Please answer question 1 and 2.

Answer:

48 or 24

Step-by-step explanation:

Answer:

It goes

Equivalent

Not Equivalent

Not Equivalent

Equivalent

Step-by-step explanation:

For the first one: First, you distribute 5 to 3y to get 15y. Then, you distribute 5 to -4 to get -20. When combining you will get an equation of 15y-20

For the second one: First, you distribute -4 to -2p to get 8p. Then, you distribute -4 to -4 to get 16. When combining you will get an equation of 8p+16

For the third one: First, you distribute 3 to -7x to get -21x. Then, you distribute 3 to -13 to get -39. When combining you will get an equation of -21-39

For the fourth one: First, you distribute -6 to -4a to get 24a. Then, you distribute -6 to 8 to get -48. When combining you will get an equation of 24a-48

 f(t) = L^(-1){1 / (s^2 + s)} Inverse Laplace transform tables or techniques, determine the time-domain function f(t) that satisfies the given integral equation.

The Laplace transform is a powerful mathematical tool that can be used to solve complex integral equations, like the one you've provided: f(t) + t * ∫(t - τ)f(τ)dτ = t.

To solve this equation using the Laplace transform, follow these steps:

1. Apply the Laplace transform to both sides of the equation. The Laplace transform of f(t) is F(s), and the Laplace transform of t is 1/s^2. The integral equation becomes:

  L{f(t)} + L{t * ∫(t - τ)f(τ)dτ} = L{t}

  F(s) + L{t * ∫(t - τ)f(τ)dτ} = 1/s^2

2. Next, apply the convolution theorem to the integral term. The convolution theorem states that L{f(t) * g(t)} = F(s) * G(s). In this case, f(t) = t and g(t) = (t - τ)f(τ):

  F(s) + L{t} * L{(t - τ)f(τ)} = 1/s^2

3. Now, substitute the known Laplace transforms for t and f(t):

  F(s) + (1/s^2) * F(s) = 1/s^2

4. Combine the terms containing F(s):

  F(s) * (1 + 1/s^2) = 1/s^2

5. Isolate F(s) by dividing both sides of the equation by (1 + 1/s^2):

  F(s) = (1/s^2) / (1 + 1/s^2)

6. Simplify the expression for F(s):

  F(s) = 1 / (s^2 + s)

7. Finally, apply the inverse Laplace transform to F(s) to obtain the solution for f(t):

  f(t) = L^(-1){1 / (s^2 + s)}

Using inverse Laplace transform tables or techniques, you can determine the time-domain function f(t) that satisfies the given integral equation.

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Answer:

31 centimeters long for each edge

Step-by-step explanation:

Answer: X = 4

(4x-1) = (2x+7)

X = 4

Answer: D

Explanation: y = 5x + 8

PLz mark brainliest:)

Answer:

The magnitude of w is approximately 26.

The angle between w and u is approximately 32.2°.

Step-by-step explanation:

The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees and this can be determined by using the given data.

Given :

a) The magnitude of 'w' is calculated using the below formula:

\(w = \sqrt{u^2+v^2+2uvcos\theta }\)

Now, substitute the values of u, v, and \(\theta\) in the above formula.

\(w = \sqrt{14^2+16^2+2\times14\times16\;cos120 }\)

Simplify the above expression.

\(w =15.1\)

b) The angle between w and u is calculated using the below formula:

\(tan\beta =\dfrac{vsin120}{u+vcos120}\)

Now, substitute the above values of u and v in the above expression.

\(tan\beta =\dfrac{14\times sin120}{14+16\times cos120}\)

Simplify the above expression in order to determine the value of \(\beta\).

\(\beta = 62.67^\circ\)

The magnitude of w is approximately 15.1, and the angle between w and u is approximately 62.67 degrees.

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Answer:

x= 18

y =45

Step-by-step explanation:

first these two angles are supplementary and add up to 180 degrees:

(6x+7) + (4x-7) = 180

find x:

10x = 180

x = 18

substitute x = 18 for the angle (6x+7)

now we know what 6x +7 =

6 (18) + 7 = 115

since angle 3y-20 = 115, solve for y

3y = 135

y = 45

Answer:

x = 18

y = 45

Step-by-step explanation:

1. First off, we know that the angle (4x-7) degrees and (6x +7) are supplementary angles because of the corresponding angles theorem. So we do: (4x-7) + (6x+7) = 180 which should get you x=18.

