Answer:
Step-by-step explanation:
If L is the length of a side, the longest diagonal in the cube is
d = √(L² + L² + L²) = √(3L²) = L√3
meaning
a) L(d) = d/√3 = ⅓d√3
b) A(d) = 6(L(d))² = 6(⅓d√3)² = 6(⅟₉d²(3)) = 2d²
c) V(d) = (L(d))³ = (⅓d√3)³ = ⅟₂₇d³3√3 = ⅟₉d³√3
Someone please help
Don’t understand the question
9514 1404 393
Answer:
22. E
23. C
Step-by-step explanation:
These questions are asking you to make use of a couple of trig identities for converting products to sums.
sin(x)cos(y) = 1/2(sin(x+y) +sin(x -y))
cos(x)cos(y) = 1/2(cos(x+y) +cos(x -y))
sin(-x) = -sin(x)
cos(-x) = cos(x)
__
22. sin(2β/3)cos(4β/3) = (1/2)(sin((2+4)β/3) +sin((2-4)β/3))
= 1/2sin(2β) +1/2sin(-2β/3) = 1/2sin(2β) -1/2sin(2β/3)
__
23. cos(3θ)cos(5θ) = (1/2)(cos(3θ+5θ) +cos(3θ -5θ)) = 1/2cos(8θ)+1/2cos(2θ)
Grace buys notebooks at a price of four for $5 and sells them at a price of three for $6. How many notebooks must she sell in order to make a profit of $120
Answer:
125 I think
I'm a lil slow
Grace needs to sell 160 notebooks to make a profit of $120
What is an equation?Two algebraic expressions having the same value and the symbol '=' in between are called as an equation.
Given:
Grace buys notebooks at a price of four for $5.
Unit cost price,
= $5 / 4
= $1.25
And sells them at a price of three for $6.
Unit cost price,
= 6/3
= $2.
Profit = sales - cost
So, the equation,
120 = 2x - 1.25x
0.75x = 120
x = 120/0.75
x = 160
Therefore, 160 notebooks need to sell to maker profit of $120.
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Find the distance between (2,0) and (8, -3)
The distance d between the points (Xy, Yı) and (x2, Y2) is
d = Vixz - x,)2 + (y2 - y)2.
O 789
15
13
O 3V5
Answer:
3√5
Step-by-step explanation:
What is the smallest power of 10 that would exceed 987,654,321,098,765,432?
Use the ^ symbol to represent an exponent.
For example, 52 would be written as 5^2.
Answer:
10¹⁸
Step-by-step explanation:
Ten to the power of x, has x many zeroes behind 1
The original numbers had 18 digits. So, 10¹⁸ is the smallest number that would exceed the original number
Suppose a certain manufacturer deposits $7,000 at the beginning of each 3 month period for 8 years in an account paying 8% interest compounded quarterly.
Required:
a. How much (in $) will be in the account at the end of the 6 year period?
b. What is the total amount (in $) of interest earned in this account?
9514 1404 393
Answer:
a) $217,212.10 after 6 years
b) $91,780.99 interest earned
Step-by-step explanation:
The future value of this "annuity due" can be found using the formula ...
FV = P(1 +n/r)((1 +r/n)^(nt) -1)
where P is the periodic payment made n times per year and r is the annual interest rate.
a) After 6 years, the value of the account is ...
FV = $7000(1 +4/0.08)((1 +0.08/4)^(4·6) -1) = $217,212.10 . . . . 6-yr balance
__
b) After 8 years, the value in the account is ...
FV = $7000(51)(1.02^32 -1) = $315,780.99
The total of payments is $7000×32 = $224,000, so the interest earned is ...
I = $315,780.99 -224,000 = $91,780.99 . . . interest earned
Please help quickly as possible thank you!
Multiply [tex]Q\cdot P[/tex], quantity and price,
[tex]1.2\cdot5.95=7.14[/tex].
Hope this helps :)
Answer:
$7.14
Step-by-step explanation:
Price of 1 pound cheese=$5.95
Price of 1.2 pounds cheese=$5.95 * 1.2
Price of 1.2 pounds cheese=$7.14
Note:if you need to ask any question please let me know.
4 over 9 divided by 12 over 27
Answer:
1
Step-by-step explanation:
4/9÷12/27
=4/9×27/12
=3/3
=1
Temperatures this cold are rare.
Another 8°F colder, and it will be
-40°F.
Pleaae show the work
Answer:
-32°F
Step-by-step explanation:
8°F - 40°F
=> 32°F
There are ten times as many silver cars than red cars. If there 88 silver and red cars altogether, find the number of cars of each colour
Answer:
80 silver, 8 red
Step-by-step explanation:
let x be the number of red cars then 10x is the number of silver cards , so
x + 10x = 88
11x = 88 ( divide both sides by 11 )
x = 8
10x = 10 × 8 = 80
There are 80 silver cars and 8 red cars
30=26-a/6
Solve for a
Answer:
the answer is 24
Step-by-step explanation:
30=26-a\6
collect like terms
30-26 =a\6
4=a\6
Cross multiply
a=4×6
a=24
The solution to the given equation is 24.
The given equation is 30 = 26-a/6.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, 30 = 26-a/6
Transpose 26 to the other side of the equation, we get
30-26 = -a/6
-4 = -a/6
4 = a/6
Transpose 6 to the other side of the equation, we get
a = 4×6
a = 24
So, the solution is 24.
Therefore, the solution to the given equation is 24.
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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =
Step-by-step explanation:
a1 = -4 = -4/1, a2 = 8/3
r = a2/a1 = (8/3) / (-4/1) = -2/3
the formula :
an = a1. r^(n-1)
so,
an = (-4). (-2/3)^(n-1)
Step-by-step explanation:
[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]
chose all that apply
Answer:
Rational
Integer
Step-by-step explanation:
B AND C NOT SURE IF ITS CORRECT
PLS HELPP , i tried solving this and i wrote 56 but it was wrong so i don’t know anymore pls pls help
Answer:
y = 68
A = 44
Step-by-step explanation:
No matter what may be true, that doesn't look like an a to me.
x = y = 68 x and y are opposite equal sides and are therefore =.
68 + 68 + A = 180 all triangles are 180 degrees.
136 + A = 180 Subtract 136 from both sides
A = 180 - 136
A = 44
Express the formula V=l x w x h in terms of the width, w. Use your formula to find the width when the volume is 192, the length is 8, and the height is 4
Answer:
6
Step-by-step explanation:
192=8*4*w
make w subject to formula
w=192/32
w=6
The expression of width is w = V/(l*h) and the value of width is 6.
What is substitution of equation to find the expression of width ?Given formula of volume is V = l * w * h .
Substituting width (w) from the above equation,
w = V/(l*h) .
Finding the value of width from the expression -Given expression after substitution is w = V/(l*h) .
⇒ w = 192/(8 * 4)
∴ w = 6 .
Thus the value of width is 6.
Therefore, the expression of width is w = V/(l*h) and the value of width is 6.
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You and your family are planning a vacation of a lifetime around the world that will cost $25,000. You borrowed this amount from your bank with an annual interest rate of 10.5%. You decided to pay it back in 5 years. What is the interest that will accrue on this loan?
$3,125.00
$131,250
$13,125.00
$312.50
Answer:
$13,125
Step-by-step explanation:
The value of the interest that will accrue on this loan will be;
⇒ $13,125
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
You and your family are planning a vacation of a lifetime around the world that will cost $25,000.
And, You borrowed this amount from your bank with an annual interest rate of 10.5%.
Now,
Since, You borrowed this amount from your bank with an annual interest rate of 10.5%.
Hence, The total interest amount after five years is,
⇒ 5 × (10.5% of $25,000)
⇒ 5 × (10.5/100 × 25,000)
⇒ 5 × 2,625
⇒ $13,125
Thus, The total interest amount after five years = $13,125
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Need the answers in 1 minute ASAP
Answer:
d=f(c)=15-c/4
Step-by-step explanation:
The expression 1/x+y
is equal to which quantities?
(1/x) + y
1/x + y
1/(x + y)
The equivalent form of the given expression is 1 /(x + y)
The given expression:
[tex]\frac{1}{x+y}[/tex]
To find:
the equivalent form of the expression:The equivalent form of the expression can be written as follows:
[tex]\frac{1}{x+y} = 1 /(x + y)[/tex]
For example, if x = 1 and y = 2, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(1 + 2)} = \frac{1}{3}[/tex]
Also, if x = 2 and y = 3, the inverse of the expression can be written as;
[tex]\frac{1}{x + y} = \frac{1}{(2 + 3)} = \frac{1}{5}[/tex]
Thus, the equivalent form of the given expression is 1 /(x + y)
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Evaluate piecewise functions
f (4) = ?
Answer:
f(4) = 9Step-by-step explanation:
x = 4 corresponds to the middle piece of the function, therefore:
f(4) = 4² - 7 = 16 - 7 = 916.
Select all transformations that carry rectangle
ABCD onto itself.
