Answer:
The geometrical relationships between the straight lines AB and CD is that they have the same slope
Step-by-step explanation:
Given
[tex]OA = 2x + 9y[/tex]
[tex]OB = 4x + 8y[/tex]
[tex]CD = 4x - 2y[/tex]
Required
The relationship between AB, CD
Since AB is a straight line and O is the origin, then:
[tex]AB = (c - a)x + (d - b)y[/tex]
Where:
[tex]OA = ax + by[/tex] ====> [tex]OA = 2x + 9y[/tex]
[tex]OB = cx + dy[/tex] ====> [tex]OB = 4x + 8y[/tex]
This implies that:
[tex]a =2[/tex] [tex]b = 9[/tex] [tex]c = 4[/tex] [tex]d = 8[/tex]
So:
[tex]AB = (c - a)x + (d - b)y[/tex]
[tex]AB = (4 - 2)x + (8 - 9)y[/tex]
[tex]AB = 2x -y[/tex]
So, we have:
[tex]AB = 2x -y[/tex]
[tex]CD = 4x - 2y[/tex]
Calculate the slope (m) of [tex]AB\ and\ CD[/tex]
[tex]m = \frac{Coefficient\ of\ y}{Coefficient\ of\ y}[/tex]
For AB
[tex]m_1 = \frac{-1}{2}[/tex]
[tex]m_1 = -\frac{1}{2}[/tex]
For CD
[tex]m_2 = \frac{-2}{4}[/tex]
[tex]m_2 = \frac{-1}{2}[/tex]
[tex]m_2 = -\frac{1}{2}[/tex]
By comparison:
[tex]m_1 = m_2 = -\frac{1}{2}[/tex]
This implies that both lines have the same slope
Help will give b if correct
Answer:
0.28
Step-by-step explanation:
28 divided by 100=0.28
Answer:0.28m
Step-by-step explanation:
Carlos is helping his grandfather paint the patio in their backyard. What is the area of the patio?
Please help! 30 points!
Use the Law of Cosines to solve the problem.
A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.
Answer: [tex]64.2^{\circ}[/tex]
Step-by-step explanation:
According to the cosine rule
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
Here, [tex]a=83, b=111, c=165,\ C=180^{\circ}-\theta[/tex]
Putting values
[tex]\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}[/tex]
So, the ship turns by [tex]64.2^{\circ}[/tex] north of west
The ship turned an at angle of 64.2 degrees north of west
Represent the angle, the ship turned due north of west with theta.
From the figure, we have the following equation
[tex]\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}[/tex]
So, we have:
[tex]\cos(A) = \frac{83^2 + 111^2 - 165^2}{2 * 83 *111}[/tex]
Evaluate the expression on the right-hand side
[tex]\cos(A) = -0.4350[/tex]
Take the arc cos of both sides
[tex]A = \cos^{-1}(0.4350)[/tex]
[tex]A =115.8^o[/tex]
The value of theta is then calculated as:
[tex]\theta = 180 -A[/tex]
This gives
[tex]\theta = 180 -115.8^o[/tex]
[tex]\theta = 64.2^o[/tex]
Hence, the ship turned an at angle of 64.2 degrees north of west
Read more about bearing and elevation at
https://brainly.com/question/19594654
Cual es el valor absoluto de 6.3
Answer:
Usamos la notación para decir "el valor absoluto de -2", lo cual significa "la distancia de -2 al 0 en la recta numérica". ... 6.3: Altitud y temperatura absoluta.
Mrs smith and i went to the shop to creme eggs at 23p each & kinder eggs at 47 peach in bulk. We bought 141 eggs altogether & it came to 48.51 how many creme eggs did we buy ?
Answer:
Step-by-step explanation:
Mrs smith and i went to the shop to creme eggs at 23p each & kinder eggs at 47 peach in bulk. We bought 141 eggs altogether & it came to 48.51 how many creme eggs did we buy ?
David uses 1/4 bag of potting soil to plant 6 tomato plants. If he uses the same amount of potting soil for each plant, what fraction of the bag of potting soil will each plant get?
1/24
24
2/3
1 1/2
Answer:
Step-by-step explanation:
A
5. Jovi solved the following system of equations by
substitution. His partner Giselle checked his work
and said she found an error. What step did Giselle
find the error?
Ann and Betty shared a sum of money in the ratio 2:3. If Ann received $120,what was the amount of money shared?
Answer:
$420
Step-by-step explanation:
Given data
GIven ratio= 2:3
The total ratio= 2+5= 7
Ann's share= $120
Let us apply the part to all approach
let the total amount be x
so for Ann
2/7= 120/x
cross multiply
2x= 120*7
2x= 840
divide both sides by 2
x= 840/2
x= 420
Hence the amount shared is $420
What is the length of a side a? Round to the nearest tenth of an inch.
Answer:
Step-by-step explanation:
a = 16 inches
NEAREST TENTH: 20
Estimate the product. 3 1/3 X 4 1/8
Answer:
55/4=13.75
Step-by-step explanation:
3+1/3=10/3
4+1/8=33/8
(10/3)(33/8)
(33x10)/(3x24)
330/24
55/4
Hope that helps :)
6v+12b=504
2v+5b=204
Answer:
Step-by-step explanation:
6v + 12b = 504 eq1
2v + 5b = 204 eq2
6v + 15b = 612 eq2 times 3
0 -3b = 504 - 612 subtraction of the two bolded eqs
-3b = -108 solve for b
b = 36
Another way to solve the problem
6v + 12b = 504 I would eliminate the v term by multiplying the bottom
2v + 5b = 204 equation by -3 on BOTH sides and then add the two eqs
2v + 5b = 204
-3(2v + 5b) = -3(204)
-6v - 15b = -612
6v + 12b = 504
-6v - 15b = -612 add the like terms
(6v + (-6v)) + (12b + (-15b) = 504 + (-612)
(6v -6v)) + (12b - 15b) = 504 - 612)
0 + -3b = - 108 solve for b divide both sides by -3
b = -108/-3
b = 36
use eq 2v + 5b = 204 to solve for v and knowing b = 36
2v + 5b = 204 b=36
2v + 5(36) = 204 substract 5 times 36 from both sides
2v = 204 - 180
v = 24 / 2
v = 12
NOW CHECK the values for b and v using the OTHER eq
6v + 12b = 504
6(12) + 12(36) = 504
72 + 432 = 504
504 = 504 IT CHECKS
Jehle and Liam a bowl serving 0.5÷200 Jehle says the question will be Less than 0.5 Liam says the quotient would be more than 0.5 which student is correct
Answer:
Jehle is correct.
Step-by-step explanation:
Given - Jehle and Liam a both solving 0.5÷200.
Jehle says the quotient will be Less than 0.5.
Liam says the quotient would be more than 0.5
To find - Which student is correct ?
Proof -
Given expression is 0.5 ÷ 200
It is equivalent to
[tex]\frac{0.5}{200} = \frac{5}{2000} = \frac{1}{400}[/tex] = 0.0025 < 0.5
∴ we get
The expression is Less than 0.5
So, Jehle is correct.
Question 1 of 10
sin = 20/29
find tan 0
Step-by-step explanation:
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
Cutt/ly.627929
13 (a) Write 2016 as the product of prime factors.
Answer: 2^5*3^2*7*1
Step-by-step explanation:
Solve these simultaneous equations:
2x + 4y = 38
7x - 4y =7
Answer:
Step-by-step explanation:
Answer:
x=5, y=7
Step-by-step explanation:
2x+4y= 38
+7x-4y= 7
9x= 45
9x/9= 45/9
x=5
2x+4y=38
2(5)+4y= 38
10+4y= 38
-10 -10
4y= 28
4y/4= 28/4
y=7
What is the diameter of the Orange below ? HINT : D = 2r
Answer:
umm don't know.....
Step-by-step explanation:
......
Problem PLS HELP MY GRADES GOING DOWN
Answer:
$248
Step-by-step explanation:
given:
4 deposits
$62
solve:
4 × $62= $248
Answer:
$248
Step-by-step explanation:
You can answer it two ways:
1) add 62 + 62 + 62 + 62 = 248
2) multiply 4 * 62 = 248
Answer: $248
A washer and a dryer cost $662 combined. The washer costs $88 less than the dryer. What is the cost of the dryer?
Answer:
Step-by-step explanation:First you have to subtract 662-88 and you work it on paper so its easier and when you find the answer its 574
Tyler has 3 times as many books as Mai. How many books does Mai have if Tyler has 21 books?
Step-by-step explanation:
Say 21 divided by 3, which gives you 7
So mai has 7 books
Answer:
Mai has 7 books
Step-by-step explanation:
Tyler has 21 books and 3 times more than Mai
21/3 = 7
Which rectangular equation represents the parametric equations x = 3t ^1/2 and y = 6t?
photo has the answer choices !
Answer:
B
Step-by-step explanation:
on edge 2021
Write an equation in point-slope form of the line that passes through the point (2, -8) and has a slope of 4. The equation is y- __=__(x-__).
Answer:
The equation is [tex]y-(-8) = 4(x-2)[/tex].
Step-by-step explanation:
The point-slope form of a line is represented by the formula [tex]y-y_1 = m (x-x_1)[/tex]. In order to write an equation of a line in point-slope form, we would need to substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex] represents the slope of the line, substitute 4 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (2,-8) in the formula as well. Substitute 2 for [tex]x_1[/tex] and -8 for [tex]y_1[/tex]. This results in the following equation and answer:
[tex]y-(-8) = 4(x-2)[/tex]
(Usually, we would simplify the double negatives on the left side to a positive, but because you have to type the values in to answer the problem and cannot change the written negative sign already visible in the equation, that would be the answer. I believe you can just type in -8 for the first box.)
Solve the following quadratic by factoring. x² + 3x – 40 = 0
A. X = -8, x=5
B. X= 8, x=5
C. X=8,x= -5
Answer:
That would be A!
Step-by-step explanation:
Please tell me if i made a mistake or misunderstood!
please hurry if answer is correct i will give brainlyyyyest thx
In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches.
Answer:
i could only get part one done
Step-by-step explanation:
Perimeter is a measurement of the distance around a shape and area gives us an idea. Understanding how much space you have and learning how to fit shapes ... If the shape is a polygon, then you can add up all the lengths of the sides to find the perimeter. ... You can write “in2” for square inches and “ft2” for square feet
Choose the graph of the solution to this inequality.
–6x < 21
Answer: A
Step-by-step explanation:
c - 12 > -16
c > -4
A
6ya +7y{a
Find the sum
O 13y^2
O O 13ay
O 13y/2a
0 13ya
Can someone please help me with math.
Answer:
Your answer would be B.
Step-by-step explanation:
Hope this helps!
HOW MANY ELEMENTS DOES A TRIANGLE HAS
?
Answer:
6
Step-by-step explanation:
3 sides, 3 angles.
The speed of boat in still water is 15km/hr if needs 4 more his to travel 63 km against the current of a river than it needs to travel down the river determine the system of equation
Answer:
[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]
Step-by-step explanation:
The systems of equations are
Let us assume the rate of the current be c
Now actual speed against the current is (15 - c)
And, the actual speed with the current is (15 + c)
Here we applied the time formula i.e. distance by speed
Also the upstream time - downstream time = 4
Now the equations are
[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]
A bag contains 90 marbles. some green and some transparent. The ratio of green
marbles to transparent ones is 3.2. How many green marbles are there?
Answer:
54 green marbles
Step-by-step explanation:
So green : transparent = 3:2
so 3+2=5 and 3*90/5 = 54 green marbles
A window shaped like a parallelogram has an area of 73 2 3 square feet. The height of the window is 8 2 3 feet. How long is the base of the window?
Answer:
8 1/2 feet
Step-by-step explanation:
Here is the complete question
A window shaped like a parallelogram has an area of 73 2/3 square feet. The height of the window is 8 2/3 feet. How long is the base of the window?
A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area = base x height
73 2/3 = 8 2/3 x base
divide 73 2/3 by 8 2/3
221/3 x 3/26 = 8 1/2 feet