The sum of 2 numbers is 27. The larger number is 3 times more than the smaller number. What are the numbers?

Answer:

160 square inches

Step-by-step explanation:

You can split the irregular figure up into regular shapes:

the top 4x6 inch rectangle

the middle section can be a 18x6 rectangle (added 7+11 for the length)

the bottom 4x7 rectangle (sibtracted 10-6 for the width)

Then, find the area of each section with the equation A = lw.

A= 4(6) = 24 square inches

A = 18(6) = 108 square inches

A = 4(7) = 28 square inches

Add these areas up to get the total area of the irregular figure.

24 + 108 + 28 = 160 square inches

Using it's concept, the expression that can be used to find the probability that a randomly selected point is in the white area of the grid is:

\(\frac{7}{16}\)

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, 7 out of 16 squares are in the white area, hence the probability is given by:

\(p = \frac{7}{16}\).

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Answer:

Translation?

Step-by-step explanation:

Answer:

The answer is 24 times

we know that

The distance between ywo points is giving by the formula

in this problem we need to calculate the distance between B and C

so

looking at the graph

B(-35,-20)=(x1,y1)

C(-20,5)=(x2,y2)

substitute in the formula

Slope of line=0

Slope of line=\(\frac{y2-y1}{x2-x1}\)

=\(\frac{-4+4}{11-7}\) =\(\frac{0}{4}\) =0

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.

The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute the slope.A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn in one of four directions: upward, downward, horizontal, or vertical.

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Answer: 12x-60

Step-by-step explanation:

-12 x 5/6 = 10

-12 x 5 = -60

10x-60+2x

12x-60

Answer:

It's going to be the graph with the straight line that intersects through 0,1 and 2,1 and 3,1 and so on.

Step-by-step explanation:

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

m [slope] = 0

Step-by-step explanation:

When the slope is 0, x cancels out so the y value will remain the same.

There are several methods to finding slope but the easiest way to do this is by dividing the second y value - first y value by the second x value - first x value.

m = ∆y/∆x = y2-y1/x2-x1

You y2 and x2 are interchangable with y and x, because y1, and x1 are part of the starting coordinate,.

The reason you subtract the second

value from the first is because in a directly proportional relationship, y increases as x increases so the next x values will have a greater y value, this is a measure of steepness.

So the slope is:

-1 - -1 / 3 - -2 = -1 + 1 / 3 + 2 = 0 / 5 = 0.

Answer:

heres what u need

Step-by-step explanation:

\(\frac{-1}{-2} \frac{-1}{3}\)

divide top from bottom

\(-2/-1=2\)

2 is your x

\(3/-1=-3\)

-3 is your y

so your slope is (2,-3)

Answer:

-4 degrees

Step-by-step explanation:

You subtract 14-18

Answer:

8

Step-by-step explanation:

24÷2=16×1=16÷2=8

am not sure I think the answer is also 16 so look at other people answer

Paul should buy 3 gallons

Unit means 'single entity', the fundamental constructing block. Usually, it is 1 in mathematics and science.

Thus, unit price of something is price of 1 thing.

Thus, suppose we're taking about price of mangoes, then unit price will denote the price of 1 mango.

There are 16 cups in a gallon, and if each person will eat 2 cups, and there are 24 people, multiply 24 by 2 to get the number of cups.

24 x 2 = 48.

Then, divide that by 16 (the number of cups in a gallon) to how many gallons.

48 ÷ 16 = 3

Therefore, he needs 3 gallons.

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Step-by-step explanation:

u decreased by 17 equals

= u-17

Answer:

u-17

Step-by-step explanation:

A compound statement is a group of two or more statements connected using words such as 'or', 'and', 'if then', 'if and only if'.

Then, we have:

This is a compound statement of conditional type where the first simple statement is the condition for the second simple statement.

Then, we have:

p: The dog is hungry.

q: She is barking.

p→q: The dog is hungry if she is barking.

Thus, this statement is a compound statement of conditional type.

We can see this statement as a conjunction of two simple statements:

• p: Bill reads books.

• q: Bill reads magazines.

Then, we have:

p ∧ q: Bill reads books and magazines.

Thus, this statement is a compound statement of conjunction type.

We can see this statement as a conjunction of two simple statements:

• p: There are wild animals on G Ranch.

• q: There are wild animals on L Ranch.

Then, we have:

p ∧ q: There are wild animals on G and L Ranch.

Thus, this statement is a compound statement of conjunction type.

Part a) Compound statement of conditional type.

Part b) Compound statement of conjunction type.

Part c) Compound statement of conjunction type.

Answer:

Step-by-step explanation:

2n = 3n - 5

This works out to n = 5.

