Answer:
238
Step-by-step explanation:
Given equation: [tex]a^2+1=6a[/tex]
Rearrange so that it is equal to zero:
[tex]\implies a^2-6a+1=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Using the quadratic formula to solve the given equation:
[tex]\implies a=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\implies a=\dfrac{6 \pm \sqrt{32}}{2}[/tex]
[tex]\implies a=3 \pm 2\sqrt{2}[/tex]
[tex]\implies a^2=17 \pm 12\sqrt{2}[/tex]
Substituting this into [tex]7\left(a^2+\dfrac{1}{a^2}\right)[/tex]
[tex]\implies 7\left(17 \pm 12\sqrt{2}+\dfrac{1}{17 \pm 12\sqrt{2}}\right)[/tex]
For [tex]17+12\sqrt{2}[/tex]:
[tex]\implies 7\left(17+12\sqrt{2}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2}{17+12\sqrt{2}}+\dfrac{1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17+12\sqrt{2})^2+1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{289+408\sqrt{2}+288+1}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{578+408\sqrt{2}}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{34(17+12\sqrt{2})}{17+12\sqrt{2}}\right)[/tex]
[tex]\implies 7(34)[/tex]
[tex]\implies 238[/tex]
For [tex]17-12\sqrt{2}[/tex]:
[tex]\implies 7\left(17-12\sqrt{2}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2}{17-12\sqrt{2}}+\dfrac{1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{(17-12\sqrt{2})^2+1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{289-408\sqrt{2}+288+1}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{578-408\sqrt{2}}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7\left(\dfrac{34(17-12\sqrt{2})}{17-12\sqrt{2}}\right)[/tex]
[tex]\implies 7(34)[/tex]
[tex]\implies 238[/tex]
Times New Roman has tiny lines at the tips of letters, creating an appearance of old-style writing with a fountain pen. Those tiny lines are called _____.
Easy question! First one to answer gets brainliest!
2x + 5 = 21
[tex]2x + 5 = 21[/tex]
Subtract both sides 5
[tex]2x + 5 - 5 = 21 - 5[/tex]
[tex]2x = 16[/tex]
Divide both sides by 2
[tex] \frac{2x}{2} = \frac{16}{2} \\ [/tex]
[tex]x = 8[/tex]
Answer:
8
Step-by-step explanation:
To determine the value of "x", we need to isolate the "x" variable completely. The first step in isolating the variable is to remove the constant on the L.H.S. This can be done by subtracting 5 both sides.
⇒ [tex]2x + 5 = 21[/tex]
⇒ [tex]2x + 5 - 5 = 21 - 5[/tex]
⇒ [tex]2x = 16[/tex]
The last step in isolating the "x" variable is to isolate the cooeficient of x. This can be done by dividing the cooeficient of x both sides.
⇒ [tex]2x = 16[/tex]
[Cooeficient of x is 2]
⇒ [tex]\frac{2x}{2} = \frac{16}{2}[/tex]
⇒ [tex]x = \frac{16}{2} = 8[/tex]
In conclusion, the value of the "x" variable is 8.
find the surface area of each rectangular prism
will someone please help me?
Answer:
x=-1
Step-by-step explanation:
1.(-9-11)(-4)/-7^2+(11*2^2)
2. =-20/-4/-7^2+11(2^2)
3. =5/7^2+11(2^2)
4. =5/-49+11(2^2)
5. =5/-49+(11)(4)
6. = 5/-49+44
7.=5/-5
8. x=-1
Isaiah is jogging near his college. he runs south along capitol street for about 0.75 miles and east along h street for about 1.2 miles. he then turns left and runs along florida avenue until he reaches his starting point. how long is his total run to the nearest hundredth of a mile? a triangle. the sides are capitol street, h street, and they hypotenuse is florida avenue. 2.89 miles 3.37 miles 3.67 miles 3.92 miles
The total distance he travelled to the nearest hundredth of a mile is; B: 3.37 miles
How to work with Pythagoras Theorem?Let F represents his starting point.
Let C represent his position from where he went to east direction.
Let H represent his position from where he went to left towards Florida Avenue.
We are given that;
FC = 0.75 miles
CH = 1.2 miles
∠FCH = 90°(This can be deduced from the question)
By Pythagoras theorem, we have;
FH = √(0.75² + 1.2²)
FH = 1.42
Thus;
Total distance he covered = FC + CH + FH
Total distance covered = 0.75 + 1.2 + 1.42
Total distance covered = 3.37 miles
Read more about pythagoras theorem at; https://brainly.com/question/7324280
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How many electrons can there be in the 5s subshell.
s orbital mentioned
Note that for all n shells electrons per shell is fixed like for p it's 6 and for d it's 10
Hence 5s contains 2electronsRule for electron in nth shell=2n²
Calculate the down payment percent using the following information:
Purchase price: $281,700.00
Closing costs: 2.4% of purchase price
Total move-in costs: $57,466.80
18.0%
20.4%
21.0%
23.5%
18.0% which is the same as 18%
==========================================================
Work Shown:
p = purchase price = $281,700
c = closing costs
c = 2.4% of purchase price
c = 0.024p
c = 0.024*(281,700)
c = 6,760.80
d = unknown down payment amount
m = total move in costs = $57,466.80
m = d + c
d = m - c
d = 57,466.80 - 6,760.80
d = 50,706
down payment percent = d/p = (50,706)/(281,700) = 0.18 = 18%
18% of the purchase price is the down payment.
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
1 1/2 or 1.5
As a simplified fraction
If this helped pls give brainlest.
An event has probability of 3/4.
How would you best describe
the likehood of this event?
Answer:
more likely
Step-by-step explanation:
3/4 is 0.75 or 75%. I would describe it as likely.
elimination-
3/4 is not equal to 1 or 0.5 or 0. It is also not equal to 0.25
The total number of balls in a bag will be 4 in which 3 balls are red and 1 ball is blue.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The probability of the event is 3/4.
Let the total number of balls be 4 of two colors that are red and blue and the probability of red color be 3/4.
There will be a total of 4 balls in the bag, 3 of which will be red and 1 blue.
More about the probability link is given below.
https://brainly.com/question/795909
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Jill usually rides her bike at a speed of 10 miles per hour. Let x represent the hours and y represent miles. Write an equation that shows the relationship between x and y.
Answer:
y = 10x
Step-by-step explanation:
If x represents the hours & y represents the miles, your equation should be in multiplication.
10 miles an hour would be 10x and y would be the total. You can also plug in the answer to check. Let's say x is 2. Plug that into 10x and you get 10(2) = 20 and since y is 20, that'd be 20 miles. Therefore, you'd be running 20 miles in 2 hours, which makes sense because your rate is 10 miles an hour.
Transformation MATHS
anyone pls help me fond a solution to this ques
======================================================
Explanation:
Transformation V reflects over the line y = 0, which is the x axis. All points on the x axis have a y coordinate of zero. Examples are (1,0) and (2,0).
To reflect over the x axis, we flip the sign of the y coordinate. The x coordinate stays the same. Example: The point (1,5) moves to (1,-5).
In general the rule is [tex](x,y) \to (x,-y)[/tex]
---------------------
Transformation W rotates the point 90 degrees clockwise around the origin (0,0). The rotation rule is [tex](x,y) \to (y,-x)[/tex].
For example, the point (1,7) rotates to (7,-1) when doing a 90 degree clockwise rotation around the origin. We move from the northeast quadrant to the southeast quadrant.
As you can see, we swap the x and y coordinates. Then we do a sign flip on the new y coordinate.
----------------------
Transformation X combines the two previous transformations. We do V first then W next. The order is important (see the next section as to why).
We're given the point (g,h) where we don't know g nor h.
The x axis reflection rule has us get to (g, -h) because we simply flip the y coordinate from positive to negative, or vice versa.
Then applying transformation W has us get to (-h, -g) as the final answer.
----------------------
As stated earllier, the order of the transformations is important. Let's say we did W first and then V next.
Apply transformation W to go from (g,h) to (h,-g)Apply transformation V to go from (h,-g) to (h,g)The point (h,g) is different from (-h, -g) showing that the order does affect where the final point ends up.
However, some transformations can be composited together without worrying about the order. An example could be having a translation followed by another different translation.
What type of number is -4/2
Answer:
It is a negative rational number. This is because it is an improper fraction that is equivalent to -2.
Step-by-step explanation:
How do I graph h(x) = 4|x+4| +3
Answer:
Move the point on the diagonal to (1,4) then move the vertex 4 units left and 3 units upwards
Step-by-step explanation:
Please answer this it would be very helpful if you did.
Answer:
See below ↓↓↓
Step-by-step explanation:
Probability of getting heads
Outcome (head) = 1Total outcomes = 2P (head) = 1/2Probability of getting an odd number
Outcome (odd) = {1, 3, 5} = 3Total outcomes = 6P (odd) = 3/6 = 1/2The outcomes are equally likely because the probabiity of each outcome is the same.
The Green Bean Coffee Shop sells muffins for $2 each. So far today, they have sold 13 muffins. 1
Part A
Write an equation that represents the amount of money, A, they’ll make if they sell, m, additional muffins today. Answer:
M
Part B
Use the equation you wrote to determine how much money they’ll make if they sell an additional 22 muffins
Answer:
A) $ = 2m + 26
B) $70
Step-by-step explanation:
For a, I know they already sold 13 for $2, meaning they made $26. I know that for each muffin, they will make $2, meaning 2m + 26.
For b, you substitute 22 for m, and solve, getting $70.
solve fox x 8 = 3a - 4
For 7 points and brainliest to the best correct answer, find the missing measures. Question is in photo, thanks.
Answer:
X = 2
AB = 39
CB = 27
Step-by-step explanation:
Since it's a parallelogram (two pairs of parallel sides), we can set each opposite side equal to each other. We know the equation for two opposite sides, side AD and side CB, therefore:
[tex]AD=CB\\14x-1=9x+9\\5x=10\\x=2[/tex]
Now that we know x, we can solve the other equations:
[tex]12x+15=AB\\12*2+15=AB\\24+15=AB\\39=AB[/tex]
And:
[tex]9*2+9=CB\\18+9=CB\\27=CB[/tex]
i cant figure this problem can you guys help/
Answer:
r = 6.998 in
D = 13.996 in
C = 43.9697 in
Step-by-step explanation:
Area = π[tex]r^2[/tex]
153.86 = π[tex]r^2[/tex]
153.86/π = [tex]r^2[/tex]
sq root(153.86/π) = r ≈ 6.998 in
Diameter = 2r
D = 2(6.998) = 13.996 in
Circumference = 2πr
C = 2π(6.998)
C = 13.996π ≈ 43.9697 in
Hope this helps!
Find the length of the midline KH in Trapezoid SQUAD.
[tex] \sf\red{the \: length \: of \: the \: middle \: kh \: is \: \frac{a \: + \: b}{2} units}[/tex]
use the midpoint formula to find the coordinates of points K and H[tex]\begin{gathered}{\boxed{\begin{array}{cccc} \sf{For \: point \: K} & \\ & \sf \\ \sf{Q( 0, 0 )\: U( c, d )}\\ \tiny \times = \times \frac{ \times 1 \: + y \: 2}{2} \: \: y = \frac{y \: 1 + y \: 2}{2} \\ \tiny{ \times = \frac{0 \: + \: c}{2} \: y = \frac{0 \: + \: d}{2} } \\ \tiny{ \times = \frac{c}{2} \: \: \: y = \frac{d}{2} } \\ \tiny \red{the \: coordinates \: of \: point \: K \: are \: ( \frac{c}{2} . \frac{d}{2} )} \end{array}}}\end{gathered} [/tex]
