[tex]\large\underline{\sf{Solution-}}[/tex]
First equation is
[tex]\rm \longmapsto\:(x - a)(y - b) = (x - 2a)\bigg(y -\dfrac{b}{2}\bigg) [/tex]
can be further simplified to
[tex]\rm \longmapsto\:xy - bx - ay + ab = xy - \dfrac{bx}{2} - 2ay + ab[/tex]
[tex]\rm \longmapsto\: - bx - ay = - \dfrac{bx}{2} - 2ay [/tex]
[tex]\rm \longmapsto\: - bx + \dfrac{bx}{2} = - 2ay + ay[/tex]
[tex]\rm \longmapsto\: - \dfrac{bx}{2} = - ay[/tex]
[tex]\rm \longmapsto\: \dfrac{bx}{2} = ay[/tex]
[tex]\rm \longmapsto\:bx = 2ay[/tex]
[tex]\rm:\longmapsto \:\boxed{\tt{ bx - 2ay = 0}} - - - - (1)[/tex]
Second equation is
[tex]\rm \longmapsto\:x\bigg(x + \dfrac{1}{2b} \bigg) + y \bigg(y + \dfrac{a}{2}\bigg) - 2xy = 5 + {(x - y)}^{2} [/tex]
[tex]\rm \longmapsto\: {x}^{2} + \dfrac{x}{2b} + {y}^{2} + \dfrac{ay}{2} - 2xy = 5 + {x}^{2} + {y}^{2} - 2xy[/tex]
[tex]\rm \longmapsto\: \dfrac{x}{2b} + \dfrac{ay}{2} = 5[/tex]
[tex]\rm \longmapsto\: \dfrac{x + aby}{2b} = 5[/tex]
[tex]\rm :\longmapsto\:\boxed{\tt{ x + aby = 10b}} - - - (2)[/tex]
So, we have two equations in simplest form as
[tex]\rm \longmapsto\:bx - 2ay = 0 [/tex]
and
[tex]\rm \longmapsto\:x + aby = 10b[/tex]
Now, Consider
[tex]\rm \longmapsto\:\dfrac{a_1}{a_2} = \dfrac{b}{1} = b[/tex]
[tex]\rm \longmapsto\:\dfrac{b_1}{b_2} = \dfrac{ - 2a}{ab} = - \dfrac{2}{b} [/tex]
[tex]\bf\implies \:\dfrac{a_1}{a_2} \: \ne \: \dfrac{b_1}{b_2} [/tex]
This implies, System of equations is consistent having unique solution.
So, The student is correct as lines are intersecting.
So, option (b) is correct.
subtract 2 3/4 - 5/16
Answer:
2 7/16
Step-by-step explanation:
2 3/4 - 5/16 → 11/4 - 5/16 (convert 2 3/4 into an improper or top-heavy fraction)
11/4 - 5/16 → 44/16 - 5/16 (multiply 11/4 by 4/4 to make a common denominator)
44/16 - 5/16 = 39/16 (Subtract 44 - 5 = 39)
Simplify (convert back into mixed number)
39/16 = 2 7/16
Hope this helps!
A square has a side length of 4 centimeters. What is the length of the diagonal of the square? What is the length from the corner to the center of the square?
Answer:
4[tex]\sqrt{2}[/tex] cm AND 2[tex]\sqrt{2}[/tex] cm
Step-by-step explanation:
The length of a diagonal of a square means finding the hypotenuse (long side) of a right triangle with legs of the length of the side of the square. This means you can use a^2 + b^2 = c^2 to solve for the diagonal. Plugging in your values gets you 4^2 + 4^2 = c^2, simplify to get 16 + 16 = c^2, simplify further to get 32 = c^2. Isolate c by taking the square root of both sides to get [tex]\sqrt{32}[/tex] = c, which you can simplify by listing out the factors of 32 and finding pairs. 32 = 2 * 2 * 2 * 2 *2 (5 of them), meaning its square root is 4[tex]\sqrt{2}[/tex], which is the length of the diagonal. Don't forget your units! (:
For the second part, remember that the distance between the corner to the center of a square is half the diagonal of the square. You already have the length of that diagonal, so all you have to do is divide it by 2. Do so and you get 2[tex]\sqrt{2}[/tex]. Once again, don't forget your units! (:
If you're required to give decimal estimates, then pop those final answers into a calculator and round to the specified number of decimal places. No one will ask you to calculate irrational square roots, or at least no one should.
Need help with number 7 and eight
Answer:
7 is d
Step-by-step explanation:
8 is b. In 7 all the sum of angles will equals 360 degres
[tex]\sqrt{108k^{7}q^{8}}[/tex]
Answer:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
6k^3*q^4√3k
What is 6(x+4) 1 hehe
Answer:
2
Step-by-step explanation:
two plus four equals six
Will give brainliest answer
Answer:
first most option is the answer
Answer:ok A is the correct answer for this test I did this plz trust me give brainpower plz
Step-by-step explanation:
Does the following system of equations
have one, none, or infinite solutions?
-4x + y = 6
-5x – y = 21
Answer:
Iv'e checked both of them and they have NO solutions so nyour answer is (None)
Step-by-step explanation:
Blanca is considering selling her blossoming art business, but is unsure what fair value would be. A friend in accounting told her she could help if she can calculate her EBIT. She has sold 120 art collages for $300. Her expenses are minimal since she usually uses recycled materials. She estimates it costs her about $4 per collage and she has created 200 collages this year. Help her calculate her EBIT. Annual Revenue Annual Expenses, and EBIT
Answer: 15x-4956
Step-by-step
this is
If triangles ABC and XYZ are similar, what is the length of side b?
What single decimal multiplier would you use to increase by 15% followed by a 14% increase?
9514 1404 393
Answer:
1.311
Step-by-step explanation:
That multiplier is the product of the multipliers for each of the increases:
(1 +15%)(1 +14%) = 1.15×1.14 = 1.311
Type SSS, SAS, ASA, SAA, or HL to
describe these triangles.
Answer:
SAS
Step-by-step explanation:
There is one common side (S)
both the triangles have 90° common (A)
Opposite sides are equal which is given (S)
They both are right angled triangles
solve pls brainliest
Answer:
a. 9m/s × 27s = 243m
b. -6°C/3hrs = -2°C/hr
help with#14 please!!!
let's solve for f :
[tex] \dfrac{1}{f} = \dfrac{1}{a} + \dfrac{1}{b} [/tex][tex] \dfrac{1}{f} = \dfrac{b + a}{ab} [/tex]Taking reciprocal of both sides :
[tex]f = \dfrac{ab}{a + b} [/tex]2/3 divided by 3/4 simplified
43% of a town has blue eyes, 46% has blonde hair, and 24% has both. What is the probability that a random person picked will have both?
Answer:
24 by 113
Step-by-step explanation:
43 + 46 + 24 = 113
the % of people with both is 24%, thus the answer will be 24 by 113
Hope its correct and helps ya :)
If an object accelerates at a rate of 3 m/s2, it will exert a force of 15 N. How much force will the same object exert if it accelerates at a rate of 7 m/s2?
Answer:
13 newtons
Step-by-step explanation:
21 N force will the same object exert if it accelerates at a rate of 7 m/s².
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to define force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given:
F = 15N
a= 3 m/s²
Now, Force = mass x acceleration
15 = mass x 3
mass = 5Kg
Now, the acceleration is 7 m/s²
F = m x a
F = 3 x 7
F = 21 N
Hence, the force exerted is 21 N.
Learn more about force here:
https://brainly.com/question/13191643
#SPJ2
Find a point E on CD such that the ratio of CE to CD is [tex]\frac{3}{8}[/tex].
Answer:
Sorry if it’s wrong. But I think the answer is: -3
Step-by-step explanation:
Formula:
E= x1 + a/b (x2 -x1)
E=-9 + 3/8(7+9)
E= -9 + 3/8(16)
E= -9 + 6
E= -3
The location of point E will be at negative 3. Then the correct option is C.
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The information is given below.
CE / CD = 3 / 8
CE / ED = 3 / 5 = m / n
Then the location of the point E will be
x = [3 × (7) + 5 × (-9)] / (3 + 5)
x = (21 - 45) / 8
x = - 24 / 8
x = -3
Thus, the location of point E will be at negative 3. Then the correct option is C.
More about the section of the line link is given below.
https://brainly.com/question/6582647
In 3 years Xavier will be 3 times older than Joanne is today. Joanne is 24. How old is Xavier?
Answer: he is currently 69 years old
Step-by-step explanation:
24x3=72-3=69 lol funni number
Answer:
78 years old
Step-by-step explanation:
In 3 years Joanne will be 27. Xavier is 3 times that age by the time Joanne is 27. 27×3=81. but we're looking for Xaviers age today. so we take 81 and subtract 3 which leaves us with 78
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.
In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.
During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:
Finishing
Beginning work-in-process units
26,400
Units transferred in this period
74,800
Units completed & transferred out
79,200
Ending work-in-process units
22,000
Material costs added
$37,400
Conversion costs
$75,460
Transferred-in costs
$141,240
What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.
In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.
During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:
Finishing
Beginning work-in-process units
26,400
Units transferred in this period
74,800
Units completed & transferred out
79,200
Ending work-in-process units
22,000
Material costs added
$37,400
Conversion costs
$75,460
Transferred-in costs
$141,240
What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.
In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.
During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:
Finishing
Beginning work-in-process units
26,400
Units transferred in this period
74,800
Units completed & transferred out
79,200
Ending work-in-process units
22,000
Material costs added
$37,400
Conversion costs
$75,460
Transferred-in costs
$141,240
What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.
In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.
During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:
Finishing
Beginning work-in-process units
26,400
Units transferred in this period
74,800
Units completed & transferred out
79,200
Ending work-in-process units
22,000
Material costs added
$37,400
Conversion costs
$75,460
Transferred-in costs
$141,240
What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
The Moon Company's equivalents units for transferred-in cost, direct materials, and conversion cost are 74,800 / 101,200 / 86,800 respectively.
Data and Calculations:
Percentage of completion:
Beginning work in process = 80%
Ending work in process = 30%
Beginning inventories:
Transferred-in costs = $30,800
Direct materials costs = $13,200
Conversion costs = $27,500
Physical Flows of Units:
Beginning WIP = 26,400
Units transferred in from Cutting Department = 74,800
Total production units available = 101,200 (26,400 + 74,800)
Units completed and transferred out = 79,200
Ending WIP = 22,000
Transferred-in Direct Materials Conversion
Units transferred out 79,200 79,200
(79,200 x 100%)
Units transferred-in 74,800 0 0
(74,800 x 100%)
Ending WIP 0 22,000 (100%) 6,600 (22,000 x 30%)
Total equivalent units 74,800 101,200 86,800
Thus, the equivalent units for the Finishing Department are determined based on the percentage of completion under the Weighted Average Method.
Learn more: https://brainly.com/question/17078653
solve pls brainliest
Answer:
162
Step-by-step explanation:
don't you have calculator app on your phone??
Answer:
bru its it 32 a
Step-by-step explanation:
1.
15% of what number is 45?
Answer:
15% of 300 is 45
Answer:
300
Step-by-step explanation:
What is the slope of the line that passes through the points 10, six and nine, five? Write your answer in simplest form
Answer:
y=x-4
Step-by-step explanation:
If you plug in the points into a graph, you can see that the slope is 1.
You can go down one and the left one, eventually you will find the y-intercept at (0,-4)
A line passes through the points (0,5) and (3,6). What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
Slope intercept form:
y = 1/3x + 5
4/8 x 4/8
i want some friends
answer if you like and comment if you want to be my friend
Answer:
i will be ur friend........ with pleasure
Answer:
1/8
Step-by-step explanation:
Have a good
bye bye
Which of the following fractions is equivalent to 4/20? 2/6 8/16 1/2 3/6 5/10 7/11
Answer:
1/2
Step-by-step explanation:
1. In the end of semester examination, 32% students failed in Economics, Mathematics, 46%in Business, 12% in Economics and Mathematics, 9% Mathematics and Business, 10% in Economics and Business and 3% in all the three. Using Venn diagram, determine, i. Number of students that failed in exactly one course. ii. Number of students that failed in exactly two courses. iii. Number of students who passed in all the three courses. iv. Number of students who failed in at least one course.
(ii) 3% of students failed all three courses, 12% failed economics and mathematics, 9% in math and business, and 10% in econ and business. In other words, the students in these groups failed at least the two mentioned courses. Then 12% - 3% = 9% failed only econ and math but not business; 9% - 3% = 6% failed math and business but not econ; and 10% - 3% = 7% failed econ and business but not math. These groups are mutually exclusive, so the total percentage of students that failed exactly two courses is (ii) 9% + 6% + 7% = 22%.
32% failed econ, which means 32% - 12% - 10% + 3% = 13% failed only econ. Similarly, 46% failed business, so 46% - 9% - 10% + 3% = 30% failed only business. But we don't know how many students failed math, so we can't determine how many failed only math... And consequently we can't determine the proportion of students that make up the other categories.
Please help! Will give brainliest if the answer is correct
Answer:
18+18√3
Step-by-step explanation:
We know that ,
Perimeter = 2(l + b)On substituting ,
P = 2 ( l + b ) P = 2 ( 2 + 5√3 + 7 + 4√3 ) P = 2 ( 9 + √3(5+4)) P = 2 ( 9 + 9√3) P = 18 + 18√3Is it fair to give only 5 points for such a big question?
Answer:
No
Step-by-step explanation:
Because you (or whoever asks) shouldn't give only 5 points to such a big question, because whoever answers the question might have worked really hard to answer it while you just gave them only 5 points...its not worth answering of only 5 points. In my opinion at least ♀️
Hope what I said makes sense :)
Suppose that $590 is deposited into an account that pays 3.5% compounded quarterly. How long will it
will take for the account to contain at least $800? Round to the nearest year.
Answer: 9 years
Step-by-step explanation:
Let 's use the compound interest formula :
[tex]\rm \displaystyle S=A\left( 1+\frac{N}{100} \right)^{\rm \big r}[/tex]
Where N- the percentage by which we raise the price ; r-years ; A-the original price
In our case
N=3,5% ; r=? ; A=590$
And we know :
[tex]\rm \displaystyle S= 800 \\\\ 590 \left( 1+ \frac{3,5}{100} \right)^{\big {r}}=800 \\\\\\(1,035)^{\big r} = \frac{80}{59}\approx1,355 \\\\\\ r= \log_{1,035}\ 1,355=8,\underline831 \approx9 \ years[/tex]
A sales person at a car dealership earns a monthly salary of $2400 and $250 for each vehicle sold
Step-by-step explanation:
8 vehicle.
Step-by-step explanation:
Given: Monthly salary of salesperson is $2400
Incentive of salesperson is $250 per vehicle sold.
First, lets compute income to earned apart from salary.
∴ Deduct salary from the target amount
\$ 4400-\$ 2400= \$ 2000$4400−$2400=$2000
∴ 2000 need to be earned only through incentive, which is2000needtobeearnedonlythroughincentive,whichis250 per vehicle sold.
Now, solving to get number vehicles to be sold to earn $2000 as incentive.
Number of vehicle= \frac{2000}{250}= 8\ vehicles2502000=8 vehicles
∴ 8 vehicles need to be sold by salesperson to get total earning as $4400