What are the coordinates of the vertices of ABC? Use the coordinates to find the lengths of ab and . bc
Answers
AC = 3
AB = 4
BC = 5
The coordinates of the vertices of the triangle are A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the coordinates of the triangle are
A ( 2 , 2 ) , B ( 6 , 2 ) and C ( 2 , -1 )
And , length of AB is given by the distance formula .
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
AB = √ ( 16 + 0 ) = 4 units
BC = √ ( 16 + 9 ) = 5 units
Hence , the lengths of AB and BC are 4 and 5 units respectively
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Related Questions
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
Answers
Find all polar coordinates of point p where p = ordered pair 5 comma pi divided by 3.
The polar coordinate of any point can be written as:
(r, θ) = (r, θ + 2nπ) --> when positive
(r, θ) = [ - r, θ + (2n + 1)π ] --> when negative
where n is any integer.
The polar coordinates of this given point P is: P = (r, θ) = (5, π/3).
When the value of r is positive, the polar coordinate is written as P= (5, π/3) = (5, π/3 + 2nπ)
where n is any integer.
When the value of r is negative, the polar coordinate is written as P = (5, π/3) = [ - 5, π/3 + (2n + 1)π] where n is any integer.
Therefore all polar coordinates of point P are (5, π/3 + 2nπ) and [ - 5, π/3 + (2n + 1)π ].
The polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
The coordinates of point p are given as:
p = (5, [tex]\pi[/tex]/3)
A point represented as (r, θ) has the following polar coordinates
(r, θ + 2n[tex]\pi[/tex]) for positive r, and (- r, θ + [2n + 1][tex]\pi[/tex]) for negative r
By comparing (r, θ) and (5, [tex]\pi[/tex]/3), we have:
r = 5
[tex]\theta = \pi/3[/tex]
So, we have:
(r,[tex]\theta[/tex]) = (r, [tex]\theta[/tex] + 2n[tex]\pi[/tex])
The equation becomes
(5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Also, we have:
(-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
Hence, the polar coordinates of point P are (5,[tex]\pi[/tex]/3) = (5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex]) to (-5,[tex]\pi[/tex]/3) = (-5, [tex]\pi/3[/tex] + 2n[tex]\pi[/tex])
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To isolate the variable in the equation -3x - 9 = -27, the first step is to add 9 to both sides. This gives you -3x = -18. What is the next step to isolate the variable?
A.+ 18 B.18 C. -3 D.+ 3x
Answers
Add 9 to both side
-3x-9+9=-27+9
-3x=-18
divided -3 to each side
-3x/-3=-18/-3
x=6
Check:
-3x-9=-27
substitute x with 6
-3(6)-9=-27
-18-9=-27
-27=-27. As a result, the next step to isolate the variable is divided -3 to both side. Hope it help!
Next step to isolate the variable is to divide by -3 .
Given,
-3x-9=-27
Firstly,
Add 9 to both side of the equation,
-3x-9+9=-27+9
-3x=-18
Now,
Divide -3 to each side
-3x/-3=-18/-3
x=6
Now,
Check:
-3x-9=-27
Substitute x with 6
-3(6)-9=-27
-18-9=-2
Thus, the next step to isolate the variable is to divide -3 to both side of equation.
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What is the range of the function g(x) = |x – 12| – 2?
{y | y > –2}
{y | y > –2}
{y | y > 12}
{y | y > 12}
Answers
What is the midpoint of (-3,-7) and (9,8)
Answers
(05.06)Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week. Finally, she spent $15 on new sunglasses.
Which part of the scenario is best represented by a linear increasing interval?
Bentley has $40 in her piggy bank.
Bentley spent $10 on new flip flops.
Bentley got $20 for her allowance.
Bentley spent $15 on sunglasses.
Answers
linear increase would be something added to an equation.
she started with 40,
she spent 10 on flip flops and also spent 15 of sunglasses those are decreases
she added 20 for allowance which is an increase and we can assume she gets the same amount of allowance every week
so that would be the linear increase
Bentley had $40 in birthday money in her piggy bank. Bentley got $20 for her allowance which is represented by a linear increasing interval.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Bentley had $40 in birthday money in her piggy bank.
She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week.
Finally, she spent $15 on new sunglasses.
linear increase would be something added to an equation.
she started with $40 in her piggy bank.
She spent 10 on flip-flops and also spent 15 on sunglasses. This show decreases.
she added 20 for the allowance which is an increase and we can assume she gets the same amount of allowance every week.
So, that would be the linear increase.
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Solve 2(x-1) = 3x+4
Answers
2x - 2 = 3x + 4
x = -6
The excel function ________ would be used to find the lowest score on a series of student test scores. min median sum dmin
Answers
The Excel function you should use to find the lowest score in a series of test scores is the MIN function. It determines the smallest number in a set of values.
Explanation:The Excel function that should be used to find the lowest score on a series of student test scores is the MIN function. This function allows you to determine the smallest number in a set of values. For instance, if you have the scores in cells A1 to A10, you would write the formula as =MIN(A1:A10).
It's important to note that the other options provided, such as median, sum, and dmin, would not accurately find the lowest score. The median would find the middle score, sum would add all the scores together, and dmin is a database function that extracts the smallest number from a selected database column based on the specified conditions.
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Find the 39th term of the arithmetic sequence that starts with 4 and has a common difference of 6.
A. 232
B. 226
C. 238
D. None of these
Answers
a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.
We are told that a=4 and d=6 so we have:
a(n)=4+6(n-1), so the 39th term is:
a(39)=4+6(38)
a(39)=4+228
a(39)=232
A swimming pool is 15 by 30 feet and a consistent 5 feet deep. you are painting the walls and floor of the pool. if a gallon can of paint covers 250 square feet, how many gallon cans would you need to buy
Answers
the bottom of the pool is 15 x 30 = 450 sq feet.
you the have 2 walls that are 30 x 5 = 150 x 2 = 300 square feet
then 2 walls that are 15 x 5 = 75 x 2 = 150 square feet
for a total of 450 +300 +150 = 900 square feet
1 can covers 250 sq ft
so 900/250 = 3.6
so you would need 4 cans of paint
If x varies inversely with y and x = 2 when y = 48, find x when y = 24.
Answers
X=k/y
X=2, y=48
2=k/48
K=2*48 = 96
X= 96/24
X=4
As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commision on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $388. If she sells $1,000, she is paid $520. Find Alysse's salary when she sells $3,300 worth of merchandise.
Answers
[tex]388=x+(y%*400)[/tex] where 388 is what she earns after her base salary, x, is paid and her commission of 400. y is the percent of the commission that she earns. As you can see, we have 2 unknowns, which COULD be a problem. But let's move on first before we freak out.
The next equation involves the other bit of info: that she earns 520 after her base salary of x and her commission of 1000 based on whatever the percentage of her sales is, which is y. That equation looks like this:
[tex]520=x+(y%*1000)[/tex]
Because her base salary is constant, the x's are the same number in both equations. So we can solve each for x:
[tex]x=-388+400y[/tex]
[tex]x=-520+1000y[/tex]
Now that these are both solved for x, and x is the exact same number, we can set those 2 equations equal to each other by the transitive property of equality:
=388+400y= -520+1000y
Solving for y gives you:
132=600y and
[tex] \frac{132}{600} =y[/tex]
Because this is a percentage, we will multiply the decimal we get by 100 to find that the percentage she earns on a sale is 22%. Now that we have that percentage, we can find her base salary. Do that like this:
Use one of your equations to solve for x:
388=x+[(.22)(400)]
388=x+88 and x = 300. That's her base salary. Now use that base salary in an equation to find out her monthly pay after she sells $3,300 worth of merchandise in a month:
x = 300 + [(.22)(3300)]
x = 300 + 726
x = $1,026
That's how much she makes after her base salary of $300 plus her earning off selling $3,300 worth of merchandise at 22% commission.
Answer:
Step-by-step explanation:
In order to solve this we just have to create a system of equations, because we have to unknown values, for the base salary we are going to use X and for the comission we will use Y, now we know that when she sold $400 in merchandise she earned $388 and and when she sold $100 se got paid $520 both equations would look like this:
[tex]x+400y=388\\x+1000y=520][/tex]
Now we can solve them by elimination, multiplying one function by -1.
[tex](-1)(x+400y=388)= -x-400y=-388\\x+1000y=388\\1000y-400y=132\\600y=388\\y=\frac{132}{600} \\y=0.22=22%[/tex]
Now we know that the percentage that she earns is 22% of the merchandise she sells.