[tex]\begin{gathered}{\boxed{\begin{array}{cccc} \sf{For \: point \: H} \\ \\ \tiny{b),d] D(a,0)} \\ \tiny \times = \frac{ \times 1 \times 2}{2} \: \: y = \frac{y \: 1 + y \: 2}{2} & \\ \tiny{ \times = \frac{a + (c + b)}{2} \: \: y = \frac{0 + d}{2} } &\\ \tiny{ \times = \frac{a + b + c}{2} \: \: \: y = \frac{d}{2} } \\ \tiny\red{ The\: coordinates\: of\: point \:H\: are ( \frac{a + b + c}{2} , \frac{d}{2} ) }\end{array}}}\end{gathered} [/tex]
b. use the distance for mula to find the length of KH[tex] \sf \: k( \frac{c}{2} . \frac{d}{2} ) \: \: \: h( \frac{a + b + c}{2} . \frac{d}{2} )[/tex]
[tex] \sf \: d = \sqrt{(x2 - \times 1) {}^{2} + (y2 - y1) {}^{2} } [/tex]
[tex] \sf \: kh = \sqrt{ \frac{[a \: + \: b \: + \: c}{2} - \frac{c}{2} {}^{2} + ( \frac{d}{2} - \frac{d}{2}) ^{2} } [/tex]
[tex] \sf \: kh = \sqrt{ (\frac{a + b}{2}) {}^{2} + (0) {}^{2} } [/tex]
[tex] \sf \: kh = \sqrt{( \frac{a + b}{2}) {}^{2} } [/tex]
[tex] \sf \: kh = \frac{a + b}{2} [/tex]
Final Answer[tex] \sf\red{the \: length \: of \: the \: middle \: kh \: is \: \frac{a \: + \: b}{2} units}[/tex]
Please Solve I will give brainliest.
each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. find the range and domain of the relation.
Using the domain and range concepts, it is found that:
For the first relation, the domain is [tex]-1 \leq x < 1[/tex], and the range is [tex]-1 \leq y \leq 0[/tex].For the second relation, the domain is [tex]-1 \leq x \leq 1[/tex], and the range is [tex]-1 \leq y \leq 1[/tex].What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence:
For the first relation, the domain is [tex]-1 \leq x < 1[/tex], and the range is [tex]-1 \leq y \leq 0[/tex]. The open circle at x = 1 means that x = 1 is not part of the domain, hence we have an open interval.For the second relation, the domain is [tex]-1 \leq x \leq 1[/tex], and the range is [tex]-1 \leq y \leq 1[/tex].More can be learned about domain and range concepts at https://brainly.com/question/27566140
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chen and megan each have a set of numbered counters chen has= 1 2 3 4 megan has= 1 2 3 4 5 they each take thier own counters without looking chen says im more likley to get a 4 is he correct? explain your answer
Answer:
Yes, Chen is correct.
Step-by-step explanation:
Chen has 1/4 chance of getting a 4, whereas Megan has 1/5 chance of getting a 4.
1/4 = 0.25
1/5 = 0.20
Therefore, Chen is correct.
(3+√3) x (2+√2) gr 9 maths sum from number system ans fast pls
(3+√3) x (2+√2)
6 + 3√2 + 2√3 + √3√2
6 + 3√2 + 2√3 + √6
Answer:
6 + 2√3 + 3√2 + √6
Step-by-step explanation:
The equation :
(3 + √3)(2 + √2)
Using Distributive Property,
3(2) + √3(2) + 3(√2) + (√3)(√2)6 + 2√3 + 3√2 + √67. What is the area of the white border?
8 cm
2 cm
9 cm
15 cm
What is the area of the white border
Answer:
119 cm^2
Step-by-step explanation:
To find the area of the white border, simply find the area of the outside rectangle and subtract the middle(dark) rectangle's area from that value.
White rectangle: 15x9 = 135
Dark rectangle: 8x2 = 16
135 - 16 = 119 cm^2
The unit is squared when finding the area of a two dimensional figure.
Lilit and Sergio sold candles for a class trip. On the first day, Lilit sold 8 candles and Sergio sold 10 candles. For the next three days, both sold another 3 candles each day.PLEASE HELP
Answer:
Lilit- 17 candles
Sergio- 19 candles
Step-by-step explanation:
this is the most probable answer.
What is the area of this triangle?
1375 ft
1500ft
3300ft
4500ft
Answer:
probably 20 man think about it
Step-by-step explanation:
Find X and y in the triangle.
Answer:
Step-by-step explanation:
Write an equation for a line that contains the point (0,4) that is parallel to the
equation below.
y= -7x+1
Step 1: Find the Slope
Parallel lines have the same slope, therefore the slope of our new line is also -7.
Step 2: Find the Y-Intercept
Once we have the slope and a point on the line, we can solve for the y-intercept. Plug in the slope and the given point into slope-intercept form and solve for b.
Slope-Intercept Form: y = mx + b
Slope = -7
Point = (0, 4)
4 = -7(0) + b
b = 4
Step 3: Form the Equation of the Line
Now that we have both the slope and the y-intercept of the new line, all that's left to do is plug those values into slope-intercept form.
Slope-Intercept Form: y = mx + b
m = -7
b = 4
Equation of the New Line: y = -7x + 4
Answer: y = -7x + 4
Hope this helps!
Answer:
y = -7x + 4
Step-by-step explanation:
Given
point = (0, 4)parallel to y = -7x + 1Solving
Slope of new line is also -7y - 4 = -7(x - 0)y - 4 = -7xy = -7x + 4What is the area of parallelogram rstu? 21 square units 24 square units 28 square units 32 square units
The area of the considered parallelogram RTSU is given by: Option A: 21 sq. units
How to find the area of a parallelogram?Area of a parallelogram = (its height × its base) sq. units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance(length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units[/tex]
For this case, the missing diagram is attached below.
If we take the base as ST then as ST is parallel to y axis, the line perpendicular to ST would be parallel to x axis. The heigth of a parallogram is the perpendicular distance between its base and top.
The base is ST and top is RU, the line segment US is perpendicular to both RU and US and its length,therefore, will serve as height as its length=perpendicular distance between the base and the top of the parallelogram.
Thus, we get:
Area of RTSU = Length of ST × Length of US
The coordinates of endpoints of ST are (4,-1), (4,-4)
Thus, the length of ST = distance between S and T = [tex]\sqrt{(4-4)^2 + (-1 - (-4))^2 }= 3[/tex]
The coordinates of endpoints of US are (-3,-1), (4,-1)
Thus, the length of US = distance between U and S = [tex]\sqrt{(-3-4)^2 + (-1 - (-1))^2 }= 7[/tex]
Thus, Area of RTSU = Length of ST × Length of US = 3 × 7 = 21 sq. units.
Thus, the area of the considered parallelogram RTSU is given by: Option A: 21 sq. units
Learn more about distance between two points here:
brainly.com/question/16410393
Answer:
21 square units I think
Step-by-step explanation:
The cost to rent a condominium at the beach is $1,500 per week. If two people share the cost, they each have to pay $750. Explain why the relationship between the cost per person varies inversely with the number of persons sharing the cost. Then write an inverse variation function that can be used to calculate the cost per person, c, of p persons sharing the rental fee.
Answer:
1. The relationship between the cost per person and the amount of persons sharing the cost is an inverse relationship because as the number of persons sharing the cost increases the cost per person decreases.
2. c = 1500 / p
Step-by-step explanation:
1. Lets look at the cost comparison per number of tenants.
1 person = $1500 per person
2 people = $750 per person
3 people = $500 per person
As you see, as the number of people increase, the cost per person decreases.
2. If you are splitting the cost, then you are dividing equally.
The rent is divided between the number of people
1500 / p
c = 1500 / p
Answer:
1. The relationship between the cost per person and the amount of persons sharing the cost is an inverse relationship because as the number of persons sharing the cost increases the cost per person decreases.
2. c = 1500 / p
Step-by-step explanation:
1. Lets look at the cost comparison per number of tenants.
1 person = $1500 per person
2 people = $750 per person
3 people = $500 per person
As you see, as the number of people increase, the cost per person decreases.
2. If you are splitting the cost, then you are dividing equally.
The rent is divided between the number of people
1500 / p
c = 1500 / p
Which fraction below represents a repeating decimal?
Answer:
22/12
Step-by-step explanation:
