We have the following:
First we calculate the slope of the line where we are given two points (6,8) and (10,0)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]repplacing:
[tex]m=\frac{0-8}{10-6}=\frac{-8}{4}=-2[/tex]now, when two lines are perpendicular:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ -2=-\frac{1}{m_2} \\ 2=\frac{1}{m_2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]now,
[tex]y=mx+b[/tex]with the point (4,5), replacing:
[tex]\begin{gathered} 5=\frac{1}{2}\cdot4+b \\ 5=2+b \\ b=5-2 \\ b=3 \end{gathered}[/tex]Therefore, the equation is:
[tex]\begin{gathered} y=\frac{1}{2}x+3 \\ y=\frac{x}{2}+3 \end{gathered}[/tex]check:
[tex]\begin{gathered} y=\frac{4}{2}+3 \\ y=2+3 \\ y=5 \end{gathered}[/tex]Therefore, the answer is y = x/2 + 3
The function 1 (2) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The
farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x)=+1, where x is the number of piglets. The farmer
always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
A function which represents the number of pens as a function of the female pigs is: p(l(z)).
How to determine the function that represents the number of pens?From the information provided, we have the following the following functions:
Function, l(z) = 4x
Where:
l(z) represents the litter of piglets born on the farm.x represents the number of female pigs on the farm.Function, p(x) = x/8 + 1
Where:
p(x) represents the number of pens required.x represents the number of piglets.Next, we would substitute the the litter of piglets born on the farm l(x) into the number of pens required as follows;
p(x) = x/8 + 1
p(l(z)) = 4x/8 + 1
p(l(z)) = 0.5x + 1
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Complete Question:
Function l(z) = 4x is used to calculate the litter of piglets born on the farm; x represents the number of female pigs on the farm. Each female pig births 4 piglets. The farmer will need pens to house all the piglets. One pen can house 8. The number of pens required is written as p(x) = x/8 + 1, where x is the number of piglets. The farmer always builds one extra pen. Which of the following functions represents the number of pens as a function of the female pigs?
p(p(x))
p(l(z))
1(p(x))
1 (1 (x))
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y = -16x2 + 261x + 130
Answer
The highest height attained by the rocket = 1194.4 feet
Explanation
The height of the rocket, y, in feet as a function of the time, x in seconds as
y = -16x² + 261x + 130
We are then asked to find the maximum height reached by the rocket
To do this, we would use the differentiation analysis to obtain the maximum of this function.
At maximum point for any function,
The first derivative = (dy/dx) = 0
The second derivative = (d²y/dx²) < 0
y = -16x² + 261x + 130
First derivative
(dy/dx) = -32x + 261 = 0
32x = 261
Divide both sides by 32
(32x/32) = (261/32)
x = 8.15625 s
We can then substitute this value of x (time) into the equation to get the maximum height (y)
y = -16x² + 261x + 130
At x = 8.15625 s,
y = -16 (8.15625)² + 261 (8.15625) + 130
= -1064.39 + 2128.78 + 130
= 1194.39
= 1194.4 feet to the nearest tenth.
Hope this Helps!!!
What is the mixed number answer 4 4/9 + 8 7/9
Hello there. To solve this question, we'll have to remember some properties about mixed numbers.
Given the mixed number a b/c, we can write it as and it is the same as
Therefore in the expression:
[tex]4\frac{4}{9}+8\frac{7}{9}[/tex]We rewrite it as
[tex]4+\frac{4}{9}+8+\frac{7}{9}[/tex]Adding the fractions, we have:
[tex]12+\frac{11}{9}=\frac{119}{9}[/tex]And we have to write the answer in mixed fraction form, therefore we perform
[tex]\frac{119}{9}=\frac{117+2}{9}=13\frac{2}{9}[/tex]This is the answer we're looking for.
Jamir is training for a race and is running laps around a field. If the distance around the field is 450 yards,how many complete laps would he need to do to run at least 4 miles?laps
We have that Jamir is training for a race and is running laps around a field:
• The distance around the field is 450 yards (per lap).
,• He needs to run at least 4 miles.
1. Now we can proceed as follows to find the number of laps Jamir needs to run as follows:
[tex]\begin{gathered} 1\text{ Mile}=1760.0065617yards \\ \\ 4\text{ Miles=}4(1760.0065617yards)=7040.0262468yards \end{gathered}[/tex]Then we have that Jamir needs to run about 7040.0262468 yards.
2. Since the distance around the field is 450 yards (per lap), then we have:
[tex]7040.0262468yards*\frac{1lap}{450yards}=15.6445027707laps[/tex]Therefore, in summary, Jamir needs to run about 15.64 laps to run at least 4 miles (almost 16 laps - if we round the result to the nearest whole number).
20. A local children's center has 47 children enrolled, and 6 are selected to take a picture for the center's advertisement. How many ways are there to select the 6 children for the picture?
Given:
Total number of children enrolled = 47
Number of children to be selected = 6
Number of ways to select 6 children for the picture are:
[tex]=^{47}C_6[/tex]Formula for combination is given as:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]Applying this, we get:
[tex]\begin{gathered} ^{47}C_6=\frac{47!}{6!(47-6)!} \\ =\frac{47!}{6!41!} \\ =10737573 \end{gathered}[/tex]Therefore, the required number of ways are 10737573.
A bag contains seven green marbles and four yellow marbles.• 2a) If you randomly pick a marble and then pick a second marble without returning the marble to the bag, what is the probability the firstmarble is yellow and the second marble is green?• 3b) If you return the first marble to the bag before picking another marble, what is the probability the first marble is yellow and the secondmarble is green?%DULUa) PIY and G without replacing) = type your answer...$6; b) PIY and G with replacing) = type your answer.4Instructions
independent vs dependent equation5х – Зу = 10 бу = kx - 42
We will assume that we want to know if the system of equations is independent or dependent:
[tex]\begin{cases}5x-3y=10\text{ (1)} \\ 6y=kx-42\text{ (2)}\end{cases}[/tex]where k is a real number. We will try to find the solutions to the system, and we will try to give values to k for which the system becomes independent or dependent.
We will use substitution, we solve for the variable x on the first equation to obtain:
[tex]\begin{gathered} 5x-3y=10 \\ 5x=10+3y \\ x=\frac{10+3y}{5} \end{gathered}[/tex]And now we replace it onto the second equation:
[tex]\begin{gathered} 6y=k(\frac{10+3y}{5})-42 \\ 6y=\frac{10k+3ky}{5}-42 \\ 6y=\frac{10k+3ky-210}{5} \\ 30y=10k+3ky-210 \\ 30y-3ky=10k-210 \\ y(30-3k)=10k-210 \\ y=\frac{10k-210}{30-3k} \end{gathered}[/tex]And the value of x will be:
[tex]\begin{gathered} x=\frac{10+3(\frac{10k-210}{30-3k})}{5}=\frac{10+\frac{10k-210}{10-k}}{5} \\ =\frac{10(10-k)+10k-210}{5(10-k)} \\ =\frac{100-10k+10k-210}{50-5k} \\ =-\frac{110}{50-5k} \\ =-\frac{22}{10-k} \end{gathered}[/tex]This means that a solution of the system will be:
[tex]\begin{cases}x=-\frac{55}{10-k} \\ y=\frac{10k-210}{30-3k}\end{cases}[/tex]Now, for finding the values which make the system dependent. This happens when the lines have the same slope, this is, when:
[tex]\begin{gathered} \frac{-5}{-3}=\frac{k}{6} \\ \frac{5}{3}=\frac{k}{6} \\ 30=3k \\ 10=k \end{gathered}[/tex]We did the division of the opposite of the coefficient of x, over the coefficient of y. This means that the system will be independent for each value of k different than 10, and will be dependent for k=10.
3. Select all the expressions that will have a remainder. 377 644 74 – 3 96 = 5 56 – 2
To obtain the term that will give a remainder, we will have to check if the dividend is a multiple of the divisor
Dividends and divisors are the two key ingredients that yield the quotient. The dividend is the number being divided, while the divisor is the number by which the dividend is divided. In other words, given a÷b, a is the dividend and b is the divisor
Looking at
37 ÷ 3 = (12 remainder 1), 37 is not a multiple of 3, so this will give a remainder of 1
64 ÷ 4 = (16 remainder 0), 64 is a multiple of 4, so this will not give a remainder
74 ÷ 3 = (24 remainder 2), 74 is not a multiple of 3, so this will give a remainder of 2
96 ÷ 5 = (19 remainder 1), 95 is not a multiple of 5, so this will give a remainder of 1
56 ÷ 2 = (28 remainder 0), 56 is a multiple of 2, so this will not give a remainder
What is the area of the circle below, in terms of ?90 metersO 457O 907O 1807O 81007134
Step 1: Write out the formula
[tex]\begin{gathered} \text{Area of a circle = }\pi r^2 \\ \text{where } \\ r=\text{ the radius of the circle} \end{gathered}[/tex]Step 2: Write out the given values and substitute them into the formula
[tex]r=90m[/tex]Therefore,
[tex]\text{ the area of the circle = }\pi(90)^2=\pi\times8100=8100\pi m^2[/tex]Hence, the area in terms of pi is
[tex]8100\pi[/tex]The last choice is the correct answer
Model -4 + -2 using counter chipsRed chip = 1 Yellow chip = 1What’s the sum?
Given the following question:
Since both are negatives and we are adding the two together:
We need 4 red chips to represent the negative four (-4)
We need 2 more red chips to present the negative two (-2)
The total sum of -4 + -2 is...
[tex]-4+-2=-6[/tex]To represent the sum using the chips we will place "six red chips."
Suppose your bank charges a $7 monthly fee and $0.11 per check. If you write 62 checks in a year, how much money in fees would you expect to pay for the year? Type out acalculations and make sure your final answer is clear.
The cost has a monthly fee and a per check fee.
We can write the bank fee as:
[tex]C(m,c)=7m+0.11c[/tex]m: months, c: number of checks.
If, in a year (m=12 months), you write 62 checks (c=62), the total fee is:
[tex]C(12,62)=7\cdot12+0.11\cdot62=84+6.82=90.82[/tex]You expect to pay a yearly fee of $90.82.
It says. Use the graph of f to determine whether the following statement is true or false. The range of f is [-5,1]
The statement is false because the range is [-5, 1)
EXPLANATION
The range of a function is the set of y-values for which the function is defined.
From the graph given the range is:
-5≤ x < 1
This can be represented by interval notation as :
[ - 5, 1)
Therefore, the statement is false because the range is [-5, 1)
i need help with math
The value of 'y' for the parallel line drawn by the Amir is 25°.
Describe the term transversal?A transversal would be any line which intersects 2 straight lines at different point in geometry. In geometry, a transversal line connects two lines within the same plane at 2 separate points. Transversals contribute to the parallelism of two or more additional straight lines inside the Euclidean plane.For the given question;
There are two parallel line cut by the transversal drawn by the Amir.
Thus, the relation of the two angles are-
The supplement angle of (4y - 45) is 180 - (4y - 45).
And,
180 - (4y - 45) = y (vertical angles)
Simplify the equation;
180 - 4y + 45 = y
5y = 125
y = 25°
Thus, value of 'y' for the parallel line drawn by the Amir is y = 25°.
To know more about the transversal, here
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Circle A' is the result of reflecting circle A across the line l.Select all of the correct statements about the unchanged properties of circle A and circle A'. Choose all answers that apply.A: The radii of circle A and circle A' have the same lengthsB: Circle A and circle A' have the same circumference.C: Circle A and circle A' have the same area.D: None of the above.
ANSWER:
A: The radii of circle A and circle A' have the same lengths
B: Circle A and circle A' have the same circumference.
C: Circle A and circle A' have the same area.
STEP-BY-STEP EXPLANATION:
A figure, when reflected, does not lose any of its arithmetic characteristics, since it does not have any type of dilation or change in its figure.
This means that it conserves its radius, and by conserving its radius it conserves the circumference and the area.
Therefore, the correct answers are:
A: The radii of circle A and circle A' have the same lengths
B: Circle A and circle A' have the same circumference.
C: Circle A and circle A' have the same area.
Answer:
A
B
C
Are correct
Step-by-step explanation:
The table shows the mean number of basketball goals made by four random samples of players from the school teamduring this year's season.Sample #Sample MeanNumber of Goals71243548Is a valid prediction for the mean of the population possible using these samples?A: No, there are not enough samples.B: Yes, the sample means are all less than 10.C: Yes, the variation of the sample means is small.D: No, the variation of the sample means is too great.
Answer:
Step-by-step explanation:
You have $20,000 that you want to deposit into a savings account. You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Problem
You have $20,000 that you want to deposit into a savings account.
You have four options to choose from, Bank A offers 4.25% compounded monthly, (Ex 2) Bank B offers 6% compounded Semi Annually, (Ex 2) Bank C offers a simple interest account with a 5.5% rate, (Chapter 8.3) Bank D offers a rate of 4% compounded continuously. (Ex 3) How much money will you have in each account if you let the money sit for 5 years? Which is the best choice?
Solution
For this case we need to take in count the compound interest formula given by:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P= 20000, r= interest rate in fraction and n= number of times that the rate is compounded in a year, t= 5 years and A is the future value
And the simple interest formula:
[tex]A=P(1+rt)[/tex]And compound continuosly:
[tex]A=\text{Pe\textasciicircum{}rt}[/tex]Let's calculate the final amount for each case
Bank A
[tex]A=20000(1+\frac{0.0425}{12})^{12\cdot5}=24726.038[/tex]Bank B
[tex]A=20000(1+\frac{0.06}{2})^{2\cdot5}=26878.328[/tex]Bank C
[tex]A=20000(1+0.055\cdot5)=25500[/tex]Bank D
[tex]A=20000e^{0.04\cdot5}=24428.055[/tex]And the best choice for this case seems to be Bank B since we will have more money at the end of the 5 year
1. In the function f(x) = 2x +3, what does the x represent?2. In the function f(x) = 2x + 3, what does the f(x) represent?
a. h(-4) = -13
b. h(t) = 23 , t = 14
c. h(13) = 21
d. h(t) = -33 , t = -14
yson does 75 sit-ups during his work out. He wants to increase his sit-ups by 15%. Which represents the new amount of sit-up
Answer:
he does 86 sit ups instead of 75 to increase by 15 percent
Step-by-step explanation:
Answer: The correct answer is 86.25 sit-ups (or round-up to 87 whole sit-ups).
Step-by-step explanation:
S = current amount of sit-ups (75)
S2 = Increased amount of sit-ups by 15%
The equation:
S2 = S + (S x .15)
S2 = 75 + (75 x .15)
S2 = 75 + 11.25
S2 = 86.25 sit-ups
find each unit rate. round to the nearest hundredth if necessary 325 meters in 25 seconds
325 meters in 25 seconds
To find out the unit rate divide the total meters by the total seconds
so
325/25=13 m/sec
therefore
the answer is
13 m/secor 13 m per one secondWrite the function whose graph is the graph of y=x^3, but is shifted to the right 3 units.y=
The Solution:
Given the function below:
[tex]y=x^3[/tex]When the function is shifted to the right by 3 units, the new function becomes:
[tex]y=(x-3)^3[/tex]Therefore, the correct answer is
[tex]y=(x-3)^3[/tex]i don’t know how to put it into an equation
x is the unknown number
The difference of a number and 4: x-4
Twice the difference of a number and 4: 2(x-4)
Twice the difference of a number and 4 equals 3: [tex]2(x-4)=3[/tex]describe the reflection (s) that carry the regular pentagon onto itself.
EXPLANATION:
The reflection that is made on a figure,reverses its position with respect to a line called the axis of reflection.
IMPORTANT NOTE:
To make the reflection of the geometric figure shown in the exercise, we need to know the vertices and coordinates of the figure that allow us to make the corresponding reflection in the Cartesian plane of the pentagon
Point M is the midpoint of segment AB. If the coordinates of Mare (2, 8) and the coordinates of Aare (10, 12), find the coordinates of B.B(x, y) =(
Using the formula
[tex](x_{m\text{ , }}y_m)\text{ = (}\frac{x_1+x_2}{2}\text{ , }\frac{y_1+y_2}{2})[/tex]x₁= 10 y₁=12 Xm=2 Ym = 8
x₂ = ? y₂=?
Substituting and solving for x₂
[tex]x_m=\frac{x_1+x_2}{2}[/tex][tex]2\text{ = }\frac{10+x_2}{2}[/tex]Multiply both-side of the equation by 2
4 = 10 + x₂
subtract 10 from both-side of the equation
-6 = x₂
x₂= -6
Similarly, substituting and solving for y₂
[tex]y_m=\frac{y_1+y_2}{2}[/tex][tex]8=\frac{12+y_2}{2}[/tex]Multiply both-side of the equation by 2
16 = 12 + y₂
Subtract 12 from both-side of the equation
4 = y₂
y₂= 2
Hence; coordinates of B are;
B(x,y) = ( -6, 2)
an item is regular priced at $60. Linda bought it on sale for 30% off the regular price. how much did Linda pay?
Given data
*An item is regular priced at $60
*Linda bought is on sale on discount is 30%
Linda pay the price on the item is calculated as
[tex]\begin{gathered} p=60\times30\text{ PERCENT} \\ =60\times0.3 \\ =18 \end{gathered}[/tex]Thus, the charged amount on an item is $18
The graph of a quadratic function with vertex (0, -1) is shown in the figure below.Find the range and the domain in interval notation please include paranthese or brackets within your answer.
The domain is all the values that the function can take on the x axis, in this case it would be all the real numbers:
[tex]domain\to(-\infty,\infty)[/tex]The range is all the values that the function can take on the y-axis. For this function it will grow from vertex to infinity:
[tex]range\to\lbrack-1,\infty)[/tex]Remember that when intervals are written, parentheses are used for open values and square brackets for exact values.
Use the two-way table on left and right-handed people to create a two-way table that shows the joint and marginal relative frequencies. Drag and drop the numbers to complete the table. Dominant Hand left. right. totalfemale 11. 104. 115Male. 24. 92. 116total. 35. 196. 231 Dominante hand left. rigth. totalfemale maletotalBank:0.0480.1520.1670.3760.3980.4500.4980.5020.5260.84810.104
1st Row (Female)
[tex]\begin{gathered} \frac{11}{231}=0.048 \\ \frac{104}{231}=0.450 \\ \frac{115}{231}=0.498 \end{gathered}[/tex]2nd Row (Male)
[tex]\begin{gathered} \frac{24}{231}=0.104 \\ \frac{92}{231}=0.398 \\ \frac{116}{231}=0.502 \end{gathered}[/tex]Third Row (Total)
[tex]\begin{gathered} \frac{35}{231}=0.156 \\ \frac{196}{231}=0.848 \\ \frac{231}{231}=1 \end{gathered}[/tex]The completed table is given below:
a family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles
A family walked 240 miles in 4 hours yesterday at this rate how many hours will it take to walk another 150 miles ?
_____________________________________________________
Rate
240 miles / 4 hours = 60 miles / hour
_______________________
Can you see the updates?
_____________________
150 miles ÷ rate = time ( 150 miles)
150 miles ÷ 60 miles/hour = 150/ 60 = 2.5 hours
___________________________________
Total time = 4 h + 2.5 h = 6.5 h
_________________________________
Answer
It will take 2.5 h to walk another 150 miles (in total 240 + 150, 6.5 h )
Draw the given angles in standard position. 110 degrees, - 80 degrees
Standard Position of Angles
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
The ray on the x-axis is called the initial side and the other ray is called the terminal side.
Positive angles are measured counterclockwise, negative angles are measured clockwise.
The angle of 110 degrees is positive so it must be measured counterclockwise. The angle -80 will be drawn clockwise.
The following image shows the required angles:
There are 3 consecutive odd integers that sum to –9. What is the least of these integers?
let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
Maggie had a number of identical flowers for sale. She sold 70 of them with a 50% loss and sold the rest with a 80% profit. On the whole, Maggie still made a 10% profit. How many flowers did Maggie have at the beginning?
ANSWER:
130 flowers
STEP-BY-STEP EXPLANATION:
Let x be the total number of flowers, we can establish the following equation:
[tex]70\left(-50\%\right)+\left(x-70\right)\left(80\%\right)=x\left(10\%\right)[/tex]We solve for x:
[tex]\begin{gathered} 70\left(-0.5\right)+\left(x-70\right)\left(0.8\right)=x\left(0.1\right) \\ \\ -35+0.8x-56=0.1x \\ \\ 0.8x-0.1x=56+35 \\ \\ 0.7x=91 \\ \\ x=\frac{91}{0.7} \\ \\ x=130 \end{gathered}[/tex]The total number of flowers, that is, the ones it had at the beginning was 130