Turner is deep-sea diving with two friends. Janelle is floating on the surface 15 meters above
Turner, and Ethan is exploring a coral reef 8 meters in front of Turner. How far apart are
Janelle and Ethan?

Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed. Therefore, the correct answer is 200%.

Speed is a measure of how quickly an object or person moves from one point to another. It is usually expressed in terms of distance traveled over time, for example, miles per hour or kilometers per hour.

To calculate this, we need to find the time taken for her to reach her home if her speed is doubled.

If her initial speed is 40 km/hr, then by doubling her speed, she will be travelling at a speed of 80 km/hr.

By travelling at this speed, she can reach her home in half an hour i.e. 30 minutes.

Therefore, the time taken to reach her destination by doubling her speed is 30 minutes.

The time taken to reach her destination while travelling at her initial speed is 2 hours.

To calculate the percentage increase in speed, we have to find the ratio of the time taken to reach her destination when the speed is doubled to the time taken to reach her destination when the speed is not doubled.

Therefore, the percentage increase in speed

= (30/120) x 100

= 25%.

Since she needs to double her speed to reach her home in half an hour, the percentage increase in speed required is 100%.

To reach her home in half an hour, she needs to double her speed twice, which is equivalent to a 200% increase in speed.

Therefore, the correct answer is 200%.

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Answer: I think that the answer is 3/4 miles

Step-by-step explanation:

The absolute value equation  that have the give solution set is

|x  - 1/12|  =  5/12

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

x−b=c

1/2 - b =  c

-1/3 - b = c

only possible

if | 1/2 - b|  = | -1/3 - b|

1/2 - b = b + 1/3

=> 2b = 1/6

=> b = 1/12

We have

|x  - 1/12|  =  5/12

The absolute value equation  that have the give solution set is

|x  - 1/12|  =  5/12

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Answer:4

Step-by-step explanation:

2+2 is 4

are you speaking another language

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

\(V = w \cdot h \cdot l\)

Where:

\(w\) - Width, measured in meters.

\(h\) - Height, measured in meters.

\(l\) - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

\(\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l\)

Where \(\dot w\), \(\dot h\) and \(\dot l\) are the rates of change related to the width, height and length, measured in meters per second.

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the volume of the box is:

\(\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)\)

\(\dot V = 54\,\frac{m^{3}}{s}\)

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

\(A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

\(\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the surface area of the box is:

\(\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)\)

\(\dot A_{s} = 18\,\frac{m^{2}}{s}\)

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

\(r^{2} = w^{2}+h^{2}+l^{2}\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

\(2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l\)

\(r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l\)

\(\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the length of the diagonal of the box is:

\(\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}\)

\(\dot r = -1\,\frac{m}{s}\)

The rate of change of the length of the diagonal is -1 meters per second.

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10."

How to solve the question?

a. The set of natural odd numbers greater than 2, but less than 11 can be expressed using the roster method as {3, 5, 7, 9}. The set includes all the odd natural numbers between 2 and 11, excluding the endpoints, since 2 is not odd, and 11 is not less than 11.

b. The set {x|x (N and 4<x<10)} can be expressed using the roster method as {5, 6, 7, 8, 9}. The set includes all the natural numbers greater than 4 and less than 10, since x is a natural number (N) and satisfies the condition 4 < x < 10.

In set-builder notation, the same set can be expressed as {x|x (N and 4<x<10)}, which reads as "the set of all x such that x is a natural number and 4 < x < 10." The vertical bar separates the description of the elements of the set (the condition) from the set itself.

The roster method and set-builder notation are both ways of describing sets, but the roster method lists all the elements of a set, while the set-builder notation describes the properties or conditions that define the set. Both methods are useful in different situations and depend on the specific context and the purpose of the set description.

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Your complete question is :-

express each set using the roster method.

a. the set of the natural odd numbers greater than 2, but less than 11

b.{x|x (N and 4

Answer:

Step-by-step explanation:

What is 8/m - 11/3m=?

8/m - 113m =

(3 - 11/3)m + 8 =

8/3m + 8

Answer:

13/3m

Step-by-step explanation:

Step-by-step explanation:

xdjdirifkf

fkckfkrrmf

fmdkrkrmfofofk

fkfofkrorof

The digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number,

A rational number is a number that can be expressed as a ratio or fraction of two integers (a numerator and a non-zero denominator).

We can see that the next three digits in the decimal points are 6, 6 and 6, respectively. Therefore, the decimal equivalent of 22/6 is:

22/6 = 3.666666...

We notice that the digits after the decimal point repeat in a pattern of 6's. This is because 22/6 is a rational number, which means that its decimal representation either terminates (ends) or repeats in a pattern. In this case, it repeats in a pattern of 6's.

Each of the digits after the decimal point will be 6 because this number is a rational number and repeating decimal with a repeating digit of 6.

The difference between 40 and the product of these digits and 6 is always 4.

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The equation for the give graph is y = 1.5x and constant of proportionality is 1.5.

What is proportionality?

Proportionality is a mathematical relationship between two or more quantities that indicates that they are related by a constant factor or ratio. In other words, proportionality refers to the idea that two quantities vary in a consistent and predictable way with respect to each other.

Given : Y=kx

from the give graph, we can substitute values of x ad y to solve for k.

when x=2 ad y = 3,

3 = 2k

∴ k = 3/2 = 1.5

hence, we can complete the table :

x                   y

0                1.5 × 0 = 0

1                 1.5 × 1 = 1.5

2                1.5 × 2 = 3

3                1.5 × 3 = 4.5

4                1.5 × 4 = 6

hence, The equation for the give graph is y = 1.5x.

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The following information regarding a dependent variable (Y) and an independent variable (X) is provided in the following blanks in the image below.

A dependent variable is the variable that changes as a result of the independent variable manipulation. It's the outcome you're interested in measuring, and it “depends” on your independent variable. In statistics, dependent variables are also called: Response variables (they respond to a change in another variable) a) least square estimate of the Y intercept  =2 b)least squares estimate of the slope is =1 c)coefficient of determination is  1-SSE/SST =0.625 d)coefficient of correlation is =(0.625)1/2 =0.7906 e) MSE =SSE/(n-2) =6/(5-2) =2

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Answer:

abdul has 15

keiko has 22

bob has 45

Step-by-step explanation:

82= a+7+3a+a

75=a+3a+a

75=5a

15=a

15=abdul

15+7=keiko

3(15)=bob

Answer:

(a) 0
(b) 0
(c) 1
The function is not continous at x = 9

Step-by-step explanation:

To the left and right of the point x = 9, the graph would seem to continue at  f(x) = 0, however on the exact point x = 9 there is a hole in the graph allowing it to be equal to 1. Due to the hole in the graph, it is not continuous

Apologies if this is wrong its been a bit since I did calculus

The 10,100 cards will be necessary to build a 100-story card tower.

To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:

Triangular number = (n * (n + 1)) / 2

In this case, n represents the number of stories in the tower (100). Plug in the value for n:

Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050

Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:

Total cards = 5,050 * 2
Total cards = 10,100

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Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure

Answer:

\(25 {x}^{2} + 125x\)

The answer to all parts is shown below.

a. To combine the two chemicals, we need to add them together. Therefore, the rational expression for C(z) is:

C(z) = C₁(z) + C₂(z)

C₁(z) = z / (z + 1)

C₂(z) = 2 / (z - 3)

Combining the two chemicals, we have:

C(z) = C₁(z) + C₂(z)

= z / (z + 1) + 2 / (z - 3)

b. To find the simplified equation of V(x), we substitute the expressions for C(z) and H(x) into the formula:

V(x) = C(x) + C₂(x) H(x)

= (z / (z + 1) + 2 / (z - 3)) (x³ - x) / x

Simplifying further, we have:

V(x) = (z(x³ - x) + 2x (z - 3)) / ((z + 1) x)

c. To find the volume when a specific number of units are produced, we substitute the value into the equation V(x) and simplify.

Let's calculate the volume for 50, 100, and 1000 units:

For z = 50:

V(x) = (50 (x³ - x) + 2x (50 - 3)) / ((50 + 1) x)

For z = 100:

V(x) = (100 (x³ - x) + 2x (100 - 3)) / ((100 + 1) x)

For z = 1000:

V(x) = (1000 (x³- x) + 2x (1000 - 3)) / ((1000 + 1) x)

d. To find the number of units needed to achieve a volume of 3000 c³, we set V(x) equal to 3000 and solve for x:

3000 = (z (x³ - x) + 2x (z - 3)) / ((z + 1) x)

Solving this equation for x will give us the number of units needed to produce a volume of 3000 c³.

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The solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

What is a nonlinear system of equations?

A system of nonlinear equations is a system of two or more equations in two or more variables containing at least one equation that is not linear. Recall that a linear equation can take the form Ax+By+C=0. Any equation that cannot be written in this form is nonlinear.

There are different methods to solve nonlinear systems of equations, but one common way is to use substitution or elimination.

Using substitution:

We can substitute the equation Y^2=6-x into the second equation, to get:

X^2 + (6-x)^2 = 36

Expanding the square and simplifying, we get:

X^2 + 36 - 12x + x^2 = 36

Combining like terms, we get:

X^2 + x^2 - 12x + 36 = 0

Rearranging, we get:

(X^2 + x^2 - 12x) + 36 = 0

Factoring out (X^2 + x^2 - 12x) = 0

Solving for X^2 + x^2 - 12x = 0 using the quadratic formula, we get:

X = ±√(6x)

Substituting this back into the first equation, we get:

Y = ±√(6-x)

So the solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

This means that there are four possible solutions, represented by the four points:

(√6, √6)

(-√6, -√6)

(√6, -√6)

(-√6, √6)

Hence, the solution to the nonlinear system of equations is:

X = ±√(6x)

Y = ±√(6-x)

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Answer:

Ed had 5 books and each book had 100 pages and it takes him 50 mins to read each book how many books can he read in a day?

sorry if it's not good I try.

Step-by-step explanation:

First find the area of the square, then the triangle.

15 times 17 = 255 sq. yd

Triangle:

(5 times 5)/2 = 12.5 sq. yd

Your answer is 267.5 sq. yd

Hope this helps.

Answer:

  19 or 26

Step-by-step explanation:

You want the value of 3n² -8n -9, given that n(n -3) = 10.

We recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.

The value of 3n² -8n -9 will be one of ...

  (3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2

or

  (3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5

The expression 3n² -8n -9 will be either 19 or 26.

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Answer:

The answer is only 2 because even numbers are divisible by 2, also 2 is a prime number.

Answer:

12 feet

Step-by-step explanation:

1 inch= 8 feet

1/2 inch= 4 feet

1/4 inch= 2 feet

(2x2)/2= 2  (one triangle)

2x4=8 (rectangle)

2+2=4 +8=12

^2 was added 2 times cause there are 2 triangles

(you did not need a 3rd measurement cause the triangle measurements were equal)

The length of BD is 18.5 units.

In the given right triangle ABC, with altitude BD drawn to hypotenuse AC, we are given the lengths AD = 22 and DC = 15. We need to find the length of BD.

Let's consider triangle ABD. Since BD is the altitude, it divides the right triangle ABC into two smaller right triangles: ABD and CBD.

In triangle ABD, we have the following sides:

AB = AD = 22 (given)

BD = ?

Now, let's consider triangle CBD. In this triangle, we have the following sides:

BC = DC = 15 (given)

BD = ?

Since triangles ABD and CBD share the same base BD, and their heights are the same (BD), we can say that the areas of these triangles are equal.

The area of triangle ABD can be calculated as:

Area(ABD) = (1/2) * AB * BD

Similarly, the area of triangle CBD can be calculated as:

Area(CBD) = (1/2) * BC * BD

Since the areas of ABD and CBD are equal, we can equate their expressions:

(1/2) * AB * BD = (1/2) * BC * BD

We can cancel out the common factor (1/2) and solve for BD:

AB * BD = BC * BD

Dividing both sides of the equation by BD (assuming BD ≠ 0), we get:

AB = BC

In triangle ABC, the lengths AB and BC are equal, which implies that triangle ABC is an isosceles right triangle. In an isosceles right triangle, the leg's length are congruent, so AB = BC = AD = DC.

BD is equal to half of the hypotenuse AC:

BD = (1/2) * AC

Substituting the given values, we have:

BD = (1/2) * (AD + DC) = (1/2) * (22 + 15) = (1/2) * 37 = 18.5

Therefore, the length of BD is 18.5 units.

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Answer: The caret symbol (^) represents a power.

Step-by-step explanation:

In short, a power or an exponent indicates the number of times a number needs to be multiplied by itself. The caret can be used to represent a number that is to be used as an exponent.

For example, 5^2 is the same thing as \(5^2\). \(5^{2} =\) 5 x 5 = 25.

In the example you provided, 1200 x (1.0041666667) ^ 48, the caret means that you need to raise 1.0041666667 to the power of 48.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12