The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
What is a equation of line?The general equation of a straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis. Key Point. The equation of a straight line with gradient m and intercept c on the y-axis is y = mx + c.
Given that,
equation of given line with a slope of m = 3
y=3x-5
A line perpendicular to that line will have a slope that is the negative reciprocal of 3.
The reciprocal of 3 is 1/3. So the negative reciprocal of 3 is -1/3.
Therefore, we want to write the equation of a line with slope, m = -1/3, and passes through the point (6, 4) = (x, y).
y = mx + b
4 = (-1/3)(6) + b
(we've set up the equation with only one unknown, b, that we can now solve for)
4 = -2 + b
b = 6
With a slope, m = -1/3, and a y-intercept, b = 6, the equation of our line relating x and y is:
y = (-1/3)x + 6
Hence, The equation of line is y = [tex]\frac{-1}{3}[/tex][tex]x[/tex]+6 .
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Find the y-intercept of the line graphed by the equation 1/2x + y = 7. (0, 14) (14, 0) (7, 0) (0, 7)
The y-intercept of the line graphed by the equation [tex]\frac{1}{2} x+y=7[/tex] is (0,7)
Option (D) is correct.
The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.
The given equation is [tex]\frac{1}{2} x+y=7[/tex]
Converting the equation in Slope-intercept form, we get
[tex]y=-\frac{1}{2} x+7[/tex] ...(1)
Now, to find the y-intercept, substitute x = 0 in the equation and solve for the value of y
Putting x = 0 in equation (1), we get
[tex]y=-\frac{1}{2} (0)+7[/tex]
[tex]y=7[/tex]
Therefore, the y-intercept of the line will be (0,y) i.e., (0,7)
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Write a system of equations that represent the graph .
To write an equation for the lines of the graph, we have to find the slope and the y-intercept of each line.
The y-intercept can be find as the value of y when the line intersects the y-axis.
For company L, that intersects at (0,10), the y-intersect is y(0)=10.
For company K, that intersects at (0,5). the y-intersect is y(0)=5.
The slope can be find using two points of the line.
For Company L we will use points (0,10) and (20,15). Then, we calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-10}{20-0}=\frac{5}{20}=0.25[/tex]For Company K, the points will be (0,5) and (20,15), and the slope will be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{15-5}{20-0}=\frac{10}{20}=0.5[/tex]With the slope and y-intercept we can write the equation of each line in slope-intercept form.
For Company L, with slope m=0.25 and y-intercept b=10 we will have:
[tex]\begin{gathered} y=mx+b \\ y=0.25x+10 \end{gathered}[/tex]For Company K, with slope m=0.5 and y-intercept b=5, we will have:
[tex]y=0.5x+5[/tex]Answer:
The system of equations will be:
Company L: y=0.25x+10
Company K: y=0.5x+5
What is the value of -7/8÷-1 2/5 pls asap
Answer:
See below
Step-by-step explanation:
-7/8 / (- 7/5) = - 7/8 *- 5/7 = 5/8
need help!! algebra 1
Answer:
f(1)= -3
Step-by-step explanation:
what f(1) means is when x is 1 what is y. I dont see the graph labeled so im just assuming that the graph is going by ones. So what i did was i found where x is one and then i checked at what point did the line match with the y axis which was 3 points below 0 on y axis ( disclaimer if the graph isnt going by ones then its going to be a different answer, but you can use the same process to find it.
Help with this special right triangle
Answer:
6 ft
Step-by-step explanation:
You want the length of the short side of a 30°-60°-90° triangle, given the longest side is 12 ft.
Special triangleA 30°-60°-90° triangle has side lengths in the ratios ...
1 : √3 : 2
Here, the longest side is given as 12 ft, so we can multiply this set of ratios by 6 ft to find the lengths of all of the sides:
1 : √3 : 2 = (6 ft) : (6√3 ft) : (12 ft)
The shortest side has length ...
k = 6 ft
__
Additional comment
You can also use trig functions to find the length k:
k/(12 ft) = cos(60°) = 1/2, or
k/(12 ft) = sin(30°) = 1/2
k = (1/2)(12 ft) = 6 ft
Bell WorkDIRECTIONSSolve the equation for the variable x.-2(x-3) = 26*Hint: Make sure to use distribution arrows and identifylike terms.
You have the following equation:
-2(x - 3) = 26
in order to solve the previous equation, proceed as follow:
-2(x - 3) = 26 use distribution property
-2(x) - 2(-3) = 26
-2x + 6 = 26 subtract 6 both sides
-2x = 26 - 6 simlify like terms right side
-2x = 20 divide by -2 both sides
x = 20/(-2)
x = -10
Hence, the solution to the given equation is x = -10
A jet’s speed in still air is 240 mph. One day it flew 700 miles with a tailwind (the wind pushing it along) and then returned the same distance against the wind. The total flying time was 6 hours. Find the speed of the wind.
Speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.
As given in the question,
Given data:
Jet speed in still air = 240mph
Let x be the speed of the wind.
Speed with tail wind = 240 +x
Distance covered with tail wind = 700miles
Time taken by jet with tail wind
= Distance/ speed
= 700 / (240 +x) __(1)
Speed against the wind = 240 - x
Distance covered against the wind = 700miles
Time taken by jet against the wind
= Distance/ speed
= 700 / (240 - x) __(2)
Total time taken is 6 hours
[700 / (240 +x)] + [700 / (240 - x)] = 6
⇒ 700( 240 -x + 240 + x) = 6 (240 +x)(240 - x)
⇒ 700 ( 480) = 6 ( 240² -x²)
⇒ 700 (80) = 57600 -x²
⇒ x² = 57600 - 56000
⇒ x² = 1600
⇒ x = √1600
⇒ x= 40 mph
Therefore, speed of the wind for jet speed in still air 240mph and jet covers 700 miles with tailwind and same distance against the wind in total time of 6 hours is equal to 40mph.
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The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 5% of all adults deliberately do a one-time fling and feel no guilt about it! In a group of six adult friends, what is the probability of the following? (Round your answers to three decimal places.)
Using the binomial distribution, the probability of no one having done a one time fling is of 0.735 = 73.5%.
Binomial distributionThe mass density formula for the probability of x successes is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters of the formula are given as follows:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.In the context of this problem, the values of the parameters are as follows:
p = 0.05, as about 5% of all adults deliberately do a one-time fling and feel no guilt about it.n = 6, as there are six adult friends in the group.The probability that no one has done a one time fling is P(X = 0), hence the probability is calculated as follows:
P(X = 0) = (0.95)^6 = 0.735 = 73.5%.
Missing informationThe problem asks for the probability that no one has done a one time fling.
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1
-2-(-7) = ?
NEXT
BOOKMARK
Answer:
5
Step-by-step explanation:
negetive two minus negative seven equal to five
Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.
Find the missing endpoint if S is the midpoint RT. R(-9, 4) and S(2, -1); Find T.
we know that
The formula to calculate the midpoint between two points is equal to
[tex]s(\frac{x1+x2}{2},\frac{y1+y2}{2}_{})[/tex]we have
S(2,-1)
(x1,y1)=R(-9,4)
(x2,y2)=T
substitute the given values in the formula
[tex]s(2,-1)=(\frac{-9+x2}{2},\frac{4+y2}{2}_{})[/tex]Find the x2 coordinate
2=(-9+x2)/2
-9+x2=4
x2=4+9=13
Find the y2 coordinate
-1=(4+y2)/2
4+y2=-2
y2=-2-4
y2=-6
therefore
the coordinates of point T(13,-6)Please show your but an short explanation, i inserted a picture of the question
With the given information we can make the following equation:
[tex]x+2x+3x=30[/tex][tex]6x=30[/tex][tex]x\text{ = 5}[/tex]Then David will have:
[tex]2\times5=10\text{ years}[/tex]Answer: 10 years.
Car 1 leaves point A at 5:30 p.m., driving due south atan average speed of 35 mph. Car 2 leaves point A at6:30 p.m., driving due north at an average speed of 45mph. How far apart will the drivers be at 9:30 p.m.?
Answer:
Explanation:
• Car 1 leaves point A at 5:30 p.m., driving due south at an average speed of 35 mph.
,• Car 2 leaves point A at 6:30 p.m., driving due north at an average speed of 45 mph.
At 9:30 pm, the time taken by the cars is:
[tex]\begin{gathered} Car\;1:9:30-5:30=4\text{ hours} \\ Car\;2:9:30-6:30=3\text{ hours} \end{gathered}[/tex]The distance covered by each car is:
[tex]\begin{gathered} Distance=Speed\times Time \\ \text{Car 1's distance}=35\times4=140\text{ miles} \\ \text{Car 2's distance}=45\times3=135\text{ miles} \end{gathered}[/tex]Since car 1 drives due South and Car 2 due North of point A:
Therefore, the distance between the drivers at 9:30 p.m. will be:
[tex]Distance=140+135=275\text{ miles}[/tex]The two drivers are 275 miles apart at 9:30 pm.
License plates in a particular state are to consist of 2 digits followed by 4 uppercase letters. a) How many different license plates can there be in this state if repetition of letters and numbers is permitted? b) How many different license plates can there be in this state if repetition of letters and numbers is not permitted? c) How many different license plates can there be in this state if the must be , and repetition of letters and numbers is not permitted? d) How many different license plates can there be in this state if the first digit cannot be , and repetition of letters and numbers is not permitted?
a)Total different number plates will be 45697600
b) Total different number plates will be 32292000
What is permutation and combination?
In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations
We are given that license plate allows 2 digits and 4 upper case letters
a) repetition is allowed
hence for 2 numbers we have 10*10=100 choices
Also letter are allowed 26*26*26*26=456976 choices
And Hence total choices are 456976*100=45697600 ways
b) Repetition is not allowed
hence for 2 numbers we have 10*9=90 choices
Also letter are not allowed 26*25*24*23= 358800 choices
And Hence total choices are 456976*100=32292000 ways
Hence
a)Total different number plates will be 45697600
b) Total different number plates will be 32292000
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Suppose that g(x) = f(x) + 5. Which statement best compares the graph ofg(x) with the graph of f(x)?
We are told that
[tex]g(x)=f(x)+5[/tex]If we were given the graph of f(x), note that in this equation we add 5 to the value of f(x) to find the value of g(x). So, in terms of the graph, as we are taking the final value of f and adding 5, this means that we are moving the graph of f 5 units up. That is the graph of g(x) is the graph of f(x) shifted 5 units up
a number increased by 6
Answer:
x + 6.
Step-by-step explanation:
a number which is x and increased by 6 is adding 6
Tareq pays $22.10 for 2.6 pound of salmon. What is the price per pound of salmon?
Answer:
22.1$ = 2.6 pound
x = 1 pound
so when we criss cross
22.1$ X 1 pound = 2.6x pound
22.1 = 2.6x
22.1/2.6 2.6x/2.6
X=22.1/2.6
x=8.5
so it costs 8.5$ per pound
solve using substitution or elimination
6x-12y=0
x-6y=4
On a coordinate plane, 2 triangles are shown. The first triangle has points F prime (1, 5), E prime (negative 1, 1), and D prime (negative 4, 2). The second triangle has points E (1, negative 1), D (2, negative 4), and F (5, 1). Complete the mapping of the vertices of ΔDEF. D(2, –4) → D' E(1, –1) → E' F(5, 1) → F' What is the rule that describes a reflection across the line y = x? rx = y(x, y) →
Answer:y
Step-by-step explanation:
Answer:
Step-by-step explanation:
I would rlly appreciate if someone helped me out on this please!
Answer:
14.7
Step-by-step explanation:
Let's say the width is x
So volume would be 24 × 2x × x = 10368
24 × 2x² = 10368
2x² = 10368 / 24 = 432
x² = 216 , width can't be negative so
x = 14.6969... ~~ 14.7
Olivia wants to buy a pizza. A plain cheese pizza costs $8.50 and each additional topping costs $0.75. Let t represent the number of toppings. How many toppings can Olivia get if she only has $8.00 to spend. Set up your inequality and solve. Then write your final answer in a complete sentence.
Olivia would be able to get 11 toppings.
Steps:
8.00 / .75 = 10.6
Round~
11
You're welcome!!!
Find the value of the variable.
Answer:
Since AB = BC,
3m + 5 = 4m - 10
m = 15
Given vectors a= (1, - 4) and b = (2, 5), find –2a+5b.Write your answer in component form.- 2a + 5b =?
We are given the following two vectors
[tex]\begin{gathered} a=<1,-4> \\ b=<2,5> \end{gathered}[/tex]We are asked to find the following
[tex]-2a+5b[/tex]First, multiply the vector a with the scaler -2 to get -2a
[tex]\begin{gathered} -2a=<-2\cdot_{}1,-2\cdot-4> \\ -2a=<-2,8> \end{gathered}[/tex]Now, multiply the vector b with the scaler 5 to get 5b
[tex]\begin{gathered} 5b=<5\cdot2,5\cdot5> \\ 5b=<10,25> \end{gathered}[/tex]Finally, add -2a and 5b to get -2a+5b
[tex]\begin{gathered} -2a+5b=<-2,8>+<10,25> \\ -2a+5b=<-2+10,8+25> \\ -2a+5b=<8,33> \end{gathered}[/tex]Therefore, the resultant vector in component form is
[tex]-2a+5b=<8,33>[/tex]Find the slope of the line with the equation 8x + 2y=12 m = -8 Om= 8 m = -4 m = 2
Simplify the equation 8x + 2y = 12 to obtain the equation in y = mx + b.
[tex]\begin{gathered} 8x+2y=12 \\ 2y=-8x+12 \\ y=-\frac{8}{2}x+\frac{12}{2} \\ y=-4x+6 \end{gathered}[/tex]In equation y = mx + b, slope is m and y-intercept is b.
So on compare the equation y = -4x + 6 with standard equation the slope is m - -4.
Answer: m = -4.
Rafael bought a bag of candy that contains 50 pieces. 30 of those pieces are chocolate and 5 are caramel. Write a ratio that compares the number of chocolate pieces to the number of pieces that are not either chocolate or caramel.
Answer:
so 50:30
=50-30=20
chocolate and 5are caramel
20:5
5can go into 20 =4
20:5
=4:1
Step-by-step explanation:
bag of candy is 50pieces 30piecesare chocolate and 5arecaramel
step 2 . you will subtract 50from30=20
step 3. 5can go into 20=4times
20:5 is equal to 4:1
Order √70,-8.2.25,-8
47
from least to greatest.
Arrange them in Ascending order :
-8(4/7) < -8.2 < 25/3 < √70
What is Ascending order?
When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given numbers,
√70 ,-8.2, 25/3, -8(4/7)
We have to Arrange these in ascending order
First lets get these terms to its simplest form
Value of √70 = 8.36
value of 25/3 = 8.33
Value of -8(4/7) = -8.57
Now we have the simplest value of all the following numbers
That is:
8.36, -8.22, 8.33, -8.57
The smallest of all is -8.57
Then -8.57 will be at first
-8.57, 8.36, -8.22, 8.33
now the second will be -8.22
-8.57, -8.22, 8.36, 8.33
Now the third would be 8.33
So the last would be 8.36 that is the greatest
-8.57, -8.22, 8.33, 8.36
Now, for the original value it would be:
-8(4/7) < -8.2 < 25/3 < √70
Hence, The ascending order of the number is -8(4/7) < -8.2 < 25/3 < √70
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If the sum of 5 consecutive analysis numbers is 170, what is the analysis number?
Answer:
The five consecutive integers whose sum is 170 are 32, 33, 34, 35, and 36
Step-by-step explanation:
hope it help
have a nice day
C>0, |u|=c is equivalent to u=
|u|=c is equivalent to u = c or u = -c.
Given that c > 0.
i.e., c is a positive number.
Then |u| = c. That is, absolute value of u = c, a positive number.
An absolute value function is defined by,
|u| = { u ; if u ≥ 0
{ -u ; if u < 0
The absolute value of any number, Positive or negative, is always a positive number.
So here |u| = c, with c > 0.
Comparing with the definition of absolute value function, c is either u or -u.
More clearly, c = u, when u ≥ 0 or c = -u , when u < 0.
Hence the value of c depends on u.
Thus, |u|=c is equivalent to u = c or u = -c.
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The cost of a Turkish cloth varies jointly as the length and width of the cloth. If the cost is TL3848 for an 8 ft by 13 ft cloth, then what is the cost of a 17 ft by 23 ft cloth?
The cost of the the 17 feet by 23 feet Turkish cloth given the constant of variation is TL14,467.
What is the cost?A variable varies jointly if the value of one variable depends on the value of two or more variables. In this question, if the length and width of the cloth increases, the cost of the cloth increases. Also, if the length and width of the cloth decreases, the cost of the cloth decreases.
The equation that represents joint variation is:
y = kab
Where:
y = dependent variable = cost of the Turkish cloth k = constant of variation a = dependent variable = length of the cloth b = dependent variable = widthTL3848 = k(13 x 8)
k = TL3848 / (13 x 8)
k = $37
The cost of 17 feet by 23 feet cloth :
37 x 17 x 23 = TL14,467
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The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8 Fahrenheit what is the difference in the record temperatures in degrees Fahrenheit
The difference in the record temperatures is 58.3° Fahrenheit.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol - , or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.
Given Data
The record high temperature on January 15 is 41.5 Fahrenheit the record low temperature on that day is -16.8.
Difference = High temperature - Low temperature
Difference = 41.5 -(-16.8)
Difference = 41.5 + 16.8
Difference = 58.3
The difference in the record temperatures is 58.3° Fahrenheit.
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Find the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300
the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300 will be A = $209314.286 or A = $209314.3 .
The formula to calculate amount,
[tex]A= \frac{P[(1+\frac{APR}{100n})^{n*N}-1 ]}{(\frac{APR}{100n}) }[/tex]
where, we are given,
N = 2 years
APR = 7%
P = 300
n = 12
subsituting these values in the equation above we get,
[tex]A=\frac{300[1+\frac{7}{100*1} ]^{12*2} -1}{\frac{7}{100*12} }[/tex]
[tex]A=\frac{300*100*12}{7}} * [\frac{107}{100}^{24} -1][/tex]
[tex]A=\frac{ 360000}{7}[5.07-1][/tex]
[tex]A=\frac{360000}{7}[4.07][/tex]
A=51428.57 * 4.07
A = $209314.286
or
A = $209314.3
What is APR?
An annual percentage rate is a calculation that includes all fees and costs associated with borrowing in addition to the interest rate.
APR is a number provided for all mortgages, loans, and credit cards, and there is a precise formula the bank must use in order to calculate the number in accordance with the Financial Service Authority's guidelines. It is simple to compare the APR between various accounts. All of the additional fees and expenditures you must pay on top of the basic interest rate are factored into the APR calculation.
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