A cake recipe called for using 6 ¼ cups of sugar before baking and another 5 ¾ cups after baking. What is the total amount of sugar needed in the recipe?

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1.

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem.

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'.

1. Image 4:

A. In image 4, the main change from the previous image (image 3) is the addition of two squares. One square is attached to the side of the triangle with length 'a', and the other square is attached to the side of the triangle with length 'b'. These squares are constructed by transforming the previous image, specifically by adding the squares and adjusting their positions accordingly.

B. If we choose figure 5 in image 4, we can see that its lengths are related to the figure in image 1. The length of the bottom side of figure 5 is equal to 'a' (the length of the side of the triangle in image 1), and the length of the right side of figure 5 is equal to 'b' (the length of the other side of the triangle in image 1).

C. The length of figure 5, which corresponds to 'a', and the length of figure 6, which corresponds to 'b', relate to the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a^2 + b^2). In this case, figure 5 represents side 'a' and figure 6 represents side 'b'. So, their lengths squared (a^2 and b^2) added together equal the length of figure 7 squared (c^2).

2. The visual proof demonstrates the Pythagorean Theorem by showing how the figures labeled 5 through 9 in image 4 are related to figures 2 and 10. Figure 5 represents side 'a' and figure 6 represents side 'b'. When we combine these two figures and the square attached to the hypotenuse (c), we see that they perfectly fill the large square in figure 10. This shows that the area of the square on the hypotenuse (c^2) is equal to the sum of the areas of the squares on the other two sides (a^2 + b^2). This visual representation provides a clear and tangible demonstration of the Pythagorean Theorem.

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The amount of money she started with is $5750

The given parameters are:

Interest = $115

Rate = 3%

Time = 8 months

The amount she start with (P) is calculated using:

P = I/(RT/12)

This gives

P = 115/(3% * 8/12)

Evaluate the product

P = 115/(0.02)

Divide

P = 5750

Hence, the amount of money she started with is $5750

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Answer:

6,561

that's a good number

0 thru 9 is 10 numbers.

Each digit can be 1 of 10 numbers:

Total combinations = 10 x 10 x 10 x 10 = 10,000

Answer: 10,000

Answer:

-0.1f + 0.4j - 13

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

-3f + 0.4j - 12 - 1 + 2.9f

Step 2: Simplify

Answer:

Step-by-step explanation:

Let B be the Boat speed in still water

Let C be the current speed.

7(B - C) = 217

7B - 7C = 217

7B = 7C + 217

         7(B + C) = 413

         7B + 7C = 413

7C + 217 + 7C = 413

                14C = 196

                    C = 14 mi/hr   WOW that a fast stream

7B = 7(14) + 217

7B = 315

 B = 45 mi/hr

Answer:

The last choice: 25. 12 / pi

Explanation:

The relationship b

Answer:

-7b^11

Step-by-step explanation:

7b^4×−b^7

Answer:

a = 6

b = 25

Step-by-step explanation:

As alternative angles in a parallel line are equal to each other,

5a = 3a + 12

So, now we can find the value of a by making "a" the subject.

5a - 3a = 12

2a = 12

Divide both sides by 2.

a = 6°

And now let us find the value of b.

We know that interior angles in a triangle are added up to 180°.

So,

2b + 4b + 3a + 12 = 180

We can replace a with 6 and then we can make "b" the subject to find the value of b.

Let us solve it now.

2b + 4b + 3 × 6 + 12 = 180

6b + 18 + 12 = 180

6b + 30 = 180

6b = 180 - 30

6b = 150

Divide both sides by 6.

b = 25°

Answer:

x=5

Step-by-step explanation:

divide 4 into both sides

\(\pmb{\frak{4x=20}}\)

\(\pmb{\frak{x=5}}\)

Answer:

C. 12π

Step-by-step explanation:

C = π2r
C = π*2*6
C = π*12
C = 12π

Hope this helps :)

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

The number of millimeters in each glass is 200ml.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.

It is important to note that some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

Since Cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. The amount in each will be:

= (2l - 400ml )/8

= (2000 - 400) / 8

= 1600 / 8

= 200ml

Therefore, based on the calculation, there'll be 200 millimeters on each glass.

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Complete question

cheetan brought a 2L bottle of milk and used 400 ml from it with the remaining amount of milk he could complely fill 8 glases of the same size and shape. How many ml will each contain?

The correct answer is: the quantity 8 over 17 end quantity squared plus the quantity 15 over 17 end quantity squared equals 1

What is a Pythagorean identity?

The Pythagorean identity for sine and cosine states that for any angle θ,

sin²θ + cos²θ = 1

We can use the given values of sine and cosine to find the missing trigonometric function:

tan(θ) = sin(θ) / cos(θ) = (8/17) / (15/17) = 8/15

Now, we can use the Pythagorean identity to determine which of the given statements is true:

1 + (8/17)² = 1 + 64/289 = 353/289 ≠ (15/17)²

1 + (15/17)² = 1 + 225/289 = 514/289 ≠ (8/17)²

(8/17)² + (15/17)² = 64/289 + 225/289 = 1

Therefore, the statement that can be proven using the Pythagorean identity is:

(8/17)² + (15/17)² = 1

Hence, the correct answer is: the quantity 8 over 17 end quantity squared plus the quantity 15 over 17 end quantity squared equals 1

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The centroid of the region is at the point (0, 2/5).

To find the centroid of the region bounded by the curves y=2-x² and y=x, we first need to find the limits of integration and the expressions for the x-coordinate and y-coordinate of the centroid.

The curves intersect at (1,1) and (-1,1), so we will integrate over the interval [-1,1].

To find the x-coordinate of the centroid, we need to evaluate the following integral:

x' = (1/A) ∫[a,b] xf(x) dx

where;

A = ∫[a,b] (f(x) - g(x)) dx

In this case, f(x) = 2 - x² and g(x) = x, so

A = ∫[-1,1] (2 - x² - x) dx

= [2x - (1/3)x³ - (1/2)x²] | from -1 to 1

= (4/3)

Now we can evaluate the x-coordinate of the centroid:

x' = (1/A)∫[-1,1] x*(2-x²-x) dx

= (1/(4/3))∫[-1,1] (2x - x³ - x²) dx

= (3/4) [(x²/2) - (1/4)x⁴ - (1/3)x³] | from -1 to 1

= 0

So the x-coordinate of the centroid is 0.

To find the y-coordinate of the centroid, we need to evaluate the following integral:

y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx

y' = (1/(4/3)) ∫[-1,1] (1/2)[(2-x²)² - x²] dx

= (3/4)[(8/15)x⁵ - (2/3)x³ + (1/2)x] | from -1 to 1

= (2/5)

So the y-coordinate of the centroid is 2/5.

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The number of elements that are in AUB is 20

From the question, we have the following parameters that can be used in our computation:

The number of elements that are in AUB is calculated as

A u B = A + B - Common elements

substitute the known values in the above equation, so, we have the following representation

A u B = 17 + 16 - 13

Evaluate

A u B = 20

Hence, the number of elements that are in AUB is 20

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Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

SOLUTION

Consider the image given below,

Since the diagonals of a kite are perpendicular, hence the angles at the center are 90 degrees.

Hence

From triangles of the shorter diagonals, triangle, ADC

Then

substituting the values we have

Then, subtracting 138 from both sides we have

Hence

The measure of angle DCE= 42 degrees

Similarly, considering the triangle CAB

Then

Hence

Subtracting 134 from both sides, we have

Hence

m < ABC =46°

Answer: m

There is no three-digit whole number that has exactly five positive factors.

The prime factorization of a number with five factors will be of the form p⁴ or p²q, where p and q are distinct prime numbers.

p⁴:

The smallest prime number greater than or equal to 10 is 11.

So, let's consider 11⁴:

11⁴ = 14641 (which is a five-digit number)

p²q:

To minimize the number, we need the smallest prime numbers possible. The two smallest prime numbers greater than 10 are 11 and 13.

Let's consider the product of these two primes:

11² × 13 = 1573 (a four-digit number)

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Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

The distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone. This can be obtained by converting the conditions to equations.

A linear function containing one dependent and one independent variable.

It can be represented using the equation,

y = mx + c

where m is the slope

It is given in the question that,

Rachel is a stunt driver and one time during a gig where she escaped from a building about to explode she drove to get to the safe zone at 24 meters per second.

After 4 seconds of driving, she was 70 meters away from the safe zone.

Let, D(t) be the distance to the safe zone (measured in meters) and t be the  time (measured in seconds)

After 4 seconds of driving, she was 70 meters away from the safe zone.

⇒ This means that at t = 4 seconds, D(4) = 70 meters

Rachel's rate is the slope of the function D(t). Since the distance is decreasing when the time is increasing, the slope must be negative

⇒ m = - 24

y = mx + c

⇒ D(t) = (-24)t + c

Put t = 4,

D(4) = (-24)4 + c

70 = -96 + c ⇒ c = 166

⇒ D(t) = 166 - 24t

Hence the distance from the safe zone after t seconds is D(t) = 166 - 24t given that drove to get to the safe zone at 24 meters per second and after 4 seconds of driving, she was 70 meters away from the safe zone.

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The effectiveness depends on your score of working.

How effective is it to go to your manager to request others take on some activities?

Certainty implies, indeed, that favorable things will happen and uncertainty  implies favorable things won't happen.

If we go to our manager, requesting that others should take some activities. It certainly depends upon the our score in the office. if we are hard working than in situations manager could approve our request and if our score is low or we are not a hard worker than result may no be in our favor.

Thus, the effectiveness depends on your score of working.

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Answer:

No

Step-by-step explanation:

\(7^{-1}\) is a fraction

using the rule of exponents

• \(a^{-m}\) = \(\frac{1}{a^{m} }\)

then

\(7^{-1}\) = \(\frac{1}{7^{1} }\) = \(\frac{1}{7}\) ← that is a fraction

If we assume that the first card drawn is green and it is replaced before the second draw, then the probability of drawing two green cards in a row is 12/51, or approximately 0.235.

If we assume that the first card drawn is green and it is replaced before the second draw, then we can say that each draw is independent of the other, and the probability of drawing a green card on each draw is the same.

Let's assume that the deck of cards contains 52 cards, with 13 green cards. Since we know that the first card drawn is green, there are now 51 cards left in the deck, with 12 green cards.

The probability of drawing a green card on the second draw is 12/51, since there are 12 green cards left in the deck out of a total of 51 cards.

To find the probability of drawing two green cards in a row, we need to multiply the probability of drawing a green card on the first draw (which we assumed to be 1 since we know the first card is green) by the probability of drawing a green card on the second draw:

P(drawing two green cards) = 1 x 12/51

Simplifying this expression, we get:

P(drawing two green cards) = 12/51

Therefore, the probability of drawing two green cards is approximately 0.235.

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Answer:

it can be 100 because percentages are out of 100

The expression in the options which is equivalent to the given expression is D. (22x + 48) / (x² - 36).

Given expression is,

[15 / (x - 6)] + [7 / (x + 6)]

Cross multiplying the two fractional expressions,

= [15 (x + 6) + 7 (x - 6)] / [(x - 6) (x + 6)]

= [15x + 90 + 7x - 42] / [x² - 6²]

= (22x + 48) / (x² - 36)

Hence the equivalent expression is D.

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The calculated output value for an input value of 5 is (c) 10

From the question, we have the following parameters that can be used in our computation:

Kerrin is making an input-output table for the rule "add 5."

This means that

Output = input + 5

In this case, we have

input = 5

substitute the known values in the above equation, so, we have the following representation

Output = 5 + 5

Evaluate

Output =10

Hence, the output is 10

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