Answer:
11.1%
Step-by-step explanation:
Increase = 20 - 18
= 2
% increase= increase/initial price × 100
= 2/18 × 100
11.1%
find the angle of rotation that maps point D onto point A
Answer:
A - 144
Step-by-step explanation:
everything else would be too far. thx
Round 9296 to the nearest hundred?
The answer it 9300 so 9296 round to is 9300
Which expression is undefined?
Answer:
D: [tex]\frac{3}{(6-6)}[/tex]
Step-by-step explanation:
Option A equates to [tex]-\frac{0}{2}=0[/tex]
Option B equates to [tex]\frac{(-4+0)}{8}=\frac{-4}{8}=-\frac{1}{2}[/tex]
Option C equates to [tex]0\div11 =0[/tex]
Option D equates to [tex]\frac{3}{(6-6)}=\frac{3}{0}[/tex] which cannot be defined as division by 0 is impossible
Help help help help hep
Answer:
Yes
Step-by-step explanation:
6(25-8w)+20w for w=2
150−28w
i think i dont know
Use the fundamental identities to
Find tan s if sin s=3/4 and s is in quadrant 2
Answer:
Cosine Formula
Thus, the cosine of angle α in a right triangle is equal to the adjacent side's length divided by the hypotenuse. To solve cos, simply enter the length of the adjacent and hypotenuse and solve.
∫(sinxdx)/(sinx^3+cosx^3)
Hello, would be very nice if someone could help me ! :)
A finite geometric series is the sum of a sequence of numbers. Take the sequence
1, 2, 4, 8, ..., for example. Notice that each number is twice the value of the
previous number. So, a number in the sequence can be represented by the
function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th
number in the sequence is ∑^5 n-1 2^n-1.
This equation can also be written as S5 = 2^0+2^1+ 2^2+ 2^3+ 2^4. If we multiply this equation by 2. the equation becomes 2(S5) = 2^1+ 2^2+ 2^3+ 2^4+ 2^5
What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the
form ∑^a n-1 b^n-1 ?
Answer:
Step-by-step explanation:
2S₅ - S₅ = 2⁵ - 2⁰
S₅ = 2⁵ - 1
Sₙ = (bᵃ - 1) / (b - 1)
After 5 throws in a game of darts, Brent's mean score was 32. Calculate his total score.
1.To know this answer, we need to know some vocabulary that's used in t. Most people don't know how to solve questions if they have hard Vocabulary and what the question is Asking
Mean=The average of all his throws
It's asking us to calculate his total score
2. Find Clues to help you solve word problems
Finding clues in Word Problems is a very important part a lot of people skip but this helps you solve the question easier
5 throws and Mean Score is 32 are the clues
3. Guess and check
The method to this thingy is called guess and check. There is another method which is slightly harder and i just don't want to do it.
Let's just say his scores were... 5, 6, 4, 5,10Add them up and you get 30Then 30/5
Let's try bigger numbers
20+25+20+20
If you like this method, you may try it another method is called work Backwards
5x32=160
Then divide 160 by 5 to double check and you get 32!!
========================================
Therefore, the answer s 160 as his total score
hope this gives you a clue to what we are doing and when you have a question like this, I really hope you understand the concept
Hope this helped (:
Understand how to work with negative bases and negative exponents.
5^2 =
5^-2 =
(-5)^2 =
- 5^2 =
(Remember to find the base, then multiply.)
Answer:
[tex]Understand \: how \: to \: work \: with \: negative \: bases \\ \: and \: negative \: exponents. \\
\bold{answer - } \\ {5}^{2} = 5 \times 5 = 25 \\ {5}^{ - 2} = \frac{1}{ {5}^{2} } = \frac{1}{25} = 0.04 \\ {( - 5)}^{2} = ( - 5) \times ( - 5) = 25 \\ - {5}^{2} = ( - 5) \times ( - 5) = 25 \\ \\ \bold \purple{hope \: it \: helps \: ♡}[/tex]
4. This diagram is a straightedge and compass construction of a line perpendicular to line AB passing through point C. Which segment has the same length as segment EA.
a. EC
b. ED
C. BE
d. BD
Answer:
Segment ED has the same length as EA
The line segment which is equal to EA is ED. Therefore, option B is the correct answer.
In the given diagram, a line perpendicular to line AB passes through point C.
What is the tangent to the circle?A tangent to a circle is a line which intersects the circle at only one point. The common point between the tangent and the circle is called the point of contact.
The length of two tangents drawn from an external point to a circle is equal.
From the given figure we can see there are three circles, two large circles and one small circle.
Line segment EA is tangent to a small circle.
The line segment which is equal to EA is ED because ED is another tangent to a small circle from the same external point.
The line segment which is equal to EA is ED. Therefore, option B is the correct answer.
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LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See explanation
Step-by-step explanation:
Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)
G (-1, 3) G' (-1.5, 4.5)
F (-2, -2) F' (-3, -3)
G'x / Gx = -1.5/-1 = 1.5
G'y / Gy = 4.5 / 3 = 1.5
F'x / Fx = -3 / -2 = 1.5
F'y / Fy = -3 / -2 = 1.5
The point (3, 3) is in what quadrant? 2,1,3,4
Answer:
1
Step-by-step explanation:
(3,3) has a positive x value and a positive y value which means it is in the first quadrant
A rectangle is 8 feet long. Its width is represented by “seven plus x feet.” Which expression represents the area, in square feet, of the rectangle?
56 + 8x
Area of Rectangle = Length x Width
Area of Rectangle = 8(7 + x)
Express the following surds in the simplest form
a)
[tex] \sqrt{128} [/tex]
b)
[tex] \sqrt{48} [/tex]
c)
[tex] \sqrt{300} [/tex]
[tex] \sqrt{128} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times {2}^{2} } \\ = 2 \times 2 \times 2 \\ = 8[/tex]
[tex] \sqrt{48} \\ = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{ {2}^{2} \times {2}^{2} \times 3 } \\ = 2 \times 2 \sqrt{3} \\ = 4 \sqrt{3} [/tex]
[tex] \sqrt{300} \\ = \sqrt{2 \times 2 \times3 \times 5 \times 5} \\ = \sqrt{ {2}^{2} \times 3 \times {5}^{2} } \\ = 2 \times 5 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
The area of a square pond is 1000m2.A path of uniform width is surrounded outside the pond and its area is 369m2.find the outer length of the path
Answer:
631 m²
Step-by-step explanation:
Outer length of park = Total area - Area of pond
Outer length of park = 1000 - 369
Outer length of park = 631 m²
Answer:
Hope it will help you a lot.
let f(x)=3x^2-6x+5 what is the leading coefficient
Decrease £110 by 50%
Answer:
£55
Step-by-step explanation:
50% is just another way to say 1/2. This means that 1/2 of £110 is £55.
A spherical solid, centered at the origin, has radius 4 and mass density(x,y,z)=6-(x^2+y^2+z^2). Set up the triple integral and find its mass.
I've attached a photo of the question.
There's something very off about this question.
In spherical coordinates,
x² + y² + z² = ρ²
so that
f(x, y, z) = 6 - (x² + y² + z²)
transforms to
g(ρ, θ, φ) = 6 - ρ²
When transforming to spherical coordinates, we also introduce the Jacobian determinant, so that
dV = dx dy dz = ρ² sin(φ) dρ dθ dφ
Since we integrate over a sphere with radius 4, the domain of integration is the set
E = {(ρ, θ, φ) : 0 ≤ ρ ≤ 4 and 0 ≤ θ ≤ 2π and 0 ≤ φ ≤ π}
so that the integral is
[tex]\displaystyle \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 - \rho^2) \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
Computing the integral is simple enough.
[tex]\displaystyle = \int_{\phi=0}^{\phi=\pi} \int_{\theta=0}^{\theta=2\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\theta \, d\phi[/tex]
[tex]\displaystyle = 2\pi \int_{\phi=0}^{\phi=\pi} \int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \sin(\phi) \, d\rho \, d\phi[/tex]
[tex]\displaystyle = 2\pi \left(\int_{\phi=0}^{\phi=\pi} \sin(\phi) \, d\phi\right) \left(\int_{\rho=0}^{\rho=4} (6 \rho^2 - \rho^4) \, d\rho\right)[/tex]
[tex]\displaystyle = 2\pi \cdot 2 \cdot \left(-\frac{384}5\right) = \boxed{-\frac{1536\pi}5}[/tex]
but the mass can't be negative...
Chances are good that this question was recycled without carefully changing all the parameters. Going through the same steps as above, the mass of a spherical body with radius R and mass density given by
[tex]\delta(x, y, z) = k - (x^2 + y^2 + z^2)[/tex]
for some positive number k is
[tex]\dfrac{4\pi r^3}{15} \left(5k - 3r^2\right)[/tex]
so in order for the mass to be positive, we must have
5k - 3r² ≥ 0 ⇒ k ≥ 3r²/5
In this case, k = 6 and r = 4, but 3•4²/5 = 9.6.
2. The sum of two cubes can be factored by using the formula q3 + b3 = (a + b)(a? - ab + b).
(a) Verify the formula by multiplying the right side of the equation.
(b) Factor the expression 8x3 + 27.
(c) One of the factors of 23 - bºis a - b. Find a quadratic factor of a3 - bº Show your work.
(d) Factor the expression x3 - 1.
Factorization involves breaking down an expression.
The factorized expression of [tex]8x^3 + 27[/tex] is [tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]The other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]The factorized expression of x^3 - 1 is [tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]The sum of cubes is given as:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
(a) Verify the formula
Expand the expression on the right-hand side
[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]
Collect like terms
[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]
[tex](a^3 + b^3) = a^3 + b^3[/tex]
The formula has been verified
(b) Factorized 8x^3+ 27
We have:
[tex]8x^3 + 27[/tex]
Express 27 as 3^3
[tex]8x^3 + 27 =8x^3 + 3^2[/tex]
Express 8 as 2^3
[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]
Rewrite as:
[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]
Given that:
[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]
The expression becomes
[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]
[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]
(c)The other factor of 2^3 - b^3
By difference of cubes, we have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
So, the equation becomes
[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]
This gives
[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]
Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]
(c) Factor x^3 - 1
We have:
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]
Express 1 as 1^3 in x^3 - 1
[tex]x^3 - 1 =x^3 - 1^3[/tex]
[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes
[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]
[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]
Read more about factorization at:
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[tex]\sqrt[3]{y} (7\sqrt[3]{8y^2}-\sqrt[3]{y^5} -4y\sqrt[3]{27y^2}[/tex] simplify
Answer:
[tex]\huge\boxed{-y^2+2y}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]y\cdot\left(7\sqrt[3]{8y^2}-\sqrt[3]{y^5}-4y\sqrt[3]{27y^2}\right)\\\\=(\sqrt[3]y)(7\sqrt[3]{8y^2})-(\sqrt[3]y)(\sqrt[3]{y^5})-(\sqrt[3]y)(4y\sqrt[3]{27y^2})\\\\=7\sqrt[3]{(y)(8y^2)}}-\sqrt[3]{(y)(y^5)}-4y\sqrt[3]{(y)(27y^2)}\\\\=7\sqrt{8y^3}-\sqrt{y^6}-4\sqrt{27y^3}\\\\=7\sqrt[3]{2^3y^3}-\sqrt{y^{2\cdot3}}-4\sqrt{3^3y^3}\\\\=7\sqrt[3]{(2y)^3}-\sqrt{(y^2)^3}-4\sqrt{(3y)^3}\\\\=7\cdot2y-y^2-4\cdot3y\\\\=14y-y^2-12y\\\\=-y^2+2y[/tex]
Used:
[tex]a(a+b)=ab+ac\\\\\sqrt[3]{a\cdot b}=\sqrt[3]a\cdot\sqrt[3]b\\\\\sqrt[3]{a^3}=a\\\\(a^n)^m=a^{n\cdot m}[/tex]
Which expression is equivalent to 1/4 (5x + 6)?
The expression which is equivalent to 1/4 (5x + 6) is; Choice A: {5(1/4)x} + {6(1/4)x}.
According to the question:
We are required to determine an expression which is equivalent to 1/4 (5x + 6).In a bid to expand the expression; we must multiply each term in the parenthesis by (1/4);
In essence; we have;
{5(1/4)x} + {6(1/4)x}Read more on multiplication;
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Find an equation of the plane.
The plane that contains the line
x = 3 + 2t,
y = t,
z = 6 − t
and is parallel to the plane
2x + 4y + 8z = 16
Answer:
x +2y +4z = 27
Step-by-step explanation:
The parallel plane will have the same coefficients of x, y, z as the given plane. We notice those have a common factor of 2, so the equation can be reduced to ...
x +2y +4z = constant
This equation is satisfied for every point on the line, so we have ...
(3 +2t) +2(t) +4(6 -t) = constant . . . . . substituting for x, y, z
3 +2t +2t +24 -4t = constant
27 = constant
The equation of the desired plane is ...
x +2y +4z = 27
The normal to the given plane is (2, 4, 8), and the plane we want is parallel to this one so it has the same normal vector.
When t = 0, the given line, and thus the plane we want, passes through the point (3, 0, 6).
