If Ф ∈ (0, pi/2) and tan(pi cosФ) = cot(pi sinФ), then cos(Ф- pi/4) is equal to?\
Answer:
please see the answer in the picture.
The volumes of two similar solids are 512cm3 and 2197cm3. If the smaller solid has a surface are of 960cm2, find the surface area of the larger solid. Part 1: find the similarity ratio by taking the cube root of each volume. Show your work. Part 2: use your answer from part 1 to find the ratio of the surface areas. Show your work. Part 3: set up a proportion and solve to find the surface area of the larger solid.
Answer:
see below
Step-by-step explanation:
Part 1:
(512) ^ 1/3
-------------------
(2197) ^ 1/3
8
-----
13
The scale factor is 8:13
Part 2
The ratios of the areas is related by scale factor squared
8^2
-----
13^2
64
------
169
Part 3
64 960
------ = ----------------
169 SA larger
Using cross products
64 * SA = 169 * 960
64 SA = 162240
Divide each side by 64
64 SA/ 64 = 162240 / 64
SA = 2535
2535 cm^2
You wait in line for hours to get the new special edition Nikes for $250, but you have to pay 5.3% in Virginia state sales tax. What is the total you will pay?
Answer:
263.25
Step-by-step explanation:
250 x .053 (5.3%) = 13.25 tax
250 + 13.25 = 263.25 price plus sales tax
Answer:
263.25
Step-by-step explanation:
Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day
Answer:
3 / 16
Step-by-step explanation:
Let The total amount = x
Fraction eaten on first day = 1/4x
Fraction left = x - 1/4x = 3/4x
Fraction of amount left eaten on second day = 3/4 of 3/4x
3/4 * 3/4x = 9/16x
Fraction left :
3/4x - 9/16x = (12x - 9x) /16 = 3/16x
Hence, fraction left = 3/16
pls pls help help help
Answer:
the diameter form for your help today with the app
Step-by-step explanation:
pa brain less
Please help ! pythagoran theaeom ! I need someone to please explain how to answer this ASAP , giving brainlist
Answer:
Floor=2*sqrt(11)
Step-by-step explanation:
Using Pythagoras theorem, we have
Wall^2+Floor^2=(Ladder)^2
Floor^2=12^2-10^2
Floor=sqrt(44)=2*sqrt(11)
Answer:The floor is 6m
Step-by-step explanation:
In this we have to solve to find B
First we know that A^2+B^2+C^2 and we know A is 10 and C is 12 so now we are going square both 10 and 12 which would be 100 and 144 then we subtract each other 144-100=44 and lastly we are going to get the square root of 44 which is 6.
Please give brainlist
geometry!!!!!!!!! helppp
Answer:
Solution given:
Centre (h,k)=(-6,-2)
end points are:
A[tex]\bold{(x_{1},y_{1})=(-1,-9) \:and \:B(x_{2},y_{2})=(-11,5)}[/tex]
Now
distance between A to M is:
AM=[tex]\sqrt{(h-x_{1})²+(k-y_{1})²}[/tex]
AM=[tex]\sqrt{(-6+1)²+(-2+9)²}=8.6[/tex]units
again
distance between B to M is:
BM=[tex]\sqrt{(h-x_{2})²+(k-y_{2})²}[/tex]
BM=[tex]\sqrt{(-6+11)²+(-2-5)²}=8.6[/tex]units
again
Since AM=BM=8.6units
so
M is the centre of the circle.:Yes
[tex]3f^{2} - 15f - 108[/tex]
Answer:
3(f - 9)(f + 4)
Step-by-step explanation:
Assuming you require to factorise the expression
3f² - 15f - 108 ← factor out 3 from each term
= 3(f² - 5f - 36) ← factor the quadratic
Consider the factors 0f the constant term (- 36) which sum to give the coefficient of the f- term (- 5)
The factors are - 9 and + 4 , since
- 9 × 4 = - 36 and - 9 + 4 = - 5 , then
f² - 5f - 36 = (f- 9)(f + 4)
Then
3f² - 15f - 108 = 3(f - 9)(f + 4)
4. PLEASE HELP ME
Which of the quadratic functions has the widest graph?
A. y= -4/5x2
B. y= -4x2
C. y= 1/3x2
D. y= 0.3x2
Answer:
D. y= 0.3x2
Step-by-step explanation:
In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.
