Find the volume. round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.

Answer:

x2+10x+25

Step-by-step explanation:

It goes like this:

X2+2*1x*5+5*5

The value of side c to the nearest tenth is 4.2.

The law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

It is expressed as:

c² = a² + b² - ( 2ab × cosC )

From the diagram:

a = 7

b = 8

Angle C = 32 degrees

Plug these values into the above formula and solve for c.

c² = a² + b² - ( 2ab × cosC )

c = √( a² + b² - ( 2ab × cosC ) )

c = √( 7² + 8² - ( 2 × 7 × 8 × cos32 ) )

c = √( 49 + 64 - ( 112 × cos32 ) )

c = √( 113 - 94.98 )

c = √18.02

c = 4.2

Therefore, the value of c is 4.2.

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Answer:

Step-by-step explanation:

2

2-9=-7

In negative numbers, the greater number that is negative is less than the smaller negative number. For example, -9<-8. Even though 9 is a bigger number when positive, it's the opposite for negative numbers. While there can be many numbers for k like 0,1, or 2, 1 will probably be the best answer.

Answer:

Step-by-step explanation:

[tex]\mathrm{ k - 9 < - 6}[/tex]

Add both sides by 9 :-

Simplify :-

___________________

Hope this helps!

Answer:

Step-by-step explanation:

To compare these two values, we first need to convert the mixed number 7 3/8 to an improper fraction. To do so, we multiply the whole number (7) by the denominator of the fraction (8), then add the numerator (3), and put the result over the denominator:

7 3/8 = (7 x 8 + 3) / 8 = 59/8

Now we can rewrite the inequality as:

(59/8) × (4/5) < 59/8

To simplify the left-hand side of the inequality, we multiply the numerators and denominators:

(59/8) × (4/5) = (59 × 4) / (8 × 5) = 236/40 = 59/10

So the inequality becomes:

59/10 < 59/8

To compare these fractions, we need to find a common denominator. The least common multiple of 8 and 10 is 40, so we can convert both fractions to have a denominator of 40:

59/10 = (59 x 4) / (10 x 4) = 236/40

59/8 = (59 x 5) / (8 x 5) = 295/40

Now we can see that 236/40 < 295/40, which means that:

59/10 < 59/8

Therefore, the inequality 7 3/8 × 4/5 < 7 3/8 is true.

To solve the problem, we need to find Julian's average speed, given that he started biking from a position behind the simulated biker at a speed of 20 km/h, and after 15 minutes, his position was reported as -214 km.

We can use the formula for average speed:

Average speed = total distance / total time

To find the total distance, we need to calculate the displacement of Julian from the initial position of -d (where d is the distance between Julian and the simulated biker when he started biking) to the position of -214 km after 15 minutes.

Displacement = final position - initial position

Displacement = (-214 km) - (-d) = d - 214 km

The total distance covered by Julian is equal to the absolute value of the displacement, since the direction of the motion does not matter when computing distance.

Total distance = |d - 214 km|

To find the total time, we need to convert 15 minutes to hours:

Total time = 15 minutes / 60 minutes/hour = 0.25 hours

Now we can substitute the values into the formula for average speed:

Average speed = total distance / total time

Average speed = |d - 214 km| / 0.25 hours

Since Julian was traveling at a constant speed of 20 km/h, we can also express the distance in terms of time:

Average speed = (20 km/h) x t / 0.25 hours

where t is the time Julian biked in hours.

Setting the two expressions for average speed equal to each other, we can solve for t:

|d - 214 km| / 0.25 hours = (20 km/h) x t / 0.25 hours

|d - 214 km| = 20 km/h x t

Solving for t:

t = |d - 214 km| / 20 km/h

Now we can substitute this expression for t into either expression for average speed:

Average speed = (20 km/h) x t / 0.25 hours

Average speed = |d - 214 km| / 0.25 hours

Substituting the expression for t:

Average speed = |d - 214 km| x 4 / |d - 214 km|

Simplifying:

Average speed = 80 km/h

Therefore, Julian's average speed so far has been 80 km/h.

