My son is 3/5 of my age. My daughter is 2/3
of my age. Altogether the sum of our ages is 136 years. How old am I?​

When a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

It's important to note that pressure increases as depth increases under water. The pressure in pounds per square foot, P, at a depth of d feet is given by the equation:

P = 0.433d + 14.7 where 0.433 is a constant for water, and 14.7 is the pressure at the surface.

In order to find the depth at which the pressure is 159 pounds per square foot, we need to solve the equation for

d.P = 0.433d + 14.7

Substitute P = 159 and solve for

d.159 = 0.433d + 14.7

Subtract 14.7 from both sides.

144.3 = 0.433d

Divide both sides by 0.433 to isolate d.

d ≈ 333.06

Hence, when a scientific team uses special equipment to measures the pressure under water and finds it to be 159 pounds per square foot, the depth is around 70 feet.

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False - division comes last

I'll show you the real steps.

4x + 5 = 25

~Subtract 5 to both sides

4x = 25

~Divide 4 to both sides

x = 6.25

Best of Luck!

Answer:

False

Step-by-step explanation:

Subtracting 5 is what starts the breaking down of the equation. It gets the answer correct. You could mess up trying to do otherwise

Answer:since X-W is 5 spaces and X-Y is also 5 spaces, the area would be 25. because area is equal to length x width

Step-by-step explanation:hope this helps brainliest

Stephanie did Step 3 wrong as instead of adding 10, she subtracted it.

We are given that Stephanie attempted to solve the equation 5 − 3 k = 2 ( k − 5 ).

5 - 3 k = 2 ( k - 5)

5 - 3 k = 2 k - 10

5 = 2 k + 3 k - 10

5 = 5 k - 10

5 + 10 = 5 k

15 = 5 k

15 / 5 = k

3 = k

We can see that she did Step 3 wrong as instead of adding 10, she subtracted it.

Therefore, she did Step 3 wrong as instead of adding 10, she subtracted it.

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We have solved the equation AB=BC for A, assuming that A, B, and C are square matrices and B is invertible, then the solution is A=C B⁻¹.

First, let's take a look at the equation AB=BC. This is an equation that involves matrices, which are essentially rectangular arrays of numbers. In this case, we have three matrices: A, B, and C. The equation tells us that the product of A and B is equal to the product of B and C.

Now, we want to solve this equation for A. This means that we want to isolate A on one side of the equation and have everything else on the other side. To do this, we can use matrix algebra.

One property of matrices is that we can multiply both sides of an equation by the inverse of a matrix without changing the solution. Since we know that B is invertible, we can multiply both sides of the equation by B⁻¹, the inverse of B:

AB B⁻¹ = BC B⁻¹

Now, we can simplify the left side of the equation, because B times its inverse gives us the identity matrix I:

A I = C B⁻¹

Again, we can simplify the left side of the equation, because anything multiplied by the identity matrix stays the same:

A = C B⁻¹

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Answer:

370.1

Step-by-step explanation:

i just got the answer

Answer:

254.94

Step-by-step explanation:

Answer:

253.94

Step-by-step explanation:

I added the whole numbers then added the decimals separate. After that I ad Dee we the decimals and the whole numbers and got 253.94.

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

y = -7x + 11

Explanation:

Just get y by itself. Subtract 7x from both sides. Substitute in each x value individually to get the next answers, which will be 25, 11, and -10.

The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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Answer:

Route A is 0.75 km longer than route B.

Step-by-step explanation:

Length of route A is 1.5 times the length of route B.

a = 1.5b

\(\frac{a}{b}=\frac{15}{10}\)

\(\frac{a}{b}=\frac{3}{2}\) --------(1)

Here, a = Length of route A

b = Length of route B

Length of route A is \(\frac{3}{4}\) of route C.

a = \(\frac{3}{4}c\)

\(\frac{a}{c}=\frac{3}{4}\) ------(2)

Here, c = Length of route C

Length of route C = 3 km

Length of route A = \(\frac{3}{4}\times 3\) [From equation (2)]

                             = 2.25 km

Length of route B = \(\frac{2}{3}\times 2.25\) [From equation (1)]

                             = 1.5 km

Difference in route A and route B = 2.25 - 1.5

                                                       = 0.75 km

Therefore, route A is 0.75 km longer than route B.

If Rudy successfully adds $50,000 to the value of his house, his new annual homeowner's insurance premium be c. $1,291.30.

The annual homeowner's insurance premium is the insurance charge that the homeowner pays as an insurance premium annually.

The insurance premium is calculated using some set formulas determined by these factors:

Insurance premium rate = $0.37 per $100

Current insurance premium = $1,106.30

Added value to the house = $50,000

Added premium = $185 ($50,000 x $0.37/$100)

New insurance premium = $1,291.30 ($1,106.30 + $185)

Thus, if Rudy successfully adds $50,000 to the value of his house, his new annual homeowner's insurance premium be c. $1,291.30.

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Answer:

it's C......................

Step-by-step explanation:

i got 100% on egde

Answer:

a=1/30

Step-by-step explanation:

6a+4a=1/3

10a=1/3

30a=1

a=1/30

1/30

is the anwser i think.i might be wront tho

Yes, it is true that if AB = BA and A is invertible, then \(A^{(-1)}B = BA^{(-1).\)

To prove this, we can start with the equation AB = BA and multiply both sides by \(A^{(-1)\) on the left. This gives:

\(A^{(-1)}AB = A^{(-1)BA\)

Simplifying the left-hand side using the associative property of matrix multiplication and the fact that \(A^{(-1)}A = I\) (the identity matrix), we get:

\(IB = A^{(-1)}BA\)

Simplifying the left-hand side further, we get:

\(B = A^{(-1)}BA\)

Now, we can multiply both sides of this equation by A on the right to obtain:

\(BA = AA^{(-1)BA\)

Using the fact that \(AA^{(-1) }= A^{(-1)}A = I\), we can simplify the right-hand side to get:

\(BA = A^{(-1)}B(AA^{(-1)})\)

Once again using the fact that \(AA^{(-1)} = A^{(-1)}A = I\), we get:

\(BA = A^{(-1)}B\)

Therefore, we can show that if AB = BA and A is invertible, then \(A^{(-1)}B = BA^{(-1).\)

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Answer:

The total cost of adding wallpaper to the room is 487.20

Answer:

The total cost of adding wallpaper to the room is $487.20

Step-by-step explanation:

Basically, how I got the answer is:

1. The shorter sides of the rectangle are 12 and the longer sides are 14.

2. The formula for a rectangle is A = l x w. The "l" means length and the "w" means width. 14 is the length and 12 is the width. So you should now have A = 14 x 12. If you multiply 14 by 12, you will get 168.

3. Since 1 square foot of carpet costs $2.90, then you should multiply by 168, which will give you $487.20 and that's pretty much it.

Hope this helps! :)

Answer:

25

Step-by-step explanation:

Step 1:

AC + BC = AB       Equation

Step 2:

18 + 7 = AB     Substitute

Answer:

25     Add

Hope This Helps :)

Answer:14

Step-by-step explanation: so if you add 21 and 264 and 20 u would get 14 hehehehhehehe im da best your not :)

ou'll notice its wings are just a blur to the human eye. ... If a bee hummingbird weighed 2 grams, about how many grams of liquid would it drink in a day?

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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Answer:

2m²

Step-by-step explanation:

Apply the prime factorization method: 2³m², 2 · 5m⁴

Find the greatest common divisor: 2m²

Answer: 2m²

Answer: ₹400

Step-by-step explanation:

The interest is 10% of ₹20,000 which is;

= 10% * 20,000

= ₹2,000

It is to be awarded to 5 scholarships of equal value. Each scholarship is there valued at;

= 2,000/5

= ₹400

Jake is presently \(0\) years old and the year is \(2036\), which is not a relevant response or there may be some missing details in the question.

A span of time that is equivalent to one year on the Calender but starts at a different period. A cycle of 365 and 366 day split into twelve month starting in January and ending in December.

Every monthly on the calender has four complete weeks since every month has at least 28 days. A few month have a few more days, but these extra days don't add up to a full week, therefore they aren't counted.

Let's first find the current year, given that the year in which their ages will sum up to \(16x\) is\(2036\).

\(2036 - (y - 2036) = 2*2036 - y\)

Simplifying this expression, we get:

\(2*2036 - y = 4072 - y\)

\(2y = 4072\)

\(y = 2036\)

Now, let's find Jake's current age by subtracting his birth year from the current year \(y - (2036 - 7x)\)

Since their ages sum up to 16x in 2036, we have:

\(x + 7x = 16x\)

\(8x = 16x\)

\(x = 0\)

This means that Jake is currently \(0\) years old, which is not a meaningful answer.

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To measure out 16 scoops of flour using the 1/2 cup measuring cup to get the correct amount of flour for the recipe.

One real problem involving the multiplication of two mixed numbers whose product is about 14 could be:

A recipe calls for 1 and 3/4 cups of flour, but you only have 1/2 cup measuring cup. How many scoops of flour do you need to measure out in order to get the correct amount of flour for the recipe?

To solve this problem, we need to multiply the two mixed numbers:

1 and 3/4 * x/2 = 14

First, we convert the mixed number 1 and 3/4 to an improper fraction:

1 and 3/4 = 7/4

Next, we solve for x:

(7/4) * (x/2) = 14

Multiplying both sides by 2 gives:

(7/4) * x = 28

Dividing both sides by 7/4 gives:

x = 16

Therefore, we need to measure out 16 scoops of flour using the 1/2 cup measuring cup to get the correct amount of flour for the recipe.

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Answer: First option, “22”

Step-by-step explanation:

Answer:

300

Step-by-step explanation:

the way to find perimeter is to add the numbers that are on the outside of the shape.

Answer: 300m

Step-by-step explanation: To find the Perimeter of the triangle or any shape, you need to add the length of the outside!

In this case, it is 104, 58, 138. Add all of them together you get 300m

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The amount of the remittance from ABC is $1,960.

The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.

Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.

To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.

In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.

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The equation 61 * 61 * 61 = (** 61 *)^2 can be replaced with 0 through 9 in various ways for the decimal equation to be correct.

In this equation, we have three instances of the number 61 being multiplied together on the left-hand side, and on the right-hand side, we have a square of a number that contains two unknown digits. We need to determine the values of these unknown digits (represented by the stars) by replacing them with digits from 0 to 9, such that the equation holds true.

To find the possible combinations, we can start by calculating the left-hand side of the equation. 61 * 61 * 61 equals 226,981. Now, we need to find two-digit numbers whose square is equal to 226,981. By taking the square root of 226,981, we find that it is approximately 476.383.

Since the square of the number on the right-hand side should be equal to 226,981, the two digits represented by the stars must be 7 and 6 in some order. Therefore, the equation can be written as 61 * 61 * 61 = (7*61 + 6)^2 or as 61 * 61 * 61 = (6*61 + 7)^2, depending on the order of the digits.

By replacing the stars with 7 and 6 in either order, we find a valid solution for the equation. It is important to note that there might be other combinations that satisfy the equation as well, but the specific values of the stars being 7 and 6 are valid options.

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The value of arcsin(1) is 90° and the value of arctan√3 is 60°

From the question, we are to determine the values of arcsin(1) and arctan√3. That is, sin⁻¹ (1) and tan⁻¹(√3)

NOTE:

If sin x° = y, then sin⁻¹ y = x°

If cos x° = y, then cos⁻¹ y = x°

If tan x° = y, then tan⁻¹ y = x°

From the trigonometry table of values, we have that

sin 90° = 1

∴ sin⁻¹ (1) = 90°

arcsin(1) = 90°

Alos, from the trigonometry table of values, we have that

tan 60° =  √3

∴ tan⁻¹(√3) = 60°

arctan√3 = 60°

Hence, the value of arcsin(1) is 90° and the value of arctan√3 is 60°

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The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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