given the diagram below, explain how you would determine the opposite, adjacent, and hypotenuse side from the given 35° angle. (HELP PLEASE!!)
Answer:
opposite=8.402402490459 ,adjacent is already given=12, hypotenuse=14.64929507
Step-by-step explanation:
to do this you will have to use the law of sines. the first thing you need to do is solve for the unknown angle by subtracting 90+35 from 180. so you get the equation 180-(90+35)=55. now that you know all your angles, you can use the law of sines to solve for the unknown sides. the law of sines state that a/sin(A)=b/sin(B). if you substitute the values of 12 and 55 into the equation, since you know those sides, you can then find a ration that you can use to find the other sides, 12/sin(55)=b/sin(B), which is equal to, 14.649... Next you pick whichever side you want to solve for next, and plug in its opposite angle (i would solve for the other leg, because then you can use pythagorean theorem to solve for the hypotenuse, so i will demonstrate that way) plug in the angle 35, since it is opposite the leg and then finish for the variable, 14.649...=b/sin(35). once you have the sin, you can multiply it by the 14.649 to get your side, 14.649...*.5736...=8.402...=b. now you have your two legs, so you can use a^2+b^2=c^2 to solve for the hypotenuse. once you plug in your values it should look like this, 12^2+8.402...^2=c^2. which simplifies down to 214.602...=c^2. so you take the square root of both sides to find c, which equals 14.649. you can check that by seeing if 14.649 is bigger then the other two sides, which it is. This number should look familiar because it was the ratio we got when we divided 12 by the sin(55). the reason that happened is because the sin(90) is 1, the 14.649*1=14.649.
If you have any questions, leave them in the comments and will try to answer them, if this helped, pls give brainliest.
How to find the radius of a circle when only the area is known?
Answer:
Divide the area by pi. Then, square root the answer.
Step-by-step explanation:
Area of a cirlce= pi r^2
Answer:
You have to divide by pi (3.14) APROXIMATELY and then divide what you get by the square root.
A school is planning to construct two rectangular play areas in the playground. The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal. Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system's solutions?
Answer:
А.The system has two solutions, but only one is viable because the other results in a negative width.
Step-by-step explanation:
Given
Let:
[tex]L_A \to[/tex] length of play area A
[tex]W_A \to[/tex] width of play area A
[tex]L_B \to[/tex] length of play area B
[tex]W_B \to[/tex] width of play area B
[tex]x \to[/tex] Area of A
[tex]y \to[/tex] Area of B
From the question, we have the following:
[tex]L_A = 1 + 4W_A[/tex]
[tex]W_B = 2 + W_A[/tex]
[tex]L_B = 2 + 3W_B[/tex]
[tex]x = y[/tex]
The area of A is:
[tex]x = L_A * W_A[/tex]
This gives:
[tex]x = (1 + 4W_A) * W_A[/tex]
Open bracket
[tex]x = W_A + 4W_A^2[/tex]
The area of B is:
[tex]y = L_B * W_B[/tex]
[tex]y = (2 + 3W_B) * ( 2 + W_A)[/tex]
Substitute: [tex]W_B = 2 + W_A[/tex]
[tex]y = (2 + 3(2 + W_A)) * ( 2 + W_A)[/tex]
Open brackets
[tex]y = (2 + 6 + 3W_A) * ( 2 + W_A)[/tex]
[tex]y = (8 + 3W_A) * ( 2 + W_A)[/tex]
Expand
[tex]y = 16 + 8W_A + 6W_A + 3W_A^2[/tex]
[tex]y = 16 + 14W_A + 3W_A^2[/tex]
We have that:
[tex]x = y[/tex]
This gives:
[tex]W_A + 4W_A^2 = 16 + 14W_A + 3W_A^2[/tex]
Collect like terms
[tex]4W_A^2 - 3W_A^2 + W_A -14W_A - 16 =0[/tex]
[tex]W_A^2 -13W_A - 16 =0[/tex]
Using quadratic calculator, we have:
[tex]W_A = -14.1[/tex] or [tex]W = 1.13[/tex] --- approximated
But the width can not be negative; So:
[tex]W = 1.19[/tex]
I reallly need help plss -m=5-plssss
Answer:
[tex]4m ^{2} = 4 \times 5 \times 5 = 100[/tex]
what is the value of x squared + 2 x y / 2 * W + 3 * z for w=2, x=5, y=8 and z=3
Answer: 114
Step-by-step explanation:
Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114
Explain how to add 5.3 + 9.079
Answer:
14.379
Step-by-step explanation:
1. Line up from left to right
2. Make sure that the decimals are lined up
3. Add the thousandths and hundredths with 0
4. Add 3 in the tenths place
5. Add up 9 and 5 to make 14
*IF YOU DID THE STEPS RIGHT, THEN YOU SHOULD HAVE 14.379 AS YOUR ANSWER*
Answer:
9.079
+5.300
_______
14.379
Step-by-step explanation:
Just line the decimals up and add zeros for 5.3 to 5.300 because you can't do 9.079
+5.3 because your decimal will be in the wrong spot and your answer will come out wrong
At a surf shop in Malibu, California, a used blue surfboard is on sale for $100. According to the salesperson, the new price represents a 20% discount from the original price. What did it sell for originally?
Answer:
$125
Step-by-step explanation:
if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price
let a = original price
this equation can be used to represent the question
a x 0.8 = 100 ]]divide both sides by 0.8
a = 100 / 0.8 = 125
how many terms does 3x + 5y - 17 - 2y + x have?
Answer:
It has 5 terms
Step-by-step explanation:
Terms are the numbers or values in a equation, so this Equation has 5 terms
x + 5y - 17 - 2y + x.
1. x
2.5y
3.17
4. 2y
5.x
(I listed the terms)
help me with this question
Answer:
960 cm³ I think it may be correct
Write the equation of the line passing through the points (0, -4) and (-2, 2).
Answer:
y=-3x-4
Step-by-step explanation:
i solved it by the two points
What is the missing justification in the proof of the angle bisector
construction?
A.symmetric property
B.congruence property
C.transitive property
D.reflexive property
Answer:
C
Step-by-step explanation:
The transitive property states that a line is congruent to itself.
Answer:
The answer is, (C) transitive property.
Step-by-step explanation:
Definition of angle bisector:The (interior) bisector of an angle, also called the internal angle bisector is the line or line segment that divides the angle into two equal parts. The angle bisectors meet at the incenter. , which has trilinear coordinates.
Then, For angle bisector construction, a statement column proof is given.
Justification for Statement.
CPCTC and MBP have the same angle.
NBP angle
Since SSS established congruence for the two triangles in the preceding sentence,
The next step is to ensure that matching angles are identical and that congruent triangle portions are congruent.
A line is congruent to itself if it has the transitive attribute.
To know more angle bisector here, https://brainly.com/question/24334771
#SPJ2
Using the image above, describe the error in the statement of the tangent ratio. answer correctly !!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
the right answer is
tan D=80/18
Find the surface area.
solve: 7 (j-5)=-14 what is the value of j?
Answer:
open bracket
7j - 35 = 14
7j = 14 + 35
7j = 49
divide thru by 7
7j / 7 = 49 / 7
j = 7
Which expression is equivalent to 10f−5−5f+2?
15f−3
5f−7
15f−7
−3+5f
Answer:
[tex]10f - 5-5f +2 =5f -3= -3+5f[/tex]
last option
Answer:
C
Step-by-step explanation:
If we solve 10f-5f+8+69+4, We get 5f+81 (put in comments if you want a step by step explanation on how i solved this).
Let's try to solve each of the options.
A) 15f + 14g + 4
It would not be option A because there isn't a variable such as g in the expression.
B) 15f + 8 + 10g
C) 5f + 69 + 12
5f+ 81
This one is correct because the expression also equals 5f+81
D) 5f + 149 +4
5f+ 153
D would be wrong as well
Hope this helps! <3
1. This system of equations has: y = 3x + 4
y = -X
A One Solution
B. Infinitely Many Solutions
C. No Solutions
Answer:
A) One Solution
Step-by-step explanation:
3x + 4 = -x
4 = -4x
x = -1
y = 3(-1)+4
y = 1
One Solution
PLS HELPPPP
Which expression is equivalent to 8x + 6?
A. -7(1 – x) + x + 13
B. 10x - 8 - 2x + 2
C. 2x + 10 - (4 + 6x)
D. 9x - 10 + x - 4
Answer:
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
Step-by-step explanation:ccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
5. If position of object x = 3 sinΘ – 7 cosΘ then motion of object is bounded between position.
9514 1404 393
Answer:
±√58 ≈ ±7.616
Step-by-step explanation:
The linear combination of sine and cosine functions will have an amplitude that is the root of the sum of the squares of the individual amplitudes.
|x| = √(3² +7²) = √58
The motion is bounded between positions ±√58.
_____
Here's a way to get to the relation used above.
The sine of the sum of angles is given by ...
sin(θ+c) = sin(θ)cos(c) +cos(θ)sin(c)
If this is multiplied by some amplitude A, then we have ...
A·sin(θ+c) = A·sin(θ)cos(c) +A·cos(θ)sin(c)
Comparing this to the given expression, we find ...
A·cos(c) = 3 and A·sin(c) = -7
We know that sin²+cos² = 1, so the sum of the squares of these values is ...
(A·cos(c))² +(A·sin(c))² = A²(cos(c)² +sin(c)²) = A²(1) = A²
That is, A² = (3)² +(-7)² = 9+49 = 58. This tells us the position function can be written as ...
x = A·sin(θ +c) . . . . for some angle c
x = (√58)sin(θ +c)
This has the bounds ±√58.
6. In 2002, the bear population in Florida was estimated to be 2,700. In 2019, it was reported to be
4050. What percent does the increase in bears represent? Pls put the steps. Pls help this is due in 15 minutes
Answer:
50% increase
Step-by-step explanation:
4050-2700 = 1350
1350/2700 = 0.5
Convert to a percentage:
0.5*100 = 50
Lines AB and CD are parallel. If mZN is 52" then what is my?
A 128
B. 38
C. 142
D. 52
Find the measure of the angle indicated.
P
A) 92°
B) 61°
C 86°
D) 34°
Answer:
92°÷^®√™÷√÷^π^π^^π^π°π°^÷
A $40 shirt now selling for $28 is discounted by what percent?
Answer:
30%
Step-by-step explanation:
Think of this as converting a fraction. 28/40 to x/100. You do this because in the situation, 40 is 100 percent of the price. So 28 is x percent of 100.
You multiply 40 by 2.5 to get to 100, so multiply 28 by the same number to get x. 28 * 2.5 = 70.
So 28 is 70 percent of 40. But the question is asking by what percentage it is discounted. If it's now selling for 70%, it has been discounted 30%. So the answer is 30%
HIII can some one please HELP ME !!!!
Answer:95
Step-by-step explanation:
Need help with math!! Provided the graph with answers
I think the first one c and the second one a
Answer please !!!!!!!!!
help no links please u^u
Answer:
∠A= 80°
Step-by-step explanation:
if they are supplementary then put them equal to 180
7x + 3 +7x + 23 = 180
14x + 26 = 180
14x = 154
x= 11
now plug in
7(11)+3
77+3= 80
Company is testing a robot.The robot is 12 inches tall and weigh 4 pounds.The employees of the company marked a grid on the floor and set the robot at(4,4). They programmed the robot to walk 4 yards east and 6 yards north each minute.What will the robot's location be after 7 minutes? The x coordinate and the y coordinate
Answer:
[tex]P(2)=(32,46)[/tex]
Step-by-step explanation:
From the question we are told that:
Height of robot [tex]h=12 inches[/tex]
Weight of robot [tex]W=4[/tex]
Start position [tex]P(1)=(4,4)[/tex]
Per minute distance [tex]d=(4,6)[/tex]
Total time [tex]T=7min[/tex]
Generally the distance traveled in 7 minutes [tex]d_T[/tex] is mathematically given by
[tex]d_T=d*T[/tex]
[tex]d_T=(4.6)*7[/tex]
[tex]d_T=(28,42)[/tex]
Generally the position of the robot after 7 minutes is mathematically given by
[tex]P(2)=P(1)+d_T[/tex]
[tex]P(2)=(4,4)+(28,42)[/tex]
[tex]P(2)=(32,46)[/tex]
Therefore the position of the robot after 7 minutes is
[tex]P(2)=(32,46)[/tex]
Macy took a Math test; her ratio of the correct to incorrect answers was 8:2.
If there were 30 questions on the test, how many did Macy get correct?
FAST RESPONSE PLEASE!!!!
Answer:
24
Step-by-step explanation:
8 correct for every 2 wrong
multiply both sides by 3
24 correct and 6 wrong
which adds up to 30
What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line x+2y=18x+2y=18?
Answer:
[tex]y=-\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slope (m) and different y-intercepts (b)1) Determine the slope (m)
[tex]x+2y=18[/tex]
Rearrange this equation into slope-intercept form (this will make it easier for us to identify the slope)
Subtract x from both sides to isolate 2y
[tex]x+2y-x=-x+18\\2y=-x+18[/tex]
Divide both sides by 2 to isolate y
[tex]y=-\frac{1}{2} x+9[/tex]
Now, we can see clearly that [tex]-\frac{1}{2}[/tex] is in the place of m. Because parallel lines have the same slope, [tex]-\frac{1}{2}[/tex] is therefore the slope of the line we're currently solving for. Plug [tex]-\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]:
[tex]y=-\frac{1}{2} x+b[/tex]
2) Determine the y-intercept
[tex]y=-\frac{1}{2} x+b[/tex]
Plug in the point (8,-7)
[tex]-7=-\frac{1}{2} (8)+b\\-7=-4+b[/tex]
Add 4 to both sides
[tex]-7+4=-4+b+4\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:
[tex]y=-\frac{1}{2} x-3[/tex]
I hope this helps!
Ahhhhhh i neeed help
Answer:
ok hiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Answer:
Option C, No real solutions
Hope this helps!