Answer: Equations (b) and (e) do not have solutions
Step-by-step explanation: b) The x cancels out (-10x + 35) = -10x + 318; 35 = 318???? NO. e) 3(x + 2) + 1 = x + 2(4 + x); 3x + 7 = 3x + 8. The x cancels out again.
The other s can be solved for x.
Hi! I'm happy to help!
To solve this, we need to simplify all of the equations. There are 3 ways equations like this can go, infinitely many solutions, 1 solution, or no solution. Infinitely many is something like 6=6, that could mean infinite solutions because 6 always equal 6, and would apply in infinitely many ways. (in the equation) One solution refers to something like x=6. This tells your exactly what x is, and that is your only solution. (for the equation) And no solution is something like 5=6, 5 will never equal 6, so that is no solution. (to the equation)
Now, let's start out with our first equation. To find if our equations have solutions or not, we need to simplify them. We do this by singling out x to see what the solution is (if there is one).
x-9=2(x-3)+12
We can multiply 2, by x and -3 inside of the parenthesis, to simplify:
x-9=2x-6+12
Since we have at least one x on both sides, we can subtract it to isolate it:
x-9=2x-6+12
-x -x
-9=x-6+12
Combine -6 and twelve:
-9=x-6+12
-9=x+6
Now, we subtract 6 to fully isolate x:
-9=x+6
-6 -6
-15=x
We see we have 1 solution, so you should not pick option 1.
Second equation:
5(-2x + 7) + 3 = -10x + 38
We should first multiply the parenthesis:
-10x+35+3=-10x+38
Since we want to simplify, let's add 10x on both sides
-10x+35+3=-10x+38
+10 +10x
35+3=38
Add 35 and 3:
38=38
Since 38 will always equal 38, there are infinite solutions, and you should not pick option 2.
Third equation:
(6x - 4) = 3(x - 2)
Since there is nothing outside of the parenthesis (right side), we don't need them:
6x-4=3(x-2)
From here, multiply the parenthesis:
6x-4=3x-6
Subtract 3x from both sides:
6x-4=3x-6
-3x -3x
3x-4=-6
Add 4 to both sides to isolate x:
3x=-2
Divide both sides by 3, to fully isolate x:
x=-[tex]\frac{2}{3}[/tex]
Since there is only 1 solution, you should not pick option 3.
Fourth equation: (not sure if the 100 is supposed to be there)
0.01x + 0.001 = (x + 10)
First, let's subtract 0.01x from both sides:
0.001=9.99x+10
Then, we subtract 10 from both sides to start isolating x:
-9.999=9.99x
Then, we divide both sides by 9.99:
______
1.000900900=x
Kind of a weird number, but regardless, you should not pick option 4, because it has 1 solution.
Fifth equation:
3(x + 2) + 1 = x + 2(4 + x)
First, let's multiply the parenthesis on both sides:
3x+6+1=x+8+2x
Combine like terms:
3x+7=3x+8
Subtract 3x from both sides:
7=8
7 will never equal 8, there will be no solution, and you should pick option 5.
You should pick option e, because it has no solution.
I hope this was helpful, keep learning! :D
please answer this question
Step-by-step explanation:
all steps are in picture
Part A
The formula for the volume V of a cylinder is V = πr2h, where r is the radius of the base and h is the height of the cylinder. Solve the formula for h.
Choose the correct formula.
A. h=Vπr2
B. h=Vπr2
C. h=Vr2π
D. h=Vπr2
Part B
Find the height of a cylinder with a volume of 36π cm3 and a base with a radius of 3 cm.
h =
cm
Answer:
Part A. [tex]h=\frac{V}{\pi r^2}[/tex]
Part B. h= 4cm
Step-by-step explanation:
I need some help with the homework problem. I have a list of formulas, but can't seem to get it done.
