Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.
Part A
Find the equation of the line passing through B and perpendicular to AC .
Answer:
[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]
Step-by-step explanation:
the slope of the line AC :
[tex]\frac{6-1}{1-2} = \frac{5}{-1} =-5[/tex]
Let y : mx + p be the equation of the line D passing through B and perpendicular to AC.
Where m is the slope and p is the y value of the y intercept point.
The line D is perpendicular to AC means the product of their slopes is −1
Therefore
(−5) × m = −1
Then
[tex]m=\frac{-1}{-5} =\frac{1}{5}[/tex]
We obtain, the equation of D is :
[tex]y : \frac{1}{5} x + p[/tex]
At this point ,we still need the value of p to get the full equation of D.
B(3, 3)∈ D
[tex]3=\frac{1}{5} \left( 3\right) +p[/tex]
[tex]\Longleftrightarrow p=3-\frac{3}{5} =\frac{12}{5} =2.4[/tex]
thus , the equation of D is :
[tex]y : \frac{1}{5} x + \frac{12}{5}[/tex]
Yes it's possible through matrix
Let's find out the area formula for our vertices
That's
[tex]\\ \rm\Rrightarrow \left|\begin{array}{ccc}\rm 2&\rm 1&\rm 1\\ \rm 3&\rm 3&\rm 1\\ \rm 1&\rm 6&\rm 1\end{array}\right|[/tex]
The determinant values modulus is the area
Slope of AC
m=6-1/1-2=-5Perpendicular lines have slopes negative reciprocal to each other
Slope of line B to AC =1/5So
Equation in point slope
y-3=1/5(x-3)y=1/5x-3/5+3y=1/5x+12/5Which function is increasing on the interval ? (-∞,∞)
A. i(x)=x^2+8x+1
B. G(x)=-4(2^X)
C. F(x)=-3x+7
D. H(x)=2^x-1
.A bicycle normally sells for $475. The bicycle was discounted 30% for a
sale. After the sale was over, the new price of the bicycle was 25%
higher than the sale price. What was the new price of the bicycle?
Answer:
415.63
Step-by-step explanation:
Multiply the price by the sales tax to find out how much money the sales tax will add.
Answer:
$415.63
Step-by-step explanation:
475
after 30%
475 times .30 = 142 5
475 - 142.5 = 332.5 <- sale price
332.5 times .25 = 83.125
332.5 + 83.125 = 415.625 <- new price
Pablo built a large wooden storage box. The box was in the shape of a rectangular prism, as shown below. He covered all the sides of the box with special wallpaper that cost a total of . How much did the wallpaper cost per square foot?
The cost of wallpaper used to cover all sides of the storage box is given by $3 per square foot
Cost of wallpaper per square footlength = 9 ftWidth = 8 ftHeight = 5 ftSurface area of a box = 2(lh + wh + lw)
= 2(9×5 + 8×5 + 9×8)
= 2(45 + 40 + 72)
= 2(157)
= 314 square foot
Total cost of wallpaper = $942Cost of wallpaper per square foot = $942 ÷ 314 square foot
= $3 per square foot
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Sum of integers from -10 to 50
Answer:
1220
Step-by-step explanation:
This can easily be done as follows,
Take the first term of the series, (a = -10)
Take the last term of the series, (l = 50)
The numbers of terms is n = 50+10+1 = 61
Now,
For sum,
S= n/2 (a+l) =60/2 (50+-10) = 61/2 (50-10) = 61/2*40 = 1220
A coordinate plane. Point A is plotted at (2, 7). Point B (2, 1). Point C (9, 8). Point D (8, 3). Point E (7, 7). A point has been translated right and up. The image of the point is point E. What point is the pre-image of point E? A B C D
Answer:
It's B
Step-by-step explanation:
Source: Trust me bro
Plus I just got done doing it
the cost of 3 dolls if 2 such dolls cost rs.120 is ...... ans pls
Answer:
Rs. 180
Step-by-step explanation:
This is a proportion problem.
We are told that 2 dolls cost Rs. 120
Thus;
Cost of 1 doll = 120/2 = Rs. 60 per doll
Then;
Cost of 3 dolls = Rs. 60 * 3 = Rs. 180
Which of the following is not a real number?
