Answer:
x₁ = 4 - √5 ; x₂ = 4 + √5Step-by-step explanation:
[tex]x^2-8x+16=5\\\\x^2-8x+11=0\\\\a=1\,,\ \ b=-8\,,\ \ c=11\\\\x_1=\dfrac{-(-8)-\sqrt{(-8)^2-4\cdot1\cdot11}}{2\cdot1}=\dfrac{8-\sqrt{20}}2=\dfrac{8-2\sqrt5}2=\dfrac{2(4-\sqrt5)}2=\\\\=4-\sqrt5\\\\x_2=\dfrac{-(-8)-\sqrt{(-8)^2-4\cdot1\cdot11}}{2\cdot1}=\dfrac{8+2\sqrt5}2=4+\sqrt5[/tex]
can you please help me with this one??? i need clear explanation
Answer:
£228.
Step-by-step explanation:
We know that each tile is 20 cm by 20 cm, which works out to be an area of 400 square cm.
The floor is 3 m by 5 m, which means it is 300 cm by 500 cm. 300 * 500 = 150000 square cm in area.
To find how many tiles are necessary, we need to find out the area of the floor divided by the area of the individual tiles.
150,000 / 400 = 1,500 / 4 = 750 / 2 = 375
So, to cover the floor, you will need 375 tiles.
Since tiles come in boxes of 10, you will need to find what is 375 divided by 10 so you can know how many boxes to buy.
375 / 10 = 37.5
Since you absolutely NEED 375 tiles to cover the floor, you need that half of a box, so you will buy 38 boxes of tiles.
Each box costs £6. 38 * £6 = £228. And that is your total cost!
Hope this helps!
The solution for the following system of linear equation 3m-2n=13 is (2,-1) true or false
Answer:
Not True
Step-by-step explanation:
>_<
[tex]\text{To find your answer, plug in the values to the equation and solve:}\\\\3(2)-2(-1)=13\\\\\text{Solve:}\\\\3(2)-2(-1)=13\\\\6+2=13\\\\8=13\\\\\text{8 does not equal 13, therefore making the equation FALSE}\\\\\boxed{\text{False}}[/tex]
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Penelope has $1,459.75 in her bank account. To pay her bills, she writes 4 checks in the amounts of $200.25, $359.45, $125, and $299.35. Then she deposits $375 into her account. Penelope’s account balance after she pays her bills and makes the deposit is $ .
Answer:
$850.7
Step-by-step explanation:
Penelope has $1459.75 in her account.
She pays different amount that are given above.
i.e.
=1459.75-200.25-359.45-125-299.35
=475.7
Then she deposit $375
Now,
=475.7+375
=850.7
So, She has $850.7 in her account after she pays her bills and makes deposits.
Answer:
$805.7 OwO
Step-by-step explanation:
Which of the following linear equations passes through points (-1, 5) and (1, -5)? y = -5x y = 5x + 10 y = -2x + 3 None of these choices are correct.
Answer:
y = -5x
Step-by-step explanation:
Which of the following linear equations passes through points (-1, 5) and (1, -5)?
y = -5x
y = 5x + 10
y = -2x + 3
None of these choices are correct.
Solution:
First find slope of equation:
slope, m = (y2-y1) / (x2-x1) = (5-(-5) / (-1-1) = 10/(-2) = -5
Now substitute m in the point slope form to find the y-intercept b
y-y1 = m(x-x1)
y-5 = 5(x- -1)
y = -5(x+1) + 5
y = -5x
Use the function below to find Fl-2).
F(x) = 3x
Help Please again ;-;
Answer:
Graph 1 shows a negative correlation, and graph 2 shows a positive correlation. This is because in graph one, as x increases, y decreases, and in graph two as x increases, y also increases.
During Thanksgiving, Anna worked 9 and 1/2 hours each day. She earned an hourly wage of $16. If she works all weekdays, how much did she earn in ONE WEEK? Solve the problem. You MUST explain your reasoning.
Answer:760$ in a week because they worked 5 out of 7 days and made 152$ a day
Step-by-step explanation:
9.5 x 16 = $152
152 x 5 (only weekdays)
<!> Branliest is appreciated! <!>
help on system of equations using substitution
Answer:
The answer is option C.
The answer is option
Step-by-step explanation:
5x + 2y = - 15 ......... 1
x - 4y = - 3 ........ 2
Make x the subject in the second equation and substitute it into the first equation
That's
x = 4y - 3
5(4y - 3) + 2y = - 15
20y - 15 + 2y = - 15
22y = - 15 + 15
22y = 0
Divide both sides by 22
y = 0
Substitute y = 0 into x = 4y - 3
That's
x = 4(0) - 3
x = - 3
x = - 3 y = 0
( - 3 , 0)Hope this helps you
Which of these systems of linear equations has no solution?
2 x + 8 y = 15. 4 x + 16 y = 30.
2 x minus y = 18. 4 x + 2 y = 38.
4 x + 7 y = 17. 8 x minus 14 y = 36.
4 x minus 3 y = 16. 8 x minus 6 y = 34.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution
Step-by-step explanation:
Examine the system
2 x + 8 y = 15
4 x + 16 y = 30
We see that these equations are identical except for a factor of 2, and thus recognize that this system has infinitely many solutions.
Next, look at the system
2 x minus y = 18
4 x + 2 y = 38
If we divide the second equation by 2, we get the system
2x - y = 18
2x + y = 19
Combining these two equations, we get 4x = 37, which has a solution.
Third, analyze the system
4 x + 7 y = 17 => 8x + 14y = 34
8 x minus 14 y = 36 => 8x - 14y = 36, or 16x = 70, which has a solution
Finally, analyze the system
4 x minus 3 y = 16 => -8x + 6y = -32
8 x minus 6 y = 34 => 8x - 6y = 34
If we combine these two equations, we get 0 + 0 = 2, which is, of course, impossible. This system has no solution.
Answer:
4 x minus 3 y = 16. 8 x minus 6 y = 34 has no solution. the 4th option.
Step-by-step explanation:
John couldn't recall the Serial number on his expensive bicycle. He remembered that
there were 6 different digits, none used more than once, but couldn't remember what
digits were used. He decided to write down all of the possible 6 digit numbers from 0 to 9. How many different possibilities will he have to create?
Answer:
151,200
Step-by-step explanation:
The possible set of numbers will be 151200
What is permutation?A permutation is an arrangement of objects in a definite order.
Given that, John want to find his bicycle's number, so he decided to write down all the possible 6-digit numbers from 0 to 9.
Here, we will use permutation to find the possible numbers,
Formula =
ⁿPₓ = n! / (n-x)!
Therefore,
¹⁰P₆ = 10! / (10-6)!
= 10! / 4!
= 10 × 9 × 8 × 7 × 6 × 5 = 151200
Hence, the possible set of numbers will be 151200
Learn more about permutation, click;
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The perimeter of a rectangular field that measures 2 feet by 18 inches is _________ ft. A. 40 B. 7 C. 84 D. 6
Answer:
B. 7
Step-by-step explanation:
What’s the answer for it
Step-by-step explanation:
I am giving you to solve the new price of Book.
[tex]new \: price \: = 13 - 29\% \: of \: 13 \\ = 13 - 0.29 \times 13 \\ = 13 - 3.77 \\ = \pounds 9.23[/tex]
Follow the same suite to find the new costs of remaining items.
in the function y+3=(1/3x)^2, what effect does the number 1/3 have on the graph, as compared to the graph of y=x^2
Answer:
I think the answer is it stretches the graph horizontally by a factor of 3.
Step-by-step explanation:
Answer: it stretches the graph horizontally by a factor of 3
Step-by-step explanation: I got it correct on a-pex
definition and example of variable
Answer:
Step-by-step explanation:
Definition: A letter that is placed in an unknown number place.
Example: 8+B+9
The variable would be B.
Answer:
a varible is a unknown quanity that is represented by a letter for example 'x ' is an variable
Step-by-step explanation
two cars are traveling down the highway with the same speed if the first car increases its speed by 1km/hr and the other car decreases its speed by 10km/hr,then the first car will cover the same distance in 2hrs as the second car in 3 hrs, what is the speed of the cars
Answer:
Their speed is 32 km/h.
