find the equation of the sides of an isosceles right angled triangle whose vertex is (-2,3) and the base is on the line x=0
Answers
Answer:
[tex]\large \boxed{y = x + 5; y = -x + 1}[/tex]
Step-by-step explanation:
This is an isosceles right triangle, so triangles ABD and CBD are congruent.
∠ ABD = ∠CBD = 45°
The slope of BC = tan(45°) = 1, and
The slope of BA = tan(-45°) = -1.
1. Equation of BC
The point-slope formula for a straight line is
y - y₁ = m(x - x₁)
x₁ = -2; y₁ = 3; m = 1
Substitute the values
[tex]\begin{array}{rcl}y - 3 & = & 1(x - (-2))\\y - 3 & = & x + 2\\y & = & x + 5\\\end{array}\\\text{The equation for the line is $\large \boxed{\mathbf{y = x + 5}}$}[/tex]
2. Equation of BA
x₁ = -2; y₁ = 3; m = -1
Substitute the values
[tex]\begin{array}{rcl}y - 3 & = & -1(x - (-2))\\y - 3 & = & -1(x + 2)\\y - 3 & = & -x - 2\\y & = & -x +1\\\end{array}\\\text{The equation for BA is $\large \boxed{\mathbf{y = -x + 1}}$}[/tex]
An isosceles right triangle has two equal length legs and the hypotenuse side as its base
The equation of the sides of the isosceles right triangle are;
x = 0 (equation of the base)
y = 1 - x
y = x + 5
The reason for arriving at the above equations are as follows:
The given parameters of the isosceles right triangle are:
The coordinate of the vertex of the triangle = (-2, 3)
The base of the triangle, x = 0
The required parameter:
The equation of the sides of the isosceles triangle
Strategy:
Define the terms and relate the given information with the given term definitions
Solution:
The base of an isosceles triangle is the side that form the equal base angles with the two equal sides of the triangle
In an isosceles right triangle, the two equal sides of the right triangle are the legs of the right triangle, and therefore, the base of the triangle is the hypotenuse side
The base angles of an isosceles right triangle, [tex]\theta _b[/tex] = 45°
The altitude of the triangle, y = (0 - (-2) = 2
The altitude is a perpendicular bisector of the base, therefore;
[tex]tan(\theta _b) = \dfrac{Altitude}{\dfrac{1}{2} \times Base \ length }[/tex]
Therefore;
[tex]Base \ length = \dfrac{Altitude}{\dfrac{1}{2} \times tan(\theta _b)}[/tex]
We get:
[tex]\mathbf{Base \ length} = \dfrac{2}{\dfrac{1}{2} \times tan(45^{\circ})} \mathbf{= 4~}[/tex]
The coordinate of the midpoint of the base is the horizontal line from the vertex to the base, and therefore, the coordinate of the midpoint of the base is x = 0, and y = 3 = (0, 3)
The base is 4 units long and half the base length = 4/2 = 2 units
The coordinates of vertex at the base is given by adding or subtracting 2 from the y-coordinates of midpoint of the base as follows;
Vertex coordinates at the base = (0, 3 + 2) = (0, 5), and (0, 3 - 2) = (0, 1)
The slope, m₁, of the side, s₁, with endpoints (-2, 3), and (0, 1), is found as follows;
m₁ = (1 - 3)/(0 - (-2)) = -1
Therefore, the equation of the side s₁ is (y - 1) = -1·(x - 0), which gives;
y = -x + 1
The slope, m₂, of the side, s₂, with endpoints (-2, 3), and (0, 5), is found as follows;
m₂ = (5 - 3)/(0 - (-2)) = 1
Therefore, the equation of the other side s₂ is (y - 5) = 1·(x - 0), which gives;
y = x + 5
The equation of the sides are; x = 0 (given), y = 1 - x, and y = x + 5
Learn more about finding the equation of a line here:
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Related Questions
Calculate the radius of the circular rug. Use 3.14 for π.
area of rug: 153.86 feet
Answers
Answer:
7 ft
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
153.86 = 3.14 r^2
Divide each side by 3.14
153.86 / 3.14 = r^2
49 = r^2
Take the square root of each side
sqrt(49) = sqrt(r^2)
7 = r
Juan examines the sequence 1, 3, 4, 7, 11, . . . and draws the conclusion that the next number in the sequence is 18. Which statements regarding the situation are accurate? Check all that apply.
