What is the area of the triangle?
2
2
units2

Answer:

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

The limits of the function for this problem are given as follows:

In this problem, we are given the graph of the function, hence the limit is given by the value of the function as the function approaches x = a, not the actual numeric value of the function at x = a.

At x = -2, we have that:

As the lateral limits are equal, lim x -> -2 f(x) = 3.

At x = 1, we have that:

As the lateral limits are different, the lim x -> 1 f(x) does not exist.

At x = 4, we have that:

As the lateral limits are equal, lim x -> 4 f(x) = -3.

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Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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Answer: 16j^3+2

Step-by-step explanation:

Answer:84

Step-by-step explanation:

Answer:

84 hamburgers were sold

Answer:

Hey there!

If you mean, to the nearest ten,  this would be 84000.

Let me know if this helps :)

Answer:

84,000

Rounded to the nearest 10 or

the Tens Place.

The length of the hypotenuse is 10.61 yd.

We have,

The sum of the angles in a triangle = 180

Now,

Two angles are 45.

This means,

The side opposite to angle 45 are equal.

So,

a = c

And,

a = 7.5 yd

Now,

Applying the Pythagorean theorem.

b² = a² + c²

b² = 7.5² + 7.5²

b² = 112.5

b = √112.5

b = 10.61

Thus,

The length of the hypotenuse is 10.61 yd.

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As a result, -3/10 csc⁵-3x + C is the antiderivative of 9csc-3xcot-3x⋅ csc³-3x.

In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or an added to the initial, the derivative which is the previous function (indefinite integral).

9csc-3xcot-3x ⋅ csc³-3x = 9csc⁴-6x cot-3x

Then, we can use u-substitution, with u = csc-3x and du/dx = -3csc-3xcot-3x dx, as in the previous problem. We get:

∫9csc-3xcot-3x⋅ csc³-3x dx = -3/2 ∫u⁴ du

= -3/2 × u⁵ / 5 + C

= -3/10 csc⁵-3x + C

Therefore, the antiderivative of 9csc-3xcot-3x⋅ csc³-3x is -3/10 csc⁵-3x + C.

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\(y = ab^{x} \)

\(y = 3 \times {4}^{x} \)

"a" is the initial amount (3), and "b" is the growth factor (4).

To find "b" plug in the knowns into the exponential function equation and solve.

\(y = ab^{x} \)

\(48 = 3 \times {b}^{2} \)

\(16 = {b}^{2} \)

\( \sqrt{16} = b\)

\(b = 4\)

Answer:

A

Step-by-step explanation:

The answer is option (A) 8560. This combination cannot be the correct combination for your brother's lock because it contains the digit '6' in the same position as the correct combination (6348), but the other digits do not match.

Answer:

yes

Step-by-step explanation:

an expression is like an equation without the equal sign, or according to the Oxford Dictionary: "a collection of symbols that jointly express a quantity."

Answer:

Yes

Step-by-step explanation:

An expression is a collection of symbols that jointly express a quantity, which means a set of symbols that equals a number. a,b, and c are all variables, meaning that its a expression

Answer:

2.8

Step-by-step explanation:

Hey there!

Well to find the amount of minutes needed to fill a 46.2 gallon bathtub we’ll divide.

46.2 / 16.5

= 2.8

2.58 minutes

Hope this helps :)

Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

Answer:

The price before tip was 35

Step-by-step explanation:

Let x = original amount

x * 20% = 7

Change to decimal form

x * .20 = 7

Divide each side by .20

x*.20/.20 = 7/.20

x =35

Answer: 34,650 permutations

Answer:

16

Step-by-step explanation:22 minus 6 is 16

The final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Hugo began his science experiment with 22 grams of sugar crystals.

During the experiment, the change in the mass of the sugar crystals was – 6 grams.

Let x be the final mass of the sugar crystals.

The value of the x can be found using:

x = 22 - 6

x = 16 grams

Thus, the final mass of the sugar crystals is 16 grams if Hugo began his science experiment with 22 grams of sugar crystals.

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Answer:

M<E=T M<T=E

Step-by-step explanation:

As you can see in the trapezoid the show you only one two sides that are equals so that's mean that the angles are congruent each other.  

Answer:

\(m\angle E=118^{\circ},\: m\angle T=118^{\circ}\)

Step-by-step explanation:

As the diagram is marked, \(WE=WT\) and \(SE=ST\). Therefore, \(m\angle E=m\angle T\). Since the interior angles of all quadrilaterals add up to be \(360^{\circ}\), we can write the following equation:

\(29^{\circ}+95^{\circ}+m\angle E+m\angle T = 360^{\circ}\)

Subtract 29 and 95 from both sides to get \(m\angle E+m\angle T=236^{\circ}\).

As we found earlier, \(m\angle E=m\angle T\).

Therefore \(m\angle E=m\angle T=\frac{236}{2}=\fbox{$118^{\circ}$}\).

a) A function that gives the area of the playground (in square meters) in terms of x is A(x) = 60x - x².

b) The side length that gives the maximum area that the playground can have is x = 30 m.

c) The maximum area that the playground can have is 900 m².

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths, we have:

120 = 2(x + W)

60 = x + W

W = 60 - x

Therefore, the area of the rectangular playground (in terms of x) is given by this function;

A = LW

A(x) = x(60 - x)

A(x) = 60x - x²

Part b.

For the side length, we would take the first derivative of the area:

A(x) = 60x - x²

A'(x) = dA/dx

A'(x) = 60 - 2x

60 - 2x = 0

x = 60/2

x = 30 m

Part c.

W = 60 - x

W = 60 - 30

W = 30 m.

Therefore, the maximum area is given by;

A = 30 × 30

A = 900 m².

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Answer:

2 and 3

2+3 = 5

3-2 = 1

is the number

Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

The total amount of money you have is $81

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

Boxes = 27

Unit price = $3

If you have 27 boxes and each box is worth $3,

The total amount of money you have can be calculated by multiplying the number of boxes (27) by the value of each box ($3).

This can be expresses this using:

Total amount of money = 27 x $3 = $81

Hence, the total is $81

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Answer:

(a) 56%

(b) 28%

Step-by-step explanation:

Hope this helps! :)

Answer:

I think it is e

Step-by-step explanation:

Hope this is correct and hope this helps

Based on the information in the image, it can be inferred that the sides of the box measure 5 cm each.

To find the measure of the sides of the box we must carry out the following mathematical procedure:

As we know the volume of a cube is the equivalent to the length of its sides raised to the cube (raised to the 3). In this case, to identify the value of the sides we must find the cube root of the volume and the result is the length of the sides.

So this cube has a volume of 125cm³, so its sides would be the cube root of 125.

\(\sqrt[3]{125} = 5\)

According to the above, the length of the sides is 5 taking into account that all the sides are equal.

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The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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Answer:

hey there

The answer is 7/10

this is true because we have two green marbles and five blue

2+5=7

Step-by-step explanation:

Answer:

20% or 2/10

Step-by-step explanation:

10 marbles in total. We want to find the probability of not picking a green marble. 10marbles-3red-5blue=2marbles left.

So the probability of picking a green marble is 2/10 or 20%

Answer:69

Step-by-step explanation:

Because i am smart.

a) In April, the number of students who had not passed their driving test decreased by 5%.

b) The equation is 1.2x + 0.95(1000 - x) = 1000.

c) 200 students passed their driving test in January.

a) At the beginning, of January, x students had passed their driving test, then the remaining number of students who had not passed their driving test was (1000 - x).

In April, the number of students who had not passed their driving test decreased by 5%, which means the remaining number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

b)

The number of students who had passed their driving test increased by 20%, which means the new number of students who passed their driving test is 1.2 times the original number (x).

The number of students who had not passed their driving test decreased by 5%, which means the new number of students who had not passed their driving test is 0.95 times the original number (1000 - x).

Therefore, we can write the equation 1.2x + 0.95(1000 - x) = 1000.

c) We can solve for x in the equation 1.2x + 0.95(1000 - x) = 1000.

Expanding the equation, we get:

1.2x + 950 - 0.95x = 1000

0.25x = 50

x = 200

Therefore, 200 students passed their driving test in January.

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Answer: q1=11 q2=15 q3=20

Step-by-step explanation: