Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ \\ \therefore y=\frac{k}{x^2} \\ where,\text{ }k\text{ is the constant of proportionality} \\ \\ when\text{ }x=1,y=\frac{7}{4} \\ \\ \frac{7}{4}=\frac{k}{1^2} \\ \\ \therefore k=\frac{7}{4} \\ \\ \text{ Thus, we can say} \\ y=\frac{7}{4x^2} \\ \\ \text{ Thus, when }x=3,\text{ we have:} \\ y=\frac{7}{4(3^2)} \\ \\ y=\frac{7}{4\times9} \\ \\ \therefore y=\frac{7}{36} \end{gathered}[/tex]Final Answer
The answer is
[tex]y=\frac{7}{4x^2};y(3)=\frac{7}{36}\text{ \lparen OPTION C\rparen}[/tex]Related Questions
Find the modulo class to which the number belongs for the indicated modulo system.14, modulo 2
Answers
Given:
Given the number 14.
Required: Modulo class where 14 belogs
Explanation:
For the case of mod 2, there are 2 modulo classes, from 0 to 1, equivalent to the remainder when a number 'n' is divided by 2.
14 is divisible by 2. So, the remainder of 14 divided by 2 gives 0. Hence 14 belongs to the modulo class [0].
Final Answer: 14 belongs to the modulo class of 0.
Enter an equation in point-slope form for the line.Slope is -8 and (1,4) is on the line.The equation of the line in point slope form is:
Answers
y - 4 = -8 ( x - 1)
Explanations:The point slope form of the equation of a line is given as:
y - y₁ = m (x - x₁)
Where m represents the slope of the line
(x₁, y₁) are the coordinates of the point
Slope is -8 and (1,4) is on the line
m = -8
x₁ = 1
y₁ = 4
Substituting these into the equation:
y - y₁ = m (x - x₁)
y - 4 = -8 ( x - 1)
Ab and CD are opposite sides so ab are congruent to CD 2a=34 a=17 find the value of each variable
Answers
Two segments of lines or two angles are congruent if the have the same length and the same measure, respectively. In a parallelogram, a geometric figure which opposite sides are parallel, opposite sides are congruent and opposite angles are also congruents.
In this case CD is opposite to AB, so they are congruent and have the same length. Since the segment AB measures 2a and the segment CD mesures 34, then we have the equation
[tex]\begin{gathered} 2a=34 \\ a=\frac{34}{2} \\ a=17. \end{gathered}[/tex]Similarly, the angles A and C are congruent since they are opposite, so their measurement is the same. Since the angle A measures 8b and the angle C measures 112, then we have the next equation
[tex]\begin{gathered} 8b=112 \\ b=\frac{112}{8} \\ b=14 \end{gathered}[/tex]
use the function g=f+4 to find the value of g when f=1use the function u=10c to find the value of u when c=5how about this one use the function u=n-5 to find the value of u when n=7this one use the function h=g+13 to find the value of h when g =1use the function w=14f to find the value of w when f =4
Answers
Given function g=f+4
To find the value of g at f=1
substitute f=1 in the given equation
[tex]\begin{gathered} g=f+4 \\ g=1+4 \\ g=5 \end{gathered}[/tex]So, at f=1, the value of g will be 5.
(b).
At u=10c
to find the value of u at c=5
substitute the value c=5 in the given equation
[tex]\begin{gathered} u=10c \\ u=10\times5 \\ u=50 \end{gathered}[/tex]The value of u at c=5 is 50
(c).
Given function u=n-5
to find the value of u at n=7
substitute the value of n=7 in the given equation
[tex]\begin{gathered} u=n-5 \\ u=7-5 \\ u=2 \end{gathered}[/tex]So the value of u at n=7 is 2
(d).
Given function h=g+13
to find the value of h at g=1
substitute the value g=1 in the given equation
[tex]\begin{gathered} h=g+13 \\ h=1+13 \\ h=14 \end{gathered}[/tex]The value of h at g=1 is 14
(e).
Given function w=14f
to find the value of w at f=4
substitute the value f=4 in the given equation
[tex]\begin{gathered} w=14f \\ w=14\times4 \\ w=56 \end{gathered}[/tex]The value of w at f=4 is 56
COMPARING METHODS Consider the equation x+ 2 = 3x – 4.a. Solve the equation using algebra.
