Answers
First thing is to find the coordinates for the two points
(-3,-2) and ( 0,2)
Then we can use the slope formula to determine the slope
m = ( y2-y1)/(x2-x1)
= ( 2 - -2) / ( 0 - -3)
= ( 2+2) / (0+3)
= 4/3
The slope is 4/3
You can also count how many you go up and then how many you go over to get from the left point to the right point.
We go up 4 and then right 3
4/3
The y intercept is where it crosses the y axis.
It crosses at y =2
The slope intercept form of the equation is
y = mx+b where m is the slope and b is the y intercept
y = 4/3x +2
Related Questions
Translate and solve: 82 less than a is at least -82 (express answer in interval notation)
Answers
Let's begin by identifying key information given to us:
82 less than a is given by:
[tex]82at least means greater than or equal to & is represented by the mathematical symbol ≥Putting this together, 82 less than a is at least -82 becomes:
[tex]82Write the inequality for this graph. Use x as your variable.
Answers
Notice that the points on the graph are all numbers greater than or equal to zero, therefore the given graph represents the following interval:
[tex]\lbrack0,\infty).[/tex]Zero is part of the graph because the circle is filled.
The above interval as an inequality is:
[tex]x\ge0.[/tex]Answer:
[tex]x\ge0.[/tex]The rectangular prism below has a base area of 38 units^2. and a height of 11.3 units. Find its volume.
Answers
Solution:
The volume of a rectangular prism is expressed as
[tex]volume\text{ = base area }\times\text{ height}[/tex]Given the rectangular prism below:
where
[tex]\begin{gathered} base\text{ area = 38 units}^2 \\ height\text{ = 11.3 units} \end{gathered}[/tex]The volume of the rectangular prism is evaluated as
[tex]\begin{gathered} volume\text{ = base area }\times\text{ height} \\ =38\text{ units}^2\times11.3\text{ units} \\ \Rightarrow volume\text{ = 429.4 units}^3 \end{gathered}[/tex]Hence, the volume of the rectangular prism is
[tex]429.4\text{ units}^3[/tex]Evaluate. (Round your answer to two decimal places.)(5pi - 9e) / (7pi + 3e)
Answers
ANSWER
-0.29
EXPLANATION
We want to evaluate the value of the fraction given to two decimal places.
To do this, we have to know the value of pi and e:
[tex]\begin{gathered} \pi\text{ = 3.1416} \\ e\text{ = 2.7183} \end{gathered}[/tex]Therefore, to simplify the fraction:
[tex]\begin{gathered} \frac{5(3.1416)\text{ - 9(2.7183)}}{7(3.1416)\text{ + 3(2.7183)}} \\ \Rightarrow\text{ }\frac{15.708\text{ - 24.4647}}{21.9912\text{ + 8.1549}} \\ \Rightarrow\text{ }\frac{-8.7567}{30.1461} \\ =>\text{ -0.2905 }\cong-0.29 \end{gathered}[/tex]That is the answer.
10. A bacteria culture is started with 200 bacteria. After 4 hours, the population has grown to 769 bacteria. If the population grows exponentially according to the formula Pt=P0(1+r)t (a) Find the growth rate. Round your answer to the nearest tenth of a percent.r = %(b) If this trend continues, how many bacteria will there be in one day? bacteria(c) How long will it take for this culture to triple in size? Round your answer to the nearest tenth of an hour. hours
Answers
Given:
A bacteria culture is started with 200 bacteria.
After 4 hours, the population has grown to 769 bacteria.
the population grows exponentially according to the formula:
[tex]P(t)=P_0(1+r)^t[/tex](a) Find the growth rate.
so, when:
[tex]\begin{gathered} P_0=200,t=4,P(t)=769 \\ 769=200(1+r)^4 \end{gathered}[/tex]Solve for r:
[tex]\begin{gathered} \frac{769}{200}=(1+r)^4 \\ 3.845=(1+r)^4 \\ \sqrt[4]{3.845}=1+r \\ 1+r=1.4 \\ r=1.4-1=0.4 \end{gathered}[/tex]So, the value of r = 0.4 = 40%
The growth rate = r = 40%
(b) If this trend continues, how many bacteria will there be in one day?
