what does coplanar mean

area of larger triangle = 1/2 x 5 x (6+4+2) =30 square mm

 area of non shaded triangle = 1/2 x 3 x 4 = 6 square mm

 area of shaded area = 30-6 = 24 square mm

any angle in a square = 90 degrees

so C=1/2x-5 has to equal 90

90=1/2x-5

95 = 1/2x

190=x

check (1/2)190-5 = 90

 x = 190

Answer:

The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400

Step-by-step explanation:

Let's suppose,

X: Number of guests

C (x) = total cost

CF (x) = fixed cost

CV (x) = variable cost

C (x) = CV (x) + CF (x)

For the situation presented,

CF (x) = 100

CV (x) = 15x

With this information, the function that provides the total cost is given by the expression:

C (x) = 15x + 100.

When there are 20 guests, the total cost of the banquet is:

C (20) = 15 (20) + 100 = 300 + 100 = 400

Conclusion: The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400

Answer:

a. 22 students per class

Step-by-step explanation:

22 students (times) 4 classes = 88 students.

Answer:

39 3/5

Step-by-step explanation:

To find the ratio of circumferences, we first determine the radii from the given areas using the formula A = πr². Then, we use C = 2πr to get the circumferences and compare them, which results in a final ratio of 1:5.

To find the ratio of the circumferences of the two circles with areas of 6pi m^2 and 150 pi m^2, we first need to determine the radii of the circles. The area of a circle (A) is given by the formula A = πr². Solving for the radius (r) gives us r = √(A/π).

For the first circle:
A = 6π m²
So the radius is r1 = √(6π/π)r1 = √6 m

For the second circle:
A = 150π m²
So the radius is r2 = √(150π/π)r2 = √150 m

Now we can find the circumferences using the formula C = 2πr.

For the first circle:
C1 = 2π√6 m

For the second circle:
C2 = 2π√150 m

Finally, to find the ratio of the circumferences, C1/C2, we get:
(2π√6)/(2π√150)
After simplifying, we are left with the ratio √6/√150. This simplifies to √(6/150) which is √(1/25) or 1/√25. And since √25 is 5, we have a final ratio of 1:5.

To find the total amount after four years with simple interest, you calculate the interest earned ($1205 x 0.025 x 4 = $120.50) and then add it to the principal ($1205 + $120.50 = $1325.50).

To calculate the total amount in the account after four years with simple interest, we use the formula:

Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)

For the given scenario:

We first calculate the simple interest earned:

SI = $1205 x 0.025 x 4 = $120.50

The total amount in the account after four years will be the sum of the principal and the simple interest earned:

Total Amount = Principal + Simple Interest

Total Amount = $1205 + $120.50 = $1325.50

Final answer:

The problem involves simple arithmetic and algebra to work out the relationship between ages at different times. Jill was twice as old as Jack 1 year ago. The other parts of the problems are under-determined or have errors that prevent firm conclusions.

Explanation:

Let's solve each problem step by step:

How many years ago was Jill twice as old as Jack? Let's call the number of years ago y. Jill's age y years ago = 9 - y, and Jack's age y years ago = 5 - y. The equation based on the problem is 9 - y = 2(5 - y). Solving this equation, y = 1. So, Jill was twice as old as Jack 1 year ago.

When Jack is three quarters as old as Jill, how old will Jill be? Let's call Jill's future age f. Jack's future age will be 3/4 * f. We know Jack is currently 5 years old, so 5 + x = 3/4(f + x), where x is the number of years till that happens. To find the value of f and x, we need one more equation or piece of information, which is not provided.

When Jill was three times as old as Jack, how old was Jack? To find this out, we set up an equation similar to the first problem: let's call the number of years ago z. So (9 - z) = 3(5 - z), solving for z gives us z = 4.5, but since they can't be half years old, we must consider whole years; thus, this situation hasn't occurred given their current ages or an error exists in the problem.

When Jill is four times as old as Jack is today, how old will Jack be? Jack is currently 5. So, when Jill is four times that age, she will be 5 * 4 = 20 years old. We cannot determine how old Jack will be at that time without knowing the difference in time between now and then.

Answer:

$22.75

Step-by-step explanation:

35% of 65 dollars is $22.75

Answer:

Multiply the fraction by StartFraction 5 over 5 EndFraction to get a denominator of 100 and then write the numerator as hundredths using a decimal point.

Step-by-step explanation:

sorry im 3 years late but help me out by giving brainliest.

The question seeks the derivatives of a function, but cannot be answered accurately due to the lack of specific information about the function provided.

The question asks to find the first, second, and third derivatives of a given function f(x). However, further details needed to answer the question, such as the specific form of the function f(x), are not provided in the question itself. Therefore, without the explicit function f(x), we cannot proceed to accurately calculate the requested derivatives.

there are 5 letters

1st letter can be any 5

2nd letter can be any 5 -1 = 4

3rd letter can be any 5 -2 = 3

5*4*3 = 60 different combinations

Answer:

The correct option is 3. The total number of different ways to answer a multiple choice test is 243.

Step-by-step explanation:

Total number of questions is 5. Each question has three options.

Total number of ways to answer the first question is 3.

Similarly, the number of ways to answer each question is 3.

Total number ways to answer a multiple choice test is

[tex]3\times 3\times 3\times 3\times 3=3^5=243[/tex]

Therefore the correct option is 3. The total number of different ways to answer a multiple choice  test is 243.

Final answer:

The radical expression ⅓∛5 simplifies to 2/3 × cubed root of 5, and cannot be simplified further since 5 is a prime number.

Explanation:

To combine and simplify the given radical expression, 2 over 3 times cubed root of 5, we first understand that the expression is in the form ⅓∛5, which can also be written as ⅓(5¹³). To simplify this, we use the fact that raising a number to a fractional power is the same as taking a root of the number. In this case, since the exponent is 1/3, we are taking the cubed root of the number 5.

Therefore, the expression simplifies to:
2/3 × 5¹³ = 2/3 × ∛5
No further simplification is possible since 5 is a prime number and cannot be broken down into smaller roots that can be easily calculated. The final simplified form of the expression remains 2/3 × ∛5.

Final answer:

To combine and simplify the expression 2/3 * 5^(1/3), rewrite 5^(1/3) as the cube root of 5 and multiply it by 2/3. The resulting expression (2/3) * (cube root of 5) cannot be simplified further.

Explanation:

To combine and simplify the expression 2/3 * 5^(1/3):

We can rewrite 5^(1/3) as the cube root of 5.

Multiplying 2/3 by the cube root of 5 gives us (2/3) * (cube root of 5).

Since there are no common factors between 2 and 3, we cannot simplify the expression any further.

Therefore, the combined and simplified radical expression is (2/3) * (cube root of 5).

Final answer:

To find the value of x in the given ellipse equation centered at (4.619, 5.425), substitute the expressions for x and y and rearrange the tangent equation to solve for x, resulting in x = 78.5.

Explanation:

To find the value of x, you are given the information related to the center and the major axis of the ellipse. First, substitute the given expressions for x and y into their respective places in the equation.

Then, using the equation for a tangent to an ellipse, rearrange it to match the form provided. This rearranged equation will give you the needed value of x.

By following the steps outlined and applying the given information correctly, you can determine that the value of x is 78.5.

Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.

Let's solve this problem using a system of equations.

Let's use the variables x, y, and z to represent the number of 1 cent stamps, 32 cent stamps, and 33 cent stamps respectively that Mildred bought. We can write the following equations based on the information given:

x + y + z = 2180  (since the total cost was $21.80)

x = z + 50  (since the number of 1 cent stamps exceed the number of 33 cent stamps by 50)

y = 2z - 10  (since the number of 32 cent stamps was 10 less than twice the number of 33 cents stamps)

Let's solve this system of equations:

After solving the system of equations, we find that Mildred bought 480 1 cent stamps, 410 32 cent stamps, and 520 33 cent stamps.