In a right triangle, the hypotenuse has endpoints XY, shown on the graph.
On a coordinate plane, line X Y has points (negative 4, 2), (negative 1, negative 3).
If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
3
4
5
6
Answers
9514 1404 393
Answer:
5
Step-by-step explanation:
A graph can be helpful. It shows possible integer coordinates of Z could be ...
(-1, 2) or (-5, 1)
These have distances 5 and 4√2 from Y, respectively. Of these, only the length YZ = 5 appears on your list of possible answers.
__
The hypotenuse of a right triangle is the diameter of the circumcircle. That is, the right angle vertex (Z) appears on a circle whose center is the midpoint of the hypotenuse. Here, that circle center is C = (-4-1, 2-3)/2 = (-5/2, -1/2). The given point Y differs from this by C - Y = (-5/2 -(-1), -1/2 -(-3)) = (-3/2, 5/2). So, a point with integer coordinates will be 2×(5/2) = 5 units above point Y, which puts it in the 2nd quadrant.
__
Adding any of the 8 combinations (±3/2, ±5/2) or (±5/2, ±3/2) to the circle center coordinates will result in integer coordinates for the right angle vertex. Of these, only the ones listed above are in the second quadrant. A couple are on the y-axis, and two of the possibilities are X and Y. The other two are in the third quadrant.
Related Questions
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Answers
Now im not 100% sure, but this is what i got (for number one).
y=2x−1
Swap sides so that all variable terms are on the left hand side.
2x−1=y
Add 1 to both sides.
2x=y+1
Divide both sides by 2.
2x/2 = y+1/2
Dividing by 2 undoes the multiplication by 2.
So therefore, X = Y+1/2.
(i couldnt explain that very well im sorry, i dont know the 2nd answer im very bad at these)
Answer:
I need 1 Brainliest before I can become Virtuoso
Step-by-step explanation:
at school there are 8 students who only play violin, 10 students who only play guitar, 3 students who play both, and 12 students who don't play any instrument at all. if a student is randomly selected from this school, what is the probability that they play violin or guitar
Answers
Answer:
[tex]\frac{7}{11}[/tex]Step-by-step explanation:
[tex]\frac{21}{33}[/tex] simplified would be [tex]\frac{7}{11}[/tex]
The probability that they play violin or guitar is 7/11 .
What is Probability ?Probability is the likeliness of an event to occur.
It is given that
The number of students who only play violin is 8
The number of students who only play guitar is 10
The number of Students who play both is 3
The number of students who don't play either is 12
Total Students = 8+10+3+12 = 33
Total favorable outcomes (violin or guitar) = 8 + 10 +3
Probability = Total favorable outcomes / Total outcomes
Probability = 21 / 33
Probability = 7/11
Therefore the probability that they play violin or guitar is 7/11 .
To know more about Probability
https://brainly.com/question/11234923
#SPJ2
y + 8 = 2
How do you show your work for this problem ?
Answers
Answer:
-6
Step-by-step explanation:
y+8=2
-8. -8 -> subtract 8 to leave y by itself
y=-6
Answer: Well you have to subtract 8 from both sides so 8-8 crosses off 2-8 equals -6 so y equals -6.
Step-by-step explanation:
Hope it helps! Mark me brainliest.
1.Encuentra de dos formas diferentes el área de las figuras mostradas en cada literal:
Answers
Answer:
Cuadrilátero A: [tex]A = y^{2}+4\cdot y +4[/tex]
Cuadrilátero B: [tex]A = a^{2}+6\cdot a + 9[/tex]
Step-by-step explanation:
Existen dos formas distintas de determinar las áreas de cada cuadrilátero:
(i) Obtener el área de cada cuadrado y sumar los resultados.
(ii) Calcular los lados del cuadrilátero grande y determinar el área.
Cuadrilátero A
Método (i)
[tex]A = y^{2}+2\cdot y +4+2\cdot y[/tex]
[tex]A = y^{2}+4\cdot y +4[/tex]
Método (ii)
[tex]A = (y+2)\cdot (y+2)[/tex]
[tex]A = y^{2}+4\cdot y + 4[/tex]
Cuadrilátero B
Método (i)
[tex]A = a^{2}+3\cdot a +9 + 3\cdot a[/tex]
[tex]A = a^{2}+6\cdot a +9[/tex]
Método (ii)
[tex]A = (a+3)\cdot (a+3)[/tex]
[tex]A = a^{2}+6\cdot a + 9[/tex]
Two of the angles are 90 degrees and 40 degrees. What is the measure of the missing angle? *
Enter only a two digit number.
