What is the slope of the line that passes through the points (1,-1) (-2,8)

Two scenarios that create right angle are 3 and 4.

In both the situations, Pythagoras theorem get satisfy with the sides which theorem is only applicable when there is right angle in the triangle.

Here's the explanation using 3 as an example :

From the statement we can assume that height of the window as the perpendicular(P) and distance from base(B) of the building to William as base of the triangle and line distance from Tom to William as hypotenuse(H) of the triangle.

Therefore, H = 130, B= 36.4 and P = 124.8

By Pythagoras theorem,

H² = P² + B²;

130² = 124.8² + 36.4²,

16900 = 15575.04 + 1324.96,

16900 = 16900

Hence satisfy the Pythagoras theorem, therefore triangle is right angle.

Similarly for the 4 statement.

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Check the picture below.

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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Answer:

Y=2/3x - 3

Gradient is 2/3

y=mx+c

Andrew made a mistake in Step 4 of his work. He incorrectly applied the associative property. To correct his work, Andrew should use the distributive property instead. Here's the correct step-by-step explanation:

Step 1: Start with the original problem: -4.5 + 4.2 + 5.6 - 7.3

Step 2: Apply the additive inverse to -7.3: -4.5 + 4.2 + 5.6 + (-7.3)

Step 3: Rearrange the terms using the commutative property: (-4.5 + 4.2) + 5.6 + (-7.3)

Step 4: Use the distributive property: -0.3 + 5.6 + (-7.3)

Step 5: Simplify the expression: -0.3 + 5.6 - 7.3 = -2

Andrew mistakenly used the associative property in Step 4 instead of the correct property, which is the distributive property. By correcting this mistake, the simplified expression is -2.

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Answer:

3/8

Step-by-step explanation:

Answer:

-5/2

Step-by-step explanation:

2x-10/4=3x

10/4=2x-3x

5/2=-x

x=-5/2

Answer:

\( = - 4 \times 2 + 4 \times ( - 4) + c \\ = - 8 - 16 + c \\ = 24 + c \\ \frac{ - c}{ - 1} = \frac{24}{ - 1} \\ c = - 24\)

Answer:

7 would be 56 in both boxes.

8 would be 75 in both of the boxes.

9 would be 3 in both of the boxes.

10 would be 60 in both of the boxes.

11 would be 62 in both boxes.

and 12 would be 5 in both boxes.

Step-by-step explanation:

If you need an explanation you can message me and I'll break it down for you

Answer:

The height of the triangle PQR is given by:

h = 4 + 8

h = 12 units

Now, the area of the triangle PQR is:

= 108 square units.

Step-by-step explanation:

The area of the triangle PQR is 108 square units

The given parameters are:

The area is then calculated using:

Area = 0.5 * base * height

So, we have:

Area = 0.5 * 18 * 12

Evaluate

Area = 108

Hence, the area of the triangle PQR is 108 square units

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Answer:

6

Step-by-step explanation:

3x-4=14

3x=14+4

3x=18

x=6

Answer:

x = 6

Step-by-step explanation:

\(x+(-4)+2x=14\\\\ \text{Distribute '+' into '-4' : }\\ x-4+2x=14\\\text{Combine Like Terms: }\\x+2x-4=14\\3x-4=14\\\text {Add 4 to Both Sides: }\\3x-4+4=14+4\\3x=18\\\text{Divide both sides by 3: }\\\frac{3x}{3}=\frac{18}{3}\\\huge\boxed{x=6}\)

Answer:

19/99

Step-by-step explanation:

Answer:

7.33

Step-by-step explanation:

Answer:

-4d - 6

Step-by-step explanation:

-1/3(12d+18)

-4d - 6

That is the simplest we can simple the function

So, the answer is -4d - 6

To find the maximum and minimum values of the function f(x, y) = exy subject to x^3 + y^3 = 54, we need to use the method of Lagrange multipliers.

Let's define g(x,y) = x^3 + y^3 - 54 as our constraint equation. Then, the Lagrangian function is:

L(x,y,λ) = exy + λ(x^3 + y^3 - 54)

Taking the partial derivatives with respect to x, y, and λ and setting them equal to 0, we get:

∂L/∂x = ey + 3λx^2 = 0
∂L/∂y = ex + 3λy^2 = 0
∂L/∂λ = x^3 + y^3 - 54 = 0

From the first two equations, we can solve for x and y in terms of λ:

x = (-ey/3λ)^(1/2)
y = (-ex/3λ)^(1/2)

Substituting these expressions into the third equation, we get:

(-ex/3λ)^(3/2) + (-ey/3λ)^(3/2) - 54 = 0

We can solve for λ in terms of e:

λ = e^(2/3)/(2*3^(1/3))

Substituting this back into the expressions for x and y, we get:

x = 3^(1/6)*e^(1/3)/y^(1/2)
y = 3^(1/6)*e^(1/3)/x^(1/2)

Now, we can find the critical points by setting the partial derivatives of f(x,y) = exy equal to 0:

∂f/∂x = ey(x) = 0
∂f/∂y = ex(y) = 0

From the expressions for x and y above, we see that x and y cannot be 0. Therefore, the only critical point is when e^(xy) = 0, which is not possible.

Thus, the function has no critical points in the interior of the region defined by the constraint equation. This means that the maximum and minimum values of the function must occur on the boundary of the region.

We can parametrize the boundary using polar coordinates:

x = 3^(1/3)cos(t)
y = 3^(1/3)sin(t)

Substituting these into f(x,y) = exy, we get:

f(t) = e^(3^(2/3)cos(t)sin(t))

To find the maximum and minimum values of f(t), we can take the derivative with respect to t and set it equal to 0:

f'(t) = 3^(2/3)e^(3^(2/3)cos(t)sin(t))(cos(2t) - sin(2t)) = 0

The solutions to this equation are t = π/4 and t = 5π/4.

Substituting these values back into f(t), we get:

f(π/4) = f(5π/4) = e^(3^(2/3))

Therefore, the maximum and minimum values of the function f(x,y) = exy subject to x^3 + y^3 = 54 are both e^(3^(2/3)).

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Answer:

16 shirts and 48 ties

Step-by-step explanation:

you start with 64 and divide it by 4 i got four cause it says that James had THREE times as many ties as shirts leaving him with leaving him with 3 groups of ties and 1 group of shirts   .  dividing 64 by 4 leaves you with 16 which is the amount of shirts he has and then you would multiply 16 by 3 to get the amount of ties he has.

Answer:

1 cart = 125

2 cart = 135

3 cart = 145

4 cart = 155

Step-by-step explanation:

Step-by-step explanation:

2(10)+2(x+4)

20 + 2x + 8

20 +8 +2x

28+2x

Answer:

Hello! answer: g = 37

Step-by-step explanation:

This is a complementary angle so it will add up to 90 degrees so we just simply have to do 90 - 53 to find the answer so... 90 - 53 = 37 so g = 37

Hope that helps!

Solving the operations:

Now we multiply by 100 to convert to percentage:

Therefore, oct-dec sales are 17.4% of the total sales.

The multimeter mode that records a measurement and displays the difference between that reading and subsequent readings is the "relative" or "delta" mode.

In relative or delta mode, the multimeter stores the initial reading as a reference point and then displays any subsequent readings as the difference between the current reading and the reference point. This mode is useful for taking measurements where the absolute value is less important than changes in the value over time, such as tracking the performance of a system or monitoring the effectiveness of a treatment. By using the delta mode, small changes in a measurement can be easily seen and tracked over time. It is important to note that this mode should not be used for measurements where the absolute value is critical, as any errors or drift in the initial reference point can lead to inaccurate results.

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Answer:

Step-by-step explanation:

Total amount with Gerald = $32

Cost of fuel per gallon = $2.75

Cost of each bottle of windshield = $3

38 miles per gallon. If Gerard must fill his car with enough fuel to drive 250 miles,

Total gallons of fuel = 250 miles / 38 miles

= 6.5789473684210 gallons

Total cost of fuel = Total gallons of fuel × cost per gallon

= 6.5789473684210 × $2.75

= $18.1

Amount left for windshield = Total amount with Gerald - Total cost of fuel

= $32 - $18.1

= $13.9

what is the maximum number of bottles of windshield washer fluid Gerard can buy?

= Amount left for windshield / Cost of each bottle of windshield

= $13.9 / $3

= 4.6333333333333 bottles

Maximum number of bottles =

4 bottles

Answer:

110x5019.2 is equal to 552169.2

Answer:

3 squares

Step-by-step explanation:

Firstly, you have to count the number of squares in the shape. As it can been seen from the diagram, there are a total 18 squares (i.e 6 squares on each row × 3 squares on each column).

Secondly you have to find 1/6 of the total number of the squares in the shape. 1/6 of the total number of the square in the shape = 1/6 × 18 = 3 squares

Therefore 3 squares would have to be shaded so that 1/6 of the shape is shaded

Answer:

1

Step-by-step explanation:

1 part

i m sorry my small brother wrote it

Answer:

multiply y x and 1 and then multiply y x and 3

Answer:

35 bagels

Step-by-step explanation:

Duh

The decimal approximation of √60, rounded to four decimal places, is 7.7450. Approximate the square root of 60 using the differential method. To do this, we will use linear approximation and the derivative of the square root function.

Let f(x) = x^(1/2), and we want to find f(60). Choose a nearby value of x that is easy to work with, such as x = 64, because f(64) = 8. Now, we will find the derivative of f(x) to determine the rate of change at x = 64.

f'(x) = (1/2)x^(-1/2)

Now, we'll find f'(64):
f'(64) = (1/2)(64)^(-1/2) = 1/16

Using the linear approximation formula, we have:
f(60) ≈ f(64) + f'(64)(60-64)
f(60) ≈ 8 + (1/16)(-4)
f(60) ≈ 8 - (1/4)
f(60) ≈ 7.75

So, the decimal approximation of √60, rounded to four decimal places, is 7.7450.

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When for the first time the United States imported more oil than it exported, Americans should have realized that an energy crisis was imminent and could happen in the future. (Option E: might be imminent).

Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.

Now,

Hence, Option E is the most accurate, i.e., When for the first time the United States imported more oil than it exported, Americans should have realized that an energy crisis was imminent and could happen in the future. (Option E: might be imminent).

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