The measure of the hypotenuse of the right-angle triangle is 53.21 feet.

Given that:

Perpendicular, P = 50 feet

Angle, Ф = 70°

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The measure of the hypotenuse of the right-angle triangle is calculated as,

sinФ = P/H

sin 70° = 50 / x

x = 53.21 feet

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Answer:

To calculate the accumulated depreciation using the MACRS method, you will need to use Table 17-1 and Table 17-2 from your textbook. Here are the steps:

1. Determine the depreciation rate for the computer system based on its class life. According to Table 17-1, the class life for computers is 5 years. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method (which is used in the first year) is 40%. Therefore, the depreciation rate for the computer system in year 1 is 40%.

2. Calculate the depreciation for year 1 using the depreciation rate and the cost of the asset. The depreciation for year 1 is the cost of the asset multiplied by the depreciation rate, which gives us:

Depreciation for year 1 = $49,500 x 40% = $19,800

3. Determine the depreciation rate for year 2. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 2 is 32%. Therefore, the depreciation rate for the computer system in year 2 is 32%.

4. Calculate the depreciation for year 2 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 1 is the cost of the asset minus the depreciation for year 1, which gives us:

Remaining book value after year 1 = $49,500 - $19,800 = $29,700

Depreciation for year 2 = $29,700 x 32% = $9,504

5. Determine the depreciation rate for year 3. According to Table 17-2, the depreciation rate for 5-year property using the 200% declining balance method in year 3 is 19.2%. Therefore, the depreciation rate for the computer system in year 3 is 19.2%.

6. Calculate the depreciation for year 3 using the depreciation rate and the remaining book value of the asset. The remaining book value of the asset after year 2 is the cost of the asset minus the depreciation for year 1 and year 2, which gives us:

Remaining book value after year 2 = $29,700 - $9,504 = $20,196

Depreciation for year 3 = $20,196 x 19.2% = $3,880.35

Answer: To find the average speed, we need to use the formula:

average speed = total distance / total time

We can first calculate the total distance, which is:

total distance = 900 km + 3000 km + 400 km + 15 km = 3315 km

To calculate the total time, we need to find the time taken for each leg of the journey:

time taken for train journey = distance / speed = 900 km / 60 km/hour = 15 hours

time taken for boat journey = distance / speed = 3000 km / 25 km/hour = 120 hours

time taken for plane journey = distance / speed = 400 km / 350 km/hour = 1.14 hours

time taken for taxi journey = distance / speed = 15 km / 25 km/hour = 0.6 hours

Therefore, the total time taken for the entire journey is:

total time = 15 hours + 120 hours + 1.14 hours + 0.6 hours = 137.74 hours

Now we can calculate the average speed:

average speed = total distance / total time = 3315 km / 137.74 hours ≈ 24.05 km/hour

Therefore, the average speed for the entire distance is approximately 24.05 km/hour.

The volume of the rectangular prism in this problem is given as follows:

84 in³.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The dimensions for the prism in this problem are given as follows:

3 in, 4 in and 7 in.

Hence the volume of the prism is given as follows:

V = 3 x 4 x 7 = 84 in³.

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The answers are explained in the solution.

Given are right triangles, we need to find the missing lengths,

Here we will use Pythagoras theorem,

Hypotenuse² = base² + perpendicular²

1) x² = 5²+2²

x = √25+4

x = √29

2) 6² = x²+4²

x = √36-16

x = √26

3) 25² = x² + √24²

x = √625-576

x = √49

x = 7

Only the 3rd is following the rule of Pythagorean triplet.

Part 2 = The Triangle Inequality :-

The Triangle Inequality (theorem) says that in any triangle, the sum of any two sides must be greater than the third side.

a) 2, 4, 8

2+4 = 6 < 8 [not a triangle]

b) 5, 6, 7

5+6 = 11 > 7

6+7 = 13 > 5

7+5 = 12 > 6

Therefore, it is forming a triangle,

7² = 49

5²+6² = 36+25 = 61

∵ 7² < 5²+6²

Therefore, the triangle is an acute triangle.

c) 6, 8, 15

6 + 8 = 14 < 15 [not a triangle]

d) 9, 12, 15

9 + 12 = 21 > 15

12 + 15 = 27 > 9

15 + 9 = 24 > 12

Therefore, it is forming a triangle,

15² = 225

9²+12² = 81 + 144 = 225

∵ 15² = 9²+12²

Therefore, the triangle is a right triangle.

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Answer:

A linear function is a function that produces a straight line when it is graphed. The equation of a linear function is of the form y = mx + b, where m is the slope and b is the y-intercept.

Looking at the four tables, we can calculate the slopes of the lines that would be produced by each table. The slope is given by the change in y divided by the change in x.

For the first table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the second table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the third table, the change in y is 1, and the change in x is 1. Therefore, the slope is 1/1 = 1.

For the fourth table, the change in y is 2, and the change in x is 1. Therefore, the slope is 2/1 = 2.

Only the first three tables have the same slope, which is 1. Therefore, only the first three tables represent a linear function.

a. WXYZ is a kite

b.In the kite mWQZ = 90° because XZ bisects WY

c. WY = 24 mm because WQ = QY

A kite is a quadrilateral that has two pairs of consecutive equal sides and perpendicular diagonals.

a. From the figure, we see that WXYZ is a kite

b. To determine mWQZ, we use the property of a kite which says that the diagonals of a kite intersect at right angles. Since XZ and WX are the diagonals of the kite, they thus intersect at right angles.

Since a right angle is 90° and the angle of intersection is mWQZ, thus mWQZ = 90°

So, mWQZ = 90° because XZ bisects WY

c. To determine WY, we know that WY is the shorter diagonal of the kite. Since one of the properties of a kite says that the longer diagonal bisects the shorter diagonal. So, XZ bisects WY. So, WY = WQ + QY. Since XZ bisects WY, WQ = QY.

So, WY = WQ + QY

= QY + QY

= 2QY

= 2(12 mm)

= 24 mm

So, WY = 24 mm because WQ = QY

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Answer:

12

Step-by-step explanation:

4(5)-8

20-8

12

The requried game should start no later than 10:30 am to ensure that the team finishes on time.

If the game is at most 1 3/4 hours long, then the latest it can end is 1:45 pm (which is 1 hour and 45 minutes after the start time).

If the team needs to be off the field by 12:15 pm, then the latest the game can start is:

12:15 pm - 1 hour and 45 minutes = 10:30 am

Therefore, the game should start no later than 10:30 am to ensure that the team finishes on time.

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An equation that can be used to describe the relationship between x and y shown in the graph is: B. y = 3x - 6

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

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

Slope (m) = 6/2

Slope (m) = 3

At data point (2, 0) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 0 = 3(x - 2)  

y = 3x - 6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

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

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Answer:

$13,080.50 + $13,080.50 x 0.06 x 30/360 = $13,393.03

Step-by-step explanation:

Adjusted balance after the first payment: $39,600 + $39,600 x 0.06 x 75/360 - $11,880 = $28,770

Adjusted balance after the second payment: $28,770 + $28,770 x 0.06 x 5/360 - $15,840 = $13,080.50 tell me if it's not clear

The requried, variance of their weights is 157.789 kg².

To calculate the variance, we need to square the standard deviation since variance is the square of the standard deviation. Thus, the variance of the weights of the 10 subjects is:

Variance = (Standard Deviation)² = (12.5602 kg)² = 157.789 kg²

Therefore, the variance of their weights is 157.789 kg².

Note that the units of the variance are the square of the units of the standard deviation.

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In 1997 the population of a small town was 700. If the annual rate of increase is about 0.8% is an example of exponential growth. Then the correct option is A.

Option A depicts exponential development among the applications provided. A tiny town's population is expanding at a 0.8% yearly rate. Because of the increasing population, the rate of rise will be higher each year as the population expands. As a result, an exponential function may be used to depict population expansion.

Option B is not an illustration of exponential development because it depicts projectile motion with a constant velocity.

Skylar spends a certain amount for each ride, therefore Option C depicts linear expenditure and is not an illustration of exponential growth.

Option D depicts exponential decline, in which the number of tree frogs falls by 3% per week. This indicates exponential decay rather than exponential growth since the amount is declining at a rate proportionate to its present value.

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A Pythagorean triple is a set of values (a,b,c) that satisfies the equation:

a^2 + b^2 = c^2

The Pythagorean theorem asserts that the square of the length of the hypotenuse (the side opposite the right angle) in a right triangle is equal to the sum of the squares of the lengths of the other two sides.

We have that;

x = √2^2 + 5^2

x = 5.4 (Not a Pythagorean triple)

x = √6^2 - 4^2

x = 4.5 (Not a Pythagorean triple)

x = √25^2 - 24^2

x = 7 (Yes, it is a Pythagorean triple)

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The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Answer:

12.   m∠C = 100° and m∠F = 100°

13.   m∠S = 89° and m∠U = 89°

Step-by-step explanation:

Question 12

The two triangles ΔABC and ΔDEF have two of their angles equal:
m ∠A = m ∠D

m∠B = m∠E

Therefore the third angles must be equal:
m∠C = m∠F

m∠C = (4x²)° and m∠F = (3x² + 25)°

Setting these two right side expressions in parentheses equal to each other gives
4x² = 3x² + 25
4x² - 3x² = 25
x² = 25
x = ±√25 = ±5

Ignoring the negative value we get
x = 5

Therefore
m∠C = (4x²)° = (4 · 5²)° = (4 · 25)° = 100°

Since, m∠F = m∠C ,
m∠F  = 100°

But we can double check
m∠F = (3x² + 25)° = (3 · 5² + 25)° = (3 · 25 + 25) = (75 + 25)° = 100°

Question 13

This is similar to question 12

The quadrilateral RSTU is divided into two triangles ΔRST and Δ RUT

We are given
m∠RTS = m∠TRU

m∠TRS = m∠RTU

Therefore the third angle of ΔRST must be equal to the third angle of Δ RUT

In other words,
m∠S= m∠U

Plugging in the expressions for each of these angles we get

(5x - 11)° = (4x + 9)°

Set the expressions inside parens equal to each other and solve for x:
5x - 11 = 4x + 9

5x - 4x - 11 = 9    (subtract 4x from both sides)
x - 11 = 9

x = 11 + 9  (add 11 both sides)

x = 20

m∠S= (4x + 9)° = (4 · 20 + 9)° = (80 + 9)° = 89°

Therefore m∠RUT is also 89°

but we can double-check
m∠U= (5x - 11)° = (5 · 20 - 11)° = (100 - 11)° = 89°

The probability of getting a number beginning and ending with even digits is 8/120= 1/15

There are six digits to choose from, but you're only taking three at a time, so the number of such numbers is

6 x 5 x 4 = 120

The first and last digits can only be even if the number takes the one of the forms "2 _ 8" or "8 _ 2".

The middle number can be any of the remaining four, so there is a total of eight such numbers.

This means the probability of getting a number beginning and ending with even digits is 8/120= 1/15

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The missing integer on the number line below is given as follows:

-7.

The missing integer on the number line is obtained applying the proportions in the context of the problem.

The vertical trace is the mean of -10 and -5, hence it is given as follows:

(-10 - 5)/2 = -7.5.

(we obtain the mean of the two numbers as the middle trace is exactly halfway between these two values).

The missing integer on the number line is the integer number exactly to the right(greater) of -7.5, hence it is of:

-7.

(nearest integer that is greater than -7.5).

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Applying the secant-tangent theorem, the length of the diameter is approximately 13.9.

Given the image above that shows a circle containing the diameter, assuming the length of the diameter is x, we can create the following equation based on the secant-tangent theorem:

25² = 19(x + 19)

625 = 19x + 361

625 - 361 = 19x + 361 - 361 [subtraction property]

264 = 19x

Divide both sides by 19:

x ≈ 13.9

The diameter is approximately 13.9.

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The solution of the logarithm equation, log₁₄ 144 = 2 is 14² = 144.

The logarithm equation can be solved using the law of logarithm. Therefore,

log₁₄ 144 = 2

If you have a single logarithm on one side of the equation, you can express it as an exponential equation and solve it.

Hence,

logₐ b = x can be represented as follows:

aˣ = b

Therefore,

log₁₄ 144 = 2

14² = 144

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pat a

π is approximately 3.1 to the nearest tenth.

√6 is approximately 2.4 to the nearest tenth.

2√6 is approximately 4.8 to the nearest tenth.

√7 is approximately 2.6 to the nearest tenth.

(b)

Ordering from least to greatest:

An approximation is described as  anything that is similar, but not exactly equal, to something else.

A number can be approximated by rounding off and  a calculation can be approximated by rounding the values within it before performing the operations .

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The number of bacteria this morning is 119000 and the surface area of the solid is 25344 square meters

Given that

So, we have

This morning = 35000 * (1 + 240%)

Evaluate

This morning = 119000

Here, we have

Fractional part = 28/70

Simplify

Fractional part = 2/5

So, the 28 is 2/5 of 70 as the fractional part

Start by calculating the base area using

base area = 1/2 * (6 + 10) * 10

base area = 80

So, we have

Volume = base area * height

Volume = 80 * 13

Volume = 1040 cubic cm

This is calculated as

Surface area = bh * (b1 + b2 + b3)l

So, we have

Surface area = 12 * 6 * (10 + 10 + 12) * 11

Evaluate

Surface area = 25344

So, the surface area of the solid is 25344 square meters

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