Square LAMP has vertices L(-2, -3), A(4, -1), M(2,5), and P(-4, 3). What is the
perimeter of the square?
Answer:
The perimeter of the square LAMP is 8[tex]\sqrt{10}[/tex] units
Step-by-step explanation:
The rule of the distance between two points (x1, y1) and (x2, y2) is
d = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}[/tex]
∵ LAMP is a square
∵ The sides of the square are equal in lengths
∴ LA = AM = MP = PL
Let us find the length of one side of it
∵ L = (-2, -3) and A = (4, -1)
∴ x1 = -2 and y1 = -3
∴ x2 = 4 and y2 = -1
→ Substitute them in the rule of the distance above to find LA
∵ LA = [tex]\sqrt{(4 - -2)^{2}+(-1--3)^{2}}[/tex]
∴ LA = [tex]\sqrt{(4+2)^{2}+(-1+3)^{2}}[/tex]
∴ LA = [tex]\sqrt{(6)^{2}+(2)^{2}}[/tex]
∴ LA = [tex]\sqrt{36+4}[/tex] = [tex]\sqrt{40}[/tex]
→ Simplify the root
∴ LA = 2[tex]\sqrt{10}[/tex] units
∵ The perimeter of the square = 4 × side
∴ The perimeter of the square = 4 × 2[tex]\sqrt{10}[/tex]
∴ The perimeter of the square = 8[tex]\sqrt{10}[/tex]
∴ The perimeter of the square LAMP is 8[tex]\sqrt{10}[/tex] units
Please help I will give brainliest!!!
Answer:
I think it is C.
Step-by-step explanation:
8. A school raffle sold 480 tickets. Students were charged $1/ticket and teachers $5/ticket. The total receipts were $560. How many of each ticket were sold? 9. An airplane travels 5432 km. On the outward trip it took 7 hours with the wind. On the return trip, it took 8 hours against the wind. What was the speed of the plane and the speed of the wind? (Remember: distance = speed x time)
Answer:
8. Number of student tickets = 460
Number of teacher tickets = 100
9. Speed of plane = 727.5 km/hr
Speed of wind = 48.5 km/hr
Step-by-step explanation:
8.
Let number of students' tickets = [tex]x[/tex]
Let number of teachers' tickets = [tex]y[/tex]
Total number of tickets = 480
[tex]x+y=480[/tex] ...... (1)
Price for one student's ticket = $1
Price for one teacher's ticket = $5
Total money collected by the tickets = $560
[tex]x +5y = 560[/tex] ...... (2)
Subtracting (1) from (2):
[tex]4y = 80\\\Rightarrow y = 20[/tex]
By equation (1):
[tex]x = 460[/tex]
Number of student tickets = 460
Number of teacher tickets = 100
9.
Let the speed of airplane in still air = [tex]u[/tex] km/hr
Let the speed of air = [tex]v[/tex] km/hr
Total distance = 5432 km
Time taken with the wind = 7 hours.
Speed with the wind = [tex]u+v[/tex] km/h
Time taken against the wind = 8 hours.
Speed with the wind = [tex]u-v[/tex] km/h
Using the formula:
Distance = Speed [tex]\times[/tex] Time
[tex]5432 = (u+v)\times 7\\\Rightarrow u +v = 776 .... (1)[/tex]
[tex]5432 = (u-v)\times 8\\\Rightarrow u - v = 679 .... (2)[/tex]
Adding (1) and (2):
[tex]2u = 1455\\\Rightarrow u = 727.5\ km/hr[/tex]
By equation (1):
[tex]v = 48.5\ km/hr[/tex]
Speed of plane = 727.5 km/hr
Speed of wind = 48.5 km/hr
18. Write an equation in point-slope form of the line that passes through the given point and with the given slope m.
(-3,1);m=3
20. Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-3,-5);y=-2x+2
21. Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(0,0);y=-3x+2
Answer:
(-4,-2); y=4x+2
Step-by-step explanation:
A laptop was originally sold for 975. The laptop is now on sale for 828.75. What percent is the percent markdown?
Answer:
15%
Step-by-step explanation:
975-828.75/975
Answer:
There was a 15% mark down.
Step-by-step explanation:
975 x 0.15 (15%) = 146.25
828.75 + 146.25 = 975
Check Work:
975 - 146.25 = 828.75
Evaluate the following expression -7x/7+9)
Answer:
− x+9
Step-by-step explanation:
−
7
7
+
9
{\color{#c92786}{\frac{-7x}{7}}}+9
7−7x+9
−
+
9=−
+
9
what is dark matter
can we travel faster than speed of light
what is chlorophyll
Step-by-step explanation:
No we can't travel faster than speed of light as it is the fastest
Chlorophyll is a pigment that absorbs light of particular wavelengths (mainly blue and red) .Chlorophyll in green plants spread out on stacks of membranes in chloroplasts.
Dark matter ia a material that we cannot see but we know that it exists because of it's effect on the objects and it is composed of particles that do not absorb,reflect or emit light.
Answer:
1. Dark matter is material that don't seen directly, it neither absorb anything, neither reflect and emit light.
2. No there is nothing which can travel faster than light.
3. In simple language, chlorophyll is those pigment which is present in all green plants and mainly responsible for the process of photosynthesis
Step-by-step explanation:
1.We can say there is dark matter but the only problem is we don't have any access to see it.
2.there is nothing faster than light because speed of light and time doesn't exist beyond any point.
A real horse is 1.8 m high. A statue of the horse is 3 m high. What is the ratio of the height of the horse to the height of the statue
Please help in this question with explanation. pls
Answer:
V = x³ - 3x² + 3x - 1
Step-by-step explanation:
The volume (V) of a cube is calculated as
V = s³ ( s is the measure of the side )
Here s = x - 1 , thus
V = (x - 1)³
= (x - 1)(x - 1)(x - 1) ← expand the second pair using FOIL
= (x - 1)(x² - 2x + 1) ← distribute
= x³ - 2x² + x - x² + 2x - 1 ← collect like terms
= x³ - 3x² + 3x - 1
Which is the fraction 14/5 written as a mixed number
PLEASE HELP ASAP!!!
3 + 2x² + 3x + 2x² + 5 = ?
Answer: 4x² + 3x + 8
Work: I combined Like Terms, put them in the right form, from the x² to the number.
I hope this helps and Happy Holidays! :)
Answer:
25
Step-by-step explanation:
3+2=5×2 ×2 +5=25
add the 10 to the other 10 and then add 5
SOMEONE PLEASE HELP ME FOR BRAINLY IF CORRECT
Paula refills the flour bin after it has been empty for a
while. She pours in the flour at a constant rate. She stops
pouring flour when the bin is full.
Which graph could represent this scenario?
Answer:
A
Step-by-step explanation:
Its A which ever is the one that is full
How is the following reciprocal function f(x)= [tex]\frac{1}{x+2}[/tex] decreasing?
Write the number in scientific notation
307,000,000
Answer:
3.07×10^8
Step-by-step explanation:
:)
hope this helps
Answer: 307,000,000 in scientific notation is 3.07 × 10^8.
Show work and I will give you brainliest
Answer: There is not enough info and I can't see because the picture is not clear enough. Sorry. :(
Merry (early) Christmas tho! :)
tan22° + tan23° tan22°. tan23° = 1 prove that
Answer:
Formula:(from trigonometry)
Tan(A+B)=(tanA+tanB)/(1-tanA*tanB)
Let A=22 degrees,B=23 degrees
Tan(22+23)=(tan22+tan23)/(1-tan22*tan23)
From trigonometry we know tan45=1
Therefore tan(45)=1=(tan22+tan23)/(1-tan22tan23)
=> 1-tan22tan23=tan22+tan23
=> tan22+tan23+tan23tan22 =1
Hence proved
what is the answer. can someone help me .
Answer:
your photo is not visible for me
Answer:
54
Step-by-step explanation:
11x=26=180
x=14
8x+p+14=180
p=54
What is 16 divided by 5
Answer:
3.2
Step-by-step explanation:
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet. What is the width of the sidewalk?
Answer:
width of the sidewalk = 1 feet
Step-by-step explanation:
Area of the pool = length × width
Length = 10 feet
Width = 6 feet
Area of the pool = length × width
= 10 feet × 6 feet
= 60 feet²
Area of the pool = 60 feet²
Total area = Area of the pool + Area of sidewalk
96 feet² = 60 feet ² + Area of sidewalk
Area of sidewalk = 96 feet² - 60 feet ²
Area of sidewalk = 36 feet²
Length of pool + sidewalk = 10 + 2x
width of pool + sidewalk = 6 + 2x
( 10 + 2 x ) ( 6 + 2 x ) -60 = 36
60 + 20x + 12x + 4x² - 60 = 36
4x² + 32x - 36 = 0
4x² + 36x - 4x - 36 = 0
4x (x + 9) -4(x + 9) = 0
(4x - 4) (x + 9) = 0
4(x - 1) (x + 9) = 0
(x - 1) = 0 (x + 9) = 0
x = 1 or x = -9
The width of the side walk can't be a negative value
Therefore, width of the sidewalk = 1 feet
A rectangular pool has a sidewalk around it. Width of the sidewalk is 1 feet.
Given
A rectangular pool has a sidewalk around it. The pool measures 6 feet by 10 feet and the total area of the pool and sidewalk is 96 square feet.
Let 'w' be the width of sidewalk
The pool measures 6 feet by 10 feet . The width of the rectangular pool with side walk is 6+x+x=6+2x
The length of the rectangular pool with side walk is 10+2x
The total area of the pool and side walk is length times width
Total area= [tex](6+2x)(10+2x)\\[/tex]
[tex]96=(6+2x)(10+2x)\\96=60+32x+4x^2\\60+32x+4x^2-96=96-96\\4x^2+32x-36=0[/tex]
apply quadratic formula to solve for x
[tex]x=\frac{-32\pm \sqrt{32^2-4\cdot \:4\left(-36\right)}}{2\cdot \:4}\\x=\frac{-32\pm \:40}{2\cdot \:4}\\x= \frac{-32+40}{2\cdot \:4}=1\\x=\frac{-32-40}{2\cdot \:4}=-9[/tex]
Width of the sidewalk cannot be negative
so the width of the sidewalk is 1 feet
Learn more : brainly.com/question/21860114
Who's ur favorite song artist?
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer. If he answered 30 questions and scored 20 points, write a system of equations.
Given:
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.
Total question answered by Steve = 30
Total score = 20 points
To find:
The system of equations for the given problem.
Solution:
Let x be the number of correct answers and y be the number of wrong answers.
Total question answered by Steve = 30
[tex]x+y=30[/tex] ...(i)
Steve gets 4 points for every correct answer and loses 1 point for every wrong answer.
Score for 1 correct answer = 4
Score for x correct answer = 4x
Score for 1 wrong answer = -1
Score for y correct answer = -y
Total score = 20 points
[tex]4x-y=20[/tex] ...(ii)
The system of equations contains (i) and (ii).
Therefore, the system of equations have two equations [tex]x+y=30[/tex] and [tex]4x-y=20[/tex].
The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?
Answer:
2 13/20 cm
Step-by-step explanation:
The screen on Brianna's new phone is 2.65 cm. Long. What mixed number represents the length of the phone screen ?
From the above question, we are converting, from decimal to mixed number , hence:
2.65 has 2 decimal places
Hence:
2.65 cm = (265/100)cm
= ( 2 + 65/100) cm
= ( 2 13/20 )cm
The mixed number that represents the length of the phone screen is 2 13/20 cm
GIVING BRAINLIEST FOR CORRECT ANSWER!!!!
Answer:
All systems have 2 real solutions.
Step-by-step explanation:
there are X and Y unknowns.
The Bailey’s spent $18.00 for 4 two-liter sodas for the birthday party this weekend. What is the number of soda bottles that could be bought for $45.00?
Answer:
10
Step-by-step explanation:
So I belive the answer consists of- 18 divided by 4 equals 4.5 and 45 divided by 4.5 is 10 so ten should be your answer.
Is linear or nonlinear?
Answer:
Linear
Step-by-step explanation:
baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each. Tickets prices for the upper deck are 75% of the cost of tickets for the lower deck. Which inequality represents all possible combinations of x, the number of tickets for the lower deck, and y the number of tickets for the upper deck, that someone can buy for no more than $800?
A.) 42x + 56y < 800
B.) 42x + 56y > 800
C.) 42x + 31.5y > 800
D.) 42x + 31.5y < 800
Answer:
b
Step-by-step explanation:
Answer:
the answer is D
Find the slope of the line that passes through (10, 10) and (3, 1).
Answer:
-7/-9 pretty sure
Step-by-step explanation:
x2-x1
y2-y1
3-10= -7
1-10= -9
Rewrite 2/100 as a percent. *
answer fast please!
Do these ratios form a proportion?
$42 per 33 customers
$28 per 22 customers
yes
no
Answer:
yes
Step-by-step explanation:
[tex]\frac{42}{33}[/tex] = [tex]\frac{14}{11}[/tex] and [tex]\frac{28}{22}[/tex] = [tex]\frac{14}{11}[/tex]
Both reduce to [tex]\frac{14}{11}[/tex] and form a proportion
The blue segment below is a radius of oo. What is the length of the diameter
of the circle?
A. 4.9 units
B. 14.7 units
C. 9.8 units
D. 19.6 units
Answer:
D. 19.6 unitsStep-by-step explanation:
diameter = 2r
where r = 9.8
plugin value of r = 9.8 into the formula:
diameter = 2(9.8)
= 19.6 units
The length of the diameter of the circle is option D 19.6 units.
What is the diameter?Diameter is defined as the line from one point in the circle to the other point through the center of the circle.
WE know that the diameter = 2r
where r = 9.8
Substitute value of r = 9.8 into the formula:
The diameter = 2(9.8)
The diameter = 19.6 units
Hence, the length of the diameter of the circle is option D 19.6 units.
Learn more about circle here;
brainly.com/question/12512221
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