A line segment has the endpoints at (-6, -10) and (23, 6) then the midpoints of the line segment will be (17, -2).
What is meant by line segment?An area or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be estimated by utilizing either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
A line segment has the endpoints at (-6, -10) and (23, 6).
Mid point of the line segment is given by [tex]$\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$[/tex]
The midpoints of the line segment will be
= [tex]$\frac{23+-6}{2}[/tex], [tex]$\frac{-10+6}{2}}[/tex]
= 17, -2
Therefore midpoints of the line segment will be (17, -2).
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Mr. Ellis has started a vegetable garden. He bought 15 bags of soil and 3 bags offertilizer for $282.72. He realized he didn't have enough supplies, so he boughtanother 5 bags of soil and 2 bags of fertilizer for $107.23. What was the cost of eachbag of soil and fertilizer? Let the cost of each bag of soil = x and the cost of eachbag of fertilizer = y. A. Each bag of soil was $12.99, and each bag of fertilizer was $16.25.B. Each bag of fertilizer was $9.75, and each bag of soil was $77.99.C. Each bag of soil was $9.75, and each bag of fertilizer was $77.99.D. Each bag of fertilizer was $12.99, and each bag of soil was $16.25.
The variables are:
x: cost of each bag of soil
y: cost of each bag of fertilizer
He bought 15 bags of soil and 3 bags of fertilizer for $282.72, that is,
15x + 3y = 282.72 (eq. 1)
He bought another 5 bags of soil and 2 bags of fertilizer for $107.23, that is,
5x + 2y = 107.23 (eq. 2)
Multiplying equation 2 by 3, we get:
3(5x + 2y) = 3(107.23)
3(5x) + 3(2y) = 3(107.23)
15x + 6y = 321.69 (eq. 3)
Subtracting equation 3 to equation 1, we get:
15x + 3y = 282.72
-
15x + 6y = 321.69
-------------------------------
-3y = -38.97
y = -38.97/-3
y = 12.99
Replacing this result into the first equation,
15x + 3(12.99) = 282.72
15x + 38.97 = 282.72
15x = 282.72 - 38.97
15x = 243.75
x = 243.75/15
x = 16.25
D. Each bag of fertilizer was $12.99, and each bag of soil was $16.25.
enter the explicit and recursive equations for sequence 2, 12,72, 432
The explicit and recursive equations of the sequence 2, 12, 72, 432 are f(n) = 2 · 6ⁿ⁻¹ and f(n) = 6 · f(n - 1).
What is the equation behind the sequence?
In this problem we find an example of a geometric progression, whose explicit and recursive forms are defined below:
Explicit form
f(n) = a · rⁿ⁻¹
Recursive form
f(1) = 2, f(n) = r · f(n - 1)
Where:
a - Value of the first element of the series.r - Common ration - Index of the n-th element of the series.If we know that a = 2 and r = 6, then we find the explicit and recursive equations below:
Explicit form
f(n) = 2 · 6ⁿ⁻¹
Recursive form
f(n) = 6 · f(n - 1)
The first four elements of the sequence are 2, 12, 72, 432.
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The graph of y=(x + 2)^2 – 1 is reflected across the x axis and then translated up 3 units and right 4 units. What is the equation for the transformed graph?
ANSWER
[tex]y=-(x-2)^2\text{ + 4}[/tex]EXPLANATION
We have that the graph of y is:
[tex]y=(x+2)^2\text{ - 1}[/tex]It is first reflected about the x axis.
A reflection about the x axis is represented as:
y = -f(x)
which means that we find the negative of the function:
[tex]\begin{gathered} \Rightarrow y=-\lbrack(x+2)^2\text{ - 1\rbrack} \\ y=-(x+2)^2\text{ + 1} \end{gathered}[/tex]Then, it is translated 3 units up (vertical shift) and 4 units right (horizontal shift).
A translation is represented as:
y = f(x - a) + b
where a = horizontal shift; b = vertical shift
So, we have to find:
y = f(x - 4) + 3
That is:
[tex]\begin{gathered} y\text{ = }-\lbrack(x-4)+2\rbrack^2\text{ + 1 + 3} \\ y=-(x-4+2)^2\text{ + 4} \\ y=-(x-2)^2\text{ + 4} \end{gathered}[/tex]Therefore, that is the equation of the transformed graph.
A study is done on the number of bacteria cells in a petri dish. Suppose that the population size P(1) after t hours is given by the following exponential function.P (1) = 2000(1.09)Find the initial population size.Does the function represent growth or decay?By what percent does the population size change each hour?
Given:
the population size P(1) after t hours is given by the following exponential function:
[tex]P(1)=2000(1.09)[/tex]Find the initial population size?
The initial size = 2000
Does the function represent growth or decay?
Growth, Because the initial value multiplied by a factor > 1
By what percent does the population size change each hour?
The factor of change = 1.09 - 1 = 0.09
So, the bacteria is increasing by a factor of 9% each hour
what is an equation of the line that passes through the point -6 and -7 and is perpendicular to the line 6x+5y=30I got y=5/6-2 but apparently its wrong
First we can find the slope. The standard form of the equation of a line is:
[tex]y=ax+b[/tex]Where a is the slope and b is the intercept.
When 2 lines are perpendicular, the slopes are reciprocal and opposite to each other. If we write the given equation of the perpendicular line in the standard form we have:
[tex]6x+5y=30\rightarrow y=-\frac{6}{5}x+\frac{30}{5}\rightarrow y=-\frac{6}{5}x+6[/tex]So you got the slope right, it's 5/6.
Now, with the given point we find the intercept. The point is x = -6 and y = -7, so we replace these values into the expression we have until now:
[tex]y=\frac{5}{6}x+b[/tex][tex]-7=\frac{5}{6}(-6)+b[/tex]And solve for b
[tex]-7=-5+b\rightarrow b=-7+5=-2[/tex]So the equation of the line is:
[tex]y=\frac{5}{6}x-2[/tex]please help! prove by bubble proof. please show you work
Statement | Reason
Points M and N are on AB | Given
AM ≅ NB | Given
AM + MN ≅ NB + MN | Addition Property of Equality
AM + MN = AN | Segment Addition Postulate
NB + MN = MB | Segment Addition Postulate
AN ≅ MB | Substitution Property of Equality
Drag "Yes" if the lengths could create a triangle, or "No" if the lengths could not create a triangle.
Okay so I’m doing this assignment and got stuck ont his question can someone help me out please
ANSWER
[tex]B.\text{ }\frac{256}{3}[/tex]EXPLANATION
We want to find the value of the function for F(4):
[tex]F(x)=\frac{1}{3}*4^x[/tex]To do this, substitute the value of x for 4 in the function and simplify:
[tex]\begin{gathered} F(4)=\frac{1}{3}*4^4 \\ F(4)=\frac{1}{3}*256 \\ F(4)=\frac{256}{3} \end{gathered}[/tex]Therefore, the answer is option B.
Nora needs to order some new supplies for the restaurant where she works. Therestaurant needs at least 478 forks. There are currently 286 forks. If each set on salecontains 12 forks, write and solve an inequality which can be used to determine s, thenumber of sets of forks Nora could buy for the restaurant to have enough forks.<
Nora needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 478 forks. There are currently 286 forks. If each set on sale
contains 12 forks, write and solve an inequality which can be used to determine s, the
number of sets of forks Nora could buy for the restaurant to have enough forks.
Let
s -----> the number of sets of forks Nora could buy for the restaurant to have enough forks
so
the inequality that represent this situation is
[tex]286+12s\ge478[/tex]solve for s
[tex]\begin{gathered} 12s\ge478-286 \\ 12s\ge192 \\ s\ge16 \end{gathered}[/tex]the minimum number of sets is 16What is the equation of this line?
A. y=4/3x−5
B. y=3/4x−5
C. y=−43/x−5
D. y=4/3x+5
Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the account in 4 years? ƒ(t) = ae^rt
To determine the amount that will be on the account after 4 years you have to apply the given exponential function that models the amount of money on the account with respect to the time.
[tex]f(t)=ae^{rt}[/tex]Where
a represents the initial amount
r represents the interest rate expressed as a decimal value
t is the time period in years
The initial amount on the account is a= $600
The time period is t= 4 years
The interest rate is r=5%, divide it by 100 to express it as a decimal value:
[tex]r=\frac{5}{100}=0.05[/tex]Using this information, you can calculate the final amount:
[tex]\begin{gathered} f(t)=ae^{rt} \\ f(4)=600e^{0.05\cdot4} \\ f(4)=600e^{0.2} \\ f(4)=732.84 \end{gathered}[/tex]After 4 years there will be $732.84 on the account. The correct option is B.
Mr. Santos cycled a total of 16 kilometers by making 4 trips to work. After 5 trips to work, how many kilometers will Mr. Santos have cycled in total? 5 Kilometers
According to the information given in the exercise, you know that he cycled a total of of 16 kilometers by making 4 trips to work.
Let be "d" the total amount of kilometers Mr. Santos will have cycled after 5 trips to work.
Based on the above, you can set up the following proportion:
[tex]\frac{16}{4}=\frac{d}{5}[/tex]Finally, you must solve for the variable "d" in order to find its value. This is:
[tex]\begin{gathered} 4=\frac{d}{5} \\ \\ (4)(5)=d \\ d=20 \end{gathered}[/tex]Therefore, the answer is:
[tex]20\operatorname{km}[/tex]what does y= 75-29 equal?
Starting with the expression:
[tex]y=75-29[/tex]Substract the numbers to find the value of y:
[tex]y=46[/tex]Answer:
if y = 75-29 the we subtract 29 from 15
75-29=46
y=46
Andre and Elena are each saving money, Andre starts with 100 dollars in his savings account and adds 5 dollars per week, Elena starts with 10 dollars in her savings account and adds 20 dollars each week.After 4 weeks who has more money in their savings account?? Explain how you know.After how many weeks will Elena and Andre have the same amount of money in their savings account? How do you know?
We can model each savings account balance in function of time as a linear function.
Andre starts with $100 and he adds $5 per week. If t is the number of weeks, we can write this as:
[tex]A(t)=100+5\cdot t[/tex]In the same way, as Elena starts with $10 and saves $20 each week, we can write her balance as:
[tex]E(t)=10+20\cdot t[/tex]We can evaluate their savings after 4 weeks (t=4) as:
[tex]\begin{gathered} A(4)=100+5\cdot4=100+20=120 \\ E(4)=10+20\cdot4=10+80=90 \end{gathered}[/tex]After 4 weeks, Andre will have $120 and Elena will have $90.
We can calculate at which week their savings will be the same by writing A(t)=E(t) and calculating for t:
[tex]\begin{gathered} A(t)=E(t) \\ 100+5t=10+20t \\ 5t-20t=10-100 \\ -15t=-90 \\ t=\frac{-90}{-15} \\ t=6 \end{gathered}[/tex]In 6 weeks, their savings will be the same. We know it beca
How many true, real number solutions does the equation n + 2 = -16-5n have?solution(s)
The equation is
n + 2 = - 16 - 5n
By collecting like terms, we have
n + 5n = - 16 - 2
6n = - 18
Dividing both sides of the equation by 6, we have
6n/6 = - 18/6
n = - 3
It has only one solution
A particle is moving along the x-axis and the position of the particle at the time t is given by x (t) whose graph is shown above. Which of the following is the best estimate for the speed of the particle as time t=4?
Given:
We are given the x(t) vs time curve.
To find:
Speed of particle at t = 4
Step by step solution:
We know that the slope of x-t curve represents the speed of the particle.
To calculate the speed of the particle at t = 4, We will calculate the slope of the curve at t = 4
[tex]\begin{gathered} Slope=\frac{y_2-y_1}{x_2-x_1} \\ \\ Slope=\frac{40-10}{6-0} \\ \\ Slope=\frac{30}{6} \\ \\ Slope\text{ = 6} \end{gathered}[/tex]From here we can say that the slope of the curve between x = 0 and x = 6 is equal to 5.
So the value of speed is also 5 units, Which is equal to option A.
Y.11 Multi-step problems with customary uni You have prizes to reveal! Go to your Tracy decides to take her puppy for a walk. After 90 feet, they stop to smell some roses. Then, Tracy runs into a friend 200 yards up the road. They start talking, and soon it's time for Tracy to go home. So, she and her puppy head back to her house. How many feet long was Tracy's walk? feet Submit
Given:
The distance travelled by Tracy till she stopped to smell roses, x=90 feet.
The distance from roses to the friend, y=200 yards.
The distance travelled by Tracy one side,
[tex]\begin{gathered} D=x+y \\ =90\text{ f}eet+200\times3feet \\ =90\text{ f}eet+600\text{ f}eet \\ =690\text{ f}eet \end{gathered}[/tex](1 yard=3 feet).
Now, the total distance travelled byTracy both sides is,
[tex]\begin{gathered} d=2D \\ =2\times690\text{ f}eet \\ =1380\text{ f}eet \end{gathered}[/tex]Therefore, Tracy walk was 1380 feet long.
What is the value of 12x if x = −5?
−60 −17 −125 −47
Answer:
-60
Step-by-step explanation:
the city pays students $50 per day to serve snow cones at the local summer festival. Analyze the potential earnings of a student who works the whole week of the festival if working partial days is not permitted. this situation can be modeled by the function f(x)=50x.What is a reasonable maximum value for the dependent variable? Explain how you arrived at your answer.
Given:
The per day earning $50
The function is
[tex]f(x)=50x[/tex]Find-:
The maximum value of earning
Explanation-:
The function is
[tex]f(x)=50x[/tex]Where,
[tex]x=\text{ Number of days}[/tex]The students work for a whole week.
[tex]1\text{ week }=7\text{ Days}[/tex]So the maximum value is
[tex]\begin{gathered} f(x)=50x \\ \\ x=7 \\ \\ f(7)=50\times7 \\ \\ f(7)=350 \end{gathered}[/tex]The maximum earning is $350
2/(x - 1) - 1/(x + 1) - 3/(x ^ 2 - 1)
The first step to solve this problem is to solve the substraction between the first two fractions:
[tex]undefined[/tex]determine how many vertices and how many edges the graph has
in the given figure,
there are 4 vertices
and there are 3 edges.
thus, the answer is,
vertiev
Write a division equation that represents the equation, How many 3/4 are in 10/9?
Given:
The number of 3/4 in 10/9.
To find the division equation that represents the given problem:
That is a number that is multiplied by 3/4 to obtain 10/9.
We need to find the number.
[tex]x\times\frac{3}{4}=\frac{10}{9}[/tex]Thus, the division equation will be,
[tex]x=\frac{10}{9}\div\frac{3}{4}[/tex]Review: Solve for Area AND Circumference. A giant holiday cookie has a radius of 5 inches. What is the area of the cookie? What is the circumference of the cookie?
Remember that the formual for the area of a circle is:
[tex]A=\pi r^2[/tex]And the formula for the circumference is:
[tex]C=2\pi r[/tex]Using this formulas and the data given,
[tex]\begin{gathered} A=\pi(5^2)\Rightarrow A=78.54 \\ C=2\pi(5)\Rightarrow A=31.42 \end{gathered}[/tex]The cookie has an area of 78.54 square inches and a circumference of 31.42 inches
2x^3-16x^2-40x=0 factor
The given expression is
[tex]2x^3-16x^2-40x=0[/tex]We extract the common factor 2x.
[tex]\begin{gathered} 2x(x^2-8x-20)=0 \\ 2x=0\rightarrow x=0 \\ x^2-8x-20=0 \end{gathered}[/tex]The first solution is 0.
Now, we solve the quadratic expression. We have to find two numbers whose product 20 and whose difference is 8. Those numbers are 10 and 2.
[tex]x^2-8x-20=(x-10)(x+2)[/tex]Hence, the given expressions expressed, as factors, is[tex]2x^3-16x^2-40x=x(x-10)(x+2)[/tex]Which of these could be the dimensions of a unit cube? Select all that apply. 1 ft. by 1 ft. by 1 ft. 1 in. by 2 in. by 1 in. 1 ft. by 1 in. by 1 cm El mm by mi byl mm 1 m by 1 m by 2 m
Since it is a cube, all its three dimensions must be equal.
Also the term 'unit cube' is used which suggests that the volume of the cube should be 1 units.
Consider that the 2nd and 5th options are incorrect as the dimensions are note equal.
Consider the third dimension, note that before analyzing the numeric part we should make sure that the units are same for all three dimensions.
Here, the units are different, and we know that,
[tex]1\text{ ft }\ne1\text{ in }\ne1\text{ cm}[/tex]So the third option is also incorrect.
Consider that the options 1st and 4th consist all three dimensions same. Also their product yields 1 in the same cubic units.
So they both represent a unit cube.
Therefore, options 1st and 4th are the correct choices.
Translate the triangle.Then enter the new coordinates.A (3,4)C(-5,0)<4,2>B(-12)A' ([?], [])B'([ ], [ ])C'([ ], [])
Given:
The coordinates of the triangle are A(-3,4), B(-1,2), and C(-5,0).
Required:
We need to translate the given triangle to <4,2> 4 units right and 2 units up.
Explanation:
The image of the point can be written as follows.
[tex](x,y)\rightarrow(x+4,y+2)[/tex]Consider point A(-3,4).
[tex]A(-3,4)\rightarrow A^{\prime}(-3+4,4+2)[/tex][tex]A(-3,4)\rightarrow A^{\prime}(1,6)[/tex]Consider point B(-1,2).
[tex]B(-1,2)\rightarrow B^{\prime}(-1+4,2+2)[/tex][tex]B(-1,2)\rightarrow B^{\prime}(3,4)[/tex]Consider point C(-5,0).
[tex]C(-5,0)\rightarrow C^{\prime}(-5+4,0+2)[/tex][tex]C(-5,0)\rightarrow C^{\prime}(-1,2)[/tex]Final answer:
A'(1, 6), B'(3, 4) and C'(-1, 2).
What is the solution to the system of equations shown below?3x+8y=-186x+16y=-54A.) The solution is (0, −18).B.) The solution is (−18, 0).C.) There are an infinite number of solutions.D.) There is no solution.
3x + 8y = -18 -----------------------(1)
6x + 16 y = - 54 ---------------------------(2)
Using elimination method,
multiply equation (1) by 6 and equation (2) by 3
18x + 48y = -108 -----------------(3)
18 x + 48y = 162 -------------------(4)
From this, we can deduce that there is no solution to the system of equations
What is 4527 written in scientific notation?A.4.527B.4.527 x 10*2C.4.527 x 10*3D.4.527 x 10*4
Solution
- The question would like us to convert the number 4527 to scientific notation.
- In order to write a number to its scientific notation, we need to follow these steps:
1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.
2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.
- We can apply these steps to solve the question given as follows:
- Thus, we have that the scientific notation of the number 4527 is
[tex]4.527\times10^3[/tex]Final Answer
The scientific notation of the number 4527 is
[tex]4.527\times10^3\text{ (OPTION C)}[/tex]
Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 362 with 54 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
We have to find the 80% confidence interval for a population proportion.
The sample size is n = 362 and the number of successes is X = 54.
Then, the sample proportion is p = 0.149171.
[tex]p=\frac{X}{n}=\frac{54}{362}\approx0.149171[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_s=\sqrt{\frac{p(1-p)}{n}} \\ \sigma_s=\sqrt{\frac{0.149171*0.850829}{362}} \\ \sigma_s=\sqrt{0.000351} \\ \sigma_s=0.018724 \end{gathered}[/tex]The critical z-value for a 80% confidence interval is z = 1.281552.
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z\cdot\sigma_s=0.149171-1.281552\cdot0.018724\approx0.1492-0.0240=0.1252[/tex][tex]UL=p+z\cdot\sigma_s=0.1492+0.0240=0.1732[/tex]As the we need to express it as a trilinear inequality, we can write the 80% confidence interval for the population proportion (π) as:
[tex]0.125<\pi<0.173[/tex]Answer: 0.125 < π < 0.173
Explain how to translate the point (5, 2) with the transformations: D2 and r(180,0). Make sure toexplain, in words, how you got your final answer, including where the point was after the firsttransformation.Edit ViewInsertFormat Tools TableΑν12ptvParagraph | BIUTv
We will have the following:
First: We dilate by a factor of 2, then we would have:
[tex](10,4)[/tex]Second: We rotate by 180°:
[tex](-10,-4)[/tex]