2. Now that you know the value of x, finding y should be pretty easy. Plug in x for (6x + 7) and you should get 115 degrees.

3. We know that the angle with (6x +7) measurement is a vertical angle to (3y-20), so we can do 3y -20 = 115.

4. find the value of y, which should be 45

Answer:

12 1/9 \(\sqrt{3}\)

Step-by-step explanation:

Answer:

10.8

Step-by-step explanation:

AB can be calculated using the formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

The coordinates of A are when x = -2, y = -2

At B, x = 8, y = -6

Let,

\( A(-2, -2) = (x_1, y_1) \)

\( B(8, -6) = (x_2, y_2) \)

Plug the values into the formula.

\( AB = \sqrt{(8 - (-2))^2 + (-6 -(-2))^2} \)

\( AB = \sqrt{(8 + 2)^2 + (-6 + 2)^2} \)

\( AB = \sqrt{(10)^2 + (-4)^2} \)

\( AB = \sqrt{100 + 16} \)

\( AB = \sqrt{116} = 10.8 \) nearest tenth

Using the percentage , the number of people that picked vanilla cupcake is 7.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

Therefore, Keith brought chocolate and vanilla cupcakes to school for his birthday. 70 students decided to take a cupcake, and 10 percent of them picked vanilla.

The number of people that picked the vanilla can be calculated as follows:

number of people that picked cupcake = 10 percent of 70 student

Therefore,

number of people that picked cupcake = 10% of 70

number of people that picked cupcake = 10 / 100 × 70

number of people that picked cupcake = 700 / 100

number of people that picked cupcake = 7

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The given differential equation dP/dt = 1.4P(1 - P/6800) models the population P. To determine if the population is increasing or decreasing, we need to analyze the behavior of the equation.

The population is increasing when the derivative dP/dt is positive, and it is decreasing when the derivative is negative. We need to find the values of P for which the population is decreasing. To find when the population is decreasing, we need to determine the range of values for P that make the derivative dP/dt negative. By analyzing the equation dP/dt = 1.4P(1 - P/6800), we can see that dP/dt is negative when the term 1 - P/6800 is negative. Solving this inequality, we get P > 0 and P < 6800. Therefore, the population is decreasing when P is in the interval (0, 6800). This means that for values of P between 0 and 6800, the population is decreasing.

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Answer:

if your trying to find the area of the square it's 1024 if your trying to find the circumference of the circle it's 32π ( also known as 32 x pi)

Answer:

Step-by-step explanation:

\(7^{2} +x^{2} =24^{2} \\49+x^{2} =576\\x^{2} =418\\x=\sqrt{418}\)

The relative frequency for La'vonn rolling a 3 is 0.15 or 15%.

Relative frequency is a measure of how often an event occurs in relation to the total number of events. It is usually expressed as a decimal or percentage.

To find the relative frequency, you take the number of times a certain event occurs (in this case, rolling a 3) and divide it by the total number of events (rolling the die 100 times). This gives you the proportion of times the event occurred out of the total number of events.

relative frequency = 15/100 = 0.15 = 15%

Hence, the relative frequency for La'vonn rolling a 3 is 15/100 = 0.15 or 15%.

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Answer:

B 10

Step-by-step explanation:

Answer:

B. Yes; diagonals of a parallelogram bisect each other.

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram.

Answer: B. Yes; diagonals of a parallelogram bisect each other.

If AE=EC and BE=DE then quadrilateral ABCD is a parallelogram because  diagonals of parallelogram bisect each other.

A parallelogram is a 2 dimensional figure whose opposite sides are equal to each other and parallel to each other. Area of parallelogram is base*height.

To be parallelogram ΔAEB and ΔEDC should be congruent.

Angle AEB= Angle DEC

AE=EC

DE=EB

so both triangles are congruent by side, side, angle.

Similarly AE=EC , DE=EB and vertical angles AED= Vertical angle BEC.

Therefore triangle AED and BEC are congruent and that makes all their corresponding sides are also congruent.

And AB=DC.

Hence both pairs of opposite sides of a quadrilateral are congruent ,then the quadrilateral is a parallelogram.

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Ram has deposited Rs. 20000 in a bank and the rate of interest is 4% compounded annually; Ram will get back Rs. 21632 after 2 years.


In this case, the principal amount deposited by Ram in the bank is Rs. 20000. The rate of interest given is 4%, which is compounded annually. The time period for which the amount is deposited is 2 years. Now, we need to calculate the amount that Ram will get back after 2 years.

To calculate the amount, we can use the formula for compound interest, which is given as A = P(1 + r/n)^(n*t) where P = principal, amount r = rate of interest, n = number of times the interest is compounded per year, t = time period in years, A = amount after time period t. Putting the values in the formula, we get A = 20000(1 + 0.04/1)^(1*2)A = 20000(1.04)^2A = Rs. 21632. Therefore, Ram will get back Rs. 21632 after 2 years.

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The length of the base and the height of the triangle in feet are 16 feet and 6 feet respectively.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let b represent the base of the triangle and h is the height, hence:

b = 2h + 4       (1)

Also, the area of the triangle is 48 square feet:

48 = (1/2)bh

96 = bh

(2h + 4)h = 96

2h² + 4h - 96 = 0

h = 6

b = 2(6) + 4 = 16

The length of the base and the height of the triangle in feet are 16 feet and 6 feet respectively.

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The Pythagorean identity and the double and half angle identities indicates that we get;

cos(2·a) = 288/337

cos((1/2)·a) = √((676 - 25·√(674))/1348)

The Pythagorean identity for tangent indicates that we get; tan²a + 1 = sec²a

Therefore; sec²a = (7/25)² + 1 = 674/625

Which indicates that we get; cos²(a) = 625/674

The double angle identity for cosines, indicates;

cos(2·a) = 2·cos²(a) - 1 = 2 × (625/674) - 1 = 288/337

The half angle identity indicates that we get; cos(a/2) = ±√((1 + cos(a))/2)

sec²a = 625/674

cos²(a) = 625/674

cos(a) = √(625/674) = -25/√(674)

Therefore; cos(a/2) = ±√((1 + (-25/√(674)))/2) = √((674 - 25·√(674))/1348)

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Answer:

2 14/18

Step-by-step explanation:

because you just multiply the numerators and denomitors you must make an improper fraction first though

Answer:

72 miles.

Step-by-step explanation:

If he uses 6 gallons of gas, you would do 6 (gallons he used) x 12 (miles per gallon) equaling 72.

Answer:

0.37

the seven is in the hundredths place

Answer:

1   600334528/1000000000

Step-by-step explanation: i don't know if this is right but it should be

Answer:

I don't think it is a fraction

Step-by-step explanation:

I used my calculator and nothing happened!

Hope I helped!

But I might be wrong....

Answer:

Answer A

Step-by-step explanation:

The coefficients of the x terms are 1, 4 and 7.  Thus, the discriminant, b^2 - 4ac, is 16 - 4(1)(7) = -12 = -3·4.  Because the discriminant is negative we know that there are two unequal, complex roots.

                               -4 ± i√3√4         -2 ±i√3

The roots are x = --------------------- =

                                       2              

This is Answer A.

Answer:

41.16 m³

Step-by-step explanation:

1/2 ( 2.8 x 4.2) * 7 = 5.88

5.88 x 7 = 41.16

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

The correct answer is a. H0: u≥2 hours and H1:u<2 hours. When testing a right-tailed hypothesis using a significance level of 0.025, a sample size of n=13, and with the population standard deviation unknown, the critical value is as follows:

To determine the critical value, we need to use the t-distribution since the population standard deviation is unknown.

Using a t-distribution table or calculator with 12 degrees of freedom (n-1), a one-tailed test, and a significance level of 0.025, the critical value is 2.1604.

If the test statistic is greater than or equal to this value, we can reject the null hypothesis in favor of the alternative hypothesis, which is a right-tailed hypothesis.

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[1] H 2.4

    Let us turn the pictures into equations, using the key given. Then, we will solve.

x + x + \(\frac{1}{4}\)x + 1 + 1 + 1 = x + x + x + \(\frac{1}{2}\)x

2x + \(\frac{1}{4}\)x + 3 = 3x + \(\frac{1}{2}\)x

\(\frac{9}{4}\)x + 3 =  \(\frac{7}{2}\)x

3 = \(\frac{5}{4}\)x

x = 2.4

[2] J

    We can tell the first two options are incorrect because there was a change in size, not position.

    Option H would make the shape bigger, but it becomes larger. This means the answer is option J.