Answer:
(14,2) and (-6/5,-28/5)
Step-by-step explanation:
The distance, d, from two points (x,y) and another point (a,b) can be calculated using
d=sqrt((x-a)^2+(y-b)^2).
Our point (a,b) is (2,7) and d=13.
Making substitutions:
13=sqrt((x-2)^2+(y-7)^2)
We are also given the relation between x and y is given as x-2y=10.
Adding 2y to both sides gives: x=10+2y
Make this insertion into our equation:
13=sqrt((10+2y-2)^2+(y-7)^2)
Simplify inside:
13=sqrt((8+2y)^2+(y-7)^2)
Square both sides:
169=(8+2y)^2+(y-7)^2
Expand binomial squares:
169=64+32y+4y^2+y^2-14y+49
Combine like terms:
169=5y^2+18y+113
Subtract 169 on both sides:
0=5y^2+18y-56
We could try to factor
0=(5y+28)(y-2)
So y=2 or y=-28/5
Recall x=10+2y
So if y=2, then x=10+2(2)=10+4=14.
So if y=-28/5, then x=10+2(-28/5)=10+(-56/5)
=50/5 +-56/5
=-6/5.
So two points satisfying given criteria is
(14,2) and (-6/5,-28/5).
the x coordinates of the point 2y-x=10 intersect the line yaxis
Answer:
Point has co-ordinates, (0, 5)
Step-by-step explanation:
If they cut y-axis, then x = 0
[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]
(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
v⃗ =
(b) Show that the point (−1,−1,1) lies on both planes. Then find a vector parametric equation for the line of intersection.
r⃗ (t)=
Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.
-4x + 2y - z = 1 ==> z = -4x + 2y - 1
3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2
==> -4x + 2y - 1 = (1 - 3x + 2y)/2
==> -8x + 4y - 2 = 1 - 3x + 2y
==> -5x + 2y = 3
==> y = (3 + 5x)/2
==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2
So if we take x = t, the line of intersection is parameterized by
r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩
Just to not have to work with fractions, scale this by a factor of 2, so that
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
(a) The tangent vector to r(t) is parallel to this line, so you can use
v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩
or any scalar multiple of this.
(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,
r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩
Please find the measure!
Step-by-step explanation:
x=72
63+45+x=180
[tex]108 + x = 180[/tex]
[tex]x = 72[/tex]
I don’t get it this ain’t make no sense
Answer:
65 m
Step-by-step explanation:
u = 6 m/s
v = 20 m/s
t = 5 s
[tex]s=\frac{1}{2} (6+20)5[/tex]
[tex]s=\frac{1}{2} (26)5[/tex]
[tex]s=(13)5[/tex]
[tex]s=65[/tex]
Hey there!
1/2(6 + 20)(5)
= 1/2 (26)(5)
1/2(26) = 13
= 13(5)
= 65
Therefore, your answer is most likely: 65m
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What transformation is described by the
notation (x, y) (x - 3, y)?
A slide left 3 units
B slide down 3 units
C slide right 3 units
Answer:
Step-by-step explanation:
Any alteration to the x value means that the function will move right. There are no exceptions to this that I can think of.
Jennifer is saving money to buy a bike. The bike costs $227. She has $106 saved, and each week she adds
$11 to her savings.
How long will it take her to save enough money to buy tho hilo?
Answer:
11 weeks.
Step-by-step explanation:
227-106=121
121 divided by 11 = no. of weeks
Therefore it takes her 11 weeks.
Answer:
It will take 11 weeks
Step-by-step explanation:
11 times 11 is 121.
121 plus 106 is 227
which is the exact number the bike costs
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer:
2x-1=3
2x=3+1
2x=4
x=2
[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]
(a) Let's try with x = - 1
[tex] \sf \: 2x - 1 = 3 \\\sf 2( - 1) - 1 = 3 \\ \sf- 2 - 1 = 3 \\ \\ \boxed{\bf- 3 \: \bcancel= \: 3}[/tex]
So, x = - 1 is not the solution to the given equation.
______________
(b) Now, try with x = 2
[tex]\sf2x - 1 = 3 \\ \sf2(2) - 1 = 3 \\ \sf4 - 1 = 3 \\ \\ \boxed{\bf3 = 3}[/tex]
Yes, we can see that x = 2 is the correct solution for the equation.