[tex]\int\frac{9}{\sqrt{1+e^{2x}}} \, dx[/tex]
I started by taking the constant out and setting u = [tex]\sqrt{1+e^{2x\\}}[/tex]
After this I can't seem to progress.
After setting [tex]u=\sqrt{1+e^{2x}}[/tex], partially solving for x in terms of u gives
[tex]u = sqrt{1+e^{2x}} \implies u^2 = 1 + e^{2x} \implies e^{2x} = u^2 - 1[/tex]
Then taking differentials, you get
[tex]2 e^{2x} \,\mathrm dx = 2u \, \mathrm du \implies \mathrm dx = \dfrac{u}{u^2-1}\,\mathrm du[/tex]
Replacing everything in the original integral then gives
[tex]\displaystyle \int \frac9{\sqrt{1+e^{2x}}}\,\mathrm dx = \int \frac9u \times \frac u{u^2-1}\,\mathrm du = 9 \int \frac{\mathrm du}{u^2-1}[/tex]
Split up the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac a{u-1} + \dfrac b{u+1} \\\\ 1 = a(u+1) + b(u-1) = (a+b)u + a-b \\\\ \implies \begin{cases}a+b=0\\a-b=1\end{cases} \implies a=\dfrac12,b=-\dfrac12[/tex]
so that
[tex]\displaystyle 9 \int \frac{\mathrm du}{u^2-1} = \frac92 \int \left(\frac1{u-1} - \frac1{u+1}\right) \,\mathrm du \\\\ = \frac92 \left(\ln|u-1| - \ln|u+1|\right) + C \\\\ = \frac92 \ln\left|\frac{u-1}{u+1}\right| + C \\\\ = \frac92 \ln\left(\frac{\sqrt{1+e^{2x}}-1}{\sqrt{1+e^{2x}}+1}\right) + C[/tex]
Given f(x) = x − 7 and g(x) = x2 .
Find g(f(4)).
g(f(4)) =
]
9514 1404 393
Answer:
g(f(4)) = 9
Step-by-step explanation:
Put the argument value where the variable is and do the arithmetic.
g(f(4)) = g(4 -7) = g(-3) = (-3)^2
g(f(4)) = 9
If f(x, y, z) = z sin (xy), find the rate of change of f at the point P(0, 0, 2) in the direction from P to Q(3, 0, 0)
Answer:
0
Step-by-step explanation:
We are looking for the directional derivative of f at P in the direction of PQ.
First we compute
[tex]\nabla f=\langle yz\cos(xy),zx\cos(xy),\sin(xy)\rangle\\\nabla f(0,0,2) =\langle 0,0,0\rangle[/tex]
But if we dot any vector to the zero vector we always get 0. So the rate of change is zero.
Complete the following equation using <, >, or =
7 _ 24/4
A. =
B. >
C. <
Answer:
7 > 24/4
Step-by-step explanation:
7 _ 24/4
Simplify 24/4
24/4 = 6
7 is greater than 6
7 > 24/4
7 is greater than the fraction 24/4 so we use the ">" symbol between them. Hence, the complete equation is 7 > 24/4.
Comparison of two numbers involves determining the relationship between them. Here are a few possible outcomes when comparing two numbers:
1: If the first number is greater than the second number, we can say that the first number is "greater than" or "larger than" the second number.
2: If the first number is less than the second number, we can say that the first number is "smaller than" or "less than" the second number.
3: If the first number is equal to the second number, we can say that the numbers are "equal" to each other.
The given numbers are:
7 and 24/4
To compare these numbers,
Convert the fraction 24/4 into the simplest form
Therefore,
[tex]\frac{24}{4} = 6[/tex]
Now since 7 is greater than 6 so we use ">" between them.
Hence,
The complete equation will be 7 > 24/4.
To learn more about the fraction visit:
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I|I is an integer between 11 and 17
Yes, there is. It's 14. Hope this helps.
Solve. − 18 + ( − 4 ) =
Answer:
-22
Step-by-step explanation:
-18 + (-4) = -18 - 4 = -22
SOMER HELP ON GIS ONEEEE
Answer:
2 one
Step-by-step explanation:
well if u go the other way for it to go right it is mf
1. If a = -1 , the value of3a + 1 is
Answer:
[tex]f(a) = 3a + 1 \\ Now,\: a = - 1 \\ f( - 1) = 3( - 1) + 1 \\ f( - 1) = - 3 + 1 \\ \boxed{ f( - 1) = - 2}[/tex]
Therefore, -2 is the right answer.When 12x +10y is subtracted from -13x + 7y, we get
Answer:
- 25x - 3yStep-by-step explanation:
-13x + 7y - (12x +10y)
= - 13x + 7y - 12x - 10y
= - 13x - 12x + 7y - 10y
= - 25x - 3y (Ans)
Write the equation of the line that
passes through (5,-7) and (0, -1)
4,3,2,1,0,-1, -2, -3, -4,
Equation of a line can be given by :
y = mx + b
Let's find the slope of the line (m) :
[tex] \mathcal{ \hookrightarrow \: \dfrac{y_2 - y_1}{x_2 - x_1} }[/tex]
[tex] \mathcal{ \hookrightarrow \: \dfrac{ - 1 - ( - 7)}{0 - 5} }[/tex]
[tex] \hookrightarrow \: \dfrac{6}{ - 5} [/tex]
[tex] \hookrightarrow \: m = \dfrac{ - 6}{5} [/tex]
now let's solve for b :
[tex] \hookrightarrow \: y = mx + b[/tex]
Let's plug the values of x and y from the coordinates of a point .
[tex] \hookrightarrow \: - 7 = (\dfrac{ - 6}{5} \times 5) + b[/tex]
[tex] \hookrightarrow \: - 7 = - 6 + b[/tex]
[tex] \hookrightarrow \: b = - 1[/tex]
now, let's put the value of m (slope) and b (y-intercept) in the equation.
[tex] \hookrightarrow \: y = mx + b[/tex]
[tex] \boxed{ \boxed{\: y = \dfrac{ - 6}{5}x - 1 }}[/tex]
That's All, I hope it helped ya
Which statement is true about the climbers’ heights?
What is the value of a in the equation 3 a plus b equals 54, when b equals 9?
15
18
21
27
simplify (2/3 of 21/4)
Answer: 3 1/2
Step-by-step explanation:
"Of" is the same as multiplication so,
2/3 × 21/4=?
For fraction multiplication, multiply the numerators and then multiply the denominators to get
2 × 2/13 × 4 = 42/12
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 42 and 12 using
GCF(4/2 , 1/2) = 6
4/2 ÷ 6 1/2 ÷ 6 = 7/2
The fraction
7/2
is the same as
7÷2
Convert to a mixed number using
long division for 7 ÷ 2 = 3R1, so
7/2 = 3 1/2
Therefore:
2/3 of 21/4 = 3 1/2
Hopefully, I Helped
Find - 36
.
Ο +6
-6
9Ο
Ο 18
Answer:
+or-6
Step-by-step explanation:
This is a trick question. The answer would be the first choice since you're multiplying -6 by +or-6, meaning that it could still end up as a negative or a positive.
Answer:
Step-by-step explanation:
John bought 3 pants for 25 dollars each and paid with a 100 dollar bill how much change did he get?
Answer:
He got $25 in change.
Step-by-step explanation:
Suppose the balance amount is x.
The cost of 3 pants is 3 × 25 = 75
John paid = $ 100
x = 100 – 75
x = 25
Answer:25
Step-by-step explanation:
25×3=75 then you subtract 100-75=25
your monthly salary increases from $2,200 to $2,376. what percent is your raise?
Answer:
8%
Step-by-step explanation:
(2376-2200):2200x100%=8%
Based on this equation 3/4 (8y +12) = 3y - 15, what is 2y - 3?
Answer:
-y+5
Step-by-step explanation:
3/4 (8y +12) = 3y - 15
3(2y+3)=3y-15
2y+3=y-5
-(2y-3)=y-5
2y-3=y-5/-1
2y-3=-y+5
Answer: -19
Step-by-step explanation:
Given equation
(3/4) (8y + 12) = 3y - 15
Divide (3/4) on both sides
(REMEMBER division of fraction can be converted to multiplication by using the reciprocal of the fraction)
(3/4) (8y + 12) ÷ (3/4) = (3y - 15) ÷ (3/4)
(3/4) (8y + 12) × (4/3) = (3y - 15) × (4/3)
8y + 12 = 4y - 20
Subtract 4y on both sides
8y + 12 - 4y = 4y - 20 - 4y
4y + 12 = -20
Subtract 12 on both sides
4y + 12 - 12 = -20 - 12
4y = -32
Divide 4 on both sides
4y / 4 = -32 / 4
y = -8
Evaluate the expression basing on the [y] value
2y - 3 ⇔ Given expression
=2(-8) - 3 ⇔ Substitute values into the expression
=-16 - 3 ⇔ Simplify by multiplication
=[tex]\boxed{-19}[/tex] ⇔ Simplify by subtraction
Hope this helps!! :)
Please let me know if you have any questions
(5pg)3=125pg. Is wrong or correct
Answer:
125 p^3 g^3
Step-by-step explanation:
(5pg)^3
We know that (ab)^c = a^c * b^c
5^3 p^3 g^3
125 p^3 g^3
A total of 574 tickets were sold for the school play. They were either adult tickets or student tickets. There were 74 more student tickets sold than adult tickets. How many adult tickets were sold?
411 is not correct
The answer is: 250 adult tickets were sold.
To be safe, prove that your answer is correct.
If there are 74 more student tickets than adult tickets, the amount of adult tickets must obviously be less.
Explanation:
74 more than 250, or 250+74 is 324.
250+324=574.
Now, you know the answer is correct. It satisfies all of the given conditions.
Also, note that the difference between the number of student tickets and adult tickets is 74.
So, there are 250 adult tickets and 324 student tickets.
How do the fuel economies of Honda and Ford
vehicles compare in 2018? Use the drop-down menus
to complete the statements.
Shape: The distribution of fuel economy for Honda is
vand for Ford is
Outliers: There appears to be an outlier of 47 mpg for
Honda. There appears to be an outlier of 40 mpg for
Ford
Center: Fuel economy for Honda tends to be
the fuel economy for Ford.
Variability: Fuel economy for Honda varies about the
same as the fuel economy for Ford.
Answer:
1. roughly symmetric
2. skewed to the right
3. greater than
Step-by-step explanation:
correct on edge 2021 :)
1. The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right. and 3. Fuel economy for Honda tends to be greater than the fuel economy for Ford.
How to compare the fuel economies of Honda and Ford vehicles in 2018?Shape: The distribution of fuel economy for Honda is roughly symmetric vand for Ford is skewed to the right.
Outliers: There appears to be an outlier of 47 mpg for Honda. There appears to be an outlier of 40 mpg for Ford
Center: Fuel economy for Honda tends to be greater than the fuel economy for Ford.
Variability: Fuel economy for Honda varies about the same as the fuel economy for Ford.
Learn more about Fuel economy here;
https://brainly.com/question/24212851
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Urgent what is the numerical answer please !!
whats the full question?
Answer:
AB slope= 4/5
CD slope= - 5/4
Step-by-step explanation:
AB: (0,-1) (5,3)
Slope= (3- -1)/(5-0) = 4/5
CD: (2,3) (6,-2)
CD slope= (-2-3)/(6-2) = -5/4
Hours worked in a week - 32; Total Pay - $160.00; What is the hourly rate?