A. √2
B. -2
C. √₁,
D. 0
Factor the expression completely
9z+15
Answer:
3(3z + 5)
Step-by-step explanation:
You have to factor out 3 from 9z+15 :)
Please mark brainliest
Find the measure of each of the interior angles of the regular hexagon using the Polygon Interior Angle Sum Theorem.
The measure of each of the interior angles of the regular hexagon using the Polygon Interior Angle Sum Theorem is 120°.
What is a polygon?A polygon is a planar figure characterized by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of the interior angle of a polygon with 'n' number of sides is given by the formula,
The sum of the interior angle = (n-2)×180°
As it is known that a hexagon has 6 number of sides, therefore, the sum of the interior angles can be written as,
The sum of the interior angle of Hexagon = (6-2)×180° = 720°
Now, the measure of each interior angle = (720°/6) = 120°
Hence, the measure of each of the interior angles of the regular hexagon using the Polygon Interior Angle Sum Theorem is 120°.
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can anyone help me identify the center and radius on these 3 pls , brainly
Answer:
See below
Step-by-step explanation:
Circle equation standard form
(x-h)^2 + ( y-k)^2 = r^2 h, k is the center
All are centered at 0,0
radii are sqrt(225) = 15 sqrt 49 = 7 and sqrt 178
Translate the phrase into an algebraic expression the product of W and 9
An expression is defined as a set of numbers, variables, and mathematical operations. The algebraic expression that can represent the product of W and 9 is 9W.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The phrase "the product of W and 9" in the form of an algebraic expression can be written as,
Expression = 9 × W = 9W
Hence, the algebraic expression that can represent the product of W and 9 is 9W.
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Find the maximum accepted height for a basketball ring which must be positioned 3050 ± 6 mm above the floor.
__MM ??
Work Shown:
3050+6 = 3056
If you wanted the min height allowed, then you'd compute 3050-6
Note: 3050 mm = 10 feet approximately
If the volume of a cylinder is 847pi yds^3 and the height is 7 yards, what is the radius?
The radius of the given cylinder of volume 847π yds³ and height of 7 yards is 11 yards
Calculating the volume of a cylinderFrom the question, we are to calculate the radius of the cylinder
The volume of a cylinder is given by the formula,
[tex]V = \pi r^{2}h[/tex]
Where V is the volume
r is the radius
and h is the height
From the given information,
V = 847π yds³
h = 7 yds
Putting the parameters into the equation, we get
[tex]847\pi = \pi r^{2} \times 7[/tex]
[tex]7r^{2} = 847[/tex]
[tex]r^{2} = \frac{847}{7}[/tex]
[tex]r^{2} = 121[/tex]
[tex]r =\sqrt{121}[/tex]
r = 11 yards
Hence, the radius of the given cylinder is 11 yards.
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Identify the type of segments as 2 CHORDS, 2 SECANTS, OR SECANT AND TANGENT. Then, find the variable.
Step-by-step explanation:
1)
SOLUTION
5(x+5) = 6. (6 +9)
90 = 5x + 25
13 = x
2)
SOLUTION
x (3) = (4) (6)
3x = 24
x= 8
3)
SOLUTION
3 (3 + x + 2) = (x+1)(x + 1 + x – 1) Use Theorem
3x + 15=2x²+2x
0 = 2x² – x – 15
0 = (x – 3) (2x + 5) Solve for x
3 = x Use positivesolution
The mean weight of college students is 154 lbs and the standard deviation is 3 lbs.
Assuming that the weight is normally distributed, determine the following percentages.
145 148
151
154 157 160 163
DO NOT write % in the box. It is already written outside the box for you"
The percentage of college students who weigh...
30
1)...less than 157 is
%
2) greater than 148 is
3)...between 145 and 160 is
%
%
Answer:(approx) 6.
Step-by-step explanation:Here μ=51 and σ=15
Z=
σ
X−μ
=
15
X−151
When X=120, Z=
15
120−151
=−2.067
When X=155, Z=
15
155−151
=0.2667
When X=185, Z=
15
185−151
=
15
35
=2.2667
(i) P(120<X<155)=P(−2.07<Z<0.27)
=∫
−2.067
0.2667
ϕ(z)dz=∫
0
0.2667
ϕ(z)dz+∫
0
2.0667
ϕ(z)dz
=0.4803+0.1026=0.5829.
Here N=500
∴ The number of students whose weight is between 120 and 155 pounds is
0.5872×500=291
(ii) P(X<185)=P(Z>2.27)=∫
2.2667
∞
ϕ(z)dz
=∫
0
∞
ϕ(z)dz−∫
0
2.2667
ϕ(z)dz=0.5−0.4881=0.0119
∴ the number of students with weight about 185 pounds.
=0.0119×500= (approx) 6.
This is geometry and I need help
Answer:
Step-by-step explanation:
Remark
The sine of an angle involves the Hypotenuse. So the first job is to find that.
When you do Sin(H) = opposite / hypotenuse
Hypotenuse
Givens
a = √3
b = √13
c = ?
c is the hypotenuse.
Equation
c^2 = a^2 + b^2 Substitute values
Solution
c^2 = (√3)^2 + (√13)^2
c^2 = 3 + 13 Combine
c^2 = 16 Take the Square Root of Both Sides
√c^2 = √16
c = 4
Sin(H) = opposite / Hypotenuse
Opposite = √3
Hypotenuse = 4
Sin(H) = √3/4
Sin(H) = 1.7321/4
Sin(H) = 0.4330
Answer
Sin(H) = 0.43
You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads.
For this case we have the following notation:
y= the number of minutes that you read
x = the number of minutes that your brother read
And we have that you decide to read 30 minutes longer than your brother, so the equation would be:
y = x+30
And for the other part of the question if x =15 we got:
y = 15+30 = 45
Step-by-step explanation:Assuming this complete question: "You and your brother are reading the same novel. You want to get ahead of him in the book, so you decide to read 30 minutes longer than your brother reads. Write an equation for the number of minutes you read, y, when your brother reads x number of minutes.
How many minutes will you read if your brother reads for 15 minutes?"
Solution to the problemFor this case we have the following notation:
y= the number of minutes that you read
x = the number of minutes that your brother read
And we have that you decide to read 30 minutes longer than your brother, so the equation would be:
y = x+30
And for the other part of the question if x =15 we got:
y = 15+30 = 45
What number line represents the solution to the inequality below
-6< -2x
Answer:
The answer is 3 or x<3.
Frank bought a pair of gloves for $9.95 and a hat for $5.25. What is the best estimate of much he spent?
$15.00
$10.00
$5.00
$25.00
Answer:
$ 15.00
Step-by-step explanation:
9.95 is JUST about 10
5.25 is close to 5
10 + 5 = 15
Solve for Unknown: x/10=43/46.
Do not put variable, only put the number value to the nearest whole number
Answer:
9
Step-by-step explanation:
x= 430/46
x=9.35 approximately 9( nearest whole number)
Grace has a 1/3 cup scoop that she uses to pour sauce on pasta. She uses one full cup for each serving of pasta. Grace has 7 cups of sauce. How many servings of pasta can she make?
Answer:
7
Step-by-step explanation:
its a trick question !!
Answer:
This seems like a tricky question... i keep second guessing myself but here goes nothing....
7 servings
please read the explanation.... it always helps....
Step-by-step explanation:
Okay... so we know from the problem that each serving takes one full cup of sauce, and we also know that Grace has seven cups of sauce.... therefore we can conclude that she can make seven servings since 7/1 is 7.
Im not really sure why the question tells us that she uses a 1/3 scoop when we don't really need that when solving the question (which is why i am second guessing myself, but oh well)
i really hope this helps!!!
Six men take five days to complete a job. How long would
the same job take fifteen men?
Answer:
2 days
Step-by-step explanation:
Understanding :
Number of men is inversely proportional to the number of days taken to complete a job6 men take 5 days to complete 1Now the number of men is 15Solving :
Rate of change of men ∝ 1/Rate of change of days15/6 ∝ 1/(d/5)2.5 = 5/dd = 2 daysFind the area: (I will give brainliest) +50 points.
