Answer:
I believe it is because he has exhausted all the different ways to use the 18 m he has. Look below.
Step-by-step explanation:
He has 18 m of wood and he has done:
8+8=16 1+1=2 16+2=18
7+7=14 2+2=4 14+4=18
6+6=12 3+3=6 12+6=18
5+5=10 4+4=8 10+8=18
So he has no more ways to use the 18 m of wood and has exhauseted all the ways.
Please mark brainliest
What is the slope of the line shown below?
Answer:
Step-by-step explanation:
x1 y1 x2 y2
-4 3 3 1
ΔY -2
ΔX 7
slope= - 2/7
Please help thank you!
Answer:
A≈376.99yd²
d= 10yd
h = 7yd
hope it helps
You are designing a rectangular fenced outdoor space for your pet rabbit. Fencing
material costs $15.25 per metre. You have $200. What dimensions give the greatest
area, to the nearest tenth of a metre? Include a sketch of the fenced area.
Answer:
2.6 x 5
Step-by-step explanation:
2.6 x 5 is 13 x 15.25 is 198.25 and you can't go any higher than that or it will go over 200 so the dimensions that give the greatest area would be 2.6 and 5, good luck
Joe receives a cake for his birthday. He eats $\frac{1}{4}$ of the cake on the first day. On the second day, he eats $\frac{3}{4}$ of the amount of cake that is left after the first day. What fraction of a whole cake is left for Joe to eat on the third day
Answer:
3 / 16
Step-by-step explanation:
Let The total amount = x
Fraction eaten on first day = 1/4x
Fraction left = x - 1/4x = 3/4x
Fraction of amount left eaten on second day = 3/4 of 3/4x
3/4 * 3/4x = 9/16x
Fraction left :
3/4x - 9/16x = (12x - 9x) /16 = 3/16x
Hence, fraction left = 3/16
Let a=(1,2,3,4), b=(4,3,2,1) and c=(1,1,1,1) be vectors in R4. Part (a) [4 points]: Find (a⋅2c)b+||−3c||a. Part (b) [6 points]: Find two perpendicular vectors p and q in R4 such that their sum is the vector b and such that p is parallel to a. Part (c) [3 points]: If T(−1,1,2,−2) is the terminal point of the vector a, then what is its initial point? Part (d) [2 points]: Find a vector in R4 that is perpendicular to b.
Solution :
Given :
a = (1, 2, 3, 4) , b = ( 4, 3, 2, 1), c = (1, 1, 1, 1) ∈ [tex]R^4[/tex]
a). (a.2c)b + ||-3c||a
Now,
(a.2c) = (1, 2, 3, 4). 2 (1, 1, 1, 1)
= (2 + 4 + 6 + 6)
= 20
-3c = -3 (1, 1, 1, 1)
= (-3, -3, -3, -3)
||-3c|| = [tex]$\sqrt{(-3)^2 + (-3)^2 + (-3)^2 + (-3)^2 }$[/tex]
[tex]$=\sqrt{9+9+9+9}$[/tex]
[tex]$=\sqrt{36}$[/tex]
= 6
Therefore,
(a.2c)b + ||-3c||a = (20)(4, 3, 2, 1) + 6(1, 2, 3, 4)
= (80, 60, 40, 20) + (6, 12, 18, 24)
= (86, 72, 58, 44)
b). two vectors [tex]\vec A[/tex] and [tex]\vec B[/tex] are parallel to each other if they are scalar multiple of each other.
i.e., [tex]\vec A=r \vec B[/tex] for the same scalar r.
Given [tex]\vec p[/tex] is parallel to [tex]\vec a[/tex], for the same scalar r, we have
[tex]$\vec p = r (1,2,3,4)$[/tex]
[tex]$\vec p = (r,2r,3r,4r)$[/tex] ......(1)
Let [tex]\vec q = (q_1,q_2,q_3,q_4)[/tex] ......(2)
Now given [tex]\vec p[/tex] and [tex]\vec q[/tex] are perpendicular vectors, that is dot product of [tex]\vec p[/tex] and [tex]\vec q[/tex] is zero.
