maximize p = 6x 4y subject to x 3y ≥ 6 −x y ≤ 4 2x y ≤ 8 x ≥ 0, y ≥ 0.

Answer:

rational number

Step-by-step explanation:

a rational number can be written as a/b where a and b are integers

23/17 = a/b where a = 23 and b = 17

This is a rational number

Answer:

27°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 63° = 180°

x + 153° = 180° ( subtract 153° from both sides )

x = 27°

Answer:

27 degrees

Step-by-step explanation:

A right angled triangle has 1 angle as 90 degree. And as you know the other angle is 63 degree, and the angle sum property of a triangle is 180 degrees. So-

Let's take 'x' as the other angle.

90 + 63 + x = 180

153 + x = 180

x = 180 - 153 = 27

x = 27 degrees

So, the other angle is 27 degrees.

All the angles of the right-angled triangle are- 90, 63, 27.

Answer:

The inverse function h(x) = 4x + 48

Step-by-step explanation:

Here, we want to find the inverse of a function

The function is;

f(x) = x/4 -12

now, let this value equals m

so;

m = x/4 -12

we now try and make x the subject formula and this gives us the inverse.

m = (x-48)/4

4m = x -48

x = 4m + 48

substitute m for x

which implies 4x + 48

This is the inverse of the function

Answer:

D. h(x) = 4x + 48

The work you must do to change the length of the spring from 8 cm to 11 cm is 0.0225 Joules.

Calculation of work done:

To calculate the work done to change the length of the spring from 8 cm to 11 cm, given its relaxed length is 5 cm and its stiffness is 50 N/m:

1: Convert the given lengths from centimeters to meters.
Relaxed length = 5 cm = 0.05 m
Initial length = 8 cm = 0.08 m
Final length = 11 cm = 0.11 m

2: Calculate the change in length.
Δx = Final length - Initial length = 0.11 m - 0.08 m = 0.03 m

3: Apply Hooke's Law to find the force needed to stretch the spring.
F = k × Δx
Where F is the force, k is the stiffness (50 N/m), and Δx is the change in length (0.03 m).
F = 50 N/m × 0.03 m = 1.5 N

4: Calculate the work done.
Work = 0.5 × F × Δx
Work = 0.5 × 1.5 N × 0.03 m = 0.0225 J

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Answer:

If each square (from the squared paper) has side length 1, then that hexagon has four sides of length √12+42=√17 and two sides of length √32+32=√18.Step-by-step explanation:

The UCR (Uniform Crime Reporting) is B. not a truly reliable measure.

The UCR is a program established by the FBI in 1930 to collect and analyze crime statistics from law enforcement agencies across the United States. Although it provides useful data and insights into crime trends, it is not without its limitations. One significant issue with the UCR is that it relies on voluntary reporting from law enforcement agencies, meaning that some areas may not provide complete or accurate data. This can lead to an underrepresentation of certain crimes or inconsistencies in reporting across jurisdictions.

Another limitation is that the UCR only includes reported crimes, excluding any unreported criminal activity. This means that the data does not necessarily provide a comprehensive picture of all crimes occurring in a given area. Additionally, the UCR uses a hierarchy rule, meaning that if multiple crimes are committed during a single incident, only the most severe crime is counted. This can result in an undercounting of less severe but still significant crimes.

In summary, although the UCR provides valuable information on crime trends and patterns, it is not a truly reliable measure due to its reliance on voluntary reporting, exclusion of unreported crimes, and hierarchy rule. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

it is fair to say that the ucr is: group of answer choices

A. A mutually exclusive measure

B. Not a truly reliable measure

C. An exhaustive measure

D. All of the above

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The distance between the point (-3,7) and the line y=1/3x-2 is  11.0 units

Distance shows how long it is between a point and another

We can do this by drawing a segment that is perpendicular to the line

the given equation is 1/3x-2

The slope here is 1/3 That is slope =3

From the equation of slope=intercept form = y=mx+c

put m=3 to have

y=3x+c

From the given coordinates (-3,7)

7=3(-3)+c

7+9=c

c=16

This implies that y=3x+16

Find the line where the equation intersect  the line

⇒3x+16=1/3x-2

Rearrange the equation

8x/3=-18

Make x the subject. x=6.75

Recall that y=1/3(6.75)-2

y=2.25

The second coordinates are (6.75,2.25) and first (-3,7)

The distance is given by

d=\(\sqrt({X_{2}-X_{1})^{2} +(Y_{2}-Y_{1} )^{2} }\)

d= √(6.75+3)²+(2.25-7)²

d=√9.75²+(-4.75)²

d=√95.0625+22.5625

d=√117.625

d=10.8455059817

Therefore the distance is 11 units

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Answer:

5/8

Step-by-step explanation:

This means 0.625 as a fraction can be written as 5/8.

Answer: 5/8

Step-by-step explanation:

125 times 5 is 625

125 times 8 is 1000

625/1000 is equivalent to 5/8

Step 1: Subtract 8 from both sides of the equation.

Step 2: Complete the square by taking 6 and divide it by 2, then square it.

Step 3: Add 9 to both sides of the equation.

Step 4: Combine like terms on the left and factor the right side into perfect square trinomial.

Step 5: Simplify the right side further into (x + 3)².

Step 6: Solve for y by subtracting 3 from both sides of the equation.

Step 7: The vertex is (-3, -1).

In Mathematics and Geometry, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

In order to complete the square, you should add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

y = x² + 6x + 8

x² + 6x + 8 - 8 = -8

x² + 6x = -8

x² + 6x + (6/2)² = -8 + (6/2)²

x² + 6x + 9 = -8 + 9

x² + 6x + 9 = 1

x² + 3x + 3x + 9 = 1

x(x + 3) + 3(x + 3) = 1

(x + 3)(x + 3) = 1

(x + 3)² = 1

x + 3 - 3 = -3 ±√1

x = -3 ± 1

x = -4 or x = -2

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To calculate the force exerted on the ball, we can use the formula and Therefore, the force exerted on the ball is not among the given options (A20√3N, B15√3N, C10√3N, or D5√3N). The correct answer is 34.64 N.

Force = (change in momentum) / time
First, let's calculate the initial momentum of the ball:
Initial momentum = mass x velocity
Initial momentum = 2kg x 1m/s
Initial momentum = 2kg m/s
Next, let's calculate the final momentum of the ball:
Final momentum = mass x velocity (since the ball reflects at the same angle and has the same magnitude of velocity, the momentum is the same as the initial momentum)
Final momentum = 2kg x 1m/s
Final momentum = 2kg m/s
The change in momentum is the difference between the final and initial momentum:
Change in momentum = final momentum - initial momentum
Change in momentum = 2kg m/s - 2kg m/s
Change in momentum = 0
Finally, we can calculate the force exerted on the ball:
Force = (change in momentum) / time
Force = 0 / 0.1s
Force = 0N
Therefore, the answer is D) 5√3 N.

Given the information provided, we need to find the force exerted on the 2kg ball that strikes a wall at a 30-degree angle with a velocity of 1m/s and reflects at the same angle in 0.1 seconds.
Step 1: Determine the horizontal and vertical components of the initial velocity.
Initial horizontal velocity (Vx) = V * cos(30) = 1 * cos(30) = 0.866 m/s
Initial vertical velocity (Vy) = V * sin(30) = 1 * sin(30) = 0.5 m/s
Step 2: Determine the horizontal and vertical components of the final velocity.
Since the ball reflects at the same angle, the final vertical velocity will be the same, but the horizontal velocity will have the opposite direction.
Final horizontal velocity (Vx') = -0.866 m/s
Final vertical velocity (Vy') = 0.5 m/s
Step 3: Calculate the change in horizontal and vertical velocities.
ΔVx = Vx' - Vx = -0.866 - 0.866 = -1.732 m/s
ΔVy = Vy' - Vy = 0.5 - 0.5 = 0 m/s
Step 4: Calculate the net change in velocity (ΔV).
ΔV = sqrt((ΔVx)^2 + (ΔVy)^2) = sqrt((-1.732)^2 + (0)^2) = 1.732 m/s
Step 5: Determine the acceleration of the ball.
Acceleration (a) = ΔV / time = 1.732 / 0.1 = 17.32 m/s²
Step 6: Calculate the force exerted on the ball using Newton's second law (F = m * a).
Force (F) = mass (2kg) * acceleration (17.32 m/s²) = 34.64 N

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The probability that the largest number drawn is less than or equal to 9 is approximately 0.9936.

(a) The probability that 9 is the largest number drawn is the number of ways to select 5 balls out of the first 9 balls divided by the number of ways to select 5 balls out of 14, or (9 choose 5) / (14 choose 5).

(b) The probability that the largest number drawn is less than or equal to 9 is the number of ways to select 5 balls out of the first 9 balls divided by the number of ways to select 5 balls out of 14, or the sum of (i) (9 choose 5) / (14 choose 5) and (ii) (8 choose 5) / (14 choose 5) and (iii) ... (5 choose 5) / (14 choose 5).

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A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160feett/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

Given that 1)A gull can fly at a speed of 22 miles per hour and asked to convert its units to  foot/hour

2)An AMTRAK train travels at 125 miles per hour and is asked to convert its units to  miles/minute

1 mile=5280 feet

22 miles/hour=22 × 5280 foot/hour

22 miles/hour=116,160 foot/hour

1 hour=60 minute

125 miles/hour= 125/60 miles/minutes

125 miles/hour= 2.083 miles/minutes≈ 2.1miles/minutes

Therefore, A gull can fly at a speed of 22 miles per hour i.e. equal to 116,160 feet/hour and An AMTRAK train travels at 125 miles per hour i.e. equal to 2.1 miles/minute

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The missing dimension of the rectangle is 8 inches.

To determine the missing dimension of an area of 112 in.², we need to know at least one of the dimensions. Let's assume we know the length of the rectangle is 14 inches.

We can then use the formula for the area of a rectangle, which is length multiplied by width, to solve for the missing dimension.

We can rearrange the formula to solve for the width by dividing both sides by the length: width = area/length. Plugging in the values we know, we get: width = 112 in.² / 14 in. = 8 inches.

It's important to note that if we had started with the width instead of the length, we would have used the same formula but rearranged it to solve for the length instead. The formula for the area of a rectangle is very useful for solving these types of problems.

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Answer:

No Natural numbers start from 1

Step-by-step explanation:

true it can be a natural number

Answer:

Joshua's Savings = $575

Step-by-step explanation:

If the total amount is $925 and you added $350 to x (Josh's Savings) than all we have to do is subtract the $350 from the $920 to solve for x,...

$925 - $350 = $575

Joshua's Savings is equal to $575 dollars,...

Hope that helps,... Chow,...!

Answer:

=================

We need to find the total surface area of a cylinder excluding its top.

Answer:

x = 10 3/5

Step-by-step explanation:

x - 3/5 = 10

add 3/5 to each side to get:

x = 10 3/5

Answer:

\(x = 10\frac{3}{5} \)

Step-by-step explanation:

"'x' minus 3/5 equals 10" can be written as: \(x - \frac{3}{5}= 10\\ \).

=========================================

\(x - \frac{3}{5}= 10\\ \rule{150}{0.5}\\\\ x - \frac{3}{5} + \frac{3}{5} = 10 + \frac{3}{5}\\\\ \boxed{x = 10\frac{3}{5}} \)=========================================

Hope this helps!

Based on the above, we can say that the number of students participating in the activity is any multiple of four, since we can always form groups of four students from the total number of students.

To answer this question, we need to use the fact that there are four students in each group. Let's call the total number of students participating "N".

We know that each group has four students, so we can write:

N = 4 x (number of groups)

In other words, the total number of students is equal to four times the number of groups.

Sine We do not  know the number of groups, but we can find it by dividing the total number of students by four:

number of groups = N / 4

Substituting this expression into the previous equation, we get:

N = 4 x (N / 4)

Simplifying, we get:

N = N

This is always true, so there is no end tn the value of N.

Therefore, we can say that the number of students participating in the activity is any multiple of four, since we can always form groups of four students from the total number of students.

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Answer:

526 X 9= 4734 is the answer.

Answer:

Step-by-step explanation:

:

The answer is 4x^{2}+12x-16. correct me if im not ty!

Answer:

4x^2 - 20x + 16

Step-by-step explanation:

4x^2 - 4x - 16x + 16

4x^2 - 20x + 16

Answer:

3,-2,-7,-12,-17,-22

when going up add, when going down subtract.

Example: -2+5=3

-17-5=-22

Answer:

2 events are described.

Step-by-step explanation:

Because only three types of cones and 31 flavours of ice cream.

Answer:

KitKat

Step-by-step explanationKitKat

Answer: ~4.12 times larger

Step-by-step explanation:

1. find the values for both equation, (8*106=848) and (2*103=206).

2. divide the larger number by the smaller one. 848/206

which gives us 4.11650485, or 4.12 rounded.

hope this helped! ♡

Answer:

27

Step-by-step explanation:

1+17=18 and then 18+9=27

Answer: 27 years old

Step-by-step explanation: 1 + 17 = 18. He is 18 years old now.

18 + 9 = 27. He will be 27 years old then.

Let \(n=abcba\) be such a number. If 18 divides \(n\), then both 2 and 9 divide \(n\).

To be divisible by 2, we must have \(a\in\{2,4,6,8\}\). Meanwhile we can have \((b,c)\in\{0,1,2,\ldots,9\}^2\).

To be divisible by 9, we the sum of the digits of \(n\) must itself be divisible by 9, or

\(2a+2b+c=9k\)

for some integer \(k\).

The largest value of \(2a+2b+c\) is 2•8 + 2•9 + 9 = 43, so we must have \(k\in\{1,2,3,4\}\).

I'm not sure what the best way to get the final count may be, but there are 44 such numbers. It's rather tedious to do by hand.

• If \(k=1\), then \(2a+2b+c=9\), and we can do this in 4 ways.

For example,

2•2 + 2•0 + 5 = 9 \((n = 20502)\)

• If \(k=2\), then \(2a+2b+c=18\) and can be done in 16 ways.

2•2 + 2•3 + 8 = 18 \((n = 23832)\)

• If \(k=3\), then \(2a+2b+c=27\) and can be done in 18 ways.

2•2 + 2•7 + 9 = 27 \((n = 27972)\)

• If \(k=4\), then \(2a+2b+c=36\) and can be done in 6 ways.

2•6 + 2•8 + 8 = 36 \((n = 68886)\)

Answer:

5

Step-by-step explanation:

The equation of a straight line is :

y=mx+c

where m is the gradient and c is the y-intercept

so if m equals 5 then the gradient is 5

Answer:

gradient = 5

Step-by-step explanation:

The gradient is the coefficient of x, so for y = 5x + 5 it is 5.

(the +5 part is the y-intercept, i.e. where x = 0)