Answer:
[tex]\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}[/tex]
Step-by-step explanation:
We can use the following trigonometrical identity:
[tex]\sin (\alpha - \beta) = \sin \alpha \cdot \cos \beta - \cos \alpha \cdot \sin \beta[/tex] (1)
Where [tex]\alpha[/tex], [tex]\beta[/tex] are angles, measured in sexagesimal degrees.
If we know that [tex]\alpha = 135^{\circ}[/tex] and [tex]\beta = 30^{\circ}[/tex], then the value of the given function is:
[tex]\sin 105^{\circ} = \sin 135^{\circ}\cdot \cos 30^{\circ} - \cos 135^{\circ}\cdot \sin 30^{\circ}[/tex]
[tex]\sin 105^{\circ} = \left(\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{\sqrt{3}}{2}\right)-\left(-\frac{\sqrt{2}}{2} \right)\cdot \left(\frac{1}{2}\right)[/tex]
[tex]\sin 105^{\circ} = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}[/tex]
[tex]\sin 105^{\circ} = \sqrt{\frac{6}{16} }+\sqrt{\frac{2}{16} }[/tex]
[tex]\sin 105^{\circ} = \sqrt{\frac{3}{8} }+\sqrt{\frac{1}{8} }[/tex]
[tex]\sin 105^{\circ} = \frac{\sqrt{3}+1}{2\cdot \sqrt{2}}[/tex]
[tex]\sin 105^{\circ} = \frac{\sqrt{6}+\sqrt {2}}{4}[/tex]
Answer: D) sqrt(2 + sqrt3)/2
Step-by-step explanation: Nah
PLEASE HELP ME ASAP :(
Solve for a.
= ✓ [?]
a
Enter the number that goes
beneath the radical symbol.
Enter
Answer that goes in the box = 28
===================================================
Explanation:
We have a white triangle shown as the empty space between the green squares.
This right triangle has the following sides:
a = unknown horizontal legb = 6 = vertical legc = 8 = hypotenuseUse the Pythagorean Theorem to solve for 'a'
a^2 + b^2 = c^2
a^2 + 6^2 = 8^2
a^2 + 36 = 64
a^2 = 64 - 36 ..... subtract 36 from both sides
a^2 = 28
a = sqrt(28) .... apply the square root to both sides
Optionally we can simplify like so
a = sqrt(28)
a = sqrt(4*7)
a = sqrt(4)*sqrt(7)
a = 2*sqrt(7)
But this would not fit the answer format your teacher has provided. So we'll stick to sqrt(28) as the final answer.
What number would you add to both sides of x2 + 7x = 4 to complete the square?
2^2
7^2
7^2/2
(7/2)^2
Answer:
(7/2)2
Step-by-step explanation:
Write an algebraic expression for "8 less than the product of 3 and j"
Answer: 3(j)-8
Step-by-step explanation: well first the product means multiplication, so u multiply 3 and j. and the second part is 8 less than that, so 8 is the last part so u do 3 times j minus 8. i graduated from high school last year so i know what im doin
According to the question,
Let,
The first number be "3".The second number be "j".The third number be "8".Now,
The product of "3" and "j" will be "3j" and the third number i.e., "8" less than the product.
Then the equation will be:
[tex]3j-8[/tex]Thus the above response is appropriate.
Learn more about equation here:
https://brainly.com/question/19800103
What is the unit rate of 600 miles in 7 hours ?
Answer:
85.7
Step-by-step explanation:
Describe the slope in the graph of the following linear function.
Answer:
the first one
Step-by-step explanation:
Answer:
2nd one
Step-by-step explanation:
because you go down 4 and across 3
help me with picture please 70 points.
Answer:
Plot the points on:
(1,2)
(3,6)
(5,12)
(9,18)
Thats it.
what is 15.5z= - 77.5 i'm confused
Answer:
z=-5
Step-by-step explanation:
divide -77.5 by 15.5, which equals -5
A salesperson at a jewelry store earns7% commission each week. Last week, jarrod sold 450$ worth of jewelry. How much did he make in commission? How much did the jewelry store make from his sales?
Answer:
he made $31.50 in commission
the jewelry store made $418.50
Step-by-step explanation:
turn the percent to a decimal by moving it 2 places 7%=.07
then multiply .07 by 450 to get his commission =31.50
then subtract 31.50 and 450 = 418.50
write the equation in slope intercept form 2x-6y-15=0
Mark jogged 3 and5/7 km. His sister jogged 2 and 4/5 km. How much farther did mark jog?
Answer: 32/35 km
Step-by-step explanation: First you have to find a common denominator between these two mixed numbers. That basically means that you have to convert them so that they both have the same denominator, that way they can be compared to one another. The easiest way to do this is to just multiply the denominators. 5 x 7 = 35. I will use 35 as my denominator. Then you multiply the numerators by the same number that you multiplied the denominator by to get 35. Since 7 x 5 = 35, 5 x 5 = 25. Same with the second fraction. 5 x 7 = 35. 4 x 7 = 28. The mixed numbers we have are now 3 and 25/35 and 2 28/35. To figure out how much farther Mark jogged we just take his distance, and subtract his sister's distance from it. 3 25/35 minus 2 28/35 = 32/35.
can anyone help me on this
Answer:its 36
Step-by-step explanation:
Answer:
32+1.8
1.8*10=18
so the answer would be 50.
Step-by-step explanation:
Can someone help me?
Answer:
The answer is 70
Help me please time Limit on this
Answer:
4 toy trains
Step-by-step explanation:
PLEASE HELP!! A community group would like to raise funds to pay for improvements to the community swimming pool. The group’s leaders are considering a number of methods to assess community interest in raising funds. Which of the following uses convenience sampling?
A. The group sends a survey through the mail to all community residents.
B. The group places a survey on a webpage where residents can register their support.
C. The group stands outside a shopping center and asks residents who enter if they support raising funds.
D. The group selects a random sample of homes in the community, and residents in those homes are interviewed.
Answer:
C
Step-by-step explanation:
Because convenience sampling is based on convenience
Also Edge 2021
Evaluate the function expression
5•f(1)+5•g(9)=
Step-by-step explanation:
By getting our values from the graph,
When x = 1, the blue line has y-value -5.
When x = 9, the dotted line has y-value -6.
Hence,
f(1) + 5 * g(9) = (-5) + 5(-6) = -35.
Answer:
From the above graph,
→When x=1, y=f(1)=-5
→When x=9, y=g(x)=-6
• 5×f(1)+5×g(9)
=5{f(1)+g(9)}
=5{(-5)+(-6)}
=5(-11)
=-55
-55 is the right answer.-75= 50 + x what is the value of x?
Answer:
x=-125
Step-by-step explanation:
-75=50+x
-50 -50
-125=x
Answer: x= -125
Step-by-step explanation:
evaluate the expression 8x + 23 for x= 3
Answer:
47
Step-by-step explanation:
8×3+23
24+23
47
is the answer
Helppppnrejeisjcjjrwhajsjfhghfjebbdbfbgbfbfbdfbfbf lol sorry help if you want
Answer:
8 tablespoons of sugar
Answer:
8 teaspoons
Step-by-step explanation:
Please help. Are they parallel?
Answer:
yes
Step-by-step explanation:
It would be great if I got some help with this thank you:)
Answer:
A or c hopes this helps!!
find the value of c to the nearest tenth
N - 8, when n = -8
please do this asap
Answer:
-8-8 is equal to -16
10 points!!HELPP ME PLEASE ❗️❗️4. Figure HJKL - Figure PQRS
Which of the following completes this proportion?
HJ/PQ =HL/?
A KL
B PQ
C RS
D PS
Answer:
B I think b djdjdjdjddhjssj
The width of a rectangular piece of paper is 8.5 inches, and the diagonal length of the piece of paper is 14 inches. What is the length of this piece of paper in inches?
At the beginning of the year, John had $40 in savings and saved an additional
$13 each week thereafter. Isaac started the year with $80 and saved $9 every
week. Let J represent the amount of money John has saved t weeks after the
beginning of the year and let I represent the amount of money Isaac has
saved t weeks after the beginning of the year. Write an equation for each
situation, in terms of t, and determine the number of weeks after the
beginning of the year until John and Isaac have the same amount of money
saved.
Answer:
J= 40+13t
I= 80+9t
they are equal at 10 weeks
Step-by-step explanation:
So we can start this by writing our equations
J= 40+13t
I=80+9t
To figure out when they're equal set the two equations equal to each other and solve for t
40+13t=80+9t
subtract 40 and 9t from both sides to get
40=4t
divide by 4 and get
t=10
helpppppp Pleaseee :)
I need help with this
Answer:
its 1.6
Step-by-step explanation:
Answer:
1.6
Step-by-step explanation:
Divide like normal, the negative signs cancel out on division and multiplication
TRUE OR FALSE:
6a - a = 5a
Answer:
false
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Find the slope of the line through
the points (-2, 1) and (0,4).
Asap taking a test!!!
Answer:
m= 3/2
Step-by-step explanation:
i need help with this
Answer:
4s[tex]{3}[/tex]
Step-by-step explanation:
4 cubes, Formula for cube is s^3