Step-by-step explanation:
Since they're at the same speed, we can assign a variable to their speed called "x". When the first car increases its speed by 1 km/h, its new speed is "x + 1", while the other car decreases its speed by 10 km/h, so its new speed is "x - 10". The distance's formula can be expressed as below:
[tex]\text{distance} = \text{speed}*\text{time}\\[/tex]
With the modifications to their speed, the distance the first car covers in 2 h and the distance the second car covers in 3 h is shown below:
[tex]\text{distance}_{car1} = (x + 1)*2 \\\text{distance}_{car1} = 2*x + 2[/tex]
[tex]\text{distance}_{car2} = \text{speed}*\text{time}\\\text{distance}_{car2} = (x - 10)*3\\\text{distance}_{car2} = 3*x - 30[/tex]
Since the distance covered by them must be the same, we can find the value of x that makes the expressions equal.
[tex]2*x + 2 = 3*x - 30\\2*x - 3*x = -30 -2\\-x = -32\\x = 32[/tex]
Their speed is 32 km/h.
Simplify the expression
4P2
A 12
B 2
C 4
D 24
Answer:
12
Step-by-step explanation:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
So in your case, n = 4 and r = 2.
n! = 4! = 4*3*2*1
(n-r)! = (4-2)! = 2! = 2*1
So....
[tex]\frac{4*3*2*1}{2*1}=\frac{24}{2}=12[/tex]
Please help me, tysm if you do :)
The length of a rectangle is 2 cm less than three times the width. The perimeter of the rectangle is 92 cm. Find the dimensions of the rectangle. A. 11, 31 cm
B. 12, 34 cm
C. 12, 38 cm
D. 13, 37 cm
Answer:
B.12.32
Step-by-step explanation:
Let y be the widht of this triangle and x the length of itFrom the first information we can write :
3y-x=2
from the second one :
2y+2x= 92
so our equation are :
3y-x=22y+2x= 92Multiply the first one by 2 then add it to the second one to get rid of x :
6y-2x= 42y+2x+6y-2x= 92+4 8y = 96 y= 12 replace y by 12 to calculate the value of x x= 34The human resources manager at a company records the length, in hours, of one shift at work, X. He creates the
probability distribution below. What is the probability that a worker chosen at random works at least 8 hours?
Probability Distribution
0.7
0.5
0.5
03
0.2
0.1
0
9 hours
10 hours
8 hours
6 hours
7 hours
Х
Answer:
.84
Step-by-step explanation:
The probability that a worker chosen at random works at least 8 hours is 0.84.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
From the given graph,
Probability of 6 hours = 0.02
Probability of 7 hours = 0.11
Probability of 8 hours = 0.61
Probability of 9 hours = 0.15
Probability of 10 hours = 0.08
The probability of at least 8 hours can be obtained as illustrated below:
P(At least 8 hours) = P(8) + P(9) + P(10)
P(At least 8 hours) = 0.61 + 0.15 + 0.08
P(At least 8 hours) = 0.84
Therefore, the probability that a worker chosen at random works at least 8 hours is 0.84.
To learn more about the probability visit:
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There are ten people in the Baking Club, including Mark. They choose $3$ people to form an executive committee. How many possible committees can be formed that do not include Mark?
Answer:
504 committees
Step-by-step explanation:
In this scenario, there are 9 choices to choose the first person (not 10 because the committee should not include Mark), 8 choices for the second person and 7 choices for the last person so the answer is 9 * 8 * 7 = 504.
I need help with this question please help
Answer:
6, 10, 8 is the correct answer.
Step-by-step explanation:
Given that, the recursive function:
[tex]a_n=a_{n-1}-(a_{n-2}-4)[/tex]
6th term, [tex]a_{6} =0[/tex]
5th term, [tex]a_{5} =-2[/tex]
To find:
First three terms of the sequence = ?
Solution:
Putting n = 6 in the recursive function:
[tex]a_6=a_{5}-(a_{4}-4)\\\Rightarrow 0=-2-(a_{4}-4)\\\Rightarrow 2=-(a_{4}-4)\\\Rightarrow -2=(a_{4}-4)\\\Rightarrow -2+4=a_{4}\\\Rightarrow a_{4}=2[/tex]
Putting n = 5 in the recursive function:
[tex]a_5=a_{4}-(a_{3}-4)\\\Rightarrow -2=2-(a_{3}-4)\\\Rightarrow -2-2=-(a_{3}-4)\\\Rightarrow 4=(a_{3}-4)\\\Rightarrow a_{3}=8[/tex]
Putting n = 4 in the recursive function:
[tex]a_4=a_{3}-(a_{2}-4)\\\Rightarrow 2=8-(a_{2}-4)\\\Rightarrow 2-8=-(a_{2}-4)\\\Rightarrow 6=(a_{2}-4)\\\Rightarrow a_{2}=10[/tex]
Putting n = 3 in the recursive function:
[tex]a_3=a_{2}-(a_{1}-4)\\\Rightarrow 8=10-(a_{1}-4)\\\Rightarrow 8-10=-(a_{1}-4)\\\Rightarrow -2=-(a_{1}-4)\\\Rightarrow 2=a_{1}-4\\\Rightarrow a_{1}=4+2\\\Rightarrow a_{1}=6[/tex]
So, first, second and third terms are 6, 10, 8.
PLEASE HELP ME WITH THIS
X is equal to 28
Hope this helps......
Can someone please help me I really need help please help me
Answer:
18.87 square cm.
Step-by-step explanation:
The area of the rectangle will be (4 + 4) * 4, since the length of the rectangle would be the diameter of the circle, and the width of the rectangle would be the radius. (4 + 4) * 4 = 8 * 4 = 32 square cm.
Then, we can calculate the area of the semicircle. The area of a circle is pi * r^2, so the area of a semicircle will be half of that. pi * (4^2) / 2 = pi * 16 / 2 = 8pi. 8 * 3.14159265 = 25.1327412 square cm.
The shaded area of the middle of the shape will then be 32 - 25.1327412 = 6.8672588 square cm.
The two triangles will have the same area. Their bases will be 14 minus the diameter of the circle, then divide that by 2 to get each separate base. 14 - 8 = 6 / 2 = 3. The heights of the triangles will be the radius of the circle, or 4 cm.
1/2 * 3 * 4 = 1/2 * 12 = 12/2 = 6. That is the area of one triangle, so the area of both triangles would be 6 * 2 = 12 square cm.
6.8672588 + 12 = 18.8672588, or 18.87 square cm.
Hope this helps!
Answer:
(44 - 8(pi)) cm^2 Exact area
18,9 cm^2 Approximate area
Step-by-step explanation:
The shaded area is the area of the trapezoid minus the area of the semicircle.
area of trapezoid = (b1 + b2)h/2
area of semicircle = (pi)(r^2)/2
The triangles at both sides are right triangles. Each of the horizontal legs has length (14 cm - 8 cm)/2 = 3 cm. Each of the vertical legs is congruent to the radius of the semicircle.
b1 = lower base = 14 cm
b2 = upper base = 14 cm - 3 cm - 3 cm = 8 cm
shaded area = (b1 + b2)h/2 - (pi)(r^2)/2
= (14 cm + 8 cm)(4 cm)/2 - (pi)(4 cm)^2 / 2
= 44 cm^2 - 8(pi) cm^2
= (44 - 8(pi)) cm^2 Exact area
= 18.9 cm^2 Approximate area
Round $535 998 to the nearest HUNDRED
Answer: 536,000
Step-by-step explanation:
Answer:
536 000
Step-by-step explanation:
because it izz what it izz
Solve -27p²q²+6p³-2p⁴-q³
Answer:
-27p^2 q^2 +6p^3 -2p^4 -q^3
Step-by-step explanation:
COMBINE LIKE TERMS
y = 5x + 2 3x = –y + 10 What is the solution to the system of equations
Answer:
x = 1 , y = 7
Step-by-step explanation:
Solve the following system:
{y = 5 x + 2 | (equation 1)
3 x = 10 - y | (equation 2)
Express the system in standard form:
{-(5 x) + y = 2 | (equation 1)
3 x + y = 10 | (equation 2)
Add 3/5 × (equation 1) to equation 2:
{-(5 x) + y = 2 | (equation 1)
0 x+(8 y)/5 = 56/5 | (equation 2)
Multiply equation 2 by 5/8:
{-(5 x) + y = 2 | (equation 1)
0 x+y = 7 | (equation 2)
Subtract equation 2 from equation 1:
{-(5 x)+0 y = -5 | (equation 1)
0 x+y = 7 | (equation 2)
Divide equation 1 by -5:
{x+0 y = 1 | (equation 1)
0 x+y = 7 | (equation 2)
Collect results:
Answer: {x = 1 , y = 7
Answer:
D) (1,7)
Step-by-step explanation:
just took the test
If the radius of a coin is 1cm than calculate its area
Answer:
3.14 square cm
Step-by-step explanation:
Since, a coin is circular in shape, hence its area would be equal to the area of a circle.
[tex]\therefore are \: of \: coin = \pi {r}^{2} \\ = 3.14 \times {1}^{2} \\ = 3.14 \times 1 \\ = 3.14 \: {cm}^{2} \\ [/tex]
44. The length of a road is 380 m, correct to the nearest 10 m. Maria runs along this road at an average
speed of 3.9 m/s. This speed is correct to 1 decimal place. Calculate the greatest possible time taken by Maria
Answer:
Time = distance/speed
max distance = 380+10 = 390 m
Max Time = 390/3.9 = 100 s
David recycles 5 cans every week. Which expression shows the total number of cans he recycles in w weeks?
5w
w over 5
5 + w
5 + 5w
Answer:
A - 5w
Step-by-step explanation:
I don't know how to explain it
TOP GUY MADE A VERY FUNNY JOKE LOL
Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports X, the claim amount divided by 1000. Actuary B reports Y, which is X rounded to the nearest integer from 0 to 10.Calculate the absolute value of the difference
This is not the complete question, the complete question is:
Automobile claim amounts are modeled by a uniform distribution on the interval [0, 10,000]. Actuary A reports X, the claim amount divided by 1000. Actuary B reports Y, which is X rounded to the nearest integer from 0 to 10.Calculate the absolute value of the difference between the 4th moment of X and the 4th moment of Y
A) 0
B) 33
C) 296
D) 303
E) 533
Answer: B) 33
Step-by-step explanation:
First lets say;
z: automobile claim amounts
x: the claim amount dived by 1000
y: x rounded to the nearest integer from 0 to 10
z ≅ V[0, 10,000]
x = z / 1000 ≅ V[0, 10 ] ⇒ Fx { 1/10, 0 ≤ x ≤ 10} 0, 0/10
y = {0, 0 ≤ x < 0.5
1, 0.5 ≤ x < 1.5
2, 1.5 ≤ x < 2.5
3, 2.5 ≤ x < 3.5
↓
9, 8.5 ≤ x < 9.5
10, 9.5 ≤ x < 10
SO 4th moment of x = E(x²) = ∫₀¹⁰x⁴ 1/10 dₓ
= 1/10 (x⁵ / 5)₀¹⁰
= 10⁵ / (10 * 5)
= 100000/50
= 2000
Now
4th moment of y = E(y⁴) = ∑/y y⁴ p( y=y)
= 0⁴p( y=0) + 1⁴p( y=1 ) + 2⁴p( y=2) + → + 10⁴p( y=10)
= 0 + 1⁴.p( 0.5 ≤ x < 1.5) + 2⁴.p( 1.5 ≤ x < 2.5) + 3⁴.p( 2.5 ≤ x < 3.5 ) + → + 10⁴.p( 9.5 ≤ x < 10 )
= 1/10 [ 1⁴(1.5 - 0.5) + 2⁴(2.5 - 1.5) + → + 9⁴(9.5 - 8.5) + 10⁴(10 - 9.5)]
= 1/10 [ 1⁴ + 2⁴ + → + 9⁴ + 1/2*10⁴] = 2033.3
now the absolute difference will be
AD = ║E(x⁴) - E(y⁴)║
= ║ 2000 - 2033.3║
= 33.3 ≈ 33
Caitlyn started collecting shells in 2005. She records how many shells are in her collection each year.
Years since 2005 # shells
0 30
1 39
2 48
3 57
What is the initial value?
0
9
30
57
Answer:
30.
Step-by-step explanation:
The initial value is the value that she starts out with. This means that she is referring to year 0. According to the chart, on year 0, she collected 30 shells.
The answer is 30.