[tex]$q_1r + 2q_2r + 3q_3r + 4q_4r = 0$[/tex]
[tex]$q_1 + 2q_2 + 3q_3 + 4q_4 = 0$[/tex] .......(3)
Also given the sum of [tex]\vec p[/tex] and [tex]\vec q[/tex] is equal to [tex]\vec b[/tex]. So
[tex]\vec p + \vec q = \vec b[/tex]
[tex]$(r,2r,3r,4r) + (q_1+q_2+q_3+q_4)=(4, 3,2,1)$[/tex]
∴ [tex]$q_1 = 4-r , \ q_2=3-2r, \ q_3 = 2-3r, \ q_4=1-4r$[/tex] ....(4)
Putting the values of [tex]q_1,q_2,q_3,q_4[/tex] in (3),we get
[tex]r=\frac{2}{3}[/tex]
So putting this value of r in (4), we get
[tex]$\vec p =\left( \frac{2}{3}, \frac{4}{3}, 2, \frac{8}{3} \right)$[/tex]
[tex]$\vec q =\left( \frac{10}{3}, \frac{5}{3}, 0, \frac{-5}{3} \right)$[/tex]
These two vectors are perpendicular and satisfies the given condition.
c). Given terminal point is [tex]\vec a[/tex] is (-1, 1, 2, -2)
We know that,
Position vector = terminal point - initial point
Initial point = terminal point - position point
= (-1, 1, 2, -2) - (1, 2, 3, 4)
= (-2, -1, -1, -6)
d). [tex]\vec b = (4,3,2,1)[/tex]
Let us say a vector [tex]\vec d = (d_1, d_2,d_3,d_4)[/tex] is perpendicular to [tex]\vec b.[/tex]
Then, [tex]\vec b.\vec d = 0[/tex]
[tex]$4d_1+3d_2+2d_3+d_4=0$[/tex]
[tex]$d_4=-4d_1-3d_2-2d_3$[/tex]
There are infinitely many vectors which satisfies this condition.
Let us choose arbitrary [tex]$d_1=1, d_2=1, d_3=2$[/tex]
Therefore, [tex]$d_4=-4(-1)-3(1)-2(2)$[/tex]
= -3
The vector is (-1, 1, 2, -3) perpendicular to given [tex]\vec b.[/tex]
Which number represents a square root of 3 (cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction pi Over 2 EndFraction) )?
a)StartRoot 3 EndRoot (cosine (StartFraction pi Over 8 EndFraction) + I sine (StartFraction pi Over 8 EndFraction) )
b)StartRoot 3 EndRoot (cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) )
c)StartRoot 3 EndRoot (cosine (StartFraction 5 pi Over 6 EndFraction) + I sine (StartFraction 5 pi Over 6 EndFraction) )
d) StartRoot 3 EndRoot (cosine (StartFraction 3 pi Over 2 EndFraction) + I sine (StartFraction 3 pi Over 2 EndFraction) )
Answer: hello your question is poorly written attached below is the complete question
answer:
[tex]\sqrt{3}(cos(\frac{3\pi }{2}) + isin(\frac{3\pi }{2}))[/tex] --- ( option d )
Step-by-step explanation:
The correct option that represents a square root of 3 as related to the question attached below is :
[tex]\sqrt{3}(cos(\frac{3\pi }{2}) + isin(\frac{3\pi }{2}))[/tex]
Answer:
D
Step-by-step explanation:
Sarah used 3/4 pound of blueberries to make 2/3 cup of jam. How many pounds of blueberries are needed per cup of jam?
3/4÷ 2/3= 3/4*3/2= 9/8= mixed fraction 1 1/8 pounds.
SOMEONE HELP ME PLEASE
Answer:
5/3
Step-by-step explanation:
Direct variation is of the form
y = kx
where k is a constant
Using the first set of point
9 = 5k
Divide by 5
9/5 = k
The equation becomes
y = 9/5 x
Using the second set of points
3 = 9/5 x
Multiply each side by 5/9
5/9 * 3 = 9/5 *5/9x
5/3 =x
this 2 pls i need help with explanation sum
9514 1404 393
Explanation:
8.An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.
The above relation tells us ...
∠PRS = ∠PQR +∠QPR = 2q +2p
Then ...
∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p
and
∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior
q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR
p = ∠QTR = 1/2(∠QPR) . . . . . subtract q
__
9.For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...
∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°
Substituting the congruent angles, this gives ...
∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation
Which choices are equivalent to the expression below ? Check all that apply sqrt(- 4)
Answer:
D 2i
Step-by-step explanation:
Answer:
B. i√4
D. 2i
Step-by-step explanation:
PLEASE HELP I WILL BE PICKING BRAINLIEST
Given the following equation where A = Area of a rectangle and w = width of the rectangle, what value of 'w' would maximize the area?
A = LW
P = 2L+2W
P = 100
w should be 625 units
w should be 25 units
w should be 0 units
w should be 50 units
Answer:
25
Step-by-step explanation:
geometry!!!!!!!!! helppp
Answer:
Solution given:
Centre (h,k)=(-6,-2)
end points are:
A[tex]\bold{(x_{1},y_{1})=(-1,-9) \:and \:B(x_{2},y_{2})=(-11,5)}[/tex]
Now
distance between A to M is:
AM=[tex]\sqrt{(h-x_{1})²+(k-y_{1})²}[/tex]
AM=[tex]\sqrt{(-6+1)²+(-2+9)²}=8.6[/tex]units
again
distance between B to M is:
BM=[tex]\sqrt{(h-x_{2})²+(k-y_{2})²}[/tex]
BM=[tex]\sqrt{(-6+11)²+(-2-5)²}=8.6[/tex]units
again
Since AM=BM=8.6units
so
M is the centre of the circle.:Yes
Solve the triangle ,find m
Answer:
m A = 63
m C = 27
Step-by-step explanation:
to find the angle of a use trigonometry by doing, cos-1(17/38) = 63
to find C, we know angles in a triangle add to 180. We know the right angle is 90 degrees so do 90 + 63 = 153
180 - 153 = 27
so C = 27 degrees
QUICK HELP PLEASE! THANK YOU SO MUCH
When the shown net containing the letters SPROUT is
folded into a cube, which letter is on the side opposite the side labeled R?
Answer:
T
fold it up =t
Step-by-step explanation:
3x+2y=4
4x+5y=10
solve the simultaneous equations (find x & y)
Answer: (0;2)
3x + 2y = 4 | * (-5)
4x + 5y = 10 | * 2
-15x - 10y = -20
8x + 10y = 20
-15x - 10y + 8x + 10y = 20 - 20
x = 0
0 + 2y = 4
2y = 4
y = 2
(0; 2)
Which of the graphs below would result if you made the leading term of the
following function negative?
F{x} = x + 3x2
Answer:
Step-by-step explanation:
A positive cubic function graphed in the coordinate plane tends from lower left to upper right while a negative cubic function tends from the upper left to lower right. That graph is D (graph A is the positive cubic. Note the difference between "lower left to upper right" and "upper left to lower right")
in how many ways can 10 people be divided into three groups of 2, 3, and 5 people respectively
Answer:
2520 ways
Step-by-step explanation:
Given
[tex]n = 10[/tex]
[tex]r = (2,3,5)[/tex]
Required
The number of selection
First, select 2 people from 10 in 10C2 ways.
There are 8 people, left.
Next, select 3 people from 8 in 8C3 ways.
There are 5 people left.
Lastly, select 5 from 5 in 5C5 ways
So, we have:
[tex]Total = ^{10}C_2 * ^8C_3 * ^5C_5[/tex]
Using combination formula
[tex]Total = 45 * 56 * 1[/tex]
[tex]Total = 2520[/tex]
Which is f(5) for the function -2x^2+2x-3
Answer:
-43
Step-by-step explanation:
f(x) = -2x^2+2x-3
Let x = 5
f(5) =-2(5)^2+2(5)-3
= -2(25)+10-3
=-50+10-3
= -43
The equation of the line that goes through the point (−10,8) and (−3,-4) can be written in the form y=mx+b
where m is:
and where b is:
Answer:
m is -12/7 and b is -64/7
Step-by-step explanation:
Use rise over run (change in y / change in x) to find the slope, m:
(-4 - 8) / (-3 + 10)
= -12/7
So, m is -12/7.
Plug in this value and a point into y = mx + b, then solve for b:
y = mx + b
-4 = -12/7(-3) + b
-4 = 36/7 + b
-64/7 = b
So, m is -12/7 and b is -64/7
The linear function is given by:
[tex]y = -\frac{12}{7}x - \frac{64}{7}[/tex]
Where:
m is [tex]-\frac{12}{7}[/tex].b is [tex]-\frac{64}{7}[/tex].What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the points are (−10,8) and (−3,-4).
The slope is given by change in y divided by change in x, hence:
[tex]m = \frac{-4 - 8}{-3 - (-10)} = -\frac{12}{7}[/tex]
Hence:
[tex]y = -\frac{12}{7}x + b[/tex]
It goes through point (−3,-4), hence when [tex]x = -3, y = -4[/tex], which is used to find b.
[tex]y = -\frac{12}{7}x + b[/tex]
[tex]-4 = \frac{36}{7} + b[/tex]
[tex]b = -\frac{64}{7}[/tex]
Hence, the equation is:
[tex]y = -\frac{12}{7}x - \frac{64}{7}[/tex]
You can learn more about linear functions at https://brainly.com/question/24808124
At 22 years of age, Nicolas and Troy have started their first full-time jobs, and Troy decides to place $10,000 in a savings plan for retirement, which pays 9% compounded every 3 months.
As usual, Nicolas thinks Troy is crazy because he wants to enjoy his money now, and then start saving when he turns 45 years of age.
Assume that both Troy and Nicolas plan to retire at age 60. If Nicolas wants to retire with the same amount of savings as Troy, how much will Nicolas need to contribute monthly to his savings account, which earns him 10% compounded monthly?
Answer:
The correct answer 8486.
Step-by-step explanation:
Given:
Troy - P pr principle amount = 10000
rate = 9%
time = 60-22 = 38
intrest at every three months so time = t = 38*4 = 132
Nicohlas
P = x
rate = 10%
time = 60 -45 = 15
every month compounded = 15*12=180
solution:
the formula of compound intrest = P (1 + r/n)^(nt)
where n = number of counded intrests per year
puting formula for troy=
10000 (1+9/4)^132
= 294,322.96 .....1
now for nicolas
I = x(1+10/12)^180
x = 294,322.96/(1+10/12)^180
= 8486.
pls pls help help help
Answer:
the diameter form for your help today with the app
Step-by-step explanation:
pa brain less
Carlos invests £4500 for 3 years.
He receives compound interest of 1.5% per year.
Carlos thinks the total of the money he invests and the interest will be more than
£4750 at the end of the 3 years.
Is he correct?
Show why you think this.
Answer:
He is incorrect.
Step-by-step explanation:
4500 x ( 1 + 1.50%)^3
= 4500 x 1.045678
= 4705.551000
4705.551000 < 4750
Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Given that, Carlos invests £4500 for 3 years.
He receives compound interest of 1.5% per year.
Here, amount =4500(1+1.5/100)³
= 4500(1+0.015)³
= 4500(1.015)³
= 4500×1.0457
= £4705.65
Carlos is not correct, because the amount at the end of the 3 years of compounding is £4705.65 not more than £4750.
To learn more about the compound interest visit:
https://brainly.com/question/14295570.
#SPJ2
solve the linear equation
x/2-3x/4+5x/8=9
I need the full solution X by 2 minus 3x by 4 + 5x by 8 equal to 9
Answer:
24
Step-by-step explanation:
x/2-3x/4+5x/8=9
Or,(4*x-2*3x+5x)/8=9. (taking LCM)
Or, (4x-6x+5x)/8=9
Or, 3x=9*8
Or, x = 72/3
so, x=24.
A bed is 0.63 m wide, and a door frame is 0.70 m wide.
By how much is the door frame wider than the bed?
Answer:
0.07
Step-by-step explanation:
0.70-0.63
Answer:
0.07
Step-by-step explanation:
subtract both and get ur answer
HELPP IS VERY MUCH NEEDED!!!!!
Since this is a right triangle, we can use the Pythagorean Theorem.
Pythagorean Theorem: a^2 + b^2 = c^2
7^2 + b^2 = 14^2
49 + b^2 = 196
b^2 = 147
b = sqrt(147) = 7 sqrt(3) miles
Hope this helps!
Solve
1+2+3+...+2017
Answer:
1 + 2 + 3 + ... + 2017
sum_(n=1)^2017 n = 2035153
Step-by-step explanation:
Please help ! pythagoran theaeom ! I need someone to please explain how to answer this ASAP , giving brainlist
Answer:
Floor=2*sqrt(11)
Step-by-step explanation:
Using Pythagoras theorem, we have
Wall^2+Floor^2=(Ladder)^2
Floor^2=12^2-10^2
Floor=sqrt(44)=2*sqrt(11)
Answer:The floor is 6m
Step-by-step explanation:
In this we have to solve to find B
First we know that A^2+B^2+C^2 and we know A is 10 and C is 12 so now we are going square both 10 and 12 which would be 100 and 144 then we subtract each other 144-100=44 and lastly we are going to get the square root of 44 which is 6.
Please give brainlist
the sum of legs for a right triangle be 21 and their product is 40. Find the perimeter of this triangle.
Answer:
The perimeter of the triangle is 40.
Step-by-step explanation:
The sum of legs for a right triangle is 12:
[tex] a + b = 21 [/tex]
[tex] a = 21 - b [/tex] (1)
And their product is:
[tex] a*b = 40 [/tex] (2)
By entering eq (1) into (2) we have:
[tex] (21 - b)b = 40 [/tex]
[tex] 21b - b^{2} - 40 = 0 [/tex]
We can find the value of "b" by solving the above quadratic equation.
[tex] b_{1} = 2.1 [/tex]
[tex] b_{2} = 18.9 [/tex]
Since the two values satisfy the equation, we can use either of them to find "a". We will use b₁.
[tex] a = 21 - 2.1 = 18.9 [/tex]
Now, the hypotenuse of the right triangle is given by:
[tex] h = \sqrt{a^{2} + b^{2}} = \sqrt{(18.9)^{2} + (2.1)^{2}} = 19 [/tex]
Hence, the perimeter is:
[tex] P = a + b + h = 18.9 + 2.1 + 19 = 40 [/tex]
Therefore, the perimeter of the triangle is 40.
I hope it helps you!
someone, please help this is due soon if you can explain them I really appreciate it (PICTURE) 15 points and brainliest.
Step-by-step explanation:
1. Given,
Sides of the shape = 3y+9, 2y+4, y+3 and 2y+4
Therefore ,
Perimeter of the shape = Sum of all the sides
= (3y+9) + (2y+4) + (y+3) + (2y+4)
= 3y + 2y + y + 2y + 9 + 4 + 3 + 4
= 8y + 20 (Ans)
2. Given,
Side of the square = 5x - 2
Therefore,
Perimeter of the square = 4 × Sides = 4s
= 4 × (5x - 2)
= 4 × 5x + 4 × (-2)
= 20x - 8 (Ans)
Can some help? Plz :)
Answer:
C. 1.05 x 10^7
Step-by-step explanation:
1.75x10^4 x 600
=1050 x 10^4
=1.05 x 10^7