How many solutions does the system have?
O One solution at (0,-4)
O One solution at (-3,0)
O No solution
O Infinitely many solutions

The boat travels a distance of [tex](1/2k) ln(61/42)^2[/tex] in the first 2 minutes after its motor quits.

We can solve this problem using separation of variables. The differential equation that models the velocity of the boat is:

[tex]dv/dt = -kv^2[/tex]

To do this, we first need to separate the variables and integrate both sides:

[tex]1/v^2 dv = -k dt[/tex]

Integrating both sides, we get:

-1/v = kt + C

where C is the constant of integration. To find C, we can use the initial condition that the boat is moving at 83 ft/s when the motor quits:

-1/83 = k(1) + C

C = -1/83 + k

Now we can substitute C back into our equation:

-1/v = kt - 1/83 + k

Solving for v, we get:

v = 1 / (k(t - 1/83 + 1))

Now we can integrate v over the time interval [1, 121] to find the distance traveled by the boat:

d = ∫[1,121] v dt

Substituting v into the integral, we get:

d = ∫[1,121] 1 / (k(t - 1/83 + 1)) dt

We can simplify the integral by using the substitution u = t - 1/83 + 1:

d = ∫[84/83, 122/83] 1 / (ku) du

Now we can integrate this expression to get:

d = ln(u) / k |[84/83, 122/83]

d = ln(122/83) / k - ln(84/83) / k

d = (1/k) ln(122/83) - (1/k) ln(84/83)

We can simplify this expression using the fact that C = -1/83 + k:

d = (1/k) ln(122/83 / 84/83)

d = (1/k) ln(61/42)

Finally, we can plug in the initial condition k > 0 to get the distance traveled by the boat:

d = [tex](1/k) ln(61/42) = (1/2k) ln(61/42)^2[/tex]

d = [tex](1/2k) ln(61/42)^2[/tex]

Since we are not given the value of k, we cannot compute the exact numerical value of the distance traveled.

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The Cupcake Café’s recipe for cheesecake calls for 2/3 cup of cream cheese.42 cups of cream cheese does the café use to make 63 cheesecakes.

What is word problem?

A word problem is a mathematical problem or puzzle that is presented in the form of a written description or narrative, rather than as a simple equation or formula. It typically involves a scenario or situation that requires mathematical calculations or problem-solving skills to arrive at a solution. Word problems can be found in a variety of settings, including in math textbooks, standardized tests, and real-life situations. They often require the reader to identify and interpret relevant information, apply mathematical concepts and formulas, and use critical thinking skills to arrive at a correct answer.

To make 63 cheesecakes, the Cupcake Café would use:

(2/3 cup of cream cheese per cheesecake) x (63 cheesecakes)

= 42 cups of cream cheese.

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The distance that a person with a height of 6 feet can see is given as follows:

10.5 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

d = 1.75h.

For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:

d = 1.75 x 6

d = 10.5 feet.

The problem asks for the distance that a person with a height of 6 feet can see.

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The required true statements are B). BC = AD, D). ∠CAD = ∠LACB, E). ∠BPC = ∠APD

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.

The statements that must be true are:

B. BC = AD (Opposite sides of a parallelogram are equal in length)

D. ∠CAD = ∠LACB (Opposite angles of a parallelogram are equal in measure)

E. ∠BPC = ∠APD (Opposite angles of a parallelogram are equal in measure)

The statements A and C are not necessarily true for all parallelograms.

Statement A (AP = CP) is only true for parallelograms that are rectangles or rhombi, where the diagonals bisect each other.

Statement C (m∠ABC = 90) is only true for parallelograms that are rectangles or squares, where each angle is a right angle.

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We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To order the bonds from slowest growing to fastest growing, we need to compare their growth rates.

The first bond grows at a fixed rate of $50 per year, regardless of how long it is held.

So its growth rate is constant and does not change with time.

The second bond is worth $500 and grows at a fixed annual rate of 6%, so its value after one year will be:

Value after one year
= $500 + 0.06 x $500

= $530

After two years, its value will be:

Value after two years.

= $530 + 0.06 x $530

= $561.80

We can see that the second bond's growth rate is increasing over time since the increase in value each year is calculated as a percentage of the new value.

The third bond is worth $100 and grows at an annual rate of 4% that is applied continuously.

The formula for the value of a continuously compounded bond after t years  = $100 x e^(0.04t)

where e is the mathematical constant approximately equal to 2.718.

After one year,

The value of the third bond.

= $100 x e^(0.04 x 1) = $104.08

After two years,

Value after two years

= $100 x e^(0.04 x 2)

= $108.24

We can see that the growth rate of the third bond is also increasing over time because the interest is being compounded continuously.

Now,

We can order the bonds from slowest-growing to fastest-growing as:

First bond: fixed growth rate of $50 per year

Third bond: growth rate of 4% per year, compounded continuously

Second bond: growth rate of 6% per year, compounded annually

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Answer:

x = 3

Step-by-step explanation:

Take the first equation-  x + 2y = (-1)

Multiply both sides by 2

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

Add first and second equations

(2x + 4y = -2)

+(4x -4y = 20)
= 6x = 18

x = 18/6

x= 3

Extra info- This method is also called as Elimination method in which Elimination (whether by addition of equations or subtraction) of any variable is done.

Hope it helps

Step-by-step explanation:

solve like this.........

The equation -13x+12-(-13x+12)-13x+12 = -13x+12   is equivalent to the given expression that is -13x+12.

10x^2 - 23x + 12 = (5x - 3)(2x - 4) = 0

So the solutions to the equation are x = 3/5 or x = 2.

Therefore, this expression is not equivalent to -23x + 12 for all values of x.

10x^2 - 7x - 12 = 0 can be factored as (2x - 3)(5x + 4) = 0.

So the solutions to the equation are x = 3/2 or x = -4/5.

Therefore, this expression is not equivalent to -7x - 12 for all values of x.

-13x+12-(-13x+12)-13x+12  = -13x+12

-13x+12  = -13x+12

This expression is equivalent to -13x+12 .

7x^2 - 23x - 77 = (7x + 11)(x - 7) = 0

So the solutions to the equation are x = -11/7 or x = 7.

Therefore, this expression is not equivalent to -23x - 7 for all value x.

The given expressions of each case are not equivalent to the given equations for all values of x, except −13x+12-(-13x+12)-13x+12  = -13x+12 which is equivalent to -13x+12 .

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______The given question is incorrect, the correct question is given below:

An expression is given on equation

Which expression is equivalent to the given expression of each case

?

A

10x2−23x+1210x^2-23x+1210x = −23x+12

B

10x2−7x−1210x^2-7x-1210x = −7x−12

C

−13x+12-(-13x+12)-13x+12 = -13x+12

D

7x2−23x−77x^2-23x-77x = −23x−7

The perimeter of the rectangle is 36 cm.

A rectangle is a two-dimensional figure with length and width.

The area of a rectangle is Length x width.

We have,

Length = 10 cm

Width = 8 cm

Now,

The perimeter of the rectangle.

= 2 (length + width)

= 2 (10 + 8)

= 2 x 18

= 36 cm

Thus,

The perimeter of the rectangle is 36 cm.

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The complete question.

The length ad width of a  rectangle is 10 cm and 8 cm.

Find the perimeter of the rectangle.

a) 28

b) 12

c) 6.4

d) 36

Answer:

162

Step-by-step explanation:

Whether the zero is in the ones position or the tens position, there are only 9 possibilities for each of the other two digits and they can occur (with possible repetition) in either order. That’s 81 for each zero position for a total of 162.

There are 171 three-digit numbers that have exactly one zero. The zero can be in either the tens or units places, yielding 90 and 81 possibilities respectively.

To determine how many 3-digit numbers have exactly one zero, we need to consider the possible placements of the zero. A 3-digit number has three positions: the hundreds place, tens place, and units place. The zero cannot be in the hundreds place, as that would make it a 2-digit number. So, the zero can only have two possible positions: the tens or units place.

For each case:

So, in total, we have 90 + 81 = 171 3-digit numbers with exactly one zero.

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We can see here that with the information given, one can prove that this quadrilateral is a parallelogram. Thus, it is yes>

A polygon with four sides and four vertices (corners) is called a quadrilateral. Its internal angles add up to 360 degrees.

Squares, rectangles, parallelograms, trapezoids, and rhombuses are all examples of quadrilaterals.

We can see that looking at the quadrilateral, we can deduce that it is parallelogram. This is because the opposites sides are equal. Also, their opposite angles are equal.

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The expression that can be used to calculate the rate per second at which the machine launches the balls is a) Fraction 12 over 2.

To calculate the rate per second at which the machine launches the balls is:

First, we need to know the meaning of rate is: it is the amount of something per unit of time. In this case, we want to find the rate at which the machine launches the balls per second.

The fraction 12 over 2 represents the number of balls launched by the machine in 12 seconds. If we want to find the rate per second, we need to divide this number by the number of seconds.

12/ 2 = 6, so the machine launches 6 balls in 1 second.

Therefore, the rate per second at which the machine launches the balls is 6.

So, the expression that can be used to calculate the rate per second at which the machine launches the balls is Fraction 12 over 2, which simplifies to 6.

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The population of Toliver town reached a maximum of 200 by the mid - 1890s.

After the Civil War, people initially began settling in Toliver, a farming community two miles northwest of the Cushing site in northwestern Nacogdoches County. There was a post office created there in 1888, and by the middle of the 1890s, there were 200 people living there.

However, the community was bypassed when the Texas and New Orleans Railroad was built through the region in 1901, and the majority of its population and businesses went to the recently founded town of Cushing, on the rail line, and the town was abandoned a few years later.

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The full question is:

What was the population of Toliver town​ at it's height ?

first one is a

Step-by-step explanation:

The table to explain the equation will be:

x (minutes) y (altitude, in feet) Worked-out equation

0                          300                 -10x + 300 = 300

5                              250                   -10x + 300 = 250

8                         220                         -10x + 300 = 220

10                         200                   -10x + 300 = 200    

30                     0                         -10x + 300 = -0

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario

I used the equation y = -10x + 300 to find the altitude of the airplane for each x value.

The altitude after 5 minutes is 250 feet and 0 after 30 minutes.

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Answer:

Top box is 2

Middle box is 10

Bottom box is 18

Step-by-step explanation:

[tex]\frac{6}{9}[/tex] = [tex]\frac{x}{3}[/tex]

9 ÷ 3 = 3

6 ÷ 3 = 2

x = 2

[tex]\frac{6}{9}[/tex] = [tex]\frac{x}{15}[/tex]

9 x [tex]\frac{15}{9}[/tex] = 15

6 x [tex]\frac{15}{9}[/tex]  = 10

x = 10

[tex]\frac{6}{9}[/tex] = [tex]\frac{12}{x}[/tex]

6 x 2 = 12

9 x 2 = 18

x = 18

The probability that, if the car selected is older than two years old,  it is not a foreign car is 57/118, so the correct option is A.

We want to find the probability that if the car selected is older than two years old,  it is not a foreign car.

Looking at the table, we can see that there are 200 - 82= 118 cars older than two years.

And of these 118 cars, 25 + 10 + 26 = 61 are foreign cars.

Then the number of non-foreign cars is:

118 - 61 = 57

And the probability will be equal to the quotient between the number of non-foreigner cars and the total number:

P = 57/118

So the correct option is A.

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Answer:

89

Step-by-step explanation:

903 - 814 =

= (900 + 3) - (800 + 14) =

= 900 + 3 - 800 - 14 = 100 - 11 =

= 89

The number of boards Mr.Kazoo should buy is given by the equation A = 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of boards Mr.Kazoo should buy be A

The total length of the board = 40 inches

The length of each board = 7 inches

So , the number of boards = total length / length of each board

Substituting the values in the equation , we get

The number of boards A = 40 / 7

The number of boards A = 5.71

The number of boards A = 6 boards

Hence , the number of boards is 6

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Answer:

-5

Step-by-step explanation:

The expression for the composition of functions t and s, (t*s)(x), is obtained by substituting the output of s(x) into t(x). So,

(t*s)(x) = t(s(x)) = t(4x) = 3(4x) + 3 = 12x + 3.

The expression for the difference of functions t and s, (t - s)(x), is obtained by subtracting the output of s(x) from t(x). So,

(t - s)(x) = t(x) - s(x) = (3x + 3) - (4x) = -x + 3.

To evaluate (t + s)(-2), we need to add the outputs of t(-2) and s(-2).

t(-2) = 3(-2) + 3 = 3

s(-2) = 4(-2) = -8

So, (t + s)(-2) = t(-2) + s(-2) = 3 + (-8) = -5.

The approximate cost of 5-hour trip if the price of fuel is R78 per liter by finding the average speed is R3000.68.

To find the the total distance travelled by the car in 5 hours at an average speed of 100 km/h is:

Distance = Speed x Time

Distance = 100 km/h x 5 h

Distance = 500 km

The total amount of fuel consumed during the trip is:

Fuel consumed = Distance / Fuel efficiency

Fuel consumed = 500 km / 13 km/l

Fuel consumed = 38.46 liters (rounded to two decimal places)

The cost of the fuel consumed during the trip is:

Cost of fuel = Fuel consumed x Price per liter

Cost of fuel = 38.46 liters x R78/liter

Cost of fuel = R3000.68 (rounded to two decimal places)

Therefore, the approximate cost of the 5-hour trip is R3000.68, assuming that the only cost incurred is for the fuel consumed during the trip.

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Answer:

5

Step-by-step explanation:

  2 1/2

+ 2 1/2

1/2 and 1/2 makes a whole which is 1

so if you have 4 and and a whole which is 5

They can also be turned into decimals. 1/2 as a decimal is .5

so 2.5 plus 2.5 = 5

Answer:

Not equal and Congruent should be your answers

Answer:

A.   112 units^2

Step-by-step explanation:

64 + 32 + 12 + 4 = 112

The height of the tree is approximately 156.7 feet.

What is Trigonometry?

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

The height of the tree can be calculated using trigonometry.

Let's call the height of the tree "h".

Then, using the right triangle formed by the height of the tree, the distance from the base of the tree to where Jerome is standing, and the angle between the ground and the top of the tree, we can set up the following equation:

tan(33°) = h / 90

Solving for h, we get:

h = 90 * tan(33°)

Using a calculator to find the value of tan(33°), we get:

h = 90 * 1.730

h ≈ 156.7 feet

So, The height of the tree is approximately 156.7 feet.

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The value of x in the equation is 8 or -27

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex.

X^2/3 + X^1/3 -6 = 0

= X^1/3(2) + X^1/3 -6 = 0

represent X^1/3 by K

= K²+k-6 = 0

(K +3k )(-2k -6)= 0

k(3+k) -2(k+3) = 0

(k+3)(k-2) = 0

k+3 = 0

k -2 = 0

k = -3 or 2

since K = x^1/3

when k =-3

-3 = x^1/3

x = -3³ = -27

when k = 2

x = 2³ = 8

therefore the value of x is -27 or 8

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The option is: Parameters summarize data or relationships in the population and are usually estimated from a sample.

Parameters are numerical values that describe a population, and they are usually estimated from a sample. Parameters summarize important characteristics of the population, such as the mean, variance, or correlation between variables. These characteristics may vary across different entities in the population, such as individuals, households, or businesses.

In statistical analysis, parameters are important because they allow us to draw inferences about the population from a sample. By estimating parameters from a sample, we can make generalizations about the population and test hypotheses about relationships between variables.

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If the scale factor of figure A to figure B is 3:8, the value of x is 9.

We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -

3/8 = x/24

Applying the cross-multiplication rule, we get,

3 * 24 = 8 * x

Further solving for the value of x, we get,

x = (3 * 24) / 8

x = 9

Hence, the value of x is 9.

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The complete question is -

If the scale factor of figure A to figure B is 3:8 find the value of x.

Yes, both methods give the same result. The chain rule is used to differentiate a composite function, while the substitution method is used to differentiate a function after substituting a variable with its expression.

The chain rule is used to differentiate a composite function, which is a function of a function. To use the chain rule, we differentiate the inner function and multiply it by the derivative of the outer function. In this case, we would have

f(x) = ([tex]x^2 + 3x + 2[/tex]) and

g(x) = [tex]2x^3 + 5[/tex]

The derivative of f(x) would be 2x + 3 and the derivative of g(x) would be [tex]6x^2[/tex]. Taking the product of these two derivatives, we get

[tex]12x^3 + 18x^2[/tex],

which is the answer we get using the chain rule. The substitution method involves substituting a variable in a function with its expression. In this case, we substitute x with ([tex]x^2 + 3x + 2[/tex]). This gives us a new function that is a function of [tex]x^2 + 3x + 2[/tex]instead of x. We then differentiate this new function and the answer we get is the same as the one we got using the chain rule. Therefore, both methods give the same result and agree with each other.

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