the Red Line in the figure is an altitude of triangle hjl. Using right angle trig and properties of equality, y sin L = x = z sin H, write the Law of Sines for this triangle
Answers
Answer:
[tex]\Large \boxed{\mathrm{\bold{C}}}[/tex]
Step-by-step explanation:
[tex]\sf \displaystyle sin(\theta) =\frac{opposite}{hypotenuse }[/tex]
[tex]\sf \displaystyle sin(L) =\frac{x}{y}[/tex]
[tex]\sf \displaystyle sin(H) =\frac{x}{z}[/tex]
[tex]\displaystyle \sf \frac{sinL}{z} =\frac{sinH }{y}[/tex]
[tex]\displaystyle \sf \frac{\frac{x}{y} }{z} =\frac{\frac{x}{z} }{y}[/tex]
Simplifying the expression.
[tex]\sf \displaystyle \frac{x}{yz } = \frac{x}{yz} \ (true)[/tex]
[tex]\displaystyle \sf \frac{z}{sinL} =\frac{y}{sinH}[/tex]
[tex]\displaystyle \sf \frac{z}{\frac{x}{y}} =\frac{y}{\frac{x}{z}}[/tex]
Multiplying both sides by x.
[tex]\sf yz=yz \ (true)[/tex]
Answer:
d
Step-by-step explanation:
The law of Sines applied to a Δ ABC is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
Using this in Δ HJL
[tex]\frac{z}{sinL}[/tex] = [tex]\frac{y}{sinH}[/tex] → (b)
Which may be expressed in reciprocal form as
[tex]\frac{sinL}{z}[/tex] = [tex]\frac{sinH}{y}[/tex] → (a)
Thus the law of Sines can be expressed as either (a) or (b)
Related Questions
A goniometer may be used to measure the range of motion of a joint. A health professional is measuring the angle of a person's back and elevated leg. The symbol theta is used to represent the angle measurement. In the picture, the angle made by the goniometer is classified as a(n) angle. ° < θ < °
Answers
Answer:
Step-by-step explanation:
Answer:
obtuse , 90 , 180 .
Step-by-step explanation:
Sena determines the remainder of 4x32−14x16+2x3−8x−1, using the remainder theorem. How does she proceed to the correct answer? Drag a value into each box to correctly complete the statements.
Answers
Explanation:
(4x^32 - 14x^16 + 2x^3 - 8)/x - 1
x - 1 = 0
x = 1
f(x) = 4x^32 - 14x^16 + 2x^3 - 8
f(1) = 4(1)^32 - 14(1)^16 + 2(1)^3 - 8
f(1) = 4 - 14 + 2 - 8
f(1) = -10 - 6
f(1) = -16
Therefore, the remainder is -16
What are some methods for finding the distance between points A and B? You can use the pen tool to explore different options on the number line?
Answers
Answer:
Ok, the straightforward thing you can do, when you have a number line like in this situation, you can just "count" the number of units that are between A and B.
Now, a more correct way:
First, A is located at the value -3, then we can write:
A = -3.
And B is located at the value 5, then:
B = 5.
Now, the distance between A and B is equivalent to the difference between A and B:
D = B - A = 5 - (-3) = 8
The distance between A and B is 8 units.
Find the exact trigonometric ratios for the angle x whose radian measure is given. (If an answer is undefined, enter UNDEFINED.) −7π
Answers
Answer:
sin(x) = tan(x) = 0
cos(x) = sec(x) = -1
cot(x) = csc(x) = UNDEFINED
Step-by-step explanation:
An angle of -7π is co-terminal with an angle of π (or 180°). Its trig ratios are ...
sin(x) = tan(x) = 0
cos(x) = sec(x) = -1
cot(x) = csc(x) = UNDEFINED
Identify whether each of the datasets is quantitative or qualitative a. Types of computer software used in a database management system. b. Life-lengths of laser printers c. Brands of calculators used by 100 engineering students on campus d. Mileage attained by 12 automobiles powered by alcohol
Answers
Answer:
a. Types of computer software used in a database management system. =Qualitative
b. Life-lengths of laser printers =Quantitative
c. Brands of calculators used by 100 engineering students on campus =Qualitative
d. Mileage attained by 12 automobiles powered by alcohol= Quantitative
Step-by-step explanation:
Data is described as quantitative when it deals with numeric values whereas qualitative data is categorical in nature. Quantitative data tells us how much, how many, or the frequency of occurrence of certain variables. Qualitative data provides answers to the what, why, which, and where questions.
1. Types of computer software are not numeric variables as they answer the 'what' question.
2. Length deals with numbers, so the life-lengths of laser printers is a quantitative variable.
3. Brands of calculators are categorical data and are thus qualitative.
4. Mileage is a numerical variable and is thus quantitative.
2x +3=11
The value of X
Answers
Answer:
x=4
Step-by-step explanation:
2x+3=11
2x+3-3=11-3
2x=8
x=4
2x+3=11
2(4)+3=11
8+3=11
11=11
Answer:
x =4
Step-by-step explanation:
[tex]2x +3=11\\\\Collect \:like\:terms\\2x =11-3\\\\Subtract\\2x =8\\\\Divide\:both\:sides\:of\:the\:equation\:by\:2\\\frac{2x}{2} =\frac{8}{2} \\\\x = 4[/tex]
can someone please help me with this
Answers
Answer:
-21
Step-by-step explanation: a negative times a positive will always be a negative
Plzzzzzzzzzzzzzzzzzzz
Answers
Answer:
Complementary
Step-by-step explanation:
Complementary Angles add up to 90°
Supplementary Angles add up to 180°
60 + 30 = 90
If there are two angles that are complementary, and the first angle has a measure of 18°, what is the measure of the second angle?
A. 180 degrees
B. 162 degrees
C. 72 degrees
Answers
Answer:
C. 72 degrees
Step-by-step explanation:
Complementary angles total 90 degrees.
The second angle is ...
90° - 18° = 72°
Solve each of the following equations. Be sure to check your solutions.
3x-5=2.5x+3-(x-4)
Answers
Answer: x=8
Step-by-step explanation:
3x - 5= 2.5x + 3 -(x-4) apply the distributive property
3x -5 = 2.5x + 3 - x + 4 combine like terms on the right side
3x - 5 = 1.5x + 7 Add 5 to both sides
+5 +5
3x = 1.5x + 12 subtract 1.5x from both sides
-1.5x -15.x
1.5x = 12 Now divide both sides by 1.5
x = 8
someone please help me with this question !!
Answers
What is the image point of (2,6) after a translation right 5 units and down 3 units?
Answers
Answer:
(7, 3)
Step-by-step explanation:
(2+5, 6-3) = (7, 3)
Evaluate the expression 2(8 − 4)2 − 10 ÷ 2.
Answers
what is the relationship between integers and natural numbers.
Answers
7-(5t - 13)= -12 need help!!!
Answers
Answer:
t = 32/5
Step-by-step explanation:
7 - (5t - 13) = -12
7 - (5t - (-13) = -12
7 - 5t + 13 = -12
-5t = -12 - 13 - 7
-5t = -32
t = -32 / -5
t = 32/5
A pizza stand offers hand-tossed, pan, and thin crust pizza. How many outcomes
are there?
Answers
Don't quite understand the question so I'm gonna provide 2 answers
The simplest one being 3
If you're making combinations then 7
hand-tossed(1), thin(2), pan(3), hand-tossed and thin(4), hand-tossed and pan(5), thin and pan(6), all 3(7)
Evaluate the expression. Write the result in simplest form. (Do not enter a mixed number.) 3 3/4 + 9 7/8
Answers
Answer:
13 5/8
Step-by-step explanation:
3 3/4+9 7/8
15/4+79/8
30/8+79/8
109/8
simplify
13 5/8
Does anyone know this? Needed ASAP
Answers
Answer:
50 square units
Step-by-step explanation:
Using the formula provided, [tex]a = \frac{1}{2}h(b_1+b_2)[/tex], substituting the height (5), b1 (8) and b2 (12), we can solve for the formula.
[tex]a = \frac{1}{2}\cdot5(8+12)\\\\a = \frac{1}{2}\cdot5(20)\\\\a = \frac{1}{2}100\\\\a = 50[/tex]
Hope this helped!
Answer:
50 units²
Step-by-step explanation:
The area of a trapezoid can be found using the following formula.
[tex]A=\frac{1}{2}h(b_{1} +b_{2} )[/tex]
The height of the trapezoid is 5 units. The bases are 8 units and 12 units.
[tex]h= 5 \\b_{1} = 8\\b_{2} = 12[/tex]
Substitute the values into the formula.
[tex]A=\frac{1}{2}*5(8+12)[/tex]
Solve inside the parentheses. Add 8 and 12.
