Step-by-step explanation:
[tex] \sin(60 - \theta) \sin(60 + \theta) \\ = \{ \sin(60) \cos( \theta) - \sin( \theta) \cos(60) \} \{ \sin(60) \cos( \theta) + \cos(60) \sin( \theta) \} \\ = \{ \frac{ \sqrt{3} }{2} \cos( \theta) - \frac{1}{2} \sin( \theta) \} \{ \frac{ \sqrt{3} }{2} \cos( \theta) + \frac{1}{2} \sin( \theta) \} \\ \\ [/tex]
from difference of two squares:
[tex]{ \boxed{(a - b)(a + b) = ( {a}^{2} - {b}^{2} ) }}[/tex]
therefore:
[tex] = \{ {( \frac{ \sqrt{3} }{2}) }^{2} { \cos }^{2} \theta \} - \{ {( \frac{ \sqrt{3} }{2} )}^{2} { \sin }^{2} \theta \} \\ \\ = \frac{3}{4} { \cos }^{2} \theta - \frac{3}{4} { \sin}^{2} \theta[/tex]
factorise out ¾ :
[tex] = \frac{3}{4} ( { \cos }^{2} \theta - { \sin}^{2} \theta) \\ \\ = { \boxed{ \frac{3}{4} \cos(2 \theta) }}[/tex]
please help will give you brainly
Answer:
-1/2
Step-by-step explanation:
3(y+13 )=36
y+13=12
y=-1
(1/2) x -1 = -1/2
3(y + 13) = 36
Distribute the 3
3y + 39 = 36
Subtract 39 from both sides.
3y = -3
Divide both sides by 3
y = -1
1/2y = 1/2(-1) = -1/2
In exercises 1-2, solve the formula for the indicated variable.
1: Surface area of a cylinder: S=2πr^2+2πrh: Solve for h.
2: Area of a trapezoid: A=1/2h(b1 + b2); Solve for b2.
The 1 and 2 are supposed to be under to the side of b like this.
Answer:
area of a trapezoid A =1Step-by-step explanation:
2
Find the area of this triangle. Round to the nearest tenth. 8m, 62°, 12m.
9514 1404 393
Answer:
42.4 m²
Step-by-step explanation:
The area can be found from the formula ...
Area = 1/2ab·sin(C)
Area = (1/2)(8 m)(12 m)sin(62°) ≈ 42.4 m²
If you can make 12 cookies in 10 minutes, how long does it take to make 200 cookies
Answer:
12 cookies = 10minutes
200 cookies = x minutes
cross multiply
200×10 = 12x
2000= 12x
divide both sides by 12
X = 166.67 minutes
Step-by-step explanation:
that is 200 cookies will take 166.67 minutes
Answer:
[tex]12 \: cookies \: in \: 10 \: minut \: \\ 1 \: cookie \: in \: \frac{10}{12} = \frac{5}{6} \: minute \\ for \: 200 \: cookies = \frac{5}{6} \times 200 = 166.67 \: minute \\ thank \: you[/tex]
Make up a data set (n = 10) that has the same minimum value, same median, and same maximum value, but a larger IQR than the boxplot shown.
a. Give your 10 numbers.
b. Give the 5-number summary for your data.
c. Describe your strategy for figuring this out.
The 10 hypothetical numbers which meets the conditions given on the question may include :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary include the maximum, minimum, lower quartile, Median and upper quartile of a distribution.
The five number summary of the hypothetical data are:
Median: 6
Minimum: 1
Maximum: 12
Lower quartile: 2.75
Upper quartile: 10
Comparing the 5 - number summary of the hypothetical data with that of the given boxplot.
From the given boxplot shown :
Minimum value = 1
Maximum value = 12
Median = 6
LOWER QUARTILE, Q1 = 4
UPPER QUARTILE, Q3 = 8
IQR = (Q3 - Q1) = 8 - 4 = 4
THE 10 made up numbers :
1, 2, 3, 5, 6, 6, 7, 10, 10, 12
The five number summary for the made up data :
Median = 1/2(n+1)th term = 5.5th term = (6+6)/2 = 6
Minimum: 1
Maximum: 12
First quartile = 1/4(n+1)th = 2.75th term = (2+3)/2 = 2.5
Third quartile: 3/4(n+1)th term = 8.25 = (10+10)/2 = 10
Interquartile Range: (10 - 2.5) = 7.5
The original data values and hypothetical data have the same minimum and maximum and median values. The hypothetical data has an higher IQR value than the original data.Learn more : https://brainly.com/question/12992903?referrer=searchResults
How much he makes in 1 hour.
Answer: $14.5
Step-by-step explanation:
PLEASE HELP MARKING BRAINLIEST
Multiply
(s - 5)(2s + 7)
(s - 5)(25+7)=(Simplify your answer.)
