Write an equation in the form r(x) = p(x) / q(x) for each function shown below.Pls see pic for details
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c.
The line equation is of the form
[tex]y=mx+c\ldots(1)[/tex]From the graph, we observe and find these points
(1,5) and (0,4) lie on the given line.
Substituting x=1, y=5 in equation (1), we get
[tex]5=m(1)+c[/tex][tex]m+c=5\ldots\text{.}(2)[/tex]Substituting x=0, y=4 in equation (1), we get
[tex]4=m(0)+c[/tex][tex]c=4[/tex]Substituting c=4 in equation (2), we get
[tex]m+4=5[/tex][tex]m=5-4[/tex][tex]m=1[/tex]Substituting c=4,m=1 in equation (1), we get
[tex]y=x+5[/tex]We need to write this equation in the form of r(x) = p(x) / q(x).
[tex]r(x)=\frac{p(x)}{q(x)}\ldots(3)[/tex]Let r(x)=x+5, q(x)=x, and subsitute in the equation , we get
[tex]x+5=\frac{p(x)}{x}[/tex]Using the cross-product method, we get
[tex]x(x+5)=p(x)[/tex][tex]x\times x+x\times5=p(x)[/tex][tex]x^2+5x=p(x)[/tex]Substitute values in equation (3), we get
[tex]x+5=\frac{x^2+5x}{x}[/tex]Hence the required equation is
[tex]x+5=\frac{x^2+5x}{x}[/tex]Related Questions
Wayne has a bag filled with coins. the bag contains 7 quarters,8 dimes,3 nickels, and 9 pennies. he randomly chooses a coins from the bag. what is the probability that Wayne chooses a quarter or nickel?
Answers
Wayne has a bag filled with coins.
Number of quarters = 7
Number of dimes = 8
Number of nickels = 3
Number of pennies = 9
So, the total number of coins is
Total = 7 + 8 + 3 + 9 = 27
What is the probability that Wayne chooses a quarter or nickel?
How many coins are either quarter or nickel?
quarter or nickel = 7 + 3 = 10
So, the probability is
[tex]P(quarter\: or\: nickel)=\frac{10}{27}[/tex]Therefore, the probability that Wayne chooses a quarter or nickel is 10/27
true or false 16/24 equals 30 / 45
Answers
True.
Given:
The equation is, 16/24 = 30/45.
The objective is to find true or false.
The equivalent fractions can be verified by, mutiplying the denominator and numerator of each fraction.
The fractions can be solved as,
[tex]\begin{gathered} \frac{16}{24}=\frac{30}{45} \\ 16\cdot45=24\cdot30 \\ 720=720 \end{gathered}[/tex]Since both sides are equal, the ratios are equivalent ratios.
Hence, the answer is true.
how to get standar form from point 1,4 and a slope of 5
Answers
Find the length of AB given that DB is a median of the triangle AC is 46
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ANSWER:
The value of AB is 23
STEP-BY-STEP EXPLANATION:
We know that AB is part of AC, and that DB cuts into two equal parts (half) since it is a median, therefore the value of AB would be
[tex]\begin{gathered} AB=\frac{AC}{2} \\ AB=\frac{46}{2} \\ AB=23 \end{gathered}[/tex]Rewrite 20 - 4x³ using a common factor.
O 4x(5-x²)
O4(5 - 4x³)
02x(10-2x²)
02(10-2x³)
Answers
Answer:
[tex]20 - 4 {x}^{3} = 4(5 - {x}^{3} )[/tex]
Rewrite 4x + 16 using a common factor.
Answer 4(x + 4)
Find the missing quantity with the information given. Round rates to the nearest whole percent and dollar amounts to the nearest cent% markdown = 40Reduced price = $144$ markdown = ?
Answers
The given information:
% mark up = 40
Reduced = $144
Markdown = ?
The formula for percentage markup is given as
[tex]\text{ \%markup }=\frac{markup}{actual\text{ price}}\times100[/tex]Let the actual price be x
Hence,
Reduced price = 60% of actual price
[tex]60\text{\% of x = 144}[/tex]Solving for x
[tex]\begin{gathered} \frac{60x}{100}=144 \\ x=\frac{144\times100}{60} \\ x=240 \end{gathered}[/tex]Therefore, actual price = $240
Inserting these values into the %markup formula gives
[tex]40=\frac{\text{markup}}{240}\times100[/tex]Solve for markup
[tex]\begin{gathered} 40=\frac{100\times\text{markup}}{240} \\ 40\times240=100\times\text{markup} \\ \text{markup}=\frac{40\times240}{100} \\ \text{markup}=96 \end{gathered}[/tex]Threefore, markup = $96
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with theafter-tax total. If the after-tax total was $357.06, and the tax rate in the area is 8.2%, what was the pre-tax subtotal?
Answers
Answer: the pre-tax subtotal is $330
Explanation:
Let x represent the pre tax total
If the tax rate in the area is 8.2%, it means that the amount of tax paid is
8.2/100 * x = 0.082x
pretax total + tax = after tax subtotal
Given that after tax subtotal is $357.06, then
x + 0.082x = 357.06
1.082x = 357.06
x = 357.06/1.082
x = 330
the pre-tax subtotal is $330
In exercises 1 and 2 , identify the bisector of ST then find ST
Answers
Given: The line segment ST as shown in the image
To Determine: The bisector of ST and the value of ST
Solution
It can be observed from the first image, the bisector of ST is line MW
[tex]\begin{gathered} ST=SM+MT \\ SM=MT(given) \\ MT=19(given) \\ Therefore \\ ST=19+19 \\ ST=38 \end{gathered}[/tex]For the second image, the bisector of ST is line LM
[tex]\begin{gathered} ST=SM+MT \\ SM=3x-6 \\ MT=x+8 \\ SM=MT(given) \\ Therefore \\ 3x-6=x+8 \\ 3x-x=8+6 \\ 2x=14 \\ x=\frac{14}{2} \\ x=7 \end{gathered}[/tex][tex]\begin{gathered} SM=3(7)-6=21-6=15 \\ MT=7+8=15 \\ ST=SM+MT \\ ST=15+15 \\ ST=30 \end{gathered}[/tex]For first exercise, the bisector is MW, ST = 38
For the second exercise, the bisector is LM, ST = 30r
a.a + 0 = 0Additive Identityb. Multiplicative IdentityCommutative Property of Additiond. Associative Property of AdditionC.
Answers
Answer:
a. Additive Identity
Explanation:
Given the equation:
[tex]a+0=a[/tex]When zero(0) is added to 'a', the result is still 'a'.
The number 0 is the additive identity of 'a'.
V256 rational or irrational
Answers
First, in order to get to know if 256 it is a rational or irrational number we have to begin with the definition of what is rational and irrational number.
Rational numbers are all the number that can be represented as fractions, while the irrational numbers are all the numbers that can not be expressed as fractions.
In this case, then we can confirm that the number 256 can be considered as a rational number because it can be expressed as the quotient of the two integers: for example 256/1.
What is the simplified form of the expression square root of -64
Answers
What is the simplified form of the expression square root of -64
we have
[tex]\sqrt[]{-64}[/tex]Remember that
64=2^6
and
i^2=-1
substitute
[tex]\sqrt[]{-64}=\sqrt[]{(-1)(2^6)}=\sqrt[]{i^2\cdot2^6}=2^3i=8i[/tex]option BUsing the equation and the ordered-pairs found previously, plot the points on the graph that would best satisfy theequation.y= 2^x
Answers
Given the following equation:
[tex]y=x^2[/tex]We will graph the given function using the points that will be written in ordered-pairs.
The given function is a quadratic function with a vertex = (0, 0)
We will graph the points using five points
The vertex and 4 points, 2 points before the vertex and 2 points after the vertex.
So, we will substitute x = -4, -2, 2, 4
[tex]\begin{gathered} x=-4\rightarrow y=16 \\ x=-2\operatorname{\rightarrow}y=4 \\ x=2\operatorname{\rightarrow}y=4 \\ x=4\operatorname{\rightarrow}y=16 \end{gathered}[/tex]So, the points are: (-4, 16), (-2, 4), (0, 0), (2, 4), (4, 16)
The graph using the points will be as follows:
What is the vertex of the parabola with thefunction rule f(x) = 5(x − 4)² + 9?
Answers
The equation f(x) = a(x - h)^2 + k gives the vertex of the parabola--it is (h, k).
In this question, h = 4 and k = 9. So the vertex is at (4, 9).
At one time, it was reported that 27.9% of physicians are women. In a survey of physicians employed by a large health system, 45 of 120 randomly selected physicians were women. Is there sufficient evidence at the 0.05 level of significance to conclude that the proportion of women physicians in the system exceeds 27.9%?Solve this hypothesis testing problem by finishing the five steps below.
Answers
SOLUTION
STEP 1
The hull hypothesis can written as
[tex]H_0\colon p=0.279[/tex]The alternative hypothesis is written as
[tex]H_1\colon p>0.279[/tex]STEP 2
The value of p will be
[tex]\begin{gathered} \hat{p}=\frac{X}{n} \\ \hat{p}=\frac{45}{120}=0.375 \\ \text{where n=120, x=}45 \end{gathered}[/tex]STEP3
From the calculations, we have
[tex]\begin{gathered} Z_{\text{cal}}=2.34 \\ \text{Z}_{\text{los}}=0.05 \end{gathered}[/tex]We obtained the p-value has
[tex]\begin{gathered} p-\text{value}=0.0095 \\ \text{level of significance =0.05} \end{gathered}[/tex]STEP4
Since the p-value is less than the level of significance, we Reject the null hypothesis
STEP 5
Conclusion: There is no enought evidence to support the claim
Finding a specify term of a geometric sequence given the common ratio and first term
Answers
A geometric sequence is defined as:
[tex]\begin{gathered} a_1=a*r^0=a*r^{1-1}, \\ a_2=a*r^1=a*r^{2-1}, \\ a_3=a*r^2=a*r^{3-1}, \\ ... \\ a_7=a*r^6=a*r^{7-1}, \\ ... \end{gathered}[/tex]Where r ≠ 0 is the common ratio and a ≠ 0 is the first term of the sequence.
From the statement, we know that r = 2/3 and the first term is a = 5.
Replacing these numbers in the expression of the 7th term, we get:
[tex]a_7=5*(\frac{2}{3})^6=5*\frac{64}{729}=\frac{320}{729}.[/tex]Answer320/729
How do I find the gif and distributive property
Answers
By using the GCF and distributive property, the sum of 15+27 = 42
The expression is
15 + 27
GCF is the greatest common factor, the greatest common factor is the highest number that divides exactly into two or more numbers.
The distributive property states that multiplying the sum of two or more variables by a number will produce the same result as multiplying each variables individually by the number and then adding the products together.
The expression is
= 15 + 27
= 3(5 + 9)
= 3 × 14
= 42
Hence, by using the GCF and distributive property, the sum of 15 + 27 = 42
Learn more about distributive property here
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What is the current population of elk at the park?
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Given the following function:
[tex]\text{ f\lparen x\rparen= 1200\lparen0.8\rparen}^{\text{x}}[/tex]1200 represents the initial/current population of elk in the national park.
Therefore, the answer is CHOICE A.
I don't get any of this help me please
Answers
Using scientific notation, we have that:
a) As an ordinary number, the number is written as 0.51.
b) The value of the product is of 1445.
What is scientific notation?An ordinary number written in scientific notation is given as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1.
For item a, to add one to the exponent, making it zero, we need to divide the base by 10, hence the ordinary number is given as follows:
5.1 x 10^(-1) = 5.1/10 = 0.51.
For item b, to multiply two numbers, we multiply the bases and add the exponents, hence:
(1.7 x 10^4) x (8.5 x 10^-2) = 1.7 x 8.5 x 10^(4 - 2) = 14.45 x 10².
To subtract two from the exponent, making it zero, we need to multiply the base by 2, hence the base number is given as follows:
14.45 x 100 = 1445.
More can be learned about scientific notation at https://brainly.com/question/16394306
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gus bought 2/3 pound of turkey and 1/4 pound of ham.The tukey cost 9 dollars per pound, and the ham cost 7 dollars per pound.In all,how much did Gus spend?
Answers
From the information given,
gus bought 2/3 pound of turkey. If tukey costs 9 dollars per pound, it means that the cost of 2/3 pound of turkey is
2/3 x 9 = 6
gus bought 1/4 pound of ham. If ham costs 7 dollars per pound, it means that the cost of 1/4 pound of ham is
1/4 x 7 = 7/4 = 1.75
Total amount spent = amount spent on turkey + amount spent on ham
Total amount = 6 + 1.75
Total amount = $7.75
Write a quadratic function whose graph passes through (3,6) and has the vertex (-2,4) what is the value of Y
Answers
The representation of a quadratic eqauation in vertex form is
[tex]y=a(x-k)^2+h[/tex]The given vertex is,
[tex](k,h)=(-2,4)[/tex]And the given point through which the graph passes is,
[tex](x,y)=(3,6)[/tex]Substitute the values in the formula of quadratic equation.
[tex]\begin{gathered} 6=a(3-(-2))+4 \\ 6=a(3+2)+4 \\ 6=5a+4 \\ 5a=6-4 \\ 5a=2 \\ a=\frac{5}{2} \end{gathered}[/tex]Hence, the equation in vertex form will be,
[tex]\begin{gathered} y=\frac{5}{2}(x-(-2))+4 \\ y=\frac{5}{2}(x+2)+4 \end{gathered}[/tex]You have to write 1/2 page for an assignment. You write 1/5 page. How many pages do you have left to write ?
Answers
To find the number of missing pages:
[tex]\frac{1}{2}-\frac{1}{5}=[/tex]rewriting the expression as homogeneous fractions:
[tex]\frac{1}{2}\times\frac{5}{5}-\frac{1}{5}\times\frac{2}{2}=[/tex]simplifying it:
[tex]\frac{5}{10}-\frac{2}{10}=\frac{3}{10}[/tex]ANSWER
you have left 3/10 page.
Jason is making bookmarks to sell to raise money for the local youth center. He has 29 yards of ribbon, and he plans to make 200 bookmarks.Approximately how long is each bookmark, in centimeters?
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The Solution:
The correct answer is 13.26 centimeters.
Explanation:
Given that Jason has 29 yards of ribbon, and he plans to make 200 bookmarks.
We are asked to find the approximate length (in centimeters) of each bookmark.
Step 1:
Convert 29 yards to centimeters.
[tex]\begin{gathered} \text{ Recall:} \\ \text{ 1 yard = 91.44 centimeters} \end{gathered}[/tex]So,
[tex]29\text{ yards = 29}\times91.44=2651.76\text{ centimeters}[/tex]Step 2:
To get the length of each bookmark, we shall divide 2651.76 by 200.
[tex]\text{ Length each bookmark = }\frac{2651.76}{200}=13.2588\approx13.26\text{ centimeters}[/tex]Therefore, the correct answer is 13.26 centimeters.
THIS IS URGENT
A line includes the points (2,10) and (9,5). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
Answers
Answer:
Step-by-step explanation:
y = 13x -12
The ship leaves at 18 40 to sail to the next port.
It sails 270 km at an average speed of 32.4 km/h
Find the time when the ship arrives.
Answers
Answer:
Step-by-step explanation:
Given:
t₁ = 18:40 or 18 h 40 min
S = 270 km
V = 32.4 km/h
____________
t₂ - ?
Ship movement time:
t = S / V = 270 / 32.4 ≈ 8.33 h = 8 h 20 min
t₂ = t₁ + t = 18 h 40 min + 8 h 20 min
40 min + 20 min = 60 min = 1 h
18 h +8 h = 26 h = 24 h + 2 h
2 h + 1 h = 3 h
t₂ = 3:00
The ship will arrive at the destination port at 3:00 the next day.
Answer:
32.4 - 27.0 = 5.4
18.40 + 54 =
7hrs:34mins
The ship arrived at
7:34pm
a quadratic function has its vertex at the point (4,6) the function passes through the point (-5,-2) find the quadratic and linear coefficients and the constant term of the function The quadratic coefficient is_____The linear coefficient is_______the constant term is_____
Answers
We have to find the equation of the quadratic function.
We know the vertex, located in (4,6), and one point (-5,-2).
The x-coordinate of the vertex (4) is equal to -b/2a, being a the quadratic coefficient and b the linear coefficient.
Now, we have 2 points to define the 3 parameters, so one of the parameters is undefined.
[tex]y=ax^2+bx+c[/tex]We start with the vertex, that we know that is:
[tex]\begin{gathered} x=-\frac{b}{2a}=4 \\ -b=4\cdot2a=8a \\ b=-8a \end{gathered}[/tex]Then, we can write the equation as:
[tex]y=ax^2-8ax+c=a(x^2-8x)+c[/tex]If we replace the point (-5,-2) in the equation, we get:
[tex]\begin{gathered} -2=a((-5)^2-8\cdot(-5))+c \\ -2=a(25+40)+c \\ -2=65a+c \\ c=-2-65a \end{gathered}[/tex]We replace the vertex coordinates and get:
[tex]\begin{gathered} 6=a(4^2-8\cdot4)+c \\ 6=a(16-32)+(-2-65a) \\ 6=-16a-2-65a \\ 6=-81a-2 \\ 81a=-2-6 \\ a=-\frac{8}{81}\approx-0.01 \end{gathered}[/tex]Then, the linear coefficient b is:
[tex]b=-8a=-8\cdot(-\frac{8}{81})=\frac{64}{81}\approx0.79[/tex]And the constant term is:
[tex]c=-2-65a=-2-65\cdot(-\frac{8}{81})=-2+\frac{520}{81}=\frac{-162+520}{81}=\frac{358}{81}\approx4.42[/tex]The quadratic coefficient is a=-0.01
The linear coefficient is b=0.79
the constant term is c=4.42
Could I assistance receive some on this question it’s very confusing
Answers
We need to translate the vertex F of triangle BDF. When we translate it 2 units to the left and 4 units down, we obtain the point F'.
We know that triangle BDF has vertices B(4,3), D(6,3), and F(6,1).
The first coordinate of each point represents its x-coordinate (the distance from the y-axis). And the second coordinate of each point represents its y-coordinate (the distance from the x-axis).
So, this triangle is shown below:
Now, we need to translate the point F 2 units to the left, to obtain the redpoint below. And then translate it 4 units down, to obtain F' (the yellow point):
Therefore, the F' has coordinates:
F'(4,-3)
Kirsten is driving to a city that is 400 miles away. When Kirsten left home, she had 15 gallons of gas in her car. Assume that her car gets 25 miles per gallon of gas. Define a function f so that f(x) is the amount of gas left in her car after she has driven x miles from home. What are intercepts for that function. What do they represent.
Answers
The equation that gives us the amount of gas left in her car, given the driven miles, is
[tex]f(x)=15-\frac{x}{25}[/tex]Notice that when x=25, there will remain 14 gallons of gas in the tank.
The x-intercept is
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow0=15-\frac{x}{25} \\ \Rightarrow x=15\cdot25=375 \end{gathered}[/tex](375,0). This is the maximum distance one can drive when the amount of gas in the tank reaches zero gallons.
On the other hand, the y-intercept is
[tex]\begin{gathered} x=0 \\ \Rightarrow f(x)=15 \end{gathered}[/tex](0,15). This is the number of gallons in the tank when we have driven 0 miles.
Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?
Answers
First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.
Let's take a look at the situation:
Since we're on a right triangle, we can say that:
[tex]\cos (22.25)=\frac{G}{R}[/tex]Solving for R,
[tex]\begin{gathered} \cos (22.25)=\frac{G}{R}\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=\frac{G}{\cos (22.25)} \end{gathered}[/tex]Since we already know that the lenght of the gym's floor is 390',
[tex]\begin{gathered} R=\frac{390^{\prime}}{\cos (22.25)} \\ \\ \Rightarrow R=421.38^{\prime} \end{gathered}[/tex]We get that the lenght of the surface we want to roof is 421.38'
Now, let's take a look at the surface we want to roof:
Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427
Our total roofing area would be:
[tex]427.38^{\prime}\cdot276^{\prime}=117956.88ft^2[/tex]We then divide this total area by the area of one of our "squares":
[tex]\frac{117956.88}{100}=1179.56[/tex]We round to the nearest integer from above, since we can't buy a fraction of a square.
(this is called ceiling a number)
[tex]1179.56\rightarrow1180[/tex]Therefore, we can conclude that Mark needs 1180 squares of roofing.
1. Is this figure a polygon?2. Is this polygon concave or convex?3. Is this polygon regular, equiangular, Equilateral, or none of these?4. What is the name of this polygon?
Answers
A polygon is a closed shape with straigh sides, then
2. Is the figure a polygon? YES.
Since the figure is a polygon
1a. Is this polygon concave or convex? It is concave. A concave polygon will always have at least one reflex interior angle, tha is, it has on interior angle greater than 180 degrees.
1b. Is this polyogn regular, equiangular, equilateral or none of these? The marks on the picture mean that all the sides have the same length. This is the definition of equilateral. Then the answer is equilateral.
1c. What is the name of this polygon? We can see it has 4 equal sides and is concave, then his name is Concave Equilateral Quadrilateral.
Radicals and Exponents Identify the choices that best completes the questions 3.
Answers
3.- Notice that:
[tex]\sqrt[]{12}=\sqrt[]{4\cdot3}=2\sqrt[]{3}\text{.}[/tex]Therefore, we can rewrite the given equation as follows:
[tex]2\sqrt[]{3}x-3\sqrt[]{3}x+5=4.[/tex]Adding like terms we get:
[tex]-\sqrt[]{3}x+5=4.[/tex]Subtracting 5 from the above equation we get:
[tex]\begin{gathered} -\sqrt[]{3}x+5-5=4-5, \\ -\sqrt[]{3}x=-1. \end{gathered}[/tex]Dividing the above equation by -√3 we get:
[tex]\begin{gathered} \frac{-\sqrt[]{3}x}{-\sqrt[]{3}}=\frac{-1}{-\sqrt[]{3}}, \\ x=\frac{1}{\sqrt[]{3}}\text{.} \end{gathered}[/tex]Finally, recall that:
[tex]\frac{1}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Therefore:
[tex]x=\frac{\sqrt[]{3}}{3}\text{.}[/tex]Answer: Option C.