A graph that represent the quadratic equation y = -x² + 8x - 12 is shown in the image attached below.

The roots of the equation are (2, 0) and (6, 0).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = -x² + 8x - 12 is negative 1, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (2, 0) and (6, 0).

In conclusion, the turning point and vertex is given by the ordered pair (4, 4).

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The end behavior of this radical function is "as x approaches positive infinity, f(x) approaches positive infinity".

As we know that the function f(x) = 4√(x − 6) is a radical function with an even index (4), which means that the function is defined for all non-negative values of x.

As x approaches positive infinity, the value of x − 6 also approaches positive infinity, and the square root function grows without bound.

Since the function is multiplied by a positive constant (4), the entire function f(x) also grows without bound as x approaches positive infinity.

Therefore, the end behavior of the function is that as x approaches positive infinity, f(x) approaches positive infinity.

Hence, option A correctly describes the end behavior of the function.

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The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.

(a) For f(x) = 0

We set the function equal to zero and solve for x:

f(0) = sec²x - 1 = 0

sec² x = 1

Taking the square root of both sides, we get:

sec x = ±1

Recall that sec x = 1/cos x = cos⁻¹ x

Therefore

x = cos⁻¹ (1) = 0 (using calculator or table)

x = cos⁻¹(-1) = pi

Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.

(b) For f(x) > 0

To get the positive values of x, we can start by factoring f(x):

f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)

Since the square of the secant function is always positive, we have:

f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0

There are two cases to consider:

sec x + 1 > 0 and sec x - 1 > 0

sec x + 1 < 0 and sec x - 1 < 0

For case 1, we have:

sec x > -1 and sec x > 1

Since secant is always positive, we have sec x > 1.

For case 2, we have:

sec x < -1 and sec x < 1 (This is not possible)

(c) For f(x) < 0

By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.

f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0

There are two cases to consider:

sec x + 1 > 0 and sec x - 1 < 0

sec x + 1 < 0 and sec x - 1 > 0

For case 1, we have:

sec x > 1 and sec x < -1 (not possible)

For case 2, we have:

sec x < -1 and sec x > 1

Since secant is always positive, this case is not possible either.

Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).

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The amount of grams that is equivalent to 3/10 of a kg is given as follows:

300 grams.

The amount of grams that is equivalent to 3/10 of a kg is obtained applying the proportions in the context of the problem.

The amount of kg is 3/10 of a kilogram is given as follows:

3/10 = 0.3kg.

(conversion of a fraction to decimal, divide the numerator by the denominator).

Each kg is composed by 1000 grams, hence the amount of grams in 0.3 kg is given as follows:

0.3 x 1000 = 300 grams.

(proportion applied to obtain the conversion).

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Answer:

36°

Step-by-step explanation:

x+27+27+90=180

x=36°

A function whose graph is the graph of y = √x, but is shifted to the left 9 units is [tex]y=\sqrt{x+9}[/tex].

In Mathematics and Geometry, the translation of a geometric figure or graph to the left means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

Conversely, the translation a geometric figure upward means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.

Based on the information provided, the transformed function should be written as follows:

y = √x

g(x) = (√x + 9)

[tex]y=\sqrt{x+9}[/tex]

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The amount of water that the plastic container can hold is -p + 3.

To determine the amount of water that can be held, we will first assume that the container can hold x quantity of water.

So, the glass jug can hold:

p + 6 - x

2 glass jugs and 2 plastic containers can hold 6p quarts of water.

= 2(p + 6 - x) - 2x = 6p

2p + 12 - 2x -2x = 6p

2p + 12 -4x = 6p

12 - 4x = 6p - 2p

-4x = 6p -2p - 12

-4x = 4p -12

x = 4p - 12/-4

x = -p - 3

or -p + 3

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Answer:

Step-by-step explanation:

Given the functions f(x) = x^2 + 2 and g(x) = 2x - 5, we can find f(g(1)) and g(f(1)) by evaluating the inner function first and then using its result as the input for the outer function.

