Answer:
Cos(15) = Cos(45-30)
Sin(15) = Sin(45-30)
Cos(45-30) - Sin(45-30)
Simplifying both brackets
Recall
Cos(A+B) = CosACosB - SinASinB (For cosine... The sign is always the opposite during expansion. If you look... Cos(A+B) became negative during its expansion;So if It was Cos(A–B)... Its expansion is CosACosB + SinASinB)]
Sin(A+B) = SinACosB + CosASinB
Now let's go!
Cos(45-30) = Cos45Cos30 + Sin45Sin30
From Trig
Cos45 = 1/√2
Cos30 = √3/2
Sin45 = 1/√2
Sin30 = 1/2
Substituting
Cos(45-30) = (1/√2).(√3/2) + (1/√2).(1/2)
= √3/(2√2) + 1/(2√2)
= 1 + √3/(2√2).
For
Sin(45 - 30)
= Sin45cos30 – Cos45Sin30
= (1/√2).(√3/2) – (1/√2).(1/2)
= √3/(2√2) – 1/2√2
= √3 – 1/(2√2)
So the question was
Cos15 - Sin15
Substituting...
1 + √3 / 2√2 – (√3 - 1)/ 2√2
When the Minus interacts with the parenthesis
We have
1 + √3 - √3 + 1 / (2√2)
= 2/2√2
= 1/√2.
THE ANSWER IS 1/√2 AND NOT 1/2.
YOU CAN VERIFY THIS WITH YOUR CALCULATOR ALSO.
YOU'LL HAVE 0.7071 WHICH IS SAME AS 1/√2.
HAVE A GREAT DAY!
Help urgent please be certain
Answer:
17 =x
Step-by-step explanation:
The angles are vertical angles, so they are equal
51 = 3x
Divide each side by 3
51/3 = 3x/3
17 =x
Answer:
C) 17
Step-by-step explanation:
Since the angle needed to be 51˚ we need to figure out which number that multiplies by 3 will get to 51˚ so 17 is the answer
17 times 3 is 51˚
Ian bought a used car. The value, y , of the car x years after his purchase is modeled by the equation y = 6500(0.875)x . What was the value of the car when Ian bought it?
Answer:
6500
Step-by-step explanation:
y = 6500(0.875)^x
When bought x = 0
y = 6500(0.875)^0
A number raise to 0 equals 1
y = 6500 * 1
y = 6500
make p the subject of the relation A is equal to 1/2 ( p + b) h
Answer:
2A /h -b =p
If you need it with a common denominator
(2A -bh)/h = p
Step-by-step explanation:
A = 1/2 ( p+b)h
Multiply each side by 2
2A = ( p+b)h
Divide by h
2A/h = ( p+b)h/h
2A/h = ( p+b)
Subtract b
2A/h -b = p+b -b
2A /h -b =p
If you need it with a common denominator
(2A -bh)/h = p
20.
Determine the type and number of solutions of 7x2 + 3x + 8 = 0.
two imaginary solutions
two real solutions
one real solution and one imaginary solution
one real solution
two real solutions
b2-4ac>0
one real solutions and one imaginary solution
b2-4ac=0
no real solution
b2-4ac<0
a=7
b=3
c=8
(3)^2-4(7)(8)=-215 no real solution
A wooden board has a volume of 0.225 cubic m and a mass of 146.25 kilograms.
What is the density of the board?
Answer:
650 kg/m³
Step-by-step explanation:
The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.
density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³
= 650 kg/m³
Hope this answer helps you :)
Have a great day
Mark brainliest
Carl can paint a room 3 hours faster than Jennifer can. If they work together, they can complete the job in 2 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jennifer to complete this job on her ow
Answer:
If they would both work at the same speed they would each take 4 hours to complete the room. So in total they would work 8 hours. But because Carl can finish three hours before Jennifer 3 hours of the eight already got to Jennifer. Then we divide the resting 5 hours by the two and then we have:
Jennifer:
3+2,5=5,5
Carl:
2,5
( if I am right)
5 + 3 + 7 = 5 + 7 + 3
O A. True
B. False
Answer:
True
Step-by-step explanation:
5+3+7=5+7+3
15=15
Hence proved.
Find the vertex of y=-2(x-4)2 + 3 and identify it as a minimum or a maximum
Answer:
Step-by-step explanation:
Remark
The minus sign in front of the 2 means that the quadratic has a maximum.
The vertex is already written in vertex form.
y= - 2 (x - 4)^2 + 3
The vertex is (4,3). Notice that the sign on the 4 changes. What you are trying to do is find the maximum point. That occurs when the minus number is made to be 0, which occurs when x = 4. The maximum y value is 3 when that happens.
I have enclosed a graph to show you all the details. Notice the maximum is when I've said it was and the roots have also been calculated.
HELP! HELP!PLEASSSSSEEEEEEEEEE HEEEEEEEELLLLLLPPPP!
Help please I don't really understand what to do here, so if somebody could find the answer that'd be great!
Answer:
See below.
Step-by-step explanation:
4.2 is 4 and 2 tenths.
4 is 40 tenths.
That means that 4.2 is 40 tenths plus 2 tenths, or 42 tenths.
First line: 4.2 / 6 = 42 tenths / 6
In the second line, we divide 42 tenths by 6. Since 42 divided by 6 = 7, then 42 tenths divided by 6 equals 7 tenths.
Second line: 4.2 / 6 = 7 tenths
In the third line, we write 7 tenths as a number. 7 tenths is the same as 0.7.
Third line: 4.2 / 6 = 0.7
what is a way of representing how the members of one group are related to the members of another group
Answer: Face
Step-by-step explanation: look at there face?
help,very easy question but i can't understand
Answer:
10
Step-by-step explanation:
10 is the greatest common factor that you can divide into both 40 and 50.
Answer:
10
Step-by-step explanation:
Try and find the prime factorization of 40 and 50.
40=2*2*2*5
50=2*5*5
Multiply the prime factors that are common to both numbers.
2*5=10
PLZ HELP ILL GIVE BRAINLIST
Answer:
[tex]14 \: 26 \: 6.5[/tex]
14
26
6.5
Which is a simplified form of the expression -3p – 4 + 4p + 8?
A. -p - 4
B. 2p - 4
C. p + 4
D. 7p + 4
Answer:
C
Step-by-step explanation:
-3p – 4 + 4p + 8
Simplify by combining like terms
-3p + 4p = p
-4 + 8 = 4
The expression in it's simplest form would be p + 4
Answer:
The answer is C.
Step-by-step explanation:
-3p - 4 + 4p + 8 can be grouped into:
-3p + 4p - 4 + 8.
If you add the p's together and the numbers together, your answer should be:
p + 4.
PLS HELPPPPP<3tyyyyyy this is due today! so please helppp tysmmm and have a great night or morning! :) (spam)
Answer:
#3: 4
#7: >
#8: =
#9: >
#10: <
Step-by-step explanation:
1 decimeter = 10 centimeters
1 meter = 10 decimeters
1 kilometer = 1,000 meters
(12y²+17y-4)+(9y²-13y+3)
Pre-calc, image attached
Answer:
[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]
Step-by-step explanation:
[tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7}[/tex]
[tex]\frac{\sqrt{x+2}-3 }{x-7}[/tex]
[tex]\frac{\frac{1}{2} (x+2)^{-\frac{1}{2} }}{1}[/tex] <-- Take derivative of numerator and denominator expressions
[tex]{\frac{1}{2} (x+2)^{-\frac{1}{2} }}[/tex] <-- Simplify
[tex]\frac{1}{2}(\frac{1}{\sqrt{x+2} })[/tex] <-- Rewrite
[tex]\frac{1}{2}(\frac{1}{\sqrt{7+2} })[/tex] <-- Use direct substitution and plug in the limit x=7
[tex]\frac{1}{2}(\frac{1}{\sqrt{9} })[/tex]
[tex]\frac{1}{2}(\frac{1}3 })[/tex]
[tex]\frac{1}{6}[/tex]
Therefore, [tex]\lim_{x \to 7} \frac{\sqrt{x+2}-3 }{x-7} = \frac{1}{6}[/tex]
In the diagram, BC = 10 and AD = 14. Find MN.
A
2.
B)
12
C)
14
D)
24
Answer:
I think D 24 but i am not sure
Answer:
B)12
Step-by-step explanation:
I took the test
What is the perimeter of triangle XYZ?
Answer:
126
Step-by-step explanation:
The dimensions of a rectangular prism are shown in the table.
Length: 10 in
Width: 12 in
Height: 16 in
What is the surface area of the rectangular prism?
If f (x) = -2x2 + 6, find f (-3).
Answer:
Step-by-step explanation:
Answer:
f(- 3) = - 12
Step-by-step explanation:
To find f(- 3) substitute x = - 3 into f(x) , that is
f(- 3) = -2(- 3)² + 6 = -2(9) + 6 = - 18 + 6 = - 12
14. A computer originally costs $1550 is on sale for 15% off. How much is
the discount? *
A. $232.50
B. $23.25
C. $15.00
D. $1,317.50
Dont mind the blue. I hit B by accident.
Select the true statement about Triangle ABC.
Answer:b
Step-by-step explanation:
Help please hurry NO LINKS!!!
Special Right Triangles (Radical Answers)
Answer:
[tex]2\sqrt{6}[/tex] = x
Step-by-step explanation:
We can use the Tan ratio to figure this out;
[tex]Tan(60) = \frac{x}{\sqrt{8} }[/tex]
Tan(60) * [tex]\sqrt{8}[/tex] = x
[tex]2\sqrt{6}[/tex] = x
Hope this helps!
The polygons are similar. The area of one polygon is given. Find the area of the other polygon.
3 cm
12 cm
A-96 cm?
Answer:
Hello! answer: area is 6 cm2
Step-by-step explanation:
Triangle area formula: base × height ÷ 2 or base × height × 1/2 so...
12 × 16 = 192 192 ÷ 2 = 96
12 ÷ 4 = 3
16 ÷ 4 = 4
3 × 4 = 12 12 ÷ 2 = 6 therefore the area is 6 hope that helps!
Answer:
6 cm²
Step-by-step explanation:
Given the sides of 2 similar figures in the ratio a : b , then
ratio of areas = a² : b²
Here the ratio of sides = 3 : 12 = 1 : 4
ratio of areas = 1² : 4² = 1 : 16
That is the area of the larger polygon is 16 times the smaller, so
area of smaller polygon = 96 ÷ 16 = 6 cm²
hey do y’all know how to solve this?:(
Answer:
27 m
Step-by-step explanation:
We know that ABC = 42 degrees
and side length BC = 24m
tan42 = 24m/a
a = 24/tan42
a = 26.65m
round to nearest whole number
= 27 m
Answer:
12 or 16 m
Step-by-step explanation:
I NEED HELP PLEASE !!
Answer:14=x
Step-by-step explanation:
Question: What is the probability of rolling one or more tails?
P(T > 1) = P(T = 1) + P(T = 2) = \ + 1
(Enter as a reduced fraction using / for the fraction bar.)
Belleview High School has 12 chaperones for 198 students on a field trip. Which of the following schools has the same ratio of chaperones to students?
Answer:
The ratio for this school is 12/186 which gives us 2/31. Just check which option has the same ratio and that will be your answer.
Step-by-step explanation:
Answer:
There is no other schools listed so I cant answer the question
Step-by-step explanation:
Which statement is not true about the absolute value of -6?
A. It descrlbes the distance between -6 and 0 on the number line.
B. It equals the absolute value of 6.
C. It describes the distance between 6 and -6 on the number line.
D. It can be expressed as |-6|.
Answer:
C
Step-by-step explanation:
All the other answers are the same worded differently except c.
The distance between 6 and -6 is 12 so that is not correct for the absolute value of -6