a) Assume y = \(x^{2}\)
\(1b=\frac{k}{1^{2} }\) k = 1b
\(y=\frac{1b}{x^{2} }\)
b) y = 25
\(x^{2}=\frac{16}{25}\)
\(x=\sqrt{\frac{4}{5} ^{2} }\)
x = ±\(\frac{4}{5}\)
x > 0, x = 4/5
{ Equation }
y=16/x² is required equation for y in terms of x and x=4/5 when y=25.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The table of values are
x 1 2 3 4
y 16 4 16/9 1
Given that y is inversely proportional to square of x.
y=k/x²
Let us consider
y=16 and x=1
16=k/1
k=16.
y=16/x²
So y=16/x² is equation for y in terms of x
b) We need to find value of x when y=25
25=16/x²
Use cross multiplication
x²=16/25
Take square root on both sides
√x²=√16/25
x=±4/5
If x>0 , so x=4/5
Hence y=16/x² is required equation for y in terms of x and x=4/5 when y=25.
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2x+6-12x=26 what is the x in this equation
Answer: x=+2
Step-by-step explanation:2x-6=12x-26
We move all terms to the left:
2x-6-(12x-26)=0
We get rid of parentheses
2x-12x+26-6=0
We add all the numbers together, and all the variables
-10x+20=0
We move all terms containing x to the left, all other terms to the right
-10x=-20
x=-20/-10
x=+2
multiply 2x^2(5+3x^2-7x)
Answer:
10x^2+6x^4-14x^3 is the answer
Rational zeros of polynomial function
Help!
Zeros of the given polynomial are -2, 2, -3/2, 3/2
What are zeroes of a polynomial?Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Given a polynomial 1/4(4\(x^{4}\) - 25\(x^{2}\) + 36)
1/4(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0
(4\(x^{4}\) - 25\(x^{2}\) + 36) = 0
4\(x^{4}\) - 16\(x^{2}\) - 9\(x^{2}\) + 36= 0
4\(x^{4}\)(\(x^{2}\) - 4) - 9(\(x^{2}\) - 4) = 0
(4\(x^{4}\)-9)(\(x^{2}\) - 4) = 0
(x+2)(x-2)(2x+3)(2x-3) = 0
x = -2, 2, -3/2, 3/2
Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2
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Sorry to ask but, may I please have help on this question? please and thank you so much!
Answer:
Angle B is 70 degrees.
Step-by-step explanation:
All 3 angles in a triangle add up to 180.
We know that angle A = 40.
So the other two angles combined = 180-40 = 140.
So add up those other 2 angles, set it equal to 140 and solve for x. Then substitute your X back into the provided equation for B. Let's go!
(2x-30) + (x+20) = 140
Combine like terms:
3x -10 = 140
3x = 150
x = 50
Angle B is 2x-30. Substitute x=50 and solve for angle B:
2(50) - 30 = 100-30 = 70
Angle B is 70 degrees.
we know that,
★ Sum of angles of a triangles is 180°
# According To The Question:-
\( \sf \: \longrightarrow \: 40 + (2x-30) + (x+20) = 180\)
\( \sf \: \longrightarrow \: 40 + 2x-30+ x+20= 180\)
\( \sf \: \longrightarrow \: 40 -30+20+ 2x+ x= 180\)
\( \sf \: \longrightarrow \: 10+20+ 2x+ x= 180\)
\( \sf \: \longrightarrow \: 30+ 2x+ x= 180\)
\( \sf \: \longrightarrow \: 30+ 3x= 180\)
\( \sf \: \longrightarrow \: 3x= 180-30\)
\( \sf \: \longrightarrow \: 3x= 150\)
\( \sf \: \longrightarrow \: x=\frac{ 150}{3}\)
\( \sf \: \longrightarrow \: x=50\degree\)
_____________________________________
★ Measure of Angle B :-
\( \sf \: \longrightarrow \: \angle B = (2x-30)\degree\)
\( \sf \: \longrightarrow \: \angle B = 2x-30\degree\)
\( \sf \: \longrightarrow \: \angle B = 2(50)-30\degree\)
\( \sf \: \longrightarrow \: \angle B = 2\times 50-30\degree\)
\( \sf \: \longrightarrow \: \angle B = 100-30\degree\)
\( \sf \: \longrightarrow \: \angle B = 70\degree\)
_____________________________________
18. If f(x) = arccos(x^2), then f'(x) =
The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)
The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.
First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.
Now we'll apply the chain rule. We have:
f'(x) = (derivative of outer function) * (derivative of inner function)
f'(x) = (-1/√(1-u^2)) * (2x)
Since u = x^2, we'll substitute that back into our equation:
f'(x) = (-1/√(1-x^4)) * (2x)
So, the derivative of f(x) = arccos(x^2) is:
f'(x) = -2x / √(1-x^4)
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Find he percent of change from 1250 to 1,755mi
in a 2015 national survey, what percentage of young adults age 18-25 were not current alcohol users?
The question is an illustration of proportion and percentages
The percentage of young adults, age 18-25 were not current alcohol users is 34.92%
The attached graph represents the proportion of those that are surveyed.
From the graph, we have:
\(\mathbf{Total = 18.6 + 27.2 + 20.8 + 11.3}\)
\(\mathbf{Total = 77.9}\)
The number of young adults 18 - 25 that are not current alcohol users are:
\(\mathbf{Young\ adults = 27.2}\)
So, the percentage of this group is:
\(\mathbf{\% Young\ adults = \frac{Young\ adults}{Total} \times 100\%} }\)
This gives
\(\mathbf{\% Young\ adults = \frac{27.2}{77.9} \times 100\%} }\)
\(\mathbf{\% Young\ adults = 0.3492 \times 100\% }\)
Multiply
\(\mathbf{\% Young\ adults = 34.92 \% }\)
Hence, the percentage of young adults, age 18-25 were not current alcohol users is 34.92%
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Select all the true statements given the figure.
A. m∠4 = m∠2
B. m∠4 = m∠1 + m∠2
C. m∠4 = 180 − m∠3
D. m∠4 = m∠1 + m∠2 + m∠3
E. m∠4 = m∠3 + m∠1
The true statement about the given triangle figure is B and C.
What are the properties outer angle of a triangle?The triangle has the following characteristics: All triangles, regardless of kind, have an angle total of 180 degrees. The length of a triangle's two longest sides added together is longer than the third side. Similarly to this, the length of the third side of a triangle third side is shorter than the difference between its two sides.
Given a triangle, where m∠4 is an outer angle. from the properties of the outer angle of the triangle, Each Exterior angle = 180° - Interior angle. This formula can be used if the corresponding interior angle is given. Exterior angle = Sum of Interior opposite angles. The sum of all the exterior angles of a triangle is 360°.
Therefore, only option B and C which is m∠4 = m∠1 + m∠2 and m∠4 = 180 − m∠3 respectively are true statements about the given triangle.
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Solve the following system of equations algebraically. Algebraically, find both the x and y
values at the point(s) of intersection and write your answers as coordinates "(x,y) and (x,y)".
If there are no points of intersection, write "no solution".
6x5= x² - 2x + 10
To find the comparing y-values, we substitute these x-values into both of the first conditions. We should utilize the primary condition:
6x + 5 = x² - 2x + 10,Subbing x = 4 + √21: 6(4 + √21) + 5 = (4 + √21)² - 2(4 + √21) + 10, Working on this situation will give us the comparing y-an incentive for the primary mark of intersection point . By playing out similar strides for x = 4 - √21, we can track down the second mark of intersection point .
Assurance of the convergence of pads - direct mathematical items implanted in a higher-layered space - is a substitute straightforward errand of straight variable based math, to be specific the arrangement of an intersection point arrangement of direct conditions.
Overall the assurance of a crossing point prompts non-straight conditions, which can be tackled mathematically, for instance utilizing Newton emphasis. Convergence issues between a line and a conic segment,
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????????? Any help :)
Answer:
I would say transroptation!
Vicki and Tamra are working on their math homework together. Vicki has worked p problems, and Tamra has worked 4 times as many problems as Vicki. The expression shows how many problems they have worked altogether.
p + 4p
Which of the following is another expression that could be used to get the same result, and what does it represent?
A.
p + 4. This represents that Vicky and Tamra have worked on p + 4 problems altogether.
B.
5p. This represents that Vicky and Tamra have worked on 5p problems altogether.
C.
p + 5. This represents that Vicky and Tamra have worked on p + 5 problems altogether.
D.
5p2. This represents that Vicky and Tamra have worked on 5p2 problems altogether.
Answer:
5p
Step-by-step explanation:
p+4p can be written as 1p+4p. And 1p+4p=5p because 1+4=5.
Can someone help me out with this question, please!?!?!
Stan wants to figure out how fast a roller coaster travels. He finds out that the speed of the roller coaster, in miles per hour, is modeled by the function below where x is time measured in seconds. How fast is the roller coaster traveling at 3 seconds?
r(x)=x^(4)-3x^(2)+5x-10
A: 9 miles per hour
B: 29 miles per hour
C: 54 miles per hour
D: 59 miles per hour
The rollercoaster is 59 miles per hour traveling at 3 seconds.
The correct option is D.
What is speed?
Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is traveling along a route.
Given:
Stan wants to figure out how fast a roller coaster travels.
He finds out that the speed of the roller coaster, in miles per hour, is modeled by the function below where x is time measured in seconds.
The function is,
r(x)=x⁴-3x² +5x -10
At 3 seconds,
r(3) = (3)⁴-3(3)² +5(3) -10
r(3) = 59 miles per hour.
Therefore, r(3) = 59 miles per hour.
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You can multiply -2.2 by 6.2 to find the total variation in water level. What decimal represents the total variation in water level that Ericka observed?
50 points
BRAINLY TO WHO EVER IS FIRST
Simplify
3(2x^4y^6)^5
——————-
(3x^6y^3)^4
Answer:
10/ 3
Step-by-step explanation:
3 × (48 xy) × 5/ (54 x y) × 4
3 × 48x y x 5/ 54 xy × 4
12 × 5/ 18
2 × 5 / 3
10/ 3
hope it helps!
How to simplify radical expressions with variables?.
To simplify radical expressions with variables, identify perfect square factors, simplify the radical by taking out the largest possible integer factor that is a perfect square, and then multiply by the remaining factor outside the radical. Repeat the process until no more simplification is possible.
To simplify radical expressions with variables, follow these steps
Factor the expression under the radical sign into its prime factors.
Identify any perfect squares within the factors.
Rewrite the expression with the perfect squares outside the radical sign and the remaining factors inside.
Simplify any remaining radicals if possible.
Combine any like terms if necessary.
For example, to simplify the expression √(12x²y), you would first factor 12x²y into 2 * 2 * 3 * x * x * y. Then, you would identify the perfect square of x² and rewrite the expression as 2x√(3y). Finally, you could simplify further if possible, but in this case, the expression is already in its simplest form.
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10
이
10
4
Which of the following are integers
2 apples for $1.50 and 8 apples for $6.50, is this a proportional relationship?
Answer:
no
Step-by-step explanation:
$1.50×8=12$ US$ so 12$ for 8ap or 6.50$ for 8ap
The circle graph shows how a family spends its annual Income. If $25,200 is used for Food, Savings, and Insurance combined, what is the total annual income?
housing 21%
food 18%
clothing 17%
auto 14%
entertaining 12%
insurance 11%
savings 7%
Answer:41,328
Step-by-step explanation:
18+7+11=36 36%
100-36=64 64%
25,200 x 164%=41,328
Simplify: 121/11 + 3(4)/2
Please and thank you. :)
Answer:
17
Step-by-step explanation:
I don't know the explanation, but hoped this helped.
help asap please:) i don’t know
Answer:
Step-by-step explanation:
area of triangle = 1/2 × b × h
here,
b = 37 m
h = 30 m
so area = 1/2 × b × h
= 1/2 × 37 × 30
= 555 m^2
hope this helps
plz mark as brainliest!!!!!!!
Tina wrote the equations 3 x minus y = 9 and 4 x + y = 5. What can Tina conclude about the solution to this system of equations?
Answer:
(2, –3) is a solution to the system of linear equations.
Step-by-step explanation:
Given: Equations:
3x - y = 9 --------(1),
4x + y = 5 --------(2),
Add Equation (1) + Equation (2),
3x + 4x = 9 + 5
7x = 14 ( Combine like terms )
x = 2 ( Divide both sides by 7 ),
From equation 1:
3(2) - y = 9
6 - y = 9
-y = 9 - 6 ( Subtraction 6 on both sides )
-y = 3
y = - 3 ( Multiplying -1 on both sides )
1. The earth travels one full rotation around the sun in approximately 365.25 days. How many minutes does it take for the earth to travel one full rotation around the sun
Answer:
Step-by-step explanation:
It takes about 525,600 minutes for the earth to fully rotate around the sun in minutes!
In which quadrant on a graph will (-5, -7) be found? *
Quadrant 1
Quadrant II
Quadrant III
Quadrant IV
Answer:
on a graph will (-5, -7) be found Quadrant III.
The temperature dropped 6°C every hour for 6 hours. What was the total number of degrees the
temperature changed in the 6 hours?
The total change in the temperature was
loc.
The principal of Oceanside middle school recorded the number of students in each class. What was the upper qualities of the class side?
Given:
The given box plot represents the class size of Oceanside middle school.
To find:
The upper quartile of the class side.
Solution:
In a box plot the starting the end or box present the first quartile and third quartile respectively. The line inside the box represents the median. The left and right end points of the segments are the minimum and maximum values respectively.
From the given box-plot it is clear that,
Minimum value = 22
First quartile or lower quartile= 24
Second quartile or median = 25
Third quartile or upper quartile= 26
Maximum value = 29
Therefore, the upper quartile of the class size is 26 student.
on a certain day, a restaurant serves 25 people breakfast and later 37 people lunch. what is the minimum number of different customers that must have visited the restaurant?
The minimum number of different customers that must have visited the restaurant is 8.
It is given that A restaurant offers breakfast to 25 people one day and lunch to 37 people the next.
So, the number of people that taken breakfast in the restaurant = 25
The number of people that took lunch in the restaurant = 37
The bare minimum number of distinct people who must have eaten at the restaurant = 37 -25 = 8
Thus, the minimum number of different customers that must have visited the restaurant is 8.
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The function f has the property that, for all x, 5(f)x=f(5x). If f(20)=40, what is the value of f(4)?
Using the given property, we conclude that:
f(4) = 8
What is the value of f(4)?
We know that our function has the property:
5*f(x) = f(5*x)
Now, we also know that:
f(20) = 40
Notice that we can rewrite:
f(20) = f(5*4)
Using the above property, we know that:
f(20) = f(5*4) = 5*f(4) = 40
Using the last part:
5*f(4) = 40
f(4) = 40/5 = 8
f(4) = 8
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Johanne packed 10 boxes of apples each day for 8 days. What is the total number of boxes Johanne packed?
Answer:
80 10x8 is 80
your welcomr
Calculate the length of AB in each of the following right-angled triangles:
Answer:
AB= 12 AB=18
Step-by-step explanation:
sin(30)=AB/AC
=> AB=Sin(30)*AC
sin(30)=0.5
=>AB=0.5*24=15
sin(30)=AB/AC
=> AB=Sin(30)*AC
sin(30)=0.5
=>AB=0.5*36=18
Answer:
part a: AB = 12cm
part b: AB = 18cm
Step-by-step explanation:
sin(angle)=OPP/HYP
sine of an angle is a ratio of two sides of a right triangle. For sine, the ratio is the opposite side over the hypotenuse. In part a the marked angle is 30° and AB is the opposite side. The hypotenuse is given, 24cm.
So the sin 30°
= opp/hyp
= AB / 24
also given is the fact that sin30°=.5
Substitute that into our equation also.
sin30° = AB/24
.5 = AB/24
multiply both sides by 24.
.5×24 = AB
12 = AB
AB is 12 cm.
Part b is an identical calculation except the hypotenuse is 36cm.
sin30° = AB/36
.5 = AB/36
.5×36 = AB
18 = AB
AB is 18cm.
They may be trying to lead you to discover some shortcut patterns in a 30°-60°-90° triangle. That is that the short leg is HALF the hypotenuse OR the hypotenuse is double the short leg.
A line passes through the point (4, -2) and has a slope of 1/2.
Answer:
a= -6
Step-by-step explanation: