Find the area of a triangle with vertices at D(2,0), B(-1,0), and R(2,-7)

The area of the enlarged figure will be 327.68 square units

The scale factor will be the ratio of the similar sides of a rectangle.

For the given triangles, the required scale factors will be expressed as:

[tex]\frac{4}{8} =\frac{a}{25.6}\\\frac{1}{2} =\frac{a}{25.6}\\2a = 25.6\\a=\frac{25.6}{2} \\a=12.8[/tex]

Next is to get the area of the bigger rectangle:

[tex]Area = Length \times Width\\Area=a\times 25.6\\Area=12.8\times 25.6\\Area=327.68 units^2[/tex]

Hence the area of the enlarged figure will be 327.68 square units

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area of a circle = PI x r^2

r = 8.4/2 = 4.2

using 3.14 for PI

 area = 3.14 x 4.2^2 = 55.3896 square cm

 round answer as needed

When dividing 1 1/2 by 1/3, the quotient 4 1/2 indicates that each person receives half of a whole unit, which in our model is half of a pizza.

(a) To model the quotient 1 1/2 ÷ 1/3, imagine you have 1 1/2 units of something, like 1 1/2 pizzas. Now, if you divide each pizza into thirds, you'd have 3 halves of pizza. So, 1 1/2 pizzas divided by 1/3 pizza per person equals 4 people, each getting 1/2 of a pizza.

(b) The half in the quotient represents the portion of each whole unit (in this case, pizza) that each person receives. In our model, it signifies that each of the 4 people receives half of a pizza.

Answer:

Troy spent $9.09.

Step-by-step explanation:

Troy spent 20 Swiss Francs to stay one night in a youth hostel.

1 U.S. Dollar = 2.2 Swiss franc

We have to convert 20 Swiss franc to U.S. dollars.

So we divide 20 by 2.2 to convert Swiss franc to U.S. dollars.

= [tex]\frac{20}{2.2}[/tex] = 9.09090909 ≈ $9.09

Troy spent $9.09 to stay one night in a youth hostel.

Answer: The answer is [tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

Step-by-step explanation:  Given that

[tex]\sin \theta=\dfrac{3}{4}[/tex] and [tex]\theta[/tex] is in Quadrant I.

We are to find the value of [tex]\cos \theta.[/tex]

We have the following trigonometric identity :

[tex]\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\sin^2\theta}\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\dfrac{9}{16}}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{\dfrac{7}{16}}\\\\\\\Rightarrow \cos \theta=\pm\dfrac{\sqrt{7}}{4}.[/tex]

Since [tex]\theta[/tex] lies in the first quadrant, so cosine of [tex]\theta[/tex] will be positive.

Thus,

[tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

I hope you got the idea

The probability that the player will make next free throw is obtained as 0.795.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The total number of free throws is 220.

And, the number of throws by the player is 175.

Now, the probability can be found as below,

P(free throws) = Throws by the Player ÷ Total throws

⇒ 175 ÷ 220 = 0.795

Hence, the probability for the next free throw can be estimated as 0.795.

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To divide 0.6 by 0.0024 using long division, adjust the numbers to remove the decimals, becoming 6000 divided by 24. The result of this division is 250.

To solve the problem of long division, specifically for 0.6 ÷ 0.0024, you need to adjust both numbers to remove the decimal points before division. Start by shifting the decimal point in each number. In this case, shift the decimal for both numbers 4 places to the right, resulting in 6000 divided by 24.

So, it becomes a simpler division problem: 6000 ÷ 24. When you divide 6000 by 24, the result is 250.

Therefore, the result of 0.6 ÷ 0.0024 is 250.

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To make [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream. This calculation is done by multiplying [tex]\frac{2}{5}[/tex] cup (the amount required for a whole pie) by [tex]\frac{3}{4}[/tex].

To calculate the amount of cream needed for making [tex]\frac{3}{4}[/tex] of a nelly cream pie when the full pie requires [tex]\frac{2}{5}[/tex] cup of cream, we simply multiply these two fractions. To do this, first convert the mixed number [tex]\frac{3}{4}[/tex] to an improper fraction. We already have it in the proper format, so we can directly multiply:

([tex]\frac{2}{5}[/tex]) * ([tex]\frac{3}{4}[/tex]) = (2*3)÷(5*4)  = [tex]\frac{3}{10}[/tex]

Therefore, for [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream.

complete square = 100 square yards

 triangle = 1/2 x base x height = 1/2 x 10 x 5 = 25 square yards

100-25 = 75 square yards

shaded area = 75 square yards

the answer is x=9

i'm not good at showing my work, but I'm positive in my answer I'm an honors student.

Let us say that:

x = width of walkway

So the area is:

(12 + 2x) (15 + 2x) = 238

2x because we must add x on both sides of length and width

Expanding:

180 + 24x + 30x + 4x^2 = 238

4x^2 + 54x = 58

By completing the square:

x^2 + 13.5x + 45.5625 = 60.0625

(x + 6.75)^2 = 60.0625

x + 6.75 = ±7.75

x = -14.5, 1

Since dimension cannot be negative, therefore:

width = 1 ft

Final answer:

The width of the walkway around the garden is 3.87 ft.

Explanation:

The width of the walkway around the garden can be found by subtracting the area of the garden from the total area of the garden with the walkway.

place the equation for g ( x^2-5) over the equation for f(4x+1)

 so you get

x^2-5/4x+1

B is the answer

it is going to be 2 1/3