The diagonal of a square unit is x units. What is the Area of the square in terms of x
Answers
d^2=s^2+s^2
d^2=2s^2 we are told that d=x so
x^2=2s^2
s^2=(x^2)/2
And since the area of a square is s^2, the area of this square is:
(x^2)/2
Or as it is shown in your answer choices...
(1/2)x^2 square units (the top answer :P)
The area of a square with a diagonal x is (1/2)x² unit²
SquareA square is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. All the sides of a square have the same length and each angle measure 90 degrees.
let l represent the length of the side of the square and x be the length of the diagonal. Using Pythagoras theorem:
l² + l² = x²x² = 2l²l = x√(1/2)Area of square = l * l = x√(1/2) * x√(1/2) = x² * 1/2 = (1/2)x² unit²
The area of a square with a diagonal x is (1/2)x² unit²
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Related Questions
suppose an investment of $8200 doubles in value every 7 years. how much is the investment worth after 28 years
Answers
131,200
Answer:
After 28 years, it will be $131,200
Step-by-step explanation:
It is given that the investment doubles in value every 7 years.
So, after 7 years, it will be 8200 × 2 = 16,400
After 14 years, it will be 16,400 × 2 = 32,800
After 21 years, it will be 32,800 × 2 = 65,600
After 28 years, it will be 65,600 × 2 = 131,200
Hence, the investment is $131,200 worth after 28 years.
match each equation with the graphs
Answers
Answer:
i) y = 2x + 3
ii) y = 3x + 3
iii) y = 5x + 5
iv) y = 5x + 2
Step-by-step explanation:
i) The first graph has the slope (m) = 2 and the y-intercept(b) = 3
Therefore, the equation of the line is y = 2x + 3
ii) The second graph has the slope (m) = 3 and the y-intercept (b) = 3
Therefore, the equation of the line is y = 3x + 3
iii) The third graph has the slope (m) = 5 and the y-intercept (b) = 5.
Therefore, the equation of the line is y = 5x + 5
iv) The fourth graph has the slope (m) = 5 and the y-intercept (b) = 2
Therefore, the equation of the line is y = 5x + 2
The total mass of Abdul and his baby brother is 15.25kg . The mass of Abdul and his father is 72.25kg . The mass of Abdul's father is 13 times as heavy as Abdul's baby brother. What is Abdul's mass?
Answers
a+f=72.25, since f=13b
a+13b=72.25 so now we have two equation in two variables...
a+13b=72.25 and a+b=15.25 so we can say:
(a+13b=72.25)-13(a+b=15.25)
a+13b-13a-13b=72.25-198.25
-12a=-126
a=10.5 kg
So Abdul's mass is 10.5 kilograms.
For f(x)=3x+1 and g(x)=x^2-6, find (f/g)(x)
A. 3x+1/x^2-6, x≠±√6
B. x^2-6/3x+1
C. x^2-6/3x+1, x≠-1/3
D. 3x+1/x^2-6
Answers
Answer:
Answer is A
Step-by-step explanation:
At the party, Aisha and her friends ate 2 1/2 pizzas. After the party, there were 1 1/8 pizzas left. How many pizzas were there at the start of the party?
Answers
Answer:
[tex]3\frac{5}{8}[/tex] pizzas were there at the start of the party.
Step-by-step explanation:
At the party let number of pizzas were = x
Aisha and her friends ate [tex]2\frac{1}{2}[/tex] pizzas after which [tex]1\frac{1}{8}[/tex] pizzas were left.
Therefore the equation formed will be
[tex]x-2\frac{1}{2}=1\frac{1}{8}[/tex]
x - (5/2) = 9/8
x = 9/8 + 5/2
x = 29/8 = [tex]3\frac{5}{8}[/tex]
Therefore [tex]3\frac{5}{8}[/tex] pizzas were there at the start of the party.
Carisa predicted she answered 9 questions correctly out of 10 on a test. She actually got 8 answers correct. By what percent was Carisa's prediction off?
Answers
Answer:
13
Step-by-step explanation:
The cost of three Ice Cream cones is $24.95. If each ice cream cone cost the same amount, what was the price,p, of one ice cream cone?
I have to write and solve an equation. If you can, can you plz just write the equation for me.
Answers
p = 24.95/3
p = 8.316 rounds to $ 8.32 per cone...wow, expensive ice cream cone
Which just means that 3 times the cost of a cone is equal to $24.95. To solve you just divide both sides of the equation by 3, which is kind of silly in this instance because it gives you a decimal value for cents :P
c≈$8.3167
c≈$8.32 (rounded to nearest cent)
fifteen less than twice a number is less than or equal to -23
Answers
but that's is what i think
Hello!
First of all, let the number be y.
"twice a number" means you should multiply that number by 2:
2y
Now, "fifteen less" means you should subtract 15:
2y-15
Now, this whole expression is less than or equal to -23:
2y-15≤-23
[tex]\rule{150}{1}~\rule{150}{2}[/tex]
Solve the inequality:
Add 15 to both sides2y≤23+15
2y≤38
Divide both sides by 2
y≤19
Hope everything is clear.
Let me know if you have any questions!
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[tex]\boxed{An~Emotional~Helper}[/tex]
What is the domain of the function f(w) = 0.5(35 – 2w)? Explain your answer.
Answers
Phil and Lorena are playing golf. Phils score after the first round is -1 Lorena score is -4 the player with the lower score is the winner Who wins?
Answers
Lorena with the score of -4 is the winner.
To determine the winner of the match, we need to look at the following given details:
In golf, the player with the lower score wins. Let's compare Phil and Lorena's scores:Phil's score: -1Lorena's score: -4We know that in negative numbers, the higher count number is lower in value than lower count.For example: -50 is lower than -20.
Hence, we know that -4 is less than -1, Lorena has the lower score and thus wins the game.
Think of the number seven. Now add eight to it. Now add four more. Now subtract nine. Now add three. Your answer is _____.
Answers
7+8= 15. 15+4= 19. 19-9=10. 10+3=13.
Answer:
7+8+4-9+3=13
Step-by-step explanation:
We have given the statements and we have to figure out the answer.
Think of the number seven i.e. 7
Now add eight to it i.e. 7+8
Now add four more i.e. 7+8+4
Now subtract nine i.e. 7+8+4-9
Now add three i.e. 7+8+4-9+3
Simplification of expression 7+8+4-9+3
Add the terms,
7+8+4-9+3=22-9
Subtract the terms,
7+8+4-9+3=13
Therefore, The answer is 13.
Which table represents a linear function?
1, 2, 3, or 4?
Answers
We can see that the first table's y-values are increasing steadily by 1/2. This makes it a linear function.
The price of pears at a farm is $1.41 per pound. Which equation can be used to determine c, the total price of n pounds of pears? c equals 1.41 over n c = 1.41 + n c = 1.41 − n c = 1.41n
Answers
We know that the price of pears at a farm is $1.41 per pound, we could use multiplication in order to find the answer. The equation that could be used to determine [tex]c[/tex] would be this:
[tex]c=1.41n[/tex]
Thanks!
-TetraFish
All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected. If adult ticket cost 7.50 each and Senior tickets cost $4 each, how many bills of each type were sold?
Answers
7.5a + 4s = 3312.50
7.5(500 - s) + 4s = 3312.50
3750 - 7.5s + 4s = 3312.50
-7.5s + 4s = 3312.50 - 3750
-3.5s = - 437.50
s = -437.50/-3.5
s = 125 <=== 125 senior tickets
a = 500 - s
a = 500 - 125
a = 375 <=== 375 adult tickets
The number of senior tickets is 375 and the adult tickets is 375 if All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
From the question:
A + S = 500
7.5A + 4S = 3312.50
-3.5S = - 437.50
S = -437.50/-3.5
S = 125
A = 500 - S
A = 375
Thus, the number of senior tickets is 375 and the adult tickets is 375 if All 500 seats to the Friday Night Seniors' Play were sold, and a total of $3312.50 was collected.
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Derek is training for a race he wants to runs a total of 100 miles over 4 weeks he only runs 16 miles in the first week if he runs the same number of miles in each of the last 3 weeks how far would he run each week
Answers
84 ÷ 3 = 28 miles
NEED HELP ASAP!!! The work of a student to solve the equation 2(4x − 4) = 8 + 4x + 4 is shown below: Step 1. 2(4x − 4) = 8 + 4x + 4 Step 2. 6x − 6 = 12 + 4x Step 3. 6x − 4x = 12 + 6 Step 4. 2x = 18 Step 5. x = 9 In which step did the student first make an error and what is the correct step?
Step 2, 8x − 6 = 2(6 + 2x + 2)
Step 2, 8x − 8 = 12 + 4x
Step 3, 6x − 4x = 12 − 6
Step 3, 6x + 4x = 12 + 6
Answers
Solve the inequality for b 10 < -2/3(9+12b)
Answers
-30/2>9+12b. (If you Multiply or divide by a negative Number the inequality Signal(<>≤≥) turns around()
-9
-15-9>12b. :12
-24:12>b
-2>b
Final answer:
To solve the inequality 10 < -2/3(9+12b), distribute -2/3 inside the parentheses, simplify, and divide by -8, which reverses the inequality. The solution is b < -2.
Explanation:
To solve the inequality 10 < -2/3(9+12b), we must first distribute the -2/3 across the parentheses:
Multiply -2/3 by 9 to get -6.
Multiply -2/3 by 12b to get -8b.
The inequality now looks like this: 10 < -6 - 8b. Next, we simplify by moving the constant term -6 to the left side:
Add 6 to both sides: 10 + 6 < -8b.
Combine like terms: 16 < -8b.
Finally, we divide both sides by -8, remembering that this reverses the inequality symbol:
Divide by -8: -2 > b or b < -2.
Therefore, the solution to the inequality is b < -2.
write an equation with an even product
Answers
product is multiplication:
2 * 2 = 4
You are considering a 5/1 ARM. What does the 5 represent?
Answers
The 1 represents the idea that the interest rate will change every year after the initial 5 years are up.
Needing this for tomorrow thanks help me please is hurry
Answers
39) 6 *15 = 90 in deposits
40) 5 + 10 + 15 = 30 withdrew
41) 35 +90 = 125 - 30 = 95 in the account
An ellipse has a vertex at (14, –1). The focus of the ellipse nearest that vertex is located at (8, –1). If the center of the ellipse is located at (–1, –1), what is the equation of the directrix on that side of the ellipse?
x =
Answers
Answer:
24
Step-by-step explanation:
edge 2022
Define a simulation to represent correct answers on a true-or-false quiz. Use the simulation to find the probability of getting exactly 4 correct answers on a ten-question quiz.
Answers
A steel cylinder with a moveable piston on top is filled with helium (He) gas. The force that the piston exerts on the gas is constant, but the volume inside the cylinder doubles, pushing the piston up.
Which of the following answers correctly states the cause for the change described in the scenario?
The temperature increased.The density of the helium atoms decreased.The pressure decreased.The helium atoms increased in size.Final answer:
To determine the probability of passing a 10-question true-false quiz with at least a 70% score when guessing, we calculate the probabilities of getting 7, 8, 9, and 10 answers correct and sum them, using the binomial probability formula.
Explanation:
A student takes a 10-question true-or-false quiz and guesses randomly without studying. To find the probability of getting exactly 4 correct answers out of 10 questions, we can use a binomial probability formula which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where 'P(X=k)' is the probability of 'k' successes in 'n' trials, 'p' is the probability of success on a single trial, and '(1-p)' is the probability of failure on a single trial.
In this case, guessing true or false correctly is a 50% chance or 'p' equals 0.5, since there are only two possible outcomes, and 'n' is 10. To calculate the probability of passing the quiz with at least a 70 percent score, we need at least 7 correct answers out of 10. We will calculate the probabilities of getting exactly 7, 8, 9, and 10 correct answers and then sum these probabilities.
The calculation for P(X=7) would be (10 choose 7) * 0.5^7 * 0.5^(10-7). Similarly, we would calculate P(X=8), P(X=9), and P(X=10) using the same formula with different values for 'k'. Once we have these probabilities, we can add them up to find the total probability of scoring at least 70 percent on the quiz.
Remember to round answers to relative frequency and probability problems to four decimal places for accurate results.
If the graph of f(x) has the point (2,7) then what is one point that will be on the graph of f-1(x)
Answers
The graph of f^-1 (x) is called the inverse function of f (x). The relationship between the two is that the point (x,y) is on the graph of f (x) if and only if the point (y,x) is on the graph of f^-1 (x).
This means that if the point (2, 7) is on f (x), therefore the point (7, 2) is on f^-1 (x).
Answer: (7, 2)
Answer: The required point is (7, 2).
Step-by-step explanation: Given that the graph of f(x) has the point (2, 7).
We are to find one point that will be on the graph of [tex]f^{-1}(x).[/tex]
We know that
if a point (a, b) lies on the graph of a function g(x), then the point (b, a) will always lie on the the graph of the inverse function [tex]g^{-1}(x).[/tex]
Therefore, the one point that will lie on the graph of [tex]f^{-1}(x)[/tex] is (7, 2).
Thus, the required point is (7, 2).
Matt and Brian were solving a system of equations. They both noticed that the two lines had the same slope. Brian said that because each line in the system had the same slope, the two lines had to be parallel, which meant the solution to the system was "no solutions." Matt disagreed, and said they should also look at the y-intercepts before determining how many solutions there were. Who is correct?
Answers
Only two lines with the same slope and different y-intercepts have no solution.
Answer: A. Matt is correct. Though two lines with equal slopes are often parallel, if they have the same y intercept, they are the same line and have infinitely many solutions.
Step-by-step explanation: Apex Answer
Rewrite each expression below using the distributive property then evaluate each expression for X equals two and Y equals five. a.8x-4= b.6y2+24y c. 7X(y -2) d. 3(9+y)
Answers
12 30+2+120 14*3 3*14
152 42 42
i hope it helps
Please help what is the additive inverse of this expression: -2.5 - 1.5 plz help
Answers
-2.5 minus 1.5= -4
|-4|=4
The additive inverse of the expression -2.5 - 1.5 is 4. This is determined by first resolving the expression to -4 and then flipping the sign of this result to its opposite, yielding 4.
Explanation:In mathematics, the additive inverse of a number is the number that when added to the original number results in zero. To find the additive inverse of the expression -2.5 - 1.5, follow these steps:
First, resolve the expression by subtracting 1.5 from -2.5 which gives -4.Second, to find the additive inverse of -4, you simply flip the sign of the term to positive, so the additive inverse of -4 is 4.This is applicable similarily like in vector subtraction we add the first vector to the negative of the vector that needs to be subtracted. This is analogous to the subtraction of scalars.
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7 to the second power minus 24 divided by 3
Answers
For the first one : 7^2-24÷3
14-24÷3
14-8 = 6
For the second one 7^2-24 all over 3
14-24 = -10
-10/3
I'm not sure which one you were asking for since you didn't include a picture, so I solved both
A student runs 100 meters in 11 second s . What is the speed of the student
Answers
to find the speed, divide these numbers, and you get .11, which is how many meters he ran per second
the speed of the student is .11 meters per second
A piggy bank containing only quarters had a mass of 850 grams when empty and 7822 grams when filled. If a quarter weighs 5.6 grams , estimate the amount of money inside the piggy bank
Answers
and if each quarter is 5.6 grams...
6972 / 5.6 = 1245 quarters are in there <===
Joyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
Answers
Joyce would have x + 5 cents after the bet.
Explanation:To determine how much money Joyce has after the bet, we need to consider the information given in the question. It states that Joyce has as much money as George, and after they bet 5 cents each, George lost and ended up with x cents. Since they both bet the same amount and George lost, it means Joyce must have won the bet and still has the original amount of money they each had, plus the 5 cents George lost.
Therefore, Joyce has x + 5 cents after the bet.