The hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2).
At which points could the vertex of the right angle in the triangle be located? Check all that apply.
(–1, 1)
(4, –2)
(1, 1)
(2, –2)
(4, –1)
(–1, 4)
Answers
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Let
(x,y) ----> the coordinates of point C
Applying the Pythagoras Theorem
[tex](-1-4)^2+(-2-1)^2=(x-4)^2+(y-1)^2+(x+1)^2+(y+2)^2[/tex]
step 1
Find the possibles values of x
[tex](-1-4)^2=(x-4)^2+(x+1)^2\\\\25=x^{2}-8x+16+x^{2}+2x+1\\\\2x^{2}-6x-8=0[/tex]
Simplify
[tex]x^{2}-3x-4=0[/tex]
Solve the quadratic equation
[tex]x^{2}-3x-4=(x+1)(x-4)[/tex]
The values of x are
x=-1 and x=4
step 2
Find the possibles values of y
[tex](-2-1)^2=((y-1)^2+(y+2)^2\\\\9=y^{2}-2y+1+y^{2}+4y+4\\\\2y^{2}+2y-4=0[/tex]
Simplify
[tex]y^{2}+y-2=0[/tex]
Solve the quadratic equation
[tex]y^{2}+y-2=(y+2)(y-1)[/tex]
The values of y are
y=-2, y=1
therefore
The possibles coordinates of point C are
(-1,1),(4,-2)
Answer:
(–1, 1)
(4, –2)
Step-by-step explanation:
Given that the hypotenuse of a right triangle has endpoints A(4, 1) and B(–1, –2), then two triangles can be formed (see figure attached).
The vertex of the right angle in each triangle are on points (-1, 1) and (4, -2), as can be seen in the figure.
Related Questions
Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.
p: An isosceles triangle has two congruent sides.
q: A right angle measures 90°.
r: Four points are always coplanar.
s: A decagon has 12 sides.
Answers
the following is a conjunction
p∧q: An isosceles triangle has two congruent sides and a right angle measures 90°.
this statement is true because both p and q are true.
The following is a disjunction :
r∨s: Four points are always coplanar or A decagon has 12 sides.
this statement is false besause both statemens r and s are false: You could have four points in the three dimensional space that are not in one plane, and a decagon is a figure with 10 sides (not 12).
luke has $5 more than sam . together they have $73.how much does each have
Answers
Sam has $31.50
a baker makes 84loaves of bread but she burns 4 of them what fraction of the loaves does the baker burn? 1/88, 1/80,1/21,1/20 ...?
Answers
Given that the baker makes 84 loaves of bread, and out of the 84, she burns 4 of them. So in fraction it will be expressed in 4/84. So to know the final answer, we will simplify this fraction and we get 1/21. So the answer would be the third option. Hope this answer helps.
given the expression below, which is the best process for simplifying the expression?
(-5sqrt[2]-sqrt[6])(sqrt[3]+2sqrt[2])
a. combine like terms, distribute the radicals; simplify the radicals
b. combine like terms, simplify the radicals; distribute radicals
c. distribute the radicals, simplify the radicals, combine like terms
d. none of the above. ...?
Answers
The best process for simplifying the expression is: combine like terms, distribute the radicals; simplify the radicals.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
Answer:
distribute the radicals, simplify the radicals, combine like terms
Step-by-step explanation:
(-5sqrt[2]-sqrt[6])(sqrt[3]+2sqrt[2])
[tex](-5\sqrt{2})-\sqrt{6} )(\sqrt{3} +2\sqrt{2} )[/tex]
To multiply it , we apply FOIL method
Distribute the radicals inside the second parenthesis
After distributing the radicals inside the second parenthesis we multiply and simplify the radical as much as we can
Then we combine like terms to simplify further
distribute the radicals, simplify the radicals, combine like terms
Add this fraction 6 3/8 4 1/8
Answers
1. Add the whole numbers
[tex]6 + 4 = 10[/tex]
2. Add the fractions
[tex] \frac{3}{8} + \frac{1}{8} = \frac{4}{8} [/tex]
[tex] 6\frac{3}{8} + 4\frac{1}{8} = 10\frac{4}{8} [/tex]
3. Reduce
[tex] 10\frac{4 / 4}{8 / 4} = 10\frac{1}{2} [/tex]
[tex] 6\frac{3}{8} + 4\frac{1}{8} = 10\frac{4}{8} = 10\frac{1}{2} [/tex]
The answer is 10 1/2
A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. False
Answers
A. True
Answer: True
Step-by-step explanation:
State if the three numbers can be the measures of the sides of a triangle
Answers
In mathematics, specifically geometry, we can determine whether three given numbers can be the sides of a triangle by applying the Pythagorean theorem (a² + b² = c²). For instance, the sides with lengths 3, 4, and 5 can form a right triangle because 3² + 4² equals 5².
Explanation:
The subject question is about determining whether three given numbers can form the sides of a triangle. This is an area of Mathematics that deals with geometry, specifically triangles.
The knowledge of Pythagorean theorem which states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, often written as a² + b² = c², helps to verify if the three given numbers are the lengths of the sides of a triangle.For example, if given lengths are 3, 4, and 5. We square each side (9, 16, and 25 respectively) and then, according to Pythagorean Theorem, add together the squares of the two smaller sides to see if they equal the square of the largest side (9 + 16 = 25), the numbers do follow the rule of the Pythagorean Theorem, hence they could form the sides of a right triangle.Learn more about Pythagorean theorem here:
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What is the simplest form of expression? 2a^2b^2/4a
Answers
Final answer:
To find the simplest form of the expression 2a^2b^2/4a, you divide both the numerator and the denominator by the common factor 2a. The resulting simplest form of the expression is ab^2/2.
Explanation:
The student has asked: What is the simplest form of the expression 2a^2b^2/4a? The simplest form is achieved by simplifying the expression through division since there are common factors in the numerator and the denominator. Here, we can divide both the numerator and the denominator by 2a, which is a common factor. This simplification process will give us the simplest form of the expression.
To simply the expression 2a2b2/4a, we can follow these steps:
Divide the numerator and denominator by the common factor 2a.This results in a2b2/2a becoming ab2/2 after reduction.Therefore, the simplest form of the expression is ab2/2.
Evaluate |3 - 5 + 7|.
-5
5
-15
15
Answers
a test is worth 80 points multiple choice questions are worth 2 points and short answer questions are worth 4 points if the test has 25 questions how many mutiple choice questions are there
Answers
For Apex Users 2m+4s=80
It costs $4 to enter a fair. each ride costs 2.50. You have $21.50. How many rides can you go on?
Answers
So the first step is subtracting 4 from both sides
So you are left with $17.50 = 2.50x
Then divide both sides by 2.50
So you get 7 = x
So you can go on 7 rides
the expression -8x3(7x6-3x5) is equivalent to
Answers
The expression -8x³(7x⁶ - 3x⁵) simplifies to -56x⁹ + 24x⁸ by applying the distributive property.
The expression -8x³(7x⁶ - 3x⁵) is an example of algebraic multiplication where we apply the distributive property. To simplify, we distribute -8x³ across the terms inside the parentheses.
Here's the step-by-step simplification:
-8x³ × 7x⁶ = -56x⁹
-8x³ × -3x⁵ = 24x⁸
Combining these results, the entire expression simplifies to:
-56x⁹ + 24x⁸
This is an algebraic expression in its simplified form, representing the product of a monomial and a binomial.
The product of 8 and a number q is at least 32.
Equation or Inequality?
Answers
In this case, 8q is at least 32 which means it can be more than 32.
8 q [tex] \geq [/tex] 32.
The ____ are two straight dotted lines, one horizontal and one vertical.
Answers
What value in place of the question mark, makes the polynomial below a perfect square trinomial?
x2+24x+? ...?
Answers
This is because half of 24 is 12, and 12 squared is 144.
Instead of the question mark, you should use 144.
Kendra owns a restaurant. She charges $3.00 for 2 eggs and one piece of toast, and $1.80 for one egg and one piece of toast. How much does Kendra charge for an egg? A piece of toast?
Answers
Let the price for one egg be x and the price for one toast be y Then: 3 = 2x+1y,
1.8 = 1x+1y.When we substract, we get x = 1.2 and y = 0.6, so the price for an egg is $1.20 and the price for a toast is $0.60.
Hope this is helpful
Which of the following sets represents the domain of the function shown?
{(2, 7}, (15, 13), (21, –4), (24, 18)}
A) {-4,2,7,13,15,18,21,24}
B) {7,2),(13, 15),(-4,21),(18,24)
C) {2,15,21,24}
D) {-4,7,13,18}
Answers
The function is { ( 2, 7 ) , ( 15, 13 ), ( 21, - 4 ), ( 24, 18 ) }
The domain is:
C ) { 2, 15, 21, 24 }
( the range is D ) )
Which is a rational function?
A. y=x^2-x+4
B. 2/x
C. x-3^3/x^2
D. x-5/2
...?
Answers
I'd say C. x-3^3/x^2 is the correct answer because of all these cubes and squares.
The correct answer is: y=2/x . A rational function is the quotient of two polynomial functions. Notice that (x - 5)/2 can be simplified into a single polynomial function, so it is not a rational function.
Ali is reviewing family video. tape totaled 2 hours and 37 minutes. video of his children was 72 minutes. how much of video is not of children?
Answers
A line segment has an endpoint at (5, 2) and has a negative slope. Which of the following points could be the other endpoint?
A. (6, 3)
B. (5, 1)
C. (4, 3)
D. (4, 1)
Answers
A blouse that cost $16.85 is on sale for 45% off. What is the amount of the discount?
Answers
Answer: the answer
Step-by-step explanation: is 7.58
The amount of the discount if A blouse that cost $16.85 is on sale for 45% off is $7.6.
What is percentage?The percentage is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given:
The cost of the blouse, c = $16.85
The discount of the sale, d = 45%,
Calculate the amount of discount as shown below,
The amount of discount = 45% of The cost of the blouse
The amount of discount = 45 / 100 × 16.85
The amount of discount = 0.45 × 16.85
The amount of discount = 7.5825
Thus, the amount of the discount is $7.6.
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What is 1/10 of 0.092?
Answers
1/10 * 0.092=0.0092
"1.Provide the reasons for the proof.
Given: m angle1 = m angle2
Prove:
Answer:
StatementsReasons
a. m angle 1 = m angle 2a. Given
b. angle 1 is supplementary to angle 2.b. Definition of supplementary angles.
c. m angle 1 + m angle 2 = 180 c.
d. m angle1 + m angle1 = 180
2(m angle1) = 180d.
e. m angle1 = 90e.
f. angle 1 is a right angle.f. GIVEN OR PROVE IF PROVE PUT REASON....EXAMPLE: SUPPLEMENTARY......"
Answers
Switch the reasons for b) and c)
b) the angles form a linear pair , from the picture, so this is linear pair postulate
C) Then the measures add to 180, because they are supplementary. Defn of supplementary.
E) you have divided both sides of the equation by 2; or multiplied by 1/2; multiplication property of equality
F) definition of right angle
G) definition of perpendicular
I hope my answer has come to your help. Have a nice day ahead and may God bless you always!
A population of insects doubles every month. If there are 100 insects to start with, how many will there be after 7 months?
Answers
100>200>400>800>1600>3200>6400>12800
After 7 month, the population of insects are 12800.
Here,
A population of insects doubles every month.
There are 100 insects to start with.
We have to find the population of insects after 7 month.
What is exponential form?
A way of writing repeated multiplication involving base and exponents, is called exponential form.
Now,
A population of insects doubles every month.
There are 100 insects to start with.
Let the population is P.
Hence, The situation is express in exponential form as;
[tex]P = 100 (2)^n[/tex]
Where, n is the number of month.
So, The population after 7 month is calculate as;
[tex]P = 100 (2)^7=100*128= 12800[/tex]
Therefore, After 7 month the population of insects are 12800.
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(Upvote. Explain?)
Which ordered pairs in the form (x, y)(x, y) are solutions to the equation 3x−4y=21
Select each correct answer.
(11, 3)
(7, 0)
(−1, −6)
(−3, 3)
Answers
Answer:
(7,0) is ur answer my dude
Step-by-step explanation:
Mel Garrett needs four new tires for his car. He can buy one tire for $87, two tires for $174, three tires for $261, or four tires for $348. Which is the best buy?
Answers
a new website didicated to helping users research their ancestry had 200 visitors in the first week. the marketing director beleives that without an advertising compaign, the site will gain 50 new users each week. how many total visitors will they have after 12 weeks?
Answers
You can acquire this answer buy multiplying 50 by 12 to get the amount of new users after 12 weeks to get 600, and then add 200 to 600 for the current users.
Your monthly living expenses are $1500 on an income of $1,650 per month. Your goal is to have an emergency fund of 4 times your monthly living expenses. Your emergency fund savings account has $2,400 and you put the remainder of your monthly income into the emergency fund each month. How much more money would you have to save each month to complete your emergency fund in 12 months?
a.
$300 per month
b.
$150 per month
c.
$75 per month
d.
$60 per month
Answers
Answer:
b. $150 per month
Step-by-step explanation:
To begin solving this let us calculate the amount of our Goal and how much we are saving per month. Our goal is to save up 4 times the amount of our monthly expenses. So we multiply our monthly expenses by 4 like so,
[tex]1,650 - 1,500 = 150[/tex] savings per month
[tex]1,500 * 4 = 6,000 goal[/tex]
We are currently saving $150 per month. Now that we know our goal is $6000. Lets calculate how far off we are with what we already have in our savings by subtracting our goal from our current savings.
[tex]6,000-2,400 = 3,600[/tex]
We need to save up $3,600 in 12 months which would be
[tex]\frac{3600}{12}=300[/tex]
Therefore we need to put $300 a month into our savings account to reach that goal in 12 months. Since we already put $150, this means we need to make an additional $150 a month to reach our goal in 12 months.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Answer: B
Step-by-step explanation:
jasmine has taken an online boating safety course and is now completing her end of course exam.As she answers each question, the progress bar at the bottom of the screen shows what portion of the test she has finished. She has just completed question 16, and the progress bar shows she is 20% complete. How many total questions are on the test.
Answers
FlybynightSavings.com is offering a savings account that pays 28% compounded continuously. How much interest would a deposit of $3,000 earn over 5 years? (Round your answer to the nearest cent.)
Answers
The continuous compound interest of a $3,000 deposit with an annual rate of 28% over 5 years would be approximately $9,156.58.
Explanation:The question pertains to continuous compound interest, which is represented by the formula A = P imes ert, where A is the final amount, P the principal amount, r is the interest rate (written in decimal), t is the time in years, and e is the base of natural logarithms.
Given that P=$3,000, r=28/100=0.28 and t=5 years, you would substitute these values into the formula to get A = $3000 imes e(0.28 imes 5).
Computing this, gives:
A = $3000 imes e1.4 = $3000 imes 4.0552 (approximately).
So, A = $12156.58 (rounded to the nearest cent).
The interest earned would therefore be: A - P.
Thus, the interest would be $12156.58 - $3000 = $9156.58.
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To find out how much interest a deposit of $3,000 would earn over 5 years with an interest rate of 28% compounded continuously, we would need to use the formula for continuously compounded interest, which is A = P*e^(rt).
Here,
A represents the total amount of money accumulated after n years including interest,
P is the principal amount, which is the initial amount of money,
r refers to the annual interest rate expressed in decimal form, and
t is the time the money is invested for in years.
Given in the problem we have P = $3000, r = 28% = 0.28, and t = 5 years.
Substituting these values into the formula we get:
A = 3000 * e^(0.28*5)
Solving this would yield the total amount accumulated after 5 years.
Next, we would need to calculate the accrued interest. This is done by subtracting the principal amount (the initial deposit) from the total amount.
So, the interest earned would be calculated as:
Interest Earned = Total Amount - Initial Deposit.
The numerical calculation of these formulas provides us the result that the total amount after 5 years would be approximately $12,165.60 and the interest earned would be approximately $9,165.60.
Thus, a deposit of $3000, with an interest rate of 28% compounded continuously over 5 years, would earn you interest of about $9,165.60.
This is of course rounded to the nearest cent as required.
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