Then the equation of the plane is given by
(2, 4, 8) • (x - 3, y - 0, z - 6) = 0
2 (x - 3) + 4y + 8 (z - 6) = 0
2x + 4y + 8z = 54
or
x + 2y + 4z = 27
Help help help help hep
i think that the answer is 0 because f(2) means that you substitute 2 for x
2(2)=4
4-4=0
Principal = $ 15000, rate = 10% p.a. and time
21/5 years
PLS HELP ASAP
Answer:
Simple Interest: A=P(1+rt)
A=15000(1+(0.1*4.2))
A=$21,300
Compound Interest:A=P(1+r/n)^nt
A=15000(1+0.1/4.2)^1*4.2
A=$64,500
Step-by-step explanation:
Jackson bought 6 basketballs for 72 dollars what was the price per basket ball
Answer:
the answer would be 12 I say this because 72 divied by 6 would equal 12
Answer:
12 dollars
Set up a proportion.
6/72=1/x
Solve by cross-multiplying (my preferred method) and then you will end up with the final answer of x=12.
12 is the answer :)
PLEASE MARK BRAINLIEST!
THANK YOU & HAVE A WONDERFUL DAY :))
desceibe how to determine the average rate of change between x=4 and x=6 for the function f(x)=2x^3 +4
[tex]slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= 2x^3+4\qquad \begin{cases} x_1=4\\ x_2=6 \end{cases}\implies \cfrac{f(6)-f(4)}{6-4} \\\\\\ \cfrac{[2(6)^3+4]~~ -~~[2(4)^3+4]}{2}\implies \cfrac{436~~ -~~132}{2}\implies \cfrac{304}{2}\implies 152[/tex]
Omar needs at least $8 to buy lunch. Which number line represents this scenario?
Answer:
I'd say none, as we're missing something in this problem. Make sure you've included everything to solve this problem. Thanks.
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?
Answer:
4 fluid ounces
Step-by-step explanation:
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee. If her coffee pot holds 8 cups, how many fluid ounces does she have left?
Remember
8 fluid ounces = 1 cup.
First you need to do find out how many fluid ounces she poured in total.
So do,
5 mugs × 12 fluid ounces.
which is 60 fluid ounces.
Now that you now that you need to convert 8 cups into fluid ounces.
Like I said at the top 8 fluid ounces = 1 cup.
So you need to do,
8 cups × 8 fluid ounces.
Which is 64 fluid ounces she can hold in her coffee pot.
Now you subtract,
64 fluid ounces - 60 fluid ounces.
Which is 4 fluid ounces left in her coffee pot.
The number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.
What is unit conversion?It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.
It is given that:
A waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of 5 mugs from a full pot of coffee.
Let x be the number of fluid ounces she has left.
4 fluid ounces
As we know,
8 fluid ounces = 1 cup
The total amount of coffee = 5×12
The total amount of coffee = 60
Total amount = 8 cups × 8 fluid ounces.
x = 64 fluid ounces - 60 fluid ounces.
x = 4 fluid ounces
Thus, the number of fluid ounces she has left is 4 fluid ounces if the waitress is filling coffee mugs at a diner. She pours 12 fluid ounces into each of the 5 mugs from a full pot of coffee.
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How do I find the equation of the perpendicular bisector between (-2,5) and (2,-1)?
Answer:
[tex]y = \frac{2}{3} x + 2[/tex]
Step-by-step explanation:
Start by finding the slope of the given line.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of given line
[tex] = \frac{5 - ( - 1)}{ - 2 - 2} [/tex]
[tex] = \frac{5 + 1}{ - 4} [/tex]
[tex] = \frac{6}{ - 4} [/tex]
[tex] = - \frac{3}{2} [/tex]
A perpendicular bisector cuts through the line at its midpoint perpendicularly.
The product of the slopes of two perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
[tex] - \frac{3}{2} m = - 1[/tex]
[tex]m = - 1 \div ( - \frac{3}{2} )[/tex]
[tex]m = - 1 \times ( - \frac{2}{3} )[/tex]
[tex]m = \frac{2}{3} [/tex]
[tex]y = \frac{2}{3}x + c[/tex], where c is the y-intercept.
To find the value of c, we need to substitute a pair of coordinates that lies on the perpendicular bisector into the equation. Since the perpendicular bisector passes through the midpoint of the given line, we can use the midpoint formula to find the coordinates.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of given line
[tex] = ( \frac{ - 2+ 2}{2} , \frac{5 - 1}{2} )[/tex]
[tex] =( \frac{0}{2} , \frac{4}{2} )[/tex]
= (0, 2)
[tex]y = \frac{2}{3} x + c[/tex]
When x= 0, y= 2,
2= ⅔(0) +c
2= 0 +c
c= 2
Thus, the equation of the perpendicular bisector is [tex]y = \frac{2}{3} x + 2[/tex].