Find the area of the circle (radius = 6)

The quadrilaterals have the following congruent angles: ∠ A ≅ ∠ W, ∠ B ≅ ∠ X, ∠ C ≅ ∠ Y, ∠ D ≅ ∠ Z.

Herein we find the case of two similar quadrilaterals, that is, two quadrilaterals that have four pairs of congruent angles and four pairs of proportional sides.

Thus, by direct observation, we have the following conclusions on congruence of angles and proportionality of sides:

Angles

∠ A ≅ ∠ W

∠ B ≅ ∠ X

∠ C ≅ ∠ Y

∠ D ≅ ∠ Z

Sides

AB / XW = BC / XY = CD / YZ = AD / WZ

To learn more on congruent angles: https://brainly.com/question/2789152

#SPJ1

The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

To know more about measurement visit:

brainly.com/question/4804936

#SPJ1

Answer:

s = 8 mi

Step-by-step explanation:

We know that the ratio of side lengths of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

     x       :    x√3     :        2x

We can apply this information to the given triangle. We know that the length of the short leg is 4 mi. This can be substituted for x:

x = 4 mi

We are trying to solve for s, which is the triangle's hypotenuse. So, we can apply the ratio to x.

s = 2x = 2(4 mi) = 8 mi

Answer:

2 cats and 2 dogs

Explanation:

Representations:

x = number of cats sold

y = number of dogs sold

Equations:

We know that it sells a total of 4 pets, so the sum of the number of cats and dogs is 4. So:

x + y = 4

On the other hand, they make $300, and they make $50 for each cat and $100 for each dog, so:

$50x + $100y = $300

So, the system of equation is:

x + y = 4

50x + 100y = 300

Graph:

Now, we need to graph the equations, so we need to identify two points for each equation:

For x + y = 4

If x = 0, then:

0 + y = 4

y = 4

If x = 4, then:

4 + y = 4

4 + y - 4 = 4 - 4

y = 0

For 50x + 100y = 300

If x = 0, then:

50(0) + 100y = 300

100y = 300

100y/100 = 300/100

y = 3

If x = 4, then:

50(4) + 100y = 300

200 + 100y = 300

200 + 100y - 200 = 300 - 200

100y = 100

100y/100 = 100/100

y = 1

Therefore, we have the points (0, 4) and (4, 0) to graph the line of the first equation and the points (0, 3) and (4, 1) to graph the line of the second equation.

So, the graph of the system is:

Therefore, the solution is the intersection point (2, 2), so they sold 2 cats and 2 dogs that day.

Answer:

Step-by-step explanation:

The thousand mark is the 4th number when going from right to left. So it would be the {6},976. When it comes to rounding, you go "5 and above, give it a shove, 4 and below, let it go. 6,976 rounded to the nearest thousand is 7,000,  3,983 rounded to the nearest thousand is 4,000,  13,560 rounded is 14,000.

7,000 + 4,000+ 14,000 = 25,000

Z (-7,-1)

When you rotate about the origin, the x and y just become negative :)

Answer:

Base rate: $120

Rate: $2 per person

Equation: f(x)=2x+120

Step-by-step explanation:

If 30 people cost $180 and 50 people cost $220, the charge for 20 extra people is $40.  This means, \(\frac{220-180dollars}{50-30people}=\frac{40dollars}{20people}=2\frac{dollars}{person}\).

These values correspond to a base rate for the bus of $120.

The function for the cost per bus with x number of people on it would be:

\(f(x)=2x+100\)

This can be checked by using the values given in the problem:

\(f(30)=2(30)+120=180\\f(50)=2(50)+120=220\)

The base rate of $120 and $2 per person satisfies the given equation and established values.

Answer:

He can buy 8 more apples because 16+6=22-30=8

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

By using the formula for the distance we will see that the correct option is B:

√52

We will use the general formula to find the distance between two points (a, b) and (c, d)

it is:

distance = √( (a - c)^2 + (b - d)^2)

Here we want to find the distance between the points (-2,-3) and (4,1), if we use the above formula we will get:

distance = √( (-2 - 4)^2 + (-3 - 1)^2) = √( 36 + 16)

distance = √52

The correct option is B.

Learn more about the distance between two points:

https://brainly.com/question/7243416

#SPJ1

Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

For more such questions on inference, click on:

https://brainly.com/question/25913650

#SPJ8

The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

Given that,

The expression is n²+2k³+3m².

We have to find how many terms are in the expression.

A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.

Take the expression,

n²+2k³+3m²

There are 3 terms

1st term n²

2nd term 2k³

3rd term 3m²

Therefore, The expression has 3 terms, that are

1st term n²

2nd term 2k³

3rd term 3m²

To learn more about expression visit: https://brainly.com/question/14083225

#SPJ1

We have the next system of equations

2x+3y=0 ...(1)

6x+9y=0 ...(2)

I order to solve this system by elimination we will multiply the first equation by -3

So we will have

-6x-9x=0

then we add the equation above with the second equation

-6x-9x=0

+6x+9y=0

As we can see we obtain 0=0 which means that we have infinity solutions

ANSWER

Infinity solutions

Answer:

8+f

Step-by-step explanation:

I'll help.

\( \frac{1}{3}x = 9 \frac{1}{2} \)

\(x = ?\)

↓

\( \frac{1}{3} x = \frac{19}{2} \)

\(x = \frac{57}{2} \)

"How it can be 57 ?"

The number 19 is multiplied by the number 3 at the bottom left.

19 × 3 = 57.

Answer:

I think it's C but I'm still thinking about this but it's C I think

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Given that,

f(x) = 2x² - 3x + 7

To find the value of f ( 2.5 ), replace x with 2.5 and solve the equation.

Let us solve it now.

f(2.5) = 2(2.5)² - 3×2.5 + 7

f(2.5) = 12.5 - 7.5 + 7

f(2.5) = 12

Answer:

\(f(x) = 2 {x}^{2} - 3x + 7 \\ f(2.5) = 2 {(2.5)}^{2} - 3(2.5) + 7 \\ f(2.5) = 12.5 - 7.5 + 7 \\ \boxed{f(2.5) = 12}\)

Answer:

According to the Pythagorean Theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So we have:

c^2 = a^2 + b^2

where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

Substituting the given values, we get:

c^2 = 14^2 + 48^2

c^2 = 196 + 2304

c^2 = 2500

Taking the square root of both sides, we get:

c = 50

Therefore, the length of the hypotenuse is 50 units.

Parent function is f(x) = 2ˣ. Graph of function f(x) = (1/2)2ˣ + 3 is attached below.

The exponential function contains an exponent. It has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function)

An exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.

Given exponential function,

f(x) = (1/2)2ˣ + 3

parent function

f(x) = 2ˣ

Putting x = 0

y = (1/2)2⁰ + 3

y = 7/2

point is (0, 7/2)

Putting x = 1

y = (1/2)2¹ + 3

y = 4

point is (1, 4)

Putting x = 2

y = (1/2)2² + 3

y = 5

point is (2, 5)

Graph of the function f(x) = (1/2)2ˣ + 3 can be drawn by plotting (0, 7/2), (1, 4) and (2, 5).

Hence, f(x) = 2ˣ is the parent function. Graph of the function f(x) = (1/2)2ˣ + 3 is attached below.

Learn more about exponential function here:

https://brainly.com/question/11487261

#SPJ1

Answer:

52+4? that's 56. the simplified version 4ft 6in

Step-by-step explanation:

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

Learn more on Intersecting secants theorem here: https://brainly.com/question/26340897

#SPJ1

Answer:

8.25

Step-by-step explanation:

first substitution

x=4 and y=7

square root(i dont have it) 4(x)7 + 9(x)4 =

square root 28+36 =

square root 64 =

8.246211251

round to 3 significant figure = 8.25

The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:18

Step-by-step explanation:

Answer:

B, you're correct

Step-by-step explanation:

1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6+1/6= 1 3/6 = 1 1/2

1+3/6= 1 1/2

A) adds up to 2.5, but the fraction model adds up to 1.5

C) adds up to 1, but the fraction model adds up to 1.5

D) adds up to 7/6, but the fraction model adds up to 1.5

The number of multiple-choice and short-answer questions on a test with 65 questions will be 40 and 25 respectively.

To determine the number of multiple-choice and short-answer questions on a test with 65 questions, we can set up a proportion based on the given ratio:

Multiple-choice questions : Short-answer questions = 8 : 5

Let x be the number of multiple-choice questions.

Let y be the number of short-answer questions.

Using the proportion, we can set up the following equation:

8/5 = x/y

8y = 5x

x = (8y)/5

Since the total number of questions on the test is 65, we have the equation:

x + y = 65

Substituting the expression for x from the previous equation:

(8y)/5 + y = 65

(8y + 5y)/5 = 65

13y/5 = 65

13y = 65 * 5

13y = 325

Dividing both sides by 13:

y = 325/13

y = 25

Substituting this value of y back into the equation x = (8y)/5:

x = (8 x 25)/5

x = 40

Therefore, there are 40 multiple-choice questions and 25 short-answer questions on the test with a total of 65 questions.

More on numerical problems can be found here: https://brainly.com/question/1774761

#SPJ1

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1