What is the value of x?
Answer:
22
Step-by-step explanation:
3x-14= 4(x-9)
3×-14= 4x-36
4x-36-3x+14=0
×-22÷0
x=22
Factorize : 4(x+y)^2 -9(x-y)^2
Answer:
Step-by-step explanation:
[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]
= -5x² + 25xy + xy - 5y²
= 5x(-x + 5y) - y(-x +5y)
= (-x + 5y)(5x - y)
Now actually compute 2 - 8
Answer:
the answer is -6. you just subtract 2 with 8
if a plane can travel 500 miles per hour with wind and 400 miles per hour against the wind find the speed of the plane with out a wind and speed of the wind.
Answer: hello there here is your answer:
Still air speed:450 mph.
Step-by-step explanation:
500-450=450-400=50 mph
Still air speed:450 mph. Wind speed:50 mph..
hope this help have a good day
On a map of a town, 3 cm represents 150 m. Two points in the town are 1 km apart. How far apart are the two points on the map?
Answer:
5000 km
Step-by-step explanation:
We are given that
3 cm represents on a map of a town=150 m
Distance between two points=1 km
We have to find the distance between two points on the map.
3 cm represents on a map of a town=150 m
1 cm represents on a map of a town=150/3 m
1 km=1000 m
1 m=100 cm
[tex]1km=1000\times 100=100000 cm[/tex]
100000 cm represents on a map of a town
=[tex]\frac{150}{3}\times 100000[/tex] m
100000 cm represents on a map of a town=5000000 m
100000 cm represents on a map of a town
=[tex]\frac{5000000}{1000} km[/tex]
100000 cm represents on a map of a town=5000 km
Hence, two points are separated by 5000 km on the map.
write the following sets in the set builder form C={1,4,9,16,25}
C={ check example in book}
Compare the subtraction problems (6/8-5/8=1/8) and (6/9-7/9=-1/9) why is the answer to the first problem positive nad the answer to the second problem negative select all that apply
6/9 - 7/9 = -1/9
is a negative number.
Order the following integers from smallest (left side) to biggest (right
side):
20, 0, 22, -35, 100, -59
Need help please
The vertical test line
Step-by-step explanation:
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. and, as a result, any vertical line in the plane can intersect the graph of a function at most once.hope it helpsstay safe healthy and happy....Answer:
It is a graphical method
19.Find dy/dx
of the function y = f(x) definded by x²+xy-y2 = 4.
Answer:
2x + y
Step-by-step explanation:
x² + xy - y² = 4
→ Remember the rule, bring the power down then minus 1
2x + y
Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Ox45)
0 - 6x - 5 < 10 - x
0 -6x + 15 < 10 - 5
E
우
-
3
5
2
-1
0
1
2
3
Answer:
45.9
Step-by-step explanation:
Thirty-six percent of customers who purchased products from an e-commerce site had orders exceeding 110. If 17% of customers have orders exceeding 110 and also pay with the e-commerce site's sponsored credit card, determine the probability that a customer whose order exceeds 110 will pay with the sponsored credit card.
Answer:
The right solution is "0.5".
Step-by-step explanation:
According to the question,
P(pay with the sponsored credit card | order exceeds $110)
= [tex]\frac{P(Pay \ with \ the \ sponsored \ credit\ card\ and\ order\ exceeds\ 110)}{P(order \ exceeds \ 110)}[/tex]
= [tex]\frac{P(A \ and \ B)}{P(A)}[/tex]
By putting the values, we get
= [tex]\frac{0.17}{0.34}[/tex]
= [tex]0.5[/tex]
Thus, the above is the right solution.
Find the solution to the system
of equations.
y = 2x + 3
([?], [ ]
2
بیر
2 3 4
-4 -3 -2 -1
-1
-2
3
-4
y=-x
Enter
Answer:
The two lines meet at (-1,1)
solve 5x^2-2=-12 by taking the square root
Answer:
[tex]x = \sqrt{-2} = 2i[/tex]
Step-by-step explanation:
[tex]5x^2-2=-12[/tex]
[tex]5x^2 =-10[/tex]
[tex]x^2 =-2[/tex]
[tex]x = \sqrt{-2} = 2i[/tex]
FastForward has net income of $19,090 and assets at the beginning of the year of $209,000. Its assets at the end of the year total $264,000. Compute its return on assets.
Given:
Net income = $19,090
Assets at the beginning of the year = $209,000.
Assets at the end of the year total = $264,000.
To find:
The return on assets.
Solution:
Formula used:
[tex]\text{Return of assets}=\dfrac{\text{Net income}}{\text{Average of assets at the beginning and at the end}}[/tex]
Using the above formula, we get
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{20900+264000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{473000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{236500}[/tex]
[tex]\text{Return of assets}\approx 0.0807[/tex]
The percentage form of 0.0807 is 8.07%.
Therefore, the return on assets is 8.07%.
In a town. the population of registered voters is 46% democrat, 42% republican and 12% independent polling data shows 57% of democrats support the increase , 38% of republicans support the increase, and 76% of independents support the increase.
Required:
a. Find the probability that a randomly selected voter in the town supports the tax increase.
b. What is the probability that a randomly selected voter does not support the tax increase?
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Answer:
a) 0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
b) 0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c) 0.1777 = 17.77% probability he or she is a registered Independent.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
57% of 46%(democrats)
38% of 42%(republicans)
76% of 12%(independents)
So
[tex]P = 0.57*0.46 + 0.38*0.42 + 0.76*0.12 = 0.513[/tex]
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
Question b:
1 - 0.513 = 0.487
0.487 = 48.7% probability that a randomly selected voter does not support the tax increase.
c. Suppose you find a voter at random who supports the tax increase. What is the probability he or she is a registered Independent?
Event A: Supports the tax increase.
Event B: Is a independent.
0.513 = 51.3% probability that a randomly selected voter in the town supports the tax increase.
This means that [tex]P(A) = 0.513[/tex]
Probability it supports a tax increase and is a independent:
76% of 12%, so:
[tex]P(A \cap B) = 0.76*0.12[/tex]
Thus
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.76*0.12}{0.513} = 0.1777[/tex]
0.1777 = 17.77% probability he or she is a registered Independent.
If BcA, AnB=(1,4,5)and AuB= (1,2,3,4,5,6) find B?
Hello,
if B ⊂ A then A∩B=B
So B={1,4,5}
As per the given value of sets, B is (1,4,5).
What is a set?A set is a collection of one or multiple data.
Given,
B ⊂ A
[tex]A[/tex] ∩ [tex]B = (1,4,5)[/tex]
[tex]A[/tex] ∪ [tex]B = (1,2,3,4,5,6)[/tex]
As B ⊂ A, therefor, B is a subset of A.
Therefore, [tex]A[/tex] ∩ [tex]B = B[/tex] and [tex]A[/tex] ∪ [tex]B = A[/tex]
Hence, [tex]B = A[/tex] ∩ [tex]B = (1,4,5)[/tex].
Learn more about a set here:
https://brainly.com/question/20516078
#SPJ2
How do I make people brainliest
Answer:
you have to wait until two people answer then you click their answer to make them brainliest
Step-by-step explanation:
i dont know
blah blah blah blah blah blah blah blah blah blah blah blah
What is the inequality shown?
Answer:
2<X ,this is because opened and facing towards x
and
–3≤X this is because the circle is closed and also facing towards x
Simplify 6/x^2−2x/x^2+3.
Answer:
3x2−2x+6/x2
Step-by-step explanation:
have a great day <33333
The circle P has a center at (0, 0) and a point on the circle at (0, 4). If it is dilated by a factor of 4, what is the distance of the diameter for circle P’.
A. 32
B. 4
C. 8
D. 16
Answer:
A. 32
Step-by-step explanation:
If the center is (0, 0) and a point is (0, 4) then the distance from the center to that point is 4 units. That distance is the radius. If you are dilating by a factor of 4, multiply the radius by 4 and you get 16. The new radius is 16 and the diameter= radius*2.
16*2=32
the angle of elevation of the top of the mast from a point 53m to its base on level ground is 61°. find the height of the mast to the nearest meter
the answer Is 95.61465. If you approximate you get 10.
Please Help NO LINKS
Suppose that
R
is the finite region bounded by
f
(
x
)
=
4
√
x
and
g
(
x
)
=
x
.
Find the exact value of the volume of the object we obtain when rotating
R
about the
x
-axis.
V
=
Find the exact value of the volume of the object we obtain when rotating
R
about the
y
-axis.
V
=
Answer:
Part A)
2048π/3 cubic units.
Part B)
8192π/15 units.
Step-by-step explanation:
We are given that R is the finite region bounded by the graphs of functions:
[tex]f(x)=4\sqrt{x}\text{ and } g(x)=x[/tex]
Part A)
We want to find the volume of the solid of revolution obtained when rotating R about the x-axis.
We can use the washer method, given by:
[tex]\displaystyle \pi\int_a^b[R(x)]^2-[r(x)]^2\, dx[/tex]
Where R is the outer radius and r is the inner radius.
Find the points of intersection of the two graphs:
[tex]\displaystyle \begin{aligned} 4\sqrt{x} & = x \\ 16x&= x^2 \\ x^2-16x&= 0 \\ x(x-16) & = 0 \\ x&=0 \text{ and } x=16\end{aligned}[/tex]
Hence, our limits of integration is from x = 0 to x = 16.
Since 4√x ≥ x for all values of x between [0, 16], the outer radius R is f(x) and the inner radius r is g(x). Substitute:
[tex]\displaystyle V=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_0^{16}(4\sqrt{x})^2-(x)^2\, dx \\\\ &=\pi\int_0^{16} 16x-x^2\, dx \\\\ &=\pi\left(8x^2-\frac{1}{3}x^3\Big|_{0}^{16}\right)\\\\ &=\frac{2048\pi}{3}\text{ units}^3 \end{aligned}[/tex]
The volume is 2048π/3 cubic units.
Part B)
We want to find the volume of the solid of revolution obtained when rotating R about the y-axis.
First, rewrite each function in terms of y:
[tex]\displaystyle f(y) = \frac{y^2}{16}\text{ and } g(y) = y[/tex]
Solving for the intersection yields y = 0 and y = 16. So, our limits of integration are from y = 0 to y = 16.
The washer method for revolving about the y-axis is given by:
[tex]\displaystyle V=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy[/tex]
Since g(y) ≥ f(y) for all y in the interval [0, 16], our outer radius R is g(y) and our inner radius r is f(y). Substitute and evaluate:
[tex]\displaystyle \begin{aligned} \displaystyle V&=\pi\int_{a}^{b}[R(y)]^2-[r(y)]^2\, dy \\\\ &=\pi\int_{0}^{16} (y)^2- \left(\frac{y^2}{16}\right)^2\, dy\\\\ &=\pi\int_0^{16} y^2 - \frac{y^4}{256} \, dy \\\\ &=\pi\left(\frac{1}{3}y^3-\frac{1}{1280}y^5\Bigg|_{0}^{16}\right)\\\\ &=\frac{8192\pi}{15}\text{ units}^3\end{aligned}[/tex]
The volume is 8192π/15 cubic units.
The largest angle in a triangle is six times the smallest angle. The middle angle is three times the smallest angle. Given that the sum of the angles in a triangle is , find the measure of each angle.
Answer:
Smallest: 18° Middle: 54° Largest: 108°
Step-by-step explanation:
We can start by writing out what we know in a series of equations:
s= smallest angle, m= medium angle, L= largest angle.
Since the largest is 6 times the smallest we have:
L=6s
Since the middle is 3 times the smallest we have:
m=3s
Since the 3 interior angle measures of a triangle always must equal 180°, we have:
s+m+L=180
Then we plug in our L and m into the third equation:
s+3s+6s=180
Combining like terms and solving:
10s=180
s=18
Then we plug in 18 for s into the first 2 equations to get:
L= 6* 18
L= 108
and
m= 3* 18
m= 54
So s= 18, m= 54, and L=108.
To check the answer we can:
Add the three to make sure they equal 180. Make sure the smallest is the smallest, and the largest is the largest.Find the third term of a geometric progression if the sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
3. Express the strength of a solution both as a ratio and as a percentage if
2 L of the solution contain 400 mg of solute.
Answer:
1 : 5000
0.02%
Step-by-step explanation:
A solution = solute + solvent
A 2 Litre solution = (2 * 1000) = 2000 mg
Having, 400 mg of solute ;
Recall ;
1 mg = 0.001 ml
400 mg = (0.001 * 400) = 0.4 ml
The strength of the solution :
Amount of solute / Amount of solution
0.4 / 2000
As a ratio :
0.4 / 2000 = (0.4 * 10) / (2000*10) = 4 / 20000 = 1 / 5000 = 1 : 5000 (as a ratio)
0.4 / 2000
= 0.0002
(0.0002 * 100%) = 0.02% (As a percentage)
it is known that the population proton of utha residnet that are members of the church of jesus christ 0l6 suppose a random sample of 46 selceted and prioon of the sample that belongs to the churh is calcutated what is the problaity of obtaining a sample priton less than 0;50 g
Answer:
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Proportion of 0.6
This means that [tex]p = 0.6[/tex]
Sample of 46
This means that [tex]n = 46[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.6[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.6*0.4}{46}} = 0.0722[/tex]
Probability of obtaining a sample proportion less than 0.5.
p-value of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.6}{0.0722}[/tex]
[tex]Z = -1.38[/tex]
[tex]Z = -1.38[/tex] has a p-value of 0.0838
0.0838 = 8.38% probability of obtaining a sample proportion less than 0.5.
What is the rate of change of the line on the graph
Answer:
A. ¼
Step-by-step explanation:
Rate of change (m) = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line, (4, 1) and (-4, -1), find the rate of change using the formula stated above:
Where,
[tex] (4, 1) = (x_1, y_1) [/tex]
[tex] (-4, -1) = (x_2, y_2) [/tex]
Plug in the values
Rate of change (m) = [tex] \frac{-1 - 1}{-4 - 4} [/tex]
= [tex] \frac{-2}{-8} [/tex]
= [tex] \frac{1}{4} [/tex]
Rate of change = ¼
Tamir wants to buy a snowboard. The original price is $760. How much will Tamir pay if he buys it during the sale?
I am having trouble with this problem. If anyone could help that would be great.
Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^2+y^2=16, 0≤z≤1, and a hemispherical cap defined by x^2+y^2+(z−1)^2=16, z≥1. For the vector field F=(zx+z^2y+4y, z^3yx+3x, z^4x^2), compute ∬M(∇×F)⋅dS in any way you like.
Answer:
Ok... I hope this is correct
Step-by-step explanation:
Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x^(2)+y^(2)=16
Center: ( 0 , 0 )
Vertices: ( 4 , 0 ) , ( − 4 , 0 )
Foci: ( 4 √ 2 , 0 ) , ( − 4 √ 2 , 0 )
Eccentricity: √ 2
Focal Parameter: 2 √ 2
Asymptotes: y = x , y = − x
Then 0≤z≤1, and a hemispherical cap defined by x^2+y^2+(z−1)^2=16, z≥1.
Simplified
0 ≤ z ≤ 1 , x ^2 + y ^2 + z ^2 − 2 ^z + 1 = 16 , z ≥ 1
For the vector field F=(zx+z^2y+4y, z^3yx+3x, z^4x^2), compute ∬M(∇×F)⋅dS in any way you like.
Vector:
csc ( x ) , x = π
cot ( 3 x ) , x = 2 π 3
cos ( x 2 ) , x = 2 π
Since
( z x + z ^2 y + 4 y , z ^3 y x + 3 x , z ^4 x ^2 ) is constant with respect to F , the derivative of ( z x + z ^2 y + 4 y , z ^3 y x + 3 x , z ^4 x 2 ) with respect to F is 0 .
