6th Grade Math! Complete the function table and write the function rule. Please explain, since this is a written answer. Tysm!

Answer: First Option

Step-by-step explanation:

The formula to calculate the volume of a cylinder is:

[tex]V = \pi(\frac{d}{2})^2*h[/tex]

Where d is the diameter of the cylinder and h is the height.

Notice that the term d is squared. This means that to increase the volume of a cylinder it is more efficient to increase its diameter as well. Therefore, look for the cylinder with the largest diameter among the options.

The first cylinder is 90 ft in diameter and 40 ft in height and its volume is

[tex]V = \pi(\frac{90}{2})^2*40[/tex]

[tex]V=254469\ ft^3[/tex]

You can verify that it is the tank that has the highest volume

12a^2b^3 / 3ab

Factor 3 out of the numerator:

3(4a^2b^3) / 3ab

Cancel out the common factors:

4a^2b^3 / ab

Cancel out the common factors again to get the final answer:

4ab^2

Answer:

c=0

Step-by-step explanation:

x² + 11x + 0 = y

x² + 11x + 0 = 0

U already know that y=0 by looking at the equations above,

But your worksheet never state "c", so we will take that c is 0   (look at the equations above.)

So c is just 0.

In a quadratic equation of the form ax^2 + bx + c=0, 'c' is the constant term. In your equation x^2 + 11x = 0, therefore the 'c' value is 0.

The equation you provided, x^2 + 11x = 0, is a quadratic equation of the form ax^2 + bx + c = 0. In this equation, 'a' is the coefficient of x^2, 'b' is the coefficient of x, and 'c' is the constant. Comparing your equation with this form, the values of 'a', 'b', and 'c' in your equation are 1, 11, and 0 respectively. Therefore, in your equation, the 'c' value is 0.

To find roots or solutions for the equation, we use the quadratic formula: -b ± √(b^2 - 4ac) / 2a. Substituting 'a', 'b' and 'c' values from your equation will help to find the value of 'x'.

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To calculate for this data set, the mean is 73, the median is 74 after sorting the numbers, and the mode is 72 as it appears more than once.

To find the mean, you add up all the numbers in the set and divide by the total count of numbers. For the provided data set:

To find the median, you first sort the data from lowest to highest, then find the middle number. If there is an even number of data points, the median is the average of the two middle numbers.

The mode is the number that occurs most frequently in the data set. For this set, the mode would be the number that appears more than once.

The period of the trigonometric function, given the graph provided, is [tex]\( 9.4 \)[/tex]units.

To determine the period of the trigonometric function from the graph, we need to find the length of one complete cycle of the function.

The period of a trigonometric function is the horizontal length between two points where the function begins repeating its pattern. For sine and cosine functions, this is typically from peak to peak, from trough to trough, or between any two identical points on the graph that are one cycle apart.

Looking at the image, we can see that the function reaches a maximum at the point (-4.7, 3.8) and then again at (4.7, -3.8). However, the points given are not one full cycle apart because they represent a maximum and the function's intersection with its midline. Instead, we should look at the distance along the x-axis between two consecutive maximums or two consecutive midline crossings.

If we assume that the graph is symmetric and the pattern repeats in the positive direction of the x-axis, the period would be twice the distance from the given midline crossing to the next one. This is because the midline crossing at (4.7, -3.8) is halfway through a cycle. Therefore, we can double this x-value to find the period.

Since the crossing occurs at x = 4.7, and it's half the period, the full period [tex]\( P \)[/tex] would be:

[tex]\[ P = 4.7 \times 2 \][/tex]

Let's compute the exact value.

The period of the trigonometric function, given the graph provided, is [tex]\( 9.4 \)[/tex]units.

complete question given below:

Answer:

37.6 units

Step-by-step explanation:

khan Academy said so

Answer:

About 57.5 inches

Step-by-step explanation:

From the points which relates height and age a linear model was made. This allow us to estimate joanna’s height in those years the points are missing. For example, when she was 11 years old, her height was about 57.5 inches.

Answer:

57.5

Step-by-step explanation:

Answer:

39.9

Step-by-step explanation:

A good trick to remember is SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we're given an angle and the opposite side, and we want to find the adjacent side.  So we need to use tangent.

tan 31° = 24 / x

x = 24 / tan 31°

x ≈ 39.9

Answer:

[tex]31\frac{1}{2}ft^2[/tex]

Step-by-step explanation:

From the information given each of the three rectangular countertops has dimension [tex]4\frac{3}{8}[/tex] by  [tex]2\frac{2}{5}[/tex] feet.

