Answers
Answer:
[tex]x = 10\\y = 5[/tex]
Step-by-step explanation:
1. Approach
The easiest method to solve this problem is to use the side ratios in a special right triangle. One should start by proving that the triangle is a (30 - 60 - 90) triangle. Since the problem gives on the information that one of the sides has a measure of ([tex]5\sqrt{3}[/tex]), one can use this combination with the ratio of the sides in a special right triangle, to find the unknown side lengths.
2. Prove this triangle is a (30 - 60 - 90) triangle
One is given a right triangle. This means the triangle has a (90) degree or right angle in it. This is indicated by a box around one of the angles. One is given that the other angle in this triangle has an angle measure of (30) degrees. The problem asks for one to find the third angle measure. A property of any triangle is that the sum of angle measures in the triangle is (180) degrees. One can use this to their advantage by stating the following:
[tex](90) + (30) + (unknown) = 180\\[/tex]
Simplify,
[tex](90) + (30) + (unknown) = 180[/tex]
[tex]120 + unknown = 180\\[/tex]
Inverse operations,
[tex]120 + unknown = 180\\[/tex]
[tex]unknown = 60[/tex]
Thus, this triangle is a (30 - 60 - 90) triangle, as its angles have the measures of (30 - 60 - 90).
3. Solve for (y)
The sides ratio in a (30 - 60 - 90) triangle is the following:
[tex]n - n\sqrt{3} - 2n[/tex]
Where (n) is the side opposite the (30) degree angle, ([tex]n\sqrt{3}[/tex]) is the side opposite the (60) degree angle and finally (2n) is the side opposite the (90) degree angle. The side (y) is opposite the (30) degree angle. This means that it is equal to the side opposite the (60) degree angle divided by ([tex]\sqrt{3}[/tex]). Therefore, one can state the following:
[tex]\frac{5\sqrt{3}}{\sqrt{3}}=y\\5=y[/tex]
4. Solve for (x)
Using the same thought process one used to solve for side (y), one can solve for side (x). The side (x) is opposite the (90) degree angle, hence, one can conclude that it is twice the length of the side with the length of (y). Therefore, one can state the following:
[tex]x = 2y\\x = 2(5)\\x = 10[/tex]
Related Questions
Find the value of the sum 219+226+233+⋯+2018.
Assume that the terms of the sum form an arithmetic series.
Give the exact value as your answer, do not round.
Answers
Answer:
228573
Step-by-step explanation:
a = 219 (first term)
an = 2018 (last term)
Sn->Sum of n terms
Sn=n/2(a + an) [Where n is no. of terms] -> eq 1
To find number of terms,
an = a + (n-1)d [d->Common Difference] -> eq 2
d= 226-219 = 7
=> d=7
Substituting in eq 2,
2018 = 219 + (n-1)(7)
1799 = (n-1)(7)
1799 = 7n-7
1799 = 7(n-1)
1799/7 = n-1
257 = n-1
n=258
Substituting values in eq 1,
Sn = 258/2(219+2018)
= 129(2237)
= 228573
find the radius of a circle if the circumference is 44cm. (take π=22/7)
Answers
Answer:
The radius of the circle if the circumference is 44 cm will be 7 cm.
Step-by-step explanation:
➝ Circumference of the circle = 44 cm
➔ Circumference = 2πr [For finding radius]
Finding the radius:-
➜ Let radius be r.
➜ 44 = 2 × 22/7 × r
➜ Multiply 2 × 22/7
➜ 44 = 44/7 × r
➜ Taking 7 to LHS.
➜ 44 × 7 = 44 × r
➜ 308 = 44 × r
➜ Taking 44 to LHS.
➜ 308/44 = r
➜ 308/44 = 7
➜ 7 = r
➜ r = 7
Nishi invests £3500 at 4% interest per year. Work out how much she will have altogether after: 2 years
Answers
Answer:
£3780
Step-by-step explanation:
P= £3500, R=4%, t=2years
I = PRT/100
I= (3500×4×2)/100 =£280
Amount in 2years = P+I = £3500+ £280= £3780
4.
A line contains the points R (-5, -6) S (1, 5) and T (x, 10). Solve for x. Be sure to show and explain all work
Answers
Answer:
x is 3.[tex]\overline{72}[/tex]
Step-by-step explanation:
The given points on the line are;
R(-5, -6), S(1, 5) and T(x, 10)
The number of points required to find the equation of the line = 2 points
The slope, m, of the line using points R(-5, -6) and S(1, 5) is given as follows;
m = (5 - (-6))/(1 - (-5)) = 11/6
The equation of the line in slope and point form, using point S(1, 5) is therefore;
y - 5 = (11/6)·(x - 1) = 11·x/6 - 11/6
y - 5 = 11·x/6 - 11/6, given that the x-value is required, we have;
x = (y - 5 + 11/6) × 6/11 = 6·y/11 - 19/11
x = 6·y/11 - 19/11
At point T(x, 10), y = 10, therefore, we have;
x = 6×10/11 - 19/11 = 41/11 = 3.[tex]\overline{72}[/tex]
x = 3.[tex]\overline{72}[/tex].
How in the world do I set this up?
The formula
c = 75 + 30(n - 5) is used to find the cost, c, of a taxi ride where n represents the number of [tex]\frac{1}{5}[/tex] miles of the ride. Find the cost of a taxi ride of 2/frac{2}{5}
Thanks
Answers
Answer:
Step-by-step explanation:
The 2 2/5 is not showing up correctly, but I think it means that you are going 2 miles + 2/5 of a mile. If that is not true, leave me a note and I'll correct it.
So 75 and 30(n - 5) represent cents (I think) per 1/5 of a mile.
1 mile has 5 fifths.
2 miles has 10 fifths
2/5 has 2 fifths.
the total is 17 fifths so n = 17
C = 75 + 30(17 - 5)
C = 75 + 30(12)
C = 75 + 360
C = 435
That means you pay 4 dollars and 35 cents.
I'LL GIVE BRAINLIEST !!! FASTER
please explain how do you get the answer
Answers
Answer:
84°
Step-by-step explanation:
angles in a quadrilateral add to 360°. 360-(114+76)=5x =170°. 170°/5 = 32°. x=32°
angles on a straight line add to 180°.
2x = 64°. 180-64=116°. y=116°.
y-x = 116-32 = 84°
Answer:
[tex]78[/tex]
Step-by-step explanation:
The inner angles of a quadrilateral all add up to 360. This means we can write the following
[tex]114 + 76 + 3x + 2x = 360\\190 + 5x = 360\\5x = 170\\x = 34[/tex]
Now that we have x we can find y. Notice that y and 2x are on the same line. Any line cutting another straight line will create two angles that add up to 180.
Therefore we can write
[tex]2x + y = 180\\2(34) + y = 180\\y = 112[/tex]
Finally computing y - x
[tex]y - x = 112 - 34 = 78[/tex]
Dorothy put $470 into a savings account for one year. The rate of interest on the account was 5.5%. Find the interest earned on the amount.
Answers
Answer: $25.85 assuming annual compounding.
Step-by-step explanation:
PV=470
I/Y=5.5
N=1
CPT_FV
Quadrilateral A'B'C'D' is a dilation of quadrilateral ABCD about point P Is this dilation a reduction or an enlargement? O reduction enlargement
Answers
Answer: reduction
Step-by-step explanation:
ABCD-> 'ABCD
its bc 'ABCD got smaller compared to ABCD
Answer:
It is a reduction.
Step-by-step explanation:
Hope this helped.
What is the slope of a line parallel to line B?
Answers
Please help explanation if possible
Answers
How do you solve this problem?
Answers
Explanation:
The square has perimeter P = 16, so each side of the square is P/4 = 16/4 = 4 cm.
This makes side KJ = 4 cm, and this is the diameter of the circle. Multiply the diameter with pi to get the circumference (aka the perimeter of the circle).
Therefore, the perimeter is pi*d = pi*4 = 4pi which points us to choice B
please show the work for it as well thank you
Answers
Answer:
2x^4+4x^2+2
Step-by-step explanation:
f(x) = x^2+1
g(x) = 2x^2
g(f(x))=
Replace x in the function g(x) with the function f(x)
=2( x^2+1)^2
= 2( x^2 +2x^2 +1)
= 2x^4+4x^2+2
helpppp please.......
Answers
The equation your teacher has given you is an identity. We can prove this by transforming one side into the other. I'll transform the right hand side (RHS) into the left hand side (LHS).
This means I'll keep the LHS the same for each line. I'll only change the RHS. The goal is to get the same thing on both sides (I could go the other way around but I find this pathway is easier).
[tex]\tan^4(\theta)+\sec^2(\theta) = \sec^4(\theta)-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\sec^2(\theta)\right)^2-\tan^2(\theta)\\\\\tan^4(\theta)+\sec^2(\theta) = \left(\tan^2(\theta)+1\right)^2-\tan^2(\theta) \ \text{ ... see note 1}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+2\tan^2(\theta)+1-\tan^2(\theta)\\\\[/tex]
[tex]\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\tan^2(\theta)+1\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta)-1+1 \ \text{ ... see note 2}\\\\\tan^4(\theta)+\sec^2(\theta) = \tan^4(\theta)+\sec^2(\theta) \ \ \Large \checkmark\\\\[/tex]
note1: I use the identity [tex]\tan^2(\theta)+1 = \sec^2(\theta)[/tex] which is derived from the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex]note2: based on the previous note, we can say [tex]\tan^2(\theta) = \sec^2(\theta)-1[/tex]So because we've arrived at the same thing on both sides, the original equation is an identity. It always true no matter what theta value you plug in, as long as theta is in the domain. So something like theta = pi/2 won't work because tan(pi/2) = undefined and sec(pi/2) = undefined. It's based on how cos(pi/2) = 0 and this value is in the denominator. Dividing by zero is undefined.
Consequently, this means all solutions to cos(theta) = 0 will be excluded from the domain. Everything else works.
functions f and g are defined as
f(x) = 5x² - 10x + 7
where x > 1
g(x) = 7x - 6
Find fg(2)
Answers
Explanation:
When dealing with composite functions, we start with the right hand function first then apply our way to the left hand side.
1) First equate g(2)
2) Equate the function f of your answer you found in g(2)
1) 7(2) - 6
2) 14 - 6
3) 8
4) f(8) = 5(8)^2 - 10(8) + 7
5) f(8) = 320 - 80 + 7
6) f(8) = 247
Hope this helps, brainliest would be appreciated :)
Please see screenshot for question you will get all 60 points plus a crown if you answer correctly
Answers
Answer:
12.73
Step-by-step explanation:
Set up ratio.
[tex]\frac{22}{100} =\frac{2.89}{x}[/tex]
Solve for x.
[tex]\frac{100}{22} =\frac{x}{2.8}[/tex]
[tex]\frac{100}{22} (2.8)=x[/tex]
x=12.73
factor and solve the problems in the photo ……….. pleaseeeee help i haven’t done algebra in 2 years
Answers
Answer:
30. 2x²-x-1=0
or, 2x²-2x+x-1=0
or, 2x(x-1)+1(x-1)=0
or, (x-1)(2x+1)=0
so, x-1 = 0 or, x = 1
and 2x+1 = 0 or, 2x = -1 or, x = -1/2
so, x = 1 and 1/2
31. 3x²-14x=5
or, 3x²-14x-5=0
or, 3x²-15x+x-5=0
or, 3x(x-5)+1(x-5)=0
or, (x-5)(3x+1)=0
so, x-5=0 or, x=5
and 3x+1=0 or, 3x=-1 or, x=-1/3
so, x = 5 and -1/3
Answered by GAUTHMATH
Find the measure of the indicated arc.
Answers
Cual es el resultado de la siguiente división (– 1/3 a^2 b^5 – 1/2 a^5 b^4 + 2/5 a^3 b – 5a^2 b^7) / ( – 5a^2 b^2)
Answers
Answer:
dont understand clearly
Step-by-step explanation:
Solve for x. Round to the nearest tenth, if necessary
Answers
Answer:
20.4
Step-by-step explanation:
cos(74) = x/74
x = 74×cos(74)
x = 20.4
Answered by GAUTHMATH
Determine the 3 digit chopping and rounding approximately of the number 0.9
Answers
Answer:
We want to "chop and round" the periodic number 0.9 at 3 digits.
First, remember that we can write our periodic number as:
0.9 = 0.9999...
Such that the nine repeats infinitely.
Now we want to chop it at the third digit, and then round.
To chop at the third digit we just "cut" the number at the third digit after the decimal point, we will get:
0.9 ≈ 0.999
Now we round.
Remember that to round a number, we need to look at the last digit after the decimal point.
If the last digit is 5 or larger, we round up, adding 1 to the previous decimal.
If the last digit is 4 or smaller, we round down, don't adding anything to the previous decimal.
in our number:
0.999
The last digit is a 9, so we round up.
Then we add "1" to the previous decimal
but the previous decimal is a 9, so when we add 1, it will transform into a 10.
So it also adds one to the previous decimal, which also is a 9, so the process repeats, this time adding 1 to the decimal to its left, in this case, that decimal will be the first decimal at the left of the decimal point.
So after rounding, we will get:
0.999 ≈ 1
Then we can conclude that:
he 3 digit chopping and rounding approximately of the number 0.9 is 1"
Please hurry due tomorrow morning!!!
Jazzie and Jocelyn are racing on a track.Jazzie runs 4 miles per hour and gets a 0.25 mile head start. Jocelyn runs 0.5 miles per hour faster than Jazzie. If Jocelyn and Jazzie run the same distance, how many hours, x, do they run?
F. 4x + 0.25 = 0.5x
G.4x + 0.25 = 4.5x
H.4x + 0.25 =3.5 x
J. 4x - 0.25 = 3.5 x
Answers
Answer:
G: 4x + 0.25 = 4.5x
Step-by-step explanation:
1. since Jazzie runs 4 mph add .5 to that to get Jocelyn's speed of 4.5 mph
2. Since Jazzie has a head start add .25 to 4x to get 4x + 0.25 = ?
3. put Jocelyn's speed in the question Mark to get 4x + 0.25 = 4.5x
How do I solve this: 12v + 10v + 14 = 80
Answers
Answer:
v = 3
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
12v + 10v + 14 = 80
Step 2: Solve for v
Combine like terms: 22v + 14 = 80[Subtraction Property of Equality] Subtract 14 on both sides: 22v = 66[Division Property of Equality] Divide 22 on both sides: v = 3how do you answer this
Answers
Answer:
19 units
Step-by-step explanation:
count the squares around the shape for the slanted part treat it like a rectangle and just count the squares from the pointy spot to the other side where it stops
Two cards are drawn from a deck of 52 playing cards. The first card is NOT replaced into the deck before the 2nd card is drawn What is the probability of drawing a King and then another King?
Answers
Answer:
probability that 2 cards drawn from a deck of 52 cards are both kings.
is probability that first card is a king times probability that second card is a king
with replacement 4/52*4/52 =0.592%
without replacement 4/52*3/51=0.452%
Step-by-step explanation:
In a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer. If the spectator has an angle of 110° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole? 70.0° 41.1° 28.9° 19.9°
Answers
Answer:
28.9°
Step-by-step explanation:
The golfer, hole and spectator form a triangle. Let ABC be the triangle and let the angle the spectator has between the golfer and the hole be A = 110°, the angle the golfer has between the spectator and the hole be B and the angle the hole has between the golfer and the spectator be C. Let the angle between the golfer and the hole be a = 200 yards, the distance between the spectator and the hole be b and the distance between the golfer and the spectator be c = 140 yards,
Using the sine rule for the triangle, we find angle C.
So, a/sinA = b/SinB = c/SinC
So, a/sinA = c/sinC
sinC = csinA/a
C = sin⁻¹(csinA/a)
Substituting the values of the variables into the equation, we have
C = sin⁻¹(csinA/a)
C = sin⁻¹( 140sin110°/200)
C = sin⁻¹( 7 × 0.9397/10)
C = sin⁻¹(6.5778/10)
C = sin⁻¹(0.65778)
C = 41.13°
We know that A + B + C = 180° (sum of angles in a triangle)
And since the angle the golfer has between the spectator and the hole be B
So, B = 180° - (A + C)
B = 180° - (110° + 41.13°)
B = 180° - 151.13°
B = 28.87°
B ≅ 28.9°
The angle that the golfer has between the spectator and the hole is 28.9°.
Angel between spectator and holes:Using the law of sines:
BC/SinΔBAC=AB/SinΔACB
Hence,
200/Sin110°=140/SinΔACB
ΔACB=41.1°
Thus,
ΔABC=180°-ΔBAC-ΔACB
ΔABC= 180° - (110° + 41.1°)
ΔABC= 180° - 151.1°
ΔABC= 28.9°
Inconclusion the angle that the golfer has between the spectator and the hole is 28.9°.
Learn more angle here:https://brainly.com/question/25770607
Can someone please exlpain how to do this???
Answers
Answer:
40. A c=60
41 B z= 40
Step-by-step explanation:
The sum of the angles in a triangle is 180
40. 61+59+c = 180
Combine like terms
120+c = 180
c = 180-120
c =60
41. 90+50+z = 180
140 +z = 180
z = 180-140
z = 40
Can someone please help me.... I am confused.
Answers
Answer:
P1 =(-6,-2)
P1=8
P2(-4,-1)
P2=5
GIVING BRAINLIEST. GRAPH ABSOLUTE VALUE INEQUALITY y<-1/3|x+4|+5
Answers
Answer:
-1/3 · Ix+4I + 5
or
y∠ - Ix+4I -15
3
Step-by-step explanation:
hope this helped
Let f(x) = 4x + 3 and g(x) = -2x + 5. Find. (g⋅f)(5)
Answers
Answer:
-41
Step-by-step explanation:
f(x) = 4x + 3 and g(x) = -2x + 5
g(f(5) ) =
First find f(5) = 4(5)+3 = 20+3 = 23
Then find g(23) = -2(23) +5 = -46+5 = -41
2( 5 1 m− 5 2 )+ 5 3 2, left parenthesis, start fraction, 1, divided by, 5, end fraction, m, minus, start fraction, 2, divided by, 5, end fraction, right parenthesis, plus, start fraction, 3, divided by, 5, end fraction
Answers
Answer:
2/5m - 1/5
Step-by-step explanation:
Given the equation :
2(1/5m - 2/5) + 3/5
First step:
Open the bracket by multiplying values in the bracket by 2
2/5m - 4/5 + 3/5
-4/5 + 3/5 = (-4 + 3) / 5 = - 1 / 5
Hence,
2/5m - 4/5 + 3/5 = 2/5m - 1/5
= 2/5m - 1/5