8+12=20
[tex]A=\frac{1}{2}*5(20)[/tex]
Multiply 5 and 20.
5*20= 100
[tex]A=\frac{1}{2}*100[/tex]
Multiply 1/2 and 100 or divide 100 by 2.
100 * 1/2= 50 or 100/2= 50
[tex]A= 50[/tex]
Add appropriate units. For this problem, the units are units².
[tex]A= 50 units^2[/tex]
The area of the trapezoid is 50 square units.
8/2=6/n+4 Solve for n
Answers
Answer:
No solution (because the n's cancel out!)
Step-by-step explanation:
Let's solve your equation step-by-step.
8
2
=
6
n
+4
Multiply all terms by n and cancel:
8n
2
=6+4n
4n=4n+6(Simplify both sides of the equation)
4n−4n=4n+6−4n(Subtract 4n from both sides)
0=6
Answer:
No solutions.
For each of the following questions, solve for the unknown quantity by rearranging the given equation.For numerical answers, make sure to express all answers in scientific notation with the proper number ofsignificant figures. Be careful to write out all units and convert if necessary.a. F=GMm/r^2a. M =b. r =b. M=kxa^3/p^2a. P =b. a =
Answers
Answer:
a. F=GMm/r^2; a. M =
[tex]M = \frac{Fr^{2} }{Gm}[/tex]
a. F=GMm/r^2; b. r =
[tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
b. M=kxa^3/p^2; a. P =
[tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
b. M=kxa^3/p^2; b. a =
[tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]
Step-by-step explanation:
For a. F=GMm/r^2; a. M =
To solve for M, we will rearrange the given equation F=GMm/r^2 such that M is the subject of the formula
From
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]Gm[/tex]
[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm} \\[/tex]
The equation becomes
[tex]\frac{Fr^{2} }{Gm} = M[/tex]
∴ [tex]M = \frac{Fr^{2} }{Gm}[/tex]
For a. F=GMm/r^2; b. r =
Also, to solve for r, we will rearrange the given equation F=GMm/r^2 such that r is the subject of the formula
From
F=GMm/r^2
[tex]F = \frac{GMm}{r^{2} }[/tex]
First, Cross multiplication, we then get
[tex]Fr^{2} = GMm[/tex]
Now, divide both sides by [tex]F[/tex], Such that we have
[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]
Then, [tex]r^{2} = \frac{GMm}{F} \\[/tex]
∴ [tex]r = \sqrt{\frac{GMm}{F} \\}[/tex]
For b. M=kxa^3/p^2; a. P =
To solve for P, we will rearrange the given equation M=kxa^3/p^2 such that P becomes the subject of the formula
From
M=kxa^3/p^2
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Divide both sides by [tex]M[/tex], such that the equation becomes
[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3}}{M}[/tex]
Then, [tex]p^{2} = \frac{kxa^{3}}{M}[/tex]
∴ [tex]p = \sqrt{\frac{kxa^{3}}{M}}[/tex]
For b. M=kxa^3/p^2; b. a =
To solve for a, we will rearrange the given equation M=kxa^3/p^2 such that a becomes the subject of the formula
From
M=kxa^3/p^2
[tex]M = \frac{kxa^{3}}{p^{2} } \\[/tex]
First, Cross multiply, we then get
[tex]Mp^{2} = kxa^{3}[/tex]
Now, Divide both sides by [tex]kx[/tex], such that the equation gives
[tex]\frac{Mp^{2}}{kx} = \frac{ kxa^{3}}{kx}[/tex]
Then, [tex]\frac{Mp^{2}}{kx} = a^{3}[/tex]
[tex]a^{3} = \frac{Mp^{2}}{kx}[/tex]
∴ [tex]a = \sqrt[3]{\frac{Mp^{2}}{kx} }[/tex]
Thanks for the help!
Answers
Answer:
A
Step-by-step explanation:
So we have the piecewise function:
[tex]f(x)= \begin{cases}\sqrt{2x} & \text{if }x<3 \\2x+10 & \text{if }3\leq x<8\\42&\text{if } x\geq 8\end{cases}[/tex]
And we want to find f(8).
Since our input value is 8, choose the equation that fits our input.
The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.
The second equation demand x to e greater than or equal to 3 and less than 8. 8 is not less than 8. So, we won't use that.
The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.
So:
[tex]f(x)=42\text{ if }x\geq 8[/tex]
[tex]f(8)=42[/tex]
There're nothing more to do, we're done :)
The answer is A.
