Answer:
this triangle is ABC with A(-2 ; -3), B(4; - 3) and C(3;5)
=> [tex]AB=\sqrt{(4-(-2))^{2}+\sqrt{(-3 -(-3))^{2} } }=\sqrt{6^{2} }=6\\\\AC=\sqrt{(3-(-2))^{2}+(5-(-3))^{2} }=\sqrt{5^{2}+8^{2} }=\sqrt{89}\\\\BC =\sqrt{1^{2}+8^{2} }=\sqrt{65}[/tex]
using Heron theorem, we have:
[tex]S=\sqrt{p(p-AB)(p-AC)(p-BC)}\\\\S=\sqrt{(\frac{6+\sqrt{89}+\sqrt{65} }{2})(\frac{\sqrt{89}+\sqrt{65}-6 }{2} )(\frac{6+\sqrt{65}-\sqrt{89} }{2})(\frac{6+\sqrt{89}-\sqrt{65} }{2}) }\\\\S=24 \\\\[/tex]
with S is the area of the triangle
[tex]p=\frac{AB+AC+BC}{2}=\frac{6+\sqrt{89}+\sqrt{65} }{2}[/tex]
Step-by-step explanation:
Area of the triangle with given vertices is equals to 24 square units.
What is Area?"Area is the surface which represents the total space occupied by any two dimensional object."
What is triangle?"Triangle is a polygon which has three sides and three vertices. Sum of all the interior angles of a triangle is equals to 180°."
Formula used
In ΔABC , A(x₁ , y₁) , B(x₂, y₂) and C(x₃, y₃)
Area of a triangle = [tex]\frac{1}{2} [ x_{1} (y_{2} -y_{3} + x_{2} (y_{3} -y_{1} +x_{3} (y_{1} -y_{2} ]\\[/tex]
According to the question,
Let ABC be the triangle with A(-2,-3) , B(4,-3) and C(3,5)
Area of the triangle = [tex]\frac{1}{2}[/tex] [ -2(-3-5) + 4(5+3) +3 (-3 +3)]
= [tex]\frac{1}{2}[/tex] [ 16 +32 + 0]
= 24 square units
Hence Area of the triangle with given vertices is equals to 24 square units.
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Write the equation for line in slope intercept form, given the point (3,-7) and slope = 9.
Answer:
y = 9x - 34
Step-by-step explanation:
(3 , -7) ; slope (m) = 9
Slope intercept form:
y - y1 = m(x -x1)
y - [-7] = 9 (x - 3)
y + 7 = 9*x - 9*3
y + 7 = 9x - 27
y = 9x - 27 - 7
y = 9x - 34
What is the square root of nine
Answer: the square root of 9 is 3.
Which graph represents a function?
HELP!!
Construct the graph of the direct proportion y=kx for k= -1
Simple answer.
-1 x 3 = -3
3 is your x and -3 is your y.
What’s the percentage as a decimal
Answer:
0.0006
Step-by-step explanation:
Gordon types 3,572 words in 47 minutes. Find the unit rate.
Answer:
Gordon types at 76 wpm
Step-by-step explanation:
You can find this by dividing the number of words typed by the number of minutes:
[tex]\frac{3572w}{47m}\\\\= \frac{3572}{47}\frac{w}{m}\\\\= 76\frac{w}{m}\\\\[/tex]
Answer:
78 Words per minute
Step-by-step explanation:
Unit Rate = 3666 Words in 47 minutes
Unit Rate = 78 Words per minute
2) An $80 text book was on sale for $49.60 at the used book store. By what percent did the book decrease in price?
The answer fam is......... 38%
Answer: 38%
Step-by-step explanation:
80x0.62=49.60
Solve for the angle x.
Answer:
x=45
Step-by-step explanation:
An entire triangle is 180 degrees and you already know that one angle is 90 degrees. 180 - 90 is 90. Now you have the equation 2x=90.
You then divide each side by 2 to get the x by itself which leaves you with x=45.
Answer:
if I did my math right it's 45 if not please fix me
Step-by-step explanation:
First thing is the the sides are congruent meant the angles have to be the same.
Next is the box indicates 90°.
Last thing is that every triangle is 180°
so if I did this right the equation is 2x+90=180
and using algebra in this you eliminate the 90 by subtract because - is the opposite of + which cancels itself and leaving the total with 90.
Then divide the 90 by 2 as it cancels out 2x leaving the answer with x=45
I hope this helps you
is this correct? help please
Answer:
yes
Step-by-step explanation:
y = -4/3x + 8 so you would multiply - 4/3 * x. Then you would add 8 to your answer and if the y value equals the value on the graph then it's correct.
A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the length of the rectangle.
