Answers
Direct variation is in the form
y = kx
a y = 7x the constant k is 7
b y = 12x the constant k is 12
c y = 1/2x the constant k is 1/2
d y = -4x the constant k is -4
Related Questions
Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.y³ - 2y² - 9y + 18/y² + y - 6Rational expression in lowest terms:Variable restrictions for the original expression: y
Answers
ANSWER
[tex]\begin{gathered} \text{ Rational expression in lowest terms: }y-3 \\ \\ \text{ Variable restrictions for the original expression: }y\ne2,-3 \end{gathered}[/tex]EXPLANATION
We want to reduce the rational expression to the lowest terms:
[tex]\frac{y^3-2y^2-9y+18}{y^2+y-6}[/tex]First, let us factor the denominator of the expression:
[tex]\begin{gathered} y^2+y-6 \\ \\ y^2+3y-2y-6 \\ \\ y(y+3)-2(y+3) \\ \\ (y-2)(y+3) \end{gathered}[/tex]Now, we can test if the factors in the denominator are also the factors in the numerator.
To do this for (y - 2), substitute y = 2 in the numerator. If it is equal to 0, then, it is a factor:
[tex]\begin{gathered} (2)^3-2(2)^2-9(2)+18 \\ \\ 8-8-18+18 \\ \\ 0 \end{gathered}[/tex]Since it is equal to 0, (y - 2) is a factor. Now, let us divide the numerator by (y -2):
We have simplified the numerator and now, we can factorize by the difference of two squares:
[tex]\begin{gathered} y^2-9 \\ \\ y^2-3^2 \\ \\ (y-3)(y+3) \end{gathered}[/tex]Therefore, the simplified expression is:
[tex]\frac{(y-2)(y-3)(y+3)}{(y-2)(y+3)}[/tex]Simplify further by dividing common terms. The expression becomes:
[tex]y-3[/tex]That is the rational expression in the lowest terms.
To find the variable restrictions, set the denominator of the original expression to 0 and solve for y:
[tex]\begin{gathered} y^2+y-6=0 \\ \\ y^2+3y-2y-6=0 \\ \\ y(y+3)-2(y+3)=0 \\ \\ (y-2)(y+3)=0 \\ \\ y=2,\text{ }y=-3 \end{gathered}[/tex]Those are the variable restrictions for the original expression.
How many factors are there for 36? What do you notice about the number of factors of 36 and the number of arrays Courtney can make with the photos
Answers
ANSWER:
9 factors
9 arrays
STEP-BY-STEP EXPLANATION:
The factors of the number 36 are:
[tex]1,2,3,4,6,9,12,18,36[/tex]Which means that there are a total of 9 factors.
The arrays would be:
1 by 36
36 by 1
2 by 18
18 by 2
3 by 12
12 by 3
4 by 9
9 by 4
6 by 6
There are a total of 9 arrays , we can see that the number of arrays is equal to the number of factors
Simplify (3.8 x 10^-2)(5.14 x 10^-10). Write the final answer in scientific notation.
Answers
Answer:
1.9532×10⁻¹¹
Step-by-step explanation:
You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.
ProductThe product is computed in the usual way, making use of the rules of exponents.
(3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)
= 19.532 × 10^(-2-10) = 19.532 × 10^-12
Moving a factor of 10 from the coefficient to the exponent gives ...
= 1.9532×10^-11 . . . . . . final answer in scientific notation
__
Additional comment
Scientific notation has 1 digit to the left of the decimal point in the coefficient.
Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.
Your calculator can display the product in scientific notation for you, as can any spreadsheet.
Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.
<95141404393>
Gene bought a living room suite for P85,000. He agreed to pay in 5 months at 12% simple interest rate. How much will he pay for the furniture?
Answers
Given the cost of the room 85000.
Rate of interest 12%
time =5 months=5/12 year
IN 5 months he will pay as interest
[tex]85000\times\frac{12}{100}\times\frac{5}{12}=4250[/tex]In total, he will pay
[tex]85000+4250=89250[/tex]given f(x)=e^-x^3 find the vertical and horizontal asymptotes
Answers
Given:
[tex]f\mleft(x\mright)=e^{-x^3}[/tex]To find the vertical and horizontal asymptotes:
The line x=L is a vertical asymptote of the function f(x) if the limit of the function at this point is infinite.
But, here there is no such point.
Thus, the function f(x) doesn't have a vertical asymptote.
The line y=L is a vertical asymptote of the function f(x) if the limit of the function (either left or right side) at this point is finite.
[tex]\begin{gathered} y=\lim _{x\rightarrow\infty}e^{-x^3} \\ =e^{-\infty} \\ y=0 \\ y=\lim _{x\rightarrow-\infty}e^{-x^3} \\ y=e^{\infty} \\ =\infty \end{gathered}[/tex]Thus, y = 0 is the horizontal asymptote for the given function.
Which of the following words best completes this sentence? "The real roots of a quadratic equation correspond to the of the graph of the related function."
Answers
This is an example of a quadratic function
The real roots are where it crosses the x axis
Where it crosses the x axis are also called the zeros of the function or the x intercepts. They can also be called the roots of the quadratic.
Without the choices, I am unsure of the words to fill in the blank.
Convert y = 9x2 + 108x - 72 to vertex form by completing the square.
Answers
Answer:
Expressing the equation in vertex form we have;
[tex]y=9(x+6)^2-396[/tex]Vertex at (-6,-396)
Explanation:
We want to convert the quadratic equation given to vertex form by completing the square.
[tex]y=9x^2+108x-72[/tex]The vertex form of quadratic equation is of the form;
[tex]f(x)=a(x-h)^2+k[/tex]To do this by completing the square;
Firstly, let's add 72 to both sides of the qeuation;
[tex]\begin{gathered} y+72=9x^2+108x-72+72 \\ y+72=9x^2+108x \end{gathered}[/tex]Them we will add a number that can make the right side of the equation a complete square to both sides;
Adding 324 to both sides;
[tex]\begin{gathered} y+72+324=9x^2+108x+324 \\ y+396=9x^2+108x+324 \end{gathered}[/tex]factorizing the right side of the equation;
[tex]\begin{gathered} y+396=9(x^2+12x+36) \\ y+396=9(x+6)(x+6) \\ y+396=9(x+6)^2 \end{gathered}[/tex]Then, let us subtract 396 from both sides;
[tex]\begin{gathered} y+396-396=9(x+6)^2-396 \\ y=9(x+6)^2-396 \end{gathered}[/tex]Therefore, expressing the equation in vertex form we have;
[tex]y=9(x+6)^2-396[/tex]Vertex at (-6,-396)
Give the slope and the y intercept of the line 92 2y - 3 = 0. Slope = y intercept = 0, Enter your answers as integers or as reduced fractions in the form A/B
Answers
Answer
Slope = (-9/2)
y-intercept = (-3/2)
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
So, to answer this question, we will express the equation of the line given in this form.
-9x - 2y - 3 = 0
-2y = 9x + 3
Divide through by -2
(-2y/-2) = (9x/-2) + (3/-2)
y = (-9/2)x + (-3/2)
Hope this Helps!!!
write as a product:y raised to the 3 - y raised to the 5
Answers
We will have the following:
[tex]y^3-y^5=y^3(1-y^2)[/tex]***Explanation***
In order to solve we factor the common values.
We can see that the smallest exponent is 3 and if we subtract y^3 from both values we will have that
[tex]y^3-y^5=y^3\cdot1-y^3\cdot y^2[/tex]So, we can see that they share the same common value, thus:
[tex]y^3(1-y^2)[/tex]We also must remember that:
[tex]y^a\cdot y^b=y^{a+b}[/tex](n-1)9. Expand11-11 + 2 + 3 + 4 + 5 + 60 + 1 + 2 + 3 + 4 + 5 + 60 + 1 + 2 + 3 +4 + 5AB(-1) + (-2) + (-3) + (-4) + (-5) + (-6)
Answers
To expand the given summation, we proceed as follows:
[tex]\begin{gathered} \text{Given:} \\ \sum ^6_{n\mathop=1}(n-1) \\ \Rightarrow\text{ }\sum ^6_{n\mathop{=}1}(n)-\text{ }\sum ^6_{n\mathop{=}1}(1) \\ \text{Now:} \\ \sum ^6_{n\mathop{=}1}(n)\text{ is the sum of the first six natural numbers (1,2,3,4,5,6)} \\ \text{And:} \\ \sum ^6_{n\mathop{=}1}(1)\text{ is simply (6}\times1)--That\text{ is, the number 1 added to itself six times } \\ \text{Therefore, we have:} \\ \Rightarrow\text{ }\sum ^6_{n\mathop{=}1}(n)-\text{ }\sum ^6_{n\mathop{=}1}(1) \\ \Rightarrow(1+2+3+4+5+6)-(1+1+1+1+1+1) \\ \Rightarrow(1+2+3+4+5+6)-(6) \\ \Rightarrow(1+2+3+4+5) \\ \end{gathered}[/tex]Therefore:
[tex]\sum ^6_{n\mathop{=}1}(n-1)\text{ = 1+2+3+4+5}[/tex]So, the correct option is option C
This is because the sum: 0+1+2+3+4+5 gives the same value as the sum: 1+2+3+4+5
Graph the system and find the vertices (corners of the darkest shaded area, where the lines intersect) of the region.f(x) = 2x-3f(x) 3XS-2(0, -3). (2.0), (0,0)(-2, 3), (-2,-6), (4,3)(0, -3), (-2,3), (4,3)(3,-2).(-2,-6), (3, 4)
Answers
We are given the following system of inequalities:
[tex]\begin{gathered} f(x)\ge\frac{3}{2}x-3 \\ f(x)\le3 \\ x\le-2 \end{gathered}[/tex]We are told to plot the graphs and find the coordinate of the vertices.
In order to find the vertices we need to plot each inequality.
Plot 1:
[tex]f(x)\ge\frac{3}{2}x-3[/tex]In order to plot this inequality, we simply choose two points because a line can be created with only two points.
The way to choose these two points, is to set x = 0 and find f(x) and set f(x) = 0 and find x. These would help us find the y-intercept and x-intercept respectively.
Let us perform this operation:
[tex]\begin{gathered} f(x)\ge\frac{3}{2}x-3 \\ \text{set x = 0} \\ f(x)\ge\frac{3}{2}(0)-3 \\ f(x)\ge-3 \\ \\ \text{set f(x)=0} \\ 0\ge\frac{3}{2}x-3 \\ \text{add 3 to both sides} \\ 3\ge\frac{3}{2}x \\ \therefore3\times\frac{2}{3}\ge x \\ \\ x\le2 \end{gathered}[/tex]From the above, we just need to plot (0, -3) and (2, 0) to find the inequality plot.
We can see the forbidden region. This is the region that does not conform to the inequalities.
Next, we move to the next system of inequality.
Plot 2:
[tex]f(x)\le3[/tex]Here, we just draw the line f(x) = 3 and then shade the forbidden region as well.
The forbidden region here is above the line because that is the region where f(x) is greater than 3, hence we shade it off.
Finally, the last inequality:
[tex]x\le-2[/tex]Plot 3:
We simply plot the line x = -2 and then shade the forbidden region
After plotting all three, we shall have the following:
j
The points V1, V2, and V3 where the lines meet are the coordinates of the vertices.
A picture of the vertices is attached below:
Thus, the vertices are (-2, 3), (4, 3) and (-2, -6)
The final answer is Option 2
Round to the nearest whole number(I) 18.32 (li) 224.9 (ili) 3.511
Answers
I
Answer:
18
Explanation:
18.32
To round to the nearest whole number, we would consider the term immediately after the decimal point. If it is greater than or equal to 5, the last term before the decimal point increases by 1. If it is less than 5, the last term remains the same. In this case, 3 is less than 5. Thus, 8 remains the same. Thus, to the nearest whole number, the answer is
18
Below is a sample space for a family with 3 children. BGG stands for the oldest child being a boy, the middle child a girl, and the youngest a girl. Use the sample space to answer the question: What is the probability (in simplest form) that the oldest child is a a girl? _____Sample Space BBB BBG BGB BGG GBB GBG GGB GGG
Answers
The probability that the oldest child is a girl is given by the quotient between two numbers:
- The number of combinations where a girl is the oldest child i.e. the number of elements in the sample space that start with a G.
- The total number of elements in the sample space.
The first number is 4 since we have 4 elements starting with G: GBB, GBG, GGB, GGG. The second number is 8. Therefore the probability that we are looking for is given by:
[tex]P=\frac{4}{8}=\frac{1}{2}[/tex]AnswerThen the answer is 1/2.
The equation that models Earth's elliptical orbit around the sun is (x+2.5)^2/22,350.25+y^2/22,344=1 in millions of kilometers. If the sun is located at one focus and it’s coordinates are (0,0), find Earth's farthest distance from the sun in millions of kilometers.
Answers
Given the equation of the elliptical orbit is (x+2.5)^2/22,350.25+y^2/22,344=1.
This equation can be written as
[tex]\begin{gathered} \frac{(x+2.5)^2}{22350.25}+\frac{y^2}{22344}=1 \\ \frac{(x+2.5)}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1 \end{gathered}[/tex]Now, if we shift this path by 2.5 units to left then we get
[tex]\frac{x^2}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1[/tex]The farthest distance of the earth from the sun will be 149.5 - 2.5 = 147 million of kilometers
Thus, option C is correct.
what can you prove congruent from your given
Answers
Answer:
a. line OL bisects angle MLN
b. triangle MLO is congruent to triangle OLN
c. line OL proves that they are congruent through reflexive property.
Step-by-step explanation:
hope this helps!
the graph shows the relationship between the length of time Ted spends knitting and the number of scars he Knits. what does 16 meak in this situation ( ima send a picture of the graph )
Answers
we have the point (1,16)
that means
1 scar
16 hours
is the option C
David and Victoria are playing ths integer card game. David drew three cards, -6, 12, and -4. What is the sum of the cards in his hands? Model your answer on the number line below. PLEASE HELP. Brainliest, will give.
Answers
The sum of -6 ,12 and -4 is,
[tex]\begin{gathered} S=-6+12-4 \\ S=2 \end{gathered}[/tex]Express it on number line implies,
list the following information about the function: y = 2 (x-3)^2-1 (parent graph y = x^2)
Answers
Given
The function is defined as:
[tex]y\text{ = 2\lparen x -3\rparen}^2\text{ - 1}[/tex]x-intercepts
The x-intercepts of the function y are the values of x when y = 0
Substituting 0 for y and solving for x
[tex]\begin{gathered} 2(x-3)^2\text{ -1 = 0} \\ 2(x-3)^2\text{ = 1} \\ Divide\text{ both sides by 2} \\ (x-3)^2\text{ = }\frac{1}{2} \\ Square\text{ root both sides} \\ x-3\text{ = }\pm\sqrt{\frac{1}{2}} \\ x\text{ = 3 }\pm\text{ }\sqrt{\frac{1}{2}} \end{gathered}[/tex]Hence, the x-intercepts are:
[tex](\sqrt{\frac{1}{2}}\text{ + 3, 0\rparen, \lparen-}\sqrt{\frac{1}{2}}\text{ + 3,0\rparen}[/tex]y-intercepts
The y-intercepts are the values of y when x = 0
[tex]\begin{gathered} y\text{ = 2\lparen0-3\rparen}^2-\text{ 1} \\ =\text{ 2}\times9-1 \\ =\text{ 17} \end{gathered}[/tex]Hence, the y-intercept is (0, 17)
Maximum or minimum of the function
The given equation is in vertex form.
[tex]\begin{gathered} y\text{ = a\lparen x-h\rparen}^2\text{ + k} \\ Where\text{ \lparen h,k\rparen is the vertex} \end{gathered}[/tex]Hence, the minimum value of the function is (3,-1)
Elizabeth wraps a gift box in the shape of a square pyramid. The figure below shows a net for the gift box. 6 in 6.8 in
Answers
The wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
Dimension of the square base:
Side = 6.8 in.
Area of the base = 6.8 in. × 6.8 in.
A = 46.24 in.²
Dimension of the triangle:
Base = 6.8 in.
Height = 6 in.
Area of 1 triangle = 1/2 × 6.8 in. × 6 in.
A (triangle) = 20.4 in.²
Area of 4 triangles = 4 × 20.4 in.²
A' = 81.6 in.²
Total area of the square pyramid = A + A'
T = 46.24 in.² + 81.6 in.²
T = 127.84 in.²
Therefore, the wrapping paper used by Elizabeth is equal to the area of the square pyramid which is 127.84 in.².
Learn more about area here:
https://brainly.com/question/25292087
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Your question is incomplete. Please refer the content below:
Elizabeth wraps a gift box in the shape of a square pyramid.
The figure below shows a net for the gift box.
How much wrapping paper did she use?
What is the positive solution for x^3 + 3x - 9 = x -1 + 2x?
Answers
Given:
[tex]\begin{gathered} x^3+3x-9=x-1+2x \\ x^3+3x-9=3x-1 \\ x^3+3x-3x=-1+9 \\ x^3=8 \\ x^3=2^3 \\ \text{Therefore, x=2} \end{gathered}[/tex]Hence, the postive solution for the gven equation is x=2
Ted has run 12 miles this month. each day he wants to run 3 miles until he reaches his goal of 48 miles. Write an equation and solve
Answers
If x is the number of days Ted is going to run, the given situation can be written in an algebraic way as follow:
12 + 3x = 48
12 because this is the number of miles Ted has already ran, 3x is the number of miles Ted has run after x days, and 48 because he wants to reach his goal of 48 miles.
In order to determine how many days he need to reach his goal, you solve the previous equation for x, just as follow:
12 + 3x = 48 subtract 12 both sides
3x = 48 - 12 simplify
3x = 36 divide by 3 both sides
x = 36/3
x = 12
Then, Ted needs 12 days to reach his goal of 48 miles
2. Damian is buying movie tickets to a movie. The tickets cost $4.35 per ticket. Damian has $40.00. What is the greatest amount of tickets he can buy?
Answers
Given:
Cost of one ticket is, c = $4.35.
Total amount with Damian is, T = $40.00.
The objective is to find the number of tickets Damian can buy with this total amount.
Consider the number of tickets as x.
The equation for this situation can be represented as,
[tex]\begin{gathered} \text{Total amount=cost per ticket}\times\text{number of tickets } \\ T=c\times x \end{gathered}[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} 40=4.35x \\ x=\frac{40}{4.35} \\ x=9.19 \\ x\approx9 \end{gathered}[/tex]Hence, Damian can buy maximum 9 tickets with total cost of $40.00.
Deb's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 34 sodas in all, 50% of which were regular. How many regular sodas did the diner serve?
Answers
We can set this equation up by saying: 34 x .50
If we plug this into a calculator we get:
17 regular sodas served by the diner
hi I don’t understand this question,can u do it step by step? Thanks!
Answers
The rule of the division of differentiation is
[tex]\frac{d}{dx}(\frac{u}{v})=\frac{u^{\prime}v-uv^{\prime}}{v^2}[/tex]The given function is
[tex]y=f(x)=\frac{x^2+3x+3}{x+2}[/tex]a)
Let u the numerator and v the denominator
[tex]\begin{gathered} u=x^2+3x+3 \\ u^{\prime}=2x+3 \end{gathered}[/tex][tex]\begin{gathered} v=x+2 \\ v^{\prime}=1 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} \frac{dy}{dx}=\frac{(2x+3)(x+2)-(x^2+3x+3)(1)}{(x+2)^2} \\ \frac{dy}{dx}=\frac{2x^2+7x+6-x^2-3x-3}{(x+2)^2} \\ \frac{dy}{dx}=\frac{x^2+4x+3}{(x+2)^2} \\ \frac{dy}{dx}=\frac{(x+3)(x+1)}{(x+2)^2} \end{gathered}[/tex]We will differentiate dy/dx again to find d^2y/dx^2
[tex]\begin{gathered} u=x^2+4x+3 \\ u^{\prime}=2x+4 \end{gathered}[/tex][tex]\begin{gathered} v=(x+2)^2=x^2+4x+4 \\ v^{\prime}=2x+4 \end{gathered}[/tex]Then substitute them in the rule above
[tex]\begin{gathered} \frac{d^2y}{dx^2}=\frac{(2x+4)(x^2+4x+4)-(x^2+4x+3)(2x+4)}{(x^2+4x+4)^2} \\ \frac{d^2y}{dx^2}=\frac{(2x+4)\lbrack x^2+4x+4-x^2-4x-3\rbrack}{(x^2+4x+4)^2} \\ \frac{d^2y}{dx^2}=\frac{(2x+4)\lbrack1\rbrack}{(x^2+4x+4)^2} \\ \frac{d^2y}{dx^2}=\frac{(2x+4)}{(x+2)^4} \\ \frac{d^2y}{dx^2}=\frac{2(x+2)}{(x+2)^4} \\ \frac{d^2y}{dx^2}=\frac{2}{(x+2)^3} \end{gathered}[/tex]b)
The turning point is the point that has dy/dx = 0
Equate dy/dx by 0 to find the values of x
[tex]\begin{gathered} \frac{dy}{dx}=\frac{(x+3)(x+1)}{(x+2)^2} \\ \frac{dy}{dx}=0 \\ \frac{(x+3)(x+1)}{(x+2)^2}=0 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} (x+3)(x+1)=0 \\ x+3=0,x+1=0 \\ x+3-3=0-3,x+1-1=0-1 \\ x=-3,x=-1 \end{gathered}[/tex]Substitute x by -3 and -1 in f(x) to find y
[tex]\begin{gathered} f(-3)=\frac{(-3)^2+3(-3)+3}{-3+2} \\ f(-3)=\frac{3}{-1} \\ y=-3 \end{gathered}[/tex][tex]\begin{gathered} f(-1)=\frac{(-1)^2+3(-1)+3}{-1+2} \\ f(-1)=\frac{1}{1} \\ y=1 \end{gathered}[/tex]The turning points are (-3, -3) and (-1, 1)
c)
To find the inflection point equate d^2y/dx^2 by 0 to find x
[tex]\begin{gathered} \frac{d^2y}{dx^2}=\frac{2}{(x+2)^3} \\ \frac{d^2y}{dx^2}=0 \\ \frac{2}{(x+2)^3}=0 \end{gathered}[/tex]By using the cross multiplication
[tex]2=0[/tex]Which is wrong 2 can not be equal to zero, then
NO inflection point for the curve
d)
Since the denominator of the curve is x + 2, then
Equate it by 0 to find the vertical asymptote
[tex]\begin{gathered} x+2=0 \\ x+2-2=0-2 \\ x=-2 \end{gathered}[/tex]There is a vertical asymptote at x = -1
Since the greatest power of x up is 2 and the greatest power of down is 1, then there is an Oblique asymptote by dividing up and down
[tex]\begin{gathered} \frac{x^2+3x+3}{x+2}=x+1 \\ y=x+1 \end{gathered}[/tex]The Oblique asymptote is y = x + 1
No horizontal asymptote
e)
This is the graph of y = f(x)
This is the graph of y = f(IxI)
f)
For the curve
[tex]y=\frac{x^2-3x+3}{2-x}[/tex]Take (-) sign as a common factor down, then
[tex]\begin{gathered} y=\frac{(x^2+3x+3)}{-(-2+x)} \\ y=-\frac{(x^2-3x+3)}{(x-2)} \end{gathered}[/tex]Since the sign of y is changed, then
[tex]y=-f(x)[/tex]Then it is the reflection of f(x) about the y-axis we can see it from the attached graph
The red graph is f(x)
The purple graph is -f(x) which is the equation of the last part
There is 1 teacher for every 18 students on a school trip. How many teachers are there if 72 students go ve values to create a proportion that can be used to solve the problem.
Answers
Proportion 1 : 18
x : 72
Ratio
1 teacher / 18 students = number of teacher / 72 students
1/18 = x/ 72
x= 72/ 18
x = 4
_____________
Answer
if 72 students go, 4 teaches are required.
_______________
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do you have any question?
What about takes four hours to travel 128 km going upstream and return it takes two hours going down stream what is the rate of the boat in Stillwater and what is the rate of a Current
Answers
Since the rate = distance/time
Since the distance is 128 km
Since the time of upstream is 4 hours
Then the rate of the boat in the still water is
[tex]\begin{gathered} R_s=\frac{128}{4} \\ R_s=32km\text{ per hour} \end{gathered}[/tex]Since the boat took 2 hours downstream, then
The rate of the current is
[tex]\begin{gathered} R_c=\frac{128}{2} \\ R_c=64km\text{ per hour} \end{gathered}[/tex]Logarithmic help is needed. Be sure to note the differences between logarithmic and exponential forms in each equation.
Answers
The pattern in converting logarithmic form to exponential form and vice versa is this:
[tex]y=b^x\leftrightarrow\log _by=x[/tex]For the first exponential equation that is 16 = 8^4/3, our y = 16, b = 8, and x = 4/3. Let's plug this in the logarithmic pattern.
[tex]\begin{gathered} \log _by=x \\ \log _816=\frac{4}{3} \end{gathered}[/tex]The logarithmic form of the first equation is log₈ 16 = 4/3.
Now, let's move to the second one.
[tex]\log _5(15,625)=6[/tex]b = 5, y = 15, 625, and x = 6. Let's plug these in to the exponential pattern.
[tex]\begin{gathered} y=b^x \\ 15,625=5^6 \end{gathered}[/tex]Hence, the exponential form of the second equation is 15, 625 = 5⁶.
Determine the inverse of the function by interchanging the variables and solving for y in terms of X
Answers
We are required to find the inverse of the function
The first step is to interchange the variable x for y
[tex]x=\frac{y}{2}-\frac{3}{2}[/tex]The next step is to make y the subject of the formula
[tex]\begin{gathered} x=\frac{y}{2}-\frac{3}{2} \\ \frac{y}{2}=x+\frac{3}{2} \\ \text{ Multiply the equation throughout by 2} \\ y\text{ = 2x + 3} \end{gathered}[/tex]The answer is y = 2x + 3
Complete the table for the given rule. Rule:y is 2 more than 4 times x
Answers
We have been given the relationship between x and y to be
y = 4x + 2
To complete the table, we will substitute the value of x = 0, 2, and 4 into the equation
when x = 0
y = 4 x 0 + 2 = 0+ 2 = 2
when x = 2
y = 4 x 2 + 2 = 10
when x = 4
y = 4 x 4 + 2 = 18
The answer is given below
Find the Midpoint of the two given endpoints of (-5, 6) and (9,7)
Answers
1) Given those endpoints, we can