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]
please find the area of the shaded region. EFGH is a square
Find the mean and the median of this data: 9, 6, 5, 3, 28, 6, 4, 7.
Answer: 9 is mean and median is 6
Step-by-step explanation:
If AB is translated right 5 units and down 2 units, what are the coordinates of A', the image of point A?
Answer:
(1,0)
PLEASE mark me brainliest!!
Answer:
1, 0
Step-by-step explanation:
Solve for xx. Round to the nearest tenth, if necessary.
sin U= |TS| / |US|
-> |US| = |TS| / sinU
-> x= 0.6 / sin 37°
-> x≈1,0
What is 20% of 60?
please and fanks
Answer:
heya! ^^
so the question demands us to calculate what is 20% of 60.
that's quite simple. so let's see how we gótta do this question.
[tex]\\\\ \fbox{20\% \: \: of \: \: 60} \\ \\ \dashrightarrow \: \frac{2\cancel0}{\cancel{100}} \times 6\cancel0 \\ \\ \dashrightarrow \: 2 \times 6 \\ \\ \dashrightarrow \: 12[/tex]
hope helpful :D
Answer:
12
▬▬How to▬▬Convert 20% to fraction.[tex]20[/tex]% ⇒ [tex]\frac{1}{5}[/tex]Flip [tex]\frac{1}{5}[/tex] to [tex]\frac{5}{1}[/tex][tex]\frac{5}{1}[/tex] also equals 5Add 5 and 1[tex]5 + 1 = 6[/tex][tex]6 * 2 = 12[/tex]Hence, the answer is 12
answer needed please
Answer:
the top answer should be stretched
What expression is equal to 6(2f + 2)
Answer:
[tex]\boxed{\sf{12f+12}}[/tex]Step-by-step explanation:
Use the distributive property.
Distributive property formula:
A(B+C)=AB+AC
6(2f + 2)
Multiply.
6*2f=12f
6*2=12
Rewrite the expression down.
12f+12
So, the final answer is 12f+12.I hope this helps! Let me know if you have any questions.
Answer:
12f + 12
Step-by-step explanation:
Step 1: Distribute
6(2f + 2)
(6 * 2f) + (6 * 2)
12f + 12
Answer: 12f + 12
F(x)=x^2. What is g(x)? point given (2,1)
A. g(x)= 4x^2
B. g(x)=1/4x^2
C. g(x)=(1/4x)^2
D. g(x)=1/2x^2
At x=2
f(2)=2²=4And
g(2)=1So the function is
g(x)=1/4f(x)g(x)=1/4x²The volume of a sphere is 2,000π m3. What is the surface area of the sphere to the nearest square meter?
Answer:
Volume of a sphere = 4/3 πr³
4/3 * 3.14 * r³ = 4000
4.19 * r³ = 4000
r³ = 4000 / 4.19
r = ∛1058
r = 10.19
Now, surface area = 4πr² = 4 * 3.14 * (10.19)²
S.A. = 12.56 * 104
S.A. = 1307
In short, Your Answer would be Option D) 1307 m²
Hope this helps!
Step-by-step explanation:
Provide the missing reasons for the proof.
Given: AB || RS
Prove: QA/QR = QB/QS
Answer:
1) given
2) reflexive property
3) corresponding angles theorem
4) AA similarity
5) Corresponding sides of similar triangles are proportional.
expand and simplify \5 (\10 +\2) ?
someone said the answer was 60, so i tried it and it didn’t work. can anyone help please?
Answer:
[tex]5\sqrt{2} +\sqrt{10}[/tex]
Step-by-step explanation:
[tex]\sqrt{5} (\sqrt{10} +\sqrt{2} ) < --Given[/tex]
[tex]\sqrt{5} \sqrt{10} +\sqrt{5} \sqrt{2} < -- Distribute[/tex]
An equation is in its simpliest form when you eliminate as many square roots as possible. Here are some rules:
1.) You cannot combine numbers through addition or subtraction if they are under square roots. However, you can combine numbers through multiplication or division if they are under square roots.
2.) You cannot take the square root of a number if the answer is not a whole number (unless the problem says you can). However, you can solve the square root if the number can be simplfied into a "rootable?" number. In other words, the number under a square root can be divided into a number that can have its square root taken.
The first part...
[tex]\sqrt{5} \sqrt{10} = \sqrt{5} * \sqrt{10} < --Multiply[/tex]
[tex]\sqrt{5} * \sqrt{10} =\sqrt{50}[/tex]
[tex]\sqrt{50} = \sqrt{25} *\sqrt{2} < --Separate[/tex]
[tex]\sqrt{25} = 5 < --Solve[/tex]
[tex]\sqrt{50} = 5 *\sqrt{2} < -- Substitute[/tex]
[tex]5*\sqrt{2} =5\sqrt{2} < --Rewrite[/tex]
The second part...
[tex]\sqrt{5} \sqrt{2} =\sqrt{5} * \sqrt{2} < -- Multiply[/tex]
[tex]\sqrt{5} *\sqrt{2} = \sqrt{10}[/tex]
Combine both parts...
[tex]5\sqrt{2} +\sqrt{10}[/tex]
Graph the solution to this inequality on the number line.
12x−3<−138
Answer:
Step-by-step explanation:
1. Solve
12x-3+3<-138+3 <=== Add three to both sides to simplify the inequality
12x÷12<-135÷12 <=== divide by 12 on both sides so we can find what x is so that we can graph the inequality
x<-11.25 <=== negative divided by positive is always negative
2. Graph
1) you find -11.25 on the number line
2) you put an ray with an empty/hollow circle facing towards the negative side
PLSSSS HELP <3
Which value of C represents a system with infinitely many solutions?
{6x+4y=14}
{9x+6y=C}
Answer: Option 2
Step-by-step explanation:
what are the answers?
Answer:
Step-by-step explanation:
hello : 12=4x and x-3=0
The area of a square garden is
1/144 km ^2 . How long is each side?
Answer:
[tex]\frac{1}{12}[/tex] Km
Step-by-step explanation:
the area (A) of a square is calculated as
A = s² ( s is the side length )
here A = [tex]\frac{1}{144}[/tex] , then
s² = [tex]\frac{1}{144}[/tex] ( take square root of both sides )
s = [tex]\sqrt{\frac{1}{144} }[/tex] = [tex]\frac{1}{\sqrt{144} }[/tex] = [tex]\frac{1}{12}[/tex]
Answer:
side= 1/12 km = 0.083km
Step-by-step explanation:
The formula of area of a square is: A=side²
To get the length of each side, square root each side of the formula as shown below:
√A=√(side)²
√(1/144)=side
side= √(1/144) = 1/12 = 0.083km
Abebi surveyed how many miles the students in her Algebra 1 class travel to get to school, and ended up with the following set of data: 4.75, 2.25, 3, 3.5, 1.75, 2.25, 1.5, 5, 4.5, 2.25, 2, 3, 2.65, 4.8, 3.5\
Match the measures of central tendency to the correct values.
Hint:
MEAN = Sum of the data/# of data values
MEDIAN = middle data value when values are listed least to greatest
MODE = value appearing the most times
RANGE = difference between the largest and smallest values
Answer:
Mean: 3.1
Median: 3
Mode: 2.25 appears 3 times
Range: 5 - 1.5 = 3.5
Mean = (4.75+2.25+3+3.5+1.75+2.25+1.5+5+4.5+2.25+2+3+2.65+4.8+3.5)/16
= 3.56625
Median = 3.50
Mode = 2.25
Range = 9.10
For each number set in this assignment, give the mean, median, mode, and range. If one of these quantities does not exist in the set, then put "0". 47, 31, 84, 50, 68, 85, 67, 56
Answer:
Mean: 54
Median: 61.5
Mode: 0
Range: 54
Step-by-step explanation:
Mean: Add everything up and divide by the amount of numbers
(47 + 31 + 84 + 50 + 68 + 85 + 67 + 56 = 488/8 = 54)
Median: Put all numbers in order from smallest to largest, the middle number is the median. Since we have 2 middle numbers, we add both 67 and 67 together, then divide them by 2.
31, 47, 50, 56, 67, 68, 84, 85
(56 + 67 = 123/2 = 61.5
Mode: The mode is the number that appears most often in the set of given numbers.
(There are no numbers that appear more than once so the mode is 0)
Range: The range is the largest number subtracted by the smallest number.
(85 - 31 = 54)
Which number line shows the solution set for Ip-31-97
-129
3
6 9 12
-12 -9
-6
-3
0
3
6
9 12
.
+
-12 -9
-6 3 0
+
9
12
o
3
-12 g 6
-3
0
12
Dersan went for a run to prepare for a long distance race coming up. From his house, he ran 6 miles directly north, and then 8 miles directly west. From there, he ran the diagnoal distance back to his house. How many total miles did Dersan run?
Answer:
24
Step-by-step explanation:
So, Dersan's path is a right triangle. You have to find the last side. You can use the triples or 6^2+8^2=c^2 but I'll use a triple.
3,4,5.
The last side is 10.
6+8+10=24
hope this helped!
Find the volume of the following. Show your work
Answer:
length * width * height = volume
10 * 2 * 5.5 = 110 cubed inches
using the similar triangles below, solve for x !
Answer:
Step-by-step explanation:
Remarks.
This can be solved as a proportion. A proportion is 2 ratios making a total of 4 parts. If we know 3 of the parts, we can solve for the 4th.
63/(8x - 2) = 49 /42
Notice that the given parts of the top triangle are the numerators of the ratios. The 2 parts of the bottom triangle are the denominators of the proportions
Proportion
63/(8x - 2) = 49 /42
Solution
63/(8x - 2) = 49 /42 Cross Multiply
(8x - 2)*49 = 63 * 42 Combine the right.
(8x - 2)*49 = 2646 Divide by 49
8x - 2 = 54 Add 2 to both sides
8x -2+2=54+2 Combine
8x = 56 Divide by 8
8x/8 = 56/8
Answer: x = 7
If the scores from an intelligence test are normally distributed, then you would predict that the largest number of people would receive an IQ score of _____ on that test.
Using the normal distribution, it is found that the prediction is that the largest number of people would receive an IQ score of 100 on that test.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.IQ scores have mean of 100, and since in the normal distribution most measures are around the mean, an IQ score of 100 is the prediction.
More can be learned about the normal distribution at https://brainly.com/question/24663213
This is the problem it’s on my screenshot
Answer:
(x = 0,y = 0),(x = 1, y = 4),(x= 2, y =8)
Step-by-step explanation:
the rule is to multiply x by 4.
when x = 0, y =4(0) = 0
when x = 1, y =4(1) = 4
when x = 2, y =4(2) = 8
Hope this helps!
Please mark as brainliest!
Tallulah's family took a road trip to the Grand Canyon. Tallulah slept for the last 129 miles of the trip. If the total length of the trip was 300 miles, what percentage of the total trip had they traveled when Tallulah fell asleep?
When Tallulah fell asleep, the family had already traveled 57% of the total trip.
A percentage is a way of expressing a number as a fraction of 100. It is often used to describe proportions, ratios, or rates. For example, if 20 out of 100 people in a room are wearing red shirts, we can say that 20% of the people are wearing red shirts.
If Tallulah slept for the last 129 miles of the trip, it means that the family had already traveled 300 - 129 = 171 miles before she fell asleep.
To calculate the percentage of the total trip that they had traveled when Tallulah fell asleep, we can use the following formula:
Percentage = (Part ÷ Whole) x 100
Where "Part" is the number of miles the family had traveled before Tallulah fell asleep (171 miles) and "Whole" is the total length of the trip (300 miles).
Percentage = (171 ÷ 300) x 100
Percentage = 0.57 x 100
Percentage = 57%
Therefore, when Tallulah fell asleep, the family had already traveled 57% of the total trip.
To know more about the Percentage visit:
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#SPJ1
7.a taxi travels with a constant speed
Answer:
Hi, not sure of what you're asking here?
Step-by-step explanation:
Try rephrasing it??
How do you write 950% as a fraction, mixed number, or whole number?
Carl is the owner of a shoe store and notices that his electricity bill has increased by 3%. Which of the expressions below represent a 3% increase?
1. a + 0.03a
2. a + 0.3a
3. 1.03a
4. 1.3a
expression 1 only
expression 2 only
expressions 1 and 3
expressions 2 and 4
Answer:
1 and 3
Step-by-step explanation:
Solve for x (literal equations)
C=b-bx
Answer:
X= (-c+b)÷b
or
X= -b×(c-b)
Step-by-step explanation:
C=b-bx
b-bx=c
-bx= c-b
-x=(c-b)÷b
x= -(c-b)÷b
or
-x= b×(c-b)
x= -b×(c-b)
plsss need help nowwww
Answer:
49/12
Step-by-step explanation:
1 ⅓ can be written as 1 + 1/3
1 ⅓
= 1 + 1/3
LCM = 3
= 3/3 + 1/3
= ( 3 + 1 )/3
= 4/3
2 ¾
= 2 + 3/4
LCM = 4
= 8/4 + 3/4
= ( 8 + 3 )/4
= 11/4
1 ⅓ + 2 ¾
= 4/3 + 11/4
LCM = 3 x 4 = 12
4/3 x 4/4
= ( 4 x 4 )/( 3 x 4 )
= 16/12
11/4
= 11/4 x 3/3
= ( 11 x 3 )/( 4 x 3 )
= 33/12
16/12 + 33/12
= ( 16 + 33 )/12
= 49/12
Answer:
I don’t know if it correct, but when I solved it I got 4 1/12
Step-by-step explanation:
(1+2) (1/3 + 3/4)
3 + 13/12
3 + 1 1/12
3 + 1 + 1/12
4 + 1 /12
4 1/12
What type of triangle is defined by the following set of side lengths
12, 8, 16
Question 3 options
Acute
Obtuse
Right
Not a triangle
The type of triangle defined by the following set of side lengths is an obtuse triangle
Properties of a triangle.Triangles are 2-dimensional shapes with 3 sides and angles.
The triangle with the sides 12, 8 and 16 is considered a triangle since the sum of two of its sides is greater than the third.
The triangle is not right angle since the sum of its longest side is not equal to the sum of the square of other two sides.
This shows that the triaangle can either be acute or obtuse. Since one of the sides differes from the other by 8 units, hence one of its angles will be greater than 90 degrees.
This shows that the type of triangle defined by the following set of side lengths is an obtuse triangle
Learn more on obtuse triangle here: https://brainly.com/question/5023725