Answer:
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
Step-by-step explanation:
Step(i):-
Let 'x' be the length of the rectangle
Given that the width is 3 feet shorter than the length
The width of the rectangle = x -3
Area of the rectangle = length × width
Step(ii):-
Area of the rectangle = length × width
= x ( x-3)
Given that the area of the rectangle = 70 square feet
x ( x-3) = 70
⇒ x² - 3x - 70 =0
⇒ x² - 10 x + 7 x - 70 =0
⇒ x (x -10) +7( x-10) =0
⇒ ( x+7) ( x-10) = 0
⇒ x =-7 and x=10
Final answer:-
we choose x=10
The length of the rectangle (l) = 10 cm
The width of the rectangle (w) = 7 cm
Susan subscribed to a video game rental service. She pays the same
amount for each video game she rents plus a monthly fee to subscribe to
the service. The cost for different numbers of video game rentals are
shown in the graph.
Answer:
C
Step-by-step explanation:
Answer: C. $6.00 monthly fee and $1.25 per video game
Step-by-step explanation:
I did the test
Parker drank 36 fluid ounces of a sports drink at her basketball game. How many pints did she drink
Answer:
2 1/4 pints
Step-by-step explanation:
create a ratio with the fact there are 16 ounces in 1 cup
let 'p' = number of pints
16 = 36
1 p
cross-multiply: 16p = 36
p = 36/ 16, which is 9/ 4, or 2 1/4
Ales read 1/3 of a book Monday. 28 pages Tuesday . still has 1/3 left to read. how many pages in book
Answer:
there are 84 pages in the book.
Step-by-step explanation:
let's call the pages in the book b.
1/3b + 1/3b + 28 = b
2/3b + 28 = b
subtract 2/3b from both sides of the equation
2/3b - 2/3b + 28 = b - 2/3b
28 = b - 2/3b
28 = b/3
multiply both sides of the equation by 3
28 * 3 = b/3 * 3
28 * 3 = b
84 = b
Answer:
The book has 84 pages
Step-by-step explanation:
Equations
Let's make:
x = number of pages of the book
Alex read 1/3x of the book on Monday, 28 pages on Tuesday, and still has 1/3x left to read. The sum of all these portions add up to the number of pages of the book, thus:
[tex]\displaystyle \frac{x}{3}+28+\frac{x}{3}=x[/tex]
Multiplying by 3:
[tex]x+84+x=3x[/tex]
Simplifying:
x = 84
The book has 84 pages
what is the equation in slope-intercept form, of the line prependicular to y= -3/5x +6 that passes through the point with coordinants (12,25)
Answer:
y=5/3x+5
Step-by-step explanation:
change slope in equation given to the negative reciprocal since the line is perpendicular:
-3/5 to 5/3
put values into point slope form y-y1=m(x-x1)
y1 = y in the point given, which is 25
m = slope, which is 5/3
x1 = x in point given, which is 12
y-25=5/3(x-12)
then solve for slope intercept form y=mx+b to get
y=5/3x+5
Find the two solutions to the equation below.
(x – 3)(x − 2) = 0
Anyone know how to do it
Answer:
You have two brackets..divide them as
x-3=0 and x-2=0
so x=3, x=2
The solutions to the equation ( x – 3 )( x − 2 ) = 0 using factors equal to zero are x = 3 and x = 2.
To find the solutions to the equation ( x – 3 )( x − 2 ) = 0, we set each factor equal to zero and solve for x. This is because the product of two factors is equal to zero only if at least one of the factors is zero.
Setting ( x – 3 ) = 0:
x – 3 = 0
x = 3
Setting ( x − 2 ) = 0:
x − 2 = 0
x = 2
Therefore, the solutions to the equation ( x – 3 )( x − 2 ) = 0 are x = 3 and x = 2.
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a scientist recorded the temperature of the first day of spring for 24 hours starting from Midnight their hours the scientist recorded a low of 44°f and a high of 67°f.
Answer:
so what is the question?
pls help me i neeed it first to answer gets a brainliest
Answer:
A
Step-by-step explanation:
Its counting up by 10 and going up by 2
Answer:
its c
Step-by-step explanation:
Write an algebraic expression for the phrase. 12 minus m
A. m/12 B. 12-m C. 12m D. m-12
Answer:
it's b
Step-by-step explanation:
literally twelve minus m
Answer:
B
Step-by-step explanation:
12 minus m is, 12 - m
Find the value of the power.
8^3 =
Answer
Answer:512
Step-by-step explanation:
Answer:
512
Step-by-step explanation:
8*8*8=512
1). Solve for n n + 46 = 67
Help helps please help
Answer:
n=21
Step-by-step explanation:
Subtract 46 from both sides.
n+46−46=67−46
n=21
Answer:
n=21
Step-by-step explanation:
46-67=21
21=n
So the answer is 21.
From a distance of 43 feet from the base of a building the angle of elevation to the top of the
building is 64º. Estimate the height of the building to the nearest foot.
A) 21 feet
B) 39 feet
C) 88 feet
D) 19 feet
Answer: B 39 ft I think
Step-by-step explanation:
A bottle holds 48 teaspoons of vanilla. The amount of vanilla remaining in the bottle decreases by 2 teaspoons per
batch of cookies. How much vanilla remains after 12 batches of cookies
Answer:
24 teaspoons
Step-by-step explanation:
2 times 12 = 24
48 - 24 = 24
The probability that A is the outcome of an experiment is 0.3
What is the probability that A is not the outcome?
Answer:
.7
Step-by-step explanation:
Ayo help a girly out
(1)Simplify each expression. (Make sure to find those "like" terms)
3x + 9 + 2x − 5
Options: 6x + 4
14x - 5
9x
5x + 4
______________________________________________________________
(2)Simplify each expression. (Make sure to find those "like" terms)
7m + 2(m − 5y)
Options: 14m - 5y
9m - 10y
9m - 5y
7m + 10y
_________________________________________________________________
If you're helping tysm my guy ily
Answer 1: 5x + 4
Answer 2: 9m + -10y
Step-by-step explanation:
To simplify 3x + 9 + 2x − 5, you have to find the like terms which are 3x and 2x, and 9 and -5. So you get 3x + 2x + 9 - 5 which gives you the result of 5x + 4. Now to simplify 7m + 2 (m − 5y), you have to distribute first, so 7m + (2) (m) + (2) (−5y) which gives you 7m + 2m + −10y. So now you just have to add. 7m + 2m = 9m and then you have -10y so basically the answer is 9m + -10y.
I hope this helps you bro
Three of the vertices of square ABCD are located at A(0,3), B(4,0), and C(7,4).
Determine the area of square ABCD.
Answer:
The area of the square ABCD is 25 square units
Step-by-step explanation:
The square ABCD has three of its vertices at A(0,3), B(4,0), and C(7,4). The fourth vertex has been also plotted in the image attached below.
The area of the square is
[tex]A = a^2[/tex]
Where a is the length of any of the square's sides. We only have to find the distance from any two consecutive vertices, for example, A(0,3), B(4,0):
[tex]a=\sqrt{(4-0)^2+(0-3)^2}[/tex]
[tex]a=\sqrt{16+9}=\sqrt{25}=5[/tex]
a = 5
Calculating the distance between any other pair of consecutive vertices would yield the same result. The area is now calculated:
[tex]A = 5^2 = 25[/tex]
The area of the square ABCD is 25 square units
PLEASE HELP WILL GIVE BRAINLIEST
travelling to France, a plane encounters a tailwind and averages 282 mph. however, on the return trip the plane, now travelling against the same wind averages 222 mph. find the speed of the wind of the plane in no wind
Answer:
.
Step-by-step explanation:
pls help solve question 3
Answer:
If m is the midpoint of ab it means am is equal to mb
am = 3x + 8 and mb = 6x-4
and ab = am + mb
first find the value of x by using am = mb
3x + 8 = 6x - 4
8 + 4 = 6x - 3x
12 = 3x
x = 4
ab = 3 (4) + 8
= 12 + 8 = 20 = mb
ab = am + mb
= 20 + 20
40
so, the value of ab is 40
Evaluate y=3x for x=2.
y=
Answer:
y=6
Step-by-step explanation:
y=3x x=2
y=3(2)
y=6
For the given expression, the value of y is 6.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ y = 3x
Now, For value of x = 2;
The value of y is,
⇒ y = 3x
Substitute x = 2;
⇒ y = 3 × 2
⇒ y = 6
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What is the total cost with sales tax price $17.95 tax 6%
Answer:
$19.03
Step-by-step explanation:
Okay, this is a standard percentage problem, so learning how to do this is necessary. First, we have to find what 6% of $17.95 is, since of is our keyword and that means to multiply, and percentages turn into decimals:
17.95 x 0.06 = 1.08
So we have our tax, then we have to add that to our original price to get the whole thing:
17.95 + 1.08 = 19.03
So the total sale price is $19.03
Find the point slope equation of the line through (10, -4) with a slope of -6.
Answer:
y=-6x+56
Step-by-step explanation:
The point-slope equation of a line is given as
y=mx+c where m is slope and c is y-intercept of a line.
We are given m=-6 and a point (10,-4) which can be put into y=mx+c to find the only unknown c. Thus,
c=-4+6x10=56.
Now we can easily form the point-slope equation of the line
y=-6x+56.
