The steps to solve the inverse variation will be:
Write the variation equation: y = k/x or k = xySubstitute in for the given values and find the value of kRewrite the variation equation: y = k/x with the known value of kSubstitute the remaining values and find the unknownHow to illustrate the variation example?The example will be y varies inversely with x and y = 2 when x = 5. Find y when x = 30
Step 1: Write the variation equation: y = k/x or k = xy:
k = xy
Step 2: Substitute in for the given values of x and y:
k = (2)(5) = 10
Step 3: Rewrite the variation equation: y = k/x with the known value of k (10):
y = 10/x
Step 4: Substitute the remaining values and find the unknown:
y = 10/30
y = 1/3
Therefore, y is 1/3 when x is 30.
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Give the equation of a line that has
a. no x-intercept
b. one x-intercept and one y-intercept
c. an infinite number of x-intercepts.
d. a y-intercept of -7.
a. x=5
b. y=x
c. y=0
d. y=x-7
Which statements accurately describe how to determine the y-intercept and the slope from the graph below? On a coordinate plane, a line goes through points (0, negative 6) and (3, 0). To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction.
Answer:
To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction.
Which of the diagrams below represents the statement "If it is an triangle,
then it has three vertices?
The answer is Figure A.
What is in a triangle?Three sides, three angles, and three vertices make up a triangle. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.Triangles are three-sided shapes. The various kinds of triangles go by various names. The angles' size and the sides' length determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.A triangle is a closed, two-dimensional object with three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. Triangles can be found in a variety of everyday objects, such as sandwiches, traffic signs, clothes hangers, and billiards racks.
Given: "If it is an triangle, then it has three vertices.
To find which diagram represents the given statement.
From the first diagram
Triangles have three vertices because they are formed by the intersection of three triangles.
using the second diagram
Three vertices make up the triangle's intersection zone.
Therefore, we cannot infer from the second diagram that a triangle has three vertices.
As a result, figure A represents the stated assertion.
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The table below shows the depth of water in a bathtub as it is being filled over time. The data can be modeled by a linear equation where x is the elapsed time in minutes and y is the depth of the water in inches. What does the y-intercept of the linear equation that models the data indicate?
In the linear equation, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
What is the Y-intercept of a Linear equation?A linear equation is modelled in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept of the equation, which is the initial value of y when x is zero.
Using two pair of points from the table, say, (1, 3) and (2, 5), find the slope (m) of the linear equation:
Slope (m) = change in y / change in x = (5 - 3)/(2 - 1)
Slope (m) = 2/1
Slope (m) = 2
To find the y-intercept (b), substitute (x, y) = (1, 3) and m = 2 into y = mx + b
3 = 1(2) + b
3 = 2 + b
Subtract 2 from both sides
3 - 2 = 2 + b - 2
1 = b
b = 1
Thus, the y-intercept, 1, suggests that: A. There was 1 inch of water in the tub when the water was turned on.
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Given the data cleanup problem of removing 0 values from a data set, the ____ algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
According to the statement
We have given that the there is a algorithm which is used to data cleanup problem of removing 0 values from a data set, and scans a list from left to right and copies every legitimate value into a new list.
and we have to explain about that algorithm.
So,
Here we given that the algorithm copies and paste the values in the new files then
the algorithm is called the copy over algorithm.
So, The copy over algorithm is a a single specimen of something that occurs in a multiple edition, such as a book, article, etc. a matter to be reproduced in print or an imitation or reproduction of an original.
So, The copy over algorithm algorithm scans a list from left to right and copies every legitimate value into a new list that it creates.
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What is the value of log5 125?
[tex] \rm log_{5}(125) \\ \rm log_{5}( {5}^{3} ) \\ \rm1 \cdot3 \\ 3 \\ \therefore \tt log_{5}(125) = 3[/tex]
Anne can make 6 headbands 3/5 from meters of cloth. Which expression shows the amount of cloth needed to make 1 headband? What is the solution to the expression?
The amount of cloth needed to make 1 headband is 10 meters.
Unit valueNumber of headbands Anne made = 6Total clothes used = 3/5 metersCloth needed to make 1 headband = Number of headbands Anne made / Total clothes used
= 6 ÷ 3/5
= 6 × 5/3
= (6 × 5) / 3
= 30/3
= 10 meters
Therefore, the amount of cloth needed to make 1 headband is 10 meters.
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A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. what is the name of the polygon?octagonhexagonheptagonquadrilateral
The name of the polygon is (B) hexagon.
What is a hexagon?A hexagon is a six-sided polygon or 6-gon in geometry. The sum of any simple (non-self-intersecting) hexagon's internal angles is 720°.To find the name of the polygon:
Let the number of sides in a polygon be n.Triangles are formed by drawing diagonals from one vertex to each of the others.Because there is no overlapping of the triangles, no diagonal will be drawn back to itself, and the diagonals to each adjacent vertex will lie on top of the adjacent sides, so the number of diagonals from a single vertex is three less than the number of sides or n - 3, and the number of triangles is one more, or n - 2. Number of triangles = number of sides in polygon - 2 Number of triangles = n - 2 n = 4 + 2 n = 6The polygon containing 6 sides is called a hexagon.Therefore, the name of the polygon is (B) hexagon.
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The complete question is given below:
A polygon is broken up into 4 non-overlapping triangles by drawing lines from one vertex to all other non-adjacent vertices. What is the name of the polygon?
A) Octagon
B) Hexagon
C) Heptagon
D) Quadrilateral
Graph. (Shade. Dashed line. Solid line?)
x+3y≥3
Answer:
Since the graph looks like this, I would say solid line
A clock has a diameter of 16 inches. how far does the hour hand travel during 5 hours? use 3.14 for pi.
Distance hour hand travel in 5 hours is 20.94 inches.
What is a diameter?A diameter of a circle is any straight line segment that passes through the center of the circle and has endpoints on the circle in geometry. It is also known as the circle's longest chord. Both definitions apply to the diameter of a sphere.To find the distance hour hand travel in 5 hours:
Let's say the hour hand completed one full round around the clock. If this was the case, it would have been 2[tex]\pi[/tex]×8 inches around. We know that the hour hand only traveled 5 hours around the clock rather than 12, thus our formula is 2[tex]\pi[/tex]×8×( 5/12 ).Distance hour hand travel is 20.94 inches.Therefore, the distance hour hand travel in 5 hours is 20.94 inches.
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Suppose we flip four coins simultaneously: a penny, a nickel, a dime, and a quarter. What is the probability that at least $15$ cents worth of coins come up heads
The probability that at least $15$ cents worth of coins come up heads is
P(H)=1/16
This is further explained below.
What is the probability that at least $15$ cents worth of coins come up heads?Generally, We are doing a simultaneous toss of four coins. How likely is it that every coin will land with the head side facing up?
It has been established by everyone who has participated so far that the solution is 116, which can be written as
(1/2)4=1/16.
On the other hand, a person who is just starting out can benefit from another method to see things.
I'm going to go ahead and make the assumption that each coin is balanced and that each side has an equal chance of facing up.
Each coin has the potential to exist in either of two states (heads or tails). Therefore, there are
2^4 = 16 different permutations (states) that the four coins may be in together as a group.
Only one of these possible permutations results in all heads. This results in the correct value of 1/16.
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Given f(x)=3x^2+kx-7 and the remainder when f(x) is divided by x-4 is 81, then what is the value of k
Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10
How to solve for k?The given parameters are:
f(x) = 3x^2 + kx - 7
Divisor = x - 4
Remainder = 81
To solve for k, we use the remainder theorem
Set the divisor to 0
x -4 = 0
Add 4 to both sides of the above equation
x - 4 + 4 = 0 + 4
This gives
x = 4
Substitute x = 4 in the function f(x) = 3x^2 + kx - 7
f(4) = 3(4)^2 + k * 4 - 7
Evaluate the exponents
f(4) = 3 * 16 + k * 4 - 7
Evaluate the products
f(4) = 48 + 4k - 7
So, we have:
f(4) = 41 + 4k
The remainder is 81.