The area of a rectangular shapes is the product of the dimensions.

Each rectangular countertop has area;

[tex]4\frac{3}{8}\times 2\frac{2}{5}=\frac{35}{8}\times \frac{12}{5} =10\frac{1}{2}ft^2[/tex]

Therefore the number of square feet tiles needed to cover all the countertops is [tex]=3\times 10\frac{1}{2}=31\frac{1}{2}ft^2[/tex]

Check the picture below.

so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5.  So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.

[tex]\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96[/tex]

For this case we have that by definition, the surface area of a regular pyramid, is given by:

[tex]SA = \frac {1} {2} p * l + B[/tex]

Where:

p: Represents the perimeter of the base

l: The inclination height

B: The area of the base

Now, since the base is square we have:

[tex]B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm[/tex]

Then, replacing the values:

[tex]SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2[/tex]

ANswer

[tex]96 \ cm ^ 2[/tex]

Answer:

B

Step-by-step explanation:

The domain is (- infinity, infinity) (or the set of all real numbers) bc the function goes never ending to the left and right

The range is f(x) is greater than or equal to 3 bc the y value 3 is the turning point. Also, it's "greater than or equal to" bc the graph opens upward

The domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number greater than or equal to 3 respectively.

The domain of a function is the set of all possible inputs of the function. The range of a function is the set of all possible outputs of that function.

The function is given:

f(x)= |x-4|+3.

We can substitute any value of x to the given function. This means that the domain of the function is the set of all real numbers.

The lowest value that the given function can have is 3. This is possible only when the value of x = 4.

It cannot go lower than that as a modulus or absolute value is used in the function.

Thus, the range of the function can be defined as the set of all real numbers greater than or equal to 3.

Therefore, we have found that the domain and range of the function f(x)= |x-4|+3 are the set of real numbers and every real number that is greater than or equal to 3 respectively.

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Answer:

y = 3x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

m = [tex]\frac{0+3}{1-0}[/tex] = 3

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = 3x - 3 ← equation of line

The equation of line l will be;

⇒ y = 3x - 3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, 0) and (0, -3).

Now,

Since, The equation of line passes through the points (1, 0) and (0, -3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 3 - 0) / (0 - 1)

m = - 3 / - 1

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 0 = 3 (x - 1)

⇒ y  = 3x - 3

Therefore, The equation of line passes through the points (1, 0) and

(0, -3)  will be;

⇒ y = 3x - 3

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Answer:

1. B nearly 70%

2. C nearly 9%

Step-by-step explanation:

1. There are 26 people which agree with the question and 61 people which disagree with the question. In total, 26+61=87 people.

So,

[tex]\dfrac{61}{87}\cdot 100\%\approx 70\%[/tex]

disagree with question 1.

2. There are 87 people in total and only 8 females agree with question, so

[tex]\dfrac{8}{87}\cdot 100\%\approx 9\%[/tex]

of females agree with the question 1.

Answer:

Q1:  about 70%

Q2:  about 9%

Step-by-step explanation:

Question 1:

The grand total number of people is the right and bottom most cell, which is the addition of the column or the row. So grand total = 60 + 27 = 87 (or 61 + 26 = 87)

The number of people (BOTH MALE AND FEMALE) that disagreed with question 1 is 61.

As a percentage, that would be (61/87) * 100 = 70.11%, which is about 70%

Question 2:

Here, the total number of people is still the same, 87. We want the number of females that agreed. So we move in line with agree and in line with female is the table. We see that it is 8, so 8 females agreed with question 1.

As a percentage, (8/81) * 100 = about 9%

Answer:

9. 1620°

10. 360°

11. 180°

Step-by-step explanation:

The answers of problems 10 and 11 give you the way to find the answer to problem 9.

__

10. The sum of exterior angles of any convex polygon is 360°.

__

11. An internal angle and an external angle are a linear pair, so always sum to 180°.

__

9. At every vertex, the sum of interior and exterior angles is 180°, so the total of those angles at all vertices is n·180°. Of that total, 360° is the sum of exterior angles, so the total of interior angles of an n-gon is ...

n·180° -360° = (n -2)·180°

For an 11-gon, the sum of interior angles is ...

(11 -2)·180° = 1620°

Answer:

y = 100x + 400

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 400) and (x₂, y₂ ) = (1, 500) ← 2 points from the table

m = [tex]\frac{500-400}{1-0}[/tex] = 100

note the line crosses the y- axis at (0, 400) ⇒ c = 400

y = 100x + 400 ← equation of line

The equation of the line represented by the following table in slope-intercept form is y = 100x + 400.

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

Slope of a straight line can be found using two given points say (x1,y1) and (x2,y2).

Slope (m) = (y2 - y1) / (x2 - x1) .

Taking any two arbitrary points, from the table given aside we have x1 = 0, x2 = 1, y1 = 400 and y2 = 500

⇒ Slope (m) = (y2 - y1) / (x2 - x1) .

=  (500 - 400)/(1 - 0)

∴  Slope (m) = 100 .

The y-intercept of the line is the value of y coordinate when the value of x = 0. In other words, y-intercept is the point where the curve touches the y-axis.

∴ From the table, y-intercept (c) = 400 .

Thus, we have slope (m) = 100 and y-intercept (c) = 400 .

The equation of straight line is y = 100x + 400 .

Therefore, the equation of the line represented by the following table in slope-intercept form is y = 100x + 400.

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Answer: (x - 3) (2x-1)

Answer:

(x+3)(2x+1)

Step-by-step explanation:

I got it right on khan academy.

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

A triangle is a three-sided polygon that consists of three edges and three vertices.

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a quadrilateral, specifically a parallelogram.

The two identical triangles, when combined in this way, will have their bases aligned and their vertices opposite each other, forming two pairs of parallel sides.

A parallelogram, which is a quadrilateral with opposite sides that are parallel and congruent.

Hence, If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

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well, let's grab a couple of points off the line hmmmm let's see, the lines runs through (0, 4) and also (3,5), so let's use those to get its slope and thus its function.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-4}{3-0}\implies \cfrac{1}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{1}{3}(x-0)\implies y-4=\cfrac{1}{3}x \\\\\\ y=\cfrac{1}{3}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Step-by-step explanation:

[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]

First, find the area of lot A.

To find the area, multiply the length by the width.

33*42=1,386

Now, subtract the area of lot a from the total area. This will give us the area of lot b.

1,848-1,386=462

The area of lot b is 462 square feet.

Finally, divide the area of lot b (462) by its length to find the width. Since they both share a side, we know that it’s length is 42 feet.

462/42=11

Lot b is 11 feet wide.

Hope this helps!

Answer:

The cost is GHC 20.00

Step-by-step explanation:

We can write a proportion to solve this

3 bottles     10 bottles

-------------- = -----------

6.00             x

Using cross products

3x = 10 *6

3x = 60

Divide by 3

3x/3 = 60/3

x = 20

The cost is GHC 20.00

Answer: d

Step-by-step explanation:

However much more you pay over the minimum will be applied to the principle, which means it will take less time to pay the credit card bill off  

When paying a credit card bill, it is recommended to pay more than the minimum amount every month to reduce the principal balance faster and avoid accruing high interest. This practice leads to less overall cost and faster debt elimination.

The recommended practice when paying a credit card bill is D. Pay more than the minimum amount every month. This is crucial because paying only the minimum amount mostly covers the interest and only a small part of the principal balance. Interest accrues on the remaining balance, leading to higher overall costs.

By paying more than the minimum, you reduce the principal balance faster, thereby reducing the amount of interest that can accumulate. For instance, if two friends both have $2,000 in credit card debt but one pays just the minimum while the other adds an additional $10 each month, the latter will pay off their debt quicker and accrue less interest overall.

Managing credit effectively involves more than just timely payments; it's also about managing your credit utilization and striving to pay off the full balance as quickly as possible. This avoids the high-interest rates that can double the initial amount over time if only minimum payments are made.

half an hour past 7, will be 7 plus 30 minutes then 7:30.

we could also come from the other way, and say is 30 minutes before 8 o'clock.

Answer: 15/4

Step-by-step explanation:

1. 12/1 - 33/4

2.  48/4 -33/4

3. 15/4

Answer:

First option: [tex]y=(x + 8)(x + 3)[/tex]

Step-by-step explanation:

Given the quadratic equation [tex]y = x^2 + 11x + 24[/tex], you need to factor it.

To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.

Therefore, knowing this, you can factor the quadratic equation:

[tex]y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)[/tex]

Then, [tex]y = x^2 + 11x + 24[/tex] is equivalent to the graph of the equation [tex]y=(x + 8)(x + 3)[/tex], which matches with the first option.

Answer:

C

Step-by-step explanation:

Given

5x + 10y - 15 ← factor out 5 from each term

= 5(x + 2y - 3) → C

Final answer:

After factoring out the common factor of 5 from the expression 5x+10y-15, we obtain the equivalent expression, which is 5(x+2y-3). Option C is correct.

Explanation:

To find an expression equivalent to 5x+10y-15, we need to factor out the common factor in all three terms. The common factor here is 5. By dividing each term by 5, we get:

Putting these together within parentheses after factoring out the 5 gives us 5(x+2y-3).

Therefore, the answer is: C. 5(x+2y-3)

Answer:

[tex]a_{n} =1.7n+(n-1)0.5[/tex]

Step-by-step explanation:

I hope this helps.

Answer:

an = .5n +1.2

Step-by-step explanation:

The formula for an arithmetic sequence is given by

an =a1 + d(n-1)  where a1 is the first term and d is the common difference

an = 1.7 + .5 (n-1)

Distribute

an = 1.7 + .5n - .5

Combine like terms

an = .5n +1.2

Answer:

Jenny would have to get a 99 on her next test to raise her average from a 94 to a 95.

Step-by-step explanation:

First you need to find her current average:

93 + 89 + 96 + 98 = 376/4 = 94

Now that you have the current average, all you need to do is find what would be the total of her grades if she had a average of 95. Since her average would be 95, and she would have completed 5 tests, it makes sense to multiply the average by the number of tests:

95 x 5 = 475

Now all you need to do is remove from this number the sum of the original 4 tests, and voila! There is her 5th test score:

475 - 376 = 99

Her 5th test score is 99%.

To raise her average to 95, Jenny needs to score a 99 on her next test.

To find out what score Jenny needs to get on her next test, we can use the average formula. We know that Jenny's average score is currently 94 (the average of 93, 89, 96, and 98). Let's call the score she needs to get on her next test 'x'. To raise her average to 95, the sum of all her test scores would be (93 + 89 + 96 + 98 + x) and the number of tests would be 5 (since she has taken 4 tests so far). We can set up the equation (93 + 89 + 96 + 98 + x)/5 = 95 and solve for x:

(93 + 89 + 96 + 98 + x)/5 = 95

Combine like terms and multiply both sides by 5:

376 + x = 475

Subtract 376 from both sides:

x = 99

Therefore, Jenny needs to score a 99 on her next test in order to raise her average to 95.

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ANSWER

"If x=7, then x - 2 = 5"

EXPLANATION

Let

[tex]p \to \: q[/tex]

be a propositional statement.

The converse of this statement is

[tex]q \to \: p[/tex]

In other words, the converse of the statement,

"If p then q" is "If q, then p"

The given given conditional statement is

"If x - 2 = 5, then x = 7"

Therefore the converse is

"If x=7, then x - 2 = 5"

Answer:

y = 8.9

Step-by-step explanation:

Use Pythagoras Theorem a² = b² + c²

In this case a = 12 and c = 8 so,

12² = b² + 8²

( Simplify )

144 = b² + 64

( Minus 64 from both sides to isolate b² )

80 = b²

( Square root to isolate b )

8.94427191 = b

Answer:

8.9

Step-by-step explanation:

The triangle is a right triangle, so we can use the Pythagorean theorem, where a and b are the lengths of the legs (the sides forming the right angle), and c is the length of the hypotenuse (the angle opposite the right angle).

a^2 + b^2 = c^2

y^2 + 8^2 = 12^2

y^2 + 64 = 144

y^2 = 80

y = sqrt(80)

y = sqrt(16 * 5)

y = 4sqrt(5)

y = 8.9

Answer:

1.27, -6.27 to the nearest hundredth,

or if you require it in exact form,

-2.5 + √14.25,   -2.5 - √14.25.

Step-by-step explanation:

x^2 = -5x + 8

x^2 + 5x  = 8

Competing the square:

(x + 2.5)^2 - 6.25 = 8

(x + 2.5) = 14.25

x + 2.5 = +/-√14.25

x = -2.5 + √14.25,   -2.5 - √14.25

x = -2.5 + 3.77,  -2.5 - 3.77

= 1.27, -6.27.