______________
Hope it helps.
RainbowSalt2222
Which exponential expression is equivalent to (4x^2 y^3)^2
Answer:
[tex] 16 {x}^{4} {y}^{6} [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} {y}^{3} {)}^{2} [/tex]
➡️ [tex] {4}^{2} \times ( {x}^{2} {)}^{2} \times ( {y}^{3} {)}^{2} [/tex]
➡️ [tex] = 16 {x}^{4} {y}^{6} [/tex] ✅
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
what is 5.5 feet in centimeters?
Answer:
167.64 cm
Step-by-step explanation:
I dont kno how to work it out
If a(x + 1) + b(x − 1) − 2 = 0 for all real x, then a =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Answer:
D) 1
Step-by-step explanation:
using the distributive property we have ax+a+bx-b-2=0. because the equation is true for all real x, ax=-bx. this means a-b-2=0 and a=-b. a-b-2=0 becomes a=b+2. then we substitute a for -b and get -b=b+2 which becomes 2b=-2 so b=-1. since a=-b, a=1
Question 4 (2 marks)
Justin works 14 hours at a normal pay rate of $24.80 per hour and 5 hours of overtime at
time and a half. How much should he be paid?
I
809 words
LE
English (Australia)
Answer:
554.7
Step-by-step explanation:
The pay=25.8*14+(25.8)*5*1.5=554.7
3)
Write an inequality for the graph below. If necessary, use
<= for < or >= for.
Kinda stuck and running out of time
Answer:
Step-by-step explanation:
不
Which line is horizontal?
O y=2
O y = 2x
O y = -2x
o y=x
Answer:
y=2
Step-by-step explanation:
A horizontal line has a slope of zero so the x term is zero
y = mx+b
y = b
y must equal a constant
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
Find the area of the figure. (Sides meet at right angles.)
Answer:
56
Step-by-step explanation:
A=(3*4)+(4*(4+3+4))=56
URGENT PLZ SAVE ME
If c varies directly as b and c = 6 when b = 2.
Find
a) the formula for c in terms of b
b) the value of c given b = 14
c) the value of b given c = 39
Answer:
Hello,
Are you still alive ?
Step-by-step explanation:
a)
c=k*b (c varies directly as b)
6=k*2 ==> k=3 ( c = 6 when b = 2.)
[tex]\boxed{c=3*b }\\[/tex]
b)
b=14 ==> c=3*14=42
c)
c=39
[tex]b=\dfrac{c}{3} =\dfrac{39}{3} =13\\[/tex]
. Sipho's dad used 4/11 of the packet of oranges to make juice. The
next day he used another 4/11 of the packet of oranges.
a) How many elevenths has he used?
Answer:
8 of the 11
Step-by-step explanation:
4+4=8 of the 11
Part of oranges usef from the orange packet used on 1st day = 4/11
Part of oranges used from the orange packet used on 2nd day = 4/11
Total part of oranges used from the orange packet
= (4/11) + (4/11)
= 8/11
So, Sipho's dad used 8 elevenths of the oranges.
hhheeeeeelllllllppppp meeee plzz
Answer:
I believe it is A
Step-by-step explanation:
PLEASE HELP
-1/2m=-9
Show your work in details if you can, I have a hard time understanding this.
[tex] \begin{cases} \\ \large\bf{\green{ \implies}} \tt \: - \: \frac{1}{2} \: m \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - \frac{1 \: m}{2} \: = \: - 9 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 9 \: \times \: 2 \\ \\ \large\bf{\green{ \implies}} \tt \: - 1m \: = \: - 18 \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{ \cancel- 18}{ \cancel - 1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: \frac{18}{1} \\ \\ \large\bf{\green{ \implies}} \tt \: m \: = \: 18 \: \\ \end{cases}[/tex]
Solve for r V=pir^2h/3
Answer: sqrt 3V/pih = r
Step-by-step explanation:
3V = (pi r^2h)3
3V = pi r^2 h
3V/pih = r^2
Sqrt (3V/pi h) = r
Hello! Please help thanks
Answer:
A. [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
Hi there!
We are given right triangle PQR, with PR=5, RQ=12, and PQ=13
We want to find the value of sin(Q)
Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]
In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse
So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]
Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A
Hope this helps!
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answer:
5,20,80,320
Step-by-step explanation:
a1 = 5
an = 4 an-1
Let n = 2
a2 = 4 * a1 = 4*5 = 20
Let n = 3
a3 = 4 * a2 = 4*20 = 80
Let n = 4
a4 = 4 * a3 = 4*80 = 320
ANSWER THE QUESTIONS PLEASE IT IS ON BEARING
9514 1404 393
Answer:
(i) x° = 70°, y° = 20°
(ii) ∠BAC ≈ 50.2°
(iii) 120
(iv) 300
Step-by-step explanation:
(i) Angle x° is congruent with the one marked 70°, as they are "alternate interior angles" with respect to the parallel north-south lines and transversal AB.
x = 70
The angle marked y° is the supplement to the one marked 160°.
y = 20
__
(ii) The triangle interior angle at B is x° +y° = 70° +20° = 90°, so triangle ABC is a right triangle. With respect to angle BAC, side BA is adjacent, and side BC is opposite. Then ...
tan(∠BAC) = BC/BA = 120/100 = 1.2
∠BAC = arctan(1.2) ≈ 50.2°
__
(iii) The bearing of C from A is the sum of the bearing of B from A and angle BAC.
bearing of C = 70° +50.2° = 120.2°
The three-digit bearing of C from A is 120.
__
(iv) The bearing of A from C is 180 added to the bearing of C from A:
120 +180 = 300
The three-digit bearing of A from C is 300.
The sum of the 3rd and 7th terms of an A.P. is 38, and the 9th term is 37. Find the A.P.
Answer:
The AP is 1, 11/2, 10, 29/2, 19, ....
Step-by-step explanation:
Let the first term be a and d be the common difference of the arithmetic progression.
ATQ, a+2d+a+6d=38, 2a+8d=38 and a+8d=37. Solving this, we will get a=1 and d=9/2. The AP is 1, 11/2, 10, 29/2, 19, ....
a day? 6. If 18 pumps can raise 2150 tonnes of water in 50 days, working 8 hours a day, how much water will be raised in 60 days by 16 out of which 10 are working 9 hours a day and the rest 7 hours a day?
Charlie's flower bed has a length of 4 feet and a width of four sixths feet. Which of the following is true
1 The area of the flower bed is equal to 6 square feet.
2The area of the flower bed is larger to 6 square feet.
3 The area of the flower bed is equal to 4 square feet
4 The area of the flower bed is smaller than 4 square feet.
Answer:
Option 4) The area of the flower bed is smaller than 4 square feet.
Step-by-step explanation:
Let’s solve for the area of the flower bed.
Consider that the flower bed is a rectangle.
The area of a recrangle is given by the formula:
A = length x width
The area of the flower bed is:
4 ft x 4/6 ft = 2 2/3 ft^2
2 2/3 ft ^2 < 4 ft^2
Therefore option 4 is the correct answer.
Given the formula A = 5h (B + b); solve for B.
2
Answer:
B = A/5h - b; You could use
B = (A - 5hb)/5h This just puts everything over a common denominator.
Step-by-step explanation:
A = 5h (B + b) Divide both sides by 5h
A/5h = B + b Subtract b from both sides.
A/5h - b = B
what is the mean of this graph?
Answer:
Step-by-step explanation:
Mean: sum of terms/ number of terms
4 + 2 + 3 + 1 + 1 + 5 = 16
Numbr of terms = 6
16/6 = 2.66
Answered by g a u t h m a th
Answer:
2 2/3
Step-by-step explanation:
The mean is the average of the values
The values on the graph are 4, 2, 3, 1, 1, and 5
Average is sum/number of values
4+2+3+1+1+5=16
16/6=2 2/3
Line A passes through the points (6, 1) and (-4, 6). Line B passes through the points (14, 3) and
(-10, -9).
Which statement is true?
Line A does not intersect line B.
Line A overlaps line B.
Line A intersects line B at exactly one point.
PLSSS HELPPP QUICKK
Answer:
Line A does not intersect line B.
Step-by-step explanation:
line A comes close, but does not touch, intersect, or overlap line A. hope this helps, please correct me if i am wrong.
