I need help with this practice I’m struggling to solve it, I have already attempted it but I’m dealing uneasy on my final answer
Answers
Answer:
y = 7 csc ( x /2) - 2
Explanation:
The parent csc x function has the range ( - ∞, -1] U [1,∞ ) infinity, meaning its "width" is 2. Now our function has range ( - ∞, -9] U [5,∞ ), with a width of 5 - (-9) = 14, which is two times as much as that of the parent function function. This tells us that the function is vertically stretched by a factor of 14 / 2 = 7, and so we have
[tex]y=7\csc x[/tex]Now, the parent function csc x has vertical asympototes at x = 0 and x = π. Our function, however, has consecutive asymptotes at x = 0 and x = 2 π. Meaning our functin is streched horizontally by a factor of 2. Therefore, we do x --> x / 2 and so we have
[tex]y=7\csc (\frac{x}{2})[/tex]Lastly, we observe that the function is not symmetric about the x-axis, whereas the parent function is. This tells us that some vertical shifting is involved. How much vertical shifting exactly?
We find the answer by finding the midpoint
[tex](-9+5)/2[/tex][tex]=-2[/tex]which is the vertical shift.
Therefore, the final form of our function is
[tex]\boxed{y=7\csc (\frac{x}{2})-2}[/tex]which is our answer!
Related Questions
Summarizing and organizing information Fill in the blanks to complete the chart
Answers
Answer
Explanation
There are different kinds of triangles
A point starts at the location (6,0) and travels 13.8 units CCW along a circle with a radius of 6 units that is centered at (0,0). Consider an angle whose vertex is at (0,0) and whose rays subtend the path that the point traveled. Draw a diagram of this to make sure you understand the context.What is the radian measure of this angle?______ radians What is the degree measure of this angle? ____degrees
Answers
Answer:
2.3 radians
131.78 degrees
Explanation:
We can model the situation as follows:
So, the length of the arc formed by an angle θ in a circumference of radius = 6 units is 13.8 units.
Therefore, we can calculate θ in radians using the following equation:
[tex]s=r\theta[/tex]Where s is the length of the arc and r is the radius of the circle.
So, replacing the values and solving for θ, we get:
[tex]\begin{gathered} 13.8=6\cdot\theta \\ \frac{13.8}{6}=\frac{6\cdot\theta}{6} \\ 2.3\text{ radians = }\theta \end{gathered}[/tex]On the other hand, 3.14 radians are equivalent to 180 degrees, so 2.3 radians are equal to:
[tex]2.3\text{ radians}\times\frac{180\text{ degrees}}{3.14\text{ radians}}=131.78\text{ degrees}[/tex]So, the measure of the angle is 2.3 radians and 131.78 degrees.
which of the following is an x-intercept of the function, f(x)=x^2-25?a. -25b. -20c. -15d. -5
Answers
We are given
[tex]f(x)=x^2-25[/tex]We want to find the x-intercept
Solution
To get the x-intercept, we need to put
[tex]f(x)=0[/tex]and we will solve for x
[tex]\begin{gathered} f(x)=0 \\ x^2-25=0 \\ (x-5)(x+5)=0 \\ x=-5,5 \end{gathered}[/tex]Thus, the intercept in the option given is -5
Option D
About 29% of the world's surface is covered by land. Shade the model below to represent the percent covered by water.
Answers
About 29% of the world's surface is covered by land. Shade the model below to represent the percent covered by water.
_____________________________
The percent covered by water
29% = (29/ 100) * 100
29/ 100 = 0.29
(1 - 0.29) = 0.71
About 0.71 of the world's surface is covered by water
Find a quadratic function with the given zeros and passing through the given point.
Answers
The Solution.
The given zeros of the quadratic function are
[tex]x=\frac{1}{7},x=0[/tex]This implies that
[tex]\begin{gathered} x=\frac{1}{7} \\ \text{cross multiplying, we get} \\ 7x=1 \\ 7x-1=0 \\ \text{ Similarly, x=0} \end{gathered}[/tex]The required quadratic function can be obtained as below:
[tex]\begin{gathered} (7x-1)x=0 \\ \text{Clearing the bracket, we get} \\ f(x)=7x^2-x=0 \end{gathered}[/tex]So, the required quadratic function is
[tex]\begin{gathered} f(x)=a(7x^2-x=0)\ldots\text{eqn}(1) \\ \text{where a is a constant, to be determined.} \end{gathered}[/tex]To find the value of a, we shall apply the given initial values, that is,
[tex](4,-3)\Rightarrow x=4,f(x)=-3[/tex]We get,
[tex]-3=a\lbrack7(4^2)-4\rbrack[/tex][tex]\begin{gathered} -3=a(7\times16-4) \\ -3=a(112-4) \end{gathered}[/tex][tex]\begin{gathered} -3=a(108) \\ -3=108a \\ \text{Dividing both sides by 108, we get} \\ a=-\frac{3}{108} \\ \\ a=-\frac{1}{36} \end{gathered}[/tex][tex]\text{ Substituting -}\frac{1}{36}\text{ for a in eqn(1) above, we get}[/tex][tex]\begin{gathered} f(x)=-\frac{1}{36}(7x^2-x=0) \\ \\ f(x)=-\frac{7}{36}x^2+\frac{1}{36}x=0\text{ } \\ Or \\ \text{Multiplying through the equation by 36, we get} \\ 7x^2+x=0 \end{gathered}[/tex]Hence, the correct quadratic function is
[tex]\begin{gathered} f(x)=-\frac{7}{36}x^2+\frac{1}{36}x=0 \\ Or \\ f(x)=7x^2+x=0 \end{gathered}[/tex]List the x-values in the graph at which the function is not differentiable. 2 X 1 2 Ox=2 O x=0, x= 1, x = 2 O x = 0 O x= 1
Answers
Answer:
x = 0
Explanation:
The function is not differentiable in a point if the limit when you get closer to that number from the right is distinct from the limit when you get closer to that number from the left.
We can also say that it is not differentiable if there isn't continuity in the graph. Therefore, the answer is x = 0.
Solve. 50/51=41/x no rounding.
Answers
Given:
[tex]\frac{50}{51}=\frac{41}{x}[/tex]Find: x
Explanation:
[tex]\begin{gathered} \frac{50}{51}=\frac{41}{x} \\ x=\frac{41\times51}{50} \\ x=\frac{2091}{50}=41.82 \end{gathered}[/tex]Final answer: the required value of x is 41.82
mr. Winston's class Works in 3 groups 1/4 of the class read 5/8 of the students works with mr. Winston the remainder of class works on an art project what part of the class who worked on the art project
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The fraction of the class working on the art project is;
[tex]\frac{1}{8}[/tex]Here, we want to calculate the fraction of the class that worked on the art project
Mathematically, at any point in time, the total fraction is 1
So, all we have to do here is to sum up the fractions that we have and subtract from 1
We have this as;
[tex]\begin{gathered} 1-\text{ (}\frac{1}{4}+\frac{5}{8}) \\ \\ =\text{ 1- (}\frac{2+5}{8}) \\ =1\text{ - }\frac{7}{8} \\ =\text{ }\frac{1}{8} \end{gathered}[/tex]-8*f(0) + 4*g(-8)I kinda get it but....
Answers
Answer
Explanation
We are asked to solve
[-8 × f(0)] + [4 × g(-8)]
f(0) will be the value of the function y = f(x) when x = 0 on the graph
g(-8) will be the value of the function y = g(x) when x = -8 on the graph
On the graph, we can
Solve for x: 2x²-2x-1=0
Answers
ANSWER
[tex]x=\frac{1}{2}+\frac{\sqrt[]{3}}{2}\text{ and }x=\frac{1}{2}-\frac{\sqrt[]{3}}{2}[/tex]EXPLANATION
Given the equation,
[tex]2x^2-2x-1=0[/tex]We have to solve it for x.
We can solve this using the quadratic formula,
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In our equation a = 2, b = -2 and c = -1,
[tex]x=\frac{2\pm\sqrt[]{(-2)^2-4\cdot2\cdot(-1)}}{2\cdot2}[/tex][tex]x=\frac{2\pm\sqrt[]{4+8}}{4}[/tex][tex]x=\frac{2\pm\sqrt[]{12}}{4}=\frac{2\pm\sqrt[]{4\cdot3}}{4}=\frac{2\pm2\sqrt[]{3}}{4}[/tex]Distribute the denominator into the addition/subtraction,
[tex]x=\frac{2}{4}\pm\frac{2\sqrt[]{3}}{4}=\frac{1}{2}\pm\frac{\sqrt[]{3}}{2}[/tex]The values of x that are solution to this equation are,
[tex]x=\frac{1}{2}+\frac{\sqrt[]{3}}{2}\text{ and }x=\frac{1}{2}-\frac{\sqrt[]{3}}{2}[/tex]What is the scale factor from drawing 2 to drawing 1?
Answers
ANSWER
5/6
EXPLANATION
We want to find the scale factor from drawing 2 to drawing 1.
The scale factor can be found by dividing the length of the corresponding side of the image by that of the pre-image.
This means that we have to divide the length of side of drawing 1 by drawing 2.
The length of side of drawing 1 is 10 and that of drawing 2 is 12.
Therefore, we have that the scale factor is:
[tex]\begin{gathered} \frac{10}{12} \\ =\frac{5}{6} \end{gathered}[/tex]That is the scale factor.
Jimmy has been collecting nickels and quarters.His coin collection consists of 154 coins.The total value of his coin collection is $18.90.
Answers
Step 1:
Use the concept below
A nickel is worth 5 cents. A dime is worth 10 cents. A quarter is worth 25 cents.
Let the number of nickel = n
Let the number of quarters = q
Step 2:
You will have to convert cent to the dollar because the total value of coin collection is in dollars.
5 cents = $0.05
25 cents = $0.25
Step 3:
The total number of coins = 154
[tex]\begin{gathered} \text{n + q = 154} \\ 0.05n\text{ + 0.25q = 18.9} \end{gathered}[/tex]Step 4:
Solve the systems of equations to find the values of n and q.
From the first equation, make n the subject of the formula and substitute in the equation 2.
[tex]\begin{gathered} \text{n = 154 - q} \\ 0.05n\text{ + 0.25q = 18.9} \\ 0.05(154\text{ - q) + 0.25q = 18.9} \\ 7.7\text{ - 0.05q + 0.25q = 18.9} \\ 0.2q\text{ = 18.9 - 7.7} \\ 0.2q\text{ = 11.2} \\ q\text{ = }\frac{11.2}{0.2} \\ q\text{ = 56} \end{gathered}[/tex]Step 5:
[tex]\begin{gathered} n\text{ = 154 - q} \\ \text{n = 154 - 56} \\ \text{n = 98} \end{gathered}[/tex]Final answer
98 nickels
56 quarters
Find the coordinates of points L, M, and N, the midpoints of the sides ABC.
Answers
Given:- ABC is a triangle and L, M and N are the mid-points of the AB, BC, and AC.
To find:- The coordinates of L, M, and N.
Solution:-
To calculate the coordinate of L, M and N. We are going to use the mid-point theorem.
The formula is:
[tex]Mid-point\text{ }coordinate=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex](a) First, calculate the coordinate of L.
Here coordinate of A is (0,0) and the coordinate of B is (6q, 6r).
So, the coordinate of L can be calculated as:
[tex]\begin{gathered} Coordinate\text{ }of\text{ }L=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ Coordinate\text{ }of\text{ }L=(\frac{0+6q}{2},\frac{0+6r}{2}) \\ Coordinate\text{ }of\text{ }L=(\frac{6q}{2},\frac{6r}{2}) \\ Coordinate\text{ }of\text{ }L=(3q,3r) \end{gathered}[/tex](b) Now calculating the coordinate of M.
Here the coordinate of B is (6q, 6r) and the coordinate of C is (6p, 0).
So, the coordinate of M can be calculated as:
[tex]\begin{gathered} Coordinate\text{ }of\text{ }M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ Coordinate\text{ }of\text{ }M=(\frac{6q+6p}{2},\frac{6r+0}{2}) \\ Coordinate\text{ }of\text{ }M=(3q+3p,3r) \end{gathered}[/tex](c) Now calculating the coordinate of N.
Here the coordinate of A is (0,0) and the coordinate of C is (6p, 0).
So, the coordinate of N can be calculated as:
[tex]\begin{gathered} Coordinate\text{ }of\text{ }N=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ Coordinate\text{ }of\text{ }N=(\frac{0+6p}{2},\frac{0+0}{2}) \\ Coordinate\text{ }of\text{ }N=(3p,0) \end{gathered}[/tex]Final answer:-
Therefore, the answer is:
[tex]\begin{gathered} Coordinate\text{ }of\text{ }L=(3q,3r) \\ Coordinate\text{ }of\text{ }M=(3q+3p,3r) \\ Coordinate\text{ }of\text{ }N=(3p,0) \end{gathered}[/tex]State if the following are perfect square trinomials. Show work that justifies your conclusion.
Answers
Solution:
Given the equation below;
[tex]x^2-6x+36[/tex]For a perfect square polynomial,
[tex]\begin{gathered} ax^2+bx+c=0 \\ (\frac{b}{2})^2 \end{gathered}[/tex]Where
[tex]b=-6[/tex][tex](\frac{b}{2})^2=(-\frac{6}{2})^2=(-3)^2=9[/tex]Where for a perfect trinomial,
[tex]x^2+2ax+a^2[/tex]And
[tex]\begin{gathered} a^2=(-3)^2=9 \\ a^2=(\frac{b}{2})^2 \\ S\imaginaryI nce,\text{ a}^236 \end{gathered}[/tex]Hence, it is not a perfect square trinomial.
Find the solution for the system of linear equations by substitution:y = 2xy-x= 1
Answers
To find the solution fo the given system of linear equation,
Let's substitute the equation y = 2x to y - x =1. We get,
[tex]\text{ y - x = 1 }\rightarrow\text{ (2x) - x = 1}[/tex][tex]\text{ x = 1}[/tex]Let's now find the value of y by substituting x = 1 to y =2x.
[tex]\text{ y =2x }\rightarrow\text{ y = 2(1)}[/tex][tex]\text{ y = 2}[/tex]Therefore, the system of the linear equation has one solution and it is (1,2).
a local department store offers two payments plans for buying a $270 skateboard.plan 1: a fixed weekly payment of $10.80plan 2: a 120 initial payment plus $6 per weekfor each plan how much money is owed after 12 weeks?plan 2: owes _______ after 12 weeksplan 1 owes ____ after 12 weeksthe blanks are the ones I need help with.
Answers
Problem Statement
The question says a store offers two payment plans; plan 1 is a fixed payment of $10.80 every week and plan 2 is a $6.00 per week payment, with an initial deposit of $120.
We are asked to find the how much would be owed after 12 weeks in both plans.
Solution
Plan 1:
The question says plan 1 is a fixed payment every week of $10.80. This means that every week, one would have to pay $10.80.
This means that:
Week 1, we pay $10.80
Week 2, we pay $10.80, so the total payment would be 2 x $10.80
Week 3, we pay $10.80, so the total payment would be 3 x $10.80
Week 4, we pay $10.80, so the total payment would be 4 x $10.80
There is a pattern to this payment. We can see that for any Week n,
we pay $10.80, so the total payment would be n x $10.80.
Thus, the total payment after 12 weeks is:
[tex]\begin{gathered} 12\times\text{ \$}10.80 \\ =\text{ \$129.60} \end{gathered}[/tex]
Plan 2:
The question says that an initial payment of $120 is made for plan 2. This would mean that the total amount paid on the very first instance of buying the skateboard would be $120.
After paying this $120, the payment becomes $6 per week.
My teacher never taught me how to find the index. i watched tons of videos but still don’t know how to solve this problem
Answers
SOLUTION
Recall that:
The index is the number outside the sqrt. (it’s 2 if it does not have a number).
The radical is the sqrt symbol.
The radicand is the number inside the sqrt symbol.
The given radical is:
[tex]\sqrt[4]{8}[/tex]Therefore, from the above definitions, the index is 4
Rafael'sngular flower bed measures 122 cm long and 63 cm wide.He wants to cover the flower bed in mulch.He knows the area each bag of mulch covers, but only in square feet.(a) Find the area of Rafael's flower bed in square feet. Do notround intermediate computations and round your finalanswer to two decimal places. Use the table of conversionfacts, as needed.A²(b) Rafael wants to cover his flower bed with mulch. He doesn'thave any to begin with and he can't buy partial bags ofmulch. Each bag of mulch covers 2.2 ft². How many wholebags of mulch does Rafael need to buy to completely coverhis flower bed?bags(c) If each bag of mulch costs $3.64, how much will he need tospend on mulch? Write your answer to the nearest cent.$0ExplanationCheckConversion facts for length2.54 centimeters (cm)1 inch (in)1 foot (ft)30.48 centimeters (cm)1 yard (yd)0.91 meters (m)1 mile (mi) 1.61 kilometers (km)Note that means "is approximately equal tFor this problem, treat as if it were =5 i need help with this problem.
Answers
Solution
Step 1:
Convert cm to feet
1 foot = 30.48cm
Step 2
a)
[tex]\begin{gathered} Area\text{ of the flower bed = Length }\times\text{ Breadth} \\ \\ =\text{ }\frac{122}{30.48}\text{ }\times\text{ }\frac{63}{30.48} \\ \\ =\text{ 8.27 square feet} \end{gathered}[/tex]b)
[tex]\begin{gathered} Number\text{ of mulch = }\frac{8.27}{2.2} \\ \\ =\text{ 3.76058} \\ \\ \approx\text{ 4} \end{gathered}[/tex]Rafael needs to buy 4 bags of mulch to completely cover his flower bed.
c)
Each bag of mulch costs $3.64
[tex]\begin{gathered} Cost\text{ for 4 bags = 4 }\times\text{ 3.64} \\ \\ =\text{ \$14.56} \\ \\ =\text{ \$15} \end{gathered}[/tex]A company has found that its rate of expenditure in hundreds of dollars on a certain type of job is given by e’(x)=2x+7, where x is the number of days since it start of the job. Find the total expenditure if the job takes three days
Answers
The given equation represents the rate of expenditure in hundreds of dollars for a certain type of job:
[tex]E^{\prime}(x)=2x+7[/tex]→ x represents the number of days since the start of the job
You have to determine the expenditure, E'(X), when the job takes three days (x=3), to do so replace the number of days into the equation and solve for E'(x)
[tex]\begin{gathered} E^{\prime}(x)=2x+7 \\ E^{\prime}(3)=2*3+7 \\ E^{\prime}(3)=6+7 \\ E^{\prime}(3)=13 \end{gathered}[/tex]The total expenditure for a job that takes 3 days will be 13 hundred dollars.
List five complex numbers that fall inside the shaded region on this graph but do not lie on the curves forming the boundaries of the region.
Answers
When they give us a graph on the Cartesian axis of complex numbers, we have to take into account that the x-axis will be the real ones and the y-axis will be the imaginary ones.
Taking this into account we identify 5 points within the shaded region and they are the following
• 2+i
,• 5-3i
,• -4+3i
,• -4-2i
,• 6-2i
Help asappppp How do you divide the polynomials(x^4+1)/(x+1)
Answers
We can divide polynomials by synthetic division, it only works when you are dividing by a polynomial of degree 1, like in this case (x+1). We are only concerned with the coefficients in the polynomials.
As a first step write the coefficients in an upside down division sign.
Then, put the opposite of the number from the divisor to the left of the division symbol. In this case, we will use -1.
-Now Take the leading coefficient and bring it down below the division symbol, then you multiply this number by the number on the left of the division symbol and place it in the next column. Add the two numbers and place the new number below the division sign, and repeat this procedure.
The numbers below your division signs represent your coefficient, and the last number the remainder.
So in this case, the answer is:
[tex]x^3-x^2+x-1[/tex]with a remainder of 2.
graph 3x +4y=12 please
Answers
To help us to graph the 3x + 4y = 12, we can isolate y
[tex]\begin{gathered} 3x+4y=12 \\ \\ 4y=12-3x \\ \\ y=\frac{12}{4}-\frac{3}{4}x \\ \\ y=3-\frac{3}{4}x \end{gathered}[/tex]Therefore it's a line with equation
[tex]y=3-\frac{3}{4}x[/tex]We have y = 3 when x = 0, and x = 4 when y = 0, therefore
What is the product?(3x-6)(2x2-7x+1)-12x2 +42x-6-12x2 + 21X+66x3 - 33x2 +45x-66x3 - 27x2-39x+6
Answers
Use the distributive property to find the product of the given polynomials:
[tex]\begin{gathered} (3x-6)(2x^2-7x+1) \\ =(3x-6)(2x^2) \\ +(3x-6)(-7x) \\ +(3x-6)(1) \end{gathered}[/tex][tex]\begin{gathered} =(3x)(2x^2)+(-6)(2x^2) \\ +(3x)(-7x)+(-6)(-7x) \\ +(3x)(1)+(-6)(1) \end{gathered}[/tex][tex]\begin{gathered} =6x^3-12x^2 \\ -21x^2+42x \\ +3x-6 \end{gathered}[/tex]Add like terms to simplify the sum:
[tex]\begin{gathered} =6x^3-12x^2-21x^2+42x+3x-6 \\ =6x^3-33x^2+45x-6 \end{gathered}[/tex]Therefore:
[tex](3x-6)(2x^2-7x+1)=6x^3-33x+45x-6[/tex]hello can you help me solve this question and if you are reading this is a homework assignment
Answers
First, we are gonna calculate y
[tex]\tan 15.8=\frac{y}{128\text{ ft}}[/tex][tex]y=128\cdot\tan 15.8[/tex][tex]y=36.22\text{ ft}[/tex]Now the total height:
[tex]\tan 32.7=\frac{h}{128\text{ ft}}[/tex][tex]h=128\cdot\tan 32.7[/tex][tex]h=82.17\text{ ft}[/tex]Now x would be the difference h - y
[tex]x=h-y[/tex][tex]x=82.17-36.22\text{ ft}[/tex][tex]x=45.95\text{ ft}[/tex]x = 46 ft
Select the correct answer.Which pair of expressions are equivalent?OA 2y- 4 and 2y - 4 + 9OB.14x- 7 and 7x - 14Oc9y+ 3 + 2 and 3(y + 1) + 2OD. x + y and x-y+ 2yOE X+ 2y and x - yResetNext© 2022 Edmentum. All rights reserved.
Answers
Remember that
Equivalent expressions are expressions that have the same value
Verify each option
Option A -----> are not equivalent
Option B ----> are not equivalent
Option C ----> are not equivalent
Option D
x+y and x-y+2y
x-y+2y=x+y
so
x+y=x+y -----> are equivalent
Option E ----> are not equivalent
therefore
the answer is option Df(x) Which function could represent this graph? (1) f(x) = (r + 1)(x² + 2) (3) f(x) = (1 - 1)(r? - 4) (2) f(x) = (x - 1)(x - 2) (4) f(x) = (x + 1)(x² + 4)
Answers
SOLUTION
Concept: graph of polynomials functions
The graph of the functions cut the x-axis at three different points from the left they are given as
[tex]x=-2,x=1,x=2[/tex]then the factor of the function becomes
[tex](x+2)(x-1)(x-2)[/tex]Simplifying further by applying difference of two squares the function becomes
[tex]f(x)=(x-1)(x^2-4)[/tex]Therefore the right option is 3
Find the y-intercept and x-intercept of the following linear equation3X-576Answer* KeypadKeyboard ShortcutsEnter the coordinates to plot points on the graph. Any lines or curves will be drawn once all required pointsare plotted.1015y-intercept (A):X105510x-intercept (B):(5-19
Answers
Y-intercept A: (0, -8.4)
X-intercept B: (8, 0)
Explanation:[tex]\begin{gathered} Given: \\ \frac{3}{4}x\text{ -}\frac{5}{7}y\text{ = 6} \end{gathered}[/tex]x-intercept is the value of x when y = 0
To get the x-intercept of the equation, we will substitute y with 0:
[tex]\begin{gathered} \frac{3}{4}x\text{ - }\frac{5}{7}\left(0\right)\text{ = 6} \\ \frac{3}{4}x\text{ - 0 = 6} \\ \frac{3}{4}x\text{ = 6} \\ multiply\text{ through by 4:} \\ 3x\text{ = 6\lparen4\rparen} \end{gathered}[/tex][tex]\begin{gathered} 3x\text{ = 24} \\ divide\text{ both sides by 3:} \\ \frac{3x}{3}\text{ = }\frac{24}{3} \\ x\text{ = 8} \end{gathered}[/tex]x-intercept = 8
In ordered pair: (8, 0)
y-intercept is the value of y when x = 0
To get the y-intercept of the equation, we will susbtitute x with 0:
[tex]\begin{gathered} \frac{3}{4}\left(0\right)\text{ - }\frac{5}{7}y\text{ = 6} \\ 0\text{ - }\frac{5}{7}y\text{ = 6} \\ -\frac{5}{7}y\text{ = 6} \\ multiply\text{ through by 7:} \\ -5y\text{ = 6\lparen7\rparen} \end{gathered}[/tex][tex]\begin{gathered} -5y\text{ = 42} \\ divide\text{ both sides by -5:} \\ y\text{ = 42/-5} \\ y\text{ = -8.4} \end{gathered}[/tex]y-intercept = -8.4
In ordered pair: (0, -8.4)
Y-intercept A: (0, -8.4)
X-intercept B: (8, 0)
Find an equation parallel to y=0 and passing through (-7,4)
Answers
a linear equation is given by the formula:
[tex]y=mx+b[/tex]In the equation y = 0 , the terms m and b are equal to zero
Y = 0x + 0
Then, a parallel equation to y = 0 has the same slope m = 0
y = 0*x + b
y = b
The equation passes through (-7,4), if we replace into the equation above, we get:
y = 0*(-7) + 4
y = 4
Answer: The equation y = 4 is parallel to y = 0 and passes through (-7,4)
Find the mean, median, and mode of the list of values. Round to the nearest tenth if necessary.5, 18, 21, 28, 24, 3, 18, 18
Answers
Given the list of values:
[tex]5,18,21,28,24,3,18,18[/tex]The corresponding frequency table is:
3: 1
5: 1
18: 3
21: 1
24: 1
28: 1
From this, we can say that the mode is:
[tex]\text{Mode }=18[/tex]There are 8 values. Ordering the list:
[tex]3,5,18,18,18,21,24,28[/tex]The position of the median can be calculated using the formula:
[tex]P=\frac{n}{2}[/tex]Where n is the number of values (n = 8). If p is a whole number, then the median is the semi-sum of the data at positions P and P+1. If it is not a whole number, the position of the median is int(P)+1, where int(P) is the integer part of P. Now, using the previous equation:
[tex]P=\frac{8}{2}=4[/tex]The values at positions 4 and 5 are 18 and 18, so the median is:
[tex]\begin{gathered} \text{Median }=\frac{18+18}{2}=\frac{36}{2} \\ \Rightarrow\text{Median }=18 \end{gathered}[/tex]Finally, to find the mean (rounded to 1 decimal place), we use the value of n:
[tex]\begin{gathered} \text{Mean }=\frac{5+18+21+28+24+3+18+18}{8}=\frac{135}{8} \\ \text{Mean }=16.9 \end{gathered}[/tex]What is the center and the radius of the circle: ( x + 6 ) 2 + ( y - 9 ) 2 = 121 ?
Answers
A circle with center at (h,k) and a radius of r has equation
[tex]\left(x−h\right)^2+(y−k)^2=r^2.[/tex]In this case our circle equation can be written as:
[tex](x-(-6))^2+(y-9)^2=11^2[/tex]So, we have: h= − 6 , k = 9 and r = 11. The answer is d. Center = ( - 6,9) and radius = 11.