Answers
WORTH 20 POINTS!! HELP PLEASEE
The function g(t) = - 16t2 + vt + h represents the height of an object, g, in feet, above the ground in relation to the time, t, in seconds, since the object was thrown into the air with an initial velocity of v feet per second at an initial height of h feet.
A model rocket is launched off the ground at an initial velocity of 80 feet per second.
Part B: What domain makes sense for the function in this context?
1. all positive numbers
2. 0 ≤ t ≤ 100
3. 0 ≤ t ≤ 5
4. all real numbers
Answers
Answer:
Step-by-step explanation:
g(t) = -16t² + vt + h
"rocket is launched off the ground at an initial velocity of 80 feet per second"
v = 80
h = 0
g(t) = -16t² + 80t
:::::
The roots of -16t² + 80t are t=0 and t=5. In other words, the rocket hits the ground after 5 seconds.
Domain: 0 ≤ t ≥ 5
A farmer wants to build a rectangular pen using 20 feet of fencing, but the length is to be 4 feet more than the width. What is the length of the pen, in feet?
Answers
Answer:
The length of the rectangular pen is 40ft. The width of the rectangular pen is 20ft
Answer:
7ft
Step-by-step explanation:
2W+2L=20
2(W+L)=20
2(W+(W+4))=20
4W+8=20
4W=12
W=3
or
If 20 is the total length of fencing used, the length of the fence is to be 4 ft longer than the width, and we know this is a rectangular pen (meaning it has 4 sides), we first multiply 4 (the additional ft for the length side) by two to get 8. Next we subtract 8 from the total amount of fencing (20) to get 12. Finally, since we know there are 4 sides to a rectangle, we divide 12 by 4 to get the width. Now since the length is 4 ft longer than the width, and we are looking for the length, then we add 3+4 to equal 7.
7 is the length.
Which property is used in the first step to solve this equation
4(x-6)=5
4x-24 = 5
4x= 29
x=29/4
Answers
Answer:
Distributive property
Step-by-step explanation:
1. A shirt, x, is discounted 20%; what is the sale price?
A. y = 2.2x
B. y = 0.8x
C. y = 1.2x
D. y = 1.02x
E. y = 0.02x
2. A family left a 20% tip after their meal. What is the final cost of their meal if the food cost x dollars?
A. y = 2.2x
B. y = 0.8x
C. y = 1.2x
D. y = 1.02x
E. y = 0.02x
3. A store adds a 120% markup to the cost of an item before selling it to the customers
A. y = 2.2x
B. y = 0.8x
C. y = 1.2x
D. y = 1.02x
E. y = 0.02x
Answers
Answer:
.8x
Step-by-step explanation:
What is the value of d in the equation?
d'= 14
Answers
So 1.75 x d = 14
14/1.75 = d
14/1.75= 8
D = 8
My new speaker costs $154.00, but I also had to
pay 61 tax. How much did I pay in total for my speakers
Answers
Answer:
$247.94
Step-by-step explanation:
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(25 + 19) + 15 = (19 + 25) + 15
What property is that equation
Answers
Answer:
Commutative Property
Step-by-step explanation:
It looks like Associative property which is when you change the GROUP, but actually it’s commutative because it didn’t change any numbers in the group, just the order of where they were.
Associative: (25 + 19) + 15 = (15 + 19) + 25
Commutative: (25 + 19) + 15 = (19 + 25) + 15
It didn’t change the numbers, only the order. Therefore, it would be commutative property
Answer:
25+19=44
44+15=59
19+25=44
44+15=59
Arlene borrows $400 on a 4-year loan. She is charged 5% simple
interest per year. How much interest is she charged for 4 years? What
is
the total amount she has to pay back?
I
Answers
Answer:
For 4 years she is charged $20. She has to pay back $420
Step-by-step explanation:
are any of you in the 9th grade and good with math? 2 (x2 - 3) + x (x - 7)
Answers
Answer:
[tex]3x^{2} - 7x - 6[/tex]
Step-by-step explanation:
[tex]2x^{2} - 6 + x^{2} - 7x[/tex]
[tex]3x^{2} - 7x - 6[/tex]
Help please! I need help with this two step equations
Answers
Answer:
search it up on goggle lll
Answer:
3
Step-by-step explanation:
7. The school librarian orders 35 new
books each year. How many new
books did the librarian order in the
past 12 years?
Answers
Answer:
420
Step-by-step explanation:
35x12
An automobile manufacturer claims that its jeep has a 59.8 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 160 jeeps, they found a mean MPG of 59.7. Assume the standard deviation is known to be 1.3. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
Answers
Answer:
The value of the test statistic is -0.97
Step-by-step explanation:
This test is two tailed test.
Null and Alternative hypothesis is as follow
Null Hypothesis is used when it is assumed that there is no significant difference between the values.
Null Hypothesis = [tex]H_{0}[/tex] = [tex]\mu =[/tex] 59.8
The Alternative hypothesis is the alternative of the Null Hypothesis. It is an experimental technique that is used when it is assumed that there is some difference
Alternative Hypothesis = [tex]H_{a}[/tex] = [tex]\mu \neq[/tex] 59.8
Test statistcs is z
The value of test statistics can be calculated using the following formula
Test Statistics [tex]= (\bar x - \mu ) / \sigma / \sqrt n[/tex]
Test Statistics [tex]= (59.7-59.8) / 1.3 / \sqrt 160[/tex]
Test Statistics = -0.97
PLEASE HELP IMMEDIATELY!!!
Answers
A=gbb/2=15x24/2=180
SOMEONE HELP I'LL MARK CORRECT ANSWER BRAINLY
Answers
Answer:
B
Step-by-step explanation:
Help me.. People who are just trying to get points by just spamming peoples questions, will be reported
Answers
Answer:
I'd say half
Step-by-step explanation:
someone help whats the work for what is 107% of 150
Answers
Answer:
If it's 107% of 50 the answer would be 53.5
If it's 107% more than 50 it would be 103.5
Step-by-step explanation:
107% of 50 is 53.5
50 × 107% = 53.5
50 × 107% = 53.5
+50
--------
103.5
Answer:
160.5
Step-by-step explanation:
you but 107% 150 = what it well give you the answer
Blakes goes from averaging 8 hours of sleep for a school night to averaging 6.5 hours of sleep on the weekend. What is the percent of change in the average hours of his sleep? (HOW DID YOU GET YOUR ANSWER PLEASE SHOW YOUR WORK. DO NOT BOTHER ANSWERING IF YOU DO NOT TELL ME HOW YOU GOT YOUR ANSWER!!)
A. 36
B. 70
C. 1/462
D. 6(4X+3Y-2)
E. 18.75
F. 23.36
G. 2.54
H. 36.3
I. 6(4X-3Y+2)
Answers
Answer:
Step-by-step explanation:
So Blakes sleep 8 hours per night during the school day
8 hours/night...................................100%
6.5 hours/night...................................?
6.5*100/8=81.25
the change in percentage is 100-81.25=18.75%
the percentage change is 18.75
if it is easier for you, another method is:
8-6.5=1.5 subtract the original amount to the new amount
1.5/8=0.1875 divide by the original amount
0.1875*100=18.75 find the percentage
Explain your answer !!
Have a great day
Will give brainlst
Answers
Answer:
1) Peru 2: Columbia 3) Brazil 4) Venezuela
Step-by-step explanation:
i found my answer by looking at which countries have the LEAST oil. Those are the countries who will be most impacted if more people use there oil. I hope this helps :)
Hellppppp........ pleasee
Answers
Answer:
Step-by-step explanation:
The set of points in the 2nd row does not represent a function, because the x-coordinate 2 is associated with more than one y-coordinate.
Functions are one-to-one: For each x value there is one y value associated.
What is the leading coefficient of the polynomial f(c) defined below? need help asap!
Answers
Answer: 7
Step-by-step explanation:
The leading coefficient is the number before the term with the highest power in your polynomial. The coefficient is just a number or constant that is before a variable in your expression.
In this case, the highest degree in this polynomial is five. If we look at the coefficient of that term, we see that it is seven.
what is the GCF of 8,12,16
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4 * 2 = 8
4 * 3 = 12
4 * 4 = 16
set up and solve a quadratic equation to work out the value of x
Answers
100 POINTS!!!
Reggie went out to eat with his family.
The cost of their food was $48.50, plus Reggie gave the waiter an 18% tip.
What was the total price of their meal, including the food and the tip!
A. $57.23
B. $48.68
C. $87.30
D. $50.30
Answers
Answer:
A) $57.23
Step-by-step explanation:
0.18 x 48.5= $57.23. Hope this helped!
A hockey team scored the following number of goals in their last 5 games:
2, 3, 5, 3, 2
Which is the mean absolute deviation of the number of goals?
Answers
Answer:
3.3
Step-by-step explanation:
Round to 2 significant figures 0.000789
Answers
Answer:
0.00079
Step-by-step explanation:
Leading zeroes dont count as sig figs, just round the final value and that gives your answer in 2 sig figs.