First, let’s find f(g(1)). We start by evaluating the inner function g(1):

g(1) = 2 * 1 - 5 = -3

Now we can use this result as the input for the outer function f(-3):

f(g(1)) = f(-3) = (-3)^2 + 2 = 9 + 2 = 11

Next, let’s find g(f(1)). We start by evaluating the inner function f(1):

f(1) = 1^2 + 2 = 3

Now we can use this result as the input for the outer function g(3):

g(f(1)) = g(3) = 2 * 3 - 5 = 6 - 5 = 1

So, f(g(1)) = 11 and g(f(1)) = 1.

A form of 1 that you can use to rationalize the denominator of the expression 8/(∛4), the rationalizing factor is 9.

In mathematics, rationalization refers to the process of eliminating radical or irrational expressions from the denominator of a fraction. This is done by multiplying both the numerator and the denominator of the fraction by a suitable expression that will result in a rational denominator.

The resulting fraction has a rational denominator, which makes it easier to work with and manipulate algebraically. Rationalization is a useful technique in algebra, trigonometry, and calculus, and is often used to simplify expressions and solve equations.

To rationalize the denominator of the expression 8/(∛4), we need to multiply the numerator and the denominator by a rationalizing factor that will eliminate the radical in the denominator.

Since the root 4 is equal to 2, we can rewrite the expression as:

8/3²

The square of 3 is 9, so we can use 9 as the rationalizing factor.

Multiplying the numerator and denominator by 9, we get:

(8/3²) x (9/9) = 72/9

Simplifying, we get:

72/9 = 8

Therefore, the rationalizing factor is 9.

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Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.

The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.

The decay factor is used in exponential decay functions to determine the depreciated value of an asset.

Current price of stereo equipment = $2,500

Annual decreasing rate = 9%

Decrease factor = 0.91 (100% - 9%)

The number of years = 8 years

Value of the equipment after 8 years = ($2,500 x 0.91^8)

= $2,116.125 ($2,500 x 0.47025)

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The best-fit linear regression equation gives us the equation y = 0.0804x + 1.1794, where the slope is 0.0804 and the y-intercept is 1.1794.

The trendline equation will give us the equation for the linear regression line, which can be written in the form of y = mx + b, where m is the slope and b is the y-intercept.

Once we have the trendline equation, we can use it to make predictions about future enrollment percentages based on the number of years after 1820.

The slope of the line tells us the rate at which the enrollment percentage is increasing or decreasing over time, and the y-intercept tells us the enrollment percentage when x is equal to zero (i.e., in 1820).

Here we have find that the best-fit linear regression equation gives us the equation

=> y = 0.0804x + 1.1794,

where the slope is 0.0804 and the y-intercept is 1.1794.

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(9,21) is a solution of y=x+12

When is an ordered pair a solution?

To find if an ordered pair (x,y) is a solution to an equation, substitute the x-value and y-value from the ordered pair into the equation, evaluate both sides of the equation individually, and see if the equation is true.

Warning: A common mistake is to use the first coordinate (the x-coordinate, on the left of the ordered pair) as the value on the left side of the equation, and the second coordinate (the y-coordinate, on the right of the ordered pair), as the value for the right side of the equation.  Make sure to substitute the x-value for the "x" in the equation, and the y-value for the "y" in the equation.

Going through the choices:

Point A (24,12)

y = x+12

(12)  ??  (24) + 12

12  ≠  36

not equal -- not a solution

Point B (-12,-24)

y = x+12

(-24)  ??  (-12) + 12

-24  ≠  0

not equal -- not a solution

Point C (9,21)

y = x+12

(21)  ??  (9) + 12

21  =  21

equal -- (9,21) is a solution

Point D (0,-12)

y = x+12

(-12)  ??  (0) + 12

-12  ≠  12

not equal -- not a solution

There were no more books checked out in March than in April.

The pictograph provided shows the number of books checked out from the library during the months of December, January, February, March, and April. Each picture represents 5 books.

The pictograph tells us that for each of these months, 5 books were checked out. So, in March, 5 books were checked out, and in April, 5 books were also checked out.

To find the difference between the number of books checked out in March and April, we subtract the number of books checked out in April from the number of books checked out in March:

5 books (March) - 5 books (April) = 0 books

Therefore, The result shows that there were no more books checked out in March than in April. Both months had the same number of books checked out, which is 5.

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The dilation of the object is given by the coordinates:

(-6,-8)
(-2, 0)
(-2, -8)

A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer.

For the first dilation

Original points are

(2,1)

(4,5)

(4,1)

Multiply by scale factor

(2,1) x 2 = (4,2)

(4,5) x 2 = (8, 10)

(4,1) x 2 = (8, 2)

This given us the coordinates of triangle B).

For the second dilation

(2,1)  

(4,5)

(4,1)
Adjust for the center of dilation which is (5,5)

(2,1)  less (5,5) = (-3, -4)

(4,5) less (5,5) = (-1, 0)

(4,1) less (5,5) =(-1, -4)

Multiply the New original point by scale factor

(-3, -4) x 2 = (-6,-8)
(-1, 0) x 2 = (-2, 0)

(-1, -4) x 2 = (-2, -8)

Thus, the new coordinates of the dilated triangle C are:

(-6,-8)
(-2, 0)
(-2, -8).

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Answer:

-9

Step-by-step explanation: Definitely correct

Answer:

The correct statement is "The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela".

The correct answer option is option A

How to solve ratio?

Mangos Used Smoothie Size

Angela 1 9 oz

Kim 3 27 oz

Bri 4 36 oz

Check the given options to determine which statement is correct;

The ratio of smoothie size to mangos used for Kim is the same as the ratio of smoothie size to mangos used for Angela.

Kim = 27 : 3 = 9 : 1

Angela = 9 : 1

True

The ratio of smoothie size to mangos used for Kim is 1:9, and the ratio of smoothie size to mangos used for Bri is 4:27.

Kim = 27 : 3 = 9 : 1

Bri = 36 : 4 = 9 : 1

False

The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.

Angela = 9 : 1

Kim = 27 : 3 = 9 : 1

False

The ratio of smoothie size to mangos used for Bri is 9:1, and the ratio of smoothie size to mangos used for Angela is 4:36.

Bri = 36 : 4 = 9 : 1

Angela = 9 : 1

False

Therefore, Kim and Angela has equal ratio of smoothie size to mangoes used.

the solution to the original rational equation is: [tex]x = 4.678[/tex] (rounded to three decimal places)

A rational number is a number that can be expressed as a ratio of two integers, where the denominator is not zero. In other words, it is a number that can be written in the form of a/b, where a and b are integers and b is not equal to zero

There are two equal signs in the equation, which is incorrect. Assuming you meant to write:

[tex]2/(x-2) + 3/(x-4) = 1/(x^2 + 6x + 8)[/tex]

We can start by finding a common denominator for the left-hand side of the equation:

[tex]2/(x-2) + 3/(x-4) = 1/[(x+2)(x+4)][/tex]

Multiplying both sides of the equation by (x-2)(x-4)(x+2)(x+4), we get:

[tex]2(x-4)(x+2)(x+4) + 3(x-2)(x+2)(x+4) = (x-2)(x-4)[/tex]

Expanding and simplifying, we get:

[tex]5x^3 - 19x^2 - 39x + 56 = 0[/tex]

This polynomial equation does not factor nicely, so we can use the rational root theorem or numerical methods to find approximate solutions. Using a calculator or computer, we find that there is one real solution to the equation:

[tex]x \approx 4.678[/tex]

Therefore, the solution to the original rational equation is:

[tex]x = 4.678[/tex] (rounded to three decimal places)

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Answer:

angle 5 is 120 since there is Z shape with angle 3

Answer:

x^2(x+5)-6(x+5)!!!!!!!!

Suppose you are a small business owner who sells handmade crafts. You have a budget of $100 to purchase materials for your next batch of products. You know that each craft requires some amount of materials, which costs $8 per unit. Additionally, you will need to pay a fixed cost of $14 for other expenses related to production and shipping.

To make a profit, you must ensure that the cost of materials and fixed expenses does not exceed the $100 budget. Therefore, you can write an inequality to represent this situation:

8x + 14 < 100

Here, x represents the number of units of materials needed for each craft. The inequality states that the total cost of materials (8x) plus fixed expenses ($14) must be less than $100.

To solve this inequality, you can subtract 14 from both sides:

8x < 86

Finally, you can divide both sides by 8:

x < 10.75

This means that for each craft, you can use no more than 10.75 units of materials in order to stay within budget and make a profit.

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Answer:

Step-by-step explanation:

You want to classify the functions shown in the tables as linear, quadratic, or exponential.

We notice all of the tables have x-values that are evenly spaced. this means we can look at the differences between y-values to determine the kind of function the table represents.

The differences have the following interpretation:

The differences of y-terms are constant at 3 -5 = -2.

The function is linear.

The differences of y-terms are constant at 5 -2 = 3.

The function is linear.

We observe that the y-values have a minimum. We don't need to take differences to know this is not linear or exponential. Of the offered choices, the only one that makes sense is "quadratic."

The differences of y-terms are ...

  1 -5 = -4, 5 -1 = 4, 17 -5 = 12, 37 -17 = 20

The differences of differences are ...

  4 -(-4) = 8, 12 -4 = 8, 20 -12 = 8

The second differences are constant.

The function is quadratic.

The first differences are ...

  3 -1 = 2, 9 -3 = 6, 27 -9 = 18, 81 -27 = 54

The second differences are

  6 -2 = 4, 18 -6 = 12, 54 -18 = 36

We note that the first and second differences are not constant, but the ratio of terms at every level is 3/1 = 6/2 = 12/4 = 3.

The function is exponential.

Note that 7th grade mean = 277.86

the 5th grade mean = 254.77

So th relationship between the mean is that the 7 th grade mean is higher than the 5 th grade mean .

To compute the means here   is what we did

7 th  grade mean = (1 × 10) + (1 × 11) +   (2 × 12) + (1 × 13) +   (1 × 14) + (2 × 15) + (3 × 16) + (3 × 17) + (2 × 18) + (2 × 19) +   (3 × 20) / 21

= 277.857142857

≈ 277.86

For the 5th grade mean

5th  grade mean = (1 × 8)   + (2 × 9) + (2 × 10) +   (2 × 11) + (2 × 12) + (1 × 13) + (3 × 15) + (2 ×16) + (1 × 17)  +  (2 × 18) + (1 × 19) + (1   × 20) / 26 = 12.5

= 254.769230769

≈ 254.77

This means that  trully,  the relationship between the mean is that the 7  th grade mean is higher than the 5 th grade mean.

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If Diego's family spent a total of $130, on a night out, then the each ticket for the fair cost's $15.

In order to find the "total-cost" of the tickets, we subtract the cost of the family dinner from the total amount spent;

⇒ Total cost of tickets = Total amount spent - Cost of family dinner,

⇒ Total cost of tickets = $130 - $55,

⇒ Total cost of tickets = $75.

Next, we divide the total cost of the tickets by the number of tickets purchased to find the cost of each ticket:

So, Cost per ticket = (Total cost of tickets)/(Number of tickets),

⇒ Cost per ticket = $75/5,

⇒ Cost per ticket = $15,

Therefore, each ticket to the fair cost $15.

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The hexagon with sides of length 5 inches, 4 inches, 4 inches, 5 inches, 3 inches, and 3 inches has a perimeter of 24 inches.

A hexagon is a regular polygon, meaning all sides and angles are equal in size. It is a symmetrical shape, which means it can be divided into two equal halves.

To calculate the perimeter of this hexagon, we must first identify the length of each side.

All sides of the hexagon have a length of either 5 inches, 4 inches, or 3 inches, as there are two sides of each length.

The perimeter of the hexagon is the sum of the length of all its sides. Adding the length of all the sides, we get

5 + 4 + 4 + 5 + 3 + 3 = 24.

Thus, the perimeter of the hexagon is 24 inches.

Hence, the sum of the length of the sides of a hexagon is always greater than the length of any one of its sides.

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