The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
x² - 6x - 27 = 0
Adding 27 to both sides:
x² - 6x - 27 + 27 = 0 + 27
x² - 6x = 27
Adding to both sides the square of half the coefficient of x, that is 9:
x² - 6x + 9 = 27 + 9
(x - 3)² = 36
taking square root of both sides:
√(x - 3)² = √36
x - 3 = ±6
x = 3 ± 6
x = 3 + 6 or; x = 3 - 6
x = 9; or x = -3
The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3
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The function f(x) = x + 21 is one-to-one.
a. Find an equation for f1(x), the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹ (f(x)) = x.
Answer:
a. D. f⁻¹(x) = x - 21, for all x
b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x
Step-by-step explanation:
See attached picture.
The required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:
x = y + 21
Now, let's solve for y:
y = x - 21
Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.
b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.
First, let's calculate f(f(x)):
f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42
Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.
Now, let's calculate f¯¹(f(x)):
f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x
Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.
Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Therefore, the required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
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please explain
Convert the angle θ= 9/14pi radians to degrees.
Answer:
280°
Step-by-step explanation:
using the relationship
π radians = 180° , then substituting gives
[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°
write a rule for the nth term of the arithmetic sequence
-11, -4, 3, 10...
Answer: aₙ = -11 + 7(n - 1)
Step-by-step explanation: The equation of an arithmetic sequence is
aₙ = a₁ + d(n - 1).
a₁ is the first term.
d is the common difference.
300 percent of m is 600. What is m?
Answer:
m=200
Step-by-step explanation:
percent means 100,so we duvude 300:by 100 then m=200
50 points Find the lateral surface area of the prism.
Answer:
Lateral surface area = 36 ft²Step-by-step explanation:
Formula:
Lateral surface area = perimeter of the base × height
………………………………………………………………
perimeter of the base = 2×(1.5+3) = 9
height = 4.
then
Lateral surface area = 9 × 4 = 36
Area of two bigger rectangles
2LB24(3)2(12)ft²24ft²Area of two smaller rectangles
2×1.5(4)2×612ft²LSA
12+2436ft²Which expression is a perfect cube
Answer: some perfect cubes are
8 (2^3)
27 (3^3)
64 (4^3)
there are many perfect cubes
maybe there is more to this question?
Step-by-step explanation:
A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.
What is 2 raised to the power of 3?
Answer:
What is 2 raised to the power of 3?
2 x 2 x 2
= 8
Step-by-step explanation:
Hope this helps.
Write the point-slope form of the equation for a line that passes through (−1, 4) with a slope of 2.
The value of x₁ is
The value of y₁ is
The point-slope form of the equation is
What is the solution for x in the equation?
9-10x=2x + 1 - 8x
x = -2
x=1/2
x=2
x=-1/2
Solve for X.
6
X = [?]
Enter the number, in decimal form,
that belongs in the green box.
Answer:
By proportional method
[tex] \frac{4}{6} = \frac{5}{x} [/tex]
4x= 30
x= 7.5
ہے
Solve for k.
4k - 10
k
k=
-
= 8
Answer:
The formation of the equation is odd, but I assume it's supposed to be:
4k - 10k = -8k
-6k = -8k
-6k + 8k = -8k + 8k
2k = 0
[tex]\frac{2k}{2}[/tex] = [tex]\frac{0}{2}[/tex]
k = 0
An insulator is installing fiberglass insulation in exterior walls that total up to 1,623 square feet after windows and doors are deducted. Each roll can insulate 49 square feet. There are 28 rolls on hand. Will this amount be sufficient? If not, how many total rolls are needed? If necessary, round your answer up to the nearest whole number, since you cannot buy part of a roll of insulation.
Answer:
2
Step-by-step explanation:
F(x)=x^2-3x-2 if shifted 4 units left. The relics it g(x). What is g(x)?
A cone has a height of 8 yards and a radius of 3 yards. What is its volume?
Use ≈ 3.14 and round your answer to the nearest hundredth.
cubic yards
Submit
Yea
The volume of the given cone.
Solution:[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]
[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]
Let's solve!
Substitute the values according to the formula.
[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]
[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]
Therefore, the volume of the given cone is 75.36 cubic yards.
The ________________ measures the spread of the middle 50% of the data set.
A. median
B. range
C. interquartile range
D. mode
Answer:
C. interquartile range
Step-by-step explanation:
using this to show im right
"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."
Hope This Helped
Coreys bank account had a balance of $55. He made a deposit of $364 and withdrawal of $67
Answer:
His bank account now has 352 dollars in it.
Step-by-step explanation:
55+364-67=352
Answer:
$352
Step-by-step explanation:
1st balance: $55
amount deposited: $364
total: $55+$364=$419
amount withdrawed: $67
amount left in account: $419-$67=$352
ans=$352
Can you help like fast
Answer:
(4, 3)
Step-by-step explanation:
Simplify surd need an answer asap please
Answer:
Step-by-step explanation:
Simplify Surd: Multiply the denominator and numerator with the conjugate of the denominator.Conjugate of denominator:[tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]
[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]
When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²
[tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]
Can you please factorize 2x²+6x
To factorize something:
⇒ need to simplify the equation to its most basic form
Let's solve:
[tex]2x^2+6x=2(x^2+3x)=2x(x+3)[/tex]
Thus the factorized form is ⇒ [tex]2x(x+3)[/tex]
Answer: 2x(x+3)
Hope that helps!