Answer:
$5
Step-by-step explanation:
Number of hours worked = 32
Total pay = $160
So, hourly rate
= Total pay/number of hours worked
= $160/32
= $5
HELP Please with this question please NO LINKs OR I WILL REPORT YOU PLEASE GIVE EXPLANATION
Answer:
87/54 = m
Step-by-step explanation:
-11/6 + m = -2/9
Here is one way to solve this:
First, we can remove the fractions. We can do this by multiplying both sides by both denominators.
multiply both sides by 6
-11 + 6m = -12/9
multiply both sides by 9
-99 + 54m = -12
add 99 to both sides to isolate the m and its coefficient
-12+99= 54m
87 = 54m
divide both sides by 54 to isolate m
87/54 = m
Homework pikcuts
Pleas
Answer:
[tex] \frac{12 - 23 \sqrt{2} }{46} [/tex]
Step-by-step explanation:
you find the LCM
Danny got a raise and now makes $58,965.95 a year. Round this number to the
nearest:
a) dollar
b) thousand dollars
c) ten thousand dollars
Answer:
c) ten thousand dollars
Step-by-step explanation:
A room has to be painted and worker A does 1/3 of the work then leaves. Next worker B does 1/4 of the remaining work and then leaves and finally worker C does 1/5 of the remaining work and then leaves.
What fraction of the room still needs to be painted?
a)3/5
b)2/5
c)13/60
d)7/15
Here, we are given that a room is painted by A, B and C so here three of them have done the work. So, we'll add all these fractions and assume the total work as 1 after that we will substract all the added ones from 1
Let us assume the room completely painted be 1
Now,
A has done 1/3, B has done 1/4 and C has done 1/5 work of the remaining
So, let us add them
A + B + C ⅓ + ¼ + ⅕Getting the L.C.M. The L.C.M of 3,4,5 is 60
20/60 + 15/60 + 12/6047/60Hence, 47/60 room has been painted
Remaining to paint
Total is assumed as 1
Work done = 47/60
Fraction of room needs to painted = 1 - 47/60
(60 - 47)/6013/6013/60 of the room needs to be painted, OPTION C IS CORRECT
When d the product of 6 and 6 is divided by the sum of 6 and 6 what is the quotient? Explain.
Two cylinders are similar the volume of one is 27cm^3 the volume of the other cylinder is 1331cm^3 what is the scale factor between them
Answer:
scale factor = 3 : 11
Step-by-step explanation:
Given 2 similar figures with scale factor a : b , then
ratio of volumes = a³ : b³
Here
ratio of volumes = 27 : 1331 . so
scale factor = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{1331}[/tex] = 3 : 11
Answer:
3:11
Step-by-step explanation:
Simplify 3 (5x-2y) +2 (4X-37)
Answer:
3x - 6y - 74
Step-by-step explanation:
Given
3(5x - 2y) + 2(4x - 37) ← distribute parenthesis
= 15x - 6y + 8x - 74 ← collect like terms
= 23x - 6y - 74
Answer:
Distribute
3
(
5
−
2
)
+
2
(
4
−
3
7
)
{\color{#c92786}{3(5x-2y)}}+2(4x-37)
3(5x−2y)+2(4x−37)
1
5
−
6
+
2
(
4
−
3
7
)
{\color{#c92786}{15x-6y}}+2(4x-37)
15x−6y+2(4x−37)
2
Distribute
1
5
−
6
+
2
(
4
−
3
7
)
15x-6y+{\color{#c92786}{2(4x-37)}}
15x−6y+2(4x−37)
1
5
−
6
+
8
−
7
4
15x-6y+{\color{#c92786}{8x-74}}
15x−6y+8x−74
3
Combine like terms
1
5
−
6
+
8
−
7
4
15x−6y+8x−74
2
3
−
6
−
7
423x}}-6y-74
23x−6y−74
Solution
2
3
−
6
−
7
4
Step-by-step explanation: