(x²+3x+2)(x²+7x+12)=24

By triangle inequality theorem  7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.

We know that the triangle inequality theorem states that the sum of any two sides of a triangle is greater than or equal to the third side.

For example, is a, b and c be sides of triangle then a + b ≥ c.

Here, the sides of triangle are:  7.7 cm, 4.0 cm, 1.7 cm

Let  a = 7.7 cm,

b = 4.0 cm,

c = 1.7 cm

consider the sum of sides b and c.

b + c = 4. 0 + 1.7

b + c = 5.7 cm

which is not greater than 7.7 cm (length of side  'a')

This means that, by triangle inequality theorem  7.7 cm,4.0 cm, 1.7 cm can not sides of the triangle.

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The complete question is:

Could 7.7 cm,4.0 cm, 1.7 cm be the side lengths of a triangle?

Hello and Greetings Brainly users.

This is an exercise in "Equation of the line that passes through two points". The equation of a line is a mathematical formula used to describe a straight line in a Cartesian plane.

To find the equation of a line that passes through two points, you must first calculate the slope using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the given points. Then, the point-slope form of the equation of the line is used to obtain the equation of the line: y - y₁ = m(x - x₁).

By solving this equation, we can obtain the equation of the line that passes through two points. If the slope of the line is zero, as in the case of two points lying on the same horizontal line, then the equation of the line is simply a horizontal line at y = k, where k is the y-coordinate of the points.

Applying the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where m is the slope of the line.

We find that the points are:

x₁ = 6 ,   y₁ = 4

x₂ = -5 , y₂ = 4

We substitute the data in the formula and solve:

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 4)/(-5-6)

m = 0/-11

m = 0

Now, we can use the point-slope form of the equation of the line to obtain the equation of the line:

Where m = 0 and (x₁, y₁) is one of the two given points. We can choose any of the two points, but for this we will choose (6,4).

So, substituting the values we have, we have:

y - 4 = 0(x - 6)

Simplifying, we arrive at:

y - 4 = 0

y = 4

The equation of the line that passes through the points (6,4) and (-5,4) is y = 4 , since it is a horizontal straight line through the values of y = 4.

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The length of the hypotenuse is given as follows:

b = 10.6 yd.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

By the 45-45-90 Triangle Theorem, the two sides have the same length, hence:

a = c = 7.5.

Hence the hypotenuse b is obtained as follows:

b² = a² + c²

b² = 7.5² + 7.5²

[tex]b = \sqrt{7.5^2 + 7.5^2}[/tex]

b = 10.6 yd.

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The projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

Explain the term projection

Projection is the process of representing a three-dimensional object or scene onto a two-dimensional surface. It involves the use of mathematical principles to create a flat image that accurately depicts the shape and position of the object or scene. Projections are widely used in fields such as engineering, architecture, and computer graphics to create visual representations of complex structures and designs.

According to the given information

The projection of a vector u onto a vector v is given by the formula proj_v(u) = (u•v)/(||v||²) * v, where u•v is the dot product of u and v, and ||v|| is the magnitude of v.

In this case, u = (-9,-5) and v = (-6,5). The dot product of u and v is u•v = (-9)(-6) + (-5)(5) = 54 - 25 = 29. The magnitude of v is ||v|| = √((-6)² + (5)²) =

√(36 + 25) = √61.

So the projection of u onto v is proj_v(u) = (u•v)/(||v||²) * v = (29/61) * (-6,5) = (-174/61, 145/61).

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The test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

The null hypothesis for this scenario is that the proportion of computer chips that do not fail in the first 1000 hours of their use is equal to or less than 61%, while the alternative hypothesis is that the proportion is greater than 61%. Mathematically:

H0: p ≤ 0.61

Ha: p > 0.61

where p is the true proportion of computer chips that do not fail in the first 1000 hours of their use.

To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:

z = (0.64 - 0.61) / sqrt((0.61 * 0.39) / 1600) = 3.46

where 0.39 is the complement of 0.61, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.02 level of significance is 2.05.

Since the test statistic (3.46) is greater than the critical value (2.05), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.02 level to support the company's claim that above 61% of the chips do not fail in the first 1000 hours of their use.

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The primary condition for which a patient is receiving care is communicated to the third-party payer through a diagnosis code on the healthcare claim.

The diagnosis code is a standardized code that represents the patient's medical condition or illness as determined by the healthcare provider. These codes are typically based on the International Classification of Diseases (ICD) coding system, which is used worldwide for reporting diagnoses and medical procedures.

By including the appropriate diagnosis code on the healthcare claim, healthcare providers can communicate to third-party payers the reason for the services or procedures provided. This information is essential for processing and reimbursing healthcare claims accurately and efficiently.

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The primary condition for which a patient is receiving care is communicated to the third-party payer through a(n) ICD (International Classification of Diseases) code on the healthcare claim.

The ICD code serves as a standardized system for classifying diseases and health conditions, enabling clear

communication between healthcare providers and third-party payers.

The primary condition for which a patient is receiving care is communicated to the third-party payer through a

diagnosis code on the healthcare claim. Diagnosis  codes, also known as ICD codes (International Classification of

Diseases codes), are standardized codes that represent the specific medical condition or disease being treated by the

healthcare provider.

These codes are used to ensure accurate and timely payment for services rendered and to track healthcare utilization

and outcomes.

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Answer:

-5

Step-by-step explanation:

if u graph it, you can see where the y-intercept is.

Answer: Symbol max-min and answer 10-4

Step-by-step explanation:

Answer:

7) 760

8) 34

Step-by-step explanation:

7)  95x8=760

8)  (103-35)/2=34

At sunrise, shadows are longest and point towards the west as the sun rises in the east. Therefore, the correct order would be:

Longest shadows of the day, and they point to the west → shadows gradually become shorter → very short shadows or no shadows → shadows gradually become longer → longest shadows of the day, and they point to the east.

As the sun moves across the sky, shadows change in length and direction, reaching their shortest length at noon when the sun is directly overhead. After noon, the sun starts to move towards the west, and shadows gradually become longer until sunset when they are longest again, but this time pointing towards the east as the sun sets in the west.

Therefore, correct order of descriptions of shadows during the day, from sunrise to sunset, would be:

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See text below



How do shadows change during the day?

Drag and drop the descriptions of shadows to show the correct order, from sunrise to sunset.

longest shadows of the day, and they point to the west

longest shadows of the day, and they point to the east

shadows gradually become shorter

very short shadows or no shadows

shadows gradually become longer

Thus,  the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

To solve this problem, we need to use algebraic equations. Let's start by assigning variables to the unknown quantities. Let x be the number of purses sold and y be the number of blouses sold.

From the problem, we know that the blouses cost $28 each and the purses cost $39 each. Therefore, the total revenue from selling x purses and y blouses is given by:

Revenue = 28y + 39x

We also know that the store sold three times as many blouses as purses. Therefore, we can write:
y = 3x

Now we can substitute y = 3x into the revenue equation and solve for x:
1107 = 28y + 39x
1107 = 28(3x) + 39x
1107 = 84x + 39x
1107 = 123x
x = 9

So the store sold 9 purses. To find the number of blouses, we can use the equation y = 3x:
y = 3x = 3(9) = 27

Therefore, the store sold 27 blouses.

In summary, the store sold 9 purses and 27 blouses on that day, and the total revenue from selling these items was $1107.

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Answer: Looks pretty good :) !

Answer:

[tex]2\sqrt{65}[/tex] cm, decimal form is about 16.1 cm

Step-by-step explanation:

Use the pythagorean theorem:

A^2 + B^2 = C^2

A and B are legs, c is hypotenuse

First leg is 16, second leg is 2

Plug it in:

16^2 + 2^2 = hypotenuse^2

256 + 4 = hypotenuse ^2

260 = h^2

[tex]\sqrt[2]{260}[/tex] = h

To simplify the square root of 260, we can factor 260 into its prime factors:

260 = 2 x 2 x 5 x 13

Then, we can take out the pairs of identical factors from under the square root symbol:

sqrt(260) = sqrt(2 x 2 x 5 x 13)

= sqrt(2 x 2) x sqrt(5) x sqrt(13)

= 2sqrt(65)

[tex]2\sqrt{65}[/tex]

Answer:

16.2 or 16.00

Step-by-step explanation:

Leg #1 --->16

Leg #2 --->2

C ---> hypotenuse

16.12452---->16.12

16.12 rounded to the nearest tenth is 16.00

Answer:

x=7.9*tan(54°)=10.87

Answer:

The slope of that line is 13/8 = 1.625

(1.63 to two decimal places).

The requried, there are 8998912 possible license plates that can be generated using this format.

There are 8 digits that can be used for each of the three digits on the license plate, with two digits (4 and 5) that cannot be used. Therefore, there are 8 choices for each of the three digits, giving us 8 x 8 x 8 = 512 possible combinations for the digits.

Similarly, there are 26 letters that can be used for each of the three letters on the license plate. Therefore, there are 26 choices for each of the three letters, giving us 26 x 26 x 26 = 17576 possible combinations for the letters.

Total number of license plates = number of choices for the digits x number of choices for the letters

= 512 x 17576

= 8998912

Therefore, there are 8998912 possible license plates that can be generated using this format.

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Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.

Toshi's prediction was that he would perform the card trick successfully 95% of the time. This means that out of 100 card tricks, he expects to perform the trick successfully in 95 of them. We can represent this mathematically by:

P(success) = 0.95

This is the probability of success for one card trick.

Toshi actually performed the card trick 30 times and was successful in 24 of them. We can represent this as:

P(actual success) = 24/30 = 0.8

This is the proportion of successful card tricks that Toshi actually performed.

To compare Toshi's prediction with his actual results, we can use probability theory. The probability of getting exactly x successes in n trials when the probability of success is p is given by the binomial distribution formula:

P(x) = (n choose x) * pˣ * [tex](1-p)^(n-x)[/tex]

In this case, we can use the formula to calculate the probability of getting exactly 24 successes in 30 trials if Toshi's prediction of 95% success rate is accurate. This is given by:

P(24 successes) = (30 choose 24) * 0.95²⁴ * 0.05⁶ ≈ 0.0045

This means that if Toshi's prediction is accurate, the probability of getting exactly 24 successes in 30 trials is very low (less than 0.5%).

Therefore, we can conclude that Toshi's actual results were significantly different from his prediction. Specifically, his actual success rate of 80% was lower than his predicted success rate of 95%.

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A. The area of the rectangle is 29.16 square inches.

B. The width of the rectangle is 2.7 inches and the height (or length) is 10.8 inches

A parallelogram in which each pair of adjacent sides is perpendicular is referred to as a rectangle.

We should utilize "w" to address the width and "l" to address the length of the square shape.

A. Since the width equals one quarter of the length, we are able to write:

w = (1/4)l

We also know that the perimeter of the rectangle is 27 inches, and

the formula for the perimeter of a rectangle is:

P = 2l + 2w

Substituting the first equation into the second equation, we get:

P = 2l + 2(1/4)l

27 = 2.5l

l = 10.8

Now that we know the length, we can use the first equation to find the width:

w = (1/4)l

w = (1/4)(10.8)

w = 2.7

As a result, the rectangle has a width of 2.7 inches and a height of 10.8 inches.

B. To find the area of the rectangle, we can use the formula:

Area = length *width

Substituting the values we found above, we get:

A = (2.7)*(10.8)

A = 29.16

Therefore, the area of the rectangle is 29.16 square inches.

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The equation that represents the line of best fit is given as follows:

y = 50x.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

When x = 10, y = 500, hence the slope m is given as follows:

m = 500/10

m = 50.

Hence the equation is given as follows:

y = 50x.

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The final answers are given below

[tex]10.[/tex]L

[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)

[tex]00000[/tex]

[tex]12[/tex]  | |

[tex]00000[/tex]

|

[tex]00000[/tex]

[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]

A number is an arithmetic value that is used to calculate and represent a quantity.

The numbers that are more than [tex]20[/tex] but less than [tex]30[/tex] are [tex]22[/tex] and [tex]26[/tex], so they should be crossed out:

[tex]31 16 48 29 53 47[/tex] X [tex]37 98[/tex] X [tex]2025[/tex]

Therefore the answers are given below.

[tex]10.[/tex]L

[tex]11.[/tex] [tex]3[/tex] (the number should be [tex]1,000,000[/tex], which has six zeros)

[tex]00000[/tex]

[tex]12[/tex]  | |

[tex]00000[/tex]

|

[tex]00000[/tex]

[tex]15. 31 16 48 29 53 47 22 37 98 26 2025[/tex]

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Answer:

Box A: 2 × 4.5 × 6 = 54 cubic inches

Box B: 6 × 2.5 × 3 = 45 cubic inches

Box C: 5 × 4.5 × 2.25 =

50.625 cubic inches

Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches

From least to greatest, the order of the boxes' volumes is D, B, C, A.

The correct option is- A. graph of two lines with the intersecting point at (negative 1, 1).

On a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Given system of equations:

y + 2x = −1  ...eq 1

3y − x = 4 ..eq 2

multiply eq 2 with 2 and add to eq 1

6y − 2x = 8 ..eq 3

6y − 2x + y + 2x = 8 - 1

7y = -7

x = -1

Now,

y + 2x = −1

y + 2(-1) = −1

y = -1 + 2

y = 1

Thus, the solution of the given system of equations. y + 2x = −1 and 3y − x = 4 is found as :(-1, 1).

The graph for the equations are attached.

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Correct question:

Choose the correct graph of the given system of equations. y + 2x = −1 and 3y − x = 4 .

Group of answer choices :

A. graph of two lines that intersect at the point (negative 1, 1)

B. graph of two lines that intersect at the point (1, 1) < Not

C. graph of two parallel lines with positive slopes

D. None of the above

the vegetable garden is 24 square feet larger than the herb garden. The area of the square vegetable garden is equal to the length of one side squared.

what is  larger than  ?

"larger than" is a comparative term used to describe a situation where one thing has a greater size, quantity, value, or magnitude than another thing. It is used to indicate a comparison between two or more objects or quantities.

In the given question,

The area of the square vegetable garden is equal to the length of one side squared. Each side of the square garden is 6 feet long, so the area of the vegetable garden is:

6 feet × 6 feet = 36 square feet

The area of the rectangular herb garden is equal to its length multiplied by its width. The length of the herb garden is 4 feet and the width is 3 feet, so the area of the herb garden is:

4 feet × 3 feet = 12 square feet

To find the difference in area between the two gardens, we subtract the area of the herb garden from the area of the vegetable garden:

36 square feet - 12 square feet = 24 square feet

Therefore, the vegetable garden is 24 square feet larger than the herb garden.

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Answer:

1. The parameter of interest is the proportion of students in the school who think of their parents or guardians as “strict”. A statistic that the students could use to estimate the parameter is the proportion of students in their sample who think of their parents or guardians as “strict”.

2. The best design for this study is a sample survey. An experiment would involve manipulating the parents' behavior and observing the effect on the students, which is not ethical. An observational study would only observe the behavior without manipulation, but it is not clear what behavior to observe in this case.

3. Here are three questions that could provide objective data related to strictness:

4. An appropriate method for obtaining a sample of 100 students is random sampling. The students could assign each student in the school a number, and then use a random number generator to select 100 numbers. They could then survey the students corresponding to those numbers. Another method could be stratified sampling, where the students divide the school into groups based on grade level, and then randomly sample a proportionate number of students from each group.

Answer:

Kailey flipping heads: 3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipping tails: 9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

Step-by-step explanation:

Kailey flipped heads 15 times and tails 5 times.

First, find the total amount of times that Kailey flipped the coin.

15+5=20

Kailey flipped the coin 20 times.

Out of those 20 times, she flipped heads 15 times. We can rewrite this as:

[tex]\frac{15}{20}[/tex]

and simplify it:

[tex]\frac{3}{4}[/tex]

3/4 as a decimal is 0.75, and to find the percentage, simply multiply the decimal form by 100.

We can find that 3/4 as a percentage is 75%.

So, the probability of Kailey flipping heads is:

3/4 as a fraction, 0.75 as a decimal, and 75% as a percent.

Olivia flipped heads 11 times and tails 9 times.

Let's find how many times she flipped the coin.

11+9=20

Olivia flipped the coin 20 times.

Out of 20 times, Olivia flipped tails 9 times.

This can be rewritten as:

[tex]\frac{9}{20}[/tex]

This fraction is already in simplest form.

To find what 9/20 is as a decimal, divide 9 by 20. You'll get 0.45.

Now, multiply 0.45 by 100 to find the percent. You'll get 45%.

So, the probability of Olivia flipping tails is:

9/20 as a fraction, 0.45 as a decimal, and 45% as a percent.

Hence, Equation of line is y= -17 x+420 and Predict the number of fan clubs in the U.S. in 2012 is -33784.

The slope of  a line is its vertical change  divided by its horizontal change, also known as rise over run. When you have 2 points  on a line on a graph  the slope is the change in y divided by the change in x.

The process of predicting inside of the observed x values observed in the data is called interpolation. The process of predicting outside of the observed x values observed in the data is called extrapolation.

according to question,

[tex](x_1,y_1)=(4,348) \\and (x_2,y_2)=(6,314)\\[/tex]

and y-intercept point=c=420

slope

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{314-348}{6-4}\\m=\frac{-34}{2}\\m= -17[/tex]

(a).now,equation of line ,y=mx+c

⇒y= -17x+420..(i)

(b). for 2012,x=2012

now value of x is substitute in (i),

⇒y= -(17*2012)+420

⇒y = -34204+420

⇒y= -33784.

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Answer:

Starting at the origin (0, 0), go right 3 units, then down 7 units. You will end at (3, -7).

The area of the composite figure is 84.85 square units

The area of the composite figure is solved by breaking it up and adding together

To find the area of a semicircle of diameter 8, we first need to find the radius of the semicircle, which is half of the diameter:

radius = diameter / 2 = 8 / 2 = 4

area of semicircle = (1/2) * pi * radius^2

= (1/2) * pi * 4^2

= 8 pi

Now, let's find the area of the parallelogram. The area of a parallelogram is given by the formula:

area of parallelogram = base * height

In this case, the base is 10 and the height is 6, so we have:

area of parallelogram = 10 * 6

= 60

total area = area of semicircle + area of parallelogram

= 8 pi + 60

= 60 + 8 pi (in exact form) or approximately 84.85 (rounded to two decimal places)

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