Answer:
The pentagon MNPQR has a perimeter of 22 units.
Step-by-step explanation:
Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:
[tex]p = MN + NP + PQ + QR + RM[/tex] (1)
[tex]p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}[/tex] (1b)
If we know that [tex]M(x,y) = (2,4)[/tex], [tex]N(x,y) = (5,8)[/tex], [tex]P(x,y) = (8,4)[/tex], [tex]Q(x,y) = (8,1)[/tex] and [tex]R(x,y) = (2,1)[/tex], then the perimeter of the pentagon MNPQR is:
[tex]p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}[/tex][tex]p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}[/tex]
[tex]p = 22[/tex]
The pentagon MNPQR has a perimeter of 22 units.
The pentagon MNPQR has a perimeter of 22 units.
Geometrically speaking, the perimeter of the pentagon is the sum of the lengths of each side, that is:
p = MN + NP + PQ + QR + RMp=MN+NP+PQ+QR+RM (1)
p = \sqrt{\overrightarrow{MN}\,\bullet \, \overrightarrow{MN}} + \sqrt{\overrightarrow{NP}\,\bullet \, \overrightarrow{NP}} + \sqrt{\overrightarrow{PQ}\,\bullet \, \overrightarrow{PQ}} + \sqrt{\overrightarrow{QR}\,\bullet \, \overrightarrow{QR}} + \sqrt{\overrightarrow{RM}\,\bullet \, \overrightarrow{RM}}p=
MN
∙
MN
+
NP
∙
NP
+
PQ
∙
PQ
+
QR
∙
QR
+
RM
∙
RM
(1b)
If we know that M(x,y) = (2,4)M(x,y)=(2,4) , N(x,y) = (5,8)N(x,y)=(5,8) , P(x,y) = (8,4)P(x,y)=(8,4) , Q(x,y) = (8,1)Q(x,y)=(8,1) and R(x,y) = (2,1)R(x,y)=(2,1) , then the perimeter of the pentagon MNPQR is:
p =\sqrt{(5-2)^{2}+(8-4)^{2}} + \sqrt{(8-5)^{2}+(4-8)^{2}}+\sqrt{(8-8)^{2}+(1-4)^{2}}+\sqrt{(2-8)^{2}+(1-1)^{2}}+\sqrt{(2-2)^{2}+(4-1)^{2}}p=
(5−2)
2
+(8−4)
2
+
(8−5)
2
+(4−8)
2
+
(8−8)
2
+(1−4)
2
+
(2−8)
2
+(1−1)
2
+
(2−2)
2
+(4−1)
2
p = \sqrt{3^{2}+4^{2}} + \sqrt{3^{2}+(-4)^{2}}+\sqrt{0^{2}+(-3)^{2}}+\sqrt{(-6)^{2}+0^{2}}+\sqrt{0^{2}+3^{2}}p=
3
2
+4
2
+
3
2
+(−4)
2
+
0
2
+(−3)
2
+
(−6)
2
+0
2
+
0
2
+3
2
p = 22p=22
The pentagon MNPQR has a perimeter of 22 units.
Which is the equation of a parabola with vertex (0,0) and directrix y= 4
a. Y^2 = -8x
b. Y^2 = -16x
c. X^2 = -8y
d X^2 = -16y
Answer:
D. [tex]x^{2} = -16\cdot y[/tex]
Step-by-step explanation:
The vertex form of the equation of the parabola centered in the origin, with axis of symmetry in the x-axis and directrix in the first and second quadrants is described by the following formula:
[tex]4\cdot p \cdot y = x^{2}[/tex], [tex]p < 0[/tex] (1)
Where:
[tex]y[/tex] - Dependent variable.
[tex]x[/tex] - Independent variable.
[tex]p[/tex] - Focus distance.
If we know that vertex is located at (0, 0) and the directrix pass through (4, 0), then the focus distance (distance of the vertex with respect to that point) is -4, and the equation of the parabola is [tex]x^{2} = -16\cdot y[/tex].
Hence, the right choice is D.
PLEASE HELP!! Find the circumference of circle K. Round your answer to the nearest hundredth. Circumference = ft
Answer:
12.57 ft
Step-by-step explanation:
Since triangle ∆EFH is a right angled triangle,side |EF| can be determined by
Sin© = Opposite side ÷ hypothenus side where © is the given angle in the triangleSin 60 = 2✓3 ÷ |EF||EF| = 2√3 ÷ sin 60|EF| = 2√3 ÷ 0.8660|EF| = 4ftSince Line |EF| is a straight line that passes through the centre of the circle and touch two sides of the circumference,
line |EF| is the diameter of the circle
Circumference = 2πr where r = radiusradius = diameter ÷ 2radius = 4 ÷ 2radius = 2 ftCircumference = 2πr Circumference = 2 × 22/7 × 2Circumference = 12.57 ftCircumference = 12.57 ftFind the length of side x in simplest radical form with a rational denominator.
