Answer
The equation in point-slope form is
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
We can calculate the slope of the line and then use any of the two points given to serve as the point (x₁, y₁) in the equation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-5, 11) and (-2, 1)
x₁ = -5
y₁ = 11
x₂ = -2
y₂ = 1
[tex]\text{Slope = }\frac{1-11}{-2-(-5)}=\frac{-10}{-2+5}=\frac{-10}{3}[/tex]Slope = m = (-10/3)
Using the point (-2, 1) as (x₁, y₁), we can write the equation of the line
y - y₁ = m (x - x₁)
y - 1 = (-10/3) (x - (-2))
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Hope this Helps!!!
(12-1) (-2-3) slope p l z
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{ - 3 - ( - 1)}{ - 2 - 12} \\ m = \frac{ - 3 + 1}{ - 14} \\ m = \frac{ - 2}{ - 14} \\ m = \frac{1}{7} [/tex]
ATTACHED IS THE SOLUTION..I also provided you with the formula used to get the gradient.
5. John had 2 Snickers bars for every 4 Kit-Kit bars. If John had a total of 16 candy bars,how many Snickers bars did he have?as
Hi, can you help me to evaluate (if possible) thesix trigonometric functions of the real number.Please.
Okay, here we have this:
Considering the provided angle, we are going to evaluate the trigonometric functions, so we obtain the following:
Sine:
[tex]\begin{gathered} \sin (-\frac{2\pi}{3}) \\ =-\sin (\frac{2\pi}{3}) \\ =-\cos \mleft(\frac{\pi}{2}-\frac{2\pi}{3}\mright) \\ =-\cos \mleft(-\frac{\pi}{6}\mright) \\ =-\cos \mleft(\frac{\pi}{6}\mright) \\ =-\frac{\sqrt{3}}{2} \end{gathered}[/tex]Cos:
[tex]\begin{gathered} cos\mleft(-\frac{2\pi}{3}\mright) \\ =\cos \mleft(\frac{2\pi}{3}\mright) \\ =\sin \mleft(\frac{\pi}{2}-\frac{2\pi}{3}\mright) \\ =\sin \mleft(-\frac{\pi}{6}\mright) \\ =-\sin \mleft(\frac{\pi}{6}\mright) \\ =-\frac{1}{2} \end{gathered}[/tex]Tan:
[tex]\begin{gathered} tan\mleft(-\frac{2\pi\:}{3}\mright) \\ =\frac{\sin (-\frac{2\pi\: }{3})}{\cos (-\frac{2\pi\: }{3})} \\ =\frac{-\frac{\sqrt[]{3}}{2}}{-\frac{1}{2}} \\ =\sqrt[]{3} \end{gathered}[/tex]Csc:
[tex]\begin{gathered} \csc \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\sin\left(-\frac{2\pi}{3}\right)} \\ =-\frac{1}{\frac{\sqrt{3}}{2}} \\ =-\frac{2\sqrt{3}}{3} \end{gathered}[/tex]Sec:
[tex]\begin{gathered} \sec \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\cos\left(-\frac{2\pi}{3}\right)} \\ =\frac{1}{-\frac{1}{2}} \\ =-2 \end{gathered}[/tex]Cot:
[tex]\begin{gathered} \cot \mleft(-\frac{2\pi}{3}\mright) \\ =\frac{1}{\tan (-\frac{2\pi}{3})} \\ =\frac{1}{\sqrt[]{3}} \\ =\frac{\sqrt{3}}{3} \end{gathered}[/tex]Use point-slope form to write the equation of a line that passes through the point (-5,7)(−5,7) with slope -5−5
The equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .
The Point - Slope form of the line passing through (x₁,y₁) with slope m is given by the equation
(y-y₁)= m(x-x₁)
In the question ,
it is given that the required line passes through the point(-5,7) and have the slope = -5 .
the point is (-5,7)
so x₁= -5 and y₁=7 and m = -5
Substituting the value in the equation of point slope form , we get
(y-y₁)= m(x-x₁)
(y-7)= (-5)(x-(-5))
simplifying further , we get
(y-7)= (-5)(x+5)
y-7 = -5x -25
5x + y = -25 +7
5x + y = -18
Therefore , the equation of the line that passes through the point (-5,7) with slope -5 in the point-slope form is 5x + y = -18 .
The given question is incomplete , the complete question is
Use point-slope form to write the equation of a line that passes through the point (-5,7) with slope -5 .
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I'll give brainliest!
Answer: D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
...................
Solve the inequality for x and identify the graph of its solution. 4[x+ 2] < 8
Answer:
x < 0
Step-by-step explanation:
4(x + 2) < 8
4x + 8 < 8
4x < 0
x < 0
◀━━━━━|──>
0
Solve the quadratic equation x2=2536.What are the solutions of the equation x2=2536?
Given
[tex]x^2=2536[/tex]Answer
[tex]\begin{gathered} x^2=2536 \\ x=5036 \end{gathered}[/tex]PLEASEEE HELP Find the rate of change of the line that contains the two points (1, 4) and (5, -4). Be sure to show all calculations and reduce your slope to a fraction in simplest form.
The rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4) is m = 2
As per the question statement, we are supposed to find the rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4).
We know slope [tex]m = \frac{y_{2}-y_{1}}{x_{2} -x_{1}}[/tex] for the line passing though the points (x1,y1) and (x2, y2)
Using the same formula and finding out the rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4).
slope m = (-4-4)/(5-1)
m=-8/4
m = -2
Hence the rate of change of the line or the slope of the line that contains the two points (1, 4) and (5, -4) is m = 2
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Aviation A plane leaves an airport and flies south at 180 mph.
Later, a second plane leaves the same airport and flies south at
450 mph. If the second plane overtakes the first one in 12 hours,
how much of a head start did the first plane have?
The first plane had a head start of 432 minutes.
The speed, time and distance of any entity can be related by the following expression as Distance = Speed × Time. The speed of the first plane is 180 mph and the time given is 12 hours whereas the speed of second plane is 450 mph. Now, the distance travelled by plane A in time 12 hours is given by
Distance = Speed × Time
Distance = 180 × 12
Distance = 2160 miles.
The second also flies 2160 miles to overtake the first plane. It does this at a rate of 450 mph. So, the time taken for it to fly will be
Time = Distance/Speed
Time = 2160/450
Time = 4.8 hours
Since, 1 hour = 60 minutes, Therefore, 4.8 hours = 4.8×60 = 288 minutes. Now, since the first plane flies for 12 hours = 12×60 = 720 minutes. So, the head start = 720 minutes - 288 minutes = 432 minutes.
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Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.noyes; ASA Congruence Theoremyes; AAS Congruence Theorem
The diagramof the triangles is shown below
Looking at the two traingles, they meet at a vertex. Vertically opposite angles are equal.
Use the graph to complete the statement. O is the origin. R(y-axis) o R(y=x): (2,3)A. (-2, -3)B. (-3, 2)C. (3, -2)D. (2, -3)
Answer:
C. (3, -2)
Explanation:
First, we need to reflect the point (2, 3) across the line y = x. To reflect this point, we need to find another point that is at the same distance but on the opposite side of the line, so the reflection is
Therefore, the reflection is the point (3, 2)
Then, reflect (3, 2) across the y-axis, to get:
So, the answer is
C. (3, -2)
Janie has $3dollar sign, 3. She earns \$1.20$1.20dollar sign, 1, point, 20 for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $13.50
The inequality to represent the situation for Janie will be 3 + 1.2c > 13.50.
How to calculate the inequality?From the information, it was illustrated that Janie has $3 and that she earns $1.20 for every chore.
Let the total number of chores that she can do be represented as c.
It should be noted that she also wants about $13.50 to buy her CD. Therefore, the inequality can be represented as:
3 + (1.2 × c) > 13.50
3 + 1.2c > 13.50
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Cynthia Besch wants to buy a rug for a room that is 25 ft wide and 31 ft long. She wants to leave a uniform strip
of floor around the rug. She can afford to buy 567 square feet of carpeting. What dimensions should the rug
have?
Answer:
21 ft by 27 ft
Step-by-step explanation:
You want the dimensions of a rug with an area of 567 square feet such that it fits in a 25 ft by 31 ft room with a uniform space all around.
SetupWe note the room is 31-25=6 ft longer than it is wide. Since the rug has a uniform border around it, the rug dimensions will be 6 ft longer than wide. We want the rug area to be 567 square feet, so for width w we have ...
w(w+6) = 567
Solutionw² +6w +9 = 576 . . . . . . add 9 to complete the square
(w +3)² = 24² . . . . . . . . express as squares
w +3 = 24 . . . . . . . . . positive square root
w = 21 . . . . . . . . . . subtract 3 to find the width
w+6 = 27 . . . . . . add 6 to find the length
The rug should have dimensions 21 ft wide by 27 ft long.
__
Additional comment
The uniform strip of floor around the rug will be 2 feet wide.
Kuta Software - Infinite Algebra 2 Graphing Absolute Value Equations Graph each equation. 1-1-11 Name Date > 1512020 2) y-lx-a 13
we have the equation
[tex]y=-3\lvert-2x+4\rvert+3[/tex]using a grahing tool
see the attached figure
[tex] \frac{x}{3} + 1 = \frac{2}{3} [/tex]find the value of x
Given:
[tex]\frac{x}{3}+1=\frac{2}{3}[/tex]Find: x
Explanation:
[tex]\begin{gathered} \frac{x}{3}+1=\frac{2}{3} \\ \frac{x}{3}=\frac{2}{3}-1 \\ \frac{x}{3}=\frac{-1}{3} \\ x=-1 \end{gathered}[/tex]Final answer: the required value of x is -1
Which postulate or theorem proves that these two triangles are
congruent?
• SAS Congruence Postulate
• ASA Congruence Postulate
O AAS Congruence Theorem
R
O HL Congruence Theorem
According to the Angle-Side-Angle Postulate (ASA), if two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, the two triangles are congruent.
What is postulate?A postulate is a statement that is assumed to be true in the absence of proof. A theorem is an unprovable true statement. Six postulates and theorems that can be proven from them are listed below. A statement, also known as an axiom, that is assumed to be true in the absence of proof. Postulates are the fundamental building blocks from which lemmas and theorems are derived. Euclidean geometry, for example, is built around five postulates known as Euclid's postulates. A postulate is a statement accepted without evidence. A postulate is another name for an axiom.To learn more about postulate, refer to:
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9.823 x 10^-9 = 9.823/ 10^ 9
9.823/ 1000000000 = 0.000000009823
the long form has the same number of zeros that 10^-9, then it have 9 zeros.
given the following trig equations find the exact value of the remaining five trig functions.cos0 = 4/9 where sin0 < 0( sin, tan, csc, cot, sec)
we have that:
[tex]\sin ^2\theta=1-\cos ^2\theta=1-\frac{16}{81}=\frac{65}{81}\rightarrow\sin \theta=-\frac{\sqrt[]{65}}{9}[/tex]having this we get that
[tex]\tan \theta=\frac{-\sqrt[]{65}}{4},\cot \theta=-\frac{4}{\sqrt[]{65}},\sec \theta=\frac{9}{4},\csc \theta=-\frac{9}{\sqrt[]{65}}[/tex]Why was the Battle of Fallen Timbers important for the new democracy?
Please write 3 paragraphs, stating 3 different reasons why the battle was important. (Paragraphs should be 4-6 sentences each
The Whiskey Rebellion put an end as a consequence of the Battle of Fallen Timbers; that had a significant outcome.
Why was Battle of Fallen Timbers important to the US?After the Battle of Fallen Timbers, the Indians agreed to the Treaty of Greenville, which gave the United States authority over most of the river crossings in the Old Northwest Territory as well as vital sites like Detroit.
The Battle of Fallen Timbers is considered to be the last battle of the American Revolution and which also helped the new country start expanding the territory to the west.
This will effectively ensured American dominance over the Indian tribes. The Whiskey Rebellion; which was the first significant confrontation between the nascent American government and it's inhabitants, which was put a stop to by it, and peace was restored.
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Solve each system using substitution show your answer as an ordered pair no solution or infinite solution
1) Given y = x+2 and y = -4x-8.
Since the left hand sides of both equations are same, equate the right hand side of both the equations.
[tex]x+2=-4x-8[/tex]Add 4x on both sides.
[tex]\begin{gathered} x+2+4x=-4x-8+4x \\ 5x+2=-8 \end{gathered}[/tex]Add -2 on both sides.
[tex]\begin{gathered} 5x+2-2=-8-2 \\ 5x=-10 \end{gathered}[/tex]Divide by 5 on both sides.
[tex]\begin{gathered} x=-\frac{10}{5} \\ =-2 \end{gathered}[/tex]Substitute the value of x into y = x+2.
[tex]\begin{gathered} y=-2+2 \\ =0 \end{gathered}[/tex]Solution is (-2,0).
2) Given y = 3x+1 and y = -2x+6.
Since the left hand sides of both equations are same, equate the right hand side of both the equations.
[tex]3x+1=-2x+6[/tex]Add 2x on both sides.
[tex]\begin{gathered} 3x+1+2x=-2x+6+2x \\ 5x+1=6 \end{gathered}[/tex]Add -1 on both sides.
[tex]\begin{gathered} 5x+1-1=6-1 \\ 5x=5 \end{gathered}[/tex]Divide by 5 on both sides.
[tex]\begin{gathered} x=\frac{5}{5} \\ =1 \end{gathered}[/tex]Substitute the value of x into y = 3x+1.
[tex]\begin{gathered} y=3\cdot1+1 \\ =4 \end{gathered}[/tex]Solution is (1, 4).
3) Given y = -3x-6 and 6x+2y = -2.
Substitute -3x-6 for y into 6x+2y = -2.
[tex]\begin{gathered} 6x+2(-3x-6)=-2 \\ 6x-6x-12=-2 \\ -12=-2 \end{gathered}[/tex]which is not possible. Hence the given system of equations has no solution.
4) Given y = -5 and -8x+4=-20.
From the second equation, -8x+4 = -20, solve for x.
Add -4 on both sides.
[tex]\begin{gathered} -8x+4-4=-20-4 \\ -8x=-24 \end{gathered}[/tex]Divide by -8 on both sides.
[tex]\begin{gathered} x=\frac{-24}{-8} \\ =3 \end{gathered}[/tex]Solution is (-5, 3).
Isaac creates a scatter plot showing the association between the height and weight of his maleclassmates. He models the association with the equation w = 6.5h - 275, where h is theclassmate's height in inches and w is the classmate's weight in pounds. What is the meaning of theslope in this equation?
solution
for this case we have the following equation:
w = 6.5h -275
For this case the slope is the number next to the h so then m = 6.5
And the best answer would be:
D) For every 6.5 inch in height , 275 pounds is subtracted to get the weight
Please help and round to the nearest minute if needed
Solution
For this case we have the following angle:
30 1/6 º
and then we need to convert to degrees and minutes so we can do this:
1 º= 60 min
then 1/6º* (60min/ 1º)= 10 min
Then the answer is:
30º 60'
Solve the following system of equations using the substitution method.
–6x + 2y = 8
y = 3x + 4
Answer:
Infinite solutions or some courses say all real numbers
Step-by-step explanation:
-6x + 2(3x + 4) = 8 substitute 3x + 4 for y
-6x + 6x + 8 = 8 Distribute the 2
8=8 The x's cancel out leaving a true statement. This means that there are infinite solutions.
i’m trying to find the slope and y intercept of number 2.. can someone help me please. thank you (:
According to the problem,
• Jennifer is 20 miles North.
,• The rate is 55 miles per hour.
Remember that rate of change refers to the slope.
Therefore, the slope is 55.
On the other hand, the y-intercept is the initial condition of the problem since Jennifer started 20 miles North, then the y-intercept is (0,20).
The length of sides of a triangle are xem, (x + 1)cm and (x + 2)cm. Determine x so that this triangle is a right- angled triangle.
The value of x = 3
3cm, 4cm, and 5cm are the sides of a right-angled triangle.
What is Pythagoras theorem?
In a right-angled triangle, the hypotenuse is the largest of the three sides, so hypotenuse is (x +2).
As a result of Pythagoras' theorem,
hyp² = base² + alt²
here ,
x² + (x+1)² = (x+2)²
by simplifying the equation,
x² + x² + 2x +1 = x² + 4 + 4x
=> 2x² + 2x + 1 = x² + 4x + 4
=> x² - 2x -3 = 0
=> x² - 3x + x - 3 = 0
=> x(x-3) + 1(x-3) = 0
=> (x+1) (x-3) = 0
so, x+1 = 0 or x-3 = 0
x = -1 or x = 3
since length cannot be negative,
x = -1 is not considered .
so x= 3.
value of x is 3.
So the triangle's three sides are 3cm, 4cm, and 5cm.
to double-check the answer
Pythagoras' theorem substitute values
hyp² = b²+a²
hyp = [tex]\sqrt{3^{2}+4^{2} }[/tex]
= [tex]\sqrt{9+16}[/tex]
= [tex]\sqrt{25}[/tex]
= 5
As a result, the three sides of a right-angled triangle are 3cm, 4cm, and 5cm.
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3. Consider the following system of equations.Line 1: 2x - y = -3Line 2: -6x - 2y = -6Part A:Is (0,3) a solution to Line 1? Explain your answer.Part B:Is coordinate (0, -3) is a solution to Line 2? Explain your answer.Part C:What are the slopes of Linel and Line 2?Part D:What are the y-intercepts of Line 1 and Line 2?
Part A
replace (0,3) on (x,y)
[tex]\begin{gathered} 2(0)-(3)=-3 \\ 0-3=-3 \\ -3=-3 \end{gathered}[/tex]the equivalence is correct so (0,3) is a solution of the first equation
Part B.
replace (0,-3) on (x,y)
[tex]\begin{gathered} -6(0)-2(-3)=-6 \\ 0-(-6)=-6 \\ 6=-6 \end{gathered}[/tex]the equivalence is incorrect so (0,-3) isnt a solution of the second equation
Part C
To find the slope we need to solve each expresion and take the coefficient of x
first equation
[tex]\begin{gathered} 2x-y=-3 \\ y=2x+3 \end{gathered}[/tex]the slope is 2
second equation
[tex]\begin{gathered} -6x-2y=-6 \\ 2y=-6x+6 \\ y=-3x+3 \end{gathered}[/tex]the slope is -3
Part D
the y-intercept is the constant without variable on each equation
first equation
[tex]y=2x+3[/tex]the y-intercept is 3
second equation
[tex]y=-3x+3[/tex]the y-intercep is 3 too
The Graph
we need two points of the line and join by a right infinite line
first equation
the points (0,3) and (-3/2,0) belong to the line 1
second equation
the points (0,3) and (1,0) belong to the line 2
Solution of the system
we can note the two lines trought the point (3,0) so this is the solution and we can check matching the equations and solving x
[tex]\begin{gathered} 2x+3=-3x+3 \\ 2x+3x=3-3 \\ 5x=0 \\ x=0 \end{gathered}[/tex]and replace x=0 on any equation to solve y I will use the first equation
[tex]\begin{gathered} y=2x+3 \\ y=2(0)+3 \\ y=3 \end{gathered}[/tex]so the solution point is (0,3)
A. Let h be the number of hours Chris worked. How many hours did Mark work?
a. We start by noting the number of hours Mark worked, given that h is the number of hours Chris worked.
To get this, we look for the relationship between the number of hours Mark worked and the number of hours Chris worked
From the question, we are told that they worked the same umber of hours, so the number of hours Mark worked is also h hours since they worked equal number of hours.
b. We shll now use the relationship with Kari for both Chris annd Mark to write two equations.
For Chris, we rae told that Kari worked twicw as many hours as he worked.
So if Chris worked h hoirs, then Kari worked 2 * h = 2h hours
For Mark, we are told that Kari worked 10 less than 3 times the number of hours Mark worked
The number of hours Mark worked was h hours, 3 times this is 3 * h = 3h
10 less than this would be (3h - 10) hours
c. An equation describing the expression above;
Since each expressin represents the number o hours Kari worked, then the two expressions must be equal.
Thus;
2h = 3h - 10
Tools Question 2 Nicolas makes toys at a toy shop. The graph represents the relationship between the number of toys (1) that Nicolas makes and the number of hours Toy Making 50 45 40 35 30 Number of Toys 25 20 15 10 2 6 10 Number of Hours Which of the following equations represents a toy-making rate, in toys per hour, that is HALF that of Nicolas's toy-making rate?
The equation of a proportional relationship between two variables x and y with a constant of proportionality k, is:
[tex]y=kx[/tex]If y represents the number of toys and x represents the number of hours, substitute the corresponding values of x and y to find the constant of proportionality k. Use, for instance, the fact that Nicholas made 40 toys in 10 hours:
[tex]40=k\cdot10[/tex]Divide both sides of the equation by 10:
[tex]k=4[/tex]Since Nicholas's toy-making rate is 4 toys per hour, half that rate would be 2 toys per hour. Then, out equation would become:
[tex]y=2x[/tex]Using the letter "t" for toys instead of y and "h" for hours instead of x, then:
[tex]t=2h[/tex]Write the equations for the lines parallel and
perpendicular to the given line j that passes
through Q. SEE EXAMPLE 4
26. y = -4x + 1; Q(6, -1)
27. y = ¾x + 4; Q(−1, 1)
LESSON 2-4 Slopes of Parallel and Perpendicular Lines 97
y = -4x + 1 and y = ¾x + 4, Clearly by values we can see that they are neither parallel nor perpendicular.
What is a slope?The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which produces the same number for every two distinct points on the same line. A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.
If a line rises from left to right, it is said to be growing. The slope is upward, or m>0.If a line slopes downward from left to right, it is diminishing. The slope, m0, is negative.The slope of a line is 0 if it is horizontal. This function is constant.A line's slope is ambiguous if it is vertical.Clearly by values we can see that they are neither parallel nor perpendicular.
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7 times blank equals 1
Answer: 0.1429.
Step-by-step explanation: To double-check our work, multiply 0.1429 by 7 to see that it equals 1.