Edit: Improved Format
Find the distance between each pair of points.
Answers
Answer: the distance is 9,
Step-by-step explanation: If you count the blocks you will see it's nine! Hope this helped you!
The acceleration of an object due to gravity is 32 feet per second. What is acceleration due to gravity in inches per second?
Answers
Answer:
384 inches per second.
Step-by-step explanation:
We are given that the acceleration of an object due to gravity is 32 feet per second.
And we want to find the acceleration in inches per second.
The acceleration can be represented as a ratio of 32 feet : second. This can be written as a fraction:
[tex]\displaystyle \frac{32\text{ feet}}{\text{second}}[/tex]
Use dimensional analysis. It is known that there is 12 inches in a feet. So, multiply by 12in/feet:
[tex]\displaystyle = \frac{32\text{ feet}}{\text{second}}\cdot\frac{12\text{ inches}}{\text{feet}}[/tex]
Cancel like units:
[tex]\displaystyle =\frac{32\cdot 12\text{ inches}}{\text{second}}[/tex]
Multiply:
[tex]\displaystyle =\frac{384\text{ inches}}{\text{second}}[/tex]
In conclusion, our answer is 384 inches per second.
Add 2 x 2 + 5 x + 6 to − 4 x 2 − x + 7
Answers
Add 2 x 2 + 5 x + 6 to − 4 x 2 − x + 7
Add the expressions.
13
A group of 8 children and 8 adults are going to a movie. Child tickets cost $2, and adult tickets cost $6. How much will the movie tickets cost in all?
Answers
Answer:
Hey there!
8(2)+8(6)
16+48=64
The total price is 64 dollars.
Let me know if this helps :)
2x8=16
6x8=48
Express (2-I) - (-1+3i) in the form of a + ib.
Answers
Answer:
[tex]=3-4i[/tex]
Step-by-step explanation:
So we have:
[tex](2-i)-(-1+3i)[/tex]
First, distribute:
[tex]=(2-i)+1-3i[/tex]
Combine like terms:
[tex]=-i-3i+2+1[/tex]
Add:
[tex]=-4i+3[/tex]
So, in the a+bi format, we will have:
[tex]=3-4i[/tex]
Answer:
3 -4i
Step-by-step explanation:
(2-i) - (-1+3i)
Distribute the minus sign
(2-i) + 1-3i
Combine like terms
3 -4i
Quadrilateral A'B'C'D'A
′
B
′
C
′
D
′
A, prime, B, prime, C, prime, D, prime is the result of translating quadrilateral ABCDABCDA, B, C, D by 555 units to the left and 555 units down.
Answers
Answer:
14.2
Step-by-step explanation:
= AB+BC+CD+DA
= 2.2+4.5+6.1+1.4
= 14.2
Answer: 14.2
Step-by-step explanation:
Khan Academy
14 + (-12)-8-5
FAST PLEASE ALSO PLEASE SHOW THE STEPS!!!
Answers
Answer:
-11
Step-by-step explanation:
start with PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
so you would first start with 14 + (-12) so the + and - become a negative so it becomes 14 - 12 which is 2
so then do -8-5 which is -13
so then you combine them and get 2-13 which is -11
(1 point) Find the volume of the parallelepiped with one vertex at (4,2,4), and adjacent vertices at (6,3,8), (6,1,10), and (0,6,3)
Answers
Answer:
8 cubic units
Step-by-step explanation:
Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D = (0,6,3)
The edges of the parallelepiped are
AB = (6,3,8) - (4,2,4) = (2,1,4)
AC = (6,1,10) - (4,2,4) = (2,-1,6)
AD = (0,6,3) - (4,2,4) = (-4,4,-1)
Therefore the volume of the parallelopiped is = |[AB,AC,AD]|
= [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]
= |2(1-24)+1(-2+24)+4(8-4)|
= |2(-23) + 1(22) + 4(4)|
= |8|
=8 cubic units
Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = (x +11)2 + .
Answers
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation:
y = 4x² + 88x
factor the expression
y = 4(x² + 22x)
complete the square
y + ? = 4(x² + 22x + ?)
y + ? = 4(x² + 22x + 121)
add 4 • 121 to the left side
y + 4 • 121 = 4(x² + 22x + 121)
multiply
y + 484 = 4(x² + 22x + 121)
y + 484 = 4(x + 11)²
subtract both sides by 484
y = 4(x + 11)² - 484
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation: