The angle of refraction is 15.6 deg.
We have given that An incident ray strikes a piece of diamond at an angle of 40. 5 degrees.
What happen when light passes through one medium to another medium?When a ray of light passes from medium 1 to medium 2, the refractive index of medium 2 with respect to 1 is the ratio of the absolute refractive index of medium 2 and medium 1
[tex]1n_{2}=\frac{^{n_{1}}}{n_{2}}[/tex]
When light passes from air into diamond, with the given values of refractive indices,
[tex]an_{d}=\frac{^{n_{d}}}{n_{a}}=\frac{2.42}{1.0003} =2.4193[/tex]
According to Snell's law,
[tex]an_{d}=\frac{^{sini}}{sin r}[/tex]
[tex]< br/ > sinr=an_{d}=\frac{^{sini}}{sin r}=\frac{sin(40.5)}{2.41930} =0.2684[/tex]
[tex]< br/ > r=arcsin(0.2684)=15.57 deg[/tex]
The angle of refraction is 15.6 deg
To learn more about the angle of reflection visit:
https://brainly.com/question/18772331
Kendall swam (n) laps in a pool. Sophia swam 12 lesd than Kendall. How many laps did they swim altogether
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS
Answer:
d and b
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 8 , then
sum = 180° × 6 = 1080°
note there are 4 angles congruent to ∠ 1 and 1 angle congruent to ∠ 2
sum the interior angles and equate to 1080
5(10x + 15) + 2(14x) + 6x - 3 = 1080 ( distribute parenthesis on left side )
50x + 75 + 28x + 6x - 3 = 1080 ( simplify left side )
84x + 72 = 1080 ( subtract 72 from both sides )
84x = 1008 ( divide both sides by 84 )
x = 12 → option d
--------------------------------------------------------------------
∠ 1 = 10x + 15 = 10(12) + 15 = 120 + 15 = 135°
∠ 2 = 14x = 14 × 12 = 168°
∠ 3 = 6x - 3 = 6(12) - 3 = 72 - 3 = 69°
the largest interior angle is 168° → option b
A laptop computer is purchased for $2300. After each year, the resale value decreases by 25%. What will the resale value be after 4 years
since its 25% on each of the 4 years then it becomes 100%, but because its decreasing then that means it is half of $2300, which is $1150.
The answer is $1150
Really easy, Really need help!
Answer:
I don't see what the question is
Write the log equation as an exponential equation. You do not need to solve for X,
log, (5x + 1) = 2
Answer:
5x+1=10²
Step-by-step explanation:
[tex]log_{x}y=n\\ y=x^{n}[/tex]
㏒(5x+1)=2
5x+1=10²
i will cry if i can't answer these
Answer:
15
Step-by-step explanation:
3 liters equals to 3000 milliliters
divide 3000 by 200 and you get 15 bowls of soup
Will literally make BRAINLIEST and marry you if you do this for me
Answer:
0.44
Step-by-step explanation:
See the picture below.
Remember that the sine is the ratio of the length of the opposite leg to the length of the hypotenuse.
Perhaps you know SOHCAHTOA, where SOH means sine, opposite, hypotenuse.
For angle J, leg LK is the opposite leg.
The hypotenuse of the triangle is the side opposite the right angle, teh angle of 90°, which is angle L, so the hypotenuse is side KJ.
[tex]\sin J = \dfrac{opposite~leg}{hypotenuse}[/tex]
[tex] \sin J = \dfrac{39}{89} [/tex]
[tex] \sin J = 0.43820... [/tex]
Answer: 0.44
Can’t solve this proof all help is appreciated
Explanation:
To get to the desired conclusion, you will want to make use of CPCTC and the fact that triangle AXB is congruent to triangle CYD. In order to show those two right triangles are congruent, it is sufficient to claim congruence of their hypotenuses and one internal acute angle (HA congruence). The corresponding internal angles are alternate interior angles where a transversal (BD) crosses parallel lines (AB║CD). It's tedious, but not terribly difficult.
__
Statement . . . . Reason
1. Congruent segment pairs are (AB, CD), (AD, BC) . . . . given
2. Perpendicular segment pairs are (AX, BD), (CY, BD) . . . . given
3. ABCD is a parallelogram . . . . definition of parallelogram (opposite sides are the same length)
4. AB ║ CD . . . . definition of parallelogram (opposite sides are parallel)
5. ∠ABX ≅ ∠CDY . . . . alternate interior angles at BD
6. ΔAXB and ΔCYD are right triangles . . . . definition of right triangle (angles at X, Y are 90°)
7. ΔAXB ≅ ΔCYD . . . . HA congruence postulate (AB, CD are the hypotenuses)
8. AX ≅ CY . . . . CPCTC
_____
Additional comment
A lot of proof has to do with working backward, answering the question, "How do I know ...?" The beginning paragraph in this answer attempts to show you the answers to those questions.
This proof works with the smaller triangles AXB and CYD. You could do the same proof with the larger triangles AXD and CYB. For that, you'd have to claim that AD║BC.
A Mexican restaurant sells quesadillas in two sizes: a "large* 10 inch-round quesadilla and a "small" 4 inch
round quesadilla. Which is larger, half of the 10-inch quesadilla or the entire 4-inch quesadilla?
Answer:
Half of the 10-inch quesadilla ↓
Here is the inequality statement:
10 ÷ 1/2 = 5 > 4
10 divided by its half equals five which is greater than 4.
A triangular pyramid has a height of 6 ft. The triangular base has a
height of 6 ft and a width of 6 ft. Explain whether doubling the
height of the base would double the volume of the pyramid.
a
Answer:
36
Step-by-step explanation:
All you have to do is 6x6 then it's 36...
Peter can paint a house in 10 hours. Melanie can paint the same house in 9 hours. How long would it take if they worked together?
Answer:
SOLUTION: It would take about 4.7 hours if they worked together.
Step-by-step explanation:
omar started to run on a treadmill after setting its timer for 78 minutes. the display says that he has finished 47% of his run. how many more minutes have gone by
Answer:
36.66 minutes have gone by
Step-by-step explanation:
x/78 = 47/100 cross multiply
x times 100 = 78 times 47
x100 = 3666
/100 /100
x = 36.66
The segments in each figure are tangent to the circle at the points shown. Find each length.
Answer:
Step-by-step explanation:
Tangents from a common point are equal.
In other words AC = AB
AC = 8x
AB = 2x^2
2x^2 = 8x Divide both sides by 2x
2x^2/2x = 8x / 2x Divide
x = 4
AC = 8x
AC = 8*4
AC = 32
AB = 2x^2
AB = 2 (4)^2
AB = 2*16
AB = 32
solve pls brainliest
Answer:
35 votes
Step-by-step explanation:
First we divide :)
56/8 = 7
Now we multiply 5 by 7
5 x 7 = 35
She recieved 35 votes :)
Have an amazing day!!
Please rate and mark brainliest!!!
Olivia goes to Larry's Lunch Place. She orders food that totals to $16. 85, Because Olivia works at Larry's Lunch Place, she gets a 15% discount on the cost of her food.
With the discount what is her total?
Answer: $ 14.32
Step-by-step explanation:
15% of 16.85 = 0.15 x 16.85 = 2.5275 ≈ 2.53
16.85 - 2.53 = 14.32
What is 226. 8 rounded to the nearest whole number
Answer:
226.8 rounded to the nearest whole number is 227
Step-by-step explanation:
226 is farther away than 227 on a number line, so it rounds to 227.
How to find the missing side of a triangle using trigonometry.
Justin is packing a container with books. The dimensions of each book are 8 inches by 6 inches by 2 inches. • The dimensions of the container are 16 inches by 12 inches by 12 inches. . All of the books and the container are rectangular prisms. Part A How many books can fit in the container if the books are packed so that there is no unused space in the container? Enter your response in the first response box. Part B Each book weighs 2 pounds. The maximum weight the container can hold is 40 pounds. What is the greatest number of books that can fit in the container without going over the container's weight limit? Enter your response in the second response box.
By finding the quotient between the volumes, we will see that 24 books can be fit on the container, and by weight, the container can hold 20 books.
How many books can be fitted on the container?Remember that the volume of a rectangular prism of length L, width W, and height H is given by:
V = L*W*H
Then the volume of each book is:
V = 6in*2in*8in = 96 in^3
And the volume of the container is:
V' = 16in*12in*12in = 2,304 in^3
The number of books that fit in the container is given by:
N = V'/V = 2,304 in^3/96 in^3 = 24
How many books the container can hold?Each book weighs 2 pounds, and the container can hold 40 pounds, then we need to solve the linear equation:
2*x = 40
To get the maximum number of books that the container can hold:
x = 40/2 = 20
x = 20
The container can hold a maximum of 20 books.
If you want to learn more about volumes, you can read:
https://brainly.com/question/1972490
Triangle DEF is shown below. Which of the following equations could be used to find the value of x?
The equation that can be used to find x in the triangle is x + 86 = 180
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the angle of x in the triangle.
Triangle DEF is shown above. Therefore, the equation that can be used to find the value of x can be calculated as follows:
49 + 37 + x = 180
Therefore, the equation is as follows:
x + 86 = 180
learn more on triangle here: https://brainly.com/question/21011159
#SPJ1
An equation that could be used to find the value of x is: B. x + 86° = 180°.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the sum of all of the interior angles of a triangle is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of the given angles are supplementary angles:
m∠1 + m∠2 + m∠3 = 180°
37° + 49° + m∠3 = 180°
86° + m∠3 = 180°
x + 86° = 180° (required equation)
Read more on triangle here: brainly.com/question/22891315
#SPJ1
The cost of a sweatshirt is 175% the cost of a T-shirt. A T-shirt costs $13.
What is the cost of 3 sweatshirts?
PLEASE SHOW HOW YOU GOT ITTT
I WILL MARK BRAINILIST
Answer:
$68.25
Step-by-step explanation:
1. First, to find the cost of one sweatshirt, we multiply 175 by 13, and then divide by 100.
[tex]175 * 13 = 2275[/tex] [tex]2275/100=22.75[/tex]2. Now, we know that one sweatshirt costs $22.75. To find the cost of three sweatshirts, we multiply 22.75 by 3.
[tex]22.75 * 3[/tex] [tex]68.25[/tex]Therefore, the cost of 3 sweatshirts is $68.25.
x^2 - y^2 = 100
x + y = 5
The solution to the given system of equations is
(x, y). What is the value of x - y?
Answer:
20
Step-by-step explanation:
Let's start by rewriting the second equation in terms of "x":
[tex]x+y=5[/tex]
Subtract y from both sides:
[tex]x=5-y[/tex]
Now, substitute "5-y" for "x" in the first equation:
[tex](5-y)^2-y^2=100[/tex]
Note that:
[tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]25-10y+y^2-y^2=100[/tex]
Cancel out like terms:
[tex]25-10y=100[/tex]
Subtract 25 from both sides:
[tex]-10y=75[/tex]
Divide both sides by -10
[tex]y=\frac{75}{-10}=\frac{15}{-2}=-\frac{15}{2}[/tex]
Now, substitute this value back into either of the equations to solve for x.
[tex]x+y=5\\x-\frac{15}{2}=5\\[/tex]
Add 15/2 to both sides:
[tex]x=5+\frac{15}{2}\\x=\frac{10}{2}+\frac{15}{2}\\x=\frac{25}{2}[/tex]
Now, find the difference:
[tex]x-y=\frac{25}{2}-(-\frac{15}{2})=\frac{25}{2}+\frac{15}{2}=\frac{40}{2}=20[/tex]
A right triangle with the dimensions given in units is shown below.
Answer: 12.5?
Step-by-step explanation: because a square is a full and half of it makes a triangle so I guess its half so 12.5?
Suppose that a and b are nonzero real numbers, and
that the equation x² + ax + b = 0 has solutions a
and b. Then the pair (a, b) is
The equation has two solutions. Means Discriminant means b^2-4ac >0
Here b = a.
a = 1
c = b
a^2 - 4b >0
a=2
b= -1
then a^2 - 4b > 0 = 4+4 > 0
therefore its 2, -1
The pair (a, b) represents the sum and product of the roots of the quadratic equation x² + ax + b = 0.
We have,
Given that the equation x² + ax + b = 0 has solutions a and b, the sum and product of the roots (a and b) can be related to the coefficients of the quadratic equation.
The sum of the roots of a quadratic equation is given by:
Sum of roots = -coefficient of x / coefficient of x² = -a
The product of the roots of a quadratic equation is given by:
Product of roots = constant term / coefficient of x² = b
From the given information, we have:
The sum of roots = a
Product of roots = b
Thus,
The pair (a, b) represents the sum and product of the roots of the quadratic equation x² + ax + b = 0.
Learn more about solutions of equations here:
https://brainly.com/question/545403
#SPJ3
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS
Answer: 125 degrees and 55 degrees
Step-by-step explanation:
Hurry please!
Which linear equation represents the graph?
A) Y= -1/3x + 3
B) y = 3x - 2
C) y= 1/3x + 3
D) y= -3x - 2
Answer:
A
Step-by-step explanation:
Fred purchased a jacket for $20 and 5 T-shirts. Each T-shirt cost the same amount. The total cost was $85. How much did each T-shirt cost?
Answer:
Each t-shirt cost 13 dollars.
Step-by-step explanation:
Since the jacket was 20 bucks, we can set that aside:
85-20=65
Now that we've set that aside, there are five t-shirts. If they all cost the same, that means we can divide!
65/5=13
How to check?
Use inverse operations: 13*5=65
Re-add the 20 bucks from the jacket, and the bill is complete again! Use inverse operations: 13*5=65
Each shirt costs $13.
PLEASE HELP !! ASAP
Find the values of X and Y. State what kind of angles are indicated in the figure.
Answer: x=61 y=29
well all the angles have to add up to 360 so its pretty simple to find,
2y=58
y=58/2=29
y=29
58*2=116
360-116=244
244/2=122
2x=122
x=122/2=61
x=61
solve for v: 56= 7v + v simplify your answer as much as possible
Answer:
v=7
Step-by-step explanation:
i just used a math website for my answers and told it to simplify. try using that website. i always get an 90-100's on my tests from using that
Given equation :
[tex]{\qquad \sf \dashrightarrow{ 56= 7v + v }}[/tex]
We can rewrite the equation as :
[tex]{\qquad \sf \dashrightarrow{ 7v + v = 56 }}[/tex]
Adding like terms :
[tex]{\qquad \sf \dashrightarrow{ 8v = 56 }}[/tex]
Dividing both sides by 8 :
[tex]{\qquad \sf \dashrightarrow{ \dfrac{8v}{8} = \dfrac{56}{8} }}[/tex]
[tex]{\qquad \bf \dashrightarrow{ v = 7 }}[/tex]
Henceforth,
The value of v is 7.Jannette says ABC ~ DEF because ABC's sides form a Pythagorean triple and DEF's side lengths are multiples of ABC's side lengths. Is she correct?
Answer: Yes
Step-by-step explanation:
DEF's side lengths are multiples of ABC's side lengths
(10, 15) and (8,3). Write the equation of the line in slope-intercept
(y = mx + b) form.
Answer:
[tex]y=6x+-45[/tex]
Step-by-step explanation:
Given the following question:
Point A = (10, 15) = (x1, y1)
Point B = (8, 3) = (x2, y2)
To find the answer we first must find the slope which we will find by using the formula for slope or rise over run. Then we use the formula for slope intercept, substitute the values, and then solve for b.
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
[tex]m=\frac{3-15}{8-10}[/tex]
[tex]3-15=-12[/tex]
[tex]8-10=-2[/tex]
[tex]=\frac{-12}{-2} =-12\div-2=6[/tex]
[tex]m=6[/tex]
Now we have the slope find the slope intercept:
[tex]y=mx+b[/tex]
[tex]y=15[/tex]
[tex]m=6[/tex]
[tex]x=10[/tex]
[tex]15=6(10)+b[/tex]
[tex]6\times10=60[/tex]
[tex]15=60+b[/tex]
[tex]60-60=0[/tex]
[tex]15-60=-45[/tex]
[tex]-45=b[/tex]
[tex]b=-45[/tex]
[tex]y=6x+-45[/tex]
Your answer is "y = 6x + -45."
Hope this helps.