which statement represents eight more than six times a number is five less than three times that number

4.  using two rectangles to estimate, the area under f(x) is approximately 5/16.

To estimate the area under the graph of the function f(x) = x² between x = 0 and x = 1 using rectangles, we can use the midpoint method.

First, let's calculate the width of each rectangle. Since we are using two rectangles, the width of each rectangle is (1 - 0) / 2 = 1/2.

For the first estimate with two rectangles:

1. Find the midpoint of the base of each rectangle:

  - The midpoint of the first rectangle is 0 + (1/2) * (1/2) = 1/4.

  - The midpoint of the second rectangle is 0 + (1/2) * (3/2) = 3/4.

2. Evaluate the function at the midpoint of each rectangle:

  - f(1/4) = (1/4)²

= 1/16.

  - f(3/4) = (3/4)²

= 9/16.

3. Calculate the area of each rectangle:

  - The area of the first rectangle is (1/2) * (1/16) = 1/32.

  - The area of the second rectangle is (1/2) * (9/16) = 9/32.

4. Sum the areas of the two rectangles to get the estimated area under the graph:

  - Estimated area = (1/32) + (9/32) = 10/32

= 5/16.

Now, let's use four rectangles for a more accurate estimate:

1. Calculate the width of each rectangle. Since we are using four rectangles, the width of each rectangle is (1 - 0) / 4 = 1/4.

2. Find the midpoint of the base of each rectangle:

  - The midpoint of the first rectangle is 0 + (1/4) * (1/4) = 1/8.

  - The midpoint of the second rectangle is 0 + (1/4) * (3/4) = 3/16.

  - The midpoint of the third rectangle is 0 + (1/4) * (5/4) = 5/16.

  - The midpoint of the fourth rectangle is 0 + (1/4) * (7/4) = 7/16.

3. Evaluate the function at the midpoint of each rectangle:

  - f(1/8) = (1/8)² = 1/64.

  - f(3/16) = (3/16)² = 9/256.

  - f(5/16) = (5/16)² = 25/256.

  - f(7/16) = (7/16)² = 49/256.

4. Calculate the area of each rectangle:

  - The area of the first rectangle is (1/4) * (1/64) = 1/256.

  - The area of the second rectangle is (1/4) * (9/256) = 9/1024.

  - The area of the third rectangle is (1/4) * (25/256) = 25/1024.

  - The area of the fourth rectangle is (1/4) * (49/256) = 49/1024.

5. Sum the areas of the four rectangles to get the estimated area under the graph:

  - Estimated area = (1/256) + (9/1024) + (25/1024)

+ (49/1024) = 84/1024 = 21/256.

using four rectangles to estimate, the area under f(x) is approximately 21/256.

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Answer:

i think it is the 4th one

Step-by-step explanation:

yo it would be cool if you would give me brainliest

The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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If the ratio of flamingos to monkeys was 6:7, then in present the number of monkeys is 18 and number of flamingo is 12.

Let "6x" be the number of flamingos and "7x" be the number of monkeys,

After the 4 monkeys were born, the number of monkeys became 7x + 4, and the ratio of flamingos to monkeys became 2:3.

This means that the number of flamingos is now 2/3 of the total number of monkeys,

Which is : 2/3(7x + 4) = 6x,

Simplifying further,

We get,

⇒ 2(7x + 4) = 18x,

⇒ 14x + 8 = 18x

⇒ 8 = 4x

⇒ x = 2

So, there were 6x = 12 flamingos and 7x = 14 monkeys in the safari park before the 4 monkeys were born.

After the 4 monkeys were born, the number of monkeys became 14 + 4 = 18, and the new ratio of flamingos to monkeys is 2:3,

Which means the number of flamingos is 2/5 of total-number of animals.

⇒ 2/5(12 + 18)

⇒ 12

Therefore, there are currently 12 flamingos and 18 monkeys in the safari park.

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The solution to the system of inequalities is (-1, 4).

To graph the system of inequalities and identify the point that represents a solution, we will plot the lines corresponding to the inequalities and shade the regions that satisfy the given conditions.

The first inequality is x > -2, which represents a vertical line passing through x = -2 but does not include the line itself since it's "greater than." Therefore, we draw a dashed vertical line at x = -2.

The second inequality is y ≤ 2x + 7, which represents a line with a slope of 2 and a y-intercept of 7.

To graph this line, we can plot two points and draw a solid line through them.

Now let's plot the points (-1, 6), (1, 11), (-1, 4), and (-3, -1) to see which one lies within the shaded region and satisfies both inequalities.

The graph is attached.

The dashed vertical line represents x > -2, and the solid line represents y ≤ 2x + 7. The shaded region below the solid line and to the right of the dashed line satisfies both inequalities.

By observing the graph, we can see that the point (-1, 4) lies within the shaded region and satisfies both inequalities.

Therefore, the solution to the system of inequalities is (-1, 4).

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Part of question :

(x-10)^2+(y-10)^2=100

(16-10)^2+(18-10)^2=100

Answer:

Yes, equation of circle is true

Step-by-step explanation:

(x-10)^2+(y-10)^2=100

(16-10)^2+(18-10)^2=100

100=100

plugging the coordinates into the equation of the circle, we observe that the equation is true since both sides of the equation are equal(value on both sides of the equal sign are same). This wouldn't be true if for instance the left side of the equation evaluated to ≠100. Therefore we can conclude that the rose bush lies on circle since the equation is true

Answer:

A.775

Step-by-step explanation:

Answer:

8 units squared

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area of quadrilateral:

\( \frac{1}{2} (b1 + b2)h\)

Where, b1 = 2 , b2 = 2+2+4 = 8 , h = 2

Now,

\( \frac{1}{2} (b1 + b2)h\)

plugging the values

\( \frac{1}{2} \times (2 + 8) \times 2\)

Calculate the sum

\( \frac{1}{2} \times 10 \times 2\)

Reduce the numbers with G.C.F 2

\( = 5 \times 2\)

Calculate the product

\( = 10 \: {units}^{2} \)

Hope this helps...

Best regards!

Answer:

-30

Step-by-step explanation:

-1x/5 = 6

-x/5 = 6

-x = 30

x = -30

Answer:

5.5

Step-by-step explanation:

Add each side of the triangle.

3z+z+1+4z-3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z-2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

Answer:

A=statististical

B=non statistical

C=non statistical

Step-by-step explanation:

i did the test and i got it all right, hope this help you!<3

Answer:

x = 4

8(4) - 2 = 30

15(4) = 60

All triangles equal 180 degrees and there is already a right angle. 60 plus 0 is 90, and 90 plus 90 (or 90 times 2) is 180

60 + 30 = 90

90 + 90 = 180

Step-by-step explanation:

Answer:

9.5

Step-by-step explanation:

Answer:

The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.

Step-by-step explanation:

I hope this helps :)

Moving line m will likely result in a change in the position or alignment of the element or object associated with line m. Moving line r, on the other hand, will likely result in a change in the position or alignment of the element or object associated with line r.

When line m is moved, it can affect the arrangement or relationship of elements or objects that are connected or associated with it. This could include shifting the position of a graphic or adjusting the layout of a design. For example, in a floor plan, moving line m could change the location of a wall, thereby altering the overall structure of the space. Similarly, in a musical composition, moving line m could involve adjusting the melody or rhythm, leading to a different arrangement of notes and chords.

Similarly, when line r is moved, it can have an impact on the position or alignment of the element or object it is associated with. This could involve repositioning a visual element, such as adjusting the angle of a line or changing the alignment of text. For instance, in a website layout, moving line r might result in shifting the position of a sidebar or adjusting the spacing between columns. In a mathematical graph, moving line r could involve modifying the slope or intercept, thereby changing the relationship between variables.

In summary, moving line m or line r can bring about changes in the position, alignment, or arrangement of associated elements or objects. The specific outcome will depend on the context in which these lines are being moved and the nature of the elements they are connected to.

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The difference quotient evaluated in x = 2 gives:

[ f(2 + h) - f(2)]/h = h + 9

So the last option is the correct one.

Here we know the function:

f(x) = x^2 + 5x + 6

And we want to find the difference quotient:

[ f(2 + h) - f(2)]/h

Let's evaluate the function:

f(2 + h) = (2 + h)^2 + 5*(2 + h) + 6

            = 2^2 + h^2 + 4h + 10 + 5h + 6

            = h^2 + 9h + 20

f(2) = 2^2 + 5*2 + 6

f(2) = 4 + 10 +  6 = 20

Then we have:

[ f(2 + h) - f(2)]/h

[h^2 + 9h + 20 - 20]/h

[h^2 + 9h ]/h

Taking the quotient we get:

[h^2 + 9h ]/h = h + 9

So the correct option is the last one.

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Answer:

i cant read it..

Step-by-step explanation:

Answer:

1x+3y=35, 2x+y=20

x=5, y=10

Step-by-step explanation:

Let x equal the number of hats and y equal number of shirts.

Solve by substitution, elimination, or graphing.

Personally, I just solved by substitution.

Solve for x (or y) in the first equation. Let's do x.

1x+3y=35 goes to 1x=35-3y or just x=35-3y.

Since we have x, plug it in the other equation. 2(35-3y)+y=20. This equals out to y=10, i assume you understand the algebra.

Plug 10 into either equation for y.

1x+3(10)=35 or x+30=35. subtract 30 on each side. X=5.

Answer:

This is an example of comparing two objects indirectly.

Step-by-step explanation:

Answer:

x = 2.74cm

Step-by-step explanation:

Soh Cah Toa

As we know from the last post that we'll be using cosine.

This will be the rearranged formula :

(Side) Cos ( Angle) = Side

8 × Cos (70) = 2.73616....cm

Answer:

200 miles

Step-by-step explanation:

1 cm = 50 miles

4 x 1   = 4 x 50 = 200

Answer:200 miles

Step-by-step explanation:

50/1 ?/4 50*4=200

The can contains 15.7 g of sugar per 100 mL. So if the can holds 330 mL of soft drink, then overall it contains

(15.7 g) / (100 mL) × (330 mL) = 51.81 g

of sugar, and this is

(51.81 g) / (90 g) ≈ 0.575667 ≈ 57.6%

so Tom's friend is correct.

Answer:

\(4x + 4 = 4x + 4\)

Step-by-step explanation:

Given

\(4x + 4 = 4x + []\)

Required

Fill in the gap to get an infinitely many solutions

Let the gap be y

\(4x + 4 = 4x + y\)

Collect Like Terms

\(y = 4x - 4x + 4\)

\(y = 4\)

The complete equation is: \(4x + 4 = 4x + 4\)

Answer:

Step-by-step explanation:

eq of first degree is a linear equation.

y=x+1

The correct answer is

2 loaves of pumpkin bread and 6 loaves of banana bread. Option C.

For the solution for the Pumpkin bread:

4 eggs

3 1/2 cups of flour

Banana bread:

1 egg

1 (0.5) cups of flour

Available ingredients:

14 eggs

16 cups of flour

Assume 2 loaves of pumpkin bread and 6 loaves of banana bread

For the solution for the Pumpkin bread:

PB=4 eggs* 2

PB= 8 eggs

PB=3 *0.5 * 2

PB = 7 cups of flour

For the solution of the Banana bread:

BB =1 *6

BB= 6 eggs

For cups

BB= 1 (0.5) * 6

BB= 9 cups of flour

In conclusion, The solution of the Total used ingredients

I=8 + 6

I= 14 eggs

For cups

IC=7 + 9

IC= 16 cups of flour

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Answer:

C 2 loaves of Pb and 6 loaves of BB

Step-by-step explanation:

The inequality used to represent the situation is 5b + 100 ≥ 150

Inequality is an expression that shows the non equal comparison of two or more numbers and expressions.

Let b represent the number of balcony seating areas that each seat 5 people.

The inequality for the situation is given by:

5b + 4(25) ≥ 150

5b + 100 ≥ 150

The inequality used to represent the situation is 5b + 100 ≥ 150

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Answer:

9+10 is 19

Step-by-step explanation: