Answer:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]
Step-by-step explanation:
The Law of Sines states that:
[tex]\frac{a}{\sin A} = \frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.
[tex]A[/tex], [tex]B[/tex], [tex]C[/tex] - Angles opposite to respective sides, dimensionless.
Given that [tex]a = 71[/tex], [tex]b = 104[/tex], [tex]\angle A = 21^{\circ}[/tex], the sine of angle B is:
[tex]\sin B = \frac{b}{a}\cdot \sin A[/tex]
[tex]\sin B = \frac{104}{71}\cdot \sin 21^{\circ}[/tex]
[tex]\sin B = 0.525[/tex]
Sine is positive between 0º and 180º, so there are two possible solutions:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex]
[tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
The remaining angle is obtained from the principle that sum of internal triangles equals to 180 degrees: ([tex]\angle A = 21^{\circ}[/tex], [tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex])
[tex]\angle C_{1} = 180^{\circ}-\angle A - \angle B_{1}[/tex]
[tex]\angle C_{1} = 180^{\circ}-21^{\circ}-31.668^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex]
[tex]\angle C_{2} = 180^{\circ}-\angle A - \angle B_{2}[/tex]
[tex]\angle C_{2} = 180^{\circ}-21^{\circ}-148.332^{\circ}[/tex]
[tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
Lastly, the remaining side of the triangle is found by means of the Law of Sine: ([tex]a = 71[/tex], [tex]\angle A = 21^{\circ}[/tex], [tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex])
[tex]c_{1} = a\cdot \left(\frac{\sin C_{1}}{\sin A} \right)[/tex]
[tex]c_{1} = 71\cdot \left(\frac{\sin 127.332^{\circ}}{\sin 21^{\circ}} \right)[/tex]
[tex]c_{1} \approx 157.532[/tex]
[tex]c_{2} = a\cdot \left(\frac{\sin C_{2}}{\sin A} \right)[/tex]
[tex]c_{2}= 71\cdot \left(\frac{\sin 10.668^{\circ}}{\sin 21^{\circ}} \right)[/tex]
[tex]c_{2}\approx 36.676[/tex]
The answer are presented below:
[tex]\angle B_{1} \approx 31.668^{\circ}[/tex], [tex]\angle B_{2} \approx 148.332^{\circ}[/tex]
[tex]\angle C_{1} \approx 127.332^{\circ}[/tex], [tex]\angle C_{2} \approx 10.668^{\circ}[/tex]
[tex]c_{1} \approx 157.532[/tex], [tex]c_{2}\approx 36.676[/tex]
Write a multiplication sentence to show how 10 gallons and 300 miles are related. How are 5 gallons ad 150 miles related? How are 1 gallon and 30 miles related?
Answer:
It shows for each gallon consumed, we multiply by 30 to get the amount of miles
This applies for the three questions
Step-by-step explanation:
10 gallons and 300 miles are related in such a way that you divide the number if miles by number of gallons.
300/10 = 30 miles per gallon.
It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.
5 gallons ad 150 miles related in such a way that you divide the number if miles by number of gallons.
150/5 = 30 miles per gallon.
It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.
1 gallon and 30 miles related in such a way that you divide the number if miles by number of gallons.
30/1= 30 miles per gallon.
It shows for each gallon consumed, we multiply by 30 to get the amount of Miles.
Kendrick is using a compass and straightedge to copy angle M. The figure shows the portion of the construction that he has already completed. Where should Kendrick place the center of the compass to do the next step of the construction?
Answer:
The question is not complete, but I found a similar question (image) that applies to this case:
The correct answer is:
Point N ( or where the arc cuts the horizontal line)
Step-by-step explanation:
From the figure attached to this answer, to copy angle in the first image on the left onto the inage in the right, Kendric first of all places tha centre of the compass at point M, and extends it to point N, to draw the first arc, which has already been done.
1. Next, the center of the compass should be placed at point N, and extended to the point where the arc touches the inclined line.
2. This measurement is then transferred to the new line, and the center of the compassed placed at point D, and a second arc drawn to cut the first arc.
3. Finally a line is drawn through the point where the two arcs meet to touch point C.
Which numbers in set ={,,,,,,,,,}eh equals left brace 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right brace are elements in both the subset of odd numbers and the subset of multiples of 3?
Enter your answer.
Answer:
D={3,9}
The numbers are 3 and 9
Step-by-step explanation:
The set A
={,,,,,,,,,}
Let B be the sub set of A containing odd numbers
B={1,3,5,7,9}
Let C be the sub set of A containing multiply of 3
C= {3,6,9}
Now let D be the be the sub set of A containing both odd numbers and multiples of 3
D={3,9}
hypothesis that there is a relationship between parents’ and children’s party identification. Would we be correct in inferring that such a relationship also exists in the population? Explain your answer. What is the probability that any relationship we found is due to pure chance?
Answer:
No
It could be purely due to chance.
Step-by-step explanation:
A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.
So it is not necessary for a population to have the same characteristics as the sample.
But it is essential for the sample to have at least one same characteristics as the population.
So we would not be correct in inferring that such a relationship also exists in the population.
It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.
For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.
It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.
Lisa owns a "Random Candy" vending machine, which is a machine that picks a candy out of an assortment in a random fashion. Lisa controls the probability of picking each candy. The machine is running out of "Honey Bunny," so Lisa wants to program it so that the probability of getting a candy other than "Honey Bunny" twice in a row is greater than \dfrac{9}{4} 4 9 start fraction, 9, divided by, 4, end fraction times the probability of getting "Honey Bunny" in one try. Write an inequality that models the situation. Use ppp to represent the probability of getting "Honey Bunny" in one try.
Answer:
[tex][P(X_{1})\times P (X_{2})]>[\frac{9}{4}\times P (H_{1})][/tex]
Step-by-step explanation:
Let the candy "Honey Bunny" be labelled as H and the other candies as X.
It is provided that the machine is running out of "Honey Bunny".
So, Lisa wants to program it so that the probability of getting a candy other than "Honey Bunny" twice in a row is greater than 9/4 times the probability of getting "Honey Bunny" in one try.
Probability of getting a candy other than "Honey Bunny" twice in a row,P (X₁) × P (X₂)
Probability of getting "Honey Bunny" in one try,P (H₁)
The inequality is as follows:
[tex][P(X_{1})\times P (X_{2})]>[\frac{9}{4}\times P (H_{1})][/tex]
Answer:
(1-p)^2>9/4p
Step-by-step explanation:
Can someone show me how to get the answer of -8 - 12 / (-4) step by step?
Answer:
-5
Step-by-step explanation:
12 ÷ -4 = -3Plug -3 in: -8 - -3Simplify: -8 + 3-8 + 3 = -5how do you Evaluate. 58−(14)2= ________
Answer:
58-(14)2
58-28
30
Step-by-step explanation:
Distribute and then combine like terms to simply the following expression -3 (2x + 4) - 2 (8 – 8x) + 52
I
Step-by-step explanation:
-6x - 12 - 16 + 16x + 52
10x + 24
Convert the following point from spherical to rectangular coordinates: (6,5π4,3π4). (x,y,z)=______
Usage: To enter a point, for example (x,y,z), type "(x, y, z)".
Answer:
nxjhbfhbfwihsfnjkfdbjbshcxbdbjibebfhdhwhhdhdhffvnfnjehrhffbfgnfjrjhhfrj
Step-by-step explanation:
Convert the following to slope-intercept form.
4x + 3y = 24
Answer:
y = -4/3x +8
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
4x+3y = 24
Subtract 4x from each side
3y = -4x+24
Divide each side by 3
y = -4/3x +24/3
y = -4/3x +8
Answer: y = -4/3x +8
HELP MEEEEE
(The problem is in the picture)
Answer:
Hey there!
We don't have enough information. 7(n+5) can be written as either the 7 times the sum of n+5, or 7 multiplied by n+5.
Let me know if this helps :)
The ares of a rectangle is 46 square inches, if the length is 4 times the width , the find the dimensions of the rectangle.
Answer:
[tex]\sqrt{11.5} =w[/tex] (Width)
[tex]4\sqrt{11.5}= Length[/tex]
Step-by-step explanation:
Area of a rectangle: 46 = w(L)
L = 4w
Substitute
46 = 4[tex]w^{2}[/tex]
Divide both by 4
[tex]11.5=w^{2}[/tex]
[tex]\sqrt{11.5} =w[/tex] (Width)
[tex]4\sqrt{11.5}= Length[/tex]
Four less than the
product of 2 and 5
Help pleasss!!!
Answer:
The answer is 6
Step-by-step explanation:
2 x 5 = 10
10 - 4 = 6
Hope this helps!
Answer:
6
Step-by-step explanation:
2 x 5 = 10
10 - 4 = 6
I hope this helps!
A customer wants to enlarge a photo to 2.75 it’s current height the photo current height is 3.25 inches what should its enlarged height be in inches
Answer:
8.9375
Step-by-step explanation:
2.75×3.25=8.9375
According to the question it said increase to and that is why I only multiplied but if the question said increase by then I would have to add my product (8.9375) to the original height of the photo.
A force of 150N is applied at an angle of 60° to the horizontal to pull a box through a distance of 50m. Calculate the work done
Answer:
Work done = 3750 Joules
Step-by-step explanation:
The force acting in the body should be resolved to it's horizontal component before we can use ut to solve for the problem
Horizontal component= 150 * cos 60
Horizontal component= 150*0.5
Horizontal component= 75N
Work done= Force * distance
Work done= 75*50
Work done= 3750 Nm
Work done = 3750 Joules
Geometry: Find the value of X
Answer:
[tex] x = \sqrt{30} [/tex]
Step-by-step explanation:
BD is the altitude of the right ∆ which divides the hypotenuse to create two line segments, CD, and AD.
According to the right triangle altitude theorem,
[tex] BD = \sqrt{CD*AD} [/tex]
CD = 3, AD = 7, therefore,
[tex] BD = \sqrt{3*7} [/tex]
[tex] BD = \sqrt{21} [/tex]
Find x using Pythagorean theorem
[tex] x^2 = BD^2 + CD^2 [/tex]
[tex] x^2 = (\sqrt{21})^2 + 3^2 [/tex]
[tex] x^2 = 21 + 9 [/tex]
[tex] x^2 = 30 [/tex]
[tex] x = \sqrt{30} [/tex]
Using this figure, A' is the ____ of A
Image
Step-by-step explanation:
It's actually called Translation but image is the same thing as translation
what is the rate of change of the linear function that has a graph that passes through the points (2, 9) and (-1, 3)
Answer:
Slope= 2
Step-by-step explanation:
Rate of change can simply be called slope
So the rate of change or slope of the linear function that passes through the points (2, 9) and (-1, 3) is
Slope = (y2-y1)/(x2-x1)
Where y2= 3
Y1= 9
X2= -1
X1= 2
Slope = (y2-y1)/(x2-x1)
Slope= (3-9)/(-1-2)
Slope= -6/-3
Slope= 2
Josie has a bag of ice that weighs 5 pounds. She left it in a sealed container and it melted. How much does the resulting water weigh
Answer:
5 pounds
Step-by-step explanation:
The only thing added or removed from the container was heat, which has no weight. The water has the same weight regardless of its chemical phase (solid, liquid, gas, plasma).
5 pounds
2) In the Tour de France, cyclists ride 3,653.6 km in 20 days. How many miles do they go per day?
Answer:
The answer is 182.68 kmStep-by-step explanation:
To solve this question we use ratio and proportion
If in 20 days they ride 3,653.6 km , then
in 1 day they will ride [tex] \frac{3653.6 \times 1}{20} [/tex]
We have the final answer as
182.68 kmHope this helps you
All of the following expressions are equivalent except.___ 2+m m+2 m-(-2) -2-m
Answer:
[tex]\Huge \boxed{-2-m}[/tex]
Step-by-step explanation:
2 + m
Rewrite with variable first.
m + 2
m + 2
Can’t be simplified further.
m - (-2)
Distribute negative sign.
m + 2
-2-m
Rewrite with variable first.
-m - 2
The last expression is not equivalent to m+2.
Solve 3x-2=1/2 - x/3
Zev read 15% of his 56-page book. Kelly read 12% of her 64-page book. Marneisha read 14% of his 68-page book Aleisha read 10% of her 72-page book.
Answer:
zev=15/100*56=9.6 pages
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Answer:
[tex]$ \frac{2187 \pi}{4}$[/tex]
Step-by-step explanation:
Using Stoke's theorem, we get
[tex]$ \int \int_S curl F.dS = \int_C F.dr$[/tex]
Now parametrize C
r(t) = ( 3 cos t, 3 - 3 sin t ) where, t in [0 2π]
[tex]$ \int_C F. dr= \int_0 ^{2 \pi}F ( 3 \cos t, 3 - 3 \sin t). r'(t)dt$[/tex]
[tex]$= \int_0^{2 \pi}(( 9 \cos^2 t)(27)(-3\sin t), \sin t \times (-27 \cos t \sin t)) . (-3 \sin t, 0 - 3 \cos t) dt $[/tex]
[tex]$ = 27 \int_0^{2 \pi} 81 \cos ^2 t \sin ^2 t + 3 \cos ^2 t \sin tdt $[/tex]
[tex]$ = 27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2t+27 [ - \cos^3 t]_0^{2 \pi}$[/tex]
[tex]$ = 27 \times \frac{81}{4} \int_0^{2 \pi} \frac{(1- \cos 4t)}{2} $[/tex]
[tex]$= \frac{2187}{8}[t-\frac{1}{4} \sin 4t]_0^{2 \pi} $[/tex]
[tex]$= \frac{2187 \pi}{4}$[/tex]
By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].
Given that,
Function F(x, y, z) = (x^2y^3z)i + sin(xyz)j + xyzk,
S is the part of the cone y^2 = x^2 + z^2 that lies between the planes y = 0 and y =3, oriented in the direction of the positive y-axis.
We have to determine,
Use Stokes' Theorem to evaluate S curl F·dS.
According to the question,
By using Stokes Theorem to evaluate S curl F .dS.
[tex]\int\ \int _s curlF.ds = \int _c F.dr\\\\[/tex]
Now parametrize C
r(t) = ( 3 cos t, 3 - 3 sin t ) ,
Where, t in [0 2π]
Then,
[tex]\int_c F.dr = \int^{2\pi }_0 F(3cost, 3-3sint).r'(t)dt\\\\[/tex]
[tex]= \int^{2\pi }_0 ((9cos^2t)(27)(-3sint),(sint) \times (-27cost.sint). (-3sint,0-3cost)dt\\\\= 27 \int^{2\pi }_0 81cos^2t .\ tsin^2t + 3 cos^2t. t sintdt\\\\= 27 \int^{2\pi }_0 \dfrac{81}{4}sin^22t+ 27[-cos^3t]^{2\pi }_0\\\\= 27 \times \dfrac{81}{4} \int^{2\pi }_{0} (\dfrac{1-cos4t}{2})\\\\= \dfrac{2187}{8}[t-\dfrac{1}{4}sin4t]^{2\pi }_0\\\\= \dfrac{2187}{8}[2\pi -\dfrac{1}{4}sin4(2\pi )- 0-\dfrac{1}{4}sin4(0 )]\\\\= \dfrac{2187\pi }{4}[/tex]
Hence, By using Stokes Theorem the required S curl F.ds is [tex]\dfrac{2187\pi }{4}[/tex].
To know more about Integration click the link given below.
https://brainly.com/question/17207150
Each of the sides of a square $S_1$ with area $16$ is bisected, and a smaller square $S_2$ is constructed using the bisection points as vertices. The same process is carried out on S_2 to construct an even smaller square $S_3$. What is the area of $S_3$?
Answer:
4 sq. units
Step-by-step explanation:
Because the vertices of S₂ are the midpoints of S₁, the area of S₂ will be half of that of S₁ which is 16 / 2 = 8. Similarly, because the same process is carried out on S₂ to make S₃, the area of S₃ is 8 / 2 = 4 sq. units.
Answer:
hope this helps friend
Step-by-step explanation:
A = a^2
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(Math question incoming) Are the Polynomials in standard form(Yes or No?) Identify the name of each Polynomial. Identify the leading coefficient. Identify the degree.
Standard polynomial form means that the terms are arranged from highest to lowest degree.
The leading coefficient is the number before the highest degree.
The degree of the polynomial is the power of the variable attached to the leading coefficient.
1) This is not in standard polynomial form.
The leading coefficient is -1.
This is a second-degree polynomial.
2) This is in standard polynomial form.
The leading coefficient is 3.
This is a fourth-degree polynomial.
3) This is not in standard polynomial form.
The leading coefficient is 3.
This is a fifth-degree polynomial.
4) This is in standard polynomial form.
The leading coefficient is -4.
This is a fifth-degree polynomial.
5) This is not in standard polynomial form.
The leading coefficient is -5.
This is a third-degree polynomial.
6) This is not in standard polynomial form.
The leading coefficient is -1.
This is a sixth-degree polynomial.
7) This is in standard polynomial form.
The leading coefficient is 2.
This is a second-degree polynomial.
8) This is in standard polynomial form.
The leading coefficient is 1.
This is a second-degree polynomial.
9) This is in standard polynomial form.
The leading coefficient is 1.
This is a third-degree polynomial.
10) This is not in standard polynomial form.
The leading coefficient is 6.
This is a fourth-degree polynomial.
3-x=5x+21
A: The solution set is (_) Simplified
B: There is no solution
Pick one and if A then simplify the answer
Answer:
[tex] \boxed{ \sf{ \bold{- 3}}}[/tex]Step-by-step explanation:
[tex] \sf{3 - x = 5x + 21}[/tex]
Move 5x to left hand side and change it's sign
⇒[tex] \sf{ - x - 5x + 3 = 21}[/tex]
Move 3 to right hand side and change it's sign
⇒[tex] \sf{ - x - 5x = 21 - 3}[/tex]
Collect like terms
⇒[tex] \sf{ - 6x = 21 - 3}[/tex]
Subtract 3 from 21
⇒[tex] \sf{ - 6x = 18}[/tex]
Divide both sides of the equation by -6
⇒[tex] \sf{ \frac{ - 6x}{ - 6} = \frac{18}{-6}} [/tex]
Calculate
⇒[tex] \sf{x = -3}[/tex]
Hope I helped!
Best regards!!
Answer:
x = - 3
Step-by-step explanation:
3 - x = 5x + 21
- x + 3 = 5x + 21
(- x + 3) + (- 3 - 5x) = (5x + 21) + (- 3 - 5x)
(- x + 3) + (- 5x - 3) = (5x + 21) + (- 5x - 3)
- x + 3 - 5x - 3 = 5x + 21 - 5x - 3
- x - 5x + 3 - 3 = 5x - 5x + 21 - 3
- 6x = 18
x = - 18/6
x = - 3
AB= please help step by step
Answer:
8x−14
Step-by-step explanation:
3x - 4 + 5x - 10
=3x+−4+5x+−10
Combine Like Terms:
=3x+−4+5x+−10
=(3x+5x)+(−4+−10)
Consider the linear equation, 2.5n + 5.2 = 35.2.
What property will be used to complete the first step in solving for n?
Answer:
Subtraction Property of Equality
Step-by-step explanation:
When solving an equation for a variable (in this case n), we want to move all of the n-terms to 1 side and the non-n terms to the other side. To do this, we can subtract 5.2 from both sides to leave 2.5n by itself. The property we used to do this is the Subtraction Property of Equality which states that if you subtract a quantity from one side of an equation, you must also subtract that same quantity from the other side of the equation.
Answer: A is the right one
Step-by-step explanation:
Consider the linear equation, 2.5n + 5.2 = 35.2.
What property will be used to complete the first step in solving for n?
subtraction property of equality
multiplication property of equality
division property of equality
distributive property
At the end of the day of teaching the skill of cutting and sewing to make capes, Ms. Ironperson and Mr. Thoro decided to go to the Shawarma Mediterranean Grill. Ms. Ironperson ordered 3 chicken shawarma wraps and 2 orders of spiced potatoes for a total bill of $42.95. Mr. Thoro ordered 5 chicken shawarma wraps and 4 orders of spiced potatoes for a total bill of $74.91. What is the cost of a chicken shawarma wrap? What is the cost of one order of spiced potatoes? If x denotes the cost of a chicken shawarma wrap and y denotes the cost of an order of spiced potatoes, what are the equations needed to solve this problem?
Answer:
The cost of a chicken shawarma wrap = $10.99
The cost of an order of spiced potatoes=$4.99
Equations needed
3x+2y =42.95
5x + 4y=74.91
Step-by-step explanation:
x = the cost of a chicken shawarma wrap
y = the cost of an order of spiced potatoes
Ms. Ironperson
3x+2y =42.95
Mr. Thoro
5x + 4y=74.91
3x+2y =42.95 (1)
5x + 4y=74.91 (2)
Multiply (1) by 2
6x + 4y=85.9 (3)
5x + 4y=74.91. (2)
Subtract (2) from (3)
6x - 5x= 85.9 - 74.91
x=$10.99
Substitute the value of x into (1)
3x+2y =42.95 (1)
3(10.99) + 2y =42.95
32.97 + 2y = 42.95
2y = 42.95 - 32.97
2y=9.98
Divide both sides by 2
y=9.98/2
=4.99
y=$4.99
Therefore,
The cost of a chicken shawarma wrap = $10.99
The cost of an order of spiced potatoes=$4.99