The translates of ''Twice a number is five less than three times the number" as,

⇒ 2 x = 3 x - 5

Here,

The written expression is,

''Twice a number is five less than three times the number" .

What is Mathematical expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Now,

The written expression is,

''Twice a number is five less than three times the number" .

Let a number is  ' x '.

Then, in mathematical expression it can be written as,

⇒ 2 x = 3 x - 5

After solving this, we get;

2 x = 3 x - 5

x = 5

So, The translates of ''Twice a number is five less than three times the number" as,

2 x = 3 x - 5

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The coordinates of the meeting place are approximately (-4.3, -4.3).

Option D is the correct answer.

We have,

Now,

Midpoint between cities A and B:

(((-16+1)/2), ((-1+6)/2)) = (-7.5, 2.5)

Midpoint between cities A and C:

(((-16+1)/2), ((-1-18)/2)) = (-7.5, -9.5)

Midpoint between cities B and C:

(((1+1)/2), ((6-18)/2)) = (1, -6)

Now we can find the intersection of the three lines formed by these midpoints.

One way to do this is to use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

The line passing through (-7.5, 2.5) and (-7.5, -9.5):

x = -7.5

The line passing through (-7.5, 2.5) and (1, -6):

y = (-8/9)x + 35/9

The line passing through (-7.5, -9.5) and (1, -6):

y = (3/5)x - 33/5

Solving for the intersection of these lines.

x = -4.3

y = -4.3

Therefore,

The coordinates of the meeting place are approximately (-4.3, -4.3).

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The value of function f(4) is 323/3 - 2sin(4).

Given, f''(x) = 9x + 6sin(x)and f'(0) = 4, f(0) = 3

The first derivative of f(x) can be obtained by integrating f''(x).f'(x) = ∫ f''(x)dx = 4.5x² - 6cos(x) + C1

Applying initial condition f'(0) = 4,f'(0) = 4.5(0)² - 6cos(0) + C1= 4=> C1 = 10/3

Thus, f'(x) = 4.5x² - 6cos(x) + 10/3The function f(x) can be obtained by integrating f'(x).f(x) = ∫ f'(x)dx= 1.5x³ - 6sin(x) + (10/3)x + C2

Applying initial condition f(0) = 3,f(0) = 1.5(0)³ - 6sin(0) + (10/3)(0) + C2= 3=> C2 = 3

Thus, f(x) = 1.5x³ - 6sin(x) + (10/3)x + 3

Now, we have to find f(4)f(4) = 1.5(4)³ - 6sin(4) + (10/3)(4) + 3= 94 - 6sin(4) + (40/3) + 3= 323/3 - 2sin(4)

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Answer:

The linear measure of an arc whose central angle is 144 on a circle of radius 35 inches is 28π inches or about 87.96 inches

Step-by-step explanation:

The linear measure of an arc is given by

\(s = 2\pi r(\alpha/360)\)

Where, α is the central angle (in degrees) of the arc

In our case,

r = 35 inches

α = 144 degrees

So, the linear measure would be,

\(s = 2\pi(35) (144/360)\\s = 28\pi \\\)

so s = 28π inches

or about 87.96 inches

Answer:

644.89

Step-by-step explanation:

Answer:

644.89 m

Step-by-step explanation:

68 / 100 * 948.37 = 0.68 * 948.37 = 644.89 m (2 d.p.)

a. From fastest to slowest, the speeds of the balls at the right ends of the tracks will depend on the curvature of the tracks.

If the tracks are of equal length but have different curvatures, the ball on the track with the least curvature will have the highest speed, followed by the ball on the track with the next least curvature, followed by the ball on the track with the most curvature.

b. From longest to shortest, the tracks in terms of the times for the balls to reach the ends will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the most curvature will have the longest time for the ball to reach the end, followed by the track with the next most curvature, followed by the track with the least curvature.

c. From greatest to least, the tracks in terms of the average speeds of the balls will depend on the curvature of the tracks. If the tracks are of equal length but have different curvatures, the track with the least curvature will have the highest average speed, followed by the track with the next least curvature, followed by the track with the most curvature.

All the balls will have the same average speed on all three tracks if the track lengths are equal, but will have different speeds at the end of each track due to the different curvatures.

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When the ball stops bouncing, it will have traveled a total vertical distance of 90 feet.

To determine how far the ball has traveled vertically when it stops, we can calculate the sum of the geometric series formed by the distances of each bounce.

Given that the ball rebounds 2/3 of the distance it falls, the distances covered by each bounce form a geometric sequence with a common ratio of 2/3.

The distance the ball initially falls is 30 feet. The subsequent distances covered by each bounce can be calculated as follows:

First bounce: 30 * (2/3) = 20 feet

Second bounce: 20 * (2/3) = 40/3 feet

Third bounce: (40/3) * (2/3) = 80/9 feet

Fourth bounce: (80/9) * (2/3) = 160/27 feet

Fifth bounce: (160/27) * (2/3) = 320/81 feet

And so on...

To calculate the total distance covered, we sum up the infinite geometric series:

Sum = a / (1 - r)

where "a" is the initial term (30 feet) and "r" is the common ratio (2/3).

Sum = (30) / (1 - 2/3)

Sum = (30) / (1/3)

Sum = 90 feet

Therefore, when the ball stops bouncing, it will have traveled a total vertical distance of 90 feet.

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Answer:

DK = 18

MJ = 3

ML = 8

Step-by-step explanation:

In this problem, we need to use the Median of a Triangle Formula. This formula states that EM/EL = FM/JF = DM/DK = 2/3. To implement this into our question, we can write ML/EL = 1/3, so we get that ML = 24/3 = 8. We also know that MJ/FM = 1/2, so MJ = 6/2 = 3. Finally, DM/DK = 2/3, so DK = (12*3)/2 = 18. Hope this is correct.

If a card is drawn from a pack of 52 playing cards, then the probability that the card will be jack is 1/13

Total number of playing cards in the pack = 52 cards

Number of jack cards in the pack = 4 cards

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability that the card will be a jack = 4/52

Simplify the answer

= 1/ 13

Therefore, the probability that the card will be jack is 1/13

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The solution to the expression -10 + |6 + -17| -- 14 is 15

The expression is given as:

-10+l 6+-17l - - 14

Rewrite properly as

-10 + |6 + -17| -- 14

Evaluate the sum and the difference

So, we have:

-10 + |6 + -17| -- 14 = -10 + |-11| + 14

Remove the absolute bracket

-10 + |6 + -17| -- 14 = -10 + 11 + 14

Evaluate the sum

-10 + |6 + -17| -- 14 = 15

Hence, the solution to the expression -10 + |6 + -17| -- 14 is 15

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Answer:

Step-by-step explanation:

distance = \(\sqrt{(7-3)^2+(-2-2)^2\) = \(\sqrt{16+16} = \sqrt{32}\), which is approximately 5.65685

Answer:

5.7

Step-by-step explanation:

\( \sqrt{(2 + 2) {}^{2} + (3 - 7) {}^{2} } = \sqrt{ {4}^{2} + {4}^{2} } = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2} = 5.7\)

Answer: (-4,16)

Step-by-step explanation:

15. x>7                   Some of them are unslovable

16. n≥−5

17. G>5

18. k≤1

19.−2<b≤6

20. −8<m<−3

21. unslovable

22. −9<x<4

23. unslovable

24. m<−9 or m>9

Answer:

work is shown and pictured

The components of the displacement gradient tensor (∇u), linear strain tensor (∇ε), strain components at point P(2l, 2a, 2a), strain along direction n = [1, 1, 1]⁺, and shear strains along directions n1 = [3, -4, 0]⁺ and n2 = [4, 3, 0]⁺ at point P can be determined using the given expressions and coordinates.

The components of the displacement gradient tensor (∇u) can be found by taking the partial derivatives of the displacement vector (u) with respect to the coordinate variables (x, y, z):

(∂u/∂x) = (2A/1) {a^2X2 + (X1^2 - X1)X2 - (X3^2 + X2X3)}

(∂u/∂y) = (2A/1) {a^2X1 + (X1^2 - 1)X2 - (X1^3 + X2X3)}

(∂u/∂z) = (2A/1) {(1 - X1)X2X3}

The components of the linear strain tensor (∇ε) can be obtained from the components of the displacement gradient tensor (∇u) using the formula:

(∂εij/∂xi) = (1/2) * [(∂u_j/∂xi) + (∂u_i/∂xj)]

To evaluate the strain components at point P(2l, 2a, 2a), substitute these coordinates into the expressions derived in step 2.

To find the strain along the direction n = [1, 1, 1]⁺, calculate the dot product of n with the strain tensor (∇ε):

Strain along n = n · ∇ε · n = ε11 + ε22 + ε33

To find the shear strain associated with the directions n1 = [3, -4, 0]⁺ and n2 = [4, 3, 0]⁺ at point P, calculate the dot product of n1 and n2 with the shear strain tensor (∇γ):

Shear strain along n1 = n1 · ∇γ · n1 = γ11 + γ22 + 2γ12

Shear strain along n2 = n2 · ∇γ · n2 = γ11 + γ22 + 2γ12

Evaluate the expressions using the derived components from step 2 at point P to find the desired strain values.

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Answer:

Step-by-step explanation:

Rate of change = (2-3.6)/(5-(-3)) = -1.6/8 = 0.2