Given:
The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).
To show:
That the triangle ABC is a right angled triangle.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The vertices of a triangle ABC are A(-3,-4), B(16,-2) and C(13,-10).
Using the distance formula, we get
[tex]AB=\sqrt{(16-(-3))^2+(-2-(-4))^2}[/tex]
[tex]AB=\sqrt{(19)^2+(2)^2}[/tex]
[tex]AB=\sqrt{361+4}[/tex]
[tex]AB=\sqrt{365}[/tex]
Similarly,
[tex]BC=\sqrt{\left(13-16\right)^2+\left(-10-\left(-2\right)\right)^2}[/tex]
[tex]BC=\sqrt{73}[/tex]
And,
[tex]AC=\sqrt{\left(13-\left(-3\right)\right)^2+\left(-10-\left(-4\right)\right)^2}[/tex]
[tex]AC=\sqrt{292}[/tex]
Now, add the square of two smaller sides.
[tex]BC^2+AC^2=(\sqrt{73})^2+(\sqrt{292})^2[/tex]
[tex]BC^2+AC^2=73+292[/tex]
[tex]BC^2+AC^2=365[/tex]
[tex]BC^2+AC^2=(AB)^2[/tex]
Since the sum of the square of two smaller sides is equal to the square of the largest side, therefore the given triangle is a right angle triangle by using Pythagoras theorem.
Hence proved.
Find all the zeroes of 2x⁴-3x³-3x²+6x-2, if you know that two of its zeroes are √2 and -√2.
Answer:
nose es algo q no se puede saber
pls help someone !!!!!!!
Answer:
Has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1)
Step-by-step explanation:
We can eliminate half the answer choices by finding whether the line passes through (1,0) or (0,1). Coordinates are read as (x,y), therefore the line passes through (0,1). The slope of the line y=x has a slope of 1. Looking at the graph, we can see that the increasing interval of the line is tilted down ever so slightly, therefore the slope must be less than one.
Therefore, the answer is has a slope of [tex]\frac{3}{4}[/tex] and passes through the point (0,1).
Answer:
Its C, or the third option.
Step-by-step explanation:
Rise/run on this graph is 3/4
and y-intercept is (0, 1)
so C, or third option is correct.
Marking brainliest
Please help!
Answer:
[tex]AB\approx 24.22[/tex]
Step-by-step explanation:
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle.
In this case, in order to form the ratio, we're looking for the angle to the bottom right of the triangle. Notice how this angle is the supplement to the angle marked [tex]130.8^{\circ}[/tex]. Since the two angles form one side of the line, we can solve for this angle.
Let's call the angle [tex]\theta[/tex]:
[tex]130.8+\theta=180,\\\theta=49.2^{\circ}[/tex]
From basic. trig for right triangles (refer to first paragraph in answer):
[tex]\sin 49.2^{\circ}=\frac{AB}{32},\\AB=32\sin 49.2^{\circ}=24.2238417809\approx \boxed{24.22}[/tex]
7. George has some quarters and some dimes. He has 6 more dimes than quarters and all of
the coins he has are worth $3.05. How many dimes and quarters does George have?
Answer:
the answer will be 18 ohkay but they will eill have more dimes than quarters
Answer:
Please the answer from the other user is completely wrong, the real answer is 7 quarters and 13 dimes
Step-by-step explanation:
0.1 (x+6) + 0.25x = 3.05
0.35x = 2.45
x = 7
therefore,
7 quarters
x+6 dimes = 13 dimes
PLEASE GIVE BRAINLIEST
write the equation of a circle that has a center of (-2,1) and a radius 3
The answer:
(x+2)²+(y–1)²=9
Help pls
Bshdndbrjdhbdbdhdjd
Answer:
just function A
A is, for every 2x (2 steps) the value of y increased linearly by 2.5
B isn't, for every 10x (10 steps), the increase of y varies
Please help me Im confused on this problem
Answer:
b = 6 sqrt(2)
Step-by-step explanation:
Since this is right triangle, we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 + b^2 = 9^2
9+b^2 = 81
b^2 = 81-9
b^2 = 72
Take the square root of each side
sqrt(b^2) = sqrt(72)
b = sqrt(36*2)
b = 6 sqrt(2)
The number of hours that each of 6 students spent reading last week is shown in the bar graph below. For the data in the bar graph, which measure is the LEAST? *
1 point
Captionless Image
What is 2 of 1,800,000÷3?
Answer:
Of is a keyword for multiplication.
So, your equation is really 2 X 1,800,000÷3=?
Final answer: 1,200,000
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
can someone please help me find f
Find the length of arc AB with an angle measure of 15 degrees and radius of 10 cm. Round to the nearest hundredth place if you get a continuous decimal when dividing with 360 degrees.
Answer:
AB ≈ 2.62 cm
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{15}{360}[/tex]
= 2π × 10 × [tex]\frac{1}{24}[/tex]
= [tex]\frac{20\pi }{24}[/tex]
≈ 2.62 cm ( to the nearest hundredth )
[tex]\frac{3}{4}- \frac{2}{3}[/tex]
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
We require the fractions to have the same common denominator
The LCM of 4 and 3 is 12 , then
[tex]\frac{3(3)}{4(3)}[/tex] - [tex]\frac{2(4)}{3(4)}[/tex]
= [tex]\frac{9}{12}[/tex] - [tex]\frac{8}{12}[/tex]
= [tex]\frac{1}{12}[/tex]
Another identity problem...
Answer:
cot(x)=-sqrt(3)/3
Step-by-step explanation:
I'm going to use the Pythagorean Identity sin^2(x)+cos^2(x)=1 to find the sine value since cotangent value is the cosine value over sine value.
Plug in:
sin^2(x)+(-1/2)^2=1
Simplify:
sin^2(x)+1/4=1
Subtract 1/4 on both sidea:
sin^2(x)=3/4
Square root both sides:
sin(x)=sqrt(3)/2. [Sine is positive since x is in 2nd quadrant]
cot(x)=(-1/2)/(sqrt(3)/2))
cot(x)=-1/sqrt(3)
Rationalize denominator by multiplying by sqrt(3)/sqrt(3):
cot(x)=-sqrt(3)/3
cot(x)=
Find the volume of a pyramid with a square base, where the side length of the base is 17 in and the height of the pyramid is 9 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
What is the answer for this question (What does the equation 100+0.05p=0.25p represent?)
Answer:
100+0.30p
hope this helps
have a good day :)
Step-by-step explanation:
X-2y=5 2x-4y=10
Put both equations in slope-intercept form
Solve the systems of equations by substitution
Solve the systems of equations by graphing
ONE HUNDRED POINTS HURRY
Step-by-step explanation:
X-2y=5 ; 2x-4y=10
• x - 2y = 5 • 2x -4y = 10
-2y = -x+5 -4y= -2x +10
y1 = ½x - 5/2 y2 = ½x -5/2
• => y1 = y2
½x -5/2 = ½x -5/2
the systems have no solution
• graph as attached
Answer:
[tex]\textsf{Equation 1}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
[tex]\textsf{Equation 2}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
True for all x (infinitely many solutions)
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y = mx + b[/tex]
(where m is the slope and b is the y-intercept)
Given equations:
[tex]\begin{cases}x-2y=5\\2x-4y=10\end{cases}[/tex]
To put both equations in slope-intercept form, rearrange both equations to make y the subject:
Equation 1
[tex]\implies x-2y=5[/tex]
[tex]\implies x-2y+2y=5+2y[/tex]
[tex]\implies x=5+2y[/tex]
[tex]\implies x-5=5+2y-5[/tex]
[tex]\implies 2y=x-5[/tex]
[tex]\implies 2y \div 2=(x-5) \div 2[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Equation 2
[tex]\implies 2x-4y=10[/tex]
[tex]\implies 2x-4y+4y=10+4y[/tex]
[tex]\implies 2x=10+4y[/tex]
[tex]\implies 2x-10=10+4y-10[/tex]
[tex]\implies 4y=2x-10[/tex]
[tex]\implies 4y \div 4=(2x-10) \div 4[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Therefore, both equations are the same as they have the same slope and y-intercept.
As both equations are the same, this system of equations is called an equivalent system.
To solve a system of equations by substitution, substitute one equation into the other:
[tex]\implies \dfrac{1}{2}x-\dfrac{5}{2}= \dfrac{1}{2}x-\dfrac{5}{2}[/tex]
As both sides are equal, the solution is true for all x.
The solution to a graphed system of equations is the point(s) of intersection.
When graphing the given system of equations, as the lines are the same, they will be on top of each other. They are called coincident lines and have infinitely many solutions since the lines have the same slope and same y-intercept.
Learn more about systems of equations here:
https://brainly.com/question/21447811
https://brainly.com/question/27357423
Draco and his friends bought Bertie Bott's Every Flavor Beans for $3 per packet and chocolate frogs for $1 per packet at Honeydukes. They spent a total of $54 to buy a total of 36 packets of Beans and frogs.
Part A: Write a system of equations that Draco can solve to find the number of packets of Bertie Bott's Every Flavor Beans and the number of packets of chocolate frogs that he and his friends bought at Honeydukes. Tell what the variables used in the equations represent. (5 points)
Part B: Solve the system of equations from Part A to find out how many packets of chocolate frogs and Bertie Bott's Every Flavor Beans Draco and his friends bought and write the answer in (x, y) form. Tell which method you used to get the answer, and explain why you selected that particular method to get the answer.
Answer:
Part A: x + y = 36, 3x + y = 54
Part B: (9, 27), I used subtraction to solve the system, because it eliminated the "y" value, so it would be easiest to solve.
Step-by-step explanation:
Amount of Bean Packets: x
Amount of Frogs: y
We are given that:
x + y = 36
3x + y = 54
This is the answer to answer A.
To solve, use subtraction. Subtract:
3x + y - (x + y) = 54 - 36
3x - x + y - y = 18
2x = 18
x = 9
Substituting x = 9 into x + y = 36, we find that y = 27
In (x, y) form, substitute x = 9 and y = 27 to get (9, 27)
I used subtraction to solve the system, because it eliminated the "y" value, so it would be easiest to solve.
Megan runs a bakery in which she can sell cakes for $12.95. Write a function for the amount of profit, in dollars, she makes for selling n amount of cakes.
Simplify this for me thanks u
[tex]4n + 3(n - 5) + 2 \\ \\ = 4n + 3n - 15 + 2\\ \\ = 7n - 13[/tex]
Option BHope This Helps You ❤️Are complementary angles adjacent?
A) Always
B) Sometimes
C) Never
Answer:
Always
Assumption:
At least how I know it.
WILL GIVE BRAINLIEST!! YOU MUST SHOW YOUR WORK! THANKS!
Jonathan is building a circular pond attached to a corner of his house. He wants to put bricks around the entire pond, including the sides that are against the house. The radius of the pond is 6ft.
Approximately how many feet of bricks does Jonathan need for the border of his pond? (Use 3.14 as an estimate for...I can’t put the sign....)
A. 28.26 ft
B. 30.84 ft
C. 37.68 ft
D. 40.26 ft
E. 46.68 ft
The formula for the circumference of a circle is 2 x 3.14 x radius
2 x 3.14 x 6 = 37.68
Which is greater 5.97 or 5.946????
Answer:
5.97
Step-by-step explanation:
Answer:
5.97
Step-by-step explanation:
5.946 = 5.94
5.97>5.94
can you answere this please? i will give brainleyest
Step-by-step explanation:
Bestie there is nothing attached
sam has a rope that is 38 feet long. He cuts the rope into 2 pieces. One piece is 1.5 feet long .
How long is the other piece?
Answer:
36.5 feet long.
Step-by-step explanation:
38-1.5 is equal to 36.5, you subtract to find the other number, therefor one piece is 1.5 feet long and the other is 36.5 feet long.
Answer:
36.5 feet long
Step-by-step explanation:
38 - 1.5
= 36.5
What is L x W X H mean
Answer:
lincth times with times hight
Step-by-step explanation:
Which statement correctly uses limits to determine an asymptote of g(x)?
Answer:
Step-by-step explanation:
When a limit has the x value approaching infinity, we are talking about end behavior of functions which implies horizontal asymptotes. As x approaches both positive and negative infinity, the tails of each branch of this function approaches 0; therefore, the correct choice for this the third one down.
Answer: c
Step-by-step explanation: got it right
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
equilateral acute
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
C. Equilateral acute
Step-by-step explanation:
The triangle is less than 90 degrees so it's an acute
change x-2y=4 into slope-intercept form.
Answer:
y = (1/2)x - 2
Step-by-step explanation:
Slope intercept form: y = mx + c
x - 2y = 4
-2y = -x + 4
[tex]\frac{-2y}{-2}=\frac{-x}{-2}+\frac{4}{-2}\\\\y = \frac{1}{2}x - 2[/tex]
Find the exact value of sin (8x) cos (3x) – cos (8x) sin (3x).
Answer:
answer is 11 x
Step-by-step explanation:
Mark brainliest
4. Given point A (3, 8) and point B (-5, 1). Find the following:
a.) The coordinates of the midpoint of segment AB. Write your answer in this form: (x, y) (7 points)
b.) Using the distance formula, find the length of segment AB. Round to the nearest hundredth. (7 points)
c.) Find the slope of segment AB. (if your answer is a fraction, use the "/" symbol) (7 points)
Answer:
a) (-1,4.5)
b)10.63 units
c)7/8
Step-by-step explanation:
a) To find this, we use the midpoint formula
(x,y) = (x1 + x2)/2 , (y1 + y2)/2
(x1,y1) = (3,8)
(x2,y2) = (-5,1)
(x,y) = (3 -5)/2 , (8 + 1)/2 = (-1, 4.5)
b) To calculate the distance D between two points, we use the formula;
D = √(x2-x1)^2 + (y2-y1)^2
D = √(-5-3)^2 + (1-8)^2
D = √(-8)^2 + (-7)^2
D = √64 + 49
D = √113
D = 10.63 units
C) We use the slope formula here
m = (y2-y1)/(x2-x1)
m = (1-8)/(-5-3) = -7/-8 = 7/8