So, we have
41 + 4k = 81
Subtract 41 from both sides
4k = 40
Divide both sides of the above equation by 4
4k/4 = 40/4
Evaluate the division
k = 10
Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem
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I cant figure this out
24 is the answer! Its all about isolation, i tried to show it a little better in the image attached. Hope this helps!!
David's car was valued at $38,000 in the year 2007. If it is continuously depreciating in value by 6% every year, how much will it be worth in 2017
The car will be worth $20467 in 2017
How to determine the worth in 2017?The given parameters are:
Initial value, a = 38000
Depreciation rate, r = 6%
The value of the car after x years is represented by the following exponential equation
V(x)= a(1 - r)^x
Substitute the known values in the above equation
V(x) = 38000 * (1 - 6%)^x
2017 is 10 years from 2007
This means that x = 10
So, we have:
V(x) = 38000 * (1 - 6%)^10
Evaluate
V(x) = 20467
Hence, the car will be worth $20467 in 2017
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Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of column relative frequencies.
The completed table will have values filled into it accordingly from left to right and the downwards.
What values are required to complete the table?The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.
Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.
For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.
For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.
For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.
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Evaluate the line integral
6 integral yzcosx ds x = t, y = cost, z = sint 0 < t < pi
It looks like the integral is
[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]
With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is
[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]
and so
[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]
Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then
[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]
where in the second-to-last equality, we have
[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]
and
[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]
by symmetry.
Given: f(x) = 2x + 5 and g(x) = x² and h(x) = -2x
h(g(f(x))) =
RETRY
X² +
X +
Answer: [tex]-8x^2 -40x-50[/tex]
Step-by-step explanation:
[tex]h(g(f(x))\\\\=h(g(2x+5))\\\\=h((2x+5)^2)\\\\=h(4x^2 +20x+25)\\\\=-2(4x^2 +20x+25)\\\\=-8x^2 -40x-50[/tex]
The value of the composite function h(g(f(x))) = -8x² - 40x - 50.
We have,
To find the composition h(g(f(x))), we need to substitute the function g(f(x)) into h(x) and simplify.
Given:
f(x) = 2x + 5
g(x) = x²
h(x) = -2x
First, we find g(f(x)) by substituting f(x) into g(x):
g(f(x)) = g(2x + 5) = (2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25
Now, we substitute g(f(x)) into h(x):
h(g(f(x))) = h(4x² + 20x + 25) = -2(4x² + 20x + 25) = -8x² - 40x - 50
Therefore,
The value of the composite function h(g(f(x))) = -8x² - 40x - 50.
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5x + 1 over 2 y2
What is the value of the expression above when x = 3 and y = 2?
Solve the inequality for w .
−9>6+5w
Hi :)
Let's use some Algebra skills to find w ^•^
————————————First off, let's subtract both sides by 6
[tex]\longrightarrow\darkblue\sf{-9-6 > 5w}[/tex]
[tex]\longrightarrow\darkblue\sf{-15 < 5w}[/tex]
Divide both sides by 5
[tex]\longrightarrow\sf{-3 < w}[/tex]
Or
[tex]\longrightarrow\sf{w > -3}[/tex]
[tex]\tt{Learn\:More;Work\:Harder}[/tex]
:)
Which equation represents a population of 370 animals that increases at an annual rate of 11% ?
The equation represents a population of 370 animals that increases at an annual rate of 11% is .
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1.
Given that,
A population of 370 animals that increases at an annual rate of 11%
a = 370, r = 11%
[tex]p=a(1+r)^{t}[/tex]
= [tex]370(1+0.11)^{t}[/tex]
p = [tex]370(1.11)^{t}[/tex]
Hence, The equation represents a population of 370 animals that increases at an annual rate of 11% is .
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can someone pls explain how to do this
The polynomial A is represented as x - 2, making option A the right choice.
In the question, we are asked to find the correct representation of A, when the algebraic expression (x² + x)/(x + 3) can be rewritten as the algebraic expression A + 6/(x + 3), where A is a polynomial.
Thus, we can write an equation,
A + 6/(x + 3) = (x² + x)/(x + 3),
or, A + 6/(x + 3) - 6/(x + 3) = (x² + x)/(x + 3) - 6/(x + 3) {Subtracting 6/(x + 3) from the both sides of the equation}
or, A = (x² + x)/(x + 3) - 6/(x + 3) {Simplifying},
or, A = (x² + x - 6)/(x + 3) {Subtracting the two fractions with the same denominator (x + 3)},
or, A = (x² + 3x - 2x - 6)/(x + 3) {Mid-term factorization},
or, A = {x(x + 3) - 2(x + 3)}/(x + 3) {Taking common},
or, A = {(x - 2)(x + 3)}/(x + 3) {Taking (x + 3) common},
or, A = x - 2 {Cancelling (x + 3) from the numerator and the denominator}.
Thus, the polynomial A is represented as x - 2, making option A the right choice.
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I need help, pls and thx
The solutions for the quadratic equation are given as follows:
x = -1, x = 7/5
What is a quadratic function?A quadratic function is given according to the following rule:
y = ax^2 + bx + c
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
For this problem, the equation is:
5x² - 2x - 7 = 0.
Hence the coefficients are a = 5, b = -2 and c = -7, and then the solutions are found as follows:
[tex]\Delta = (-2)^2 - 4(5)(7) = 144[/tex][tex]x_1 = \frac{2 + \sqrt{144}}{10} = \frac{7}{5}[/tex][tex]x_2 = \frac{2 - \sqrt{144}}{10} = -1[/tex]The solutions are:
x = -1, x = 7/5
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Is the given point interior, exterior, or on the circle (x 2)2 (y - 3)2 = 81? p(8, 4) click on the graphic to choose the correct answer.
From the equation we see that the center of the circle is at (-2,3) and the radius is 9.
So using the distance formula we can see if the distance from the center to the point (8,4) is 9 units from the center of the circle...
d^2=(8--2)^2+(4-3)^2 and d^2=r^2=81 so
81=10^2+1^2
81=101 which is not true...
So the point (8,4) is √101≈10.05 units away from the center, which is greater than the radius of the circle.
Thus the point lies outside or on the exterior of the circle...
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Can someone help me? And possibley tell me how to solve this as well? I'm totally clueless haha
Answer:
3
Step-by-step explanation:
-2 * 3= -6
-1 * 3= -3
0 *3= 0
1 *3 = 3
2* 3 = 6
3 * 3 =9
Answer:
? = 3
Step-by-step explanation:
To find the value of ?, substitute one of the ordered pairs from the table [except (0, 0)] into the given formula and solve for ?.
Given formula:
[tex]\sf y=\boxed{?} \:x[/tex]
Substitute x = 1 and y = 3 into the formula:
[tex]\sf 3=\boxed{?} \:1[/tex]
To isolate ? divide both sides by 1:
[tex]\implies \sf \dfrac{3}{1}=\dfrac{\boxed{?} \:1}{1}[/tex]
[tex]\implies \sf 3=\boxed{?}[/tex]
Therefore, ? = 3:
[tex]\implies \sf y=3x[/tex]
Check by inputting another value of x from the table into the found formula and comparing the calculated y-value:
[tex]\sf x=-2 \implies y=3(-2)=-6 \quad \boxed{\sf correct}[/tex]
[tex]\sf x=3 \implies y=3(3)=9 \quad \boxed{\sf correct}[/tex]
A pizza shop advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. In addition, it is discovered that the quantity of cheese put on the population of all medium pizzas has a normal distribution with mean 0.495 and standard deviation 0.025. Calculate the minimum number of pounds of mozzarella cheese necessary to say that your medium pizza ranked in the top 3% of all medium pizzas in terms of cheese content.
The minimum number of pounds of mozzarella cheese is necessary to say that your medium pizza ranked in the top 3% of all medium pizzas in terms of cheese content.
P(z < 0.2) = 0.5793
What is a normal distribution?Generally, The normal distribution, also known as the Gaussian distribution, is a kind of probability distribution that is symmetric around the mean. This means that it demonstrates that data that are closer to the mean are more likely to occur than data that are farther away from the mean. When represented graphically, the normal distribution takes the shape of a "bell curve."
In conclusion, To begin, we calculate the z score to determine the crucial value. If
[tex]z =\frac{ (x - u)}{ s}[/tex]
x = critical value = 0.5
u = mean = 0.495
Hence
[tex]z =\frac{ (x - u)}{ s}[/tex]
z= 0.2
Therefore, by making use of a table or some other kind of technology, the left-tailed area of this is
P(z < 0.2) = 0.5793
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Complete Question
A pizza shop advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. In addition, it is discovered that the quantity of cheese put on the population of all medium pizzas has a Normal distribution with a mean of 0.495 and standard deviation 0.025. The probability that a randomly selected pizza has less than the advertised amount of mozzarella cheese is:
a) 0.2000
b) 0.5793
c) 0.4207
d) 0.800
A herd of 21 horses has 6 white and some black horses. What is the ratio of white to black horses
The ratio of white to black horses is 2:5.
What is the ratio of white to black horses?Ratio expresses the relationship between two or more numbers. Ratio is used to compare two or more numbers with each other. It shows the frequency that one value is contained within other value(s).
The ratio of white to black horses = number of white horses : number of black horses
number of white horses = 6 number of black horses : total number of horses - number of white horses: 21 - 6 = 15The ratio of white to black horses = 6 : 15
6 : 15 is not expressed in its simplest form yet. To convert the ratio to its simplest form, divide the numbers by a common factor of 6 and 15. A common factor is a number that divides two or more numbers perfectly with leaving any remainder. A common factor of both numbers is 3
(6/3) : (15/3) = 2 : 5
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Please solve quickly
The degenerate conic that is formed when a double cone is sliced at the ap-ex by a plane parallel to the base of the cone is a Point.
What degenerate conic is formed?When a plane that is parallel to the base of a double cone is used to slice the ap-ex, the conic section formed is a circle.
Circles lead to a Point degenerate conic being formed because a single point will be formed on the double cone that separates the shape.
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5 1/2 divided by 1 3/8
Answer:
4
Step-by-step explanation:
1. Convert from mixed number to fraction
[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]
[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]
2. Divide fractions
[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]
Hope this helps
9) In the standard co-ordinate system, which of the following points in the greatest distance from origin? A. (-4, -1) B. (-3, 3) C. (4,0) D. (2, 3)
The point with the greatest distance to the origin is given by:
B. (-3, 3).
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:
D = sqrt(x² + y²).
Hence the distances for each point given in the problem are:
A. Distance = sqrt((-4)² + (-1)²) = sqrt(17).B. Distance = sqrt((-3)² + (3)²) = sqrt(18).C. Distance = sqrt((4)² + 0²) = sqrt(16).D. Distance = sqrt((2)² + 3²) = sqrt(13).Hence option B has the greatest distance.
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Design an experiment that you could conduct in any branch of earth science. identify the independent variable and dependent variable. what safety precautions would you have to take?
Earth science is made of many branches of knowledge concerning all aspects of the Earth system. The main branches are geology, meteorology, climatology, oceanography, and environmental science. Astronomy uses principles understood from Earth to learn about the solar system, galaxy, and universe.
Overview of Earth Science:Only recently have humans begun to understand the complexity of our planet Earth. We have only known for a few hundred years that Earth is just a tiny part of an enormous galaxy, which in turn is a tiny part of an even greater universe.
An important component of experiments is the different variables involved. A variable is any parameter in the experiment that can change. This could be a parameter like temperature, weight or height, or it could be more complex, such as life expectancy or growth rate. Depending on how you set up your experiment, you will use different kinds of variables. There are three basic types to be familiar with.
Independent variable:The first type is the independent variable. This is the variable that is manipulated during an experiment. For example, when experimenting with how fertilisers affects plant growth, the fertiliser is the independent variable because this is the variable that you change. It might help to think of the independent variable as the cause of change in the experiment.
Dependent variable:In contrast to this, the dependent variable is the variable that is affected during an experiment. In our experiment, our dependent variable would be plant growth since this is affected by the amount of fertiliser applied. If you think of the independent variable as the cause, then the dependent variable is the effect.
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