Now to know how much does she makes on her base pay we just put the value into one of the functions:
[tex]x+1000y=520\\x+1000(.22)=520\\x+220=520\\x=300[/tex]
So her base pay is $300.
To calculate how much she will earn when she sells $3,300 in merchandise we just put that value into the formula:
[tex]x+3300y=\\300+3300(.22)\\300+726=1026[/tex]
So when she sells 3300 she will make 1026 total.
which function is equivalent to the inverse of y=sec(x)
a. y=cot^-1(x)
b. y=cos^-1(1/x)
c. y=csc^-1(x)
d. y=sin^-1(1/x)
Answers
[tex]sec(x)= \frac{1}{cos(x)} [/tex]
[tex]f(x)=sec(x)= \frac{1}{cos(x)} [/tex]
the inverse of f is g such that f(g(x))=x,
we must find g(x), such that [tex] \frac{1}{cos[g(x)]}=x [/tex]
thus, [tex]cos[g(x)]= \frac{1}{x} [/tex]
[tex]g(x)=cos^{-1} (\frac{1}{x}) [/tex]
Answer: b. g(x)=cos^-1(1/x)
Answer: B) csc^-1(x)
Step-by-step explanation: EDGE 2021
Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. Use 3.14 for pi.
a) 89 miles per hour
b) 117 miles per hour
c) 149 miles per hour
d) 129 miles per hour
Answers
frequency = 4.9 / 5 seconds = 0.98 / second
Angular velocity = 2π radian * 0.98/sec = 6.1544 radian / sec
To pass it to radian per hour multiply by the factor 3600 sec / hour
=> 6.1544 rad / sec * 3600 sec / hour = 22,155.84 rad/hour.
Now, you have to realize that the answer choices are not angular velocities. They have units of miles per hour, which means that they are linear velocities
To calculate linear velocities you need the radius of the circular path described by the object.
With the radius, then you use the formula V = angular velocity * radius =>
For example if the radius is 0.0402 miles, the linear velocity is 0.00402 miles * 22,155.84/hour = 89 miles per hour
If the radius is 0.00528 miles, V = 0.00528 miles * 22,155.84 / hour = 117 mph
If the radius is 0.00673 miles, V = 0.00673 miles * 22,155.84 / hour = 149 mph
If the radius is 0.00582 miles, V = 0.00582 miles * 22,155.84 / hour = 129 mph.
Now you know how to calculate the angular and linear velocities.
if acircle is inscribed in a hexagon, which of the following must be true ? Check all that apply.
A. The hexagon is circumscribed about the circle.
B. Each vertex of the hexagon lies inside the circle.
C. The circle is congruent to the hexagon.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Answers
D. Each vertex of the hexagon lies outside the circle .
E. The circle is tangent to each side of the hexagon .
Answer: A. The hexagon is circumscribed about the circle.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Step-by-step explanation:
Given: A circle is inscribed in a hexagon.
Then the hexagon is circumscribed about the circle.
Each vertex of hexagon lies outside the circle.
As each side of hexagon is just attached to the circle not passing through the circle, thus the circle is tangent to each side of the hexagon.
Since circle is a closed curve and hexagon is regular polygon with 6 sides, they cannot be congruent because they have different shapes.
What is the probability that the student will have score between 71 and 80
Answers
Help please. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
A.5√2 /2
B.5√3
C.5√2
D.5√3 /2
Answers
Answer: The value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Step-by-step explanation: We are given to find the value of the variable 'x' in the figure.
We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:
h = 5 units.
Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.
That is, p = x units.
From relations between trigonometric ratios, we have
[tex]\sin 45^\circ=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{p}{h}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{x}{5}\\\\\\\Rightarrow x=\dfrac{5}{\sqrt2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{(\sqrt2)^2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{2}.[/tex]
Thus, the value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Factor y2 + 10z - 10y - yz.
Answers
First, let's write the problem.
[tex]y^2+10z-10y-yz[/tex]
First, we have to factor the y from [tex]y^2-10y[/tex], so we would be left with,
[tex]y\left(y-10\right)[/tex]
Next, we factor the [tex]-z[/tex] from [tex]10z-yz[/tex]. This would leave us with,
[tex]=y\left(y-10\right)-z\left(y-10\right)[/tex]
The common term is [tex]\left(y-10\right)[/tex], so let's factor it out.
[tex]=\left(y-10\right)\left(y-z\right)[/tex]
That would be our final answer.
Thanks!
-TetraFish
GCF of y^2 and -yz
GCF of 10z and -10y
y(y-z)+10(z-y)
Now, (z-y) is the opposite of (y-z), so turn the +10 into -10 and change sign inside parenthesis.
y(y-z) - 10 (y-z)
(y-10)(y-z)
A mosaic is made by having 1 cm square tiles glued onto a photograph. the photograph is a 6 cm by 8 cm rectangular photo. It is enlarged by a scale factor of 1.5. how many tiles are needed to cover the enlarged photo
Answers
Old photo = 6 cm x 8 cm
New photo = 6 cm x 1.5 x 8 cm x 1.5
= 9 cm x 12 cm
Number of tiles = Area of photo / Area of tiles
Area of photo = 9 x 12 = 108 cm^2
Area of tiles = 1 cm x 1 cm = 1 cm^2
Number of tiles = 108 cm^2 / 1 cm^2 = 108 tiles
The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. what is the temperature of the coldest point in the plane?
Answers
can be written as follows:
[tex] x^{2} -4x+ y^{2}+2y[/tex]
[tex](x^{2} -4x+4)-4+ (y^{2}+2y+1)-1[/tex]
[tex] (x-2)^{2}+(y+1)^{2} -5[/tex]
since [tex](x-2)^{2}[/tex] and [tex](y+1)^{2}[/tex] are always positive, except for x=2 and y=-1, when they become 0,
the minimum value of this expression is when x=2, and y=-1, that is -5
Answer: -5
find the center of the circle that can be circumscribed about triangle EFG, E(6,4) F(6,2) and G(10,2)
Answers
Final answer:
The center of the circumscribed circle about triangle EFG with given vertices is found by calculating the perpendicular bisectors of the triangle's sides and locating their intersection point, which is the center (8,3).
Explanation:
To find the center of the circumscribed circle about triangle EFG with vertices E(6,4), F(6,2), and G(10,2), we need to determine the perpendicular bisectors of at least two sides of the triangle and then find their intersection point, which will be the center of the circumscribed circle.
First, find the midpoint of side EF, which has the same x-coordinate (since E and F have the same x-coordinate), so the midpoint is (6,3).Next, we need the equation of the perpendicular bisector of EF. Since EF is vertical, its perpendicular bisector is a horizontal line that passes through the midpoint, hence the equation is y = 3.Then, find the midpoint of side FG. As the endpoints have the same y-coordinate, the midpoint will have that y-coordinate (2) and the x-coordinate will be the average of the x-coordinates of F and G, which is (6+10)/2 = 8. So, the midpoint of FG is (8,2).The slope of side FG is 0 (since it's horizontal), so the slope of its perpendicular bisector is undefined, meaning it's a vertical line. Consequently, the equation of this perpendicular bisector is x = 8.Last, by solving the system of equations formed by the two perpendicular bisectors x = 8 and y = 3, we find the intersection point, which is the center of the circumscribed circle: (8,3).Find y' if x = tan(y)
Answers
[tex]x=\tan y[/tex]
[tex]\dfrac{\mathrm d}{\mathrm dx}x=\dfrac{\mathrm d}{\mathrm dx}\tan y[/tex]
[tex]1=\sec^2y\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]1=\sec^2y\,y'[/tex]
[tex]y'=\dfrac1{\sec^2y}=\cos^2y[/tex]
Furthermore, if you restrict the domain of [tex]y[/tex], we could write
[tex]x=\tan y\iff \tan^{-1}x=y[/tex]
and so we could also have
[tex]y'=\cos^2(\tan^{-1}x)=\left(\dfrac1{\sqrt{x^2+1}}\right)^2=\dfrac1{x^2+1}[/tex]
Find the measure of each angle: Complementary angles with measures (5x)° and (4x−18)°.
Answers
so
5x+4x-18=90
9x-18=90
add 18 both sides
9x=108
divide both sides by 9
x=12
5x is one angle
5x=5(12)=60 degrees
the other one is 4x-18
4x-18=4(12)-18=48-18=30
the angles are 60 degrees and 30 degrees
and x=12 degree
The measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
What are complementary angles?Complementary angles are a pair of angles whose sum is always equal to 90°.
If A and B are complementary angles, then A + B = 90°.
How to solve the given question?In the question, we are asked to find the measure of each angle, given that the angles (5x)° and (4x - 18)° are complementary angles.
As we know that these angles are complementary, we can write the equation to solve for x as,
5x + (4x - 18) = 90
or, 5x + 4x - 18 = 90
or, 9x = 90 + 18 = 108
or, x = 108/9 = 12.
Therefore, the value of these angles are:
(5x)° = (5*12)° = 60°.(4x - 18)° = (4*12 - 18)° = (48 - 18)° = 30°.Therefore, the measure of the complementary angles (5x)° and (4x−18)° are 60° and 30° respectively.
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Help a sphere has a radius of 8ft if the radius is doubled what is the effect on volume
Answers
What is the slope of a line that is perpendicular to the line v= 3/4x-6?
A. 3/4
B. -4/3
C. -3/4
D. 1/6
Answers
The reciprocal of 3/4 is 4/3. The negative of that is -4/3.
Final answer: B
The slope of line which is given to be perpendicular to the line represented by equation "v = (3/4)x - 6" is : (b) -4/3.
To determine the slope of a line that is perpendicular to the given line v = (3/4)x - 6, we use the property that perpendicular lines have slopes that are "negative-reciprocals" of each other.
The slope of the given line is 3/4. To find the slope of the perpendicular line, we take the negative reciprocal of 3/4.
The negative reciprocal of 3/4 is -4/3. So, the slope of the line that is perpendicular to the given-line v = (3/4)x - 6 is -4/3.
Therefore, the correct answer is (b) -4/3.
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find the common ratio of the following geometric sequence: 3.512,12.292,43.022,150.577,527.020
A) 2.5
B) 3.5
C) 8.78
D) 0.29
Answers
Start from the right end and divide the by the previous term.
527.020/150.577 = 3.5
150.577/43.022 = 3.5
43.022/12.292 = 3.5
12.292/3.512 = 3.5
r = 3.5 LETTER B
Bobby knows that the perimeter of the original rectangular is 120 meters he also knows that the perimeter of the reduced rectangular is 30 meters and the reduced length is 9 meters
Answers
Answer:36meters
Step-by-step explanation:
The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?
Answers
a^2 = y^2 + 11^2
x^2 - 5^2 = y^2 - 11^2.......... (1)
Also consider the whole triangle:
x^2 + y^2 = 16^2..........(2)
x^2 - y^2 = -96 .........(3) (from equation (1))
adding 2 x^2 = 256 + -96 = 160
x^2 = 80
x = sqrt80
= 8.94 to nearest hundredth
find the value of x.
Answers
X + X + (X - 26) + (X - 26) = 360
2X + X - 26 + X - 26 = 360
4X - 52 = 360
4x = 412
X = 103.
The value for X, I believe would be 103 degrees. You can verify this by plugging in the value into both expressions, X and X-26 and see that if adding all the expressions together does it equal 360 degrees.
Larry's dining room table measures five feet in diameter. what scale diameter will he use if the scale he is using is 1 inch = 2 feet?
Answers
1/2 = x/5
2x = 5
X = 5/2
2.5 inches would measure 5 feet according to the scale
Answer: 2.5 inches.
Step-by-step explanation:
The given statement : Larry's dining room table measures five feet in diameter.
i.e. We are given that the diameter of Larry's dining room table = 5 feet
The scale used by him 1 inch =2 feet
i.e. [tex]\text{1 feet =}\dfrac{1}{2}\text{ inch}[/tex]
Now, [tex]\text{5 feet =}5\times\dfrac{1}{2}\text{ inches}=2.5\text{ inches}[/tex]
Therefore, the scale diameter he will use = 2.5 inches.
The record ski jump for women is 110 meters. What is this length in feet?
Answers
Answer:
The record ski jump for women is 360.89 feet.
Step-by-step explanation:
The record ski jump for women is 110 meters.
Record ski jump = 110 m
We need to find what is this length in feet.
We have the conversion 1 m = 3.28084 ft
Using the above conversion
We will get
1 m = 3.28084 ft
110 m = 110 x 3.28084 = 360.89 ft
The record ski jump for women is 360.89 feet.