Answer:
[tex]A_{total} = 16\ cm^2[/tex]
Step-by-step explanation:
Step 1: Determine the area of the top rectangle
We can tell that the total shape seems like two rectangles glued together. We can separate the top rectangle and determine the area of it and then determine the area of the bottom rectangle and combine them. Lets first solve the left rectangle.
[tex]A=l*w[/tex]
[tex]A_{top\ rectangle}=6\ cm * 2\ cm[/tex]
[tex]A_{top\ rectangle}=12\ cm^2[/tex]
Step 2: Determine the area of the bottom rectangle
[tex]A=l*w[/tex]
[tex]A_{bottom\ rectangle}=2\ cm * 2\ cm[/tex]
[tex]A_{bottom\ rectangle}=4\ cm^2[/tex]
Step 3: Determine the total area
[tex]A_{total}=A_{top\ rectangle}+A_{bottom\ rectangle}[/tex]
[tex]A_{total}=12\ cm^2+4\ cm^2[/tex]
[tex]A_{total} = 16\ cm^2[/tex]
Answer: [tex]A_{total} = 16\ cm^2[/tex]
Break in middle horizontally
For square (Below)
Area =Side²=2²=4cm²For rectangle
Area =LB=6(2)=12cm²Total area
12+416cm²Kate has $17. She wants to hire a bike for 5 hours. There are two companies.
The table shows the cost C, in $, of hiring the bike for n hours from each company.
Company A C = 2n + 6
Company B C = 3n + 3
Find the cost of hiring a bike from Company A and Company B.
Answer:
It's 8 yuan per hour in company A and 9 yuan per hour in company B
the volume of a cone is 2307.9 mm^3. The height is 5 mm. What is the radius?
Answer:
21 mm
Step-by-step explanation:
Given,
Volume of cone ( V ) = 2307.9 mm³
Height ( h ) = 5 mm
To find : Radius ( r )
Formula : -
Volume of cone = πh/3 r²
Note : -
The value of π is 3.14
Volume of cone = πh/3 r²
2307.9 mm³ = 3.14 x 5/3 x r²
2307.9 = 5.23 x r²
Divide 5.23 on both sides,
r² = 2307.9 / 5.23
r² = 441
r² = 21 x 21
r² = 21²
r = 21 mm
Select all the correct answers.
If the measure of angle 0 is 2pi/3, which statements are true?
A. The measure of the reference angle is 60 degrees
B. Cos(0)= 3/2
C. The measure of the reference angle is 30 degrees.
D. Sin(0)= -1/2
E. Tan(0)= -3
F. The measure of the reference angle is 45 degrees.
The correct answers: tan 120= -√3.
The correct answer is (E)
What is an angle?Angles are the angles between bisecting lines or surfaces at or near their meeting point.
Given : [tex]\theta\\[/tex] = 2π/3
= 2*180/3= 120
So, First and the fourth statement is not correct.
and, cos 120= -1/2
sin 120= √3/2
So, B and D statement is also wrong
tan 120= -√3.
Hence, the only correct statement is tan 120= -√3.
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Diana has a tool box in the shape of a right rectangular prism. The volume of the tool box is 1.62 cubic feet. The height of the tool box is 0.75 feet, and the length is 1.8 feet. What is the width of Diana's tool box? Enter your answer as a decimal in the box. ft
Answer:
I think you just have to multiply 0.75 and 1.8 then divided with 1.62.
Step-by-step explanation:
0.75*1.8=a
1.62/a= answer?
Answer:
the answer in 1.2 i just took the unit test on K12
Kay cut a cheese stick into
sixths and ate a sixth. Jake
cut a cheese stick into thirds
and ate a third. Which child
ate less cheese?
Answer:
Jake
Step-by-step explanation:
The two formats used in an observation checklist are:
A. Video recording and audio recording
B. Performance profiles and Tallies
C. Tallies and video recording
D. Performance profiles and SMART Targets
The most likely formats used in an observation checklist includes the video recording and audio recording.
What is an observation checklist?This refers to the list of things that an observer is going to look at when observing a class or sample elements.
Most time, the checklists techniques are put in a sequenced way to observe and evaluates the samples from one point to another.
Therefore, the Option A is correct.
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