helpppppppppppppppppppppp

Answer:

The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.

Step-by-step explanation:

Answer:

7m

Step-by-step explanation:

not sure if youre referring to that question! you didnt have a pic.

"Basically, from point A up to B is 4m and from B east to C is 3m."

a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:

b) The total cost of the purchase by Mrs. Singh is $58.50.

Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).

The unit cost of folders = $2.50

The unit cost of notebooks = $4.00

The number of folders bought = 9

The number of notebooks bought = 9

Let the number of folders bought = x

Let the number of notebooks bought = y

Folders: 2.50x

Notebooks: 4.00y

Folders: 2.50x = $22.50 ($2.50 x 9)

Notebooks: 4.00y = $36.00 ($4 x 9)

Total costs = $58.50

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Answer:

61

Step-by-step explanation:

Quick maths

Answer:

Step-by-step explanation:

DE = EF

DF = DE + DF

     = DE + DE

DF = 2DE

2DE = DF

DE = (1/2)DF

The Remainder when dividing f(x) by x - 3 is 840

The remainder when dividing the polynomial f(x) = 3x^5 + 4x^3 + 3 by the binomial x - 3, we can use the polynomial remainder theorem. According to the theorem, if we substitute the divisor, x - 3, into the polynomial f(x) and evaluate it at x = 3, the resulting value will be the remainder.

Let's calculate the remainder using this approach:

Substituting x = 3 into the polynomial f(x), we have:

f(3) = 3(3)^5 + 4(3)^3 + 3

    = 3(243) + 4(27) + 3

    = 729 + 108 + 3

    = 840

Therefore, when f(x) = 3x^5 + 4x^3 + 3 is divided by x - 3, the remainder is 840.

In summary, the remainder when dividing f(x) by x - 3 is 840.

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The value of x in the triangle is 10 units

From the question, we have the following parameters that can be used in our computation:

The triangle

On the triangle, we have the following equivalent ratio

x : 15 = 4 : 6

Express as fraction

So, we have

x/15 = 4/6

This gives

x = 15 * 4/6

Evaluate

x = 10

Hence, the value of x is 10

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Answer:

The starting height of the chairlift

Answer:

< S = 32

Step-by-step explanation:

< S = 180 - (< R + < T)

< R = < T

15x - 31 = 9x + 11

6x = 42

x = 7

< R = 74

< S = 180 - (74 + 74)

< S = 180 - 148

< S = 32

Answer:13 years,1 month, and 29 days

Step-by-step explanation:

The area of the third side of the triangle is either 20 square unit or 12 square units.

Triangle:

in math, triangle refers a simple closed curve made of three line segments and it has three vertices, three sides and three angles.

Given,

Two sides of a right triangle measure 2 units and 4  units.

And we need to find the area of the square that shares a side with the third side of the triangle  ​

Let us consider is  Two sides of a right triangle measure 2 units and 4  units.

Here if sides are perpendicular sides, then by using Pythagorean theorem

=> third side² = 2² + 4²

When we simplify this one, then we get,

=> third side² = 4 + 16

So, the  third side² = 20

Then the area of the square that shares a side with the third side of the triangle =  third side² = 20 sq units

Similarly, if 4  units is hypotenuse side, then by using Pythagorean theorem, the third side is calculated as,

=> third side² = 4² - 2²

And when we simplify this one, then we get,

=> third side² = 16 - 4

Therefore, the third side² = 12

And the area of the square that shares a side with the third side of the triangle =  third side² = 12 sq units

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Answer:

Step-by-step explanation:

\(1\)

The required   inverse function is:\($t = \frac{r - 1.13}{0.83}$$\)

A function that reverses the effects of another function is called an inverse function. When y=f(x) and x=g, a function g is the opposite of a function f.(y).

We are given the function that relates the fork length r to the total length t of a requiem shark as:

\($$r = 0.83t + 1.13$$\)

To find the inverse of this function, we need to solve for t in terms of r

We start by isolating t on one side of the equation:

\($r = 0.83t + 1.13$$\)

\($r - 1.13 = 0.83t$$\)

\($\frac{r - 1.13}{0.83} = t$$\)

So the inverse function is:

\($t = \frac{r - 1.13}{0.83}$$\)

Therefore, the inverse function is:

\($t = \frac{r - 1.13}{0.83}$$\)

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I believe its 35 but im thinking it can be 40 too

Answer: The probability is 1/4

Step-by-step explanation:

The odds of rolling a 1,2, or 3 on the first roll is 3/6 or 1/2.

The odds of rolling a 4,5, or 6 on the second roll is also 3/6 or 1/2

The odds all together is 1/4 because 1/2 divided by 1/2 is 1/4.

If I’m wrong tell me

Option C, y = e^(x+y) + x^2 + 3x - 2, requires the use of implicit differentiation to find dy/dx.

The expression that requires the use of implicit differentiation to find dy/dx is option C: y = e^(x+y) + x^2 + 3x - 2.

Implicit differentiation is a technique used to differentiate equations where the dependent variable y is not explicitly expressed as a function of x. It involves differentiating both sides of the equation with respect to x, treating y as an implicit function of x.

Let's apply implicit differentiation to option C:

Starting with the equation: y = e^(x+y) + x^2 + 3x - 2

To find dy/dx, we differentiate both sides of the equation with respect to x:

d/dx(y) = d/dx(e^(x+y) + x^2 + 3x - 2)

Using the chain rule on the right side of the equation, we get:

dy/dx = d/dx(e^(x+y)) + d/dx(x^2) + d/dx(3x) - d/dx(2)

The derivative of e^(x+y) with respect to x requires the use of implicit differentiation. We treat y as an implicit function of x and apply the chain rule:

d/dx(e^(x+y)) = e^(x+y) * (1 + dy/dx)

The derivatives of the remaining terms on the right side are straightforward:

d/dx(x^2) = 2x

d/dx(3x) = 3

d/dx(2) = 0

Substituting these derivatives back into the equation, we have:

dy/dx = e^(x+y) * (1 + dy/dx) + 2x + 3

Next, we isolate dy/dx on one side of the equation by moving the term involving dy/dx to the left side:

dy/dx - e^(x+y) * dy/dx = e^(x+y) + 2x + 3

Factoring out dy/dx, we get:

(1 - e^(x+y)) * dy/dx = e^(x+y) + 2x + 3

Finally, we solve for dy/dx:

dy/dx = (e^(x+y) + 2x + 3) / (1 - e^(x+y))

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Answer:

4/9

Step-by-step explanation:

I did the butterfly method to see which one is the bigger one

Answer:

4/9

Step-by-step explanation:

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

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All the condition for to show whether cost is proportional to area in the situation represented are shown below.

Since, we know that;

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y = kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin.

Now, We can Verify each case;

case 1) Sod that is quoted at a set price per square yard plus a labor fee

The Cost is NOT proportional to Area, because the line don't pass though the origin (the equation has an y-intercept equal to the labor fee)

case 2) Pavers that cost a set amount per square foot

The Cost is Proportional to Area

In this problem the constant of proportionality k is equal to the set amount per square feet

case 3) Hardwood flooring that cost $16 for every 2 square feet

The Cost is Proportional to Area

The constant of proportionality k is equal to

k = y/x

k = 16 / 2

k = 8

The linear equation is,

⇒ y = 8x

case 4) The given graph

Is a line that passes though the origin

So, The Cost is Proportional to Area

case 5) The given table

Find the constant of proportionality k for each ordered pair

If all values of k are the same, then the cost is proportional to area

For x=2, y=3,000

k = 3000/2

k = 1500

For x=4, y=4,000

k = 4000/4

k = 1000

For x=6, y=6,000

k = 6000 / 6

k = 1000

Thus, the values of k are different

Therefore, The Cost is NOT proportional to Area.

case 6) A concrete patio quoted at a bulk cost for 50 square feet

Not enough information.

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The line that passes through the given point and is parallel to the graph

y = -4x - 23.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Equation: y=-4x+3

As, we know that the slope of parallel line are same.

Now, using slope- intercept form

y = mx+ b

y = -4x+ b

Now, the line passes through (-4, -7).

So, y= -4x + b

-7 = -4(-4) + b

-7 = 16 + b

b = -23

So, the equation of parallel line is

y = -4x - 23

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\(m = \frac{y_2 - y_1}{x_2 - x_1} \)

Let these points

\( \begin{cases}(x_1, y_1) = ( - 4, - 1) \\ (x_2, y_2) = ( 2, 8) \end{cases}\)

\(m = \frac{8 - ( - 1)}{2 - ( - 4)} \\ m = \frac{8 + 1}{2 + 4} \Longrightarrow \frac{9}{6} \Longrightarrow \frac{3}{2} \\ m = \frac{3}{2} \)

\(y = mx + b \\ m = slope \\ b = y - intercept\)

Substitute the value of m in the equation.

\(y = \frac{3}{2} x + b\)

\((x_, y) = ( - 4, - 1)\)

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

\( - 1 = \frac{3}{ \cancel{2}} ( \cancel{ - 4}) + b\\ - 1 = 3( - 2) + b \\ - 1 = - 6 + b \\ - 1 + 6 = b \\ 5 = b\)

\(y = \frac{3}{2} x + 5\)

\( \large \boxed{y = \frac{3}{2} x + 5}\)

If you have any questions related to the answer, feel free to ask via comment.

Answer: 10

Step-by-step explanation:

Set the equal angles as x, as shown below.

Then, \(sin(x)=\frac{x+4}{8}\) and \(sin(x)=\frac{2x+1}{12}\). Set them equal to each other and solve for x:

\(\frac{x+4}{8} =\frac{2x+1}{12} \\ \\12(x+4)=8(2x+1)\\12x+48=16x+8\\48-8=16x-12x\\4x=40\\x=10\)

This is assuming those two triangles are right triangles. I'm actually not sure if they're right triangles.

Answer:

x=3

Step-by-step explanation:

so...

13=x²+4.

start by subtracting 4 from each side to get the numbers on one side.

13-4=, and 4-4=0

now, we just have 9=x².

to undo a square, one must square root. so,

\( \sqrt{9} = 3\)

and

\( \sqrt{x {}^{2} } = x\)

now, x=3.

Answer:

we have

x²+4=13[From the same external point, the tangent segments to a circle are equal.]

x²=13-4

x²=9

x²=3²

x=3

Answer:50.50

Step-by-step explanation:

Answer:

8) 4(n)+12

9) 21 + 4(m) + (2(m)+7)

10) 3 (S+21)

Step-by-step explanation:

I did this quickly, hopefully they are correct. May not be the same format as you wish (especially for 9)

Answer:$2800

Step-by-step explanation: Lets first figure out how much money a box of candy bars is worth. We know that each candy bar is worth $5 and that there are 7 candy bars per box. We can multiply 7*5 to figure out that each box is worth $35.

Now lets figure out how many boxes can be sold each day. Each student can sell two boxes a day. 5 students selling 2 boxes each is 5*2= 10 boxes total sold a day.

Now finally we use what we found to figure out the amount of money made per day. We know that there are 10 boxes being sold and that each box makes them $35. We just multiply 10 boxes by $35 to get $350 dollars each day.

Since they sell for 8 days we just multiply 8*$350 to get $2800.

Answer:

Refraise it please

Step-by-step explanation:

Step-by-step explanation:

3 x 2÷4y

3/2y

hope it helps ☺️