Given the points (-8,5) and (6,5), we can find the equation of the line first by finding the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case, we have the following:
[tex]\begin{gathered} (x_1,y_1)=(-8,5) \\ (x_2,y_2)=(6,5) \\ \Rightarrow m=\frac{5-5}{6-(-8)}=\frac{0}{6+8}=0 \\ m=0 \end{gathered}[/tex]since the slope is m = 0, we have that the line is a horizontal line that goes through the points (-8,5) and (6,6), then, the equation of the line is:
[tex]y=5[/tex]in slope-intercept form the equation would be:
[tex]y=0x+5[/tex]Jackie planted a tomato plant that was 4 inches tall. The plant grew by 150% of its height after 3 weeks. How tall was the plant after the 3 weeks?
1) Problems like these, we can solve by writing an equation.
2)Since that tomato plant grew 150% after three weeks we can write the following
[tex]\begin{gathered} 4\cdot(1+1.5)= \\ 4(2.5)=10 \\ \end{gathered}[/tex]Note that in the parentheses we have the factor of growth. Since it's 150% we can add to 1 and write 1 +1.5=2.5
3) Thus, the answer is:
[tex]10\:inches[/tex]A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 12.5 ft by 13.5 ft by 13 ft. The container is entirely full. If, on average, its contents weigh 0.18 pounds per cubic foot, and, on average, the contents are worth $7.18 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The volume of a right rectangular prism is given by
[tex]V=\text{height}\times length\times width[/tex]From the given information, we know that
[tex]\begin{gathered} \text{ height=13.5 ft} \\ \text{ length=13 ft} \\ \text{width = 12.5 ft} \end{gathered}[/tex]So, the volume is given by
[tex]V=13.5\times13\times12.5ft^3[/tex]which gives
[tex]V=2193.75ft^3[/tex]Now, since the content weigh 0.18 pound per cubic foot and worth $7.18 per pound, the value of the container is given by,
[tex]\text{ Value=}2193.75\times0.18\times7.18[/tex]Therefore, by rounding to the nearest cent, the answer is:
[tex]\text{Value}=\text{ \$2835.20}[/tex]let f ( x ) = 6356 x + 5095 . Use interval notation. Many answers are possible.
The equation of the function has its domain representation in interval notation as (oo, oo)
How to determine the domain of the functionFrom the question, the equation of the function is given as
f ( x ) = 6356 x + 5095
Rewrite the equation of the function properly by removing the excess spaces
So, we have
f(x) = 6356x + 5095
The above equation is a linear equation
A linear equation is represented as
f(x) = mx + c
As a general rule;
The domain of a linear equation is all set of real numbers
This is the same for the range
i.e. the range of a linear equation is all set of real numbers
When the set of real numbers is represented as an interval notation, we have the following representation
(oo, oo)
Hence, the domain is (oo, oo)
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Possible question
let f ( x ) = 6356 x + 5095 . Use interval notation to represent the domain of the function.
Many answers are possible.
An object moves at a rate of 9,400 inches each week. How many feet does it move per minute?
To answer this question, we need to transform each of the values into the corresponding other units:
• Inches ---> Feet
,• Week ---> minutes
And we also have here a ratio:
• Inches/week ---> Feet/minute.
Then we can proceed as follows:
Inches to FeetWe know that the conversion between inches and feet is:
[tex]1ft=12in[/tex]Then
[tex]1in=\frac{1}{12}ft[/tex]If we have 9,400 inches, then:
[tex]9400in=\frac{9400}{12}ft\Rightarrow9400in=783ft+\frac{1}{3}ft=783.33333333ft[/tex]Week to minutesWe know that:
[tex]1\text{hour}=60\min [/tex]In one day we have 24 hours, then:
[tex]24\text{hours}=24\cdot60\min =1440\min [/tex]Then we have 1440 minutes in a day. A week has 7 days. Therefore, we will have:
[tex]1440\frac{\min}{day}\cdot7days=10080\min [/tex]Therefore, we have that there are 10,080 minutes in one week.
Now, to find the ratio of feet per minute, we need to divide:
[tex]\frac{783\frac{1}{3}ft}{10080\min}=0.0777116402116\frac{ft}{\min }[/tex]In summary, we can say that the object moves:
[tex]0.0777116402116\frac{ft}{\min }[/tex]into the
In basketball, " one on one" free throw shooting ( commonly called foul shooting) is done as follows: if the player makes the first shot(1point), she is given a second shot. If she misses the first shot, she is not given a second shot. Christine, a basketball player, has a 70% free throw record. (she makes 70% of her free throws). Find the probability that, given one-on-one free throw shooting opportunity, Christene will score one point.
If she will be able to shoot the first shot and miss the second shot, then she will obtain 1 point.
Thus, the probability that Christine will get the first shot is as follows:
[tex]P(1pt)=(0.7)(0.3)=0.21[/tex]where the first factor is the probability that she will shoot the first shot and the second factor is the probability that she missed the second shot. Thus, the probability of obtaining 1 point is 21% or 0.21.
NO LINKS!! Please help me with this problem
0.3821, 0.8745
========================================================
Work Shown:
pi/2 = 3.14/2 = 1.57 approximately
The solutions for t must be in the interval 0 ≤ t ≤ 1.57
[tex]3\cos(5t)+3 = 2\\\\3\cos(5t) = 2-3\\\\3\cos(5t) = -1\\\\\cos(5t) = -1/3\\\\5t = \cos^{-1}(-1/3)\\\\5t \approx 1.9106+2\pi n \ \text{ or } \ 5t \approx -1.9106+2\pi n\\\\t \approx \frac{1.9106+2\pi n}{5} \ \text{ or } \ t \approx \frac{-1.9106+2\pi n}{5}\\\\[/tex]
where n is an integer.
Let
[tex]P = \frac{1.9106+2\pi n}{5}\\\\Q = \frac{-1.9106+2\pi n}{5}\\\\[/tex]
Then let's generate a small table of values like so
[tex]\begin{array}{|c|c|c|} \cline{1-3}n & P & Q\\\cline{1-3}-1 & -0.8745 & -1.6388\\\cline{1-3}0 & **0.3821** & -0.3821\\\cline{1-3}1 & 1.6388 & **0.8745**\\\cline{1-3}2 & 2.8954 & 2.1312\\\cline{1-3}\end{array}[/tex]
The terms with surrounding double stars represent items in the interval 0 ≤ t ≤ 1.57
Therefore, we end up with the solutions 0.3821 and 0.8745 both of which are approximate.
You can use a graphing tool like Desmos or GeoGebra to verify the solutions. Be sure to restrict the domain to 0 ≤ t ≤ 1.57
Answer:
[tex]\textsf{c)} \quad 0.3821, \; 0.8745[/tex]
Step-by-step explanation:
Given equation:
[tex]3 \cos (5t)+3=2, \quad \quad 0\leq t\leq \dfrac{\pi}{2}[/tex]
Rearrange the equation to isolate cos(5t):
[tex]\begin{aligned}\implies 3 \cos(5t)+3&=2\\3 \cos(5t)&=-1\\\cos(5t)&=-\dfrac{1}{3}\end{aligned}[/tex]
Take the inverse cosine of both sides:
[tex]\implies 5t=\cos^{-1}\left(-\dfrac{1}{3}\right)[/tex]
[tex]\implies 5t=1.91063..., -1.91063...[/tex]
As the cosine graph repeats every 2π radians, add 2πn to the answers:
[tex]\implies 5t=1.91063...+2\pi n, -1.91063...+2 \pi n[/tex]
Divide both sides by 5:
[tex]\implies t=0.38212...+\dfrac{2}{5}\pi n,\;\; -0.38212...+\dfrac{2}{5} \pi n[/tex]
The given interval is:
[tex]0\leq t\leq \dfrac{\pi}{2}\implies0\leq t\leq 1.57079...[/tex]
Therefore, the solutions to the equation in the given interval are:
[tex]\implies t=0.3821, \; 0.8745[/tex]
distance between (11,-5) and (0,1)
Here,point can be written as:
[tex]\begin{gathered} x1=11, \\ y1=-5 \\ x2=0 \\ y2=1 \end{gathered}[/tex]The formula for the distance between the points as follows;
[tex]\begin{gathered} d=\sqrt{(x1-x2)^2+(y1-y2)^2} \\ d=\sqrt{(11-0)^2+(-5-1)^2} \\ d=\sqrt{121+36} \\ d=\sqrt{157} \\ d=12.53 \end{gathered}[/tex]Thus, the distance between the point is 12.53.
O DESCRIPTIVE STATISTICInterpreting relative frequency-histogramsStudents at a major university in Southern California are complaining about a serious housing crunch. Many of the university's students, they complain, have tocommute too far to school because there is not enough housing near campus. The university officials' response is to perform a study. The study, reported in theschool newspaper, contains the following histogram summarizing the commute distances for a sample of 100 students at the university:Relative frequencyCommute distance (in miles)Based on the histogram, find the proportion of commute distances in the sample that are at least 16 miles. Write your answer as a decimal, and do not roundyour answer
Since the graph gives us the relative frequency we just have to add those who are more or equal to 16; in this case we have to add 0.11 and 0.06, therefore the proportion in this case is 0.17
Solve for w.4w²-24w=0If there is more than one solution, separate them with commas.If there is no solution, click on "No solution".W =0U08Nosolution
ANSWER
[tex]\begin{equation*} w=0,\text{ }w=6 \end{equation*}[/tex]EXPLANATION
We want to solve the given equation for w:
[tex]4w^2-24w=0[/tex]To do this, we have to factorize the equation and simplify it.
Let us do that now:
[tex]\begin{gathered} (4w*w)-(4w*6)=0 \\ \\ 4w(w-6)=0 \\ \\ \Rightarrow4w=0\text{ and }w-6=0 \\ \\ \Rightarrow w=0,\text{ }w=6 \end{gathered}[/tex]That is the answer.
In planning her retirement, Liza deposits some money at 4.5% interest, with twice as much deposited at 5%. Find the amount deposited at each rate if the total annual interest income is $1595.
Let
x ----> amount deposited at 4.5%
y ----> amount deposited at 5%
we have that
y=2x----> equation A
4.5%=0.045
5%=0.05
so
0.045x+0.05y=1,595 ----> equation B
solve the system
substitute equation A in equation B
0.045(x)+0.05(2x)=1,595
solve for x
0.045x+0.10x=1,595
0.145x=1,595
x=11,000
Find y
y=2(11,000)=22,000
The amount deposited at 4.5% was $11,000 and the amount deposited at 5% was $22,000Which expression is undefined? O A. 11 B.- 3 C.6-6) D. -4+0
Answer:
Option C
Step-by-step explanation:
Undefined expression:
Division by 0, or fraction in which the denominator is 0. In this question, this is in option C, since 3/(6-6) = 3/0.
what is the sum of -1 1/3 + 3/4
Here, we want to add two fractions
What we have to do here is to make the mixed fractin an improper one
To do this, we multiply the denominator by the standing number, and add to the numerator, then we place the value over the denominator
Thus, we have it that;
[tex]\begin{gathered} 1\frac{1}{3}\text{ = }\frac{4}{3} \\ -\frac{4}{3}+\frac{3}{4}\text{ = }\frac{-16+9}{12}=\text{ }\frac{-7}{12} \end{gathered}[/tex]The basic wage earned by a truck driver for a 40 - hour week is $560 How can I calculate the hourly rate for overtime, the driver is paid one and a half times the basic hourly?
First, find the hourly rate by dividing the total wage of $560 by the amount of time worked, which is 40 hours:
[tex]\frac{\text{\$}560}{40h}=\text{ \$}14\text{ per hour}[/tex]To find the hourly rate for overtime, multiply the basic hourly rate by 1.5:
[tex](\text{\$}14\text{ per hour})\times1.5=\text{ \$}21\text{ per hour}[/tex]Therefore, the hourly rate for overtime is $21.
A statement of Chandler's biweekly earnings is given below. What is Chandler's gross pay?
SOLUTION:
Step 1:
In this question, we are asked to calculate Chandler's gross pay from the statement of bi-weekly earnings.
Step 2:
To get the Gross pay, we need to do the following:
[tex]\text{Gross pay - Total Deductions = Net Pay}[/tex]Now, we need to calculate Total Deductions:
[tex]\text{ \$ 105.00 + \$ 52.14 + \$ 10.62 + \$ 26. 15 = \$ 193.91}[/tex]Now, we have that the Net Pay = $ 780. 63
Then,
[tex]\begin{gathered} \text{Gross Pay - \$ 193. 91 = \$ 7}80.\text{ 63} \\ \text{Gross pay = \$ 780.63 + \$ 193.91} \\ \text{Gross Pay = \$ 974. 54} \end{gathered}[/tex]CONCLUSION:
Chandler's Gross Pay = $ 974. 54
23 – 4u < 11 what is the answer
23 - 4u < 11
23 is adding on the left, then it will subtract on the right
-4u < 11 - 23
-4u < -12
-4 is multiplying on the left, then it will divide on the right. Remember that dividing by a negative number changes the sign.
u > (-12)/(-4)
u > 3
3(4x+1)^2-5=25 using square root property
Answer:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]Explanation:
Given the equation:
[tex]3\left(4x+1\right)^2-5=25[/tex]To solve an equation using the square root property, begin by isolating the term that contains the square.
[tex]\begin{gathered} 3(4x+1)^{2}-5=25 \\ \text{ Add 5 to both sides of the equation} \\ 3(4x+1)^2-5+5=25+5 \\ 3(4x+1)^2=30 \\ \text{ Divide both sides by 3} \\ \frac{3(4x+1)^2}{3}=\frac{30}{3} \\ (4x+1)^2=10 \end{gathered}[/tex]After isolating the variable that contains the square, take the square root of both sides and solve for the variable.
[tex]\begin{gathered} \sqrt{(4x+1)^2}=\pm\sqrt{10} \\ 4x+1=\pm\sqrt{10} \\ \text{ Subtract 1 from both sides} \\ 4x=-1\pm\sqrt{10} \\ \text{ Divide both sides by 4} \\ \frac{4x}{4}=\frac{-1\pm\sqrt{10}}{4} \\ x=\frac{-1\pm\sqrt{10}}{4} \end{gathered}[/tex]Therefore, the solutions to the equation are:
[tex]x=\frac{-1+\sqrt{10}}{4}\text{ or }x=\frac{-1-\sqrt{10}}{4}[/tex]
which equation represents the function modeled by the graph? (picture of graph below)
Answer:
The parent function of the graph is given below as
[tex]y=\sqrt[3]{x}[/tex]The parent function has undergone transformation
Hence,
Using a graphing calculator, we will have the graph be
Hence,
The final answer is
[tex]\Rightarrow f(x)=\sqrt[3]{4x+2}[/tex]The FIRST OPTION is the right answer
The table below shows distance as it relates to how many seconds have passed.1510time(seconds)distance, y =y = f(x)(meters)30150 300Write a formula to describe the distance as a linear function of time.
Zales sells diamonds for $1,100 that cost $800. What is Zales’s percent markup on selling price? Check the selling price.
Zales's percent markup on the selling price as required in the task content is; 37.5%.
Percentages and markup priceIt follows from the task content that the percent markup on the selling price be determined according to the given data.
Since the cost of diamonds is; $800 while the diamonds sell for $1,100. It follows that the markup on the selling price of the diamonds is;
Markup = Selling price - Cost price.
Hence, we have;
Markup = 1,100 - 800.
Therefore, the markup is; $300.
On this note, the percent markup can be determined as follows;
= (300/800) × 100%.
= 37.5%.
Ultimately, the percent markup on the diamonds is: 37.5%.
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octavius wants to write the equation of a line perpendicular to y=-4x + 5 that passes through the point (8,-3). Describe the mistake octavius made and write the correct equation of the line.
The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:
[tex]y = \frac{1}{4} x-5[/tex].
What is a equation of line?These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.
Given equation of line is:
y=-4x + 5
Let [tex]m_{1}[/tex] be the slope of given line
Then,
[tex]m_{1}[/tex] = -4
Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line
As we know that product of slopes of two perpendicular lines is -1.
[tex]m_{1}*m_{2} = -1\\- 4*m_{2}=-1\\ m_{2} = \frac{1}{4}[/tex]
The slope intercept form of line is given by
[tex]y = m_{2}x+c[/tex]
[tex]y = \frac{1}{4} x+c[/tex]
to find the value of c, putting (4,-1) in equation
[tex]-3= \frac{1}{4} *8+c\\-3-2 = c\\c = -5[/tex]
Putting the value of c in the equation
[tex]y=\frac{1}{4} x-5[/tex]
Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is [tex]y=\frac{1}{4} x-5[/tex].
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David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
Given,
The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair.
Explain what each part of the expression represents in the context of the problem.
Now, According to the question:
Given the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the variable r represents the original cost of the repair while 0.07r most likely represents the amount of money charged as tax. Lastly the expression (r – 20) represents the discount on fixing David’s broken watch.
What each part of the expression represents in the context of the problem include the following:
→ r represents the original cost of the repair.
→ 0.07r represents the tax.
→ (r – 20) represents the discount
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In the figure to the right, ABC and ADE are similar. Find the length of EC.
The length of EC is ___.
Answer:
ninety 90 feet or foot long
The difference between the graph of a radical function and the graph of a rational function
The difference between the graph of a radical function and that of a rational function is:
A radical graph is drawn from a function that contains a root, it could be a square root, cube root, etc. Whenever you are graphing a radical function, we first need to consider the domain. Because of the square root sign, the domain and range are always restricted.
But a rational graph is drawn from the ratio of two polynomial functions where the function in the denominator is not equal to zero. A rational graph is characterized by asymptotes.
The major difference would be that a radical graph has a restricted domain due to the root, and usually without an asymptote, while a polynomial graph has a restricted domain and sometimes range which forms the asymptote (vertical, horizontal asymptote).
Using solving systems using elimination addition method3x-7y=5-3x+7y=-9help
In the elimination method, we need to eliminate one of the variables using addition or subtraction.
In this case, if we add both equations, we have that:
Since we obtained a FALSE result, we can say that this system of linear equations has NO SOLUTIONS.
In summary, using the elimination method, we add both equations. The result for that was a false r
Find the x- and y-intercepts of the graph of the equation.5x + 3y = 15x−intercept (x, y) = ( ) y−intercept (x, y) = ( )
Consider that the intercept form of equation of a line whose x-intercept is (a,0) and y-intercept is (0,b), is given by,
[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]The equation of the line is given as,
[tex]5x+3y=15[/tex]Convert this equation into intercept form,
[tex]\begin{gathered} \frac{5x}{15}+\frac{3y}{15}=1 \\ \frac{x}{3}+\frac{y}{5}=1 \end{gathered}[/tex]Comparing with the standard equation,
[tex]\begin{gathered} a=3 \\ b=5 \end{gathered}[/tex]Thus, the x-intercept and y-intercept of the equation, respectively, are,
[tex](3,5)\text{ and }(0,5)[/tex]a large human population of both globally and within individual countries has been a concern since the time of Thomas Malthus. country X is 95% desert. the government of country X is concerned about not having enough arable land (land capable of being used to grow crops) in the country to produce the food needed to feed its population without increasing food imports the demographic for Country X for the year 2020 is provided in the table below. 1. calculate the national population growth rate for a country X 2. using the rule of 70 calculate the doubling time for this population
Firstly, we want to calculate the growth rate of the population
While birth would increase the population, death and migration will decrease the population
So when we subtract the migration rate and the death rate from the birth rate, we can get the population growth rate;
Thus, we have;
[tex]\begin{gathered} \frac{38}{1000}\text{ - (}\frac{24}{1000}\text{ + }\frac{2}{1000}) \\ \\ =\text{ }\frac{38}{1000}\text{ - }\frac{26}{1000} \\ \\ =\text{ }\frac{12}{1000} \end{gathered}[/tex]The national population growth rate for a country X is 12/1000
Secondly, we are to use the rule of 70 to calculate the doubling time for the population
Mathematically;
[tex]\begin{gathered} No\text{ of years to double = }\frac{70}{\text{annual growth rate}} \\ \\ No\text{ of years to double = 70 divided by }\frac{12}{1000} \\ \\ No\text{ of years = 70 }\times\frac{1000}{12}=5833\frac{1}{3}years^{} \\ \\ \frac{1}{3}\text{ years is same as 4 months} \\ \\ So\text{ it will take 5833 years and 4 months for the population to double} \end{gathered}[/tex]Need help determining if h. F(x)= 3^x is even, odd or neither
Recall that:
1) f(x) is an even function if:
[tex]f(-x)=f\mleft(x\mright).[/tex]2) f(x) is an odd function if:
[tex]f(-x)=-f(x).[/tex]Now, notice that:
[tex]\begin{gathered} f(-x)=3^{-x}\ne3^x=f(x), \\ f(-x)=3^{-x}\ne-3^x=-f(x). \end{gathered}[/tex]Therefore f(x)=3^x is neither an even function nor an odd function.
Answer: Neither an even function nor an odd function.
simplify the following expression:7^-6 × 7^3
To solve this question, we will apply the knowledge of exponents and indices
The values have the same bases (7) but different powers and they are separated by a multiplication sign.
So we can use the law:
[tex]a^{x\text{ }}\text{ x a}^{y\text{ }}=a^{x\text{ + y}}[/tex]so that
[tex]7^{-6}\text{ x 7}^3=7^{-6\text{ + 3}}[/tex]on simplifying will give
[tex]7^{-3}[/tex]=>
[tex]7^{-3}\text{ =}\frac{1}{7^3}[/tex]in the experiment of the preceding exercise, the subjects were randomly assigned to the different treatments. what is the most important reason for this random assignment?
The most important reason for random assignment on the subjects in the experiment, is because random assignment would be the best way in creating group of subjects to the different treatments.
Note that; the group of subjects are roughly equivalent at the beginning of the experiment.
Using random assignment will allow the allocation of different patients to various treatments at a random order. From this there will be objective results obtained altogether from the experiment under investigation.
Random assignment will eliminate any biasness that may occur when conducting the experiment. It prevents favoritism of any event from occurring. It will ensure that all the different patients have an equal chance of being selected for various treatment.
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which methods correctly solve for the variable x in the equation 2/5m = 8?
Ok, so the equation is (2/5)m=8
1st option: Divide by 2 on both sides, then multiply by 5 on both sides:
[tex]\begin{gathered} \frac{2}{10}m=4 \\ \frac{10}{10}m=20 \\ m=20 \end{gathered}[/tex]2nd option: Multiply both sides by 5/2
[tex]\begin{gathered} \frac{2}{5}\cdot\frac{5}{2}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]3rd option: First dristibute 2/5 to (m=8), the multiply by 5/2 in both sides
[tex]\begin{gathered} \frac{2}{5}m=8 \\ \frac{5}{2}\cdot\frac{2}{5}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]4th option: Divide both sides by 2/5:
[tex]\begin{gathered} \frac{\frac{2}{5}}{\frac{2}{5}}m=8\cdot\frac{5}{2} \\ m=20 \end{gathered}[/tex]5th option: First, multiply by 5. Then, divide by 2.
[tex]\begin{gathered} 5\cdot\frac{2}{5}m=40 \\ 2m/2=40/2 \\ m=20 \\ \end{gathered}[/tex]All the methods are correct