11. (15 pts) Salt and pepper sit on a table, and they are 1 meter apart from each other. The top of the table is 0.8 meters above the hard tile floor, and Salt is near the edge of the table. A cat jumps on the table and gently pushes Salt over the edge. Salt's vertical velocity is v(t) = -31 m/sec., where t is the time after being knocked over, and the negative direction is downward toward the floor. At what rate is the distance between Salt and pepper changing at any time after Salt falls off the edge of the counter and before Salt hits the floor? Salt Pepper

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

x=23

Step-by-step explanation:

A and D are equal to eachother so you write the equation (x-4)=19. To solve all you have to do is add 4 to each side and you will get the answer of x=23

Answer:

48.95

Step-by-step explanation:

Answer:

Since rational numbers can be written as a ratio, such as a/b, then irrational numbers can not be written that way.

Step-by-step explanation:

Square roots of non-perfect squares are irrational numbers because they are non-terminating and non repeating decimals

Answer:

3131 meters

3332 - 210 = 3122

3122 +9 = 3131 meters

Step-by-step explanation:

Answer:

x = 23

Step-by-step explanation:

Hello There!

We are given that AC and BD are diagonals of a rectangle

If you didn't know diagonals are congruent

So given that BC = 56 and AC = 2x + 10 we can use this equation to solve for x

56 = 2x + 10

now we solve for x

step 1 subtract 10 from each side

56 - 10 = 46

10 - 10 cancels out

now we have 46 = 2x

step 2 divide each side by 2

46/2=23

2x/2=x

we're left with x = 23

Answer:

x=23 is the answer

Step-by-step explanation:

good luck

Answer:

1/9 chance

Step-by-step explanation:

Answer:

Look at step-by-step explanation.

Step-by-step explanation:

The answer to 14 is 70 dollars.

The answer to 16 is 7 miles per hour or 7mph.

To find (f ∘ g)(x), we need to substitute g(x) into f(x) wherever we see x in the expression for f(x).

So we have:

f(g(x)) = f(3x + 1) = (3x + 1)^2 - 8 = 9x^2 + 6x - 7

Therefore, the correct answer is: 9x^2 + 6x - 7.

Answer:

A. 8

Step-by-step explanation:

6.0061 x 10^7

/                        = 6/8 x 10^7/10^6

7.8483 x 10^6

0.75 x 10^7-6

0.75 x 10^1

A: 0.75 = 7.5 = 8.

The area of the Pacific Ocean is 8 times larger than the area of the Southern Ocean.

Option A is the correct answer.

It is a result that is not exact, but close enough to be used.

We have,

Area of the Pacific Ocean:

= 6.0061 x \(10^{7}\) square miles

Area of the Southern Ocean:

= 7.8483 x \(10^{6}\) square miles

The area of the Pacific Ocean is larger than the area of the Southern Ocean by:

Area of the Southern ocean x M = Area of the Pacific Ocean

M = 6.0061 x \(10^{7}\) / 7.8483 x \(10^{6}\)

M = 7.7

Approximating we get,

M = 8.

Thus the area of the Pacific Ocean is 8 times larger than the area of the Southern Ocean.

Option A is the correct answer.

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Answer:

m <5 = 65°

m<8 = 115°

Step-by-step explanation:

m<2= m<5 = 65° (vertically opposite angles are equal)

m<5 + m<4 = 180 (co-int angles, parallel lines)

65+ m<4 =180

m<4 = 115°

Therefore

m<4=m<8 = 115° (vertically opposite angles are equal)

Answer:

m<5 = 65 degrees  m<8 = 115 degrees

Step-by-step explanation:

m<2 = 65 degrees

m<2 = m<5 so

m<5 = 65 degrees

A line is 180 degrees, so

180 degrees - 65 degrees = 115 degrees

m<8 = 115 degrees

Answer:

11/12 is the answer

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

The area represented by g(x) is a triangular region with base 1 and height (7/3) x, where x is the variable along the horizontal axis. The resulting shape will be a right triangle with vertices at (0,0), (1,0), and (0, (7/3) x).

It seems like you are asking to sketch the area represented by the function g(x) given as the integral of x with respect to t from 1 to 2. However, there seems to be a typo in your question. I will assume that you meant g(x) = ∫[1 to x] t^2 dt. Please follow these steps to sketch the area represented by g(x):

1. Draw the function y = t^2 on the coordinate plane (x-axis: t, y-axis: t^2).

To sketch the area represented by g(x) = x t2 dt 1, we first need to evaluate the definite integral. Integrating x t2 with respect to t gives us (1/3) x t3 + C, where C is the constant of integration. Evaluating this expression from t=1 to t=2 gives us (1/3) x (2^3 - 1^3) = (7/3) x.

2. Choose an arbitrary x-value between 1 and 2 (e.g., x = 1.5).
3. Draw a vertical line from the x-axis to the curve of y = t^2 at x = 1.5. This line represents the upper limit of the integral.
4. Draw another horizontal axis from the x-axis to the curve of y = t^2 at x = 1. This line represents the lower limit of the integral.
5. The area enclosed by the curve y = t^2, the x-axis, and the vertical lines at x = 1 and x = 1.5 represents the area for the given value of x.

In conclusion, the area represented by g(x) = ∫[1 to x] t^2 dt can be sketched by plotting the curve y = t^2, choosing a specific x-value between 1 and 2, and then finding the enclosed area between the curve, x-axis, and the vertical lines at x = 1 and x = chosen x-value.

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Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

If Rashid spent 30 minutes on each piece of homework for three subjects, we can calculate the total time he spent by multiplying the time spent per subject (30 minutes) by the number of subjects (3).

30 minutes * 3 = 90 minutes.

To convert this into hours and minutes, we divide 90 minutes by 60 since there are 60 minutes in an hour.

90 minutes ÷ 60 = 1 hour and 30 minutes.

Therefore, Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.

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Answer: 1/4

Step-by-step explanation:

Say you have a square, and each side is two units. The area of that square is 4 because 2 times 2 is 4. Now multiply each side by two, causing the area to go from 4 to 16 because each side is now 4. 16 times 1/4 is 4.

The area of the given triangle is 20 square kilometers.

Here, we are given a triangle as shown in the figure below.

There are many ways of calculating the area of a triangle but since here, we are given only one angle and 2 sides of the triangle we will use the following formula to calculate the area-

area of triangle = 1/2 × sinФ × side 1 × side 2

where, Ф = angle formed by side 1 and side 2

Here, Ф = 35

Sin 35 = 0.5736

Thus, the area of the triangle will be-

1/2 × 0.5736 × 7 × 10

= 35 × 0.5736

= 20.076

20.076 rounded off to nearest hundredth is 20

Thus, the area of the given triangle is 20 square kilometers.

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Your question was incomplete. Check for the missing figure below

Step-by-step explanation:

ABE is isoceles, so both legs are equally long.

so, AB = AE.

BD = CE

that means that BC = DE.

and therefore also ACD is isoceles.

so, AC = AD

we therefore know that all 3 pairs of corresponding sides of the 2 triangles are equivalent.

so, via SSS ABC is equivalent to AED.

Considering the numeric values of the function, the points and ordered pairs are given as follows:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

An ordered pair is given by:

(x, f(x)).

In which f(x) is the numeric value.

For this problem, the function is given by the following rule:

y = 3x + 1.

When x = 2, the numeric value is given by:

y = 3 x 2 + 1 = 6 + 1 = 7.

Hence the ordered pair is (2,7).

When x = 3, the numeric value is given by:

y = 3 x 3 + 1 = 9 + 1 = 10.

Hence the ordered pair is (3,10).

When x = -1, the numeric value is given by:

y = 3 x -1 + 1 = -3 + 1 = -2.

Hence the ordered pair is (-1,2).

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A p-value conveys the type of probabilistic result known as "statistical significance." Statistical significance refers to the likelihood that a given result occurred by chance.

A p-value is a measure of this likelihood, with a smaller p-value indicating a smaller likelihood that the result occurred by chance. In other words, a smaller p-value indicates a higher level of statistical significance.

For example, if a p-value is 0.01, this means that there is a 1% chance that the result occurred by chance. This is considered to be statistically significant, as it is unlikely that the result occurred by chance. On the other hand, if a p-value is 0.5, this means that there is a 50% chance that the result occurred by chance. This is not considered to be statistically significant, as it is equally likely that the result occurred by chance or not.

In summary, a p-value conveys the type of probabilistic result known as statistical significance, with smaller p-values indicating a higher level of statistical significance.

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Answer:

Diverges

There is no sum.

Step-by-step explanation:

A geometric series has a general formula of:

\(\sum ar^n\)

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges, but if |r| > 1, than the series diverges.

In this problem, the initial term is a = 36, the ratio can be found by:

\(r = \frac{39.6}{36}=\frac{43.56}{39.6}\\ r=1.1\)

Since the ratio is r =1.1 and 1.1 > 1.0, the series diverges.

In a diverging series, it is not possible to determine the sum of infinite terms, since it would be infinite.

The geometric series diverges and the sum does not exists.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms .

A geometric series has a general formula of:

∑arⁿ

Where 'a' is the initial term, 'n' is the number of terms, and 'r' is the constant ratio. If |r| < 1 than the series converges.

In this particular case, the initial term is a=36 and each term is multiplied by 1.1 to get the next term

Therefore r = 1.1 and as it is >1 therefore the series diverges.

The sum of a divergent series is not finite so the sum does not exists.

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the approximate area of the base of the paint can is 53.5 square centimeters.by using Volume formula is Base Area × Height

To find the approximate area of the base of the paint can, we can use the formula for the volume of a cylinder:

Volume = Base Area × Height

We are given the volume (535 cubic centimeters) and the height (10 cm). We need to solve for the Base Area. Rearranging the formula to solve for Base Area, we get:

Base Area = Volume ÷ Height

Now, substitute the given values:

Base Area = 535 cubic centimeters ÷ 10 cm

Base Area ≈ 53.5 square centimeters

So, the approximate area of the base of the paint can is 53.5 square centimeters.

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The approximate area of the base of the can is 53.5 square centimeters

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

Volume = 535 cubic centimeters of paint

Height of container = 10 cm

The area of the base of the can is calculated as

Base area = Volume/Height

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

Base area = 535/10

Evaluate

Base area = 53.5

Hence, the base area is 53.5 square centimeters

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Answer:

\(\frac{36}{g}\)=9

Answer: (5,1)

Step-by-step explanation:

Look for the point of maximum or minimum, where the graph changes direction.

The test score is 91.5.

z-score:

A z-score is the number of standard deviations from the mean value of the reference population.

Here we have to find the test score.

Mean(μ) = 90

Standard deviation(б) = 15

z-score = 0.1

Formula for z-score:

z = X - μ / б

Now putting the values in the equation:

0.1 = X - 90 / 15

1.5 = X - 90

X = 91.5

Therefore the test score is 91.5.

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The equation of the line in point-slope form and in​ slope-intercept form are both y = 1/2x.

1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.

3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.

If a line has a slope of 1/2 and passing through the origin, then:

m = 1/2

(x1, y1) = (0,0)

Plug in the values in the point-slope form and in​ slope-intercept form.

point-slope form

y - y1 = m(x - x1)

y - 0 = 1/2(x - 0)

y = 1/2x

slope-intercept form

y = mx + b

y = 1/2x + b

Substitute the values of x and y and solve for the y-intercept, b.

0 = 1/2(0) + b

b = 0

y = 1/2x + 0

y = 1/2x

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Answer:

It opens downward and crosses the x axis at (-3,0) and (1,0) this means for any x value less than -3 or greater than 1, the function is negative.

The answer would be:

The function is negative for all real values of x where

x < –3 and where x > 1.

Answer:

It's C

Step-by-step explanation:

Edge 2021 Test

The volume of the remaining piece of ice cube is 6911.5 cubic cm

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

The figure

Where, we have

Radius, r = 20/2  = 10 cm

Height, h = 33 cm

The volume of the remaining piece is calculated is

V = 2/3πr²h

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

V = 2/3 * 22/7 * 10² * 33

Evaluate

V = 6911.5

Hence, the volume of the remaining piece is 6911.5 cubic cm

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