The measure of the angle between tangent and secant AB in a circle with arcs in a 1:5 ratio is 120°, calculated using arc measures.
Let's denote the measures of the arcs subtended by chord AB as x and 5x, where x is the measure of the smaller arc.
Now, according to the properties of angles formed by a tangent and a secant, the measure of the angle formed between the tangent and the secant AB is equal to half the difference of the measures of the intercepted arcs.
So, the measure of the angle [tex]\( \angle A \)[/tex] formed between the tangent and the secant AB is:
[tex]\[ \angle A = \frac{1}{2} \left|5x - x\right| \\\[ \angle A = \frac{1}{2} \left|4x\right| \][/tex]
Now, since x represents the measure of the smaller arc, it must be greater than 0. Thus, the expression simplifies to:
[tex]\[ \angle A = 2x \][/tex]
Now, we need to find the value of x. Since the sum of the measures of the arcs in a circle is 360°, we have:
[tex]\[ x + 5x = 360^\circ \\\[ 6x = 360^\circ \\\[ x = \frac{360^\circ}{6} \\\[ x = 60^\circ \][/tex]
Now, we can find the measure of the angle [tex]\( \angle A \)[/tex]:
[tex]\[ \angle A = 2x \\\[ \angle A = 2(60^\circ) \\\[ \angle A = 120^\circ \][/tex]
So, the measure of the angle between the tangent and secant AB is 120°.
Answer:
The measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]
Explanation:
To solve this problem, let's denote the measures of the two arcs subtended by chord AB as [tex]\(x\)[/tex] and [tex]\(5x\)[/tex], respectively.
We know that when a tangent line intersects a secant line, the angle formed between the tangent and the secant is equal to half the difference of the measures of the intercepted arcs.
So, the angle between the tangent and secant AB, let's call it [tex]\(\theta\)[/tex], is given by:
[tex]\[ \theta = \frac{1}{2}(5x - x) = \frac{1}{2}(4x) = 2x \][/tex]
Now, let's find the value of [tex]\(x\).[/tex]
Since chord AB subtends two arcs with measures in the ratio of [tex]\(1:5\)[/tex], the total angle around the circle is [tex]\(1x + 5x = 6x\)[/tex], which is [tex]\(360\°\)[/tex](since the total angle around a circle is [tex]\(360\°\)[/tex]).
So, we have:
[tex]\[ 6x = 360\° \][/tex]
Solving for [tex]\(x\):[/tex]
[tex]\[ x = \frac{360\°}{6} = 60\° \][/tex]
Now, we can find the measure of the angle [tex]\(\theta\):[/tex]
[tex]\[ \theta = 2x = 2 \times 60\° = 120\° \][/tex]
So, the measure of the angle between the tangent and secant AB is [tex]\(120\°\).[/tex]
Evaluate 9n -15 for n = 5.
Answer:
the answer is 30
Step-by-step explanation:
9(5)=45
45-15=30
➷ Substitute 5 into everywhere you see 'n'
9(5) - 15
Simplify:
9 x 5 = 45
45 - 15 = 30
The answer is 30.
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Can you help me put these into slope intercept form so I can graph them and if u can find the slope that would be great sry for bad English
1) 20x + 80y=0
2) 30x + 50y-100=0
3) 3x - 15y - 30 =0
Answer:
Part 1) [tex]y=-(1/4)x[/tex]
Part 2) [tex]y=-(3/5)x+2[/tex]
Part 3) [tex]y=(1/5)x-2[/tex]
Step-by-step explanation:
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
Part 1) we have
[tex]20x+80y=0[/tex]
Simplify
Divide by 20 both sides
[tex]x+4y=0[/tex]
isolate the variable y
Subtract x both sides
[tex]4y=-x[/tex]
Divide by 4 both sides
[tex]y=-(1/4)x[/tex] ------> equation of the line into slope intercept form
[tex]m=-(1/4)[/tex]
[tex]b=0[/tex]
Part 2) we have
[tex]30x+50y-100=0[/tex]
Simplify
Divide by 10 both sides
[tex]3x+5y-10=0[/tex]
isolate the variable y
Subtract (3x-10) both sides
[tex]5y=-(3x-10)[/tex]
Divide by 5 both sides
[tex]y=-(3/5)x+2[/tex] ------> equation of the line into slope intercept form
[tex]m=-(3/5)[/tex]
[tex]b=2[/tex]
Part 3) we have
[tex]3x-15y-30=0[/tex]
Simplify
Divide by 3 both sides
[tex]x-5y-10=0[/tex]
isolate the variable y
Subtract (x-10) both sides
[tex]-5y=-(x-10)[/tex]
Divide by -5 both sides
[tex]y=(1/5)x-2[/tex] ------> equation of the line into slope intercept form
[tex]m=(1/5)[/tex]
[tex]b=-2[/tex]
A system of equations is shown below:
2x = 5y + 4
3x − 2y = −16
What is the solution to this system of equations?
(−8, −4)
(8, 4)
(−4, −8)
(4, 8)
Answer:
(-8, -4) is the solution
Step-by-step explanation:
Determine whether or not (-8, -4) is a solution to this system. It is a solution if we can substitute -8 for x and -4 for y in both equations and find that both equations are true:
2(-8) = 5(-4) + 4 TRUE
3(-8) - 2(-4) = -16 TRUE
So (-8, -4) is a solution to the given system.
Check out the second possible solution in the same way:
2(8) = 5(4) + 4 FALSE
Check out the third possible sol'n in the same way:
2(-4) = 5(4) + 4 FALSE
Check out the fourth in the same way:
2(4) = 5(8) + 4 FALSE
So we conclude that (-8, -4) is the sole solution to the given system.
Answer:
(-8, -4)
Step-by-step explanation:
Select all of the equations that represent linear relationships. 5 + 2y = 13 y = 1/2x^2+7 y – 5 = 2(x – 1) y/2 = x + 7 x = –4
Answer:
FIRST OPTION.
THIRD OPTION.
FOURTH OPTION.
FITH OPTION.
Step-by-step explanation:
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope, b the y-intercept and the exponent of x is always 1 or 0.
Solve for y from the equations shown below:
[tex]5+2y=13\\2y=8\\y=4[/tex]
(In this linear function the slope is 0)
[tex]y-5=2(x-1)\\y=2x-2+5\\y=2x+3[/tex]
(It is a linear function)
[tex]\frac{y}{2}=x+7\\ y=2(x+7)\\y=2x+14[/tex]
(It is a linear function)
Equation of the line whose slope is not defined:
[tex]x=-4[/tex]
Answer:
1, 3, 4, and 5
Step-by-step explanation:
Edge 2021!
Proof:
One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 400 square meters, what are the lengths of the diagonals?
Answer:
20m and 40m
Step-by-step explanation:
The area (A) of a kite is calculated using the formula
A = [tex]\frac{1}{2}[/tex] product of diagonals
Let one diagonal be d then the other diagonal is 2d ( twice as long )
Hence
[tex]\frac{1}{2}[/tex] × 2d × d = 400
d² = 400 ← take the square root of both sides
d = [tex]\sqrt{400}[/tex] = 20
and 2d = 2 × 20 = 40
The diagonals are 20m and 40m in length
The lengths of the diagonals of a kite, where the area is 400 square meters and one diagonal is twice the length of the other, are 20 meters for the shorter diagonal and 40 meters for the longer diagonal.
Explanation:You asked how the lengths of the diagonals of a kite can be determined given that the area is 400 square meters and one diagonal is twice as long as the other. To find the diagonals, we'll use the formula for the area of a kite, which is Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals.
Let's denote the shorter diagonal as d, which means the longer diagonal is 2d. Plugging these into the area formula gives us:
400 m2 = (d * 2d) / 2
Multiplying both sides by 2 gives us 800 m2 = d * 2d, which simplifies to 800 m2 = 2d2.
Dividing both sides by 2 gives us 400 m2 = d2. Taking the square root of both sides, we find that d = 20 meters. Hence, the longer diagonal is 2 * 20 meters = 40 meters.
The lengths of the diagonals of the kite are 20 meters and 40 meters.
Can you help me please
Answer:
[tex]\large\boxed{A=(120+32\pi)cm^2}[/tex]
Step-by-step explanation:
Look at the picture.
We have the half of circle and a triangle.
The fromula of an area of a circle:
[tex]A_O=\pi r^2[/tex]
r - radius
We have r = 8cm. Substitute:
[tex]A_O=\pi(8)^2=64\pi\ cm^2[/tex]
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b- base
h - height
We have b = 8cm + 8cm = 16cm and h = 15cm. Substitute:
[tex]A_\triangle=\dfrac{(16)(15)}{2}=(8)(15)=120\ cm^2[/tex]
The area of the figure:
[tex]A=\dfrac{1}{2}A_O+A_\triangle[/tex]
Substitute:
[tex]A=\dfrac{1}{2}(64\pi)+120=32\pi+120=(120+32\pi)cm^2[/tex]
Jonael dropped a sandbag from a hot air balloon at a target that is 250 meters below the balloon. At this moment, the sandbag is 75meters below the balloon.
Which of the following expressions represent the distance between the sandbag and the target?
Choose 1 answer:
Answer:
175 I believe.
Step-by-step explanation:
The distance between the sandbag and the target is 325 meters.
Explanation:The distance between the sandbag and the target can be calculated by subtracting the distance of the sandbag from the balloon's height from the total distance between the balloon and the target. In this case, the balloon is 250 meters above the target and the sandbag is 75 meters below the balloon. So, the distance between the sandbag and the target is 250 + 75 = 325 meters.
Situation: A 22 gram sample of a substance that's used to sterilize surgical instruments has a k value of 0.138. n equals ne^-kt no=initial Mass( at time t=0) N= mass at time t k= a positive constant that depends on the substance itself and on the units used to measure time t= time, in days find the substances Half-Life, in days. Round your answer to the nearest tenth
The half-life of the substance is calculated using the decay constant and is found to be 5.0 days when rounded to the nearest tenth.
To find the half-life of a substance, we use the decay formula N = [tex]N0e^{-kt}[/tex], where N is the remaining mass at time t, N0 is the initial mass, k is the decay constant, and t is the time in days. For a substance to reach its half-life, the remaining mass (N) will be half of the initial mass (N0).
Let's substitute the known values to find the half-life:
Initial mass N0 = 22 g
The decay constant k = 0.138
Half of the initial mass would be 11 g, so N = 11 g
Using the formula for half-life:
0.693 / k = t1/2
Substitute k = 0.138 into the equation:
t1/2 = 0.693 / 0.138
Calculate the half-life:
t1/2 = 5.0 days
Thus, we round to the nearest tenth to get the half-life as 5.0 days.
a circular swimming pool has a circumference of 188.4 feet. if kelly swims across the pool. how far will she swim
Answer:
C.) 60 feet
Step-by-step explanation:
Knowing that the formula for finding the circumference of a circle is [tex]\pi d[/tex] or [tex]2\pi r[/tex], we are able to set up the equation to be:
[tex]188.4=3.14d[/tex]
[tex]\frac{188.4}{3.14} =d[/tex]
[tex]60=d[/tex]
and done! :)
Joe spends $1.75 every time he buys a snack with his lunch. He has $16.25 to spend. Write an inequality showing how many times (x) that Joe can buy a snack with his lunch.
Answer:
16.25=1.75x
Step-by-step explanation:
so write it like this to that the bigger number(16.25) is on the left then write the other number(1.75)then put the X by the 1.75
The lines given by the equations y = 6x and y = 6x + 2 are _____. A. parallel B. perpendicular C. neither perpendicular nor parallel
Answer:
A. Parallel
Step-by-step explanation:
The given lines are
[tex]y=6x[/tex]
and
[tex]y=6x+2[/tex]
The slope of [tex]y=6x[/tex] is [tex]m_1=6[/tex].
The slope of [tex]y=6x+2[/tex] is [tex]m_2=6[/tex].
Since the two lines have the same slope, the two lines are parallel.
Answer:
The correct answer option is A. parallel.
Step-by-step explanation:
We are given the following two lines and we are to determine if they are parallel, perpendicular or none of them:
[tex]y = 6x[/tex] and [tex]y = 6x + 2[/tex]
According to the standard equation of a line, [tex]y=mx+c[/tex], the coefficient of x ([tex]m[/tex]) is the slope of the line.
Slope of [tex]y = 6x[/tex] = 6
Slope of [tex]y = 6x + 2[/tex] = 6
Since both the lines have same slope, therefore the two line are parallel.
How many significant figures does the number 12 have
Answer:
It has 2.
Step-by-step explanation:
Since the numbers aren't zeroes they are automatically significant figures.
Answer:
2
Step-by-step explanation:
There are 2 digits needed to nail down the precise value of 12: a 1 in the tens place and a 2 in the ones place, giving it 2 significant figures.
For a few more examples, the number 1.23 would have 3 significant figures, the number 56.89 would have 4, and the number 1.00000 would have 1, as the trailing zeroes don't contribute anything to the number's actual value.
A sphere and a cylinder have the same radius and height. The volume of the cylinder is Amie found the volume of the sphere.
Answer:
The answer is the first
Amie should have multiplied 54 by 2/3
Step-by-step explanation:
* Lets start with the rule of the volume of each solid
∵ Volume the sphere = 4/3 π r³
∵ Volume the cylinder = π r² h
∵ The radii and the heights of the sphere and the cylinder are equal
∴ The ratio between there volumes are
4/3 π r³ : π r² h
- Lets divide each part by π r²
∴ 4/3 r : h
∵ The height of the sphere = the diameter of it = 2r
∴ The height of the cylinder = 2r
∴ The ratio will be:
4/3 r : 2r
- Now divide each part by 2r
∵ (4/3)r ÷ 2r = 2/3
∵ 2r ÷ 2r = 1
∴ The ratio is 2/3 : 1
∴ The volume of the sphere = 2/3 the volume of the cylinder
∵ The volume of the cylinder = 54 m³
∴ The volume of the sphere = 2/3 × 54 = 36 m³
∴ The answer is Amie should have multiplied 54 by 2/3
Answer:
The answer is Amie should have multiplied 54 by 2/3
Step-by-step explanation:
Help please 2 questions(25 points)
First one is C and second one is A
how do you solve this?
3x(x+4)=0
Answer:
3x=0 or x+4=0
x=0 or x=−4
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3x2+12x=0
Step 2: Factor left side of equation.
3x(x+4)=0
Step 3: Set factors equal to 0.
3x=0 or x+4=0
x=0 or x=−4
Billy has been to three more than four times as many baseball games as Brendan. Brendan has been to 11 baseball games. Complete the equation below to find out how many baseball games Billy has been to.
11 x __ + __ = __
Answer:11x4+3=47
Step-by-step explanation:
Answer:
47
Step-by-step explanation:
11 x 4 + 3 = 47
PLEASE HELP ASAPPP
Line d is parallel to line c in the figure below.
Which statements about the figure are true? Check all that apply.
Vertical angles prove that <2 = <5
In the two similar triangles, <1 and <4 are corresponding angles.
Vertical angles prove that <3=<6.
The triangles are similar because alternate interior angles are congruent.
In the two similar triangles, <2 and <4 are corresponding angles.
The triangles are similar because corresponding sides are congruent.
The correct answers are 2,3, and 4.
(if not 4, then the last one)
Answer:
C.Vertical angles prove that angle 3= angle 6
D.The triangles are similar because alternate interior angles are congruent.
Step-by-step explanation:
When line d is parallel to line c.
We have to find the true statements about the figure.
Then, [tex]\angle 3=\angle 6[/tex](Vertical angles are equal)
[tex]\angle 1=\angle 4[/tex]
[tex]\angle 2=\angle 5[/tex]
Reason: Alternate interior angles
Two triangles are similar by AA postulate
Reason:Alternate interior angle are congruent.
Option C and D are true.
