To find the length of the diagonal of a square garden, you can use the Pythagorean theorem. In this case, the length of the diagonal is approximately 14.14 meters.
Explanation:To find the length of the diagonal of a square garden, we can use the Pythagorean theorem. The Pythagorean theorem 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 two shorter sides of the right triangle are the sides of the square garden. Let's call each side x. The hypotenuse (the diagonal) will be the side we are trying to find.
Using the Pythagorean theorem, we have: x^2 + x^2 = diagonal^2. Since the area of the square garden is 200 m², we can set up the equation: x^2 + x^2 = 200. Combining like terms, we get: 2x^2 = 200. Dividing both sides by 2, we have x^2 = 100. Taking the square root of both sides, we find that x = 10.
Therefore, each side of the square garden is 10 meters. And using the Pythagorean theorem one more time, we can find the length of the diagonal: diagonal^2 = 10^2 + 10^2. Simplifying, we get diagonal^2 = 200. Taking the square root of both sides, we find that the length of the diagonal is approximately 14.14 meters.
which situation involving raul's Bank account would be modeled by a positive number?
A.Raul deposited his paycheck.
B.Raul wrote a check to his grandmother
C.Raul withdrew cash from an ATM
D.Raul paid for groceries with his debit card.
positive means add
so it would be a deposit into the account
so A is the correct answer
the question is............
given that (6 3) is on the graph of f(x) find the corresponding point for the function f(-1/2x)
Answer:
this answer is wrong on plato, trust me
Step-by-step explanation:
We need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
To find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x), we need to substitute the x-coordinate of (6, 3) into the function -1/2x and determine the resulting y-coordinate.
Given that (6, 3) is on the graph of f(x), it means that f(6) = 3.
Now let's substitute -1/2x into the function:
f(-1/2x) = f(-1/2 * 6) = f(-3)
Therefore, we need to find the corresponding y-coordinate for x = -3. Unfortunately, since we don't have additional information about the function f(x), we cannot determine the value of f(-3) and provide the corresponding point.
In summary, without more information about the function f(x), we cannot find the corresponding point for the function f(-1/2x) when (6, 3) is on the graph of f(x).
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How can I do this with the function (x+2)/x-3
Create a rational function with a linear binomial in both the numerator and denominator.
Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and intercepts.
Part 2. Show all work to identify the vertical asymptote, the x-intercepts, and the y-intercept.
A right triangle has a side with length 12 in and a hypotenuse with length 20 in. find the length of the second leg (in inches). (round to the nearest hundredth if needed)
Solve 3x2 + 2x + 7 = 0. Round solutions to the nearest hundredth. (5 points)
x ≈ −1.90 and x ≈ 1.23
x ≈ −1.23 and x ≈ 1.90
x ≈ −0.44 and x ≈ −3.56
No real solutions
Answer:
The answer is No Solutions Look Below
Step-by-step explanation:
If tan y = 3 over y and cos x = y over z what is the value of sin x??
A. sin x = 3/z
B. sin x = 3y
C. sin x = z/3
D. sin x = 3z
Answer: (A) sin x° = 3/z
Step-by-step explanation: i couldnt find it anywhere else but i figured it out and dont worry i got it right on the quiz
Show that the equation is not an identity by finding a value of x for which both sides are defined but not equal. cos x - cos x sinx = cos3 x
Answer:
The answer is pi/4
Step-by-step explanation:
You substitute each x for "pi/4", you will see that the equation is incorrect, the two values are no longer equal.
The equation is not an identity. Value of x = nπ, where n∈I , I → set of integers, for which both sides are defined but not equal.
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
We have the equation,
cos x - (cos x) (sin x) = cos³x
Simplifying,
cos x [ 1 - (sin x) ] = cos²x (cos x)
1 - sinx = cos²x
1 - sinx = 1 - sin²x
1 - sinx = 1² - sin²x
1 - sinx = (1 - sinx)(1 +sinx)
1 = 1 + sinx
sinx = 0
x = nπ, where n∈I , I → set of integers.
