Make a table of ordered pairs for the equation y = 1/2x -3then plot two points to graph the equation
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We are asked to find two ordered pairs for the line y = 1/2x - 3.
Our equation y = mx + b has defined two of the variables that we will need:
• b: the y-intercept of the equation
• m: the slope of the equation
If we examine a basic graph, we can see that when there is a y-intercept, the value for x is equivalent to 0. This gives us our first ordered pair in (x, y) form: (0, -3).
We will now find the next ordered pair that is 1 unit up and 2 units horizontal of -3. This will be one unit up (going from -3 to -2) and two units to the right (going from 0 to 2). Therefore, the second ordered pair is (2, -2).
An image of the graph is provided below as well as the table.
Related Questions
=O EXPONI NTIAL AND LOKARITHMIC FUNCTIONSEvaluating an exponential function that models a real-world...The radioactive substance uranium-240 has a half-life of 14 hours. The amount A (1) of a sarthe following exponential function.A(!)(*47001Find the amount of the sample remaining after 7 hours and after 60 hours.Round your answers to the nearest gram as necessary.Amount after 7 hours:gramsAmount after 60 hours:gramsX5?
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We have the next function to find the solutions:
[tex]A(7)=4700\cdot(\frac{1}{2})^{\frac{7}{14}}=3323.4019\approx3323gr[/tex][tex]A(60)=4700\cdot(\frac{1}{2})^{\frac{60}{14}}=240.9735\approx241gr[/tex]Then, the amount after 7 hours is 3323 grams, and after 60 hours is 241 grams.
Which of the following is an extraneous solution of V-3x-2-X+2?O x=-6O x = -1O X = 1O x = 6
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We have the expression:
[tex]\sqrt[]{-3x-2}=x+2[/tex]The square root, to be defined in the domain of real numbers, has to have a 0 or positive argument. Then, -3x-2 has to be greater or equal than 0.
We can write:
[tex]\begin{gathered} -3x-2\ge0 \\ -3x\ge2 \\ x\le-\frac{2}{3} \end{gathered}[/tex]Then, solutions for x that are greater than -2/3 are not valid.
We are left with x=-6 and x=-1.
We can test both:
[tex]\begin{gathered} x=-6\Rightarrow\sqrt[]{-3(-6)-2}=-6+2 \\ \sqrt[]{18-2}=-4 \\ \sqrt[]{16}=-4 \\ 16=(-4)^2 \\ 16=16 \end{gathered}[/tex]x=-6 is a valid solution.
We now test the other solution:
[tex]\begin{gathered} x=-1\longrightarrow\sqrt[]{-3(-1)-2}=-1+2 \\ \sqrt[]{3-2}=1 \\ \sqrt[]{1}=1 \\ 1=1 \end{gathered}[/tex]x=-1 is also a valid solution.
Hello could someone help me with a and c ? I keep getting those wrong
Answers
Answer:
Explanation:
Part A
The price per item when q units are sold is given by the function:
[tex]D(q)=-1.3q+260[/tex]When 30 units are sold:
[tex]\begin{gathered} \text{The price per item, }D(30)=-1.3(30)+260 \\ =-39+260 \\ =\$221 \end{gathered}[/tex]Therefore, the total revenue from selling 30 items is:
[tex]R(q)=30\times221=\$6,630[/tex]Part B
• Fixed Cost = $4000
,• Variable Cost = $8 per Item
[tex]\begin{gathered} \text{ Total Cost for 30 items, }C(q)=4000+(8\times30) \\ C(30)=\$4,240 \end{gathered}[/tex]Part C
[tex]undefined[/tex]You and 4 friends go to a restaurant to eat. The bill comes to a total of $110 before tax and tip. You want to leave a 20% tip for the $110 bill. You must also pay an 8.25% tax on the $110 bill. After you include the tax and tip, what is the price of the bill? Write out your process for solving this problem. Explain exactly what you do.
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Bill = $110.
Tip: 20% So:
[tex]\begin{gathered} If\text{ \$110 - 100\%} \\ Then\text{ x- 20\%} \\ x=\text{ }\frac{\lparen20\%\rparen\lparen\$110\rparen}{100} \\ \\ x=\frac{2200}{100} \\ \\ x=\text{ \$22} \end{gathered}[/tex]Tax: 8.25%
[tex]\begin{gathered} If\text{ \$110 -100\%} \\ Then\text{ x - 8.25\%} \\ \\ x=\frac{\lparen8.25\%\rparen\lparen\$110\rparen}{100\%} \\ \\ x=\frac{907.5}{100} \\ \\ x=\text{ \$9.075} \end{gathered}[/tex]Therefore, they will pay $22 in tips and $9.075 in taxes. Therefore the final price of the bill will be:
[tex]110\text{ + 22 + 9.075 = \$141.075}[/tex]Find the first and third quartile for the quantitative data.х X2.42.86.58.61113.726.428.729.430Q1 =?Q3=?
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Given: The data is,
[tex]2.4,2.8,6.5,8.6,11,13.7,26.4,28.7,29.4,30[/tex]The number of terms is 10.
The first quartile is calculated as,
Take the lower half of the data,
[tex]\begin{gathered} 2.4,2.8,6.5,8.6,11 \\ \text{Median is 6.5} \\ Q_1=6.5 \end{gathered}[/tex]Now, the third quartile is,
Take the upper half of the data,
[tex]\begin{gathered} 13.7,26.4,28.7,29.4,30 \\ \text{Median is 28.7} \\ Q_3=28.7 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} Q_1=6.5 \\ Q_2=28.7 \end{gathered}[/tex]which of the following statements describes the rate of change of f over the interval 1.5 < x<3? the rate of change is 1/2. the rate of change is 2. the rate of change is constant. the rate of change is increasing.
Answers
Remember that
the average rate of change is equal to
(f(b)-f(a))/(b-a)
in this problem we have
a=1.5
b=3
f(a)=f(1.5)=1
f(b)=f(3)=4
substitute
(4-1)/(3-1.5)
3/1.5
=2
therefore
the rate of change is 2
Linear equation- (6+Step 1: -3r-5 = 13Step 2:-3x = 18Step 3: x=-610) = 13Which sequence describes the inverse operations usedfor steps 2 and 3 to solve the linear equation?O the addition property of equality and then thedivision property of equalitymultiplication property of equalitythe subtraction property of equality and then theO the addition property of equality and then thedivision property of equalityO the subtraction property of equality and then themultiplication property of equality
Answers
1. The Addition property of equality states that, if:
[tex]a=b[/tex]Then:
[tex]a+c=b+c[/tex]2. The Subtraction property of equality states that, if:
[tex]a=b[/tex]Then:
[tex]a-c=b-c[/tex]3. According to the Division property of equality, if:
[tex]a=b[/tex]Then:
[tex]\frac{a}{c}=\frac{b}{c}[/tex]4. According to the Multiplication property of equality, if:
[tex]a=b[/tex]Then:
[tex]a\cdot c=b\cdot c[/tex]In this case, you have the following equation:
[tex]-\frac{1}{2}(6x+10)=13[/tex]You can identify in the picture that in Step 1, each term inside the parentheses was multiplied by the fraction, then the Distributive property was applied:
[tex]-3x-5=13[/tex]In Step 2
8. Nate wrote the polynomial shown below on the board. Which value(s) of "n" would make the polynomial factorable? 16x2 - I. q 9 II. -9 III. 25 a. I only b. I and III only w c. I and II only d. I, II and III
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By definition, a Perfect square trinomial has the following form:
[tex]a^2\pm2ab+b^2[/tex]Perfect square trinomials can be expressed in Squared-binomial form, as following:
[tex](a\pm b)^2[/tex]In this case, you know that the first term of the Perfect square trinomial Tia wrote on the board, is:
[tex]4x^2[/tex]And the last term is:
[tex]25[/tex]Then you can identify that:
[tex]a^2=4x^2[/tex]Solving for "a", you get:
[tex]\begin{gathered} a=\sqrt[]{4x^2} \\ a=2x \end{gathered}[/tex]Notice that:
[tex]b^2=25[/tex]Solving for "b", you get:
[tex]\begin{gathered} b=\sqrt[]{25} \\ b=5 \end{gathered}[/tex]Knowing "a" and "b", you can write the following Squared-binomial:
[tex](2x+5)^2[/tex]And determine that the missing term is:
[tex]2ab=2(2x)(5)=20x[/tex]Therefore, the missing value is not a Perfect square, because it is not obtained by multiplying two equal Integers.
The answer is: Option B.
1. In a certain game, it is advantageous to have in- game friends who visit you daily. Player A has 150 in-game friends, and 45 of them visit her daily. a. What percent of her friends visit her daily? b. How many more friends need to visit her daily if her goals is to have 70% of her friends visit her daily?
Answers
Answer:
(a)30%
(b)60 more friends
Explanation:
The number of in-game friends Player A has = 150.
The number that visits daily = 45.
Part A
The percent of her friends that visit her daily will be:
[tex]\begin{gathered} \frac{\text{Number of daily visits}}{Total\text{ number of in-game friends}}\times100 \\ =\frac{45}{150}\times100 \\ =0.3\times100 \\ =30\% \end{gathered}[/tex]30% of her friends visit her daily.
Part B
• If her goal is to have 70% of her friends visit her daily.
,• Let the number of additional friends = x.
Therefore:
[tex]\begin{gathered} \frac{x+45}{150}\times100=70 \\ \mleft(x+45\mright)\times\frac{100}{150}=70 \\ Multiply\text{ both sides by }\frac{150}{100} \\ (x+45)\times\frac{100}{150}\times\frac{150}{100}=70\times\frac{150}{100} \\ x+45=105 \\ x=105-45 \\ x=60 \end{gathered}[/tex]Therefore, if her goal is to have 70% of her friends visit her daily, she needs 60 more friends to visit her daily.
Determine whether each parabola has a horizizontal or vertical directrix
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we know that
A vertical parabola of the form
y=a(x-h)^2+k has a vertical directrix (x=h)
and a horizontal parabola of the form
x=a(y-k)^2+h has a horizontal parabola (y=k)
therefore
In this problem
option 1 ----> horizontal directrix
option 2 -> horizontal directrix
option 3 ---> vertical directrix
option 4 -> vertical directrix
4x−6x+15−x−4. I don't know
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state all integer values of x in intervals [3,9] that satisfy for[tex]4x - 7 =\ \textless \ 11[/tex]
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Given:
[tex]4x\text{ - 7 }\leq11[/tex]To find the values of x in intervals [3, 9} that satisfy the inequality, we have:
Let's check all values between 3 to 9:
4(3) - 7
PLEASE HELPPP. Jessie is playing a game in which each player spins the spinner shown two times. The player with a sum of 7 from the two spins wins the game.24Which first spin would give Jessie the best chance of winning the game?OAOB 2c. 3ОООD. 4) E. 5
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The player with a sum of 7 from the two spins wins the game.
Which first spin would give Jessie the best chance of winning the game?
the answer for the first spin is 2, the 2 would give her the best chance of winning the game
Find the linearization L(x) of f(x)= tan x at x=3*Pi/4.
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The linearization L(x) of f(x)= tan x at x=3*Pi/4 is L(x) = -1 - [tex]\sqrt{2}[/tex](x - 3π/4) .
Given:
f(x) = tanx at x = 3π/4
we know that:
L(x) = f(x) + f'(x)(x - a).
f(x) = tan(x)
= tan(3π/4)
= tan(π/2 + π/4)
= -cot(π/4)
f(x) = -1
f'(x) = (tan x)'
= [tex]sec^{2}[/tex]x
= [tex]sec^{2}[/tex](3π/4)
= [tex]sec^{2}[/tex](π/2 + π/4)
= -cosec(π/4)
f'(x) = -[tex]\sqrt{2}[/tex]
f(x) and f'(x) substitute in L(x) function.
L(x) = f(x) + f'(x)(x - a)
= -1 + (-[tex]\sqrt{2}[/tex])(x - 3π/4)
L(x) = -1 - [tex]\sqrt{2}[/tex](x - 3π/4)
Therefore the linearization L(x) of f(x)= tan x at x=3*Pi/4 is L(x) = -1 - [tex]\sqrt{2}[/tex](x - 3π/4).
Learn more about the linearization here:
https://brainly.com/question/26139696
#SPJ1
Given f(x) = cos^2 (x), find the equation of the tangent line at x = π/6
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GIVEN THE EQUATION :
[tex]f(x)\text{ = cos }^2(x)\text{ }[/tex](i) Find the derivative of cos^2 (x)
[tex]\begin{gathered} f^{\prime}(x)=\frac{d}{dx}(cos\text{ }^2(x)\text{ \rparen.... apply the chain rule } \\ \Rightarrow2\text{ cos \lparen x\rparen }\frac{d}{dx\text{ }}(cos\text{ \lparen x\rparen\rparen} \\ \Rightarrow2cos\text{ x \lparen-sinx\rparen ..... simplify } \\ \Rightarrow-sin(2x)\text{ } \\ \therefore f^{\prime}(x)\text{ = -sin\lparen2x\rparen } \\ \\ \end{gathered}[/tex](ii) Now that we have calculated the derivative of cos^2 (x) = -sin(2x)
at x = /6 :
[tex]\begin{gathered} f(\frac{\pi}{6})\text{ = -sin \lparen2 * }\frac{\pi}{6}) \\ \text{ = -sin }\frac{2\pi}{6} \\ \text{ = -sin }\frac{\pi}{3} \\ \text{ = -0.018} \end{gathered}[/tex]This means that our point is ( /6 ;- 0.018)
(iii) Calculate the slope of the tangent line :
m = f'( /6 )
= -sin2
Write 22% as a fraction in simplest form.
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Solution
Step 1
22%
To write 22% in fraction you will divide it by 100.
Step 2
[tex]\begin{gathered} 22\text{ \% = }\frac{22}{100} \\ \\ Divide\text{ by numerator and denominator by 2 to reduce the fraction to} \\ \text{it lowest term.} \\ \\ =\text{ }\frac{11}{50} \end{gathered}[/tex]Final answer
[tex]\frac{11}{50}[/tex]Solve the equation.1/2K-(k+1/5)=1/10(k+2)
Answers
The equation is the following:
[tex]\frac{1}{2}k-(k+\frac{1}{5})=\frac{1}{10}(k+2)[/tex]First let's eliminate the denominators. We can do that by multiplying both sides of the equation by 10:
[tex]\begin{gathered} \frac{10}{2}k-10(k+\frac{1}{5})=k+2 \\ 5k-10k-2=k+2 \end{gathered}[/tex]Then, we isolate the terms with the variable in one side of the equation, and the terms without the variable in the other side:
[tex]\begin{gathered} 5k-10k-k=2+2 \\ -6k=4 \end{gathered}[/tex]Finally, we divide both sides by the number multiplying the variable:
[tex]\begin{gathered} \frac{-6k}{-6}=\frac{4}{-6} \\ k-\frac{-4}{6}=-\frac{2}{3} \end{gathered}[/tex]So the value of k is -2/3
The sum of a number and twice it’s reciprocal is 11/3. Find the numbers
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In order to find the answer you first write the statement of the question in an algebraic form. Just as follow:
[tex]\begin{gathered} x+\frac{2}{x}=\frac{11}{3} \\ x^2+2=\frac{11}{3}x \\ x^2-\frac{11}{3}x+2=0 \end{gathered}[/tex]Then, you obtained a quadratic equation. The general form of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]where a=1, b=-11/13 and c=2
The quadrativ formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]you replace:
[tex]\begin{gathered} x=\frac{-(11/3)\pm\sqrt{(11/3)^2-4(1)(2)}}{2(1)}=\frac{-11/3\pm2.33}{2} \\ x_1=-3 \\ x_2=0.66 \end{gathered}[/tex]BRAINLIEST FOR ANSWERAnswer choices: A. The interquartile range is 7, and the range is 7.B. The interquartile range is 7, and the range is 11.C. The interquartile range is 2.75, and the range is 17.D. The interquartile range is 2.75, and the range is 11.
Answers
Range = 17 - 6 = 11
Q1 = (8 + 9)/2 = 8.5
Q2 = (14+15)/2= 14.5
Interquartile range = Q2 - Q1
14.5 - 8.5
6
Option B will be the best fit for the answer.
The sum of two numbers is 17. One number is 3 less than of the other number. What is the lesser number?what is the answer
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Let the numbers be a and b
Given that the sum is 17 then
a + b = 17
also given that one number is 3 less than the other
a = b + 3
substituting
b + 3 + b = 17
2b + 3 = 17
subtract 3 from both sides
2b = 17 - 3
2 b = 14
divide both sides by 2
b = 14/2
= 7
The lesser of the two is 7
What is the image of (1, -8) after a dilation by a scale factor of 5 centered at the origin?
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If you are dilating a coordinate (a, b) by the scale factor "z", the new coordinate will be (za, zb).
It simply means that we multiply each cordinate, x and y, by the scale factor given.
Here,
The coordinate is (1, -8) and hte scale factor is "5". Thus, we multiply each coordinate by "5". So, it becomes:
[tex]\begin{gathered} (5\times1,5\times-8) \\ =(5,-40) \end{gathered}[/tex]The image is at (5, - 40)
alkanun Write the coordinates of ench plint.
Answers
The x coordinate coresponding to point is 3 units forward , y coordinate is 4 unit left side (or -4 units) and z coordinate is 2 units up side. So coordinate of the point is,
[tex](3,-4,2)[/tex]So answer is (3,-4,2).
Pretest Unit 2Question 13 of 21What is the greatest common factor of the polynomial below?20x^2 -14xO A. 2xB. 6x2с. БхO.D. 2x
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Given the polynomial;
[tex]20x^2-14x[/tex]The greatest common factor is is the largest positive integer that divides evenly into all numbers with zero remainder.
[tex]20x^2-14x=2x(10x-7)[/tex]Thus, the greatest common factor of the polynomial is 2x.
Find the diameter of a circle withan area of 615.75 cm^2.
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Question: Find the diameter of a circle with an area of 615.75 cm^2.
Solution:
Remember that the area of the circle is given by the following equation:
[tex]A=\pi r^2[/tex]where r is the radius of the circle. Now notice that the diameter is 2r, which is two times the radius. Therefore, from the previous equation, we find the radius of the circle, and with this its diameter:
[tex]r^2=\frac{A}{\pi}\text{ = }\frac{615.75cm^2}{3.1416}=195.99cm^2[/tex]Taking the square root to the previous equation, we have that the radius is:
[tex]r\text{ = 13.99}\approx14[/tex]then, we can conclude that the diameter is:
[tex]d\text{ = 2r = 2(13.99) = 27.99}\approx28[/tex]
Find the product for 7-9 and write your answer in simplest form. 7. 1/4 x 3/5 = 3/20 8. 3 1/2 x 4 2/3 =. 2 x 5/6 =
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7) 1/4 * 3/5 we use direct multiplication of fractions and get:
1/4 * 3/5 = (1 * 3) / (4 * 5) = 3 / 20
which is already in simplest form
8) 3 1/2 * 4 2/3 These are mixed numbers, so we first convert them into improper fractions and then multiply as shown below:
3 1/2 = 6/2 + 1/2 = 7/2
and
4 2/3 = 12/3 + 2/3 = 14/3
Now we multiply these fractions:
7/2 * 14/3 = (7 * 14) / (2 * 3) = 98/6 where we can cancel a common factor of "2"from numerator and denominator, leading to: 49/3 and in mixed number form = 16 1/3
9) 2 * 5/6 = 2/1 * 5/6 where we wrote the integer "2" as the fraction 2/1 in order to be able to use the convention for multiplying fractions. Then:
2 * 5/6 = (2 * 5) / (1 * 6) = 10/6 here we can again simplify a common factor of 2 in numerator and denominator, leading to: 5/3
Then 2 * 5/6 = 5/3
if y=a(b)^t is an exponential decay function, then b must be...a. less than oneb. less than 100c. less than zero d. a whole number
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if y=a(b)^t is an exponential decay function, then b must be less than one
Solve the inequality for v.- 20> -4vSimplify your answer as much as poss
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We are given the following inequality:
[tex]v-20>-4v[/tex]To solve for "v" we will add "4v" on both sides:
[tex]\begin{gathered} v+4v-20>-4v+4v \\ \end{gathered}[/tex]Adding like terms:
[tex]5v-20>0[/tex]Now, we add 20 to both sides:
[tex]5v-20+20>20[/tex]Adding like terms:
[tex]5v>20[/tex]Now, we divide both sides by 5:
[tex]\frac{5v}{5}>\frac{20}{5}[/tex]Solving the operations:
[tex]v>4[/tex]Since we can't simplify any further this is the final answer.
Can someone help me with this equation. I am unable to get the paper version because of my quarantine and am looking for extra help.
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Solution:
The quadaratic equation is given below as
[tex]x^2+4x=18[/tex]Step 1:
Take half of the x term and square it
[tex](4\times\frac{1}{2})^2=2^2=4[/tex]Then add the result to both sides
Hence, We will have
[tex]x^2+4x+4=18+4[/tex]Step 2:
Rewrite the perfect square on the left
Hence,
We will have
[tex](x+2)^2=22[/tex]Step 3:
Take the square root of both sides, we will have
[tex]\begin{gathered} x+2=\sqrt{22} \\ x+2=\pm4.7 \end{gathered}[/tex]Step 4:
Isolate the x on the left side and
solve for x (1)
[tex]\begin{gathered} x+2=4.7 \\ x=4.7-2 \\ x=2.7 \\ \\ x+2=-4.7 \\ x=-4.7-2 \\ x=-6.7 \end{gathered}[/tex]Hence,
The final answers will be shown in the image below
Labeling endpoints on a histogram (can add or remove columns is necessary)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
hearing experiment:
25, 22, 18, 35, 37, 34, 27, 36, 36, 36, 33, 33, 30, 30, 26
Step 02:
histogram:
we must analyze the data to find the solution.
general histogram:
[tex][/tex]11.Find the approximated area of a circle whose diameter is 3.12
Answers
The area of a circle is pi times the radius squared; (A = π r²)
If the diameter is 3.12, then the radius is: r = 1.56.
So, the area will be:
A = π r²
A = π x (1.56)² = 7.64