Answers
Answer: 2
We are given the equation
x + 2 = 3x - 4
To solve for x.
Firstly, we need to collect the like terms
x - 3x = -4 - 2
-2x = -6
Divide both sides by -2
-2x/-2 = -6/-2
x = -6/-2
Negative sign will cancel negative sign
x = 6/2
x = 2
The answer is 2
If A= { 1,2,4,5,7,9} and B= {2,3,4} and U = {1,2,3,4,5,6,7,8,9} Find A’
Answers
SOLUTION
Given the sets in the question tab, the following are the solution steps to get the answer
Step 1: Write the given sets
[tex]\begin{gathered} A=\mleft\lbrace1,2,4,5,7,9\mright\rbrace \\ B=(2,3,4\} \\ U=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace \end{gathered}[/tex]Step 2: Find A'
A' denotes the complement of set A. The complement of set A is defined as a set that contains the elements present in the universal set but not in set A. The Universal set is denoted by capital letter U.
Hence, the elements in set A' will be the elements present in the set U but not set A
[tex]A^{\prime}=\mleft\lbrace3,6,8\mright\rbrace[/tex]Which expression represents the relationship between the step number n and the total number of small squares in the pattern? A Step 1 Step 2 Step 3 n²-n n2-1 n²+n n²+1
Answers
We can see in the sequence is :
[tex]0,3,8[/tex]That is a squar of side 1 minus one square so the solution will be:
[tex]n^2-1[/tex]and we can replace the first 3 steps to be sure of the answe so:
[tex]\begin{gathered} 1\to1^2-1=0 \\ 2\to2^2-1=3 \\ 3\to3^2-1=8 \end{gathered}[/tex]The slope of a graph is ratio of the change in the y - variable to the change in the x - variable True or false
Answers
ANSWER
True
EXPLANATION
We want to understand the meaning of slope.
The slope of a graph is known as the rate of change of the dependent variable with the independent variable.
It is the rate of change of the graph.
This means that it tells us how the y values of the graph vary with the x values.
Therefore, the slope of a graph is ratio of the change in the y - variable to the change in the x - variable.
You survey 100 people in your school and ask them if they feel your school has adequate parking.
Only 30% of the sample feels the school has enough parking. If you have 728 students total in your school, how many would you expect out of all the student body that felt there was enough parking?
Answers
Answer:
218 students feel there is enough parking.
Step-by-step explanation:
First, we convert 30% into a decimal by moving the decimal point over twice to get 0.30. Then, we set up this equation:
0.30 x 728 = 218.4
Now, you can't have a fraction of a person, so we round to the nearest whole number to get 218 students.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 6 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Events A and B are independent. The P(A) = 3/5, and P(not B) = 2/3. What is P(A and B)?
Answers
Given:
Events A and B are independent.
P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Required:
P(A and B).
Answer:
We have given that P(A)=
[tex]\frac{3}{5}[/tex]P(not B)=
[tex]\frac{2}{3}[/tex]Then P(B)=
[tex]\begin{gathered} P(B)=1-P(not\text{ B}) \\ P(B)=1-\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Hence, P(A and B)=
[tex]P(A)\cdot P(B)=\frac{3}{5}\times\frac{1}{3}=\frac{1}{5}[/tex]Final Answer:
P(A and B)=
[tex]\frac{1}{5}[/tex]What is the approximate area of the circle? Use 3.141 for pi and do not round your answer.
Answers
The radius of the circle is 2 units and the value of pi is 3.141.
Hence the area of the circle is given by:
[tex]\begin{gathered} A=\pi\times r^2 \\ A=3.141\times2^2 \\ A=12.564 \end{gathered}[/tex]Hence the area is 12.564 square units.
Find the equation for the line that passes through the point (-4,-3) and that is perpendicular to the line with the equation y=3/4x-1
Answers
Given,
The coordinate that lie on the line is (-4, -3).
The equation of line is y = 3/4x-1.
The standard equation of line is,
[tex]y=mx+c[/tex]Here, m is the slope of the line.
On comparing, the slope of the line y = 3/4x-1 with the standard equation of line then m = 3/4.
The relation of two perpendicular line is,
[tex]\begin{gathered} m_1\times m_2=-1_{} \\ \frac{3}{4}\times m_2=-1 \\ m_2=\frac{-4}{3} \end{gathered}[/tex]The equation of line passing through the point (-4,-3) and perpendicular to line y = 3/4x-1 is,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-3)=\frac{-4}{3}(x-(-4)) \\ y+3=\frac{-4}{3}(x+4) \\ 3y+9=-4x-16 \\ 3y=-4x-25 \\ y=\frac{-4x-25}{3} \end{gathered}[/tex]Hence, the equation of line perpendicular to y = 3/4x-1 is y = (-4x-25)/3.
draw out the system on the bottom of the graph and chose what postulate proves the triangle is congruent hlsssaassasasa
Answers
The given postulates are:
hl: Two right triangles are congruent if the hypotenuse and one corresponding leg are equal in both triangles.
sss: Two triangles have the corresponding three sides congruent (3 corresponding sides have the same measure)
aas: Two angles and a side not between those angles are congruent.
sas:Two sides and an angle between those sides are congruent.
asa: Two angles and a side between those angles are congruent.
---------------------
In the system you have two triangles that share side AC. Then one side is congrent in the triangles.
The line AC bisects angles BAD and BCD, it means taht the angle is equal up and down that line.
Then, the system has two angles and the side between those angles congruent. Triangles are congruent by asaThe following sets of data show the high temperatures in four different cities for a week in December
Answers
the data that have the greatest spread are
(3, 12, 25, 34, 51)
Hello, I need some assistance with this homework question please for precalculusHW 23
Answers
ANSWER
slope = 1
EXPLANATION
Given:
Points (1, 2) and (8, 9).
Desired Outcome:
Slope of the line
Applying the slope formula
[tex]slope\text{ = }\frac{y_2\text{ - y}_1}{x_2\text{ - x}_1}[/tex]where:
y2 = 9,
y1 = 2
x2 = 8 and
x1 = 1
Substituting the values
[tex]\begin{gathered} slope\text{ = }\frac{9\text{ - 2}}{8\text{ - 1}} \\ slope\text{ = }\frac{7}{7} \\ slope\text{ = 1} \end{gathered}[/tex]Hence, the slope of the line containing the points (1, 2) and (8, 9) is 1.
suppose that R(x) is a polynomial of degree 12 whose coefficients are real numbers. Also, suppose that R(x) has the following zeros. Answer the following.Edit: if its ok please double-check the answers.
Answers
According to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
It is given to us that -
R(x) is a polynomial of degree 12 whose coefficients are real numbers.
The zeroes of R(x) are -
-6, -2+3i, -2-3i, 5+i
We have to find out -
(a) Another zero of R(x)
(b) The maximum number of real zeroes that R(x) can have
(c) The maximum number of non-real zeroes that R(x) can have
Since R(x) is a polynomial of degree 12, there are in total 12 roots.
(a) If a non-real, complex, root 5+i exists, then so it's conjugate 5-i exists which is another zero of R(x).
(b) Now, the total number of zeroes of R(x) can be stated as -
-6, -2+3i, -2-3i, 5+i, 5-i
From the above list of zeroes, we can see that there are at least 4 non-real zeroes. So, R(x) has a total of 12 zeroes and we know that there are at least 4 non-real zeroes.
Thus, we can say that the maximum number of real zeroes that R(x) can have is 12-4 = 8 real zeroes.
(c) The non-real complex zeroes always exist in conjugate pairs. And the total number of zeroes that R(x) can have is 12. And we already have determined that R(x) can have a maximum of 8 real zeroes.
Thus, the maximum number of non-real zeroes that R(x) can have is 12-8 = 4 non-real zeroes.
Therefore, according to the polynomial roots description, we can conclude that 5-i is another zero of R(x), the maximum number of real zeroes that R(x) can have is 8, and the maximum number of non-real zeroes that R(x) can have is 4.
