Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs in simplest form.
Answer:
The area of the triangle is 18 square units.
Step-by-step explanation:
First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:
AB
[tex]AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}[/tex]
[tex]AB \approx 7.616[/tex]
BC
[tex]BC = \sqrt{(-1-5)^{2}+(4-6)^{2}}[/tex]
[tex]BC \approx 6.325[/tex]
AC
[tex]AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}[/tex]
[tex]AC \approx 5.831[/tex]
Now we determine the area of the triangle by Heron's formula:
[tex]A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}[/tex] (1)
[tex]s = \frac{AB+BC + AC}{2}[/tex] (2)
Where:
[tex]A[/tex] - Area of the triangle.
[tex]s[/tex] - Semiparameter.
If we know that [tex]AB \approx 7.616[/tex], [tex]BC \approx 6.325[/tex] and [tex]AC \approx 5.831[/tex], then the area of the triangle is:
[tex]s \approx 9.886[/tex]
[tex]A = 18[/tex]
The area of the triangle is 18 square units.
1.Which answer below represents the
line 5y= 15x+ 10 in the form "y= mx +
c" .
1. 5y= 3x + 2
2.y= 3x + 2
3.y= 5x + 2
O4.y= 3x + 5
3x + 0 = 3x
Need help
Answer:
x is equal to all real numbers.
Step-by-step explanation:
3x = 3x
No matter what number you substitute for x, 3x will always equal 3x.
plsss help i’ll give brainliest if you give a correct answer
Answer:
x = 7
Step-by-step explanation:
15-8=7
Richard is frustrated. He knows the line to the right should have a 3 and a 4 in the equation but he can't remember if it is y = 4x + 3 or y = 3x + 4. a. Which equation is correct? How do you know?
Answer:
The correct equation is "y=4x+3"
Step-by-step explanation:
Given equation:
[tex]y= 4x+3 \ \ or \ \ y=3x+4[/tex]
As per the given line formula:
[tex]\to y=mx+c[/tex]
The slope(m) of the line is [tex]\frac{4}{1} = 4[/tex] and y-intercept at 3, that is the point (c). So, the correct equation of the line: [tex]y = 4x + 3[/tex]
1-x⁴
is it polynomial?
Are the figures congruent? Explain.
A boy has 11 coins in dimes and quarters. Their value is $170. How many of each does he have? (Hint: Let x be the number of quarters and 11 - x be the number of dimes.)
Answer:
x - number of dimes, y - number of quarters
x + y = 11
0.10 x + 0.25 y = 1.70
0.10 x + 0.25 ( 11 - x ) = 1.70
We can solve it:
0.10 x + 2.75 x - 0.25 x = 1.70
0.15 x = 1.05
x = 1.05 : 0.15
x = 7 ( a boy has 7 dimes and 4 quarters )
Answer: D ) 0.10 x + 0.25 ( 11 - x ) = 1.70
Step-by-step explanation:
the length of one side of the base of a square pyramid is 15 cm. the height of each face is 40 cm. what is the surface area of the pyramid?
Answer:
B. 1,425 square centimeters
Step-by-step explanation:
Area of the square pyramid = b² + 2bs
Where,
b = length of square base = 15 cm
s = slant height of each face = 40 cm
Surface area of the pyramid = 15² + 2(15)(40)
= 225 + 1,200
Surface area = 1,425 cm²
1/3x1/6 7 more and I’m done
Answer: 1/18
Step-by-step explanation:
Multiply both Numerators
1x1=1
Multiply both Denominators
3x6=18
1/18
Can someone pls help im new to this
Answer:
5
Step-by-step explanation:
[tex]\frac{-10}{-2} \\\\5[/tex]
−(x − 7)+ 5/3 = 2(x + 9)
simplify
please help me!!!!
Rewrite the expression in the form x^n
Answer:
[tex]x^{-2}[/tex]
Step-by-step explanation:
[tex]\frac{x^{6}}{x^{8}}\\ = x^{6-8} = x^{-2}[/tex]
Write the numerical expression that represents the following: 6 times the sum of 12 and 8
Answer:
12+8*6
Step-by-step explanation:
(-8,-2);m=3/4 in point slope form
Answer:
y + 2 = ³/₄(x + 8)Step-by-step explanation:
The point-slope form of the equation that describes the line with a slope of m and containing the point (x₀, y₀) is: y - y₀ = m(x - x₀)
m = ³/₄
(-8, -2) ⇒ x₀ = -8, y₀ = -2
Therefore:
y - (-2) = ³/₄(x - (-8))
y + 2 = ³/₄(x + 8)
Circumference of a circle is 14 pi what is the area in square inches express your answer in terms of pie
Answer: 49π inches²
Step-by-step explanation:
The formula for the circumference of a circle = 2πr
Since the circumference is 14π, we have to find the radius in order to solve the area.
2πr = 14π
r = 14π/2π
r = 7
Since area = πr²
= π × 7 × 7
= 49π inches²
Find the volume of the cylinder.
Either enter an exact answer in terms of " or use 3.14 for T.
2
units3
Answer:
56.52
Step-by-step explanation:
pi×r²h
=3.14×3²2
=3.14×9×2
=3.14×18
= 56.52³
Testimated the ceiling was 10 ft tall.
The acutal height of the ceiling was
12 ft tall. What is my percent of error?
Jenny wants to buy an MP3 player that costs $30.98. Write an equation so find how much change (x) she receive if she gives the cashier $40. *
Answer:
40.00-30.98=x
Anacondas are snakes found in South America. Anacondas can measure over 1612 feet in length. How many inches are in 1612 feet?
Answer:
165 inches
Step-by-step explanation:
WORTH 100 POINTS NEED DONE ASAP WRONG ANSWERS WILL BE REPORTED THANK YOUUU
Answer:
3.
1.x=√(15²-12²)=√81=9
2.x=√(6²+6²)=6√2
3.c=√(√19²-√7²)=√(19-7)=√12
Step-by-step explanation:
4.h=10
a=b=x
we have
by using Pythagoras law
h²=x²+x²
100=2x²
x²=50
x=√50=5√2
both legs =5√2
HELP I HAVE 5 MINS :(
Answer:
y intercept is (0,-5)
Step-by-step explanation:
Is at x = 0
Intercepts the y axis
pls help me with #3 I don’t understand
Answer:
h ≈ 235
Step-by-step explanation:
We know there is a tower with h height. There is also a wire (that's diagonal) travelling to the ground. It touches the ground. The angle it makes with the ground is 57°.
Refer to the image below of what the problem should look like.
Refer to the trigonometric ratios:
tangent = opposite side/adjacent side
sine = opposite side/hypotenuse
cosine = adjacent side/hypotenuse
We can use sine because we are looking for the opposite side (to the angle) and we have the hypotenuse. So:
sine = opposite side/hypotenuse
sin(57) = h/280
sin(57) / 1 = h / 280
Cross multiply:
sin(57) (280) = 1 (h)
Input to calculator:
h = 234.827759...
h ≈ 235
Multiply (5x - 2)^2
Answer: that would b 25x^2-20x+4!
Step-by-step explanation:
Answer:
25x^2-20x+4
Step-by-step explanation:
Ed wants to bicycle at least 75 miles this week. The inequality 11 + 4b > 75 can be used to find the average number of miles he should bike on his remaining 4 bike rides this week.
Sorry for the inconvenience, but I need this done and I need help. This is the last question of this quiz. Please Help.
Answer: Ed should bike at least more than 16 miles
Step-by-step explanation:
11 + 4b > 75
4b > 64
b > 16
Simplify. Write your answer in standard form.
(4x^3+6x−7)+(3x^3−5x^2−5x+9)
answer: 7x^ - 5x^2 + x + 2
step-by-step explanation: i think thats it
Solve the following equation.
PLEASE HELP ASAP NO ROCKY THE EQUATION IS ON THE PICTURE !!!
HELP DUE IN 7 MINUTES
Answer:
1. 0,5
2. Move 5 units east
3. You need to plot checkpoint B on a graph, then you need to follow the instructions then you end up on 0,5. Which Ultimately is checkpoint C.
Hope this Helps!
WILL GIVE BRAINLIEST!
A custom-illustrated sign or banner can be commissioned for a cost of $20 for the material and $12.50 per square foot for the artwork. The equation that represents this cost is given by y = 12.50x + 20, where y is the cost and x is the number of square feet in the sign.
Graph this equation for values of x from 0 to 20.
The point (5, 82.5) is on the graph. Select a sentence that describes the meaning of this ordered pair.
A. It costs $5 for a custom sign 82.5 ft2 in area.
B. It costs $12.50 for a custom sign 20 ft2 in area.
C. It costs $20 for a custom sign 12.50 ft2 in area.
D. It costs $82.50 for a custom sign 5 ft2 in area.
E. It costs $270 for a custom sign 20 ft2 in area.
Answer:
D
Step-by-step explanation:
12.50 x 5 = 62.5
62.5 + 20 = 82.5