Answer:
x=2√5
Step-by-step explanation:
1st method:
sin(30)=opposite/hypotenuse=√5/x
sin(30)x=√5
x=√5/sin(30)
x=2√5
2nd method:
cos(60)=adjacent/hypotenuse=√5/x
cos(60)x=√5
x=√5/cos(60)
x=2√5
3rd method:
This is a 30-60-90 triangle, so we can multiply the short side, √5, by 2, to get x=2√5
How do I do this I don’t understand it
Answer:
you graph it on the LINE and find the slope
The radius of a circle is 18 in. Find its circumference in terms of T.
Answer:
36πStep-by-step explanation:
NOTE : I am assuming that T means π.
The formula for circumference is 2πr, so 2*r = 2*18 = 36.
Since we are leaving it in terms of π, the answer is 36π
HELP FOR TEST PLZ
find measure of angle 1
Answer:
the answer should be 98
Step-by-step explanation:
try it
ANSWERS FOR THESE PLEASE DOESNT HAVE TO BE ALL OF THEM
Step-by-step explanation:
y-intercept: first one is -6
slope:
(-6,0) (0,-3)
-3-0/ 0- -6 = -3/6 = -1/2
3. TBD
4. slope is 3/6 = 1/2
y - 3 = 1/2(x-2)
y = 1/2x +2
5. -4/2 = 2 slope
y-2 = 2(x-3)
y = 2x -4
Find the magnitude of a vector with initial point A(3, 4, 10) and terminal point B(8, 4, –2).
A: 0
B: 13
C: 8
D:16
Answer:
B
Step-by-step explanation:
Use the distance formula in 3 dimensions
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2 }[/tex]
with (x₁, y₁, z₁ ) = (3, 4, 10) and (x₂, y₂, z₂ ) = (8, 4, - 2)
d = [tex]\sqrt{(8-3)^2+(4-4)^2+(-2-10)^2}[/tex]
= [tex]\sqrt{5^2+0^2+(-12)^2}[/tex]
= [tex]\sqrt{25+144}[/tex]
= [tex]\sqrt{169}[/tex]
= 13 → B
in a regular polygon each interior angle is 140 greater than each exterior angle calculate the number of sides of each polygon .
Answer:
9
Step-by-step explanation:
Exterior sides = 180 - 140 = 40
number of sides = 360 / 40 = 9 sides
If the function y=1/x is translated to the left 2 units and up 6 units, what is the new horizontal asymptote
Answer:
y=6
Step-by-step explanation:
The horizontal asymptote for y = 1/x is the x-axis, y = 0.
Shifting the graph up 6 makes the asymptote move up, too, to y = 6.
See the attached image:
y = 1/x is purple
y = 1/(x + 2) + 6 is black
Find the area of the figure.
A. 180 sq. ft
B. 38 sq. ft
C. 152 sq.ft
D. 150 sq.ft
E. 44 sq.ft
Answer:
D 150 sq ft
Step-by-step explanation:
10x12 = 120
1/2(10)(6) = 30
120+30 = 150
I need Help please!!
Elsa drove 864 miles in 12 hours.
At the same rate, how many miles would she drive in 8 hours?
Answer:
576 miles
Step-by-step explanation:
Answer:
else will drive 567 miles in 8h
Step-by-step explanation:
take 864÷ 12 to get how many hours she drives in one hour
you get 72
then you take 864÷2 to get how many miles she'll drive in 6h
you get 432
then you take 432 and add 144 or 72 + 72
and you get 567 miles in 8h
hope this helped!!
Francis surveyed a random sample of 70 7070 students at Franklin High School about their favorite season. Of the students surveyed, 18 1818 chose fall as their favorite season. There are 1816 18161816 students at Franklin High School. Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall? Choose 1 answer: Choose 1 answer:
Answer:
467
Step-by-step explanation:
Determine the percentage of those sampled whose favourite season is fall
(18/70) x 100 = 25.7%
the sample is representative of the population of students. So, 25.7% of the students would like fall
number of students at Franklin High School whose favourite season is fall = 25.7% x 1816 = 466.7 students
rounding off to the nearest whole number gives 467
Answer:
467
Step-by-step explanation:
4·(4+32+42) please help fast
Answer:
Uhm so I did 4×4=16 than 4×32=128 than 4×42=168
You add 16+128=144 than you divide 144÷168 which gives you a decimaled number which I got 0.8 if you round up its 1.0
What is the equation of function g?
g(x)= f(x)
Answer:
f=gx-4/x-2
f=x^3+2/x
Match each statement with its corresponding value for the system below:
y = -2(3)x and y = 9x - 2
1. The number of points of intersection.
2. The x-coordinate of the solution.
3. The y-coordinate of the solution.
the options as the answers are:
0, -2, and 1
Answer:
The X Coordinate equals 0.