It is not an identity equation.
cos x - (cos x) (sin x) ≠ cos³x
Therefore, both sides are defined but not equal.
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Find the value of cos θ for the angle shown. A line is drawn from the origin through the point four comma negative square root of thirty-three. The angle theta is given as the measurement from the positive x axis counterclockwise to the line.
cos θ = seven-fourthsAnswer
Cos θ = 4/7
Explanation
The angle θ is in the 3rd quadrant. So, it is positive.
cos θ = adjacent / hypotenuse
hypotenuse = √(4² + (√33)²)
= √(16 + 33)
= √47
= 7
Cos θ = 4/7
Answer:
Step-by-step explanation:
cos 0= 4/7
reason: i took the test
The gold leaf on your necklace is 0.000045 of an inch thick. How do you write 0.000045 in scientific notation?
a hot air balloon holds 3,249 cubic meters kf helium. the density of the helium is 0.1785 kilograms per cubic meter. how many kilograms of helium does the balloon contain, round to the nearest tenth of a kilogram?
equations that look different but have the same solution are said to be
a. equivalent
b. expressions
c. equals
d. similar
e. radical
How many different 1010-letter permutations can be formed from 88 identical h's and two identical t's?
The sum of three numbers is 91 . the third number is 2 times the first. the first number is 9 more than the second. what are the numbers?
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
In a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N. Which must be true?
A) N||L
B) N||P
C) L||O
D) P||L
Answer:
The correct answer is option B) N || P
Step-by-step explanation:
N || P.
As it is given, in a plane, line N is parallel to line O, Line O is parallel to P, and line L is perpendicular to line N.
Since, N is parallel to O, and O is parallel to P, then N must be parallel to P.
So, option B is correct.
Sarah decides to take her six-year-old son to the circus the price for the child ticket is $4.75 dollars Less in the price for the adult ticket if you represent their price for the child ticket using the variable X how would you write the algebraic expression for an adult ticket price?
Let f(x) = 2x − 6. Solve f−1(x) when x = 2. (1 point) explanation please! algebra 2 makes no sense to me!
Charmaine pays $848 for landscaping rocks for a project. The cost per pound is 32 cents. How many pounds did she purchase?
Answer:
D
Step-by-step explanation:
if a circle is inscribed in a triangle, the center of the circle is called the _____ of the triangle.
A. radius
B. incenter
C. circumcenter
Answer:
The correct answer to the following question will be Option B (Incenter).
Step-by-step explanation:
The middle of the circle which is carved in a triangle is the triangle incenter, the point where the triangle angle bisectors cross.
There are following steps to construct an inscribed circle in a triangle are as follows:
Step 1: Create the incenter.
Step 2: Construct a line that passes through incenter, perpendicular to one side of the triangle. The segment which connects the incenter with the triangle intersection point and the perpendicular line is the circle radius.
Step 3: Build a centered circle at the incenter with radius spotted in step 2.
If one honey bee makes 1/2 teaspoon of honey during its lifetime, how many honey bees are needed to make 1/2 teaspoon of honey
A license plate comprised of 3 letters followed by 3 numbers is to be chosen (repetition is allowed). If the first letter cannot be a "Z", how many different ways can this occur? In your answer, include the set up and calculations for the license plate.
In a group of students 25% are enrolled in physics, 23% in sociology, 17% in chemistry, 14% in political science, 12% in anthropology, and 9% in math. you are going to select an individual from the group of students. the probability of event a is equivalent to the probability that you select someone who studies social science (sociology, political science and anthropology) or physics. what is the probability of the event a’s complement?
The probability of event A's complement, which signifies selecting a student not studying social science or physics, is 26%.
The probability of selecting someone who studies social science (sociology, political science, and anthropology) or physics is the sum of the individual probabilities for those subjects: 23% (sociology) + 14% (political science) + 12% (anthropology) + 25% (physics) = 74%. To find the probability of the event A's complement, which is selecting a student not studying any of these subjects, we subtract the probability of event A from 100%: 100% - 74% = 26%. Therefore, the probability of selecting a student not enrolled in any of the mentioned social science subjects or physics is 26%.
The camera melissa wanted for her birthday is on sale at 27%off the usual price. theamount of the discount is $99.90.what was the original price of the camera?$nothing
divide the discount by the percentage off
so:
99.90/0.27 = 370
the original price was 370 dollars
You are taking a multiple-choice test that has 10 questions. each of the questions has four answer choices, with one correct answer per question. if you select one of these four choices for each question and leave nothing blank, in how many ways can you answer the questions?
Find the area of the square.
A parent rewards a child with 50 cents for each correctly solved mathematics problem and fines the child 30 cents for each incorrectly solved problem. if the child nets $22.00 after 100 problems. how many problems were solved correctly?
x = correct answer
y = incorrect answer
0.50x-0.30(100-x)=22.00
0.50x-30.00+0.30x=22.00
0.80x=22.00+30.00
0.80x=52.00
x=52.00/0.80
x= 65
y=100-65 = 35
0.5x65 = 32.50
35*0.30=10.5
32.5-10.5 = 22
there were 65 correct answers
Answer:
65 problems were solved correctly, 35 incorrecly.
Step-by-step explanation:
1. Data:
Total answers= 100
50 cent = $0.50 for each correct answer
-30 cent = -$0.30 for each incorrect answer
Net reward= $22.00
2. Define Variables:
x= Correct answers
y= Incorrect answers
3. Formulate the Equations
Total number of answers (Eq 1)
[tex]x+y=100\\y=100-x[/tex]
Net reward (Eq 2)
[tex]0.50*x-0.30*y=22.00[/tex]
4. Solve by replaccing the Eq 1 in Eq 2 as follows:
[tex]0.50*x-0.30*y=22.00\\0.50*x-0.30*(100-x)=22.00[/tex]
5. Apply distrivutive property and operate:
[tex]0.50x-(0.30*100)+(0.30*x)=22.00\\0.50x-30.00+0.30x=22.00[/tex]
6. Separate numbers and variables on each side of the equation and solve
[tex]0.50x+0.30x=22.00+30.00\\0.80x=52.00[/tex]
7. Solve x
[tex]x=\frac{52.00}{0.8} \\x=65[/tex]
Now you know that correct answers are equal to 65
8. Find Incorrect Answers with Eq 1.
[tex]y=100-x\\y=100-65\\y=35[/tex]
Now you know that incorrect answers are equal to 35
9. Answer
65 problems were solved correctly, 35 incorrecly.
Use the drop-down menus to complete each statement to show why √65 is between 12 and 18.
Answer:
12 < 6√5 < 18
Step-by-step explanation:
It has been given in the question 4 < 5 < 9 and we have to show 6√5 is between 12 and 18.
For box number 1.
4 < 5 < 9 ⇒ √4 < √5 < √9
For the box number 2.
√4 < √5 < √9 ⇒ 2 < √5 < 3
For the box number 3.
we multiply the inequality by 6.
6×(2 < √5 < 3) ⇒ 6×2 < 6×√5 < 6×3
Therefore final answer is 6×2 < 6×√5 < 6×3 ⇒ 12 < 6√5 < 18
The square root of 65 (√65) falls between 8 and 9, as these are the square roots of the closest perfect square numbers (64 and 81 respectively). The range of 12 to 18 provided in the question seems incorrect.
Explanation:The student's question is referring to the mathematical concept of square roots of numbers. The square root of a number is a value which, when multiplied by itself, yields the original number. In the case of √65, we need to locate it between two perfect square numbers, which are 64 (8^2) and 81(9^2). As a result, √65 should fall between 8 and 9.
However, the interval of 12 and 18 as stated in the question seems to be a mistake, as they are not the correct boundaries for the value of √65. Please verify the numbers in your question.
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What is the fifth term in the expansion of (3x - 3y)7?
__ x3y4
Answer:
76545
Step-by-step explanation:
got it write on edge :)