Juan used inductive reasoning.
Juan's conclusion is a conjecture.
Juan's conclusion is not possible.
Juan's conclusion is a counterexample.
Juan based his conclusion on patterns.
Answers
Answer:
Juan conclusion is counterexample
Answer:
1, 2, and 5
Step-by-step explanation:
Jada and Noah wanted to find the total volume of a cube and a rectangular prism. They know the prism's volume is 20 cubic units, and they know the cube has side lengths of 10 units. Jada says the total volume is 27,000 cubic units. Noah says it is 1,020 cubic units. Here is how each of them reasoned: Jada's method: Noah's method: 20 + 10^3 20 + 10^3 30^3 20 + 1000 27,00 1,020 Question: Do you agree either of them? Explain
Answers
Answer:
Only Noah is correct.
Step-by-step explanation:
Volume of the cube = 10^3 = 1000 units.
Total volume of the cube + the prism = 1000 + 2
= 1020 cubic units.
Answer:
Only Noah is correct.
Step-by-step explanation:
Volume of the cube = 10^3 = 1000 units.
Total volume of the cube + the prism = 1000 + 2
= 1020 cubic units.
Step-by-step explanation:
-6x+2y=-18. -3x-2y=54
Answers
Answer:
x = -4
y = -21
Step-by-step explanation:
To solve this, we will need to set up a system of equations and get rid of a variable.
-3x - 2y = 54
-6x + 2y = -18
From this, we can see that the 'y' variables can be cancelled out if we add the two together. This means that we must add these equations to each other to cancel out the 'y' variables:
-3x - 2y = 54
-6x + 2y = -18
-------------------- +
-9x = 36
x = -4
Since we have solved for 'x', we can simply plug this value into an equation to find 'y'.
-3(-4) -2y = 54
12 - 2y = 54
-2y = 42
y = -21.
Kai bought 6 new Pokemon cards to add to his collection. The next day, his dog ate half his collection! There are only 27 cards left now. How many cards did Dan start with?
Answers
Jamila babysits to earn money. The mean amount she
earns each time she babysits is $24. If she babysits
nine evenings and earns the following amounts: $15,
$20, $10, $12, $20, $16, $18, and $25, how much did she
earn the ninth evening?
Answers
Answer:
$80Step-by-step explanation:
Give jamila's Mean earning = $24
let her ninth earning be x
we know that mean= (∑sumation of earnings)/number of earnings
[tex]24= \frac{15+20+ 10+ 12+ 20+ 16+ 18+ 25+x}{9}[/tex]
[tex]24= \frac{136+x}{9} \\24*9=136+x\\216=136+x\\x=136-216\\x=80[/tex]
Her ninth earning is $80
Help me for brainliest...
The scale on a map is 1:320 000. What is the actual distance represented by 1 centimere? Give your answer in kilometres.
Answers
Answer:
1cm = 320 km?
Step-by-step explanation:
Answer:
[tex]3.2km[/tex]
Step-by-step explanation:
[tex]1 \: : 320000 \\ 1cm = 320000cm[/tex]
[tex]1cm = 100m \\ [/tex]
[tex]1cm = 320000cm \\ 1cm = 3200m[/tex]
[tex]1km \: \: = 1000m[/tex]
[tex]1cm = 3200m \\ 1cm = 3.2km[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Given that M angle KLH equals 120° which statement about the figure must be true?
Answers
Answer:
m∠HLI = m∠ILM
Step-by-step explanation:
Name and classify the basic geometric object each real life object represent using correct mathematical notation. a. The location of a city on a map b. The angle of a recliner c. Row of corn in a garden d. The angle of a lawn chair when laid all the way down e. An arrow f. The angle of a jet taking off at an airport g. The angle a flag pole sits with the ground
Answers
Answer:
a. A point
b. Obtuse angle
c. A line segment
d. 180 degrees
e. A ray
f. An acute angle
g. 90 degrees
Step-by-step explanation:
a. A point (a place on a plane that has no dimension)
b. Obtuse angle (any angle over 90 degrees)
c. A line segment (a part of a line)
d. 180 degrees (The angle of a line or line segment)
e. A ray (a line segment with one end extending forever)
f. An acute angle (Any angle under 90 degrees)
g. 90 degrees (the pole is perpendicular to the ground)
Aball is thrown downward from a window in a tall building. Its position at time tin seconds is s = 16t ^ 2 + 32t , where s is in feet. How long to the nearest will the ball to fall 276 ?
Answers
Answer:
3secondsStep-by-step explanation:
If a ball thrown downward from a window in a tall building is modeled by the equation, s = 16t² + 32t where s in feet, in order to know the time it will take to fall a distance of 276, we will substitute s = 276feet into the equation and calculate for the value of t as shown;
276 = 16t² + 32t
16t² + 32t = 276
Dividing through by 4
4t² + 8t = 69
4t² + 8t - 69 = 0
Using the general formula to find t
t = -b±√b²-4ac/2a
a = 4, b = 8 and c = -69
t = -8±√8²-4(4)(-69)/2(4)
t = -8±√64+1104/8
t = -8±√1168/8
t = -8±34.176/8
t = -8+34.176/8 or -8-34.176/8
t = 3.272 or -5.272
neglecting the negative time, t = 3secs to the nearest seconds
It will take the all 3secs to fall 276 feets
Peter is making an "X marks the spot" flag for a treasure hunt. The flag is made of a square white flag with sides of 12 centimeters. He will make the "X" by stretching red ribbon diagonally from corner to corner.
How many centimeters of ribbon will Peter need to make the "X"?
Round your answer to the nearest centimeter.
Answers
Answer: 34 cm
Step-by-step explanation:
Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem (to one triangle)
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between corners) and a and b are the other sides.
Replacing with the values given:
c^2 = 12^2 + 12^2
c^2 =144+144
c^2 = 288
c = √288
c = 16.97 cm = 17 cm (rounded)
The other diagonal has the exact same lenght (because the flag is a square)
So, we have to multiply the length of the ribbon by 2:
17 x2 = 34 cm
Feel free to ask for more if needed or if you did not understand something.
Answer:
34
Step-by-step explanation:
I did it on Khan
Please help with this!!! My grade depends on it!!!
Answers
Answer:
52 degree
Step-by-step explanation:
So using cos again again :v
AC^2 = AB^2 +BC^2 - 2ABBCcosB
AC = 31.796cm
then
BC^2=AB^2 + AC^2 -2ABACcosA
Cos A = 0.61
A=52.17degree
How do i find the area i dont understand the formula
Answers
Answer:
The answer is A (97.5)
Step-by-step explanation:
Formula Using the Diagonals
That means the two diagonals form two sides of a square that is twice the size of the rhombus. You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals (d1 and d2 ) and dividing by two.
(13)(15) /2 = 195 /2
(Decimal: 97.5)
Please mark brainliest!
Is the relation a function
Yes
No
Answers
Answer:
Yes
Step-by-step explanation:
As long as the input has an output it will always be a function.
Answer:
Yes
Step-by-step explanation:
Because there isn't a number in the input colum that is repeated like:
1
1
2
3
Instead each number is individual and they aren't repeated.
If they were repeated then it would NOT be a function.
Have a good day. :)
Hope this helps!
(brainliest would be appreciated)
Joe spent $48 on fruit at the grocery store. He spent a total of $50 at the store. What percentage of the total did he spend on fruit?
Answers
Answer:
96%
Step-by-step explanation:
Take the amount spent of fruit and divide by the total
48/50
Percent means out of 100 so multiply the top and bottom by 2
96/100
96%
Answer:
If Joe has a total of 50 dollars and uses only 48 dollars and you are trying find the percentage of how much he spent, all you need to do is take the amount of money he use dives it by how much money he had in the beginning. Then multiply the number by 100 to get the percentage.
48/50=.96
.96*100=96%
In total he spent 96% of his money.
An empty cup in the shape of a cylinder (pictured below) is being filled with water.
7
cm
7 cm
3
cm
3 cm
The cup is filled at a constant rate. The table below shows the amount of water in the cup at specific times.
Number of seconds Amount of water
(
cm
3
)
(cm
3
)left parenthesis, start text, c, m, end text, cubed, right parenthesis
0
00
0
00
3
33
75
7575
6
66
150
150150
Find the percent of the cup that is filled with water after
7
77 seconds.
Use
3.14
3.143, point, 14 for
π
πpi and round your final answer to the nearest percent.
%
Answers
Answer:
The answer is 88%
After 7 seconds the cup is about 88% filled with water.
5. Shirley buys a fax machine and sells it to De
at a gain of 25% on the cost price. Devi then ses
the fax machine to Amirah at a loss of 250 on the
price at which she buys it from Shirley. If Amirah
pays $360 for the fax machine. how much die
Shirley pay for it
Answers
Answer:
Shirley bought a fax machine and sells to Devi at a profit of 25% on the cost price.
Shirley buy price:: x
Devi buy price:: 1.25x
Devi sells the fax machine to Amirah at a loss of 250 on the price which she buys it from Shirley.
Amirah buy price = 1.25x -250
if Amirah pays $360 for the fax machine,how much did Shirley pay for it?
Equation:
1.25x - 250 = 360
1.25x = 360 + 250
x = 610 / 1.25
x = 488
Ans: x = $488 (Price Shirley paid)
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
Answers
Answer:
[tex]4x^2 + 12x + 8[/tex]
Step-by-step explanation:
Area of rectangle
= height * width
[tex]=4(x^2 +3x +2)\\= 4x^2 + 12x + 8[/tex]
Answer:
add 2 and 4
Step-by-step explanation:
x²+3x+6
In a box of crayons 2/5 the crayons are green and 1/6 of purple how much greater is the fraction of green crayons than that of purple A) 1/3 B)3/11 C)1/30 D)7/30
Answers
Answer: 7/30
Step-by-step explanation: 2/5-1/6= 7/30, if it helps pls mark me as brainliest
Jennifer bought 1 apple and 3 oranges for 5.10 and Linda bought 5 oranges and 1 apple for 7.50 what is the price of 1 apple and 1 orange
Answers
Answer:
$2.70
Step-by-step explanation
Jennifer and Linda both bought one apple, but they bought different numbers of oranges. Looking at the numbers, we see that Linda bought 2 more oranges than Jennifer (they bought the same number of apples, so disregard apples for now, we will look at them later).
Subtracting Jennifer's cost from Linda's cost, 7.50 - 5.10 = 2.40
So, we know that 2 oranges cost $2.40, so 1 orange will then cost $1.20.
Now we know the cost of 1 orange. So, we can find the price of an apple by finding the cost of 3 oranges. 3 x 1.20 = 3.60. So, Jennifer's 3 oranges cost 3.60, and subtract this cost from the total cost and we find that 1 apple costs $1.50.
Add the price of 1 apple and 1 orange. $1.50 + $1.20 = $2.70
What is the range of the function shown in the graph?
Answers
Answer:
D. -∞ < y < 5
Step-by-step explanation:
The range are all the possible values for y that the function can take. In the graph we can see that the highest value for y is 5 and there isn't a lowest value for y. It means that the range are values between -∞ and 5.
So the range is:
-∞ < y < 5
Solve for f.
–7f − 9 = 9 − 4f
f =
Answers
-7f -9=9-4f
3f-9=9
3f=18
F=6
Answer:
[tex] \boxed{f = -6} [/tex]
Step-by-step explanation:
[tex] = > - 7f - 9 = 9 - 4f \\ \\ = > - 7f + 4f - 9 = 9 \\ \\ = > - 3f = 9 + 9 \\ \\ = > - 3f = 18 \\ \\ = > 3f = - 18 \\ \\ = > f = - \frac{18}{3} \\ \\ = > f = - 6[/tex]
The slope of the line whose equation is 6x = 4y - 7 is 1. 4 2. 2/3 3. 3/2
Answers
Answer:
3/2
Step-by-step explanation:
Divide by 4 to get 6x/4 = 3x/2
HELP ASAP PLEASE!!! A patient is to take 60 milligrams (mg) of an antibiotic on day 1, take 45 milligrams (mg) on day 2, take 30 milligrams (mg) on day 3 and take 15 milligrams (mg) on day 4. How many total milligrams (mg) will the patient take? (Show your work)
Answers
Answer:
150 mg
Step-by-step explanation:
This is an addition problem. Simply add the mg of the antibiotic that the patient takes each day.
So you would do:
60+45+30+15 = 150
Since you get a result of 150, 150 mg is the answer.
The addition is one of the four fundamental mathematical operations. The patient will take a total of 150 mg of antibiotics.
What is Addition?The addition is one of the four fundamental mathematical operations, the others being subtraction, multiplication, and division. When two whole numbers are added together, the total quantity or sum of those values is obtained.
The total amount of antibiotics the patient will take is,
Total Antibiotic = 60mg + 45mg + 30mg + 15mg = 150 mg
Hence, the patient will take a total of 150 mg of antibiotics.
Learn more about Addition:
https://brainly.com/question/14092461
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PLEASEEE HELP ME WITH THIS QUESTION!!!!!!! ASAP PLEASE ANSWER IT CORRECTLY AND NO GUESSING!!!!!!
Which of the following is true about Debit Cards?
A= When you use a Debit Card you pay the bill at the end of the month with interest.
B= Debit cards withdraw money from your bank account
C= Debit cards are a way for you to borrow money.
Answers
Answer:
the answer
is b
i hope that helps
what is an equation of a line that is perpendicular to the line whos equation is
2y+3x=1
Answers
[tex]\text{First, simplify the equation into slope intercept form:}\\\\2y+3x=1\\\\2y=-3x+1\\\\\text{Divide by 2}\\\\y=-\frac{3}{2}x+1\\\\\text{Now, the perpendicular line is the opposite of the slope, and the opposite}\\\text{value}\\\\\text{Since our original equation is negative, the perpendicular lien will be positive}\\\\\text{And then you would just flip the fraction}\\\\\text{Your perpendicular line should be:}\\\\\boxed{y=\frac{2}{3}x+1}[/tex]
Which of the following is the function for the graph shown?
Answers
Answer: A. [tex]y = x^{2} + 6x + 8[/tex]
Step-by-step explanation:
You can plug in the know point of (-3, -1) to each equation to see which one fits. The correct one in this case is [tex]y = x^{2} + 6x + 8[/tex]
Expand: (1 + 6x)(1 - 6x)
Answers
Answer:
6 x(6x)+6x*-1+1(6x)+1*-1 SIMPLIFIED: 36x^2-1
Step-by-step explanation:
Use foil and distributive property
ax+by=(a-b) , bx - ay =(a+b) simultaneous linear equations using cross multiplication
Answers
Answer:
[tex]x=1\,,\,y=-1[/tex]
Step-by-step explanation:
Given: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]
To solve: the given linear equations
Solution:
Consider the equations:
[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]
By method of cross multiplication:
[tex]\frac{x}{B_1C_2-B_2C_1}=\frac{y}{C_1A_2-C_2A_1}=\frac{1}{A_1B_2-A_2B_1}[/tex]
For equations: [tex]ax+by=a-b\,,\,bx-ay=a+b[/tex]
[tex]ax+by-(a-b)=0\\bx-ay-(a+b)=0[/tex]
Take [tex]A_1=a\,,\,B_1=b\,,\,C_1=-(a-b)\,,\,A_2=b\,,\,B_2=-a\,,\,C_2=-(a+b)[/tex]
So,
[tex]\frac{x}{-b(a+b)-a(a-b)}=\frac{y}{-b(a-b)+a(a+b)}=\frac{1}{-a^2-b^2}\\\frac{x}{-ab-b^2-a^2+ab}=\frac{y}{-ab+b^2+a^2+ab}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\\frac{x}{-(a^2+b^2)}=\frac{1}{-(a^2+b^2)}\,,\,\frac{y}{a^2+b^2}=\frac{1}{-(a^2+b^2)}\\x=1\,,\,y=-1[/tex]
Please help: 3x+10=-5. What is x?
Answers
Answer:
-5
Step-by-step explanation:
3x + (10-10) = -10 - 5
3x = -10 - 5
3x = -15
Divide both sides by 3
3x/3 = -15/3
X = -5
