Answer:
565.3 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.
Sine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
In triangle KLM:
∠K + ∠L + ∠M = 180° (sum of angles in a triangle)
∠K + 107 + 18 = 180
∠K + 125 = 180
∠K = 55°
We can find the length of k using sine rule:
[tex]\frac{l}{sinL}=\frac{k}{sinK} \\\\substituting:\\\\\frac{660}{sin(107)}=\frac{k}{sin(55)} \\\\k=\frac{660}{sin(107)}*sin(55)\\\\k=565.3\ cm\\[/tex]
Work out the percentage change to 2 decimal places when a price of £110 is
decreased to £98.
Answer:
10.91% decrease
Step-by-step explanation:
98/110 x 100 = 89.090909
100 - 89.0909 = 10.909090 to 2dp is 10.91%
Which angles are adjacent to each other?
a) Angle 12 and Angle 7
b) Angle 6 and Angle 9
c) Angle 12 and 9
d) Angle 5 and Angle 11
Answer:
(c). Angle 12 and 9
Step-by-step explanation:
9, 3, 1, 7, 1, 44
Mean ??
Mode ??
Median ??
Answer:
Step-by-step explanation:
mean:[tex]\frac{65}{6}[/tex]
mode:1
median:5
Answer:
Mean: 10.83
Mode: 1
Median: 5
Step-by-step explanation:
I did mean as a decimal but you might have to change that if your teacher doesn't prefer it as decimals
Helppppp please. I am stumped..
Answer:
D
Step-by-step explanation:
w = width
length = w + 0.6
A = l · w
A = w (w + 0.6)
A = w² +.6w
Answer:
D
Step-by-step explanation:
w = width
l = length = w + 0.6
Area = ( l ) * ( w )
Area = ( w + 0.6 ) ( w )
Area = w^2 + 0.6w
Solve.
3/5x - 7 = 23
A. x = 40
B. x = 45
C. x = 50
D. x = 55
Answer:
(C) x=50
Step-by-step explanation:
[tex]\frac{3}{5 }x -7=23[/tex]
[tex]\frac{3x}{5} -7=23[/tex]
[tex]\frac{3x}{5} -7+7=23+7[/tex]
[tex]\frac{3x}{5}=30[/tex]
[tex]3x=30* 5[/tex]
[tex]3x=150[/tex]
[tex]x=50[/tex]
Answer:
(C) X = 50
Step-by-step explanation:
(3/5)*x-7 = 23 // - 23
(3/5)*x-23-7 = 0
3/5*x-30 = 0 // + 30
3/5*x = 30 // : 3/5
x = 30/3/5
x = 50 (Sorry if it's wrong)
Last Friday Kali had $22.62. Over the weekend she received some money for cleaning the attic. She now has $33.99. How much money did she receive?
Which inequality represents this situation? The number of students, s, who ride in a bus is less than 30. A. S < 30 B. S > 30 C. S ≥ 30 D. S ≤ 30
Answer:
A.s<30
Step-by-step explanation:
We are given that
Number of students who ride in a bus=s
We have to find the inequality which represents the given situation.
According to question
s<30
A.s<30
It is true.
B.s>30
It is false because s is less than 30
C.[tex]s\geq 30[/tex]
It is false because s<30
D.[tex]s\leq 30[/tex]
It is false because s<30
Option A is true.
Find the surface area of the cuboid shown below
Answer:
Surface area of cuboid = 352 cm
Step-by-step explanation:
Given that:
Height of cuboid = 8 cm
Length of cuboid = 12 cm
Width of cuboid = 4 cm
Surface area = 2lw + 2lh + 2hw
Putting all the values;
Surface area = 2*12*4 + 2*12*8 + 2*8*4
Surface area = 96 + 192 + 64
Surface area = 352 cm
Hence,
Surface area of cuboid = 352 cm
Examples of long division?
Graph the line given by the equation y=2x-6.
PLS HELP QUICKLY ILL ITS TIMED
Find the locus of a point such that the sum of its distance from the point ( 0 , 2 ) and ( 0 , -2 ) is 6.
~Thanks in advance !
Answer:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.
First, we will need the distance formula, given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let the point on the locus be P(x, y).
So, the distance from P to (0, 2) will be:
[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]
And, the distance from P to (0, -2) will be:
[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]
So sum of the two distances must be 6. Therefore:
[tex]d_1+d_2=6[/tex]
Now, by substitution:
[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]
Simplify. We can subtract the second term from the left:
[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]
Square both sides:
[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]
We can cancel the x² terms and continue squaring:
[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]
We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:
[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]
We can divide both sides by -4:
[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]
Adding 9 to both sides yields:
[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]
And, we will square both sides one final time.
[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]
Distribute:
[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]
The 36y will cancel. So:
[tex]4y^2+81=9x^2+9y^2+36[/tex]
Subtracting 4y² and 36 from both sides yields:
[tex]9x^2+5y^2=45[/tex]
And dividing both sides by 45 produces:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.
which expression are equivalent to this exponential expression
Answer:To create an equivalent expression, you simply need to move the base and exponent to the other side of the fraction line and change the exponent to positive: 1/(24)
Step-by-step explanation:
Given right triangle XYZ with altitude WZ, let WY = 10 cm and XY = 13 cm. Find the
length of WZ.
A.5.4
B.11.4
C.7.3
D.3
Seth is two-thirds as tall as his father. If Seth is 54 inches tall, how tall is his father?
Answer:
81 inches tall
pls mark me brainliest
The blue dot is at what value on the number line?
Pls help my brain is fried and this is my last question
Answer: 14, 16, 18, 20 in that order
Step-by-step explanation:
If the bottom response square is asking for a general equation, it would be y=x+7
A store purchases baseball hats from two different manufacturers in 3 different colors, summarized
below. One hat is chosen at random. Give your answer as a decimal out to at least 4 places.
Black Blue Red Total
Manufacturer A 23 21 29 73
Manufacturer B 27 17 10 54
Total 50 38 39 127
х
a) Find the probability that the hat was was Black or was from Manufacturer A. 0.3150
O 0.78740157480315
b) Find P(Red).
c) Find P(Manufacturer B and Red),
d) Find P(Manufacturer B or Red).
Answer:
See below
Step-by-step explanation:
a)
P(A or Black) = (73 + 27)/127 = 100/127 = 0.7874015748
b)
P(Red) = red/total = 39/127 = 0.30708661417
c)
P(Manufacturer B and Red) = (B and red)/total = 10/ 127 = 0.0787401575
d)
P(Manufacturer B or Red) = (B or red)/total = (54 + 29)/127 = 0.65354330708
What is the price of a $500 tv after a 20% discount?
Find the ratio (red to blue) of the perimeters of the similar triangles. Write your answer in simplest form.
Answer:
I think the answer is 9/2
Find the angle of this sector.
6 cm
NEED ASAP
5 cm
Answer:
x ≈ 68.8°
Step-by-step explanation:
The length of the arc of a sector is calculated as
arc = circumference × fraction of circle , that is
6 = 2πr × [tex]\frac{x}{360}[/tex] = 2π × 5 × [tex]\frac{x}{360}[/tex] = 10π × [tex]\frac{x}{360}[/tex] ( multiply both sides by 360 )
2160 = 10πx ( divide both sides by 10π )
68.7549... = x , that is
x ≈ 68.8° ( to 1 dec. place )
The Furry Friends Hotel, a kennel in Sparrowtown, needs to bring in at least $1,100 per day to cover its operating costs. The kennel charges $26 per day to house a large dog and $23
per day to house a small dog.
write an inequality to represent the situation
Answer:
23x >= 1100
Step-by-step explanation:
if 10% of a group of children are girls, what is the ratio of girls to boys
Answer:
9 boys to 1 girl
Step-by-step explanation:
Which graph represents the function f(x)=-|x|-2?
Answer:
ind the absolute value vertex. In this case, the vertex for y=−|x|−2 is (0,−2).
(0,−2)
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
(−∞,∞)
Set-Builder Notation: {x|x ∈ R}
For each x value, there is one y value. Select few x values from the domain. It would be more useful to select the values so that they are around the x value of the absolute value vertex.
x y
−2 −4
−1 −3
0 −2
1 −3
2 −4
Step-by-step explanation:
Answer:
The answer is C.
I hope this helps you!
Solve the system of equations using elimination, or write “no solutions” or “infinite solutions” where applicable
4x-y = 7
Answer:
no solutions
Step-by-step explanation:
i guess im
Plz help this one is the last one of the day plz help
What is the value of 20+6•5/-2
Answer:
The answer is 25
Step-by-step explanation:
6•5=30
30+20=50
50/-2=25
A parachutist's speed during a free fall reaches 135 miles per hour. What is this speed in feet per second? At this speed, how many feet will the parachutist fall during 5 seconds of free fall? In your computations, use the fact that I mile is equal to 5280 feet. Do not round your answers.
Answer:
198 ft/s speed
99 ft distance
Step-by-step explanation:
Answer:
7.33333ft
Step-by-step explanation:
x-3y=7
2х-6у=12
Solve the following systems
Answer:
Step-by-step explanation:
this system doesnt have any solutions
if you multiply the first equation by 2 you will get
2x-6y=14
second equation is
2x-6y=12
the result will -12=14
no solutions
Can someone help please
Answer:
B
Step-by-step explanation:
Stella wnats to buy an atlas that costs 510, a novel that costs $8, and a comc that costs $6. She saved 516 from her pocket money. How much
more money does she need to save? What equation is correct?
Answer:
where are the equations
Step-by-step explanation:
m is how much more she needs to save
510+8+6=516+m
m=8