C.Vertical angles prove that angle 3= angle 6
D.The triangles are similar because alternate interior angles are congruent.
x/2+3=-5 what does x equal?
x/2+3=-5
x/2 = -5+3
x/2 = -2
x = -2(2)
x = -4
Answer:
X = - 16
PLEASE RATE AND THANKS ME IF THIS HELPED
HELP ASAP! GIVING BRAINLIEST!!
∆ABC has A(-3, 6), B(2, 1), and C(9, 5) as its vertices. The length of side AB is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side BC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units. The length of side AC is
A) (50)^1/2
B) (65)^1/2
C) (105)^1/2
D) (145)^1/2
units.
∠ABC ≈ °
A) 55.21
B) 85.16
C) 105.26
D) 114.11
Answer:
AB is A
BC is B
AC is D
Step-by-step explanation:
To find the length of each side, use the formula for the distance between coordinate pairs.
We can find the distance using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (2,1) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(2--3)^2+(1-6)^2} \\d=\sqrt{(2+3)^2+(-5)^2} \\d=\sqrt{25+25}\\d=\sqrt{50}[/tex]
BC
We then substitute (2,1) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9-2)^2+(5-1)^2} \\d=\sqrt{(-7)^2+(4)^2} \\d=\sqrt{49+16}\\d=\sqrt{65}[/tex]
AC
We then substitute (-3,6) as [tex](x_1,y_1)[/tex] and (9,5) as [tex](x_2,y_2)[/tex].
[tex]d=\sqrt{(9--3)^2+(5-6)^2} \\d=\sqrt{(12)^2+(-1)^2} \\d=\sqrt{144+1}\\d=\sqrt{145}[/tex]
What is the distance from (−3, 1) to (−1, 5)? Round your answer to the nearest hundredth
Answer:
4.46Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have (-3, 1) and (-1, 5). Substitute:
[tex]d=\sqrt{(-1-(-3))^2+(5-1)^2}=\sqrt{2^2+4^2}=\sqrt{4+16}=\sqrt{20}\\\\=\sqrt{4\cdot5}=\sqrt4\cdot\sqrt5=2\sqrt5\approx2\cdot2.23=4.46[/tex]
Answer:
it 4.47
Step-by-step explanation:
I TOOK THE TEST
Solve for the roots in the equation below.
x4 + 3x2 - 4 = 0
Answer: x = {1, -1, 2i, -2i}
Step-by-step explanation:
x⁴ + 3x² - 4 = 0
∧
-1 +4 = 3 this works!
(x² - 1)(x² + 4) = 0
x² - 1 = 0 and x² + 4 = 0
x² = 1 and x² = -4
x = ±1 and x = ± 2i
x = 1, -1 and x = 2i, -2i
Need help don’t understand
Answer:
4 units left and 2 units up
Step-by-step explanation:
Translation notation is the words you would use to describe the translation of the point or shape. It says that the point was translated 4 units left and 2 units up, and that is the translation notation.
A princess hat for a costume is shaped like a cone. The base of the cone is 12 in across and the height is 8
in. The slant height of the outside edge, which is unknown, is the hypotenuse of the right triangle formed with
the radius and the height of the cone.
(a) Sketch the princess hat. Label the known lengths as described and label the unknown length as x.
(b) What is the slant height of the outside edge?
Answer:
Part a) The drawn in the attached figure
Part b)The slant height of the outside edge is [tex]x=10\ in[/tex]
Step-by-step explanation:
Part a) The drawn in the attached figure
Part b) What is the slant height of the outside edge?
we have that
The diameter of the base of the cone is 12 in
so
[tex]r=12/2=6\ in[/tex] ----> the radius is half the diameter
[tex]h=8\ in[/tex]
Applying the Pythagoras Theorem find the slant height x
[tex]x^{2}=r^{2}+h^{2}[/tex]
substitute the values
[tex]x^{2}=6^{2}+8^{2}[/tex]
[tex]x^{2}=100[/tex]
[tex]x=10\ in[/tex]
What is 8.79 rounded to the nearest hundredth
Answer:
8.79
Step-by-step explanation:
Rounding the nearest hundredth would be using the thousandths place to determine if the hundredths place must be rounded up or down. Because there is no visible thousandths place in 8.79, then it stays as 8.79. Because technically, there is an infinite number of zero's after the 9- and because 0 is less than 5, we leave the number as it is.
Read the following statement:
Line segment CD is congruent to line segment EF.
Which of the following is an equivalent statement?
EXPLANE HOW YOU GOT IT AND WHY
CD overbar similar to EF overbar
CD overbar equal to EF overbar
CD overbar element to EF overbar
CD overbar congruent to EF overbar
Here is your answer
d. CD overbar congruent to EF overbar.
REASON:
Since, line segment CD is congruent to line segment EF and im geometry an overbar represents a line segment.
So, we can say that CD overbar means line segment CD and EF overbar means line segment EF.
Hence, the statement is justified.
HOPE IT IS USEFUL
Here is your answer
d. CD overbar congruent to EF overbar.
REASON:
Since line segment CD is congruent to line segment EF and in geometry an overbar represents a line segment.
So, we can say that CD overbar means line segment CD and EF overbar means line segment EF.
Hence, the statement is justified.
hope this helps :)
remember to love urself <3
The graph of r = -9 cos theta has which of the following characteristics?
Answer:
A
Step-by-step explanation:
The center is at (-4.5,0) because -9/2 = -4.5
9 is the diameter in the above equation
Answer:
"circle; diameter of 9; center at (-4.5,0)"
Step-by-step explanation:
The polar equation of a circle centered on an axis, would take the forms:
1. Positive x-axis
r = (diameter) Cos θ
2. Positive y-axis
r = (diameter) Sin θ
3. Negative x-axis
r = - (diameter) Cos θ
4. Negative y-axis
r = - (diameter) Sin θ
As we see from the equation given, the diameter is 9 and it is centered n negative x-axis. And the center is Diameter divided by 2. So negative x axis has the center at (-9/2, 0) = (-4.5, 0)
The first choice is correct.
I need the answer please
Answer:
22 degrees
Step-by-step explanation:
Since both triangles correspond, side x is correspondent to 22 degrees, Since that is also the only given piece of information, that is your answer.
16 square meters is equivalent o how many square yards
Answer: 19.13 yd²
Step-by-step explanation:
1. By definition, you have that 1 square meter is equal to 1.19599 square yards. You can express it as following:
1 m²= 1.19599 yd²
2. Then, keeping the information above on mind, you can make the conversion from 16 m² to yd² as it is shown below:
[tex](16m^2)(\frac{1.19599yd^2}{1m^2})=19.13yd^2[/tex]
Therefore, you have that 16 m² is equivalent to 19.13 yd².
You can convert square meters to square yards by multiplying by 1.196. Therefore, 16 square meters is equivalent to 19.14 square yards.
Explanation:You're asking about the conversion between square meters and square yards, which is used in measuring areas in mathematics and geometry. To do this conversion, we can use the conversion factor given in the references - 1 m² = 1.196 square yards.
Therefore, to find out how many square yards are equivalent to 16 square meters, we multiply 16 m² by 1.196 (the number of square yards in one square meter). Doing this math gives us an equivalent area of 19.136 square yards.
So, your 16-square meter area is roughly equivalent to 19.14 square yards, when rounded to two decimal places.
Learn more about Area Conversion here:https://brainly.com/question/28977968
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Find the area of a 9-gon with apothem length 7. Round to a whole number.
Answer:
Step-by-step explanation:
This time we'll do this using 1 formula to get the answer.
Givens
n = 9 (number of sides in an 9-gon.
inradius (apothem) = a= 7
Formula
Area = a^2 * n * tan(180/n) Substitute
Solution
Area = 9^2 * 9 * tan(180/9) Combine
Area = 81 * 9 * tan(20)
Area = 729 * tan (20)
Area = 265.33
Area rounded = 265
Kesha has scored 85 92 84 71 and 94 on her previous five Tess what score did she just she need to receive an excess of the average or mean is 86
85+92+84+71+94+x /6>86
Multiply both sides by 6
426+x>516
Subtract 426 from both sides
X>90