Two similar triangles, the perimeter of the first is 74cm and the side lengths of the other one are 4.5cm 6cm and 8 cm. Find the length of the longest side of the first triangle.

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

I think its 0.03 but I'm not a 100 percent sure

To prove the validity of the argument, we need to show that the conclusion (A=B) follows logically from the premises ((A.B)=C and (A.B)V-C).

To prove the validity of the argument (A.B) = C, (A.B) V-C /: A = B, we can use the following steps:

1. Assume that A ≠ B, and then use the distributive law of conjunction and disjunction to rewrite the premise as follows: (A.B) V (-A.-B) V C
2. Apply De Morgan's laws to simplify the above expression to: (-A V -B) V (A V -C) V (B V -C)
3. Use the distributive law of disjunction over conjunction to further simplify the expression to: (-A V -B V A V -C) V (-A V -B V B V -C)
4. Use the law of excluded middle to simplify the first part of the expression to: (-A V -C) V (-B V -C)
5. Apply the rule of inference known as disjunctive syllogism to conclude that: -C
6. Substitute -C into the original premise to obtain (A.B) V -(-C), which is equivalent to (A.B) V C
7. Use the distributive law of conjunction over disjunction to rewrite the above expression as follows: (A V C).(B V C)
8. Apply the rule of inference known as simplification to obtain A V C and B V C
9. Use the law of excluded middle to simplify the second part of the expression to: -C V B
10. Apply the rule of inference known as disjunctive syllogism to conclude that: A
11. Use a similar argument to show that B must also be true.
12. Therefore, we have shown that if (A.B) = C and (A.B) V-C, then A = B, which proves the validity of the argument.

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Answer:

i dnt know what you are asking for but if it is area it will be the area times 5/6

Step-by-step explanation:

The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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None of the statements a, b, c, or d can be determined to be true based solely on x ⇒ y and y ⇒ z.

Given that x ⇒ y and y ⇒ z, we can determine the valid implication between x and z.

To evaluate the possible truth values, let's consider the following cases:

If x is true and y is true:

Since x ⇒ y, the implication holds.

If y ⇒ z, the implication holds.

Therefore, z can be true in this case.

If x is true and y is false:

Since x ⇒ y, the implication does not hold.

The truth value of y ⇒ z is not relevant in this case.

Therefore, we cannot determine the truth value of z.

If x is false:

Since x ⇒ y, the implication holds vacuously, regardless of the truth value of y.

The truth value of y ⇒ z is not relevant in this case.

Therefore, we cannot determine the truth value of z.

Based on the above analysis, we cannot definitively conclude the truth value of z from the given information. Therefore, none of the statements a, b, c, or d can be determined to be true based solely on x ⇒ y and y ⇒ z.

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John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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Answer:

x = 4

Step-by-step explanation:

For this problem, we simply need to convert the words into the left hand side of the equation and solve for x:

The quantity of implies a grouping

x plus 20 is the quantity

And we want the quantity over 2 all equal to 3x:

( x + 20 ) / 2  = 3x

( x + 20 )  = 6x

20 = 5x

4 = x

And now we can check to see if x is correct by plugging back into the equation:

( x + 20 ) / 2 = 3x

( (4) + 20 ) / 2 ?= 3(4)

( 24 ) / 2 ?= 12

12 == 12

Therefore, we have shown the value of x to be equal to 4.

Cheers.

Answer:

x+20/2=3x.

6x=x+20.

6x-x=20.

5x=20.

x=4.

Answer:

9.75

Step-by-step explanation:

first we are going to subtract the bonus

142.25 -35 = 107.25

assuming that you are not takeing breaks you work a total of 11 hours (7+4)

so 11/107.25  = 9.75

so you would make 9.75 an hour before taxs

Therefore, the approximate value of the integral is 0.42 (rounded to the nearest hundredth).

To approximate the integral ∫ from 1 to 2 of √(1 + cos(x)) dx using a Left Riemann sum with 20 subintervals, we need to divide the interval [1, 2] into 20 equal subintervals.

The width of each subinterval, Δx, is given by:

Δx = (b - a) / n = (2 - 1) / 20 = 1/20 = 0.05

Now, we evaluate the function at the left endpoint of each subinterval and sum the areas of the rectangles formed by multiplying the function value by the width.

Approximation using Left Riemann sum:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ Σ[√(1 + cos(xᵢ)) Δx] for i = 0 to 19

where xᵢ = a + iΔx, and a = 1.

Calculating the approximation:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ Σ[√(1 + cos(1 + i*0.05)) * 0.05] for i = 0 to 19

Now, we calculate the sum by substituting the values:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ (√(1 + cos(1))*0.05) + (√(1 + cos(1.05))*0.05) + ... + (√(1 + cos(1.95))*0.05)

Evaluating this expression using a calculator or software, we get the approximation to the nearest hundredth:

∫ from 1 to 2 of √(1 + cos(x)) dx ≈ 0.42

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Answer:

38 × 38 is larger than 37 × 37 by 75!

The second cylindrical container with a base radius of 14 inches and height of 7 inches requires more metal.

For the first container with a base radius of 7 inches and height of 14 inches:

The area of each base is

= π x 7²

= 49π square inches.

and,  lateral surface area is

= 2π x 7 x 14

= 196π square inches.

So, total surface area = 2(49π) + 196π = 294π square inches.

For the second container with a base radius of 14 inches and height of 7 inches:

The area of each base is

= π x 14²

= 196π square inches.

and,  lateral surface area is

= 2π x 7 x 14

= 196π square inches.

So, total surface area = 2(196π) + 196π = 588π square inches.

Comparing the two surface areas, we can see that the second container requires more metal, as its surface area is greater.

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The maximum possible area of the rectangle is (9.005)^2 = 81.08 square units.

The maximum possible area of a rectangle that can be placed inside an isosceles triangle with base 9 and height 11 occurs when the rectangle is a square.

Let the base of the rectangle be x, then the height of the rectangle is (11/x)*x = 11. By the Pythagorean theorem, the length of each side of the isosceles triangle is sqrt(11^2 + (9/2)^2) = 11.704.

Since the rectangle is placed with one side on the base of the triangle, its diagonal is a hypotenuse of a right triangle with legs 11 and x. Using the Pythagorean theorem again, we have:

(x^2 + 11^2)^(1/2) <= 11.704

Solving for x, we get:

x <= 9.005

Therefore, the maximum possible area of the rectangle is (9.005)^2 = 81.08 square units.

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Answer: x ≈ 18 ft

Step-by-step explanation:

We will use our trig knowledge to solve this.

The man is standing 10 ft away, but we also need to add the 5 ft shadow as well as that is a point on our triangle.

We can set up a simple trig equation of: tan(50) = x/15

x being the height of the lamppost.

Now we solve.

tan(50) = 1.1918

1.1918 *15 = x

x = 17.876

Now round to the nearest foot.

x ≈ 18 ft

\(5 + n = 12 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

Answer:

No, only for right angle Δ

Step-by-step explanation:

It is only used for right angle triangles

Answer:

3$:4

Step-by-step explanation:

12/3= 4  9/3= 3

3$:4

The simplified value of the given expression 0 + (1/2)×(2. 219^2)*9. 81 is 24.143810005.

To simplify the expression, we can use the Order of Operations (PEMDAS): 1. Parentheses 2. Exponents 3. Multiplication 4. Division 5. Addition 6. Subtraction. Hence, to simplify the expression 0 + (1/2)×(2.219^2)*9.81, we need to follow the order of operations (PEMDAS).

1. The parentheses must be solved first: (2.219^2) = 4.924361

2. The exponents are solved next: there are none in this expression

3. The multiplication must be carried out next: 4.924361x9.81 = 48.30405741

4. The division is done next: (1/2)x48.30405741 = 24.143810005

5. The addition and subtraction are carried out last: 0 + 24.143810005 = 24.143810005

Therefore, the simplified expression is 24.143810005.

Note: The question is incomplete. The complete question probably is: Simplify the question 0 + (1/2)×(2. 219^2)*9. 81

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The correct answer is not listed in the answer choices provided.To find the total cost of the fence and the gate, we need to first calculate the perimeter of the rectangular garden. The perimeter is the sum of all four sides of the garden. We know that the garden is 18 feet wide and 27 feet long.

The two shorter sides (width) will have a length of 18 feet each, while the two longer sides (length) will have a length of 27 feet each. Therefore, the perimeter of the garden is:

Perimeter = 2(18) + 2(27) = 54 + 36 = 90 feet

However, we need to subtract the length of the gate from the width of the garden as the fence will not be installed in that area. The width of the garden after the gate is taken into account will be 18 - 3 = 15 feet.

Therefore, the perimeter of the garden with the gate included is:

Perimeter = 2(15) + 2(27) = 30 + 54 = 84 feet

Now, we can multiply the perimeter by the cost per foot of the fence to find the total cost of the fence:

Cost of fence = 84 x 43 = $3,612

Finally, we add the cost of the gate to the cost of the fence to find the total cost of the fence and gate:

Total cost = 3,612 + 128 = $3,740

Therefore, the correct answer is not listed in the answer choices provided.

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Answer:

hello your question has a missing diagram attached below is the missing diagram

answer :  

Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )

Step-by-step explanation:

when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between  the given circles and then construct a line through it

Answer:

Mark the point of intersection S of circles R and P, and construct line QS.

Step-by-step explanation:

This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points.  If your in FLVS, it would be in lesson 7.04.  I also got this right on my test.  Good luck!

Answer:

0,-24,-3/4

You have to substitute the values for x and y to get the other output. When I put 0 into the equations I get back 0

Given that:

Cost of the new plumbing fixtures = $160

Labor charge per hour = $50

Let x denotes the number of hours of labor. Then,

It represents the required relation.

The volume of the concrete piece is 1000 cubic inches.

What is the Volume?

Volume is a measure of the amount of space that an object occupies. It is a three-dimensional measurement that is typically expressed in cubic units.

The given diagram shows a rectangular concrete piece with dimensions 5 inches, 10 inches, and 20 inches. The volume of a rectangular prism can be calculated as:

V = l × w × h

Where "l" is the length, "w" is the width, and "h" is the height. So, for the concrete piece, the volume is:

V = 5 in. × 10 in. × 20 in. = 1000 cubic inches.

Hence, the volume of the concrete piece is 1000 cubic inches.

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The value of the integral is 4ln|x| - 4ln|x² + 7| + C.

To evaluate the integral ∫(x² - x + 28)/(x³ + 7x) dx, we can first decompose the rational function into partial fractions. Let's perform the partial fraction decomposition:

(x² - x + 28)/(x³ + 7x) = A/x + (Bx + C)/(x² + 7),

where A, B, and C are constants to be determined.

Multiplying both sides by (x³ + 7x), we have:

x² - x + 28 = A(x² + 7) + (Bx + C)x.

Expanding and collecting like terms, we get:

x² - x + 28 = Ax² + 7A + Bx² + Cx.

Comparing the coefficients of like powers of x, we have the following system of equations:

A + B = 1 (for the x² term)

C = -1 (for the x term)

7A = 28 (for the constant term)

From the last equation, we find A = 4. Substituting this into the first equation, we find B = -3. Finally, from the second equation, we find C = -1.

Therefore, the partial fraction decomposition is:

(x² - x + 28)/(x³ + 7x) = 4/x - (3x + 1)/(x² + 7).

Now, let's integrate each term separately:

∫(4/x - (3x + 1)/(x² + 7)) dx.

The integral of 4/x is 4ln|x|.

For the second term, we can perform a substitution u = x² + 7, du = 2x dx:

∫-(3x + 1)/(x² + 7) dx = ∫-(3x + 1)/u du.

This integral can be evaluated by using the natural logarithm:

-∫(3x + 1)/u du = -3∫(x/u) du - ∫(1/u) du = -3ln|u| - ln|u| + C = -4ln|u| + C.

Substituting back u = x² + 7, we have:

-4ln|x² + 7| + C.

Putting it all together, the integral becomes:

∫(x² - x + 28)/(x³ + 7x) dx = 4ln|x| - 4ln|x² + 7| + C.

Therefore, the value of the integral is 4ln|x| - 4ln|x² + 7| + C.

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Answer:

\(33\%, ~\dfrac 3{10},~0.32,~ \dfrac 13\)

Step-by-step explanation:

\(33\% <\dfrac 3{10}<0.32<\dfrac 13\)

Answer:

????

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

The whole line (DF) equals 9x - 39. So you need to make that equal to 47+3x+10 and work out like so. I hope this helps!

The word phrase for h + 6 is Six more h or the sum of six and h.

Converting algebraic expression to word phrase:

An algebraic expression is a mathematical phrase that uses variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Converting an algebraic expression to a word phrase means expressing the mathematical expression in words.

This can be useful in situations where mathematical symbols may not be understood or when communicating mathematical concepts to someone who may not be familiar with them.

Here we have the expression h + 6

Where 6 is added to h

Hence,

The word phrase for h + 6 is Six more h or the sum of six and h.

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