Answer:
Solution:
→ 2x(x + 3)
Step-by-step explanation:
Method:
Grouping→ Common factor
2x² + 6x2(x² + 3x)→ Rewrite in factored form
2(x² + 3x)2x(x + 3)I need help asap!!! I will without hesitation give brainliest to whomever gets this
Answer:
A. [tex]y\leq \frac{1}{2}x+2[/tex]
Step-by-step explanation:
First, let's find the slope of the line, so we can eliminate some answers.
From point (0,2) we can go up 1 and over to the right 2 to the point of (2,3). Slope is rise over run so 1 over 2.
This eliminates C and D.
The last part is to recognize that y being less than the equation will result in the shaded region being below the line. If y was greater than the equation then the shaded region would be above the line.
Therefore, the correct answer would be A. [tex]y\leq \frac{1}{2}x+2[/tex].
Hope this helps! If you have questions about my work please let me know down in the comments!
Answer:
[tex]y\leq \frac{1}{2}x+2[/tex]
Step-by-step explanation:
The first part of finding our answer is finding the slope of the line. The image attached shows this.
[tex]\frac{rise}{run} = \boxed{\frac{1}{2}}[/tex]
This means the slope is [tex]\frac{1}{2}[/tex], removing the bottom 2 answer choices.
Now we have to choose between the [tex]\leq[/tex] and [tex]\geq[/tex] sign. Since the shaded area is below the line, it will be the [tex]\leq[/tex]. (If it was the [tex]\geq[/tex] sign, the shaded area would be above the line.) This marks the first answer as the correct answer.
what is the mean of 7,5,6,5,4,4,8,6,6,7,4,5,56,6
Answer:
5.6
Step-by-step explanation:
If you add all the numbers together then divide it by 15 you would get 5.6
When 2(3/5 x + 2 3/4 y - 1/4 x - 1 1/2 y + 3) is simplified, what is the resulting expression?
Answer:
6 + 7/10x + 2/y
Step-by-step explanation:
Hope this helps :)
a girl spent 1/6 of her pocket money on sweets and 2/5 on toys what fraction of her pocket money did she spend what fraction of her pocket money did she have remaning
Answer:
She spent 17/30 of her money and still has 13/30 of her money
Step-by-step explanation:
The first step to solve is to find a common denominator. The common denominator of this problem is 30. So 1/6 turns into 5/30, and 2/5 becomes 12/30. Then you add them together to get 17/30. If you subtract 17 from 30 you will get your answers.
A line is parallel to y=-2x-5 and intersects the point (-1,3) input the correct values into the point slope formula y-[?] = [__}(x- [__])
The equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
A line is parallel to y=-2x-5 and intersects the point (-1,3)The equation of the new line will be:-
y - y₁ = m ( x - x₁ )
Since the line is parallel to the line y = -2x - 5 so slope will be same m = -2 now the coordinates are ( -1, 3).
y - ( 3) = -2 [( x - (-1) ]
y - 3 = -2x - 2
y = -2x + 3 -2
Y = -2x + 1
Therefore the equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.
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The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya?
Answer:
12.6
Step-by-step explanation:
4.2×3=12.6
I hope this answer can help you
Answer:
1.4 kg
Step-by-step explanation:
Given :
⇒ Watermelon (Peter) = 3 × Papaya (Paul)
⇒ Watermelon (Peter) = 4.2 kg
=============================================================
Solving :
⇒ 4.2 = 3 × Papaya (Paul)
⇒ Papaya (Paul) = 1.4 kg
Therefore the mass of the papaya is 1.4 kg.
I'd appreciate the help!!
Answer:
B
Step-by-step explanation:
look at the graph. y is negative from x>2, so interval is 2<x<infinity.
in other case y=0 for x=2, y<0 for infinity<x<2
Answer:
The intervel that describes where the graph is negative is C :)
I hope this helps you!
Step-by-step explanation:
Which of the following is the graph of the inverse of F(x) = 2x - 3?
what is mean by migration
who will give me brainlest then I am follow you
Step-by-step explanation:
Movement from one place to another
b solve each problem . use ñ= 3.14 1. what is the volume of a regular cylinder whose base has radius of 5 cm and has height of 4 cm? 2. the diameter of sphere is 10 cm. find the volume. 3. juice is sold in aluminum cans that measure 7 inches in height and 4 inches in diameter. how many cubic inches of juice are contained in a full can? 4. the square pyramid has a volume of 297 cm³. the area of the base is 81 cm². What is the height.? 5. A glass is 10 cm deep and 8 cm wide . How much liquid the glass hold?
#1
Volume
πr²hπ(5)²(4)100π3.14(100)314cm³#2
Radius=10/2=5cm
Volume
4/3πr³4/3π(5)³125(4/3π)500π/3523.3cm³#3
Volume
π(4/2)²(7)2²(7π)28π87.92in³#4
V=1/3a²hV=1/3(81)h27h=297h=11cm#5
radius=8/2=4
Volume
π(4)²(10)160π502.4cm³502.4mLAnswer:
1) 314 cm³
2) 523.33 cm³
3) 87.92 in³
4) 11 cm
5) 502.4 cm³
Step-by-step explanation:
Part 1[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 5 cmh = 4 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]
Part 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]
Given:
d = 10 cm ⇒ r = 5 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]
Part 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 4 in ⇒ r = 2 inh = 7 inπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]
Part 4[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]
Given:
Volume = 297 cm³Area of base = 81 cm²[tex]\implies 81=a^2[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9\: \sf cm[/tex]
Substitute the given values into the formula and solve for h:
[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]
Part 5[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
d = 8 cm ⇒ r = 4 cmh = 10 cmπ = 3.14Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]
Can someone tell me what is 9x46288