Answer:
1)Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Step-by-step explanation:
We need to solve the expressions:
1) [tex]1-2(2x+1)=1-(x-1)\\[/tex]
Solving
[tex]1-2(2x+1)=1-(x-1)[/tex]
First solving the brackets
[tex]1-4x-2=1-x+1[/tex]
Simplifying
[tex]-1-4x=-x[/tex]
Adding 4x on both sides
[tex]-1-4x+4x=-x+4x\\-1=3x[/tex]
Switching the sides
[tex]3x=-1[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=-\frac{1}{3}\\x= -\frac{1}{3}[/tex]
So, Solving the expression [tex]1-2(2x+1)=1-(x-1)[/tex] we get [tex]\mathbf{x=-\frac{1}{3}}[/tex]
2) [tex]3.6x-6.1=5.9-2.4x[/tex]
Solving:
[tex]3.6x-6.1=5.9-2.4x[/tex]
Adding 6.1 on both sides
[tex]3.6x-6.1+6.1=5.9-2.4x+6.1\\3.6x=12-2.4x[/tex]
Adding 2.4x on both sides
[tex]3.6x+2.4x=12-2.4x+2.4x\\6x=12\\[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}=\frac{12}{6}\\x=2[/tex]
So, solving the equation [tex]3.6x-6.1=5.9-2.4x[/tex] we get [tex]\mathbf{x=2}[/tex]
Solve each system .If a system's equations are dependent or if there is no solution,state this .
Please answer!
9514 1404 393
Answer:
(x, y, z) = (-8 2/7, -10, -7 3/7)
Step-by-step explanation:
A graphing calculator or matrix solver can find the solution easily. It is ...
(x, y, z) = (-8 2/7, -10, -7 3/7)
__
You can find y by subtracting the second equation from the third:
(2x -y +z) -(2x -3y +z) = (-14) -(6)
2y = -20
y = -10
Putting this value into the first equation and either of the others gives ...
x -3z = 14
2x +z = -24
Subtracting twice the first of these from the second gives ...
(2x +z) -2(x -3z) = (-24) -2(14)
7z = -52
z = -52/7 = -7 3/7
x = 14 +3(-7 3/7) = -8 2/7
So, the solution is (x, y, z) = (-8 2/7, -10, -7 3/7).
Answer:
Step-by-step explanation:
No Solution!
What is the following quotient?
Answer: Choice B) [tex]\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\[/tex]
==========================================
Work Shown:
[tex]\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\[/tex]
This shows why choice B is the answer.
---------------
Explanation:
In the second step, I multiplied top and bottom by [tex](\sqrt{11}+\sqrt{3})[/tex]This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.So in general, if the denominator is [tex]\sqrt{a}-\sqrt{b}[/tex] and you want to rationalize the denominator, then you should multiply top and bottom by [tex]\sqrt{a}+\sqrt{b}[/tex]. The same applies in reverse as well.
This leads to the denominator becoming [tex](\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b[/tex]
Keep in mind that [tex]a \ge 0[/tex] and [tex]b \ge 0[/tex]
i’m not asking for much :(
Answer:
c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
mcfluffythebigrubberducky
Find the value of x and y. Show all your work neat and
in order.
Answer:
x = 21°
y = 29°
Step-by-step explanation:
a) Solving for x
Note that:
(3x - 3)° and 60° are Alternate interior angles, and alternate interior angles are equal to each other, hence:
3x - 3 = 60° (Alternate interior angles)
Add 3 to both sides
3x - 3 +3 = 60 + 3
3x = 63°
x = 63°/3
x = 21°
b) Solving for y
Notes that:
(3x - 3)° and (4y + 4)° are Consecutive interior angles and the sum consecutive interior angles is 180°
3x - 3 + 4y + 4 = 180°
3x + 4y - 3 + 4 = 180°
3x + 4y + 1 = 180°
Note that x = 21
Hence
3(21) + 4y + 1 = 180°
63 + 1 + 4y = 180°
64 + 4y = 180°
Subtract 64 from both sides
64 - 64 + 4y = 180° - 64
4y = 116°
y = 116/4
y => 29°
In a flower basket, the ratio of red roses to white roses is 2 to 3. There are a total of 20 roses in the basket. How many red roses are in the basket?
Analyze each step to identify if Andy made an error. Yes, he made an error in Step 1. He switched the x and y values. Yes, he made an error in Step 2. He did not distribute StartFraction 3 Over 4 EndFraction properly. Yes, he made an error in Step 3. He should have subtracted 2 from both sides. No, his work is correct.
Answer:
Step 3, because the values for x for which y^1 < y^2 also include values between 3 and 5.
Step-by-step explanation:
Just took the test.
Answer:
c
Step-by-step explanation:
it just is
work out the subtraction equation of 5 1/4 divided by 2 5/7 equals
Answer:
calculater or hackmath
Step-by-step explanation:
f(x) = -2x^3 + 3(x + 2). Does this mean that it's f(3) = -39
Answer:
Step-by-step explanation:
lets replace x with 3
f(3)= -2(3)^3+3(3+2)=-2*27+15=-54+15=-39
Please help me asap
Answer:
She walked 1.5 miles, then 0.75 miles. Hence 1.5 + 0.75= 2.25 or 2 and 1/4 a mileBased on the data given in the..etc help fast
I don't really know but I believe it is:
Rounded to the nearest thousandth, the conditional relative frequency that an eleventh grader likes tennis is 69%.
ROunded to the nearest thousandth, the conditional relative frequency that a twelfth grader likes tennis is 51%.
Since 51% is less than 69%, a greater percent of eleventh grader like tennis.
A shoe store costs 1800 dollars a month to operate. The average wholesale cost of each pair of shoes is 25 dollars, and the average price of each pair of shoes is 65 dollars. How many pairs of shoes must the store sell each month to break even?
Answer: 45
Step-by-step explanation:
The store has to sell
45
pairs of shoes.
Explanation:
The store has a base cost of
$
1800
, the cost per pair of shoes is
$
25
. Each pair of shoes is sold for
$
65
, therefore the profit per pair of shoes is
$
65
−
$
25
=
$
40
The formula for calculating the amount that needs to be sold would look like this;
40
x
=
1800
To determine the value of
x
, we take this formula;
x
=
1800
40
x
=
45
Therefore, the store needs to sell
45
pairs of shoes to break even.
There are 10 triangles and 4 circles. What is the simplest ratio of circles to total shapes?
Answer: 5:2
Step-by-step explanation:
Well, you are going to find a number they both divide by in this case it is 2
10/2=5
4/2=2
Now when rewriting your numbers make sure to put what comes first first
5:2
5 and 2 can not be divided evenly anymore so your final answer is 5:2
Hope this helped!
The number N(t) of people in a community who are exposed to a particular advertisement is governed by the logistic equation. Initially, N(0) = 200,and it is observed that N(1) = 400. Solve for N(t) if it is predicted that the limiting number of people in the community who will see the advertisement is 20,000. (Round all coefficients to four decimal places.)n(t) = ?
9514 1404 393
Answer:
n(t) = 20,000/(1 +99e^(-0.7033t))
Step-by-step explanation:
One way to write the logistic function is ...
n(t) = L/(1 +a·e^(-kt))
where L is the maximum value and parameters 'a' and k depend on boundary conditions.
Here, we have n(∞) = L = 20,000 and n(0) = L/(1+a) = 200. We also have n(1) = L/(1+a·e^-k) = 400.
Solving for 'a', we get ...
n(0) = 20000/(1+a) = 200
20000/200 -1 = a = 99
Solving for k, we get ...
n(1) = 20000/(1 +99e^-k) = 400
20000/400 -1 = 99e^-k = 49
e^-k = 49/99
k = -ln(49/99) ≈ 0.7033
So, the desired function is ...
n(t) = 20000/(1 +99e^(-0.7033t))
What is the equation of the line that crosses the y-axis at 2 and has a unit rate of 8/2
Answer:
Step-by-step explanation:
P1 = (0,2)
M =8/2= 4
y-2=4(x-0)
y-2 = 4x
y= 4x +2
:)
The graph shows the soulution
Answer:
B. (3, -2)
Step-by-step explanation:
The solution of the system of the equations given, can be determined using the graph. The coordinate of the point where the two lines of both equations intersect is the solution.
Both lines intersect at x = 3, when y = -2.
Therefore, the solution would be (3, -2).
the perimeter of a rectangle is 40m. one of the lengths or the sides is 5m. find the lengths of the other 3 sides.
The perimeter of a rectangle is 40m and one side of it is 5m. What is the length of the other side using an equation?
Perimeter of the rectangle =2(l+ b)=40m
If one of its side b=5, then l = (40/2)-5
= 20–5
= 15 m Therefore
Length= 15 cm
Breadth =5 cm
Answer:
perimeter means the total distance of all sides of a shape. Rectangle has 2pairs of 2 sides with the same length. If one is 5 the other pair would be 5. So 40-5-5 would be the total of the second pair , 30. 30/2=15. So there's 2 sides with 5m each, and another 2 sides with 15m each
Allan bought a sweater
for $78 and a shirt for
$29. How much more did
the sweater cost than
the shirt
Answer:
$49
Step-by-step explanation:
78 - 29 = 49
To get 49, I subtracted 29 from 78.
8/12 = 2/9
What is the answer hurry please due today
Answer:
1/3
Step-by-step explanation:
mr johnson is grading english essays hes determined that he must grade 124 essays and that he can grade 8 per day how many days will it take mr johnson to grade all of the english essays
Answer:
16
Step-by-step explanation:
It shows the mulitplication bettween eachother.
I need help, I will give the brainiest
Also, KJL is 54
Answer:
Step-by-step explanation:
Traingle 72 LN
which statement best describes the solution to the system of equations?
Answer:
option a is correct
Step-by-step explanation:
I think
Answer:
D - It has a single solution: x = -3, y = 26.
Step-by-step explanation:
What fractions are equivalent to terminating decimals?
Option B since -7/15 equals -0.4666...
Hope it helps!
PLEASE ANSWER IM DESPERATE
Lincoln bought 3 bottles of an energy drink for $4.50. Write an equation relating the total cost y to the number of energy drinks bought?
Answer:
y=1.50x ...........
Step-by-step explanation:
Let x be the per-bottle price of the energy drink. Then:
3x=y=4.50
x=4.50/3
=1.50
Then:
y=1.50x ...................
A band expects to put 16 songs on their next CD. The band writes and records 50% more songs than
they expect to put on the CD. During the editing process, 62.5% of the songs are removed. How many
songs will there be on the final CD?
Answer: this is wrong there will be 28
Step-by-step explanation:
Answer:
Its 9
Step-by-step explanation:
Evaluate the expression for the given values.
4ab8c, where a = 8, b = 4, and c=12
Enter your answer in the box.
plz halp
Answer:
4ab8c
4(8)(4)(8(12)
(32)(38)(12)
(1216)(12)
14592
Step-by-step explanation:
2x2−3x−4=0 Solve using the quadratic formula.
Answer:
Step-by-step explanation:
2x2−3x−4=0
For this equation: a=2, b=-3, c=-4
2x2+−3x+−4=0
Step 1: Use quadratic formula with a=2, b=-3, c=-4.
x=
−b±√b2−4ac
2a
x=
−(−3)±√(−3)2−4(2)(−4)
2(2)
x=
3±√41
4
The price of a video game was reduced from 60 to 45 . By what percentage was the price of the video game reduced
Answer:
The price was reduced from $60 to $45 - So the price was reduced by $15. $15 is what percent of the original price of $60? Percentages can be expressed as fractions or decimals. For example, 30% is the same as 0.30 or 30/100.
Use the graph to answer the questions help!
Answer:
0; 2; 6; 0 or -1
Step-by-step explanation:
If the question says "f(a)=" they are asking for the y value with the given x such as the two first ones.
If it's "f(x)=a than x=" they are asking you what x is when the (bolded) x is a given value.
what is the area of this trapezoid?
plss help
i will telling you a brainlist!!!
Answer:
30in²
Step-by-step explanation:
A=1/2(4)(5+10)
A=2x15
A=30in²
-12 + 3p = 3
what does p equal
Answer:
p=5
Step-by-step explanation:
Answer:
p = 5
Step-by-step explanation:
-12 + 3p = 3
3p = 3 + 12
= 15
p = 15 ÷ 3
p = 5