For one day, t = 24 hours
so,
[tex]\begin{gathered} P_t=200\cdot(1+0.4)^{24} \\ P_t=200\cdot1.4^{24}=642,840 \end{gathered}[/tex]Bacteria = 642,840
(c) How long will it take for this culture to triple in size?
So,
[tex]\begin{gathered} P_t=3\cdot200=600 \\ 600=200\cdot(1+0.4)^t \end{gathered}[/tex]Solve for t:
[tex]\begin{gathered} \frac{600}{200}=1.4^t \\ 3=1.4^t \\ \ln 3=t\cdot\ln 1.4 \\ t=\frac{\ln 3}{\ln 1.4}\approx3.265 \end{gathered}[/tex]Round your answer to the nearest tenth of an hour.
So, t = 3.3 hours
I need help with this. Also when you’re done explaining it can you place the answer on top of the answer tab?
Answers
answer is option A
answer is option A
Recently, more money 4u offered a annuity that pays 5.4% compounded monthly. If 878 is deposited into this annuity every month, how much is in the account after 8 years ? How much of this is interest
Answers
Step 1
State the formula for Future value compounded monthly.
[tex]FV=PMT(\frac{(1+i)^n-1)}{i})[/tex]where;
[tex]\begin{gathered} PMT=878 \\ i=\frac{5.4}{100\times12}=0.0045 \\ n=8\times12=96 \end{gathered}[/tex]Step 2
Find the future value
[tex]\begin{gathered} FV=878(\frac{(1+0.0045)^{96}-1^{}}{0.0045}) \\ FV=878(\frac{(1.0045)^{96^{}}-1}{0.0045}) \\ FV=\frac{473.1042497}{0.0045} \\ FV=105,134.2777 \\ FV\approx\text{ \$105134.28 to 2 decimal places} \end{gathered}[/tex]Find how much of the future value is interest
[tex]\text{Money paid in = 878}\times8\times12=\text{ \$84288}[/tex][tex]\begin{gathered} \text{Interest}=\text{ Future value - money paid in=}105134.27771-\text{ 84288}= \\ \text{Interest}=105134.27771-\text{ 84288}=20846.2777 \\ \text{Interest}\approx\text{\$}20846.28\text{ to 2 decimal places} \end{gathered}[/tex]Hence, the answers are;
How much is in the account after 8 years = $105134.28 to 2 decimal places
How much of this is interest = $20846.28 to 2 decimal places
in the figure below, two seconds are drawn to a circle from an exterior point E. Suppose that EZ = 16.8, EX = 14, and EW =35. Find XY.
Answers
Knowing that two secants are drawn to a circle from an exterior point, you need to use the Intersecting Secant Theorem.
Based on the Intersecting Secant Theorem, you can write the following equation:
[tex]EZ\cdot EW=EX\cdot EY[/tex]Knowing that:
[tex]\begin{gathered} EZ=16.8 \\ EX=14 \\ EW=35 \end{gathered}[/tex]Substitute those values into the equation:
[tex](16.8)(35)=(14)\cdot EY[/tex]Solve for EY:
[tex]\begin{gathered} 588=14EY \\ EY=\frac{588}{14} \\ EY=42 \end{gathered}[/tex]Notice that:
[tex]EY=EX+XY[/tex]Then you can substitute values and solve for XY:
[tex]\begin{gathered} 42=14+XY \\ 42-14=XY \\ XY=28 \end{gathered}[/tex]The answer is:
[tex]XY=28[/tex]name the point of intersection –2x = −2y - 4 -6 = 3у – бх
Answers
–2x = −2y - 4
-6 = 3у – бх
Solve the first equation for x:
x = (-2y-4) /-2
x= y + 2
Replace x in the second equation and solve for y
-6= 3y - 6 (y+2)
-6= 3y -6y - 12
-6= -3y -12
-6+12= -3y
6=-3y
6/-3= y
y= -2
Replace y on any equation and solve for x
x= y + 2
x= -2+2 = 0
Point of intersection = (0,-2)
Graph the quadratic function f(x) = 2(x - 3)2 - 2 and select all of the following which are true.maximum at (-3,-2)minimum at (3,-2)x-intercept at (2,0)x-intercept at (4,0)y-intercept at (0, -16)
Answers
Graph:
By looking at the graph we can see that:
It opens upwards, so it has a minimum at (3,-2)
I crosses the x axis at x=2 and x=4
x- intercepts at (2,0) and (4,0)
It doesn't cross the y axis
- Which list represents the numbers arranged in descending order? :A)1.55x10^1,√155,155%,1/5,-15/3.B)√155,155%,1/5,1.55x10^1,-15/3.C)155x10^1,√155,155%,1/5,-15/3.D)-15/3,1.55x10^1,√155,155%,1/5.
Answers
Arranging in descending order means arraging the numbers frim the largest to the smallest.
Given the following values according to the options
1.55x10^1, √155, 155%, 1/5, -15/3.
Let us rewrite all the values as whole numbers and decimals
1.55x10^1 = 15.5
√155 = 12.45
155% = 155/100 = 1.55
1/5, = 0.2
-15/3 = -5
The largest value is 15.5, followed by 12.5 then 1.55, 0.2 and then -5th
The negative vakue there is the lowest value i.e -15/3
The arrangement from largest to smallest are;
1.55x10^1, √155, 155%, 1/5, -15/3
Option A is corect
One of these seven students will be selected at random. Which of these events describes students 1, 4, 5, 6, and 7 without including any of the other students?
Answers
ANSWER
Plays a fall sport or a spring sport
EXPLANATION
Student 1 plays a fall sport
Student 4 plays a fall sport and a winter sport
Student 5 plays a fall sport and a spring sport
Student 6 plays a spring sport
Stydent 7 plays a fall sport
Of these five students, 1, 4, 5 and 7 play a fall sport and student 6 plays a spring sport. So of these group each student plays a fall sport or a spring sport.
Which choice is equivalent to the product below when x> 0? 3x xli 3x ОАА O A. ОВ. Ос. C. Ž O D. D. x 2.
Answers
We can use the following properties of radicals:
[tex]\begin{gathered} \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\Rightarrow\text{ Product property} \\ \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}\Rightarrow\text{ Quotient property} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} \text{ Apply the product property} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x\cdot x}{2\cdot6}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x^2}{12}} \\ \text{ Simplify the expression inside the radical} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{3x^2}{3\cdot4}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\sqrt[]{\frac{x^2}{4}} \\ \text{ Apply the quotient property} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\frac{\sqrt[]{x^2}}{\sqrt[]{4}} \\ \sqrt[]{\frac{3x}{2}}\cdot\sqrt[]{\frac{x}{6}}=\frac{x}{2} \end{gathered}[/tex]Therefore, the choice that is equivalent to the given product when x > 0 is:
[tex]\frac{x}{2}[/tex]12. Derek scored a total of 42 points in the first 4 basketballgames. If he continues to score at this rate, how manypoints will he score during the entire 18-game season?
Answers
Given data:
The numbers of points scored in 4 games are 42.
The expression for the given statement is,
[tex]\begin{gathered} 4\text{ games= 42 points} \\ 1\text{ game = 10.5 points} \end{gathered}[/tex]Multiply the above expression by 18 on both sides.
[tex]\begin{gathered} 18(1\text{ game) =18(10.5 points)} \\ 18\text{ games =189 points} \end{gathered}[/tex]Thus, in 18 games 189 points achieved.
A map shows a garden with a width of 2 inches and a length of 6 inches. The map uses a scale of 1 inch for 10 yards. What is the actual length and width of the garden? Don't Forget the units.
Answers
Scale
1 inches = 10 yards
Width = 2 inches
2 * 10 = 20 yards
Length = 6 inches
6 * 10 = 60 yards
So, actual :
length = 60 yd
width = 20 yd
.........................answer explanation of another question shown on session....................
2 cake = 9 person
1 person = 2/9th cake
So,
45 person would take up:
45 * 2/9 = 10 cakes
Question 1)A line with slope = 6 that passes through the point (3, 1) written in point-slope form is
Answers
The equation of a line in slope-intercept form is given as
[tex]y-y_1=m(x-x_1)[/tex]The slope of the line is 6
Hence, m = 6
Since the line passes through the point (3, 1)
Hence,
[tex]x_1=3,y_1=1[/tex]Substitute the values into the equation
This gives
[tex]y-1=6(x-3)[/tex]Simplify the equation
[tex]\begin{gathered} y-1=6x-18 \\ y=6x-18+1 \\ y=6x-17 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=6x-17[/tex]The sequence is arithmetic or geometric and the common difference or ratio is 5.
Answers
1. Arithmetic
2. common difference
1) Examining that sequence we can see that:
[tex]\begin{gathered} -6,-1,4,9 \\ -6+5=-1 \\ -1+5=4 \\ 4+5=9 \end{gathered}[/tex]So as we can see this sequence is an Arithmetic one, whose common difference is 5
2) That is the answer.
The Third Floor residence of a building were Polled about whom they would vote for in the upcoming city election for comptroller. what are the sample amd population in this poll?the population is the registered voters in the building, the sample is the residence on the third floor.the population is the registered voters in the city. the sample is the residence of the third floorthe population is the registered voters in the city. the sample is the residence of the building the population is the registered voters of the building. the sample is the registered voters in the city
Answers
Answer:
The population is the registered voters in the city. the sample is the residence of the third floor
Explanation:
The population is the group that you want to know information about and the sample is a small group of the population that you select to collect the data.
In this case, the purpose is to know whom they would vote for the upcoming city election, so the population will be the registered voters in the city. Additionally, you only ask to the third floors residence of a building, then the sample will be the residence on the third floor.
So, the answer is:
The population is the registered voters in the city. the sample is the residence of the third floor
Hello, I need some help with this homework question, please?HW Q24
Answers
Given:
[tex]h=-3t^2+147[/tex]Required:
We need to find the number of seconds will the plane be at a height of 20.25 feet.
Explanation:
Substitute h = 20.25 in the equation.
[tex]20.25=-3t^2+147[/tex]Subtract 147 from both sides of the equation.
[tex]20.25-147=-3t^2+147-147[/tex][tex]-126.75=-3t^2[/tex]Divide both sides of the equation by -3.
[tex]\frac{-126.75}{-3}=\frac{-3t^2}{-3}[/tex][tex]42.25=t^2[/tex]Take square root on both sides.
[tex]\pm\sqrt{42.25}=\sqrt{t^2}[/tex]Time is of positive value.
[tex]\sqrt{42.25}=t[/tex][tex]6.5=t[/tex]Final answer:
After 6.5 seconds the plane will be at a height of 20.25 feet.
when your family gets together to exchange gifts things get a little crazy you counted a128 gifts 1/4 of them have your name on the tag 1/8 of them are for your cousin. Howw many gifts are not for you or your cousin?you came to the 128 gifts 1/4 of them have your name on the tag and 1/8 of them are for your cousins how many gifts are not for your cousins
Answers
Total gifts: 128
1/4 have your name. Multiply the total number of gifts by 1/4 to get the number of gifts that are for you:
Multiplication of a whole number and a fraction:
[tex]a\cdot\frac{b}{c}=\frac{a\cdot b}{c}[/tex]gifts that are for you:
[tex]128\cdot\frac{1}{4}=\frac{128\cdot1}{4}=\frac{128}{4}=32[/tex]1/8 of them are for your cousins. Multiply the total number of gifts by 1/8 to get the number of gifts that are for your cousins:
[tex]128\cdot\frac{1}{8}=\frac{128\cdot1}{8}=\frac{128}{8}=16[/tex]Then, subtract the number of gifts that are for you and the number of gifts that are for your cousins to get the answer of "How many gifts are not for you or your cousin?":
[tex]128-32-16=80[/tex] There are 80 gifts that are not for you or your cousins.To get the number of gifts that are not for your cousins substract 16 from the total of gifts:
[tex]128-16=112[/tex]There are 112 gifts that are not for your cousinsSuppose that the relation S is defined as follows.s={(-2,8), (5.-9).(-9,0).(-6, -6)}Give the domain and range of S.Write your answers using set notation.Domain=Range=
Answers
Remember that
The Domain is the set of all the input values, which are the x-coordinate of each ordered pair (the first number in each pair).
The Range is the set of all output values, which are the y-coordinate of each ordered pair (the second number in each pair)
In this problem we have
s={(-2,8), (5.-9).(-9,0).(-6, -6)}
therefore
The domain is [-9,-6,-2,5]The range is [-9,-6,0,8]Graph triangle ABC with vertices A(0,5) B(4,3) and C(2,-1) and it’s image after a reflection in the line y=2I starting by graphing triangle ABC just so you know!
Answers
Given the triangle ABC, you can identify that the coordinates of its vertices are:
[tex]\begin{gathered} A\mleft(0,5\mright) \\ B\mleft(4,3\mright) \\ C\mleft(2,-1\mright) \end{gathered}[/tex]You know that it is reflected over the following line:
[tex]y=2[/tex]Notice that it has the form of a horizontal line. It intersects the y-axis at this point:
[tex](0,2)[/tex]Knowing that you can graph the line. See the picture below:
By definition, when a figure is reflected over a line, the points of the Image (the figure obtained after the transformation) and the points of the Pre-Image (the original figure), have the same distance from the line of reflection.
Notice that:
- Point A is 3 units away from the line of reflection.
- Point B is 1 unit away from the line.
- Point C is 3 units away from the line.
See the picture attached:T
Therefore, the points of the Image will have this distance from the line of reflection:
- Point A' will be 3 units away from the line of reflection.
- Point B' will be 1 unit away from the line.
- Point C' will be 3 units away from the line.
A right square pyramid has the following dimensions: • The side length of the base is 5 inches. • The height is 9 inches. What is the volume of the pyramid? o 135 cubic inches O 115 cubic inches O 75 cubic incheso 90 cubic inches
Answers
Explanation:
Height = 9 inches
Length = 5 = inches
Area of the square is = l^2
Area = 5 x 5
Area = 25 square inches
Volume = 1/3
A car travels according to the table of values shown. What equation can be used topredict the distance (d) the car travels in a number of hours (h)?Hours1234Distance(miles)4590135180
Answers
SOLUTION
From the table, we can see that in 1 hour, the car covered 45 miles and in 2 hours, 90 miles, and in 3 hours 135 miles.
This means that the distance was increased by 45 miles for every additional 1 hour, that is
[tex]\begin{gathered} d=1hr\times45 \\ d=2hr\times(45+45) \\ d=3hr\times(45+45+45),\text{ that means } \\ d=45\times number\text{ of hours, since number of hours is h} \\ d=45\times h \\ d=45h \end{gathered}[/tex]Hence the first option d = 45h is the answer
The temperature in Springfield at 10:00 am was 78 degrees F. During the day, it dropped to 56 degrees F. Write and solve an equation to find the decrease in temp.
Answers
Step 1. The initial temperature at 10:00 am was 78 degrees F, then there was a decrease in temperature and it dropped to 56 degrees F.
Let x be the decrease in temperature.
Step 2. The equation that will help us solve the problem is:
[tex]78-x=56[/tex]This is because 78 is the original temperature, and after a decrease of x degrees, the final temperature is 56.
Step 3. Now that we have the equation, we need to solve for x.
To solve for x, subtract 78 to both sides of the equation:
[tex]\begin{gathered} -x=56-78 \\ -x=-22 \\ \downarrow\downarrow \\ x=22 \end{gathered}[/tex]The decrease in temperature was 22 degrees.
Answer: The equation is
78-x=56
The solution
x=22
in order to build a shee you need to build 6 inches of height for a base that is 26 inches long. What is the height of a shed thats is 156 inches long?Part A: What id the equation that represents this relationship y= blankPart B: A shed that is 156 inches long is blank inches high
Answers
The sheds must be similar so we han have the relation:
[tex]\frac{y}{6}=\frac{156}{26}[/tex]So we can solve for y to have an expression so:
[tex]y=\frac{6\cdot156}{26}[/tex]and we can solve it so:
[tex]y=36[/tex]So the shed that is 156 inches long has a high of 36 inches
Based on the 2017 season, the Houston Astros have a winning percentage of 623. Use the binomial model to find the probability that the Astros will win 4 of their next 6 games. P (1) = ( z Xn-3) p'ai O A 12.4% O B. 24.7% O C. 32.1% O D. 62.3%
Answers
a pilot took 1/2 hour to complete 1/3 of hjis trip. How much longer will it take him to complete his trip
Answers
It took the pilot half an hour to complete one-third of the trip, to determine how much it will take him to complete the trip, you can use cross multiplication to determine it.
1/3 of the trip → 1/2 hour
Whole trip → x hours
Let "1" represent the whole trip, that is, all three parts of it. Both relationships are at the same ratio so that:
[tex]\begin{gathered} \frac{\frac{1}{2}}{\frac{1}{3}}=\frac{x}{1} \\ \frac{\frac{1}{2}}{\frac{1}{3}}=x \end{gathered}[/tex]When you divide by a fraction, is the same as multiplying the dividend by the reciprocal fraction of the divisor, you can write the expression as follows:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{3}{1}=x \\ \frac{1}{2}\cdot3=x \\ x=\frac{3}{2}=1.5 \end{gathered}[/tex]It will take him one and a half hours to complete the trip.
5. ). A cosmetic company has developed a new after-shave lotion. If the company goesinto small-scale production its annual fixed costs will be $200,000 and it can produce theproduct for a variable cost of $3 per unit. If the company goes into large-scale production itsannual fixed costs will be $400,000 and it can produce the product for a variable cost of$1.25 per unit.Assume that the selling price is $7 per unit.a) Determine the break-even points for small scale and large scale production.b) If the expected sales are for 500,000 units, which production process is more profitablesmall-scale or large-scale?c) Determine profits for both cases,d) Find the number of units for which one would be indifferent between small-scale andlarge-scale production
Answers
This is a simple question to solve.
First, we need to understand what is a break-even point.
Well, a break-even point is a point in sales where your company know it has covered all money they spent on fixed and variable costs but still don't have a profit. It means --> no loss but also no profit.
Letter A) To calculate a break-even point we can use the following equation:
[tex]BEP=\frac{C_{fixed}}{S_{price}-C_{variable}}[/tex]Where:
BEP = Break-even point;
Cfixed = Fixed Cost;
Sprice = Selling price; and
Cvariable = Variable cost.
So, for small-scale we have:
[tex]\begin{gathered} BEP=\frac{C_{fixed}}{S_{price}-C_{variable}} \\ BEP=\frac{200000_{}}{7_{}-3_{}} \\ BEP=50000 \end{gathered}[/tex]And, for large-scale:
[tex]\begin{gathered} BEP=\frac{C_{fixed}}{S_{price}-C_{variable}} \\ BEP=\frac{400000_{}}{7_{}-1.25_{}} \\ BEP\cong69565.217 \end{gathered}[/tex]Letter B:
We can see above the break-even point for small-scale(50000) is lower than large-scale(69565.217). That means for small-scale we need to sell fewer units to cover all our cost and start profit after that point, so if the expected sales are for 500000 units, the small production is more profitable.
Letter C:
The profits for small-scale starts after 50000 units sold and for large-scale starts after 69565 units sold approximately.
Letter D:
As we understand what is a break-even point, we know the number of units for each one would be indifferent between small-scale and large-scale is 50000 units and approximately 69565 respectively because at these points for both (small and large scale) we have neither a profit nor a loss.
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6), and all the outcomes are equally likely. Find P (6). Express your answer in exact form.P() =DOX
Answers
Sample space = {1, 2, 3, 4, 5, 6)
• P (1) = 1/6 or 16.67%
,• P (2) = 1/6 or 16.67%
,• P (3) = 1/6 or 16.67%
,• P (4) = 1/6 or 16.67%
,• P (5) = 1/6 or 16.67%
,• P (6) = You can complete it