To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.
Explanation:To solve the system of linear equations:
6x + 20y = -62
3x - 9y = -12
We can use the method of substitution:
From the first equation, solve for x: x = (-62 - 20y) / 6Substitute the value of x into the second equation: 3((-62 - 20y) / 6) - 9y = -12Simplify and solve for y:After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.
Mrs. Milleman looked at another hotel. She waited a week before she decided to book nights at that hotel, and now the prices have increased. The original price was $1195. The price for the same room and same number of nights is now $2075. What is the percent increase? Round to the nearest whole percent.
Every two years, a manufacturer's total yearly sales decline 20%. She sells 400 total units in her first year. Rounded to the nearest unit, how many total units will she sell her ninth year?
146.54 units are the total units will she sell her ninth year.
Here, we have,
periodic exponential decay is:
[tex]A = I(1-r)^{t/p}[/tex]
where,
A = amount
I = initial amount
r = rate
t = time
p = period
we know, the first year she sold 400 units,
thus year 0, 400 units, t = 0, A = 400.
so, we get,
periodic exponential decay is:
[tex]A = I(1-r)^{t/p}[/tex]
=> 400 = I × 1
=> 400 = I
therefore then, when, rate = 20 %
we get,
periodic exponential decay is:
[tex]A = I(1-r)^{t/p}[/tex]
[tex]= > A = 400(1-0.2)^{t/2}[/tex]
now, how many units will it had decreased by the 9th year? t = 9
so, we get,
[tex]= > A = 400(1-0.2)^{9/2}[/tex]
=> A = 146.54
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what is the answer of 9X23+3X39-28=n
Answer: n=296
Step-by-step explanation: 9 x 23 + 3 x 39 - 28 + n = 296
Hope this helps! <3
What's 24.67 to one significant figure?
Use the chain rule to find dw/dt. w = xey/z, x = t7, y = 4 − t, z = 2 + 9t
The derivative[tex]\( \frac{dw}{dt} \) is \( \frac{7t^6 e^{4-t}}{2+9t} - \frac{t^7 e^{4-t}}{2+9t} - \frac{9t^7 e^{4-t}}{(2+9t)^2} \).[/tex]
To find [tex]\( \frac{dw}{dt} \)[/tex] using the chain rule for the given function[tex]\( w = \frac{x e^y}{z} \), where \( x = t^7 \), \( y = 4 - t \), and \( z = 2 + 9t \)[/tex], follow these steps:
1. **Express ( w ) in terms of ( t ):**
Substitute ( x ), ( y ), and ( z ) into ( w ):
[tex]\[ w = \frac{x e^y}{z} = \frac{(t^7) e^{(4 - t)}}{2 + 9t} \][/tex]
2. **Apply the chain rule:**
The chain rule states that for a function ( w(t) ) defined implicitly by ( w = f(x(t), y(t), z(t)) ), the derivative [tex]\( \frac{dw}{dt} \)[/tex] is given by:
[tex]\[ \frac{dw}{dt} = \frac{\partial w}{\partial x} \cdot \frac{dx}{dt} + \frac{\partial w}{\partial y} \cdot \frac{dy}{dt} + \frac{\partial w}{\partial z} \cdot \frac{dz}{dt} \][/tex]
3. **Compute partial derivatives of ( w ) with respect to ( x ), ( y ), and ( z ):**
[tex]\( \frac{\partial w}{\partial x} = \frac{e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial y} = \frac{x e^y}{z} \)[/tex]
[tex]\( \frac{\partial w}{\partial z} = -\frac{x e^y}{z^2} \)[/tex]
4. **Compute [tex]\( \frac{dx}{dt} \), \( \frac{dy}{dt} \), and \( \frac{dz}{dt} \):**[/tex]
[tex]\( \frac{dx}{dt} = 7t^6 \)[/tex]
[tex]\( \frac{dy}{dt} = -1 \)[/tex]
[tex]\( \frac{dz}{dt} = 9 \)[/tex]
5. **Substitute these into the chain rule formula:**
[tex]\[ \frac{dw}{dt} = \frac{e^y}{z} \cdot 7t^6 + \frac{x e^y}{z} \cdot (-1) + \left(-\frac{x e^y}{z^2}\right) \cdot 9 \][/tex]
6. **Substitute[tex]\( x = t^7 \), \( y = 4 - t \), \( z = 2 + 9t \)[/tex] into the expression:**
[tex]\( e^y = e^{4 - t} \)[/tex]
Substitute these values into the formula for [tex]\( \frac{dw}{dt} \):[/tex]
[tex]\[ \frac{dw}{dt} = \frac{e^{4 - t}}{2 + 9t} \cdot 7t^6 - \frac{t^7 \cdot e^{4 - t}}{2 + 9t} - \frac{9t^7 \cdot e^{4 - t}}{(2 + 9t)^2} \][/tex]
Therefore, [tex]\( \frac{dw}{dt} \)[/tex] is:
[tex]{\frac{dw}{dt} = \frac{7t^6 e^{4 - t}}{2 + 9t} - \frac{t^7 e^{4 - t}}{2 + 9t} - \frac{9t^7 e^{4 - t}}{(2 + 9t)^2} } \][/tex]
A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form? A=–n2 + 3n + 5 B=n2 + 6n + 1 C=2n2 + 6n – 1 D=3n2 + 5
Answer:
B
Step-by-step explanation:
What is the answer to the problem below?
Solve the system of equations graphically.
x=3
y=4
What can be used as a reason in a two-column proof?
Select each correct answer.
conjecture
postulate
definition
premise
Answer:
Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.
Therefore, what can be used as a reason in a two-column proof are:
Postulates
Definitions
The five-number summary for scores on a statistics test is 11, 35, 61, 70, 79. in all, 380 students took the test. about how many scored between 35 and 61
Answer: There are 95 students who scored between 35 and 61.
Step-by-step explanation:
Since we have given that
The following data : 11,35,61,70,79.
So, the median of this data would be = 61
First two data belongs to "First Quartile " i.e. Q₁
and the second quartile is the median i.e. 61.
The last two quartile belongs to "Third Quartile" i.e. Q₃
And we know that each quartile is the 25th percentile.
And we need "Number of students who scored between 35 and 61."
So, between 35 and 61 is 25% of total number of students.
So, Number of students who scored between 35 and 61 is given by
[tex]\dfrac{25}{100}\times 380\\\\=\dfrac{1}{4}\times 380\\\\=95[/tex]
Hence, There are 95 students who scored between 35 and 61.
The number of students who scored between 35 and 61 is 95
The 5 number summary is the value of the ;
Minimum Lower quartile Median Upper quartile and Maximum values of a distribution.The total Number of students = 380
The lower quartile (Lower 25%) = 35
The median (50%) = 61
The Number of students who scored between 35 and 61 : 50% - 25% = 25%This means that 25% of the total students scored between 35 and 61.
25% of 380 = 0.25 × 380 = 95Hence, 95 students scored between 35 and 61.
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605 mi in 11 hours at the same rate how many miles would he drive in 13 hours
Determine whether the function f : z × z → z is onto if
a.f(m,n)=m+n. b)f(m,n)=m2+n2.
c.f(m,n)=m.
d.f(m,n) = |n|.
e.f(m,n)=m−n.
D is the midpoint of CE.E has coordinates (-3,-2), and D has coordinates (2 1/2, 1). Find the coordinate of C.
The coordinate of point C on line CE will be (8, 4).
What is Coordinates?
A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Given that;
D is the midpoint of CE.
E has coordinates (-3,-2), and D has coordinates (2 1/2, 1).
Now, By the definition of midpoint;
Let the coordinate of point C = (x, y)
Then,
((x + (-3))/2 , (y + (-2))/2) = (2 1/2, 1)
By comparison we get;
x + (-3) / 2= 2 1/2
x - 3 = 2 (5/2)
x - 3 = 5
x = 3 + 5
x = 8
And, (y + (-2))/2 = 1
y - 2 = 2
y = 2 + 2
y = 4
Thus, The coordinate of point C = (x, y) = (8, 4)
So, The coordinate of point C on line CE will be (8, 4).
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$185 DVD player 6% markup
Round 5836197 to the nearest hundred
Answer:
5836200.
Step-by-step explanation:
Given : 5836197 .
To find : Round 5836197 to the nearest hundred.
Solution : We have given 5836197
Step 1 : First, we look for the rounding place which is the hundreds place.
Step 2 : Rounding place is 97.
Step 3 : 97 is greater than 50 then it would be rounded up mean next number to 97 would be increase to 1 and 97 become 00.
Step 4 : 5836200.
Therefore, 5836200.
Find a solution x = x(t) of the equation x′ + 2x = t2 + 4t + 7 in the form of a quadratic function of t, that is, of the form x(t) = at2 + bt + c, where a, b, and c are to be determined.
To find a, b, c for the solution:
Let's start by writing down the expression for the function x(t) and its derivative:
We have:
x(t) = at² + bt + c
and
x'(t) = 2at + b
Using x' and x into the differential equation x′ + 2x = t² + 4t + 7 gives us:
2at + b + 2*(at² + bt + c) = t² + 4t + 7
Expanding this gives:
2at² + 2bt + b + 4at + 2c = t² + 4t + 7
By equating the coefficients of equivalent powers of t on both sides, we get three equations:
For t² :
2a = 1
So, a = 1/2
For t:
2b + 4a = 4
Substitute a = 1/2 into the equation gives b = 1 - 2 = -1
For the constant term:
b + 2c = 7
Substituting b = -1 gives c = 4.
So the solution is a = 1/2, b = -1, c = 4.
So the specific solution of this differential equation is given by x(t) = (1/2)t² - t + 4.
The perpendicular bisector of side AB of ∆ABC intersects side BC at point D. Find AB if the perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
Answer:
Hence, AB=12.
Step-by-step explanation:
We are given that the perpendicular bisector of side AB of ∆ABC intersects side BC at point D.
this means that side AE=BE.
Also we could clear;ly observe that
ΔBED≅ΔAED
( since AE=BE, side ED common, ∠BED=∠AED
so by SAS congruency the two triangles are congruent)
Now we are given that:
the perimeter of ∆ABC is 12 cm larger than the perimeter of ∆ACD.
i.e. AB+AC+BC=AC+AD+CD+12
AB+BC=AD+CD+12
as AD=BD
this means that AD+CD=BD+CD=BC
AB+BC=BC+12
AB=12
Hence AB=12
Answer:
The required length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
Step-by-step explanation:
Given: The perpendicular bisector of side [tex]AB[/tex] of [tex]\bigtriangleup{ABC}[/tex] intersects side [tex]BC[/tex] at point [tex]D[/tex] and the perimeter of [tex]\bigtriangleup{ACD}[/tex].
From the figure,
[tex]AE=BE[/tex] .......(1) (as [tex]DE[/tex] is perpendicular bisector of side [tex]AB[/tex])
Now, In [tex]\bigtriangleup{BED}[/tex] and [tex]\bigtriangleup{AED}[/tex]
[tex]AE=BE[/tex] ( from equation 1 )
[tex]\angle {BED} =\angle {AED}[/tex] ( Both [tex]90^\circ[/tex] )
[tex]ED=ED[/tex] ( Common side)
[tex]\bigtriangleup{BED}\cong\bigtriangleup{AED}[/tex] ( by SAS congruence rule)
[tex]BD=AD[/tex] .........(2) (by CPCT)
As per question,
The perimeter of ∆ABC is with 12 cm larger than the perimeter of ∆ACD.
[tex]AB+BC+AC=AC+CD+AD+12[/tex]
[tex]AB+BC=AD+CD+12\\AD+CD=BD+CD\\AB+BC=BC+12\\[/tex]
[tex]AB=12\rm\;{cm}[/tex]
Hence, the length of [tex]AB[/tex] is [tex]12\rm\;{cm}[/tex].
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The diagram represents a reduction of a triangle by using a scale factor of 0.8.
What is the height of the reduced triangle?
4.0 inches
4.8 inches
5.2 inches
7.5 inches
The reduction factor of 0.8 means the lengths in the reduced triangle are 0.8 times those of the original.
Then the original 6 inch length is reduced to 0.8×6 inches = 4.8 inches in the reduced triangle.
Answer:
4.8 inches
Step-by-step explanation:
The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:
6 inches * scale factor
6 inches* 0.8= 4.8 inches
So the resultant triangle will have a height of 4.8 inches.
What is the completely factored form of x3 – 64x? x(x – 8)(x – 8) (x-4)(x2+4x+16) x(x – 8)(x + 8) (x – 4)(x + 4)(x + 4)
After factoring x from both terms, you can factor the difference of two squares.
= x(x² -64)
= x(x -8)(x +8)
_____
It is worth remembering the "speciall form" that is the difference of two squares:
... a² - b² = (a -b)(a +b)
Answer:
x(x -8)(x +8)
Step-by-step explanation:
how can I adjust a quotient to solve a division problem
write a fraction less than 1 with a denominator of 6 that is greater than 3/4
Answer:= 5/6
Step-by-step explanation:hope this helps
4r+3=r+21
How do I do this?
If the radius of a circle measures 2 inches, what is the measure of its diameter?
what 5x(4+gy) if x= 1 g= 20 Y=14
please show work
"unable to determine because x can't take on the value 5.5"
How do you figure out what 1/10 of 1,7000.000 km squared is?
Suppose you have two credit cards. The first has a balance of $415 and a credit limit of $1,000. The second has a balance of $215 and a credit limit of $750. What is your overall credit utilization?
Compute for the total balance:
total balance = $415 + $215 = $630
Then we compute for the total credit limit:
total credit limit = $1,000 + $750 = $1,750
The credit utilization would simply be the percentage ratio of total balance over total credit limit. That is:
credit utilization = ($630 / $1,750) * 100%
credit utilization = 36%
15 children voted for their favorite color. The votes for red and blue together we're double the votes for green and yellow together. How did the children vote?
What is the expanded notation for 2.918?
Given sina=6/7 and cosb=-1/6, where a is in quadrant ii and b is in quadrant iii , find sin(a+b) , cos(a-b) and tan(a+b)
sin(a+b) = -1/7 +√455/42 = 0.8721804464845457
cos(a-b) = √13/42 - √35/7 = -0.7761476987942811
tan(a+b )= (6√13/13 + √35) / (1 - 6√455/13) = -0.525
Given sin(a) = 6/7 and cos(b) = -1/6, with a in quadrant II and b in quadrant III, we need to utilize trigonometric identities to find sin(a+b), cos(a-b), and tan(a+b).
Firstly, since a is in quadrant II, cos(a) is negative. We use the identity sin²(a) + cos²(a)=1 to find cos(a):
cos(a) = -√(1 - sin²(a)) = -√(1 - (6/7)²) = -√(1 - 36/49) = -√(13/49) = -√13/7Similarly, since b is in quadrant III, sin(b) is also negative. We use the identity sin²(b) + cos²(b)=1 to find sin(b):
sin(b) = -√(1 - cos²(b)) = -√(1 - (-1/6)²) = -√(1 - 1/36) = -√(35/36) = -√35/6Now we can use the angle addition and subtraction formulas:
1. sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin(a + b) = (6/7)(-1/6) + (-√13/7)(-√35/6) = -1/7 + √(13×35)/(7×6) = -1/7 + √455/42 = -1/7 +√455/422. cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
cos(a - b) = (-√13/7)(-1/6) + (6/7)(-√35/6) = √13/(7×6) - (6√35)/(7×6) = √13/42 - √35/73. tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
Using tan(a) = -sin(a)/cos(a) = -(6/7)/(-√13/7) = 6/√13 and tan(b) = sin(b)/cos(b) = (-√35/6)/(-1/6) = √35:tan(a + b) = (6/√13 + √35) / (1 - (6/√13)(√35)) = (6√13/13 + √35) / (1 - 6√455/13)What is the unit rate for 822.6 km in 18 hours? Enter your answer, as a decimal, in the box. Please Help