To learn more about polynomial roots visit https://brainly.com/question/11906453
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18 in3.4.35 km5.6.15.6 amy7 mm7.8.58 yd10.2 m78-* 306.3: 243.47: 144:: 497: 8171 267*: 8417
Answers
We need to calculate the area of the circle
[tex]\begin{gathered} \text{Area of circle =}\pi r^2 \\ \text{radius of circle = 29ft,} \\ Area\text{ of circle = }\pi\text{ }\times(29ft)^2 \\ \text{Area of circle = }\pi\text{ }\times841ft^2 \\ \text{Area of circle = 84}1\pi ft^2 \end{gathered}[/tex]Therefore
The area of the circle is 841 square feet
the sum of z and 24 is equal to 116
Answers
Given that the sum of z and 24 equals 116, we can represent this statement as follows
We can then proceed to solve the equation by following the steps below:
[tex]z+24=116[/tex]Step 1: subtract 24 from both sides
[tex]z+24-24=116-24[/tex]Step 2: simplify the expression
[tex]z=92[/tex]Thus the value of Z = 92
y=8x+3 ordered pairs
Answers
Answer: (1, 11) and (-1, -5), OPTION C
We are given the equation
y = 8x + 3
This implies that the value of y is a function of x
Firstly, we need to test the options
For (1, 11)
From the point given, let x = 1 and y = 11
Substitute the value of x and y in the above equation
Since, y = 8x + 3
11 = 8(1) + 3
11 = 8 + 3
11 = 11
This implies that (1, 11) satisfied the equation y = 8x + 3
For (-1, -5)
Let x = -1 and y = -5
-5 = 8(-1) + 3
-5 = -8 + 3
-5 = -5
The point (-1, -5) satisfies the equation y = 8x + 3
Hence, the answer is (1, 11) and (-1, -5)
What is the area of parallelogram ABCD?This is a diagram of parallelogram ABCD. Point A is located at (2,1). Point B is located at (8,1). Point C is located at (11,5). Point D is located at (5,5).A. 30 units²B. 55 units²C. 24 units²D. 12 units²
Answers
If we draw the given points, we have the following:
The area of a parallelogram can be calculated as the height of it multiplied by its lenght of the base.
In this case, the height will be the distance of the coodinate y = 1 to the coordinate y = 5, which is equal to Δy = 5-1 = 4.
And the base is the distance from the point A to point B, which can be calculated as Δx = 8 - 2 = 6
Now, using the formula, we have:
[tex]\begin{gathered} A_{parallelogram}=b\times h \\ \\ A_{parallelogram}=6\times5 \\ \\ A_{parallelogram}=30\text{ }units² \end{gathered}[/tex]From the solution developed above, we are able to conclude that the correct answer for the present question is:
A. 30 units²Evaluate the expression 25 – 14 +3.
Answers
ANSWER
14
EXPLANATION
We want to evaluate the expression given:
25 - 14 + 3
First, let us evaluate the subtraction (25 - 14). We are left with:
11 + 3
Now, evaluate:
14
That is the answer
calculate the female's BMI. Round your answer to one decimal place.
Answers
For the 17 year old female with:
Weight: 145 lbs
Height: 5'4''→64 inches
[tex]BMI=\frac{703w}{h^2}[/tex]w= weight (pounds)
h= height (inches)
Replace the given values in the formula to determine the girl's BMI
[tex]\text{BMI}=\frac{703\cdot145}{(64)^2}=24.89[/tex]The girl's BMI is 24.89
A helthy weight is considered to be w
Some the quadratic equation by completing the square.x^2+4x-11=0First choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution separate them with commas.
Answers
By completing the square, we have:
[tex]\begin{gathered} x^2+4x=11 \\ x^2+4x+2^2=11+2^2 \\ (x+2)^2=11+4 \\ (x+2)^2=15 \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} (x+2)=\pm\sqrt[]{15} \\ x=+\sqrt[]{15}-2\text{ OR x= -}\sqrt[]{15}-2 \\ x=3.8729-2\text{ OR -3.8729-2} \\ x=1.873\text{ OR -5.873} \end{gathered}[/tex]Derive the following functionsa) (2x+1)⁴b) f(x) = [tex] \sqrt{6x + 3} [/tex]
Answers
Given:
18.
[tex]f(x)=\sqrt[]{6x-3}[/tex]To find the derivative of the given function, we apply chain rule first:
Therefore, the answer is :
[tex]\frac{3}{\sqrt[]{6x-3}}[/tex]a)Kat's equation b) Carter's equation c) After how many car washes will they both have the same amount of money? d) How much money will they each have
Answers
Answer:
a) Kat's equation is 10 + 12x = Amount
b) Carter's equation is 85 + 7x = Amount
c)
Explanation:
Kat has $10 saved up in her account and charges $12 for each car she washes, the equation representing this is:
10 + 12x
Where x is the number of cars she washes.
Carter's equation is:
85 + 7x
I
Please ensure that you provide the important points (the x and y - intercepts, and the vertices),and please clearly label them on the Cartesian coordinate system. [15 points]
Answers
Given the piece-wise function
[tex]k(x)=\begin{cases}|x|,x\ge3 \\ \\ 2x^2-4x+3,x<3\end{cases}[/tex]The graph of
[tex]|x|\text{ for x }\ge3[/tex]Is shown below
The graph of
[tex]2x^2-4x+3\text{ for x < 3}[/tex]Is shown below
The graph of the piece-wise function is shown below
The blue curve represents the quadratic function and the red line represent the absolute function
Add (c + 3) + ( + 6) Add and Subtract polynomials
Answers
The given polynomial expression is
(c + 3) + (c + 6)
By opening the brackets, we have
c + 3 + c + 6
By collecting like terms, we have
c + c + 3 + 6
2c + 9
The final answer is 2c + 9
Solve the inequality. −2x+3>x−18 Enter the exact answer in interval notation.
Answers
Step 1
Given;
[tex]-2x+3>x-18[/tex]Required; To solve the inequality
Step 2
Bring like terms together
[tex]-2x-x>-18-3[/tex]Step 3
Simplify
[tex]-3x>-21[/tex]Step 4
Multiply both sides by -1
[tex]-3x(-1)<-21(-1)_{}[/tex]Step 5
Simplify
[tex]3x<21[/tex]Step 6
Divide by 3 and get the answer
[tex]\begin{gathered} \frac{3x}{3}<\frac{21}{3} \\ x<7 \\ In\text{ in}terval\text{ notation;} \\ (-\infty,7) \end{gathered}[/tex]Hence, the exact answer in interval notation is;
(-∞,7)
2m + 7 =9 solution please
Answers
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is y=-0.2x + 1. Graph the equation and use it to answer questions 1 and 2. a. What is the x-intercept? What does it represent? b. What is the y-intercept? What does it represent?c. After how many hours is the battery power at 75%d. what is the percentage of battery power remaining at 3 hours?
Answers
The percent y (in decimal form) of battery power remaining x hours after you turn on a laptop computer is given by
[tex]y=-0.2x+1[/tex]Let us graph the above equation
a. What is the x-intercept? What does it represent?
The x-intercept is the point where the line intersects the x-axis.
From the graph, we can see that the x-intercept is (5, 0)
The x-intercept represents that it takes 5 hours for the battery power to go to 0%
You can manually find out the x-intercept by substituting y = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ 0=-0.2x+1 \\ 0.2x=1 \\ x=\frac{1}{0.2} \\ x=5 \end{gathered}[/tex]Therefore, the x-intercept is (5, 0)
b. What is the y-intercept? What does it represent?
The y-intercept is the point where the line intersects the y-axis.
From the graph, we can see that the y-intercept is (0, 1)
The y-intercept represents that the battery power is 1 (100%) when x = 0 hours.
You can manually find out the y-intercept by substituting x = 0 into the given equation
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(0)+1 \\ y=1 \end{gathered}[/tex]Therefore, the y-intercept is (0, 1)
c. After how many hours is the battery power at 75%
We need to substitute y = 0.75 (that means 75%) into the equation to find out x (number of hours)
[tex]\begin{gathered} y=-0.2x+1 \\ 0.75=-0.2x+1 \\ 0.75+0.2x=1 \\ 0.2x=1-0.75 \\ 0.2x=0.25 \\ x=\frac{0.25}{0.2} \\ x=1.25\: \text{hours} \end{gathered}[/tex]Therefore, after 1.25 hours, the battery power is at 75%
d. what is the percentage of battery power remaining at 3 hours?
We need to substitute x = 3 hours into the equation to find out y (remaining battery power)
[tex]\begin{gathered} y=-0.2x+1 \\ y=-0.2(3)+1 \\ y=-0.6+1 \\ y=0.4 \end{gathered}[/tex]Therefore, the remaining battery power is 40% after 3 hours.