The most appropriate choice for equation of line in slope intercept form will be given by-
line K is parallel to line P
line M is not parallel to both line K and line P.
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx +c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line
For M
y + 1 = -3(x - 1)
y + 1 = -3x + 3
y = -3x + 3-1
y = -3x + 2
Slope of M = -3
For K
y = 3(x+2)
y = 3x + 6
Slope of K = 3
For P
y + 4 = 3x
y = 3x - 4
slope of P = 3
Since Slope of K = Slope of P,
line K is parallel to line P
Since slope of M is different from slope of both K and P,
line M is not parallel to both line K and line P.
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I need help with this problem Math relatedsimplify in radical form:^3{120a^4b^5c
Sara, this is the solution:
∛ 120a^4b^5c
Lets solve factor by factor:
∛ 120 = ∛ 8 * 15 = 2∛ 15
∛a^4 = a^4/3
∛b^5 = b^5/3
∛c (We can't simplify this factor)
In consequence, we have:
2a^(4/3) b^(5/3)∛ 15c
Represent each sum as a single rational number. -14+(-8/9) due tomorrow pls answer
the given expression is
-14 + (-8/9)
so,
[tex]\begin{gathered} =-14+\frac{-8}{9} \\ =-14-\frac{8}{9} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-126-8}{9} \\ =-\frac{134}{9} \end{gathered}[/tex][tex]=-\frac{134}{9}=-14\frac{8}{9}[/tex]so the answer is -14 8/9 or -134/9
The boats rate is ____ mph(Type an integer or decimal)
Let
x ----> rate of the boat in still water (mph)
y ---> rate of the current (mph)
Remember that
The speed is equal to dividing distance by the time
speed=d/t
d=speed*time
so
Upstream
speed=x-y
time=5 hours
100=(x-y)*5
x-y=20 --------> equation 1
Downstream
speed=x+y
time=4.5 h
100=(x+y)*4.5
x+y= 100/4.5 --------> equation 2
Adds equation 1 and equation 2
x-y=20
x+y= 100/4.5
-----------------
2x=20+(100/4.5)
2x=190/4.5
x=190/9
x=21.11 mph
therefore
The answer is 21.11 mphdetermine the lateral surface area of the cylinder
Question:
Solution:
Remember that the total area surface of the cylinders is given by the formula:
[tex]S\text{ = 2}\pi rh+2\pi r^2[/tex]where r is the radius of the cylinder and h is its height. Now, in this case, we have that r= 10 m and h = 5m, then replacing these values in the previous equation we obtain:
[tex]S\text{ = 2}\pi(10)(5)+2\pi(10^2)=942.48^{}[/tex]then, we can conclude that the correct answer is:
[tex]S\text{ =}942.48^{}[/tex]Solve the system using any method. State your solution as an ordered pair. DO NOT include spaces in your answer.
Answer: (- 4, - 7)
Explanation:
The given equations are
y = 5x + 13
y = 2x + 1
We would equate both equations. We have
5x + 13 = 2x + 1
5x - 2x = 1 - 13
3x = - 12
x = - 12/3
x = - 4
Substituting x = - 4 into y = 2x + 1, we have
y = 2(- 4) + 1 = - 8 + 1
y = - 7
The solution is
(- 4, - 7)
Solve the equation below by completing the square and then solving for x.2 + 14x + 24 = 0A. X=-12 or x= -2B. x=2 or x=-2C. X=-2 or x=-5D. X= 8 or x= 3
2x^2 + 14x + 24 = 0
x^2 + 7x + 12 = 0
Then
x^ + (14/2) x + 12 + [7x + 49 ] = 7x + 49
Now form square
[ x + 7x + 7x + 49 ] = 7x + 49 - 12
[ x + 7]^2 = 7x + 37
Then now find x
x^2 + 7x = -6
x^2 + 7x + 7^2/4 = 7^2/4 - 6
then
( x + 7/2)^2 = 49/4 - 24/4
(x + 7/2) = ±√ (25/4)
. x = 5/2 - 7/2
and. x = 5/2 + 7/2
Then solutions are
x = -2
x= -12
ANSWER IS
OPTION A
Linda's medicine bottlesays "If you will be driving, then youshould not take this medicine." What arethe inverse, converse, and thecontrapositive of this statement?
For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
Omoro bought 2 2/3 pounds of takis that he is going to bring to school for lunch each day in plastic bags that carry 1/8 of a pound.how many bags can omoro fill completely ?
Given:
Amount of takis bought = 2⅔ pounds
Amount the plastic bag can carry = 1/8 pounds
First convert 2⅔ to a simple fraction:
2⅔ = 8/3
To find the amount of bags Omoro can fill completely, we have to divide the amount of takis bought by the amount of takis the plastic bag can carry:
(8/3) ÷ (1/8)
[tex]\begin{gathered} =\text{ }\frac{8}{3}\text{ }\ast\text{ }\frac{8}{1} \\ =\text{ }21.3\text{ bags} \end{gathered}[/tex]Therefore, Omoro can fill approximately 21 bags completely
ANSWER:
21 bags
Which best represents the number of square centimeters in a square foot?A 366 square centimeters B 144 square centimeters C 930 square centimeters D 61 square centimeters
Answer:
C. 930 square centimeters
Explanation:
First, recall the standard conversion between cm and ft.
[tex]1\text{ ft}=30.48\operatorname{cm}[/tex]Therefore:
[tex]\begin{gathered} (1\times1)ft^2=(30.48\times30.48)cm^2 \\ =929.03\operatorname{cm}^2 \\ \approx930\text{ square cm} \end{gathered}[/tex]The correct choice is C.
Which expression can be used to find the nth term in this sequence position: 1 2 3 4 5 nvalue of term: 2 5 10 17 26 ?
n²+1 where n is the position of the sequence
1) Considering the sequence (2,5,10,17,26,...) corresponding to 1,2,3,4,5,...
Let's figure out how that sequence grows:
5 -2 = 3
10 -5 = 5
17-10= 7
26-17= 9
And examining the differences from each difference we have:
5-3 =2
7-5 = 2
9-7 =2
2) So we can write the following table, where the first line is the sequence, then the positions, then the subtraction between them.
As it is a quadratic formula, we can write in the general form and then plug x=0
[tex]\begin{gathered} a_n=n^2 \\ 2\text{ 5 10 17 26} \\ 1\text{ 2 3 4 5 6 } \\ 1\text{ 4 9 25 36} \\ a_n=n^2+0n+1 \\ a_n=n^2+1 \end{gathered}[/tex]3) Hence, to find the 6th term, for instance, we plug n=6 so
6²+1 = 31. So the formula to find the nth term is n² +1
3) Finally, the sequence is given by n² +1 where n is the position of the term.
Convert the following percent to a simplified fraction: 6%
Given:
6%
To convert the given percent into simplified fraction, we first divide it by 100 as shown below:
[tex]\begin{gathered} 6\%=\frac{6}{100} \\ Simplify \\ =\frac{3}{50} \end{gathered}[/tex]Therefore, the answer is:
[tex]\frac{3}{50}[/tex]One cubic foot holds 7.48 gallons of water, and 1 gallon ofwater weighs 8.33 pounds. How much does 6 cubic feet ofwater weigh in pounds? In tons?
We know that
• 1 cubic foot holds 7.48 gallons of water.
,• 1 gallon of water weighs 8.33 pounds.
The given information is about ratios that we must use to find the answer. Remember that a ratio is a quotient between two magnitudes, that means each statement above represents a fraction which must multiply "6 cubic feet" in order to get the answer. As follows
[tex]6ft^3\cdot\frac{7.48gallons}{1ft^3}\cdot\frac{8.33lb}{1gallon}=\frac{6\cdot7.48\cdot8.33}{1}lb=373\text{.}85lb[/tex]Therefore, 6 cubic feet weighs 373.85 pounds.
On the other hand, 1 ton is equivalent to 2000 pounds. Knowing this, we calculate
[tex]373.85lb\cdot\frac{1ton}{2000lb}\approx0.19ton[/tex]Therefore, 6 cubic feet weighs about 0.19 tons.
Which can be the first step in finding the equation of the line that passes through the points (5,-4) and (-1,8) in slope-intercept form?8-(-4) 12-12--2Calculate -1-5Calculate 8-(-4) 12-1-5 -6Find that the point at which the line intersects with the line y = 0 is (3,0).Find that the point at which the line intersects with the line X=Y is (2, 2).
The first step to finding the equation of the line in the slope-intercept form is to find the slope.
So, to find the slope we can use the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x1, y1) and (x2, y2) are points of the line.
Therefore, if we replace (x1, y1) by (5, -4) and (x2, y2) by (-1, 8), we get that the first step is to calculated:
y2 - y1 = 8 - (-4) = 8 + 4 = 12
x2 - x1 = -1 - 5 = -6
Answer: Calculate 8 - ( - 4 ) = 12
Calculate - 1 - 5 = -6
Find the area of the shapes below. Must show all steps includingformula and units! If needed, round your answer to the nearest tenth. This is a parallelogram
Answer: Area = 120 cm^2
Explanation:
The formula for calculating the area of a parallelogram is expressed as
Area = base x height
From the information given,
base = 15
height = 8
Area = 15 x 8
Area = 120 cm^2
help meeeeeeeeee pleaseee !!!!!
The value of the composite function is as follows:
(gof)(5) = 6How to find composite function?The composite function can be solved as follows:
Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is a function that depends on another function.
f(x) = x² - 6x + 2
g(x) = -2x
Therefore,
(gof)(5) = g(f(5))
So we need to find g(f(x)) first.
Therefore,
g(f(x)) = -2(x² - 6x + 2)
g(f(x)) = - 2x² + 12x - 4
Therefore,
g(f(x)) = - 2x² + 12x - 4
(gof)(5) = g(f(5)) = - 2(5)² + 12(5) - 4
(gof)(5) = g(f(5)) = -50 + 60 - 4
(gof)(5) = g(f(5)) = 6
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A car travels 273 miles in 6 hours. How muchtime will it take traveling 378 miles
hello
the car travels 273 miles in 6 hours, how many hours will it take to travel 378 miles.
let the number of unknown hours be represented by x
[tex]\begin{gathered} 273mi=6\text{hrs} \\ 378mi=\text{xhr} \\ \text{cross multiply bith sides} \\ 273\times x=6\times378 \\ 273x=2268 \\ \text{divide both sides by 273} \\ \frac{273x}{273}=\frac{2268}{273} \\ x=8.3076\text{hrs} \end{gathered}[/tex]the car spent approximately 8.31 hours to travel a distance of 378 miles
Max packs cereal boxes into a larger box. The volume of each cereal box is 175 cubic inches. What is the approximate volume of the large box? Please help!!
Using mathematical operations, we can conclude that the volume of the larger box is approximately 2,800 in³.
What are mathematical operations?The rules governing the order of operations specify the order in which multiple operations should be performed to solve an expression. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are the order in which the operations are performed (from left to right).So, in the image, we can observe that the large box contains 6 boxes of cereals in front and possibly 8 boxes of cereals at the back.
In total, there are 16 small boxes in the big box.Then, the volume of the larger box can be:
175 × 16 = 2,800 in³Therefore, using mathematical operations, we can conclude that the volume of the larger box is approximately 2,800 in³.
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Create a polynomial of degree 6 that has no real roots. Explain why it has no real roots. Is it possible to have a polynomial with an odd degree that has no real roots? Explain.
Create a polynomial of degree 6 that has no real roots.
y = ( x^2 + 4) ( x^2 +7 ) ( x^2+5)
Multiplying all the terms together
y =x ^6 + 16 x^4 + 83 x^2 + 140
Using the zero product property
0= x^2 +4 x^2+7 =0 x^2 + 5 =0 will each give a complex solution
x^2 = -4 x^2 = -7 x^2 = -5
This means x = 2i or -2i x = i sqrt(7) or -i sqrt(7) x = i sqrt (5) or - i sqrt(5)
These solutions can be in the form a+bi
Therefor it will have no real roots
y = x^6 + 16 x^4 + 83 x^2 + 140 has no real solutions
Complex solutions come in pairs, so an odd degree must have a real solution
In a student council election there are 2 people running for treasure 3 people running for secretary 4 running for vice president and 2 people running for class president How many possible outcomes are there?
Given:
There are given that the 2 people running for treasure, 3 people running for secretary, 4 running for vice president, and 2 people running for class president.
Explanation:
According to the concept of outcomes:
The outcomes are defined for the possible results of an experiment.
Then,
In the given question, the outcomes are:
[tex]\text{Outcomes}=2+3+4+2=11[/tex]Final answer:
Hence, the total number of outcomes is 11.
Find the probability that a dart hits one of the shaded areas. Thewhite figure is a rectangle. Be sure to show all work.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Get the angles of the hexagon
The internal angles of an hexagon is given as:
[tex]\begin{gathered} \frac{180(n-2)}{n} \\ n=6\text{ since hexagon has 6 sides} \\ So\text{ we have:} \\ \frac{180(6-2)}{6}=\frac{180(4)}{6}=\frac{720}{6}=120\degree \end{gathered}[/tex]Therefore each angle of the hexagon is 120 degrees.
STEP 2: find the length of the sides
We remove the right triangles as seen below:
Using the special right triangles, we have:
STEP 3: find the area of the extracted triangle above
[tex]\begin{gathered} b=1,h=\sqrt{3} \\ Area=\frac{1}{2}\cdot1\cdot\sqrt{3}=\frac{\sqrt{3}}{2}units^2 \end{gathered}[/tex]Since there are two right triangles, we multiply the area by 2 to have:
[tex]Area=2\cdot\frac{\sqrt{3}}{2}=\sqrt{3}[/tex]There are two triangles(both sides), therefore the total area of the shaded area will be:
[tex]\sqrt{3}\cdot2=2\sqrt{3}[/tex]STEP 4: Find the area of the whole hexagon
[tex]\begin{gathered} Area=\frac{3\sqrt{3}s^2}{2} \\ s=hypotenuse\text{ of the right triangle}=2 \\ Area=\frac{3\sqrt{3}\cdot4}{2}=6\sqrt{3} \end{gathered}[/tex]STEP 5: Find the probability
[tex]\begin{gathered} Probability=\frac{possible\text{ area}}{Total\text{ area}} \\ \\ Possible\text{ area}=2\sqrt{3} \\ Total\text{ area}=6\sqrt{3} \\ \\ Probability=\frac{2\sqrt{3}}{6\sqrt{3}}=\frac{1}{3}=0.3333 \end{gathered}[/tex]Hence, the probability that the dart hits one of the shaded areas is approximately 0.3333
Hello,
I have paid the $29.00 monthly subscription for my son (jalen); I have signed up only to pay the monthly payment. Sorry to say, he does not live with me. I earlier sent you an email explaining the same with no reply from you. So how does he proceed using his information to freely access your program?
Looking forward to hearing from you shortly.
THANKS,
climacus
Answer:
Step-by-step explanation:
Solve the system of inequalities by graphing.y\ge-3
1. Canada has the longest coastline of any country. It is 202,080 km. China has 22,147 km of borders - more than any other countries. What is the difference between the two lengths? Label your answer!!
Canada has a coastline if 202,080km and China has 22,147 of borders, so the difference between them can be writen like this:
[tex]202080-22147[/tex]And we can made this operation so the answer is:
[tex]202080-22147=179,933[/tex]This means that the coastline of canada is 179,933 longer than the border of china
helppppppppppppppppppppppppppppppppppp
Harold Hill borrowed $16,400 to pay for his child's education at Riverside Community College. Harold must repay the loan at the end of 15 months in one payment with 3 3/4 % of interest.
A. How much interest must Harold pay? (Round answer to the nearest cent.)
B. What is the maturity value? (Round answer to the nearest cent.)
The interest that Harold pay is $768.75 and his maturity value is $17168.75.
Harold Hill borrowed $16,400
Harold must repay the loan at the end of 15 months in one payment with 3 3/4 % of interest
First we need to calculate the interest amount
= loan amount x rate of interest x number of months
interest = (16400 x 3 3/4 x 15/12)/100
interest = $768.75
The maturity value = loan amount + interest
= 16400 + 768.75
= 17168.75
Therefore, the interest that Harold pay is $768.75 and his maturity value is $17168.75.
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What is the value of 3÷5?
Answer:
0.6
Step-by-step explanation:
Jamie paid the rent well past the due date for the months of April, May and June. As a result, he had been charged a total of $75 as a late fee. Howmuch did he pay as late fee per month?Use 'f to represent the late fee $$ per month.
Total fee = $75
Number of months = 3
Divide the total fee by the number of months
75/3 = $25 per month
Graph the intersection or union, as appropriate, of the solutions of the pair of linear inequalities
See graph below
Expanation:The given inequalities:
[tex]\begin{gathered} x\text{ + y }\leq\text{ 4} \\ x\text{ }\ge2 \end{gathered}[/tex]To plot the graphs, we will assing values to x in order to get the corresponding values of y for each of the inequality:
let x = 0, 2, 4
x + y = 4
from the above: y = 4 - x
when x = 0
y = 4
when x = 2
y = 4 - 2 = 2
when x = 4
y = 4 -4 = 0
we only have x in the second inequality
we will have a vertical line for x = 2
But the shading will be towards the right because the inequality is greater than x
plotting the graph:
The solution of the inequalities is the point of intersection of both graphs (the darker shade)
Test scores are normally distributed with a mean of 86 and a standard devotion of 2.2 what percent scored between 83.8 and 92.6? What percent scored below 83.8?
Z- Score formula is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z\text{ is the z-score (Standard score)} \\ X\text{ is the value to be standardized} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Here, the mean is 86, while the standard deviation is 2.2
Percent between 83.8 and 92.6 is;
[tex]P(\frac{83.8-86}{2.2}The percent between 83.8 and 92.6 = 0.83999[tex]P(Z<-1)=\text{ 0.15866}[/tex]Percent score below 83.8 is 0.15866
Please provide deep explanation, so i can understand and learn. Thank you
Assume the height of the box is x.
5 reams of paper have 5 x 500 = 2500 sheets of paper.
This means that each sheet of paper has a thickness of x/2500.
Two sheets of paper have a thickness of 2 times x/2500.
Simplifying the fraction:
[tex]2\cdot\frac{x}{2500}=\frac{x}{1250}[/tex]Two sheets of paper have a thickness of 1/1250th of the height of the box.
Assume the height is x = 20 cm, then two sheets are 20/1250 = 0.016 cm thick.