[tex]3x=x+10[/tex]
We tripple something and get 10 more than something.
Put the x-es on the left and non x-es to the right,
[tex]2x=10[/tex]
Divide both sides by 2,
[tex]x=5[/tex]
Et Viòla.
Hope this helps :)
When a number is tripled, its value increases by 10 then the original number is 5.
Let's call the original number "x". According to the problem, when this number is tripled, its value increases by 10. Mathematically, we can represent this as an equation:
3x = x + 10
Now, we can solve for "x" step by step:
1. Subtract "x" from both sides of the equation:
3x - x = 10
2. Simplify the left side:
2x = 10
3. Divide both sides by 2 to solve for "x":
x = 10 / 2
x = 5
So, the original number "x" is 5.
In other words, if you take a number, triple it (multiply by 3), and then increase the result by 10, you would end up with the value 5. This can be verified by checking:
3 * 5 = 15
15 + 10 = 25
The equation 3x = x + 10 represents the relationship between the original number and its tripled value with an increase of 10. Solving this equation helps us find the original value that satisfies the given condition.
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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
2 sec^2(t)/tan^2(t) + 14 tan(t) + 48 dt
Complete the square in the denominator to get
tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1
… = (tan(t ) + 7)² - 1
Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]
Separate the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]
Then we get
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]
-3x > 12
What is the value of x? Use substitution to support your answer.
Answer:
x < -4
Step-by-step explanation:
-3x > 12
----- ----
-3 -3
12 ÷ -3 = -4
Which means:
x < -4
(The sign changes because the equation is divided by a negative number)
Hope this helped.
Answer:
x <-4
Step-by-step explanation:
-3x > 12
Divide each side by -3. remembering to flip the inequality
-3x/-3 > 12/-3
x <-4
a potter is making cups and saucers. each cup takes c minutes to produce, and each saucers takes s minutes. Th epotter can produce three cups and two saucers in 19 mnutes
Answer:
1) 3c+2s=19
4c+5s=30
2) c=5 s=2
3)42minutes
Step-by-step explanation:
The potter need 3c minutes to make three cups and 2s to make two saucers, then he needs 3c+2s minutes to make both of them
3c+2s=19
He needs 4c+5s minutes to produce 4 cups and 5 saucers
4c+5s=30 (half of an hour is 30 minutes)
So the equations are
3c+2s=19
4c+5s=30
2) to solve you should express c from the first equation and use it in the second equation
3c=19-2s
c=19/3-(2/3)*s
4(19/3-(2/3)*s) +5s=30
76/3-(8/3)*s+5s=30
(7/3)*S= (14/3)
s=2
3c=19-4
3c=15
c=5
3) 6c+6s= 6(c+s)= 6(5+2)=6*7=42
Complete the equation: x^ 2 +6x+__ =(_)^ 2
Answer:
x^2+6x+9= (x+3)^2
Step-by-step explanation:
x^ 2 +6x+__ =(_)^ 2
The formula is a^2+2ab+b^2= (a+b)^2
x^2= a^2
x=a
6x=2ab where a=x
6x=2x*b
b=3
b^2=9
x^2+6x+9= (x+3)^2
Correct the formula
Please
Answer:
The addition should be divided by 4 and not 3 since there are 4 meals.
Step-by-step explanation:
look at the image below plzz urgant help !!!!!! NEED DONE IN TEN MINUTES
Answer:
V≈113.1
Step-by-step explanation:
V=πr2h
3=π·32·12
3≈113.09734
2. The table shows the probabilities of winning or losing when the team is playing away or is playing at home.
Home Away Total
Win 0.2 0.05 0.25
Loss 0.6 0.15 0.75
Total 0.8 0.20 1.00
(a) Are the events “winning” and “playing at home” independent? Explain why or why not.
(b) Are the events “losing” and “playing away” independent? Explain why or why not.
Answer:
A tank containing 6312 litres of water fills several buckets of capacity 8 litres each. Will there be any
water left in the tank after filling all the buckets?
YES/NO and state reason for your answer.
Answer:
NO
Step-by-step explanation:
6312/8= 789
here, 6312 is devisable by 8.
Therefore, there will not be any water left in the tank.
x+2y=9 and x=2y+1
helppppppppppppppppp meeeeereeer
Answer: y = 2
Step-by-step explanation:
we need to use systems of equations, basically since we know what x equals, we plug that into first equation so:
since x=2y+1,
we can say that:
(2y+1)+2y=9
then we solve this equation,
first we expand the brackets- 2y+1+2y=9,
then we combine like terms- 4y+1=9
then we take 1 away from both sides- 4y=8
then we divided both sides by 4
y=2
Hope this helps xx
Answer:
(5, 2)Step-by-step explanation:
Given system:
x + 2y = 9x = 2y + 1Solve for y by substitution:
(2y + 1) + 2y = 94y + 1 = 94y = 8y = 2Find the value of x:
x = 2*2 + 1x = 51+9+40-40+40+10x2 equals what?
Answer:
70
Step-by-step explanation:
1+9+40-40+40+10*2
----------------------- 20
10+40-40+40+20
50 (-40+40 cancels out to 0) +20
50+20= 70
(Following PEMDAS)
Multiply, add, subtract.
if you were to instead go through it left to right, you would get 120, which is incorrect.
how far from 0" is the green rectangle for both
Answer:
C. 3 3/4
Step-by-step explanation:
just is
id k how to explain
11. A surveyor at point S discovers that the angle between peaks A and B is 3 times as large as the angle
between peaks B and C. The surveyor knows that ZASC is a right angle. Find mzASs and m2BSC.
The measures of the angles between the peaks are;
m∠BSC = 22.5°
m∠ASB = 67.5°
The reason for arriving at the above angles is as follows:
The known values are;
The location of the surveyor = Point S
The angle between peaks A and B = m∠ASB = 3 times as large as the angle between peaks B and C = 3 × m∠BSC
The measure of angle m∠ASC = A right angle = 90°
Required:
To find m∠ASB and m∠BSC
From the given diagram, we have;
m∠ASC = 90°
m∠ASC = m∠ASB + m∠BSC (angle addition postulate)
m∠ASB = 3 × m∠BSC
∴ m∠ASC = 3 × m∠BSC + m∠BSC = 4 × m∠BSC
m∠ASC = 4 × m∠BSC = 90°
m∠BSC = 90°/4 = 22.5°
m∠BSC = 22.5°
m∠ASB = 3 × m∠BSC
∴ m∠ASB = 3 × 22.5° = 67.5°
m∠ASB = 67.5°
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find the missing side. round your answer to the nearest tenth. PLEASE HURRY!
Answer:
44.8
Step-by-step explanation:
Using the Cosine formula, we first have Cos 48 = 30/x. So then we just solve for x and get 44.8342965, which rounds to 44.8
I hope this helped! :D
Can someone help me please need the answer ASAP
Answer: 445.5 (choice C)
Work Shown:
[tex]S_n = \frac{n}{2}(a_1+a_n)\\\\S_{11} = \frac{11}{2}(8+73)\\\\S_{11} = 5.5(81)\\\\S_{11} = 445.5\\\\[/tex]
Adding the first 11 terms of this arithmetic sequence yields the sum 445.5
A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can sell 300 plates but for each Ghc5 she raises the price,10 less plates are sold. A.Draw a table relating 5 different price levels with their corresponding number of plates sold.
B.Use the table to find the slope of the demand
C.Find the equation of the demand fraction.
D.Use your equation to determine the price in Ghc if she sells one plate of food to maximize her revenue
The demand equation illustrates the price of an item and how it relates to the demand of the item.
The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85From the question, we have:
[tex]Plates = 300[/tex]
[tex]Price = 20[/tex]
The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:
[tex]\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{25-20}{290-300}[/tex]
[tex]m = \frac{5}{-10}[/tex]
[tex]m = -\frac{1}{2}[/tex]
The equation of the demand is as follows:
The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).
Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).
So, the demand equation is:
[tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]
Open the brackets to calculate the maximum revenue
[tex]R(x) =6000 + 1500x - 200x - 50x^2[/tex]
[tex]R(x) =6000 + 1300x - 50x^2[/tex]
Equate to 0
[tex]6000 + 1300x - 50x^2 =0[/tex]
Differentiate with respect to x
[tex]1300 - 100x =0[/tex]
Collect like terms
[tex]100x =1300[/tex]
Divide by 100
[tex]x =13[/tex]
So, the price at maximum revenue is:
[tex]Price= 20 + 5x[/tex]
[tex]Price= 20 + 5 * 13[/tex]
[tex]Price= 85[/tex]
In conclusion:
The slope of the demand function is -1/2The equation of the demand function is: [tex]R(x) = (300 - 10x) \times (20 + 5x)[/tex]The price that maximizes her revenue is: Ghc 85Read more about demand equations at:
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Solve for x in the equation x2 - 4x-9= 29
In the diagram, the perimeter of the rectangle is 56. What is its area?
write two properties of Zero
Answer:
the addition properties of zero and multiplication properties of zero
zero is even, not odd not neutral.
zero is neither positive or negative.
Workbook
WB-21
38. What is the circumference of a circle that has a diameter of 12 inches? (Use
3.14 for 1.)
a. 15.14 inches
b. 37.68 inches
c. 376.8 inches
d. 9.42 inches
Answer:
37.68
Step-by-step explanation:
Formula for finding the circumference of a circle is C = 2πr
If you substitute the numbers in you should get 37.68.
PLEASE ANSWER ASAP THANK YOU!!! How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.....
Answer:
10 bucks
Step-by-step explanation:
Money=9*(1+0.05)^3
Money=9*(1.05)^3=10.41≈10
Find m∠DFC.
A. 23
B. 167
C. 46
D. 69
Answer:
A.23
maaf kalosalah !(!)!(!)!(!)!(!)!(!)!(!)!(!)!(!)!
brainliest to correct
Answer:
27
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
-9 × -3
= 27
Note: When you multiply two integers with same sign, then their product is positive.
what is the lub and glb of the following sets, in the set of real numbe if exists E={ 0.2,0.23,0.234,0.2343,0.23434,0.23434,...}
Answer:
Hello,
Step-by-step explanation:
[tex]LUB(E)=0.2=\dfrac{1}{5} \\\\GUB(E)=0.2 34 34 34 ....=0.2+\dfrac{1}{10} *0.343434....\\\\=\dfrac{1}{5} +\dfrac{1}{10} *\dfrac{34}{99} \\\\=\dfrac{198+34}{990} \\\\=\dfrac{116}{495}[/tex]
which of the following are ordered pairs for the given function f(x)=1+x.? (1,2) (3,3) (0,2) (1,0) (0,1)
Answer:
no,
(
1
,
0
)
is not an ordered pair of the function
f
(
x
)
=
1
+
x
.
Step-by-step explanation:
Ordered pairs are usually written in the form
(
x
,
y
)
by tradition.
so usingthe function,
f
(
x
)
=
1
+
x
we can rewrite it as,
y
=
1
+
x
any pair of x and y that satisfy this equation are solutions to the equation.
so subbing in
(
1
,
0
)
,
0
=
1
+
(
1
)
0
=
2
which is not true so the point does not make the function true.
It might be easier to see graphically,
graph{1+x [-10, 10, -5, 5]}
any combination of x and y on this line make the equation true and as such are an ordered pair of the function.
Answer:
Step-by-step explanation:
which is an example of an algebraic expression
A.4(3+8)
B.18^2
C. 3-a
D. 12•4
Answer:
C: 3-a
Step-by-step explanation:
The answer is C because an algebraic expression needs to have a variable in it. The variable is "a," so the answer has to be C.
Answer:
Option C : as in algebraic expression there must a variable and constant.
Someone PLEASE HELP!!! Nowwww
What is the remainder when 62,710 is decided by 541
Answer:
the quotient is is 115.915 and the remainder is 495
Step-by-step explanation:
Hope it helps you
Mark my answer as brainlist
have a nice day
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than twice the third side, what are the possible lengths for the second and third sides?
Answer: One side could be 18 and the other side will be 33.
Step-by-step explanation:
Side #1 = 18Side #2 = 2x - 3Side #3 = xOne way of setting up the inequality is: Side #2 + Side #3 > Side #1
[tex]2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7[/tex]
Another way of setting up the inequality is: Side #1 + Side #3 > Side #2
[tex]18+x>2x-3\\18+3>2x-x\\x<21[/tex]
Final way of setting up the inequality is: Side #1 + Side #2 > Side #3
[tex]18+2x-3>x\\15>x-2x\\15>-x\\x>-15[/tex]
Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.
Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. What conclusion can be made based on the data
a cubical water tank is 80 CM broad how many CC of water does it hold
Answer:
I think: vol of h20 inside = side³ = (80cm)³ =512000 cm³
Please refer!
Step-by-step explanation:
I'm not sure but hope it helps.