A. Rotate by 90 degrees clockwise using center P.
B. Rotate by 180 degrees clockwise using center P.
C. Reflect across line m.
D. Reflect across diagonal AC.
E. Translate by the directed line segment from A to B.
Answer:
I got B and C.
Step-by-step explanation:
When you rotate by 180° you turn it so that it is facing the other way (ie D is B, C is A, etc) since it's a rectangle, when you rotate by 180°, you still have the same rectangle with angles in the same corners. when you reflect across the midpoint, you are just flipping your rectangle over, and so would again have the same effect as turning it 180°.
4/8 divided by 4/6
thank you for your answer
Answer:
[tex] \frac{3}{4} [/tex]
Step-by-step explanation:
[tex] \frac{4}{8} \div \frac{4}{6} [/tex]
[tex] \frac{4}{8} \times \frac{6}{4} [/tex]
[tex] \frac{1}{4} \times 3[/tex]
[tex] = \frac{3}{4} [/tex]
Hi fellow Army^^
Maggies brother is 4 years younger than three times her age the sum of there ages is 28 how old is maggie
Answer:
24
Step-by-step explanation:
19. Solve 5x^2 - 6x + 1 = 0 using the quadratic formula.
Please give detailed steps!!
Answer:
x = -b ± √b²-4ac /2a
a = 5
b= -6
c= 1
x = -(-6) ± √(-6)² - 4(5)(1) /2(5)
x = 6 ± √36 - 20 / 10
x = 6 ± √16 /10
x = 6 ± 4/10
Breaking into respective signs
x = 6 + 4/10 or 6 - 4/10
x = 10/10 or 2/10
x = 1 or 1/5
x = 1 or 1/5.
Answer:
1/5 and 1
Brainliest, please!
Step-by-step explanation:
5x^2 - 6x + 1 = 0
a = 5, b = -6, c = 1
(-b +-sqrt(b^2 - 4ac))/2a
(-(-6) +-sqrt((-6)^2 - 4(5)(1))/2(5)
(6 +- sqrt(16)/10
(6 +- sqrt(16))/10
(6 +- 4)/10
2/10 and 10/10
1/5 and 1
2. Which type of variation is represented by the following equation?
indirect variation
Verification
[tex]\\ \rm\Rrightarrow s\propto \dfrac{1}{y}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{s_1}{t_2}=\dfrac{s_2}{t_1}[/tex]
[tex]\\ \rm\Rrightarrow s_1t_1=s_2t_2[/tex]
Evaluate 5x -3x when x=2
Answer:
4
Step-by-step explanation:
5*2-3*2=10-6=4
Write the scientific notation for 127.5. Please! And tell me how so I can learn too.
-4x+9y=9
x-3y=-6
solve. systems of equations
Answer:
-3x + 6y = 3
Step-by-step explanation:
-4x + x = -3x
9y - 3y = 6y
9 - 6 = 3
9514 1404 393
Answer:
(x, y) = (9, 5)
Step-by-step explanation:
My preferred method is to solve a system using a graphing calculator. That result is attached.
__
Here, you can multiply the second equation by 4 and add the first equation.
4(x -3y) +(-4x +9y) = 4(-6) +(9)
-3y = -15 . . . . . . . . . . simplify
y = 5 . . . . . . . . . . . . divide by -3
x -3(5) = -6
x = -6 +15 = 9
The solution is (x, y) = (9, 5).
I know the answer don’t know how though
Answer:
16384Step-by-step explanation:
As,
[tex] {2}^{15} [/tex]
Meaning that 2 multiplied 15 times here,
Equals 32 768
Now,
[tex] {2}^{14} [/tex]
Meaning that 2 multiplied 15 times then divided by one time 2,
Equals 32 768 ÷ 2 = 16384 (Ans)
If y = -18 when x = 3, find x when y =30
Answer:
when x = 18. Putting x = 18 into the equation y = 6/x, we have y = 6/18. Simplifying the fraction gives us y = 1/3.
Step-by-step explanation:
if a metalic cylinder having volume 18cm3 is melted to form a hemisphere. find the radius of the hemisphere.
Answer:
R = 2.05 cm
Step-by-step explanation:
Volume of a hemisphere
V = ½(4/3)πR³ = (2/3)πR³
18 = (2/3)πR³
R³ = 27/π
R = 2.04835218...
A school store buys pencils in bulk and sells them to students for a small profit. The school pays $2.00 for 100 pencils and sells them for 10 cents each. How many pencils would they have to sell to make a $100 profit?
Answer:
Step-by-step explanation: