Answer:
(3, 2) and (1, 4)
Step-by-step explanation:
Plot the two points on a graph.
The other two points are (3, 2) and (1, 4).
To do this with algebra, it takes a few steps.
The diagonals of a square are perpendicular and bisect each other. You are given opposite vertices, so first, find the midpoint of that diagonal.
((1 + 3)/2, (2 + 4)/2) = (2, 3)
The midpoint of the diagonal is (2, 3).
This diagonal has slope 1 and y-intercept 1, so its equation is
y = x + 1
The perpendicular bisector has equation
y = -x + 5
The two vertices we are looking for, lie in a circle whose center is the midpoint of the diagonals, (2, 3), and whose radius is half of the diagonal.
Use Pythagoras to find the diagonal's length.
2^2 + 2^2 = c^2
c^2 = 8
c = sqrt(8) = 2sqrt(2)
Half of the diagonal is sqrt(2). This is the radius if the circle.
The equation of the circle is
(x - 2)^2 + (y - 3)^2 = (sqrt(2))^2
(x - 2)^2 + (y - 3)^2 = 2
The points of intersection of this circle and the second diagonal are the two vertices you are looking for.
System of equations:
(x - 2)^2 + (y - 3)^2 = 2
y = -x + 5
Use substitution and substitute y with -x + 5 in the equation of the circle.
(x - 2)^2 + (-x + 5 - 3)^2 = 2
(x - 2)^2 + (-x + 2)^2 - 2 = 0
x^2 - 4x + 4 + x^2 - 4x + 4 - 2= 0
2x^2 - 8x + 6 = 0
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0
x - 3 = 0 or x - 1 = 0
x = 3 or x = 1
Now we find corresponding y values.
y = -x + 5
x = 3
y = -3 + 5 = 2
This gives us (3, 2).
y = -x + 5
x = 1
y = -1 + 5 = 4
This gives us (1, 4).
Answer: (1, 4) and (3, 2)
what is the answer to -22/9r = 11/9
Answer:
2
Step-by-step explanation:
for this question you've to cross multiply
-22/9r=11/9
99r=-198
then you divide both sides by 99 inorder to remain with r on one side
99r/99=198/99
r=2
I hope this helps
Solve A=1/2(bh) for h
Answer: 2A/b = h
Step-by-step explanation: First, get rid of the fraction by multiplying both sides of the equation by 2. That gives us 2A = bh.
Don't be thrown off by the capital A in this problem.
Just treat it like any other variable.
To get h by itself on the right side of the equation, we now simply
divide both sides of the equation by b and our answer is 2A/b = h.
Take a look back at the formula now in the
original problem, A = 1/2bh, does that look familiar?
Proportion problems
8 chickens would lay 20 eggs in 3 days.
If chickens always lay eggs at the same rate,
a) how many days would it take to chickens to lay 100 eggs?
= 10 days
b) how many chickens would be required if a farmer needed 30 eggs each day?
i need help how to do question b. i know answer bu,.t i need explaining.
:]
Find y.
A. √2/2
B. 4
C. √6/2
D. √2
Answer:
Step-by-step explanation:
the answer is option D
WHEN YOU SUBSTITUTE THE VALUES YOU WILL GET IT............
What is the factorization of 2x^2 + 5x + 3?
A. (x+3)(x + 3)
B. (x+3)(x + 1)
C. (2x+3)(x + 1)
D. (2x + 3)(x + 3)
Answer:
( 2x +3) (x+1)
Step-by-step explanation:
2x^2 + 5x + 3
2 factors to 2 and 1
3 factors to 3 and 1
We need to get 5x in the middle
( 2x +3) (x+1)
Find the solutions to $x^2 + 64 = 0.$[tex]Find the solutions to $x^2 + 64 = 0.$[/tex]
Answer:
x=8i,\:x=-8i
Step-by-step explanation:
x^2+64-64=0-64
x^2=-64
x=\sqrt{-64},\:x=-\sqrt{-64}
x=8i,\:x=-8i
a car averaged 72 kph .on a trip if the car travelled for 9 hours how far did it go
Answer:
648 km
Step-by-step explanation:
distance travelled= speed * time
distance= 72kph * 9 hours
distance= 648 km
To bake 12 cookies, I use 2 quarts of milk. There are 2 pints in a quart. How many pints of milk do I need to bake 3 cookies?
Answer:
1 pint
Step-by-step explanation:
You need 2 * 2 = 4 pints to make 12 cookies. Since 3 cookies is 1/4 of 12 cookies, you would need 1/4 * 4 = 1 pint of milk to make 3 cookies.
Answer:
1 pint
Step-by-step explanation:
12c=4p
divide both sides by 4
3 cookies needs 1 pint!!!!
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
[tex]\huge\boxed{x = 36\°}[/tex]
Step-by-step explanation:
According to secant angle theorem:
[tex]x = \frac{1}{2} (mCDF-mBJH)[/tex]
Where mCDF = 140 , mBJH = 68
[tex]x = \frac{1}{2} (140-68)[/tex]
[tex]x = \frac{1}{2} (72)[/tex]
x = 36°
5/6 = b/12 help please
Answer:
[tex]b = 10[/tex]
Step-by-step explanation:
We can use the cross products property and solve for b.
[tex]\frac{5}{6} = \frac{b}{12}\\\\\\b=(12\cdot5)\div6\\b=60\div6\\b=10[/tex]
Hope this helped!
Answer:
The answer is b=10
Step-by-step explanation:
All you need to do is think 12/6 is what, the answer would be 2, then you would multiply the numerator by 2, which would be 5*2 which is 10.
Thank you, Hope this helps you.
one tree is 6 feet tall. Another tree is 3 1/4 feet tall. How much taller is the larger of the two trees?
Answer:
2 3/4 feet
Step-by-step explanation:
I need help on this question!!!
Answer:
The answer is 17.
Step-by-step explanation:
200/3 is approximately 67, and divided by 4 again to represent the second checkpoint will become 16.75. Obviously there can't be a fraction of a bag, so the answer is 17.
Answer:
16
Step-by-step explanation:
the lcm for 3 and 4 is 12
200 ÷ 12 = 16.667
≈16
What is the y−intercept of the line that passes through the point (4,9)and is parallel to the line y=12x+2?
Answer:
y- intercept = - 39
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 2 ← is in slope- intercept form
with slope m = 12
Parallel lines have equal slopes, thus
y = mx + c ← is the partial equation
To find c substitute (4, 9) into the partial equation
9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept
Answer:
y-intercept = -39
Step-by-step explanation:
if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line
y=mx+c
y=12x+2
comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use
y-y1=m(x-x1)
y1=9 and x1=4
y-9=12(x-4)
y-9=12x-48
y=2x-48+9
y=2x-39
comparing to the default equation of a line y=mx+c where c is the y-intercept
therefore the y-intercept is -39
2.5 kg of oranges cost $ 1.40, what is the cost of
1 kg of orange?
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The students in Shawn's class got to choose whether to visit the zoo or the aquarium. 3 students went to the zoo and 15 students went to the aquarium. What is the ratio of the number of students who went to the zoo to the number of students who did not go to the zoo?
A. 1:6
B. 1:1
C. 1:3
D. 1:5
Answer:
D. 1:5
Step-by-step explanation:
3 students went to the zoo
15 students went to the aquarium, which is no the zoo
students who went to the zoo : students who did not go to the zoo =
= 3:15
Now we simplify the ratio by dividing both numbers by 3.
= 1:5
Answer: D. 1:5
what is 2/5 divided by -1/2 minus 3/2
Answer:
[tex] - \frac{23}{10} [/tex]
Step-by-step explanation:
[tex] \frac{2}{5} \div \frac{ - 1}{2} - \frac{3}{2} [/tex]
➡️ [tex] - \frac{2}{5} \times 2 - \frac{3}{2} [/tex]
➡️ [tex] - \frac{4}{5} - \frac{3}{2} [/tex]
➡️ [tex] - \frac{23}{10} [/tex]
the sum of 35 and one fifth part of itself is added to the sum of one seventh of 11 and 8
Answer:
313/7
Step-by-step explanation:
Here, we are interested in turning the wordings of the statement to numeric values.
We take it one at a time.
Sum of 35 and 1/5(35) = 35 + 7 = 42
This is added to 1/7(11 + 8)
= 1/7(19) = 19/7
So we have;
42 + 19/7 = (294 + 19)/7 = 313/7
Please help me i don’t know if I’m right
Answer:
your choice is correct
Step-by-step explanation:
The magnitude of the difference between the target amount and the actual amount will be no greater than the allowed error.
|x -34| ≤ 0.25
Suppose the graph in part A can be represented by the function f(x)=1.5x+750/x . What is the domain of this function? Consider the context of the function in your answer.
Answer:
Domain:
( − ∞ , 0 ) ∪ ( 0 , ∞ ) , { x | x ≠ 0 }
Step-by-step explanation:
i used math. way for help
PLEASE HELP ME !!!!!!!!!!!!!!!!!
Answer:
2
Step-by-step explanation:
The series is a geometric series with a common ratio (r) of 1/2 and a first term (a1) of 1/2^0 = 1. The sum of such a series is given by ...
S = a1/(1 -r) 1/(1 -1/2) = 2
The sum of the series is 2.
Last year, there were 245 pies baked for the bake sale. This year, there were k pies baked . Using k, write an expression for the total number of pies baked in the two years.
Answer:
245 + k
Step-by-step explanation:
Since we know that,
245 = amt. of pies baked for the bake sale last year.
--> and k = (unknown) amt. of pies baked for the bake sale this year.
Using k, we need to write the total amt. of pies baked for bake sales in the 2 years.
last year + this year =>
respectively, 245 and k
Thus, we get 245 + k
3T-2 + T -5T= -1
Solve it out please
Answer: T = -1
Step-by-step explanation:
**Disclaimer** I assume that the [T] is a variable. If it was, then you may refer to my answer. If it was not, then you may point it out and I'll redo it.
Given
3T - 2 + T - 5T = -1
Combine like terms
-T - 2 = -1
Add 2 on both sides
-T - 2 + 2 = -1 + 2
-T = 1
Divide -1 on both sides
-T / (-1) = 1 / (-1)
T = -1
Hope this helps!! :)
Please let me know if you have any questions
___H2 + ___Br2 → ___HBr
Answer:
H2+Br2 HBrH2+Br2. 2HBrOn his return trip, Zen descends from the Calloway Peak Summit to an elevation of 2,402.5 feet, arriving at the Flat Rock Junction. So, the elevation at Flat Rock is feet.
Complete question :
Zen is participating in an all-day hike to the Grandfather Mountain Summit on the Blue Ridge Parkway.
Starting at elevation zero, Zen climbs to an elevation of 4,646.4 feet to reach the Cragway Trail. From there, he hikes up another 1,817.6 feet to the Calloway Peak Summit, the highest point on Grandfather Mountain. Based on these numbers, the Calloway Peak Summit is at a height of _____ feet.
On his return trip, Zen descends from the Calloway Peak Summit to an elevation of 2,402.5 feet, arriving at the Flat Rock Junction. So, the elevation at Flat Rock is ______ feet.
Answer:
6,464 Feets; 4,061.5 Feets
Step-by-step explanation:
Given the following:
Starting elevation = 0
Elevation of the Cragway Trail = 4,646.4 feets
Elevation of Cragway Trail to Calloway peak summit = 1,817.6
From Calloway peak summit, Zen descends to an elevation of 2,402.5 Feets (flat Rock junction)
The Calloway Peak Summit is at a height of _____ feet.
Height of Calloway Peak Summit:
(Starting elevation to Cragway trail) + (Cragway trail elevation to Calloway peak Summit)
4,646.4 Feets + 1,817.6 Feets = 6,464 Feets
B) Elevation at Flat Rock Junction:
Height of Calloway peak summit - 2,402.5
(6464 - 2402.5) Feets = 4,061.5 Feets
3. Create and write a real-world situation that could be represented by the equation below:
5x + 15 = 45
Answer:
You ordered 5 tickets for a show on line...
The cost was $5 a ticket Plus a one time ordering fee of $15.
you total cost was $45 ....
Solving for x will determine the cost of one ticket
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a taxi charges $5 a mile plus $15 "pull fee" ...
you ride cost a total of $45 ... x is the number of miles that you got driven
Step-by-step explanation:
You rent a car for a down payment of $15 and $5 is charged per mile driven. The total charge is therefore, $45. In essence, x is the no. of miles driven.
According to the question;
We are required to create a real-world problem that could be represented by the equation; 5x + 15 = 45.In essence, x is the no. of miles driven in this scenario.
By solving for x in 5x + 15 = 45, we may determine the no. of miles driven.
Read more:
https://brainly.com/question/2319353
(6e−3f−4)⋅2= what is the answer for this?
Answer:
12e-6f-8 is the answer
Step-by-step explanation:
did work on peice of paper
Answer:
12e - 6f - 8
Step-by-step explanation:
By using the distributive property,, the answer is
(6e x 2) - (3f x 2) - (4 x 2)
12e - 6f - 8
Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[tex]Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.[/tex]
Hello, please consider the following.
[tex]x^2 + 10x + 25 = 8\\\\\text{\bf We can notice that } x^2+10x+25=(x+5)^2 \text{ so}\\\\x^2 + 10x + 25 = (x+5)^2=8\\\\\text{\bf We take the root.}\\\\x+5=\pm\sqrt{8}\\\\\text{\bf We subtract 5}\\\\\boxed{x=-5-\sqrt{8}} \ \ or \ \ x=-5+\sqrt{8}[/tex]
In the box, you can find the smallest solution.
Thank you.
Last week Andi had exams in Chemistry and in Spanish. On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65. For which class should Andi expect the better grade?
Answer:
Chemistry
Step-by-step explanation:
To solve the above question, we use the z score formula
Andy took two Exams, Chemistry and Spanish. So we find the z score for both exams.
a) Chemistry Exam
On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45
z-score is given as: z = (x-μ)/σ
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z = (x-μ)/σ
z = (45 - 30)/5
z = 15/5
z = 3
b) On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65.
z-score is given as: z = (x-μ)/σ
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z = (x-μ)/σ
z = (65 - 60)/6
z = 5/6
z = 0.8333333333
Comparing the z score of both Exams,
Andy had a z score of 3 in the Chemistry exam and 0.8333333333 in the Spanish exam.
Therefore, Andy should be expecting a better grade in the Chemistry exam because his z score in the Chemistry exam was higher than that of the Spanish exam.
a line is perpendicular to y=4x-2 and intersects the point (4,-11). what is the equation of this perpendicular line?
Answer:
y = -1/4x - 10
Step-by-step explanation:
Hey there!
Well to the slopes of 2 perpendicular lines are reciprocals of each other meaning if the line has a slope of 4 then it’s perpendicular line has a slope of -1/4.
Now to find the y intercept we need to graph,
y = -1/4x and point (4, -11)
Look at the image below.
By looking at the image below we can tell that in order for the perpendicular line to go through point (4,-11) it would be -10.
The equation is y = -1/4x - 10
Hope this helps :)
The loudness, L , of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d , from the source of the sound. When a person 14 feet from a jetski, it is 70 decibels loud. How loud is the jetski when the person is 46 feet away?
Answer:
Loudness (L) = 6.48 dB
Step-by-step explanation:
Given:
Loudness (L) = k / d² , where k = constant
So,
70 = k / 14²
k = 13,720
New distance = 46 feet
Find:
Loudness (L) = ?
Computation:
Loudness (L) = 13,720 / 46²
Loudness (L) = 13,720 / 2,116
Loudness (L) = 6.48 dB