Can a triangle be constructed with the following side lengths?
12 6 9

Answer:

the answer for this problem is x^2+2x-15

Step-by-step explanation:

(x+5)(x-3)

x(x-3)+5(x-3)

x^2-3x+5(x-3)

x^2-3x+5x-15

=x^2+2x-15

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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Answer:

76°

Step-by-step explanation:

Applying trigonometry :

Angle x ;

Tan x = opposite / adjacent

Tan x = (30/20)

x = tan^-1(30/20)

x = 56.31°

Angle y;

Tan y = opposite / adjacent

Tan y = (22/20)

x = tan^-1(22/20)

x = 47.73°

The angle θ ;

Sum of angles in a straight line = 180

56.31 + 47.73 + θ = 180°

θ = 75.96°

Answer:

a

Step-by-step explanation:

19.50 cost of pizza

Step-by-step explanation:

$8.00-$1.50 = $6.50 × 3 =19.50

Answer:

67 times

Step-by-step explanation:

33,500 divided by 500 is equivalent to 67

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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The equation y = -1/7x + 1 represents a line with a slope of -1/7 and a y-intercept of 1.

The equation of the line is in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.

For the equation y = -1/7x + 1, the slope (m) is -1/7, and the y-intercept (b) is 1.

To graph this line, you can start by plotting the y-intercept, which is the point (0, 1) on the coordinate plane. Then, you can use the slope to find additional points and connect them to form the line.

To find other points, you can choose any x-value, substitute it into the equation, and calculate the corresponding y-value.

For example, when x = 7, substituting it into the equation gives:

y = -1/7(7) + 1

y = -1 + 1

y = 0

So, when x = 7, y = 0, giving us another point (7, 0) on the line.

By repeating this process for other x-values, you can find more points on the line and connect them to create the graph.

Alternatively, you can use online graphing tools or graphing software to visualize the line using the equation y = -1/7x + 1.

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Answer:

this is a binomial because its separated by a negative sign

Step-by-step explanation:

Answer:

180°

Step-by-step explanation:

ABCD is a parallelogram.

Measures of the opposite angles of a parallelogram are equal. Here \( \angle A, \:\: \angle C \: \: and\:\: \angle B, \:\: \angle D\) are opposite angles.

\( \therefore m\angle A = m\angle C = 110\degree \)

\( \& \:m\angle B = m\angle D = 70\degree \)

\( m\angle A + m\angle B =110\degree + 70\degree \)

\( m\angle A + m\angle B =180\degree \)

Answer:

A.

Step-by-step explanation:

The minimum sample size required to construct a 90% confidence interval with an error of no more than 0.06, given a population mean of 3 fast food meals per week and a population variance of 1.69, is 166.

To find the minimum sample size required to construct the specified confidence interval, we need to use the following formula

n = [Z² × σ²] / E²

where n is the sample size, Z is the Z-score for the desired level of confidence (90% in this case), σ² is the population variance, and E is the maximum error or margin of error.

First, we need to find the Z-score for the 90% confidence level using a standard normal distribution table or calculator. For a two-tailed test, the Z-score is 1.645.

Next, we plug in the given values

n = [1.645² × 1.69] / 0.06²

n = 165.82

We round up to the nearest whole number since we cannot have a fraction of a person in our sample

n = 166

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Answer: The different ways can he line the textbooks up on his bookshelf =24

Step-by-step explanation:

The number of ways to arrange n things = n!

Given:  Number of different books = 4

Number of different ways to arrange 4 different books =4!

Number of different ways to arrange 4 different books= 4 x 3 x 2 x1

Number of different ways to arrange 4 different books = 24

Hence, the different ways can he line the textbooks up on his bookshelf =24

The location of point N is -20.

We  can see a number line with 3 points.

Here we know taht MN is 2/7 of MP, so first let's find the length of MP.

The length is equal to the difference between the two values, we can see that:

P = -5

M = -26

Then the length of MP is:

-5 - (-26) = 21

And MN is 2/7 of that, then:

(2/7)*21 = 2*3 =6

Then we can write:

N - M = 6

N - (-26) = 6

N = 6 - 26 = -20

The location of N is -20.

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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The area of a square is 14 times larger than the area of a triangle, so the length of a side of the square is 49 inches. The area of the triangle is 1/2  base  height, while the area of the square is 14 times larger.

Given, The area of a square is 14 times as large as the area of a triangle One side of the triangle is 7 inches long, and the altitude to that side is the same length as a side of the square. We need to find the length of a side of the square. Area of the triangle = 1/2 × base × height We know the base = 7 in and the height is equal to the side of the square. Let's say the side of the square is x. Area of the triangle = 1/2 × 7 in × x in = 7x/2 in²Area of the square = x²Given, the area of a square is 14 times as large as the area of a triangle.=> x² = 14(7x/2) in²=> x² = 49x in²=> x = 49 in Therefore, the length of a side of the square is 49 inches.

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Answer:

(a) These are the same function

Step-by-step explanation:

Given

\(x + x^2\) and \(u + u^2\)

Required

Are they the same?

Yes, they are the same function and this is proved below.

\(x + x^2\)

Represent as a function:

\(f(x) = x + x^2\)

\(u + u^2\)

Represent as a function

\(f(u) = u + u^2\)

Let x = u

Substitute u for x in \(f(x) = x + x^2\)

\(f(u) = u + u^2\)

This implies that:

\(f(x) = f(u)\)

\(x + x^2 =u + u^2\)

PS: The information that x and u are real numbers are for all real numbers; So, we can not assume that x and u are different numbers

Hence:

(b) and (c) are wrong

The slope-intercept form of a linear equation is given by:

y = mx + b. The value of w is 13 and the value of r is 5.

To find the value of w and r, we need to use the slope-intercept form of a linear equation and the given slope.

The slope-intercept form of a linear equation is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given that the line passing through (3, 5) and (-3, w) has a slope of 3/4, we can substitute the values into the slope-intercept form to get two equations:

5 = (3/4)(3) + b       -- Equation 1

w = (3/4)(-3) + b      -- Equation 2

Simplifying Equation 1, we have:

5 = 9/4 + b

To solve for b, subtract 9/4 from both sides:

5 - 9/4 = b

(20/4) - (9/4) = b

11/4 = b

Now we substitute b = 11/4 into Equation 2:

w = (3/4)(-3) + 11/4

w = -9/4 + 11/4

w = 2/4

w = 1/2

Therefore, the value of w is 1/2.

To find the value of r, we need to calculate the distance between the two x-coordinates of the given points. The distance between 3 and -3 is 3 - (-3) = 6.

Since r represents the value of the x-coordinate of the point (-3, w), we have r = -3.

Therefore, the value of r is -3.

In conclusion, the value of w is 1/2 and the value of r is -3.



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The function f(x) = 2x + 1, where f is defined from the positive integers (Z+) to the real numbers (R), is a one-to-one function, but not a bijection or onto function.

A one-to-one function, also known as an injective function, is a function in which each input value (x) maps to a unique output value (f(x)). In the given expression, f(x) = 2x + 1, every positive integer will have a unique real number output since the coefficient of x is 2, ensuring distinct outputs for distinct inputs. Hence, f is a one-to-one function.

However, a bijection requires that a function be both one-to-one and onto. An onto function, also known as a surjective function, means that every element in the codomain (R) has a corresponding element in the domain (Z+) such that f(x) maps to that element. In this case, the function f(x) = 2x + 1 is not onto because there are real numbers that do not have corresponding positive integers. For example, there is no positive integer x that can satisfy f(x) = 2x + 1 = 0.

In conclusion, the function f(x) = 2x + 1 is a one-to-one function, but it is not a bijection or an onto function.

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Answer:

\(x^{2} +11x-10\)

Step-by-step explanation:

\((13x^{2} +9x-4)-(12x^{2} -2x+6)\)

Remove the brackets and multiply the minus sign through all the numbers in the second polynomial

\(13x^{2} +9x-4-12x^{2} +2x-6\)

Rearrange in the highest order

\(13x^{2} -12x^{2} +9x+2x-4-6\)

Simplify

\(x^{2} +11x-10\)

Answer:

A

Step-by-step explanation:

If  the relationship is graphed with the number of rolls sold on the x-axis and the money earned on the y-axis

Then the two points on that line will be (14,17.50) and (16,20)

We know that the slope of a lien with points  is give by:-

Hence, the slope of the graph with points  (14,17.50) and (16,20) is given by :-

Therefore, the slope of the graph = 1.25 dollars per roll.

Hi! I'm happy to help!

Our total line is JL (4x), and it is split into two parts: JK, and KL. We have our values, and we know that JK+KL=JL, so we can substitute our values and solve for x:

4x=(2x+3)+(x)

4x=3x+3

To solve for x, we have to isolate it on one side of the equation.

First, let's subtract 3x from both sides so that we can isolate x:

4x=3x+3

-3x -3x

x=3

So, our x=3, which means that KL=3.

I hope this was helpful, keep learning! :D

The possible lengths( in whole elevation) for the third side is

9 elevation< x< 45 elevation, i.e in between 9 and 45 elevation.

 For the below question, we've a rule from the properties of triangle, the sum of the length of any two  sides of the triangle must be lesser than the length of the third side.

Hence

She has two sides of length 18 elevation and 27 elevation

Let the third side = x

Hence

a) 18 27> x

45> x

b) 18 x> 27

x> 27- 18

x> 9

thus, the possible lengths( in whole elevation) for the third side is

elevation< x< 45 elevation

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Answer:  73

Step-by-step explanation:

8² = 64    3² = 9    64 +9 = 73

8 to the power of 2 means 8 × 8 that is 64

3 to the power of 2 means 3 × 3 that is 9