A triangle has vertices at (-2,-3),(4, -3), and (3,5). What is the area of the triangle?
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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What is the value of the expression below when w=2 8w2+2w+8
Answer:
44?? maybe
Step-by-step explanation:
Fill in the missing
number to make the
number sentence
true.
| 148 +___= 179
Answer: 31
Step-by-step explanation:
179 - 148 = 31
The answer is 31.
Step-by-step explanation:
179 -- 148 = 31.
148 + 31 = 179
geometric mean of 384 and 6
Answer:
48 is the geometric mean of 384 and 6
Which of the following situations are equal to 20%?
Select all that apply.
A) 5 out of 25
B) 8 out of 40
C) 2 out of 8
D) 16 out of 80
E) 12 out of 24
Answer:
A and B
Step-by-step explanation:
you divide 5 and 25
like this 5/25 and then multiply by 100
For B you do the same thing but is 8/40 and then you multiply by 100
Rational equations intro (Khan Academy)
Answer:
y = 17/7
Step-by-step explanation:
Question 5
For the following right triangle, find the side length x. Round your answer to the nearest hundredth.
6
11
X
Step-by-step explanation:
a^2 + b^2 = c^2
a = 6
b = x
c = 11
6^2 + b^2 = 11^2
36 + b^2 = 121
b^2 = 121 - 36
b^2 = 85
Find the square root of both sides.
b = 9.22
There are 16 ounces in one pound. If 3.4 pounds of beef cost $4.95, what is the cost per ounce, to the nearest cent?
$0.09
$0.31
$1.05
$1.46
$10.99
On an airplane flight, Steve watch the display that showed the number of minutes since the flight to cough and the number of miles away from the destination. He recorded various points and fit the line why equals 2426-8x To the data, Where x is The number of minutes flying and why is the number Have miles from the Have miles from the destination. According to the model, how far was Steve from his destination after 120 minutes of flying?destination A. 960 miles B. 2410 mikes C. 1466 !miles D. 3386 miles
Answer:
3386 miles was her destination......
The bakers at Healthy Bakery can make 310 bagels in 2 hours. How many
bagels can they bake in 20 hours? What was that rate per hour?
Answer:
The number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
Step-by-step explanation:
Given;
number of bagels in 2 hours = 310 bagels
The rate per hour is calculated as;
[tex]Rate = \frac{310 \ bagels}{2 \ hours}\\\\Rate = 155 \ bagels \ per \ hour[/tex]
In 20 hours, the number of bagels made is calculated as;
Number of bagels = 155 (bagels/hour) x 20 (hour)
= 3100 bagels.
Therefore, the number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
You are traveling at 75 km/hr to make it to school on time. You have to be at school in .25 hour or you will be late. You have 15 km to travel. Will you make it to school on time?
Answer:
Yes
Step-by-step explanation:
.25 hour = 1/4 hour
75 * 1/4 = 18 3/4
You travel 18 3/4km in 1/4 hr(.25 hr).
What is the inverse of 2x^2
Answer:Interchange the variables.
x
=
2
y
+
2
Solve for
y
.
Tap for more steps...
y
=
x
2
−
1
Solve for
y
and replace with
f
−
1
(
x
)
.
Tap for more steps...
f
−
1
(
x
)
=
x
2
−
1
Step-by-step explanation:
The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. (a) What is the point estimate of the population mean? 8.75 Incorrect: Your answer is incorrect. (b) What is the point estimate of the population standard deviation? (Round your answer to three decimal places.) (c) With 95% confidence, what is the margin of error for the estimation of the population mean? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the population mean? (Round your answer to one decimal place.) to
Answer:
10 ; 3.464 ; 2.4 ; (7.6, 12.4)
Step-by-step explanation:
Given the data :
10, 8, 12, 15, 13, 11, 6, 5
Point estimate of population mean :
m = ΣX / n
n = sample size = 8
(10+8+12+15+13+11+6+5) / 8
= 10
Point estimate of population standard deviation :
Sqrt(Σ(X - m)^2 / n-1)
((10-10)^2 + (8-10)^2 + (12-10)^2 + (15-10)^2 + (13 - 10)^2 + (11-10)^2 + (6-10)^2 + (5-10)^2) / 7
= sqrt(84/7)
= 3.464
Margin of error at 95%:
Zcritical * sqrt(sd²/n)
Zcritical at 95% = 1.96
1.96 * sqrt(3.464^2 / 8)
Margin of Error = 2.4
Confidence interval :
m ± Z(s/sqrt(n))
10 - 1.96(3.4634/sqrt(8)) = 7.6
10 - 1.96(3.4634/sqrt(8)) = 12.4
11. Which of the following points is on the
line 3x - 5y=1
A. (1, 2)
B. (2, 1)
C. (3/5, 1)
D. (2,3)
a
Step-by-step explanation:
because it's is very important
ALGEBRA II // MODULE 1
FUNCTIONS AND INVERSES - 1.2
1.2
READY, SET, GO!
Name
Period
Date
READY
Topic: Solving for a variable
Solve for x.
1.
17 = 5x + 2
2. 2x² – 5 = 3x2 – 12x +
31
3. 11 = 2x + 1
Answer:
1. x = 3
2.x = 6
3. x = 5
I hope this helps you :D
To solve for variables, we start by isolating the variable term and then solve for the variable. The values of x in the given equations are 3, 6 and 5, respectively.
Equation (1)
[tex]17 = 5x + 2[/tex]
Collect like terms
[tex]5x = 17 -2[/tex]
[tex]5x = 15[/tex]
Divide both sides by 5
[tex]x =3[/tex]
Equation (2)
[tex]2x^2 - 5 = 3x^2 - 12x + 31[/tex]
Collect like terms
[tex]3x^2 - 2x^2 - 12x + 31 +5=0[/tex]
[tex]x^2 - 12x + 36=0[/tex]
Expand
[tex]x^2 - 6x - 6x + 36=0[/tex]
Factorize
[tex]x(x - 6) - 6(x -6)=0[/tex]
Factor out x - 6
[tex](x - 6)(x -6)=0[/tex]
This means that:
[tex]x -6=0[/tex]
Solve for x
[tex]x = 6[/tex]
Equation (3):
[tex]11 = 2x + 1[/tex]
Collect like terms
[tex]2x = 11-1[/tex]
[tex]2x = 10[/tex]
Divide both sides by 2
[tex]x =5[/tex]
Hence, the values of x in the given equations are 3, 6 and 5.
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What is the square root of nine
Answer: the square root of 9 is 3.
How is a constant term different from a variable term
for an expression that represents a real-world situation?
Answer:
Constants are the terms in the algebraic expression that contain only numbers. That is, they're the termswithout variables. We call them constants because their value never changes, since there are no variablesin the term that can change its value.
Step-by-step explanation:
Share 56 sweets in the ratio 2 : 5.
56 sweets can be shared in the ratio 2 : 5 as 16 sweets and 40 sweets.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Share 56 sweets in the ratio 2 : 5.
First share is = (2/2+ 5)×56.
= (2/7)×56.
= 16.
And the second share is (5/2 + 5)×56.
= (5/7)×56.
= 40.
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Megan and noah were splitting nachos. Megan ate 1/4 of the nachos and noah ate 5/12 of the nachps. What fraction of the nachos did they eat
Answer:
3/5
Step-by-step explanation:
Answer:
They ate 6/12 of the nacho
Step-by-step explanation:
hope that helps
Plz help me with the problem
Answer:Step-by-step explanation:
Just tell me the problem
What is the solution to Three-fourths a greater-than negative 16?
a greater-than negative 21 and one-third
a less-than negative 21 and one-third
a greater-than 21 and one-third
a less-than 21 and one-third
will give brainliest
Answer:
a greater-than negative 21 and one-third
Step-by-step explanation:
3/4a>-16
divide both sides by 3/4
a>-16*4/3
a>-64/3
a>-21 1/3
so then
a greater-than negative 21 and one-third
Good luck on the test.
What is the inverse of -1/2x+5
On a treasure map, a X is placed at point (9, -7). if the pirates are currently on point (9,3), how many units away are they?
Answer:
They are 10 units away from the treasure
Step-by-step explanation:
Notice that the points (9, -7) and (9, 3) are both located at the same x-value (9) while their y-values are in one case 3 units above the x-axis, and in the other 7 units BELOW the x-axis. Therefore thy differ by 3 - (-7) units , which totals 10 units.
Use the information and diagram to answer the following question.
An airplane makes a 20° angle of elevation from the runway when it takes off.
The airplane shown is 2.500 feet along the ground from its take-off point.
Take-off point
20
2500 ft
Note: The figure is not drawn to scale.
At what height, h, is the airplane? Round the answer to the nearest foot. Show
your work.
Answer:
910 ft
Step-by-step explanation:
This question sets up the equation tan20°=x/2,500. Solve for X by multiplying 2,500 on both sides giving you x = 2,500tan20°. Finally, plug that in a calculator and you get 909.92. Round it to the nearest foot and you get 910
The required height where the plane is given as 910 ft, as of the given condition.
Given that,
An airplane makes a 20° angle of elevation from the runway when it takes off. The airplane shown is 2500 feet along the ground from its take-off point.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
here,
base length = 2500
Angle of inclination = 20°
let the perpendicular height = h
Now,
tan20° = h / base
h = 2500 [tan20°]
h = 910 ft
Thus, the required height where the plane is given as 910 ft, as of the given condition.
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What’s the answer please??
Answer:
your answer will be x=1.13504161
9514 1404 393
Answer:
{-1.47, 1.14}
Step-by-step explanation:
The solution to ...
ax^2 +bx +c = 0 is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Filling in the values a=3, b=1, c=-5, the solutions are ...
[tex]x=\dfrac{-1\pm\sqrt{1^2-4(3)(-5)}}{2(3)}=\dfrac{-1\pm\sqrt{61}}{6}\\\\\boxed{x\approx\{-1.47,1.14\}}[/tex]
Find the size of the angle a.
Diagram not drawn accurately
Answer:
45°
Step-by-step explanation:
Since,
3a + a + 2a + 2a = 360°
Riley used the distributive property to find the product of 37 and 24. Which expression could Riley have used to find the product of the two numbers?
20(30)+7
37(20)+4
24(30+7)
30(24+7)
Answer:
Step-by-step explanation:
The second one
Answer:
distributive property
Step-by-step explanation:
u should be use the 2nd one...
37(20)+7
Simplify.
Rewrite the expression in the form 4^n.
4^8
4^3
how many cells are in the human body
Answer:
There should be 37.2 trillion, however this is not a finite number and there might be more or less depending on the person.
Step-by-step explanation:
what is the P.O.I for 5.2x-y=4 1/2x+y=1
Answer:
X = 4/13
Y = - 5/13
Step-by-step explanation:
Since all of the equalities are true, the ordered pair is the solution of the system