Given A(2,4) and B(5,-4) from problem #1. What is the slope of a line that is parallel to (AB) ⃡?What is the slope of a line that is perpendicular to (AB) ⃡?
Answers
Solution
Given that
[tex]\begin{gathered} A(2,4) \\ B(5,-4) \end{gathered}[/tex]To find the slope, m, of the line passing through the given points, the formula is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)\Rightarrow A(2,4) \\ (x_2,y_2)\Rightarrow B(5,-4) \end{gathered}[/tex]Substitute the coordinates into the formula to find the slope, m, of a line
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-4}{5-2}=\frac{-8}{3}=-\frac{8}{3} \\ m=-\frac{8}{3} \end{gathered}[/tex]The slope of the line AB passing through the given points is m = -8/3
A) If two lines are parallel, their slopes are equal.
Hence, the slope, m₁ of the line that is parellel to line AB is
[tex]m_1=-\frac{8}{3}[/tex]Thus, the slope of a line parallel to line AB is m₁ = -8/3
B) If two lines are perpendicular, the formula to find the slope m₂ of the line perpedicular to the slope of a given line
[tex]m_2=-\frac{1}{m_{}}[/tex]Where m = -8/3, the slope, m₂, of a line perpendicular to line AB will be
[tex]\begin{gathered} m_2=-\frac{1}{m_{}} \\ m_2=-\frac{1}{\frac{-8}{3}_{}}=\frac{3}{8} \\ m_2=\frac{3}{8} \end{gathered}[/tex]Thus, the slope of a line perpendicular to line AB is m₂ = 3/8
Related Questions
CJ loves Girl Scout cookies. He eats 3 cookies per hour. After 5 hours, there are 24 cookies left in the box. Write an equation in slope intercept form. Determine how many hours it will take CJ to eat the entire box of cookies.
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To solve this problem: y will represent the number of cookies, and x the number of hours.
To find the number of cookies that CJ eats per hour, we multiply 3 (since he eats 3 per hour) by x (the number of hours)
Since there we only 24 cookies left in the box, we will need to substract 3 by the number of hours that have passed, from 24 to find the number of cookies "y":
[tex]y=24-3(x-5)[/tex]This equation represents that the number of cookies "y" is equal to the 24 cookies that where left after 5 hours, and to that we substract 3 (which is the number of cookies per hour) by total number of hours that have passed since those 5 hours (x-5) because 5 hours that have already passed we substract them from x.
We need to simplify that equation to represent in slope-intercept form:
[tex]\begin{gathered} y=24-3x+15 \\ y=-3x+39 \end{gathered}[/tex]Now we need to determine the number of hours it would take to finish the cookies. So we are looking for the value of x, that makes y=0:
[tex]0=-3x+39[/tex]solving for the number of hours x:
[tex]\begin{gathered} -3x=-39 \\ x=-\frac{39}{(-3)} \\ x=13 \end{gathered}[/tex]It would take 13 hours for CJ to eat the entire box of cookies.
8. A farm water tower (with a capacity of 615 cubic metres) has sprung a leak. It loses water at the rate of 1 cubic metre an hour. If no one fixes it, when would the tower be empty? (Answer in weeks, days and hours; for example, 2 weeks, 2 days and 5 hours.)
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Given: A farm water tower (with a capacity of 615 cubic metres) has sprung a leak. It loses water at the rate of 1 cubic metre an hour
Find: when would the tower be empty.
Explanation: A capacity of farm water tower is 615 cubic meters.
if it loses water at the rate of 1 cubic meter an hour
it means it take 615 hours to be empty.
[tex]615\text{ hours=}\frac{615}{24}=25.625\text{ days}[/tex]25.625 conatins 3 weeks= 21 days.
25.625-21=4.625 days.
4.625 days contains 4 days and
[tex]0.625\times24=15\text{ hours}[/tex]Hence the final answer will be 3 weeks, 4 days and 15 hours .
please let me know when I come to work with this
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Comparing the blue bars (8 - 12 yrs old) and orange bars (13 - 17 yrs old), we can see that most of the blue bars centered between 1 - 1.9 hours of screen time while the orange bars somehow centered between 3 - 3.9 hours of screen time.
If more screen time mean less exercise, then, we can infer that on average, 13 to 17-year-olds gets less exercise compared to 8 to12-year-olds. (Option 3)
Question 4: -12a - 4 and -4(3a - 1) are equivalent expressions. True False > false
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If we use the distributive property on the second expression, we get the following:
[tex]-4\cdot(3a-1)=-4\cdot(3a)-4(-1)=-12a+4[/tex]therefore, the expressions are not equivalent
All changes 4. What are the coordinates of the midpoint of the line segment with endpoints (7, 2) and (3, 4)? O (5,3) O (4, -2) O (4,2) 0 (2, 1)
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We will find the coordinates of the mid-point using the following expression:
[tex]mp=(\frac{_{}x_2+x_1}{2},\frac{y_2+y_1}{2})_{}_{}_{}[/tex]So, when we replace we obtain the mid-point coordinates:
[tex]mp=(\frac{7+3}{2},\frac{2+4}{2})\Rightarrow mp=(5,3)[/tex]So, the coordinates of the mid-point are (5, 3).
The Knitting Club members are preparing identical welcome kits for new members. The Knitting Club has 45 spools of yarn and 75 knitting needles. What is the greatest number of identical kits they can prepare using all of the yarn and knitting needles?
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Common factors of 45 : 1,3,5,9,15,45
Common factors of 75 : 1,3,5,15,25,75
Common factors: 1,3,5,15
GReatest common factor = 15
15 identical kits
this is factor by grouping. did I do 1a right and how do I continue on 1b
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We will have the following:
*First: ( f ° g) (x):
[tex](f\circ g)(x)=\frac{(\frac{1}{x})+1}{(\frac{1}{x})-2}\Rightarrow(f\circ g)(x)=\frac{(\frac{1+x}{x})}{(\frac{1-2x}{x})}[/tex][tex]\Rightarrow(f\circ g)(x)=\frac{(1+x)(x)}{(x)(1-2x)}\Rightarrow(f\circ g)(x)=\frac{1+x}{1-2x}[/tex]Domain:
[tex](-\infty,\frac{1}{2})\cup(\frac{1}{2},\infty)[/tex]*Second: (f ° f) (x):
[tex](f\circ f)(x)=\frac{(\frac{x+1}{x-2})+1}{(\frac{x+1}{x-2})-2}\Rightarrow(f\circ f)(x)=\frac{(\frac{(x+1)+(x-2)}{x-2})}{(\frac{(x+1)-2(x-2)}{x-2})}[/tex][tex]\Rightarrow(f\circ f)(x)=\frac{(\frac{2x-1}{x-2})}{(\frac{-x+5}{x-2})}\Rightarrow(f\circ f)(x)=\frac{(2x-1)(x-2)}{(x-2)(-x+5)}[/tex][tex]\Rightarrow(f\circ f)(x)=\frac{2x-1}{-x+5}[/tex]Domain:
[tex](-\infty,5)\cup(5,\infty)[/tex]Carbon-14 is used for archeological carbon dating. Its half-life is 5730 years. How much of a 50-gram sample of Carbon-14 will be left in 1000 years?
Answers
Given:
The half-life of carbon-14 is 5730 years.
The initial amount of carbon is I = 50 grams.
Explanation:
To find the final amount of carbon after 1000 years.
The fundamental decay equation is,
[tex]\begin{gathered} F=Ie^{-\lambda t} \\ \text{Where, }\lambda=\frac{\ln 2}{t_{\frac{1}{2}}} \end{gathered}[/tex]Let us find the radioactive constant first.
[tex]\begin{gathered} \lambda=\frac{\ln 2}{5730} \\ \lambda=0.00012096809 \end{gathered}[/tex]Then, the final amount of the corban-14 is,
[tex]\begin{gathered} F=50e^{-0.000121(1000)}^{} \\ =44.30g \end{gathered}[/tex]Hence, the amount of a 50-gram sample of Carbon-14 will be left in 1000 years is 44.30 g.
Describe and correct the error in performing the operation of complex numbers and write the answer in standard form.
Answers
Answer:
-20+48i
Explanation:
The solution erroneously began by expressing the square as the square of each of the terms.
[tex](4+6i)^2=(4)^2+(6i)^2^{}[/tex]However, the correct way is to take the square of the entire expression inside the bracket as shown below:
[tex](4+6i)^2=(4+6i)(4+6i)[/tex]Next, we expand and simplify our result below:
[tex]\begin{gathered} =4(4+6i)+6i(4+6i) \\ =16+24i+24i+36i^2 \\ =16+48i+36(-1) \\ =16-36+48i \\ =-20+48i \end{gathered}[/tex]The result of the operation in standard form is -20+48i.
If the sample space, S = {1, 2, 3, 4, …, 15} and A = the set of odd numbers from the given sample space, find Ac.A.{1, 2, 3, 4, 5, 6, …, 15}B.{1, 3, 5, 7, 9, 11, 13, 15}C.{1, 2, 3, 4, 15}D.{2, 4, 6, 8, 10, 12, 14}
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A^c is the complement of set A.
Given that A is a subset of S, then A^c contains the elements present in set S but not in set A.
The sets are:
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A = {1, 3, 5, 7, 9, 11, 13, 15} (odd numbers present in S)
Therefore, the elements present in set S but not in set A are:
[tex]A^c=\mleft\lbrace2,4,6,8,10,12,14\mright\rbrace[/tex]
Multiples of 36 and the square root of 49
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
36
√49
Step 02:
multiples:
36:
The multiples of thirty-six are the numbers that contain it a whole number of times.
36, 72, 108, 144, 180, ...
√49:
[tex]\sqrt[]{49}=7[/tex]The multiples of seven are the numbers that contain it a whole number of times.
7, 14, 21, 28, 35, 42, ...
That is the full solution.
? Question The table shows certain values of a fourth-degree polynomial function with no repeated factors. -12 -10 -6 -4 2 4 8 10 12 у 280 81 -14 0 0 -24 0 126 400 The function must have a zero between the x-values of -12 and -10 Between the x-values of 2 and 8, the graph of the function should be drawn the x- The function must be positive for all x-values between Submit
Answers
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Answer: (-10 and 06), below, (-4, 2)
Step-by-step explanation:
From Edmentum.
the function f(x) = |2x-4| is not a one-to-one function. graph the part of the function that is one-to-one and extends to positive infinity.
Answers
Here, we want to graph the part of the graph that is one-to-one
What we have to do here is to remove the absolute value signs and plot the graph of the line that it normally looks like
Generally, we have the equation of a straight line as;
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
Looking at the function f(x) = 2x-4; -4 is simply the y-intercept value
So, we have a point at (0,-4)
To get the second point, set f(x) = 0
[tex]\begin{gathered} 2x-\text{ 4 = 0} \\ 2x\text{ = 4} \\ x\text{ =}\frac{4}{2}\text{ = 2} \end{gathered}[/tex]So, we have the second point as (2,0)
By joining (2,0) to (0,-4) ; we have the plot of the part of the function that extends to infinity
Apply zero product theorem to solve for x[tex]x ^{2} = 9[/tex]
Answers
Answer:
[tex]\begin{gathered} x_1=-3 \\ x_2=3 \end{gathered}[/tex]Step-by-step explanation:
To apply the zero product theorem, put all the terms on the left side to equal zero.
[tex]x^2-9=0[/tex]Factoring the binomial:
[tex]\begin{gathered} (x+3)(x-3)=0 \\ x_1+3=0 \\ x_1=-3 \\ \\ x_2-3=0 \\ x_2=3 \end{gathered}[/tex]A corporation distributes a 10% common stock dividend on 30000 shares issued when the market value of its common stock is $24 per share and its par value is $2 per share dollars per share on the distribution date a credit for $___ would be journalized.A. $30,000B. $6,000C. $72,000D. $66,000
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A corporation distributes a 10% common stock dividend on 30,000 shares.
The market value is $24 per share.
The par value is $2 per share.
We have to find the credit that is journalized the moment the distribution is made.
They paid a total amount in dividends that is 10% of the par value of the stock times the number of stocks:
[tex]\begin{gathered} 10\%\cdot2\cdot30000 \\ 0.1\cdot2\cdot30000 \\ 6000 \end{gathered}[/tex]Answer: the credit is $6,000 [Option B]
which equation has a solution of x = 4
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Answer
Option B is correct.
Only the equation, 3x + 9 = 21, has a solution of x = 4.
Explanation
We are told to pick the equation(s) with x = 4 as a solution from the equations,
5x - 8 = 44
3x + 9 = 21
4x = 24
x - 10 = -8
The step to solving this is to insert x = 4 and check if that is consistent with the given equation.
Option A
5x - 8 = 44
If x = 4
5(4) - 8 = 44
20 - 8 = 44
12 ≠ 44
Hence, this is not an answer
Option B
3x + 9 = 21
If x = 4
3(4) + 9 = 21
12 + 9 = 21
21 = 21
Hence, this is an answer for this question.
Option C
4x = 24
If x = 4
4(4) = 24
16 ≠ 24
Hence, this is not an answer to this question.
Option D
x - 10 = - 8
If x = 4
4 - 10 = -8
-6 ≠ -8
This is also not an answer to this question.
Hope this Helps!!!
simplify the following giving the answer with a positive exponent 2n^4*2n^3÷4
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so the answer is n^7
x + y =5 x + y = 6 one solution no solutions infinitely many solutions
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Problem
x + y = 5
x + y = 6
method
A system has no solution if the equations are inconsistent, they are contradictory.
for example
2x + 3y = 10
2x + 3y = 12 has no solution.
Final answer
x + y = 5
x + y = 6
are inconsistent
hence, the equations has no solution
NO SOLUTION
X1 2 Given f(x) = 35 - 2 - 2
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Use the rule of correspondence of the case when x>3, since 5>3.
[tex]\begin{gathered} f(5)=5+2 \\ =7 \end{gathered}[/tex]Therefore, f(5)=7.
what are the roots of the equation?-3= -6x^2+7x
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We have the next equation
[tex]-3=-6x^2+7x[/tex]First, we need to set the equation to zero
[tex]6x^2-7x-3=0[/tex]then we will use the general formula to find the roots of a second-degree equation
[tex]x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where
a=6
b=-7
c=-3
then we substitute the values
[tex]x_{1,2}=\frac{7\pm\sqrt[]{(-7)^2-4(6)(-3)}}{2(6)}[/tex][tex]\begin{gathered} x_{1,2}=\frac{7\pm\sqrt[]{49^{}+72}}{12} \\ x_{1,2}=\frac{7\pm\sqrt[]{121}}{12} \\ x_{1,2}=\frac{7\pm11}{12} \\ \end{gathered}[/tex][tex]x_1=\frac{7+11}{12}=\frac{18}{12}=\frac{3}{2}[/tex][tex]x_2=\frac{7-11}{12}=\frac{-4}{12}=-\frac{1}{3}[/tex]the roots of the equation are x=3/2, x=-1/3
Using the compound interest formula, determine the total amount paid back and the monthly payment. Buying a $6000 used sedan taken out with $500 paid up front and the rest borrowed at 8.3%annual interest compounded daily (365 days per year) over 2 years.
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The final value of an investment or loan with compound interest is given by:
[tex]FV=P(1+\frac{r}{m})^{m\cdot t}[/tex]Where P is the initial value (principal or loan), r is the annual interest rate, t is the duration of the investment/loan, and m is the number of compounding periods per year.
The following values are given in the problem:
P = $6000 - $500 = $5500
r = 8.3% = 0.083
t = 2 years
m = 365
Applying the formula:
[tex]FV=5500(1+\frac{0.083}{365})^{365\cdot2}[/tex]Calculating:
[tex]FV=5500(1+0.0002273926)^{730}[/tex]FV = $6493.03
The total amount paid back is $6493.03
This is equivalent to an approximate monthly payment of:
[tex]R=\frac{$ 6493.03 $}{24}=270.54[/tex]The monthly payment is approximately $270.54
For a standard normal distribution, find the z-value that goes with a left tail area=0.9931
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The z-value that goes with a left tail Area= 0.9931 is 2.4 .
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, also known as the Gaussian distribution. Data close to the mean are more common than data far from the mean. The normal distribution is displayed as a "bell curve" on the chart.
What is left rear area?
The area under the curve to the left of x* in Figure 5.19, “Right and left tails of the distribution” is known as the left tail of the density curve for a continuous random variable X whose limit is x* (a).
According to the Z-value normal distribution table, its value is 2.4 .
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If P = (-3,5), find the imageof P under the following rotation.180° counterclockwise about the origin([?], []).Enter the number that belongs inthe green box.Enter
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The rule for a 180° counterclockwise rotation is-
[tex](x,y)\rightarrow(-x,-y)\text{.}[/tex]So, we just have to change the sign of each coordinate.
[tex](-3,5)\rightarrow(3,-5)[/tex]Hence, the image is (3,-5).Solve the equation for all real solutions. 9z^2-30z+26=1
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Weare given the following quadratic equation, and asked to find all its real solutions:
9 z^2 - 30 z + 26 = 1
we subtract "1" from both sides in order to be able to use the quadratic formula if needed:
9 z^2 - 30 z + 26 - 1 = 0
9 z^2 - 30 z + 25 = 0
we notice that the first term is a perfect square:
9 z^2 = (3 z)^2
and that the last term is also a perfect square:
25 = 5^2
then we suspect that we are in the presence of the perfect square of a binomial of the form:
(3 z - 5)^2 = (3z)^2 - 2 * 15 z + 5^2 = 9 z^2 - 30 z + 25
which corroborates the factorization of the trinomial we had.
Then we have:
(3 z - 5)^2 = 0
and the only way such square gives zero, is if the binomial (3 z - 5) is zero itself, which means:
3 z - 5 = 0 then 3 z = 5 and solving for z: z = 5/ 3
Then the only real solution for this equation is the value:
z = 5/3
I need all solved, As soon as possible Question 1
Answers
Given:
[tex]f(x)=3^x[/tex]To find:
The type of function by completing the table and graphing the function
Explanation:
When x = -2,
[tex]\begin{gathered} y=3^{-2} \\ =\frac{1}{3^2} \\ =\frac{1}{9} \\ =0.11 \end{gathered}[/tex]When x = -1,
[tex]\begin{gathered} y=3^{-1} \\ =\frac{1}{3} \\ =0.33 \end{gathered}[/tex]When x = 0,
[tex]\begin{gathered} y=3^0 \\ =1 \end{gathered}[/tex]When x = 1,
[tex]\begin{gathered} y=3^1 \\ =3 \end{gathered}[/tex]When x = 2,
[tex]\begin{gathered} y=3^2 \\ =9 \end{gathered}[/tex]Therefore, the table values are,
Then, the graph will be,
Since the domain of the function is real numbers and the range of the function is a set of positive real numbers.
Therefore, it is an exponential function.
what is 39 ÷ (2+ 1) - 2 × (4 + 1)
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The given expression is
[tex]36\colon(2+1)-2\times(4+1)[/tex]First, we solve the additions inside the parenthesis
[tex]36\colon3-2\times5[/tex]Then, we solve the produce and the division
[tex]12-10[/tex]At last, we subtract
[tex]12-10=2[/tex]Hence, the answer is 2.I need help with the question
Answers
B
For this problem Let's work in parts
1) Coin
Heads
Tails
Flipping the coin once, the Probability is:
[tex]P\text{ =}\frac{1}{2}[/tex]For there are two possible results, Heads or Tails, and there was one flipping.
2) Spinner
1 to 6 sections
The Probability of this spinner lands on a number lesser than 3
[tex]P\text{ =}\frac{2}{6}\text{ = }\frac{1}{3}[/tex]is 1 out of 3 for this spinner, since only 1, 2 are valid results.
So, the answer to this experiment
[tex]P\text{ = }\frac{1}{3}\cdot\frac{1}{2}\text{ = }\frac{1}{6}[/tex]Is the probability of both happen, both spinner and coin are 1 in six flipping. Since there are only two numbers < 3 on the spinner and two possibilities for the coin.
B
Heads, 1
Tails 1
Heads2
Tails 2
The number of visits to public libraries increased from 1.3 billion in 1999 to 1.5 billion in 2004. Find the average rate of change in the number of public library visits from 1999 to 2004.The average rate of change between 1999 and 2004 was: billion: Simplify your answer. Type an integer or a decimal.)
Answers
The average rate of change is defined as:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]using the information given
a=1999
b=2004
f(a)=1.3
f(b)=1.5
then,
[tex]\begin{gathered} \frac{1.5-1.3}{2004-1999} \\ \frac{0.2}{5} \\ 0.04 \end{gathered}[/tex]The average rate of change between 1999 and 2004 was 0.04 billion.
Convert 5 1/4 lb to oz.
Answers
The conversion factor for lb to oz is
[tex]1lb=16oz[/tex]I will put the pounds first in terms of the improper fraction. We have
[tex]5\frac{1}{4}=\frac{21}{4}[/tex]Using the conversion factor to convert lb to oz, we have
[tex]\frac{21}{4}lb\times\frac{16oz}{1lb}=\frac{21\cdot16}{4}=\frac{21\cdot4}{1}=84oz[/tex]Hence, 5 1/4 lb is equal to 84 oz.
Answer: 84 oz
A clothing manufacturer has 1,000 yd. of cotton to make shirts and pajamas. A shirt requires 1 yd. of fabric, and a pair of pajamas requires 2 yd. of fabric. It takes 2 hr. to make a shirt and 3 hr. to make the pajamas, and there are 1,600 hr. available to make the clothing. i. What are the variables? ii. What are the constraints? iii. Write inequalities for the constraints. iv. Graph the inequalities and shade the solution set. v. What does the shaded region represent? vi. Suppose the manufacturer makes a profit of $10 on shirts and $18 on pajamas. How would it decide how many of each to make? vii. How many of each should the manufacturer make, assuming it will sell all the shirts and pajamas it makes?
Answers
Let the number of shirts is x and the number of pairs of pajamas is y
Then the variables are x and y which are the numbers of shirts and pajamas
Since each shirt needs, 1 yard and a pair of pajamas needs 2 yards
Since there are 1000 yards to make them
Then the first inequality is
[tex]\begin{gathered} (1)x+(2)y\leq1000 \\ x+2y\leq1000 \end{gathered}[/tex]Since the time to make a shirt is 2 hours and the time to make a pair of pajamas is 3 hours
Since there are 1600 hours available, then
The second inequality is
[tex]\begin{gathered} (2)x+(3)y\leq1600 \\ 2x+3y\leq1600 \end{gathered}[/tex]Then let us answer the questions
i. The variables are x and y
ii. The constraints are 1000, 1600
iii. The inequalities are
[tex]\begin{gathered} x+2y\leq1000 \\ 2x+3y\leq1600 \end{gathered}[/tex]iv. Let us draw the graph
The red area represents the 1st inequality
The blue area represents the 2nd inequality
The area of the two colors is the area of the solutions of the 2 inequalities
V.
The shaded region represents the solution of the 2 inequalities, the numbers of shirts and pajams
Vi.
The intersection point between the 2 lines is (200, 400)
Then we will take this point to represents the number of shirts and pajamas
vii.
Since the profit on shirts is $10 and on pajama is $18
Then we should make 200 shirts and 400 pajamas