what is the radius of a circle with a circumference 31 m?

A) Consider the equation [tex]10x^2-3x-1=0[/tex]

We have to describe the solutions to this equation.

We will determine the radicand = [tex]b^2-4ac[/tex]

= [tex](-3)^2 - 4(10)(-1) = 9+ 40 = 49[/tex] which is greater than zero,

Therefore, the given equation ha real roots.

B) Consider the equation [tex]16x^2-2x-5=0[/tex]

We will use middle splitting term method to solve this equation.

[tex]16x^2+8x-10x-5 =0[/tex]

[tex]8x(2x+1) -5(2x+1)=0[/tex]

[tex](2x+1)(8x-5)=0[/tex]

So, [tex]2x+1=0[/tex]

[tex]x = \frac{-1}{2}[/tex] and [tex]x = \frac{5}{8}[/tex]

I chose this method, because this is more easier and takes less time.

The distance that a tortoise will cover in 6 hours is:

                        16.47735 feet.

It is given that :

A tortoise travels 11 feet in one hour.

In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.

[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]

which is equal to:

[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet[/tex]

                     Hence, the answer is:

                               16.47735 feet

In 100g of 15% sugar syrup, there is 15g of sugar.

Sugar syrup is a thick viscous liquid that mostly contains water and dissolved sugar in it. therefore, a 20% sugar syrup means having a 20:80 ratio of sugar and water in a unit of sugar syrup.

100g of sugar syrup 15% sugar,

Now, 15% of sugar means having a 15:85 ratio of sugar and water in 100g of sugar syrup. Let the sugar in 100g of sugar syrup be x. so, the water in the syrup is (100-x), therefore,

[tex]\bold{\dfrac{15}{85} = \dfrac{sugar}{water}}[/tex]

Substituing the values we get,

[tex]\dfrac{15}{85} = \dfrac{x}{100-x}\\\\15\times(100-x) = 85x\\1500 - 15x = 85x\\1500 = 85x +15x\\1500 = 100 x\\\\x = \dfrac{1500}{100}\\\\x = 15[/tex]

Hence, In 100g of 15% sugar syrup, there is 15g of sugar.

Learn more about sugar syrup:

https://brainly.com/question/7459847

Answer:no mode

Step-by-step explanation:

The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.

The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.

To calculate it:

Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.

Answer:

114 cm∧3

Step-by-step explanation:

V= area of base x height

1) calculate the area of the base with formula: 1/2 bh

   B=1/2 (8) (6)=24 then Multiply to get the area: Bh

2) (24) (6)= 144cm∧3

hope this helps.

Here, we need to find express 0.2444... as a fraction in simplest form.

Let the fraction be expressed as x

Now,

x = 0.2444....

Since, x is recurring in 1 decimal places, we multiply it by 10.

10x = 2.4444....

From left hand-side, x is subtracted and from 0.24444... from right hand side

10x - x = 2.4444.... - 0.24444....

So now,

9x = 2.2

x = [tex] \frac{2.2}{9} [/tex]

x = [tex] \frac{22}{90} [/tex]

x = [tex] \frac{11}{45} [/tex]

Thus, fraction as simplest form = [tex] \frac{11}{45} [/tex]

Answer: Quadrilateral fxyh is a trapezoid

Step-by-step explanation: Hi, the correct answer is trapezoid.

A trapezoid is a Quadrilateral ( a polygon with four sides) with a pair of opposite sides parallel. These parallel sides are called the bases of the trapezoid, and the other non-parallel sides are known as the "legs" of the trapezoid.

Feel free to ask for more if it´s necessary or if you did not understand something.

The 1258 cm³ is equal to 1.258 liters.

To convert 1258 cm³ to liters, you can use the fact that 1 liter is equal to 1000 cm³. Therefore, the conversion from cubic centimeters to liters is straightforward.

Identify the given volume: 1258 cm³.

Know the conversion factor: 1 liter = 1000 cm³.

Perform the conversion:

[tex]1258 \ cm^3 \times \left( \frac{1 \ liter}{1000 \ cm^3} \right) = 1.258 \ liters[/tex]

The length of the fence Matt needs is 26 ft.

To find the length of the fence, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the width of the garden is one side of the right triangle, the length of the garden is the other side, and the fence is the hypotenuse.

So, we can calculate the length of the fence as follows:

Length of the fence = √((Width)^2 + (Length)^2)

Substituting the given values, we get:

Length of the fence = √((10 ft)^2 + (24 ft)^2)

Length of the fence = √(100 ft^2 + 576 ft^2)

Length of the fence = √676 ft^2

Length of the fence = 26 ft

Final answer:

To calculate the length of fence needed for Matt's garden, the Pythagorean theorem is used, resulting in needing a fence that is 26 feet long.

Explanation:

Calculating the Fence Length Across a Rectangular Garden

Matt has a rectangular garden with dimensions of 10 feet in width and 24 feet in length. To find the length of the fence that Matt needs to build from one corner of the garden to the opposite corner, we will use the Pythagorean theorem, since the corners of the garden and the fence form a right triangle.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².

For Matt's garden, the length is 'a' = 24 ft and the width is 'b' = 10 ft. Plugging these values into the formula, we get:

c² = 24² + 10²

c² = 576 + 100

c² = 676

We then take the square root of both sides to solve for 'c':

c = √676

c = 26 ft

Therefore, Matt needs 26 feet of fence to reach from one corner of the garden to the opposite corner.

Answer:

It's 0.088.

Step-by-step explanation:

So the males who carpool is 9 right? Well relative frequency is the frequency divided by the total. So we must divide 9 by 102.

9÷102 = 0.088

Final answer:

To find the area of the floor not covered by the rug, calculate the total floor area (120 square feet), subtract the rug's area (58.5 square feet), resulting in 61.5 square feet of uncovered floor.

Explanation:

To find the area of the floor that is not covered by the area rug, we first need to calculate the area of the entire floor and then subtract the area of the rug.

The area of the floor is calculated by multiplying its length and width. So for a floor that measures 10 feet by 12 feet, the area is 10 feet × 12 feet = 120 square feet.

The area rug measures 6.5 feet by 9 feet, which means its area is 6.5 feet × 9 feet = 58.5 square feet.

Now, subtract the area of the rug from the area of the entire floor to find the part of the floor not covered by the rug:

120 square feet - 58.5 square feet = 61.5 square feet.

Therefore, the area of the floor not covered by the rug is 61.5 square feet.

The marked price of the shoes that Morgan bought at a 25% discount for $1000 is $1333.33. The calculation was done by dividing the discounted price by (1 minus the discount percentage in decimal form).

The question involves finding the marked price of an item given the discounted price and the discount percentage. Morgan paid $1000 for a pair of shoes after getting a 25% discount. To find the original marked price, we can use the formula:

Discounted Price = Marked Price × (1 - Discount Percentage)

Here, the Discounted Price is $1000, and the Discount Percentage is 25%, which is equivalent to 0.25 in decimal form.

By rearranging the formula to solve for the Marked Price, we get:

Marked Price = Discounted Price ÷ (1 - Discount Percentage)

Now we can calculate:

Marked Price = $1000 ÷ (1 - 0.25) = $1000 ÷ 0.75 = $1333.33

Therefore, the marked price of the shoes was $1333.33.