The Y Coordinate equals -2
And the number of points of intersection is 1.
Hope this helps!
Step-by-step explanation:
Answer:
The X Coordinate equals 0.
The Y Coordinate equals -2
And the number of points of intersection is 1.
Hope this helps!
Step-by-step explanation:
Which graph does not represent a function?
I need help with this question pls
Answer: the third one
Step-by-step explanation:
Can you solve my question please, you will get brainlest, points, and stars!!!
IMPORTANT::: Write the #? Next to the answer.
Like for example there’s question #1,
Answer: #1 : .........e.t.c.
Then you write the answer.
Hope you get it!
Answer:
Below.
Step-by-step explanation:
One standard form of the equation of a straight line is
y = mx + c where m = the slope and c = the y-intercept.
Comparing this with y = 3x - 6 we see that:
The slope = 3 and the y-intercept is -6.
The error was in the y-intercept.
#2.
The error is in stating the intercepts
x - intercept is (8, 0) and y-intercept = (0, 2), (NOT (8, 2)).
#3.
The error is in stating the intercepts
x - intercept is (5, 0 and y-intercept = (0, 2).
Please Help me on this question
Answer:
yellow
Step-by-step explanation:
A + B = C which is correct.
|C| = A
|C| > |A|
C > 0
C < 0
Answer:
i think a is correct
Step-by-step explanation:
The height of a seat on a Ferris wheel can be modeled as
H (t) = 47 sin (Fot+ 3 + 52, where tis time in seconds and h(t) is
height in feet.
How far off the ground is a seat when it is at the top of the Ferris wheel?
A. 99 feet
B. 94 feet
C. 104 feet
D. 52 feet
Answer:
Step-by-step explanation:
Its 99
I just took it
Point B has coordinates (3,1). The x-coordinate of point A is negative 1. The distance between point A and point B is 5 units. What are the possible coordinates of point A?
Answer:
Given in quesion:Point B (3,1) and point A is -1. Distance between A and B is 5 units.
Using distance formula for AB we obtain,
AB^2=(x2-x1)^2 + (y2-y1)^2
5^2=(3+1)^2 + (1-y)^2
25-16=(1-y)^2
9=(1-y)^2
1-y=3
y= -2
Therefore the possible co-ordinates of A are(-1,-2).This is your required answer.
please help immediately
Answer:
the answer should be 1920
hope this helped and have a good weekend :D
How do I solve this arithmetic sequence?
Answer:
The 6ᵗʰ term of this sequence is 82
Step-by-step explanation:
Here,
First Term = a₁ = 13
Common Difference = (d) = 4
Now, For 6ᵗʰ term, n = 16
aₙ = a + (n - 1)d
a₆ = 13 + (6 - 1) × 4
a₆ = 13 + 5 × 4
a₆ = 13 + 20
a₆ = 33
Thus, The 6ᵗʰ term of this sequence is 33
-TheUnknownScientist
The angle of elevation of the top of a tower from two points 121 m and 144 m away from the foot of the tower on th same side are found to be complementary. find the height of the tower.
Answer:
132 m
Step-by-step explanation:
Refer to attachment for figure.
In smaller triangle with angle theta , we have ,
⇒ tanθ = p/b
⇒ tanθ = h/121m
⇒ tanθ = h/121 m
In triangle with angle 90-∅
⇒ tan(90-θ) = p/b
⇒ cot θ = h/144 m
Multiplying these two ,
=> tanθ . cotθ = h/121 m × h/144m
=> 1 = h²/ (121 m × 144m )
=> h² = 121m × 144m
=> h= √ ( 121m × 144m)
=> h = 11m × 12m
=> h = 132 m
Write an equation for the function that includes the points (-2,4) and (-1,8)
Answer:
If its a linear then the equation is 4x + 8
Step-by-step explanation:
a-b³
pls telll
i neeed
Answer:
a-b³=a³-3a²b+3ab²-b³
hope it is helpful to you
Select the correct answer. What are the solutions of this quadratic equation?
6x^2 + 6 = 12x + 18
[tex]x = 1 + \sqrt{3} [/tex]
[tex]x = 2 + 2 \sqrt[]{3} [/tex]
[tex]x = 2 + \sqrt{6} [/tex]
[tex]x = - 1 \: and \: x = 3[/tex]
Answer:
x=1+√3
Step-by-step explanation:
Let's solve your equation step-by-step.
6x^2+6=12x+18
Step 1: Subtract 12x+18 from both sides.
6x^2+6−(12x+18)=12x+18−(12x+18)
6x^2−12x−12=0
For this equation: a=6, b=-12, c=-12
6x^2+−12x+−12=0
Step 2: Use quadratic formula with a=6, b=-12, c=-12.
x=−b±√b2−4ac/2a
x=−(−12)±√(−12)2−4(6)(−12)/2(6)
x=12±√432/12
x=1+√3