(SOMEONE PLEASE ANSWER)
(s - 5)(2s + 7) =
= 2s² + 7s - 10s - 35 =
= 2s² - 3s - 35
Answer:
2s² - 3s - 35 {final answer}
Step-by-step explanation:
Let's find simplest form of equation,
→ (s - 5)(2s + 7)
→ 2s² + 7s - 10s - 35
→ 2s²- 3s - 35
Thus, the answer is 2s²- 3s - 35.
Alix is 6 inches shorter thelan Ben. Alix is p inches tall. Write an expression to show how tall Ben is
Answer:
p+6
Step-by-step explanation:
Loretta earns $10 a week
and puts $7.50 a week
into savings account and spends
the rest. How much does she
spend in six weeks?
PLEASE HELP POINTS AND BRAINLIEST WILL BE GIVEN
Answer:
- 376
Step-by-step explanation:
8u = 8(- 8i + 3j ) ← multiply each element by 8
= - 64i +24j
Then
(- 64i + 24j ) • (4i - 5j )
= (- 64 × 4) + (24 × - 5)
= -256 + (- 120)
= - 256 - 120
= - 376
please show work 3d – 4 + d = 8d – (-12)
Answer:
d = -4
Step-by-step explanation:
3d – 4 + d = 8d – (-12)
3d - 4 + d = 8d + 12
4d - 4 = 8d + 12
(4d - 4d) - 4 = (8d - 4d) + 12
-4 = 4d + 12
-4 - 12 = 4d (+ 12 - 12)
-16 = 4d
-16/4 = 4d/4
d = -4
Answer:
d= -4
Step-by-step explanation:
3d- 4 +d = 8d + 12
4d - 4 = 8d + 12
4d = 8d + 16
-4d = 16
d= -4
Check
-12 - 4 - 4 = -32 + 12
-20 = -20
Can someone help (Geometry)
Answer:
∠DAC is 35°
Step-by-step explanation:
Given:
Measure of ∠DAB = 64°
Measure of ∠CAB = 29°
Solution:
∠DAB shows the value of the overall angle.
∠CAB shows the value for almost half of the angle.
∠DAB - ∠CAB = ∠DAC
64° - 29° = ?
∴ 64° - 29° = 35°
Hence, the value of ∠DAC is 35°
Evaluate expression
a) -19 + 3(-13 + 4*3)
b) | -7(2) |
c) 15 – 3 | - 4-2 |
Answer:
well i know the first one
-19+3(-13+4*3)
= -19+3(-13+12)
= -19+3(-1)
= -19-3
= -22
evaluate the expression -(5/7)^0
Answer:
1
Step-by-step explanation:
There are 6 times as many dogs as cats . If the total number of dogs and cats is 21 , how many dogs are there?
Answer:
126 cats .................
126 dogs........
-.0666
Rational or
Irrational?
WHY
Answer:
It's irrational
Step-by-step explanation:
An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point.
Answer:
Rational
Step-by-step explanation:
Irrational numbers go on FOREVER.
An example is
1. π
2.[tex]\sqrt{2}[/tex]
....
Surds are irrational. A surd is a square root of a number that goes on forever.
Some irrational numbers have recurring digits (repeating digits)
10/3 is an example:
3. 333333333333333333333333333333333333333333............
Hello Brainly User please help me I will mark brainliest. Its really east math please help me
Using BODMAS, I think but please help!!!
And show the steps
Answer:
= 12
Step-by-step explanation:
2 × {4 ÷ 2 -5}^2 -6
Solve the brackets first
2 × { 2 -5}^2 -6
2 ×{-3 }^2 -6
2 × 9 -6
18 -6
= 12
Step-by-step explanation:
[ 4 ÷ 2 - 5 ] ² - 6
(2 - 5)² - 6
(-3)² - 6
9 - 6
= 3
Could you help please i really dont get it
Answer:
[tex]3.4 \: apple \: pounds = 5.61 \: dollars \\ 1 \: apple \: pound = \{ \frac{(1 \times 5.61)}{3.4} \} \: dollars \\ \\ = { \boxed{ \boxed{1.65 \: dollars \: per \: pound}}}[/tex]
Answer:
1.65
Step-by-step explanation:
5.61/3.4=1.65
A rectangular tank 160 cm long and 80 cm wide is filled with some water. John puts a cube with side 40 cm long into the water. What is the rise in water level if the cube is completely immersed?
Answer:
The water level would rise by [tex]5\; \rm cm[/tex].
Step-by-step explanation:
Assume that the initial water level is [tex]h\; \rm cm[/tex].
Before the cube was placed in the tank, the volume of the water was the same as the volume of a rectangular prism with a length of [tex]160\; \rm cm[/tex], a height of [tex]80\; \rm cm[/tex], and a height of [tex]h\; \rm cm[/tex]:
[tex]\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times h\; {\rm cm} \\ =\; & (80 \times 160) \, h \; \rm cm^{3} \end{aligned}[/tex].
Let the rise in the water level in the tank be [tex]x\; \rm cm[/tex]. The new water level would be [tex](x + h)\; \rm cm[/tex].
The volume of the water and the submerged cube, combined, would be the same as that of a rectangular prism with a length of [tex]160\; \rm cm[/tex], a width of [tex]\rm 80\; \rm cm[/tex], and a height of [tex](x + h)\; \rm cm[/tex]:
[tex]\begin{aligned} & 160\; {\rm cm} \times 80\; {\rm cm} \times (x + h)\; {\rm cm} \\ =\; & (80 \times 160) \, (x + h) \; \rm cm^{3} \end{aligned}[/tex].
In other words:
Volume of water in this tank: [tex](80 \times 160)\, h\; \rm cm^{3}[/tex], whereasVolume of water in this tank, plus the volume of the submerged cube: [tex](80 \times 160) \, (x + h) \; \rm cm^{3}[/tex].Therefore, the volume of the submerged cube could be expressed as:
[tex]\begin{aligned} & (80 \times 160) \, (x + h) \; {\rm cm^{3}} - (80 \times 160) \, h \; \rm cm^{3} \\ =\; &(80 \times 160)\, x\; {\rm cm^{3}}\end{aligned}[/tex].
On the other hand, the volume of the cube could be expressed as:
[tex](40\; \rm cm)^{3} = 64000\; \rm cm^{3}[/tex].
Equate these two expressions for the volume of the cube and solve for [tex]x[/tex], the rise in the water level in the tank:
[tex](80 \times 160)\, x = 64000[/tex].
[tex]x = 5[/tex].
In other words, the rise in the water level in this tank would be [tex]5\; \rm cm[/tex].
Evaluate x + 2.7 for x= -1.5.
The value of the expression is
[tex]\text{x}=-1,5\\\\\text{x}+2,7=-1,5+2,7=2,7-1,5=\boxed{1,2}[/tex]
Luis buys 0.56 pound of power pasta. Mariana buys 0.27 pound of power pasta. How much do they buy in all?
Add the two amounts together:
0.56 + 0.27 = 0.83 pounds total
Luis buys 0.56 pound of power pasta. Mariana buys 0.27 pound of power pasta. How much do they buy in all?
Solution:First, understand the problem.
Luis buys 0.56 pounds of power pasta.
Mariana buys 0.27 pound of power pasta.
Then, add the bus of Luis and Mariana.
Luis buys + Mariana buys = N0.56 + 0.27 = NN = 0.83Answer:Therefore, 0.83 buy in all.Solve for the value of R
Answer:
13
Step-by-step explanation:
Since the angles form 180 degrees, it will be what the equation is equal to.
Make the equation:
8r + 5 + 5r + 6 = 180
Combine like terms:
8r + 5 + 5r + 6 = 180
13r + 5 + 6 = 180
13r + 11 = 180
Solve:
13r + 11 = 180
-11 -11
---------------------
13r = 169
------ ------
13 13
r = 13
Hope this helped.
solve for x. y = 1/3 (x + w)
What is the quotient of (x3 – 3x2 + 5x – 3) ÷ (x – 1)?
x2 – 2x – 3
x2 + 2x + 7
x2 – 3x + 8
x2 – 2x + 3
Answer:
the answer would be x^2 - 2x + 3
have a good day !! :D
Step-by-step explanation:
Answer:
D. x2 – 2x + 3
Step-by-step explanation:
Edge 2023
How to solve -3/9 + ( -2 9/10)
[tex] - 3 \sqrt{8 + ( - 2 \times \frac{9}{10} } [/tex]
9514 1404 393
Answer:
-3 7/30-7.46994Step-by-step explanation:
We understand this to be two separate problems.
-3/9 +(-2 9/10) = -(3/9 +2 9/10)
= -(10/30 +87/30) = -97/30 = -3 7/30
__
-3√(8 +(-2(9/10))) = -3√(8 -1.8) = -3√6.2 ≈ -7.46994
__
Additional comment
A calculator can help with these, especially if it is able to deal with rational numbers. (Many graphing calculators and some scientific calculators will do that more or less nicely. My favorite Android calculator app makes arithmetic with fractions and mixed numbers very easy.)
14 644 552 + 25 625 568
ayud estoy haciendo tarea :3
Answer:
14644552+25625568
=40270120
Step-by-step explanation:
is right answer
Find the area of this figure. round your answer to the nearest hundredth.
Answer:
49.12 ft^2
Step-by-step explanation:
The triangle:
Area = 1/2 * base * height
= 1/2 * 6 * 8
= 24
The semicircle:
Area = 1/2 * 3.14 * 4^2
= 25 .12
Total area = 24 + 25.12
= 49.12 fT^2
if (a^-1+b^-1)(a+b)^-1=a^mb^n.prove that a^(m-n)=1.
Answer:
46666
Step-by-step explanation:
