Answers
Find the POI.
[tex] \left \{ {{3x+2y=12} \atop {6x+3y=21}} \right. [/tex]
Multiply Equation #1 by 2.
[tex] \left \{ {{2(3x+2y)=2(12)} \atop {6x+3y=21}} \right. [/tex]
[tex] \left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. [/tex]
Eliminate with subtraction.
[tex] \frac{\left \{ {{6x+4y=24} \atop {6x+3y=21}} \right. }{0x+y=3} [/tex]
[tex]y=3[/tex]
Substitute the value of y.
[tex]6x+3y=21[/tex]
[tex]6x+3(3)=21[/tex]
Simplify.
[tex]6x+9=21[/tex]
Add -9 to both sides.
[tex](6x+9)+(-9)=(21)+(-9)[/tex]
[tex]6x=12[/tex]
Divide both sides by 6.
[tex] \frac{6x}{6}= \frac{12}{6} [/tex]
[tex]x=2[/tex]
The Solution/POI is:
[tex](2,3)[/tex]
Hope this helps.
-Benjamin
Related Questions
What is the product of the roots of the equation x^3-4x^2+x+6=0?
Answers
ABC = -r where the equation is written as x^3 + px^2 + qx + r
comparing this to the equation in question:- - r = -6
Answer is -6.
The product of the roots of the equation x³ - 4x² + x + 6 = 0 will be - 6.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ x³ - 4x² + x + 6 = 0
Now,
We know that;
If u, v, w are the roots of the equation ax³ + bx² + cx + d = 0
Then, The product of roots (uvw) = - d / a
Here, The equation is,
⇒ x³ - 4x² + x + 6 = 0
Let the three roots of the equation = a, b, c
Then, We get;
⇒ a × b × c = (-6) / 1
⇒ abc = - 6
Thus, The product of the roots of the equation x³ - 4x² + x + 6 = 0
will be - 6.
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A veterinary office takes out a loan to purchase a new set of digital animal scales that costs $12,250. The interest rate is 6.5%, and the total interest paid is $2,388.75. How many years is the loan for?
Answers
The loan is for approximately 3 years.
Explanation:To find the number of years for the loan, we can use the formula for simple interest:
Interest = Principal * Rate * Time
Given that the principal is $12,250, the rate is 6.5%, and the total interest paid is $2,388.75, we can rearrange the formula to solve for time:
Time = Interest / (Principal * Rate)
Plugging in the values, we get:
Time = 2,388.75 / (12,250 * 0.065)
Simplifying the expression, we have:
Time ≈ 3 years
Change the equation x^2+8x+y^2-12y=12 to graphing form
Answers
Im not sure if this is what your looking for
If a rider stops 15 mile to take a break and Another stops at 25 miles at what distance will they stop at the same time
Answers
multiples of 15: 15,30,45,60,75
multiples of 25: 25, 50, 75
they will stop together at 75 miles
Solve the following for y: 9x − 3y = 18
y = −3x − 6
y = 3x − 6
y = −3x + 6
y = 3x + 6
Answers
Hope I helped love! <3
Which one describes the translation of f(x) to g(x) ?
Answers
Answer:
a
Step-by-step explanation:
PLESSE HELP!! this question is super hard. it’s due tomorrow and i’m not understanding.
Answers
Mitchell has a balance of $1,200 in his first state bank checking account. he deposits a $387.89 pay check, a $437.12 dividend check, and a personal check for $250 into his account. He wants to receive $400 in cash. How much will he gave in his account after the transaction ????
Answers
hope this helps if it does please click the heart and give me five stars
The total present money in his account after all the $400 withdrawals is $1875.01.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Total present money initially = $1200
Deposits check = 387.89 + 437.12 + 250 = $1075.01
Total money after deposit = 1200 + 1075.01 = $2275.01
Money remains after withdrawals of $400
⇒ $2275.01 - $400 = $1875.01.
Hence "The total present money in his account after all the $400 withdrawals is $1875.01".
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List the following numbers from least to greatest -5/3, 7/3, -3/4, 7/5.
Answers
An interior decorator bought 12 1/2 yards of material to make drapes. He used 8 2/3 yards on one pair of drapes. How much material does he have left?
Answers
12 1/2 - 8 2/3
Next would be to change the mixed fractions to improper fractions.
25/2 - 26/3
Now, we need to find a common denomintor, since we can't just subtract like it is now. The Lowest Common Denominator would be 6 because 2*3 = 6. So we need to multiply the numerator and the denominator of both fractions, so that they will have the same denominator.
3( 25/2 ) - 2( 26/3 )
75/6 - 52/6
Now we just subtract the numerators and leave that new answer over the same denominator.
75/6 - 52/6 = 23/6
If it asks to simplify into fraction, we can put it as,
3 5/6
the senior classes at high school A and high school B planned separate trips to the indoor climbing gym. the senior class at high school A rented and filled 13 vans and 5 buses with 353 students. high school b rented and filled 9 vans and 5 buses with 309 students. each van and bus carried the same number of students. find the number of students in each van and in each bus.
Answers
9v + 5b = 309.....multiply by -1
--------------------
13v + 5b = 353
-9v - 5b = -309 (result of multiplying by -1)
-------------------add
4v = 44
v = 44/4
v = 11 <=== a van holds 11 students
9v + 5b = 309
9(11) + 5b = 309
99 + 5b = 309
5b = 309 - 99
5b = 210
b = 210/5
b = 42 <=== a bus holds 42 students
For high school A:
Total number of students = 353 students
number of vans = 13
number of buses = 5 buses
This means that:
13x + 5y = 353 ............> equation I
For high school B:
Total number of students = 309 students
number of vans = 9 vans
number of buses = 5 buses
This means that:
9x + 5y = 309
5y = 309 - 9x ..............> equation II
Substitute with equation II in equation I:
13x + 5y = 353
13x + 309 - 9x = 353
4x = 44
x = 44/4 = 11
Substitute with the value of x in equation II as follows:
5y = 309 - 9x
5y = 309 - 9(11)
5y = 309 - 99
5y = 210
y = 42
Based on the above calculations:
one van can hold 11 students
one bus can hold 42 students
What is the value of g? 3g + 4 5 = 4g - 8 4?
Answers
So, just move like numbers near each other. This way, you get 4g-3g=45-84, which means g= -39.
Answer: g=7
Step-by-step explanation:
The height of a triangle is 4 feet more than four times the length of the base. The area is 24 square feet. Find the base and the height. Show your work and explain the steps you used to find the solution in order to receive full credit.
Answers
H= 4+ 4B
A=24 square feet
Know that the area of a triangle formula is 1/2 x b x h.
A=1/2 x b x h
Plug in the known values and solve for the base.
24= .5 x B x (4+4B)
48=B(4+4B)
48=4B+4B^2
12= B + B^2
0=B^2 + B -12
0=(B+4)(B-3)
B= -4, 3
This solution gives us two answers, so plug both into the formula to find the correct answer.
24=.5 x -4 x (4+4(-4))
48= -4 x (-12)
48=48
24= .5 x 3 x (4+4(3))
48= 3 x (4+12)
48= 3(16)
48=48
It looks like both work, so either answer is correct.
if five more than three times x is equal to 32, find the value of x.
it also says to show all work so that would really be appreciated!!
Answers
-5 -5
3x = 27
/3 /3
x = 9
3x + 5 = 32
Now, let's subtract both sides by 5:
3x + 5 = 32
-5 -5
3x = 27
Now divide both sides by 3
x = 9
Hope this helps!
what is the value of x?
Answers
What surprised or impressed Xuanzang on his visit to India? What features of Indian life might seem most strange to a Chines visitor?
Answers
Actually what surprised Xuanzang the most was the way how Indians ran things and their way of life because this is completely unlike to Chinese cultures. The strangest thing he found was that how everyone in India practiced Buddhism and how structured it was. Because back in China at that time, Buddhism was still much unorganized and not very popular.
30 points to who answers this first and will get brainliest answer
In which quadrant of the coordinate graph does point J lie?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
Answers
Determine the range of this set of data.
89,73,84,91,87,77,94
Answers
94+73= 167
Divide 167 by 2 because you added only 2 numbers
167 divided by 2 is 83.5
So your answer is 83.5 or 84 if you want to round it up
When is the sum of two complex numbers a real number? When is the sum of two complex numbers an imaginary number?
Answers
w = a+bi
z = c+di
where a,b,c,d are real numbers and i = sqrt(-1)
---------------------------
When is w+z purely real? When there is no imaginary part at all. Adding w and z gives
w+z = (a+bi) + (c+di)
w+z = (a+c) + (bi+di)
w+z = (a+c) + (b+d)i
The imaginary part here is (b+d)i. If we set it equal to zero, then we get
(b+d)i = 0
b+d = 0
b = -d
So if b = -d, then w+z is purely real. For instance, if w = 2+3i and z = 7-3i then
w+z = (2+3i)+(7-3i) = (2+7)+(3-3)i = 9+0i = 9
The result 9 being purely real without any imaginary part.
--------------------------
When is w+z purely imaginary? We'll follow the same path of logic but instead of setting the imaginary part to zero, we do that to the real part
Again,
w+z = (a+bi) + (c+di)
w+z = (a+c) + (bi+di)
w+z = (a+c) + (b+d)i
Set the real part (a+c) equal to zero and solve for zero
(a+c) = 0
a+c = 0
a = -c
When a = -c, then the sum of the complex numbers is purely imaginary
Example:
w = 9+12i
z = -9-14i
w+z = (9+12i)+(-9-14i)
w+z = (9-9)+(12i-14i)
w+z = (9-9)+(12-14)i
w+z = (0)+(-2)i
w+z = -2i
which is purely imaginary (with no real parts)
--------------------------
Both cases are very similar: if the corresponding values are equal but opposite, then we have cancellations to go from complex to purely real or purely imaginary. Depending of course on which values you set opposite.
The exception is that if a = -c and b = -d together, then w+z = 0 is purely real
The sum of two complex numbers resulting in a real or imaginary number depends on the cancellation of their real or imaginary components upon addition.
When the sum of two complex numbers is a real number: For the sum of two complex numbers to be a real number, their imaginary parts must cancel each other out. This happens when the imaginary parts have equal magnitude but opposite signs, resulting in the cancellation upon addition.
When the sum of two complex numbers is an imaginary number: The sum of two complex numbers is an imaginary number when the real parts cancel each other out. This occurs when the real parts have equal magnitude but opposite signs, leading to the elimination of the real components.
Len and three of his friends decide to rent a house and split the cost evenly. They each paid $725 towards the total move-in cost of first month's rent, last month's rent, and a security deposit. If rent is $800 per month, how much was the security deposit?
a.
$575
b.
$725
c.
$1,300
d.
$2,100
Answers
Answer:
its 1300
Step-by-step explanation:
When Angela begins her drive, she is 400 mi from home. She drives at an average of 50 mph until she gets home. Graph the situation.
Answers
PLZ HELP
Lakita has 65 water bottles for the 5K race participants. In addition, she is considering buying boxes of water bottles that have 16 water bottles each. All of the boxes cost the same. Lakita can buy up to 5 boxes of water bottles given the amount of money she has. Let x represents the number of boxes of water bottles Lakita buys. Write a function rule to describe how many water bottles Lakita will have based on the number of boxes she buys. Find a reasonable range for the function.
A - f(x) = 65x + 16
{145}
B - f(x) = 16x + 65
{65, 81, 97, 113, 129, 145}
C - f(x) = 65x + 16
{81, 97, 113, 129, 145}
D - f(x) = 16x + 65
{65, 81, 97, 113, 129}
Answers
The function rule representing the total number of bottles Lakita will have based on the number of boxes she buys would be f(x) = 16x + 65. The reasonable range for this function, considering she can buy up to 5 boxes, is {65, 81, 97, 113, 129, 145}.
Explanation:In this problem, we want to find out the total number of water bottles Lakita will have based on the number of boxes she buys. We know that Lakita already has 65 water bottles and each box she buys contains 16 water bottles. The function rule to represent this would be: f(x) = 16x + 65. Here, x is the number of boxes she buys.
The range of the function is the possible values that f(x) can have based on the scenario. Since Lakita can buy up to 5 boxes, the range would be the number of bottles she will have if she buys 0 through 5 boxes, which is: {65, 81, 97, 113, 129, 145}.
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The function rule to describe the number of water bottles is f(x) = 16x + 65. The range for the function is {65, 81, 97, 113, 129, 145}, which represents the total water bottles counts depending on the number of boxes Lakita buys.
Explanation:The function that will describe how many water bottles Lakita will have based on the number of boxes she buys is f(x) = 16x + 65. To explain, x represents the number of boxes, each with 16 water bottles (16x), and the 65 represents the water bottles she initially has. The total number of water bottles is the sum of these two amounts.
A reasonable range for the function is the set of all possible total water bottles counts, depending on the number of boxes bought. As she can buy up to 5 boxes, we substitute values from 0 to 5 into the function to find the range. So the range will be {65, 81, 97, 113, 129, 145}, corresponding to Lakita buying 0, 1, 2, 3, 4, or 5 boxes (respectively).
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How many atoms are there in 2.50 mol of carbon dioxide? complete the response using standard scientific notation?
Answers
In this question, the carbon dioxide unit is already in mol so you don't need to find the molecular weight of the carbon dioxide. Carbon dioxide chemical formula would be CO2 which means every 1 carbon dioxide molecule is made of 3 atoms, 1 carbon atom and 2 oxygen atoms.
Then, the number of atoms in 2.5 mol of carbon dioxide would be:
2.5 mol * 3 * 6.02 *10^23 atoms/mol =
45.15 * 10^23 =
4.52 * 10^24 atoms
Tracy deposited $59 into a bank account that earned 3.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 112 years?
Answers
HELP ASAP 30 POINTS GIVEN
The coordinates of the vertices of quadrilateral JKLM are J(−3, 2), K(4, −1), L(2, −5), and(−5, −2). Drag and drop the choices into each box to correctly complete the sentences.
Answers
The slope of LK is 2
The slope of ML is -3/7
The slope of MJ is 2
Quadrilateral JKLM is a parallelogram because both pairs of opposite sides are parallel. YOU'RE WELCOME :D
Answer:
[tex]-\frac{3}{7}[/tex],[tex]2[/tex],[tex]-\frac{3}{7}[/tex],[tex]2[/tex],is,both pairs of opposite sides are parallel
Step-by-step explanation:
Given two points
[tex]A=(a1,a2)[/tex] and
[tex]B=(b1,b2)[/tex]
We define the slope ''m'' between this points as :
[tex]m=\frac{b2-a2}{b1-a1}[/tex] or either
[tex]m=\frac{a2-b2}{a1-b1}[/tex]
The slope between the points J and K is
[tex]m=\frac{-1-2}{4-(-3)}=-\frac{3}{7}[/tex]
The slope between the points L and K is
[tex]m=\frac{-1-(-5)}{4-2}=2[/tex]
The slope between the points M and L is
[tex]m=\frac{-2-(-5)}{-5-2}=-\frac{3}{7}[/tex]
The slope between the points M and J is
[tex]m=\frac{-2-2}{-5-(-3)}=2[/tex]
We find all the slopes between the points.
For the quadrilateral JKLM the side JK is opposite to the side ML and the side KL is opposite to the side JM
The definition of parallelogram is :
A figure with 4 sides in which their opposite sides are parallel.
The side JK is parallel to the side ML because they have the same slope.
The side JM is parallel to the side KL because they have the same slope.
We answer that JKLM is a parallelogram because both pairs of opposite sides are parallel.
(04.07)the balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
Answers
The balance in two separate bank accounts grows each month at different rates. the growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12. in what month is the f(x) balance greater than the g(x) balance?
Answer:
6 months
If growth rates for both accounts are represented by the functions f(x) = 2x and g(x) = 4x 12 thn in 6 months the f(x) balance is greater than the g(x) balance.
What type of financial institution account grows?excessive-yield financial savings accounts stand out from conventional financial savings bills in that they praise you with a better interest rate, permitting your cash to grow even quicker as it sits on your account. The interest charge that these debts provide is noted as APY or annual percentage yield.
What account grows the most cash?fees and minimal balance: CDs tend to pay the very best hobby prices of the 3 varieties of savings bills. They commonly require around $1,000 to open, but there are CDs without a minimum beginning balance requirement. CDs typically don't rate a month-to-month rate.
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How is a rational number that is not an integer different from a rational number that is an integer?
Answers
Real numbers can either be rational or irrational. ... A rational number is a numberwhich can be written as a ratio of two whole numbers (integers). For example 5 is arational number since 5 can be written as ratio of 5 : 1 . 5 is also an integer. 2.5 is arational number since it is a ratio of 5 : 2 .
Hope it helps :)
dora gets paid an hourly wage, which increases if she works over 40 hours per week. she worked a total of h hours last week, and the number of dollars she got paid was 30 ×40+45 ×(h-40). what does 45 represent in this situation?
A. the number of dollars per hour she got paid for all hours under 40
B. the number of dollars per hour she got paid for all hours over 40
C. the number of hours she worked over 40
D. the total number of hours she worked
Answers
let me try to explain this...
the 30 * 40 is saying that she normally gets paid $ 30 per hr for 40 hrs
the (h - 40) is the number of hrs after 40 hrs
the 45 is saying that for any hrs after 40 hrs, she gets paid $ 45 per hr
so ur answer is : B. the number of dollars per hr she got paid for all hrs over 40.
I hope this helps and have a wonderful day filled with joy!!
ASAP HELP FOR NUMBER 13!!
13a, b, c, and d!!
CORRECT ANSWERS PLS
THANK U GUYS SO MUCH!!!
Answers
Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.
Another point on this line is (3,8) which is drawn from the second column.
Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2
Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2
Plug those into y = mx+b and we get y = 2x+2
Answer: y = 2x+2
==============================================
Problem 13b
(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20
Another point on this line is (3,8) as drawn from the second column
Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4
Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20
Answer: y = -4x+20
==============================================
Problem 13c
(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.
Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5
Note: the fraction 3/2 is equivalent to the decimal form 1.5
Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2
So we can now update y = mx+b to y = 1.5x+2
Answer: y = 1.5x+2
Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write [tex]y = \frac{3}{2}x+2[/tex]
==============================================
Problem 13d
(0,20) is on the line. So the y intercept is 20, indicating that b = 20
(3,11) is also on the line
Again as done with 13a-13c, I'm only looking at the first two columns.
Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3
Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier
Answer: y = -3x+20
A storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 20 feet with a hemisphere attached to each end. determine the radius x so that the resulting volume is 216π ft3.
Answers
V = (π)(r^2)(h) where
V = right circular cylinder volume
π = the constant pi
r = radius
h = height or altitude
With a hemisphere on each end, if I calculate the volume of a sphere, that will include both hemispheres. So the volume of a sphere =
V = (4/3)(π)(r^3) where
V = sphere volume
π = the constant pi
r = radius
So the total volume of the entire propane gas storage tank =
Vt = volume of cylinder + 2(volume of hemishere)
Vt = volume of cylinder + volume of sphere
Vt = (π)(r^2)(h) + (4/3)(π)(r^3)
216π = (π)(r^2)(20) + (4/3)(π)(r^3)
Divide both sides by π to eliminate it.
216 = 20r^2 + (4r^3)/3
Multiply both sides of the equal sign by 3 to eliminate the denominator.
648 = 60r^2 + 4r^3
Factor a common 4 from the right side of the equal sign.
648 = 4(15r^2 + r^3)
162 = (15r^2 + r^3)
r = 3
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. We can set up a cubic equation to find the value of r, and then calculate the radius x.
To determine the radius x of the storage tank, we need to break down the shape into smaller parts. First, let's consider the cylinder. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the altitude. In this case, the altitude is 20 feet. So, the volume of the cylinder is Vcylinder = πr^2(20).
Next, let's consider the hemispheres attached to each end. The volume of a hemisphere is given by V = (2/3)πr^3. Since there are two hemispheres, the total volume of the hemispheres is Vhemispheres = (2/3)(2)(πr^3) = (4/3)πr^3.
Given that the resulting volume is 216π ft3, we can set up the equation:
216π = Vcylinder + Vhemispheres = πr^2(20) + (4/3)πr^3
Simplifying and rearranging the equation, we get:
3r^3 + 60r^2 - 216 = 0
By solving this cubic equation, we can find the value of r. Once we have the value of r, we can determine the radius x by subtracting the radius of the hemispheres (r) from the total radius of the tank (x+r).
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