Use special right triangle ratios to find the lengths of the other leg and the hypotenuse
Answer:
leg = 18
hypotenuse = 18 sqrt(2)
Step-by-step explanation:
We know that sin theta = opp side / hypotenuse
sin 45 = 18 / hyp
hyp sin 45 = 18
hyp = 18 / sin 45
hyp = 18 sqrt(2)
Since this is an isosceles triangle ( the two angles are the same measure), the two legs have to be the same length
leg = 18
the lengths of the other leg and the hypotenuse
is 18 units and 18[tex]\sqrt{2}[/tex]units respectively.
Answer:
Solution given:
Let <C=<B=45°
AB=18 units
BC=?
AC=?
again
By using
By usingspecial right triangle ratios
sin C=opposite/hypotenuse=AB/AC=18/AC
Sin 45=18/AC
AC=18/sin45
AC=hypotenuse=18[tex]\sqrt{2}[/tex]units
again
Tan A=opposite/adjacent=BC/AB=BC/18
Tan45=BC/18
BC=Tan45*18
BC=length of another leg=18 units.
Which graphs are the graphs of even functions?
What are the steps to this problem (along with the answer)?
Answer:
x = 3
Step-by-step explanation:
In this piece-wise function, there are three defined sections, each for a different range of x. To find an x where y is -9, we have to set all parts of it equal to -9.
-x, x < -3
So, we can start by setting -x equal to -9 and solve for x:
-x = -9
x = 9
Our domain for this piece of the function is supposed to be x < -3. x = 9 does not fit into this range, meaning, in this range, there is no x for y = -9.
2x, -3 ≤ x ≤ -2
We can set the value 2x equal to -9 and, again, solve for x:
2x = -9
x = -4.5
The solution x = -4.5 does not fit into the defined domain of -3 ≤ x ≤ -2, therefore it is not a solution.
-x^2, x > -2
One last time, we can set -x^2 equal to -9 and solve for x:
-x^2 = -9
x^2 = 9
x = 3, x = -3
We are looking for a solution that fits into the domain, x > -2, x = -3 does not work, but x = 3 does.
In conclusion, the only solution where it fit the domain was x = 3
Answer:
x = 3
Step-by-step explanation:
x = - 3 in interval - 3 ≤ x ≤ - 2 then f(x) = 2x , so
f(- 3) = 2(- 3) = - 6 ≠ - 9
x = 9 in interval x > - 2 then f(x) = - x² , so
f(9) = - 9² = - 81 ≠ - 9
x = 3 in interval x > - 2 then f(x) = - x²
f(3) = - 3² = - 9
x = - 4.5 in the interval x < - 3 then f(x) = - x , so
f(- 4.5) = - (- 4.5) = 4.5
Thus
y = - 9 when x = 3
According to the synthetic division below, which of the following statements are true?
Answer:
Step-by-step explanation:
That 3 sitting outside there in that little "box" thing is a root/solution/zero of the polynomial. The numbers underneath the line are the coefficients of the depressed polynomial, which means that the polynomial is 1 degree lower than the degree with which we started. If we started with an x-squared, this degree is a single x, better known as linear (a line). Anyway, (x - 3) is a zero of the polynomial, which also means that it's a factor. So A applies. x = 3 is a root, so C applies. And F also because the depressed polynomial, the remainder, is 2x + 4.
The width of a rectangle is twice as long as the length. if the length is increased by 50% and the width is decreased by 20%, the perimeter becomes 248. find the width and length of the original rectangle.
Answer:
Step-by-step explanation:
The percents here make this more tricky than it originally seems to be. We'll make a table and see where it takes us:
original new
length
width
And we'll fill it in according to our rules given. Starting with the original, we are told that the width is twice as long as the length. We don't know the length, so we'll call that L, and if the width is twice that, the width is 2L:
original new
length L
width 2L
Now here's the tricky part. What I'm going to do is fill in the "new" column with the expressions and then we'll simplify them in the next step.
The length is increased by 50%. So we have 100% of the original length and we are adding another 50% to that:
original new
length L 100%L + 50%L
width 2L
The width is decreased by 20%, so we have 100% of 2L and we are subtracting 20% of 2L from that:
original new
length L 100%L + 50%L
width 2L 100%(2L) - 20%(2L)
And now we'll simplify that "new" column:
original new
length L 150%L = 1.5L
width 2L 80%(2L) = 160%L = 1.6L
Now we're ready for the perimeter part. The formula for the perimeter of a rectangle is P = 2L + 2w, so filling in from our "new" column, since 248 is the perimeter given for AFTER the rectangle's length and width are manipulated:
248 = 2(1.5L) + 2(1.6L) and
248 = 3L + 3.2L and
248 = 6.2L so
L = 40 and that means that w = 80 (because in the "original" column, the width is twice the length)
in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Answer:
2520 ways
Step-by-step explanation:
Given
[tex]n = 10[/tex]
[tex]r = (2,3,5)[/tex]
Required
The number of selection
First, select 2 people from 10 in 10C2 ways.
There are 8 people, left.
Next, select 3 people from 8 in 8C3 ways.
There are 5 people left.
Lastly, select 5 from 5 in 5C5 ways
So, we have:
[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]
Using combination formula
[tex]Total = 45 * 56 * 1[/tex]
[tex]Total = 2520[/tex]
(c+d)^2+11(c+d)+30
Factor completely.
Answer:
firstable give c+b a polynomial value like x
so its will be x^2+11x+30
after the we have to factor it
30=6×5
and 11=6+5
so its will become
(x+6)×(x+5)=x^2+11x+30
x=c+d
(c+d+6)×(c+d+5)=(c+d)^2+11(c+d)+30
have a great day
someone, please help this is due soon if you can explain them I really appreciate it (PICTURE) 15 points and brainliest.
Step-by-step explanation:
1. Given,
Sides of the shape = 3y+9, 2y+4, y+3 and 2y+4
Therefore ,
Perimeter of the shape = Sum of all the sides
= (3y+9) + (2y+4) + (y+3) + (2y+4)
= 3y + 2y + y + 2y + 9 + 4 + 3 + 4
= 8y + 20 (Ans)
2. Given,
Side of the square = 5x - 2
Therefore,
Perimeter of the square = 4 × Sides = 4s
= 4 × (5x - 2)
= 4 × 5x + 4 × (-2)
= 20x - 8 (Ans)
HELP PLEASE!!! The expected value of a random variable X is 35. The variable is transformed
by multiplying X by 4 and then adding 1 to it. Find the expected value (mean)
of the transformed variable. A. 135 B.117 C. 154 D.141
Answer:
Expected value x= 35
linear transformation is defined as a + bx
here, b=4, a=1
The transformation is [tex]z=1+4x[/tex]
now, expected value, [tex]l_z=l_z(a+bx)[/tex]
[tex]=l(a)+l(bx)[/tex]
[tex]=a+b\:l\:x[/tex]
substitute the value of a=1, b=4 and l=35
[tex]l_z=1+4\times35[/tex]
[tex]=1+140[/tex]
[tex]=141[/tex]
So, the expected value of the transformed variable is 141.
OAmalOHopeO
=======================================================
Explanation:
Let's consider a set of three values such that they're all equal to 35
{35,35,35}
This rather boring set has a mean of 35 and it's hopefully very clear why this is the case. The terms "mean" and "expected value" are interchangeable.
If we multiply everything by 4, then we get the new set {140,140,140}
Then add 1 to everything and we arrive at {141,141,141}. You can quickly see that the mean here is 141.
-----------------------------
You could play around with that original set of 3 values to make things more interesting. Let's say we subtract 1 from the first item and add 1 to the last item. So we could have {35,35,35} turn into {34,35,36}. You should find that the mean is still 35 here.
If we quadruple each item, then we have {34,35,36} turn into {136,140,144}
Finally, add 1 to everything to get {137,141,145}. Computing the mean of this set leads to 141.
These are just two examples you could do to help see why the answer is D) 141
-----------------------------
In a more general theoretical sense, we're saying the following
Y = mX+b
E[Y] = E[m*X+b]
E[Y] = E[m*X] + E[b]
E[Y] = m*E[X] + b
where Y is the transformed variable based on the random variable X. In this case, m = 4 and b = 1. Also, E[X] = 35.
So,
E[Y] = m*E[X] + b
E[Y] = 4*35 + 1
E[Y] = 141
-----------------------------
Why go through all this trouble? Well consider that you know a certain distribution is centered around 35. Then consider that you want to convert those measurements to some other unit. This conversion process is us going from variable X to variable Y. Think of it like a batch conversion of sorts.
A more real world example would be something like "we know the average temperature is 35 degrees Celsius. The question is: what is the average temperature in Fahrenheit?" The numbers would be different, but the idea still holds up.
Use the expression, X^2-7
What is the value of the expression above when n=5
Answer:
18
Step-by-step explanation:
X^2 - 7 =
Since we need to evaluate the expression when X = 5, we replace X with 5.
= 5^2 - 7
Now, according to the correct order of operations, we need to do the exponent first. 5^2 = 5 * 5 = 25
= 25 - 7
Finally, we subtract.
= 18
Answer: 18
What is 1/4 0.75 1/3 0.5 greatest to least
Answer:
1/4 = 1 ÷ 4 = 0.251/3 = 1 ÷ 3 ≈ 0.330.750.50.75 → 0.5 → 1/3(0.33) → 1/4(0.25)
What is the area of this triangle
Answer:
14
Step-by-step explanation:
7*4*1/2=14
Can someone please help me out
Step-by-step explanation:
[tex] \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} [/tex]
ASAP HELP!! PLEASEEEE!!
Answer:
Step-by-step explanation:
5.1, please this is just a guess from using my head to calculate
ahla
S : Assignment
乡,一石
Answer
what's the question?
Step-by-step explanation:
looks like your question is missing information
Which of the following lines is parallel to the line
y = 1/2x -6
Select one:
a) y=-1/2x-6
b) y=2x+1
c) y=-1/2x+5
d) y=1/2x-3
Answer:
y = 1/2x - 3 (option - d)
Step-by-step explanation:
The lines are parallel if they have the same slope/gradient. So by comparing with y = mx + c (where 'm' is the slope and 'c' is the y-intercept).
Line y = 1/2 x - 6 has the slope m = 1/2
and the line in option 'd'
y = 1/2 x -3 has the slope m = 1/2
Slopes are equal and lines are parallel.
Thank-you.
#Muhib
Help me to prove it
Answer:
see explanation
Step-by-step explanation:
Using the identities
cotA = [tex]\frac{1}{tanA}[/tex]
cot²A = cosec²A - 1
tan²A = sec²A - 1
Consider the left side
(cotA + tanA)² ← expand using FOIL
= cot²A + 2cotAtanA + tan²A
= cosec²A - 1 + 2 .[tex]\frac{1}{tanA}[/tex] . tanA + sec²A - 1
= cosec²A - 1 + 2 + sec²A - 1
= sec²A + cosec²A - 2 + 2
= sec²A + cosec²A
= right side, thus proven
Select the true statement about triangle ABC.
A. cos A = cos C
B. cos A = sin C
C. cos A = sin B
D. cos A = tan C
Answer:
B
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
cosC = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{5}{13}[/tex]
sinC = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{12}{13}[/tex]
tanC = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{12}{5}[/tex]
Then
cosA = sinC → B
Two boys together have $12. One of them has $10 more than the other. How much money does each of them have
3. A rectangle has a length of 2x – 9 and a width of x2 + 3x – 4. What is the polynomial that models the area
of the rectangle?
Answer:
(C) 2x^3 - 3x^2 - 35x + 36
Step-by-step explanation:
First multiply 2x by x^2 + 3x - 4:
(2x)(x^2 + 3x - 4)
2x^3 + 6x^2 - 8x
Next multiply -9 by x^2 + 3x - 4:
(-9)(x^2 + 3x - 4)
-9x^2 - 27x +36
Now add the two polynomials by adding like terms:
(2x^3 + 6x^2 - 8x) + (-9x^2 - 27x +36)
2x^3 + 6x^2 - 9x^2 - 8x - 27x + 36
2x^3 - 3x^2 - 35x + 36
Hope this helps (●'◡'●)
write 5 lcms of 100 and 120
Answer:
The LCM of 100 and 120 is 600.
The LCM of 5 and 120 is 120.
LCM of 5 and 100 is 100.
Step-by-step explanation:
I think this is the answer . If it is not sorry .
