The length 2.3 and 7.8 units
We have given that ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees.
What is the formula for low of cosine?The Law of Cosines, which tells us
[tex]a^{2}=b^{2} +c^{2} -2bccosA[/tex]
giving us a quadratic equation for b we can solve. But let's do it with the Law of Sines as asked.
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
We have c,a,A so the Law of Sines gives us sin C
[tex]sinC=\frac{csina}{a} =\frac{5.4sin20}{3.3} =0.5597[/tex]
There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse
[tex]C_{a}=arcsin(0.5597)=34.033^{0}[/tex]
[tex]C_{0}=180-C_{a} =145.96^0[/tex]
Both of these make a valid triangle with A=20°. They give respective B's:
[tex]B_{a}=180-A-C_{a} =125.96^0[/tex]
[tex]B_{0}=180-C_{0} =14.033^0[/tex]
So we get two possibilities for b:
[tex]b=\frac{asinB}{sinA} \\\\b_{a} =\frac{3.3sin125.96}{sin 20} \\\\b_{a}=7.8\\\\ b_0=2.3[/tex]
2.3 units and 7.8 units
Therefore we get the length 2.3 and 7.8 units
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Answer: 2.3 units and 7.8 units
Let's check it with the Law of Cosines:
There's a shortcut for the quadratic formula when the middle term is 'even.'
Looks good.
Which of the following is the graph of a quartic function?
A. Graph A.
B. Graph B.
c. Graph C
D. Graph D
Answer: D
Step-by-step explanation:
If f(x)=2x^2 + 5 sqrt(x-2), complete the following statement f(6)
Answer:
f(6) = 82
Step-by-step explanation:
substitute x = 6 into f(x) and evaluate
f(6) = 2(6)² + 5[tex]\sqrt{6-2}[/tex] = 2(36) + 5[tex]\sqrt{4}[/tex] = 72 + 5(2) = 72 + 10 = 82
A transit train from Boston to New York and a passenger train from New York to Boston both departed at 3:00 pm. The distance between the New York station and the Boston station is 280 miles. The speed of the transit train was 80 mph. The speed of the passenger train was 60 miles per hour. Which train will arrive at their station first?
Answer:
The passenger train
Step-by-step explanation:
if its going 60 mph then it makes it way to a stop of 280 miles then the passenger train will just go 60 so thats 5 in a half hours
Answer:
5:00 pm
Step-by-step explanation:
The rate of closure is (80 mi/hr + 60 mi/hr) = 140 mi/hr
At 140 mi/hr, it will take 2 hours to travel 280 miles
The engines of the trains will meet in 2 hours past 3:00
Simplify the expression 8+(10+x).
Answer:
18+x
Step-by-step explanation:
since the plus is between the 8 and the perinthesis, you can basically just get rid of them and the expression is then
8+10+x
which is equal to 18+x
Answer:
18 + x
Step-by-step explanation:
combine 10 and 8 to make 18, then add x.
answer quickly only if you know
PLEASE HELP!!! ASAPPPPP
Can y’all pls help me I need help!!
Answer:
D
Step-by-step explanation:
I hope this helps :) Have a lovely day!!!
please help this is due tomorrow.,.
What is the theoretical probability of picking a
yellow counter in simplest form?
4/6
1/2
2/6
1/3
The radius of a circle is 6.5 ft. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
The circumference of the circles should be 40.84 (rounded is 40.8)
Step-by-step explanation:
You find the circumference by doing 2 x pi * 6.5 which = 40.84
It is 3:13 when Lavender gets home from school. She works on her homework, and by the time she finishes math, the clock says that it is 4:37. How much time has passed?
Answer:
An hour and 24 minutes have passed.
Step-by-step explanation:
4:37 minus 3:13 is an hour and 24 minutes.
Heather is 1.6 m tall and casts a shadow of 3.5 m.
At the same time, a barn casts a shadow of
17.5 m. Find the height of the barn in meters.
Answer:
Heather is 1.6 m tall and casts a shadow of 3.5 m. At the same time, a barn casts a shadow of 17.5 m. Find the height of the barn in meters. (6y +11307 IH=71° 20.
Step-by-step explanation:
Circle P has a radius of 3 centimeters. What is the length of Arc RS?
Round to the nearest tenth.
[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=3\\ \theta =143 \end{cases}\implies s=\cfrac{(143)\pi (3)}{180}\implies s=\cfrac{143\pi }{60}\implies s\approx 7.5[/tex]
A and B are two brothers. A weigh 50 kg and B weigh 45 kg. if they divide 285 g of roasted meat in the ratio of their weight, how many grams does each get?
Answer:
Share of A = 150 grams
Share if B = 135 grams
Step-by-step explanation:
Weight of A = 50 kg
Weight of B = 45 kg
ratio of weights = 50 : 45 = 10 : 9
Let the common multiplier of the ratio be x.
-> 10x + 9x = 285
-> 19x = 285
-> x = 285/19
-> x = 15
-> 10x = 150
-> 9x = 135
Share of A = 150 grams
Share if B = 135 grams
HELP PLEASE! What is the area of a cube with 5 inches height?
A. One hundred twenty-five inches
B. Three hundred and six inches cubed
C. One hundred twenty-five inches cubed
D. Three hundred and six inches
Answer:
C. One hundred twenty-five inches cubed
Step-by-step explanation:
To find the answer,
The volume of a cube is side * side * side
In a cube all the sides are the same.
5 * 5 * 5 = 125
Answer:
c
Step-by-step explanation:
bc i say so, And also With volume it is always cubed
KE is twice as KI.If its perimeter is 42cm, how long is KI?
please
Call KE as a, KI as b
To calculate the perimeter of a kite, we use the formula : 2(a+b)
The perimeter is 42cm, hence a + b = 42/2 = 21 cm
Now, we can write the ratio between a and b as 2:1 (because KE is twice as long)
So, we can calculate KI by taking the sum and divide by the total ratio parts
21 : (2 + 1 ) = 7
Recheck : KI = 7 -> KE = 14
Perimeter = (7+14) x 2 = 42, and 14 is indeed 2 x 7.
HELP FASTT PLEASE
An account earns annual simple interest. Find the balance of the account. $2000 at 9% for 6 months
Answer:
2000 × 9% × 6/12 = 90
2000+90 =2090
How do you find x in the question \frac{x}{10}=0.1 how do you find out what x is???
A scientist is growing bacteria, starting with a culture of 10 bacteria. The colony of bacteria doubles every 3 hours. Which equation represents the relationship between the number of bacteria (b) and the number of hours (t) that have elapsed?
A) B= 10(2)^t
B) B= 10(2)^t/3
C) B= 10(2)^3t
D) B= 10(e)^2t
E) B= log₂(t)
Answer:
B) B=10(2)^(t/3)
Step-by-step explanation:
The Formula used to find Exponential Growth is
[tex]y=a*b^{\frac{t}{t_{1} } }[/tex]
where y is the Final Amount
a is the Initial Amount
b is the Growth Factor
t is Time
t1 is Time to Complete one Growth
so for our Problem
a=10 and b=2 and t1=3 and y=B
so B=10(2)^(t/3)
So
The expression is
[tex]\\ \rm\rightarrowtail B=10(2)^{\frac{t}{3}}[/tex]
Option B is correct
solve pls brainliest
Answer:
1/3
Step-by-step explanation:
3/9 = 1/3 in simplest form
7/9 - 4/9 = 3/9
If you need further help, let me know!
- profparis
The trinomial x2 – 3x – 4 is represented by the model. an algebra tile configuration. 0 tiles are in the factor 1 spot and 0 tiles are in the factor 2 spot. 10 tiles are in the product spot in 2 columns with 5 rows: 1 is labeled x squared, 1 is labeled x, the 4 tiles below x squared are labeled negative x, and the 4 tiles below the x tile are labeled negative. what are the factors of the trinomial? (x 1) and (x – 4) (x 4) and (x – 1) (x 5) and (x – 4) (x 4) and (x – 5)
Trinomial is an expression. The factors of the given trinomial x²-3x-4 are (x+1)(x-4).
What is a trinomial?An algebraic expression with three non-zero terms and more than one variable is known as a trinomial.
To know the factors of the trinomial, we need to find the factors of the given trinomial. therefore, we need to divide the middle term of the trinomial into two parts, such that the sum of that two terms is the middle term(-3x), while their product is equal to the product of the first and the last term(ac=-4x²).
Later on, we need to take the common terms out of the first two and the last two terms.
[tex]x^2-3x-4\\\\= x^2-4x+x-4\\\\=x(x-4)+(x-4)\\\\=(x+1)(x-4)[/tex]
Hence, the factors of the given trinomial x²-3x-4 are (x+1)(x-4).
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Factor the polynomial: 3x^4+6^3+9^2
Answer:
3x^4+297
Step-by-step explanation:
First, simplify 6³ and 9².
6³ = 6•6•6 = 36•6 = 216
9² = 9•9 = 81
Add.
3x^4+216+81
3x^4+297
Note:
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Tracy wants to determine the coordinates of the minimum value of a quadratic function. She
writes the equation for the function in different forms.
Which form of the function would be MOST helpful to determine the coordinates of the
minimum value? *
O y = (x + 1)2 - 25
O y = x² + 2x - 24
O y = 2(x - 12) + x?
O y = (x - 4) (x + 6)
The most helpful form to find the coordinates of the minimum is the vertex form.
Which form is better to find the minimum?Remember that for a quadratic equation with a positive leading coefficient, the minimum is at the vertex.
So the better form to determinate the coordinates of the minimum value will be the vertex form, where if the vertex is (h, k), we get:
y = a*(x - h)^2 + k
In this case, the first option is in that form:
y = (x + 1)^2 - 25
so:
h = -1
k = -25
This means that the coordinates of the minimum are (-1, -25)
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What is the raitio for chaperones to students if there is 180 students and 35 chaperones
lighting if a 25-foot-tall house cast a 75-foot shadow at the same time that a streetlight casts a 60-foot shadow how tall is the streetlight
Answer:
The street light is 20 feet tall.
Step-by-step explanation:
This question depends on a proportion. Keep your height of the object in one ratio and the length of the shadow in the other.
25/x = 75/60 Notice the height of the structure is on the left. The length of the shadow is on the right. Cross multiply
75x = 60 * 25 Combine the right
75x = 1500 Divide by 75
x = 1500/75
x = 20
The street light is 20 feet tall.
x-y=136
x+y=360
what do x and y equal?!
Answer:
x=13
y=234
Step-by-step explanation:
Points S and T are midpoints of the sides of triangle FGH.
Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.
What is GF?
4 cm
6 cm
8 cm
16 cm
Answer: 16 cm
Step-by-step explanation:
By the triangle midsegment theorem, 2(ST)=2(8)=16=GF
The length of GF in the triangle illustrated will be 16cm.
How to compute the value?From the information given, the lengths of HT and T F are 6 centimeters, the lengths of HS and SG are 4 centimeters, and the length of ST is 8 centimeters.
Therefore, the length of GF will be:
= 2 × ST
= 2 × 8
= 16 cm
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Please help!!! Photo below!! Any work helps
Answer:
296.1 yards
Step-by-step explanation:
The surveyor is interested in solving a triangle with two sides and the enclosed angle known. The Law of Cosines is used for that purpose.
The angle interior to the triangle where the surveyor turned is the supplement of the turning angle:
180° -110° = 70°
The law of cosines tells us the relation of the given sides (a, b) and angle (C) to the unknown side (c) is ...
c² = a² +b² -2ab·cos(C)
c² = 245² +270² -2·245·270·cos(70°) ≈ 87675.7350
c ≈ √87675.7350 ≈ 296.10
The length of the lake is about 296.1 yards.
please solve quickly
Answer:
x = 31°
Step-by-step explanation:
z is the length of the midsegment of the triangle. (Given)
[tex]\implies[/tex] midsegment will be parallel to the third side of the triangle.
[tex]\implies x=31\degree[/tex] (Corresponding angles)
Prove each of these identities.
a (1 + secx) (cosec x - cotx) = tan x
b (1 + sec x)(1 - cos x) = sin x tan x
➲ ( 1 + sec x )( cosec x - cot x ) = tan x
Solving for L.H.S[tex] \implies\quad \sf{(1+sec\:x)(cosec\:x-cot\:x) }[/tex]
[tex] \implies\quad \sf{ \left(1+\dfrac{1}{cos\:x}\right)\left(\dfrac{1}{sin\:x}-\dfrac{cos\:x}{sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{1+cos\:x}{cos\:x}\right)\left(\dfrac{1-cos\:x}{sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{1-cos^2 x}{cos\:x.sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left( \dfrac{sin^2 x}{cos\:x.sin\:x}\right)}[/tex]
[tex] \implies\quad \sf{ \left( \dfrac{sin\:x.\cancel{sin\:x}}{cos\:x.\cancel{sin\:x}}\right)}[/tex]
[tex] \implies\quad \sf{\left( \dfrac{sin\:x}{cos\:x}\right) }[/tex]
[tex] \implies\quad\underline{\underline{\pmb{ \sf{tan\:x}}} }[/tex]
➲ ( 1+ sec x )( 1- cos x ) = sin x. tan x
Solving for L.H.S[tex] \implies\quad \sf{ ( 1+ sec\:x)(1-cos\:x)}[/tex]
[tex] \implies\quad \sf{\left(1+\dfrac{1}{cos\:x} \right) \left( 1-cos\:x\right)}[/tex]
[tex] \implies\quad \sf{ \left(\dfrac{cos\:x+1}{cos\:x} \right)(1-cos \:x)}[/tex]
[tex] \implies\quad \sf{\dfrac{1-cos^2 x}{cos\:x} }[/tex]
[tex] \implies\quad \sf{\dfrac{sin^2x}{cos\:x} }[/tex]
[tex] \implies\quad \sf{sin\:x.\left( \dfrac{sin\:}{cos\:x}\right) }[/tex]
[tex] \implies\quad\underline{\underline{\pmb{ \sf{sin\:x.tan\:x}}} }[/tex]