how are rational numbers written as decimals?

Answer:

Length of each side of the square = 8 cm

Step-by-step explanation:

In the figure attached, diagrams of a right triangle and a square have been given.

"Area of the square is twice the area of the triangle."

Let one side of the square = x cm

Therefore, area of the square = x²

Area of the given triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                           = \(\frac{1}{2}(16)(4)\)

                                           = 32 cm²

Therefore, x² = 2 × 32

x² = 64

x = 8 cm

Therefore, length of each side of the square will be 8 cm.

Answer:

No, because 30 is not equal to 2.5 times 6

Step-by-step explanation:

2.5 times 6 = 15

Step-by-step explanation:

The proportion of similar triangles are

\( \frac{3}{4} = \frac{9}{r} \)

Solving for r

\( \frac{4}{3} = \frac{r}{9} \)

\( \frac{9 \times 4}{3} = r\)

\(12 = r\)

The argument is valid. If a number is not prime, it does not imply that the number is odd.

The given argument is invalid. The argument's structure follows the form of denying the consequent (modus tollens). However, the argument itself contains a logical flaw. While it is true that all prime numbers greater than 2 are odd, it does not follow that a number being not prime implies it is not odd.

The argument assumes that the negation of being prime automatically leads to not being odd, which is not necessarily true. There exist non-prime numbers that are odd, such as 9, 15, and 21. Therefore, the fact that a number is not prime does not guarantee that it is not odd.

To establish the conclusion that a number is not odd based on it not being prime, additional information or reasoning is needed. Hence, the argument is invalid.

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Answer:

Collect, analyze, interpret and present quantitative data

Answer: Collect, analyze, interpret and present quantitative data

Answer:

Jupiter :)

Step-by-step explanation:

Answer:

1 radian ≈ 57.2958

Answer:

Below

Step-by-step explanation:

The answer I got was (-5/2, -9/2) but in your case the answer is:

(-2.5, -4.5)

Answer:uyuy uy

the rang is 5 times 6 is 9 the rang is 5 times 6 is 9 the rang is 5 times 6 is 9

Step-by-step explanation:

The shortest length of cable needed is approximately 3464 ft.

.To find the shortest length of cable needed for the cable car running to the top of the mountain. We'll use the terms: mountain height (3400 ft), inclined angle (74 degrees), and distance from the base (1000 ft).

Step 1: Draw a right triangle where the hypotenuse represents the cable, the vertical leg represents the mountain's height (3400 ft), and the horizontal leg represents the distance (1000 ft) from the base of the mountain.
Step 2: We are given the inclined angle (74 degrees) between the hypotenuse and the horizontal leg. We can use the sine function to find the ratio between the height (opposite leg) and the length of the cable (hypotenuse).

\(sin(74 degress) = \frac{height}{hypotenuse}\)
Step 3: Plug in the height (3400 ft) and solve for the hypotenuse.

\(sin(74 degress) = \frac{3400}{hypotenuse}\)
\(hypotenuse = \frac{3400}{sin(74 degrees)}\)
Step 4: Calculate the value hypotenuse = 3464.45 ft
Step 5: Round the answer to the nearest foot.

The shortest length of cable needed is approximately 3464 ft.

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Answer:

0

Step-by-step explanation:

anything multuplied by 0 is 0

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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3 < x < 44

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

Explanation:

For triangles ABC and DEF we have these two pairs of congruent sides

In between sides AB and BC is angle ABC = 82

In between sides DE and EF is angle DEF = 2x-6

Since AC > DF, this must mean angle ABC is larger than angle DEF. This is because the longer a side is, the larger the opposite angle will be.

Therefore, this leads to angle ABC > angle DEF

--------------------------------------------------

This is what the steps will look like

angle ABC > angle DEF

angle DEF < ABC

0 < angle DEF < angle ABC

0 < 2x-6 < 82

0+6 < 2x-6+6 < 82+6

6 < 2x < 88

6/2 < 2x/2 < 88/2

3 < x < 44

x is between 3 and 44, excluding both endpoints.

The rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground is 0.05 radians per second.

To find the rate of change of the angle of elevation of the balloon from the observer, we can use trigonometry. Let's denote the distance between the observer and the point directly below the balloon as 'x', the height of the balloon above the ground as 'h', and the angle of elevation as 'θ'.

Given:

Rate of change of the height of the balloon (h) = 3 meters/sec

Distance between the observer and the point directly below the balloon (x) = 30 meters

Height of the balloon above the ground (h) = 30 meters

To find the rate of change of the angle of elevation (dθ/dt), we need to determine the relationship between the variables x, h, and θ.

From the right triangle formed by the observer, the point below the balloon, and the balloon itself, we can write the following trigonometric relationship:

tan(θ) = h / x

To find the rate of change of the angle of elevation, we need to differentiate this equation with respect to time (t):

d/dt(tan(θ)) = d/dt(h / x)

Using the quotient rule, the left side becomes:

(sec^2(θ)) * (dθ/dt) = (1/x) * (dh/dt)

Now, let's substitute the given values:

sec^2(θ) = (h^2 + x^2) / x^2

dh/dt = 3 meters/sec

h = 30 meters

x = 30 meters

Plugging in these values and rearranging the equation, we can solve for dθ/dt:

(sec^2(θ)) * (dθ/dt) = (1/x) * (dh/dt)

(sec^2(θ)) * (dθ/dt) = (1/30) * (3)

(sec^2(θ)) * (dθ/dt) = 0.1

Since sec^2(θ) is always positive, we can divide both sides of the equation by sec^2(θ):

dθ/dt = 0.1 / sec^2(θ)

Now, we need to find the value of sec^2(θ) when the balloon is 30 meters above the ground. Let's denote this value as sec^2(θ_0).

In the right triangle, when the balloon is 30 meters above the ground, we have:

sec^2(θ_0) = (h^2 + x^2) / x^2

sec^2(θ_0) = (30^2 + 30^2) / 30^2

sec^2(θ_0) = (900 + 900) / 900

sec^2(θ_0) = 2

Now, we can substitute this value back into the equation for dθ/dt:

dθ/dt = 0.1 / sec^2(θ_0)

dθ/dt = 0.1 / 2

dθ/dt = 0.05

Therefore, the rate of change of the angle of elevation of the balloon from the observer when the balloon is 30 meters above the ground is 0.05 radians per second.

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It already is to the nearest cent. 25 cents.

Answer:

0

Step-by-step explanation:

Answer:l=p/2-w=198/2-3=96

Step-by-step explanation:yes

Answer: 3x-x+2=4

Step-by-step explanation:

12/X=3/6 CROSS MULTIPLY.

3X=12*6

3X=72 X=72/3 X= 24 FEET TALL.

Answer:

45

Step-by-step explanation: i know what im talking about :)

Problem 11

Work Shown:

P = 4x^2-x+1

Q = -6x^2+x-4

P+Q = sum of P and Q

P+Q = (4x^2-x+1)+(-6x^2+x-4)

P+Q = (4x^2-6x^2)+(-x+x)+(1-4)

P+Q = -2x^2+0x-3

P+Q = -2x^2 - 3

2*(P+Q) = twice the sum of P and Q

2*(P+Q) = 2*(-2x^2 - 3)

2*(P+Q) = 2(-2x^2) + 2(-3)

2*(P+Q) = -4x^2 - 6

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

Problem 12

Work Shown:

y = 3x^3 + x^2 - 5

z = x^2 - 12

2(y+z) = 2(3x^3 + x^2 - 5      +   x^2-12)

2(y+z) = 2(3x^3 + 2x^2 - 17)

2(y+z) = 2(3x^3) + 2(2x^2) + 2(-17)

2(y+z) = 6x^3 + 4x^2 - 34

Answer:

11. 3

12. 1

Step-by-step explanation:

11.

\((4x^2-x+1)+(-6x^2+x-4)\\4x^2-x+1-6x^2+x-4\\-2x^2-3\)

Double that

\((2)(-2x^2-3)\\-4x^4-6\)

----------------------------------------------------------

12.

\(y=3x^3+x^2-5\\z=x^2-12\)

\(2(y+z)\\2(3x^3+x^2-5+x^2-12)\\2(3x^3+2x^2-17)\\6x^3+4x^2-34\)

The function is increasing on the interval (-∞, 5/3), where it has a relative maximum at (5/3, 10/3). The function is decreasing on the interval (5/3, ∞).

Let's start by finding the first derivative of the function f(x)= x - 6x²+9x:

f'(x) = 1 - 12x + 9

Simplifying this expression, we get:

f'(x) = -6x + 10

Now, we need to find where f'(x) is equal to zero or undefined to determine where the function is increasing or decreasing. Setting f'(x) equal to zero, we get:

-6x + 10 = 0

Solving for x, we get:

x = 5/3

This tells us that the function has a critical point at x=5/3. To determine whether this is a relative maximum or minimum, we will use the first derivative test.

If f'(x) is positive to the left of x=5/3 and negative to the right of x=5/3, then the function has a relative maximum at x=5/3. If f'(x) is negative to the left of x=5/3 and positive to the right of x=5/3, then the function has a relative minimum at x=5/3.

Evaluating f'(x) for values less than and greater than 5/3, we get:

f'(-1) = 16 > 0, so f(x) is increasing on (-infinity, 5/3) f'(2) = -2 < 0, so f(x) is decreasing on (5/3, infinity)

Therefore, the function has a relative maximum at x=5/3. To find the y-coordinate of this point, we can plug x=5/3 into the original function:

f(5/3) = (5/3) - 6(5/3)² + 9(5/3) = 10/3

So the relative maximum is at (5/3, 10/3).

Next, we need to find the second derivative of the function to determine where it is concave up or concave down:

f''(x) = -6

Since f''(x) is a constant (-6), the function is concave down everywhere.

To find any inflection points, we need to set f''(x) equal to zero or undefined. However, since f''(x) is a constant, it is never zero or undefined, so there are no inflection points.

Now that we have all the necessary information, we can sketch the graph of the function f(x)= x - 6x²+9x.

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Step-by-step explanation:

making a the subject of the eqaution am=n+p we will have to divide both terms of the equation by m

\( \frac{am}{m} = \frac{n}{m} + \frac{p}{m} \\ a = \frac{n}{m} + \frac{p}{m} \)

Answer:

Chelsea has $48, Essence has $144

Step-by-step explanation:

Answer: You can see if the graphs of the two populations meet at a given point.

Step-by-step explanation:

If we have a graph of population vs time

such that y = population and x = time, two different populations will be exactly the same for a given time if we have an intersection of the two graphs. The value (x0, y0) where the graphs cross is the time = x0 and the population y0, this means that both populations have y0 individuals at the same time.

Answer:

Can I see the graph?

Step-by-step explanation:

The original price of milk is Rs. 14.

Let the original price of milk be Rs. x and the original quantity of milk purchased be y liters. After the rise, the new price of milk becomes 14.28% + 100% of the original price of milk i.e. (100% + 14.28%) = 114.28% of the original price of milk. Therefore, the new price of milk becomes (114.28/100)*x = 1.1428x. Now, due to the 14.28% rise in price, the milkman is able to purchase 20 liters less of milk for Rs. 5600. Using this information, let's set up an equation as follows:(x/y) - (1.1428x)/(y - 20) = 5600/y where the left-hand side of the equation represents the original cost of the milk minus the new cost of the milk after the price rise. The above equation can be simplified as follows:(x/y) - (1.1428x)/(y - 20) = (5600/y) * (y/(5600 + 20x)).After simplification, the equation becomes :x(y - 20) = (5600 + 20x)*y. Now,  substitute the values given in the question to get the original price of milk as follows: x(y - 20) = (5600 + 20x)*y x(y - 20) = 5600y + 20xy - 400xy = 5600yx - 20xy - 5600y = -400xy = (5600y)/(x - 20y) = 5600/400 = 14.

Original price=Rs14

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Answer:

25 feet x 18

Step-by-step explanation:

Answer:

x = 245

Step-by-step explanation:

In similar polygons the corresponding sides are in same proportion.

       \(\dfrac{x}{105}=\dfrac{98}{42}\)

           \(x =\dfrac{98}{42}*105\\\\\\x = 7 * 35\\\\x = 245\)

Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

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Carl deposited 10,000 into the savings account.

We can use the formula for compound interest to solve this problem:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A = the final amount

P = the initial principal (what Carl deposited)

r = the annual interest rate (8%)

n = the number of times interest is compounded per year (2 for semiannual compounding)

t = the number of years (1)

Plugging in the given values and solving for P:

\(10,816 = P(1 + 0.08/2)^{(2\times 1)}\)

\(10,816 = P(1.04)^2\)

10,816 = 1.0816P

P = 10,000

Therefore, Carl deposited 10,000 into the savings account.

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