The value |x−9|≤9 is equivalent to [18,0] in interval notation.
According to the statement
We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.
So, For find all x value we use absolute value inequalities.
distance of 9 from number 9.
So, when we draw the number line
we see that the number will become
The distance from x to 9 can be represented using an absolute value symbol, |x−9|.
Write the values of x that satisfy the condition as an absolute value inequality.
So, it become
|x−9|≤9
Now write two inequalities then it become
x−9≤9 and x−9≥−9
x≤18 and x≥0
So, The solution set is x≤18 and x≥0,
then the solution set is an interval including all real numbers between and including 18 and 0.
So |x−9|≤9 is equivalent to [18,0] in interval notation.
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30% of what number is
165
Answer:
550
Step-by-step explanation:
165 x 100= 16500/30=550
question:
|x-2|, if x > 5
simplify without the absolute value sign
Answer:
x - 2, if x > 5
Step-by-step explanation:
The vertical lines either side of the expression mean absolute value.
The absolute value of a number is its positive numerical value.
if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive. Therefore, we can disregard the absolute value.
Therefore:
x - 2, if x > 5
To find the range (output values) of the expression, substitute x = 5 into the expression:
⇒ 5 - 2 = 3
Therefore, |x - 2| > 3, if x > 5
In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and
130 play both the games. Find
(i) The number of pupils who play Football only,
(ii) The number of pupils who play Hockey only,
(iii) The total number of pupils in the school
Answer:370 play football and 20 play hockey
Step-by-step explanation: because 400 - 130 equals 370 for football
then hockey 150-130 equals 20
Then the total students are 420
150+400-130 equals 420
HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Write each expression in the standard form for the complex number a + bi.
1. [ 4 ( cos (7pi/9) + i sin (7pi/9))]^3
2. The complex fifth roots of 5 - 5 sqrt(3)i
1. By de Moivre's theorem,
[tex]\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}[/tex]
2. First write the given number in exponential/trigonometric form.
[tex]z = 5-5\sqrt3\,i[/tex]
has modulus
[tex]|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10[/tex]
and since it lies in the second quadrant of the complex plane, its argument is
[tex]\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3[/tex]
So, we have
[tex]z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)[/tex]
Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For [tex]k\in\{0,1,2,3,4\}[/tex], the fifth roots of [tex]z[/tex] are
[tex]z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}[/tex]
[tex]k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}[/tex]
[tex]k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}[/tex]
[tex]k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}[/tex]
[tex]k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)}[/tex] [tex]k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}[/tex]
You purchase a very basic cell phone plan that charges $24.99 a month. This plan allows for data usage but that will cost you $5 for every GB you use in a month. Write an equation below in slope-intercept form that models this situation.
The equation of this given condition in the intercept form would be
y = 5x + 24.99
The slope-intercept is the most “popular” form of a straight line. Many students find this useful because of its simplicity. One can easily describe the characteristics of the straight line even without seeing its graph because the slope and y-intercept can easily be identified or read off from this form.
The linear equation written in the form
y = mx + b
is in slope-intercept form where: m is the slope, and b is the y-intercept.
In the given question the slope of the equation is 5 as $5 is charged for every GB used while $24.99 would be the intercept.
Thus the equation of this given condition in the intercept form would be
y = 5x + 24.99
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A
a = 10
C = 15
B
b
Find the length of b using
the Pythagorean Theorem.
Hint: a² + b² = c²
Round your answer to the nearest tenth.
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
What is the Pythagorean Theorem?The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
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Find the last number of the following series
10 8 16 13 39 35
1)75
2)100
3)130
4)140
The answer is 4) 140.
If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.
10 - 2 = 88 × 2 = 1616 - 3 = 1313 × 3 = 3939 - 4 = 35The next step, according to the pattern, would be to multiply 4.
35 × 4140What is the solution to x2 – 9x < –8? x < 1 or x > 8 x < –8 or x > 1 1 < x < 8 –8 < x < 1
In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.
x²− 9x < − 8Let's find the critical points of the inequality.
x² − 9x = − 8x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)
x² − 9x + 8 = 0(x − 1)(x − 8) = 0 (Factor left side of equation)
x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)
x=1 or x=8Check intervals in between critical points. (Test values in the intervals to see if they work.)x < 1 (Doesn't work in original inequality)
1 < x < 8 (Works in original inequality)
x > 8 (Doesn't work in original inequality)
Answer:1 < x < 8
The third option is the correct one.
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Ali’s ate 1/3 of a pizza for lunch. Later, she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
Will mark brainliest
The plot of [tex]\sqrt{25-x^2}[/tex] is that of the top half of a circle with radius 5. The interval [-5, 0] captures the left half of this semicircle.
Adding 5 to this shifts the plot up by 5 units. The area under this curve is then the combined area of a square with side length 5 and the area of a quarter circle with radius 5.
So we have
[tex]\displaystyle \int_{-5}^0 5 + \sqrt{25-x^2} \, dx = 5^2 + \frac\pi4\cdot5^2 = \boxed{25 + \frac{25\pi}4}[/tex]
Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using
a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3;
-2 and 7+5 i are zeros;
f(2)=200
f(x) =
(Type an expression using x as the variable. Simplify your answer.)
possible
4
Answer:
f(x) = x³ -12x² +46x +148
Step-by-step explanation:
When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.
Factored formGiven the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...
f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))
Rearranging a bit, this is ...
f(x) = (x +2)((x -7) -5i)((x -7) +5i)
The latter two factors are recognizable as the factors of the difference of squares, so this is ...
f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)
Standard formMultiplying the factors, we have ...
f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)
f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property
f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms
3a²+ab²-b² x a²-2ab²-3b²
/a+b
Answer:
It might be - c² or b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)
Step-by-step explanation:
I agree with the person above ^^^
Question
Which of the following equations is equivalent to 8x - 6y = 12?
y = ³x - 1²/2 3
y=x-2
y = 2x - 12
y = 8x - 6
The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
What are Equivalent Equations?Equations that are equivalent to each other have the same value when evaluated or simplified.
Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.
8x - 6y = 12
Subtract 8x from both sides of the equation
8x - 8x - 6y = -8x + 12
-6y = -8x + 12
Divide both sides of the equation by -6
-6y/-6 = -8x/-6 + 12/-6
y = 4x/3 + (-2)
y = 4x/3 - 2
Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.
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I hope you could get this answer
Answer: -12
Step-by-step explanation: x is -4 so -(-4) is positive 4. d = 3 so -3 = -3. -3x4 = -12.
SOLVE THE FOLLOWING PROBLEMS.
A) IN HOW MANY WAYS CAN THE LETTERS OF THE WORD “TRACK” BE ARRANGED?
B) A STUDENT MUST SELECT AND ANSWER SIX OUT OF TEN QUESTIONS ON AN EXAM. IN HOW MANY WAYS CAN THIS BE DONE?
C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE
The answers to the question are:
12021038760How to solve for permutations and combinations1. The letters of the word track can be arranged in 5! ways
These are 5 x 4 x 3 x 2 x1
= 120
2. The way that the student would be able to select 6 out of 10 questions would be by 10C6
= 210 ways
C)This teacher would be able to make the decision of the prices to the students using =20C6= n!(n-r!r!)
= 38760
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A COUPLE PLAN TO HAVE THREE CHILDREN.
A) LIST ALL THE POSSIBILITIES FOR THE SAMPLE SPACE.
B) WHAT IS THE PROBABILITY THAT THEY HAVE AT MOST TWO BOYS?
C) WHAT IS THE PROBABILITY THAT THEY HAVE AT LEAST TWO GIRLS?
D) WHAT IS THE PROBABILITY THAT THEY ARE ALL OF THE SAME SEX?
Relate ratios in right triangles
Consider right triangle ADEF below. Which Expressions are equivalent to cos(E)?
Answer:
B
Step-by-step explanation:
Cos is the adjacent side over the hypotenuse. The adjacent side to <E is side ED. The hypotenuse is side EF. ED/EF. They do not go right out and give you this choice, but you see that B says the same thing.
Application
I
3. Ray has a stride of about 1.4 m. He runs 9 km daily to train for a marathon. Approximately
how many strides does he need to run 9 km?
He needs to run with approximately 6429 for a distance of 9 km
How to determine the number of strides?The given parameters are:
Length of stride = 1.4 m
Distance for marathon = 9 km
The number of strides needed is then calculated as:
Number of stride = Distance for marathon/Length of stride
Substitute the known values in the above equation
Number of stride = 9km/1.4m
Convert km to m
Number of stride = 9000m/1.4m
Evaluate the quotient
Number of stride = 6428.57143
Approximate the estimate
Number of stride = 6429
Hence, he needs to run with approximately 6429 for a distance of 9 km
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Landon Wallin is an auto mechanic who wishes to start his own business. He will need $4200 to purchase tools and equipment. Landon decides to finance the purchase with a 36-month fixed installment loan with an APR of 5.5% a) Determine Landon's finance charge. b) Determine Landon's monthly payment.
Landon's finance charge is $613.2
Landon's monthly payment is; $80.22
How to find the finance charge?
It is convenient to compute the monthly payment first, then figure the total amount repaid and the finance charge.
The amortization formula is:
A = Pr/(1 - (1 + r)⁻ⁿ)
where;
A is the monthly payment
P is the loan amount
r is the monthly interest rate
n is the number of months
b) Using the above formula, we can get the monthly payment as;
A = $4200(0.055/12)/(1 - (1 +0.055/12)⁻⁶⁰) = $19.708333/0.23995049
A = $80.22
The monthly payment amount is $80.22
a) 60 monthly payments add up to;
$80.22 × 60 = $4813.2
Since $4200 of that amount is principal, the finance charge is;
$4813.2 - $4200.00 = $613.2
Landon's finance charge is $613.2
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Armando tiene 25 chocolates en una caja y caja y cada chocolate tiene un relleno de 4 posibles fresa, mora y piña. De los 25 chocolates de la caja de armando sabes que tiene 8 tienen relleno de mora y 5 de piña si una persona torna al azar un chocolate de la caja
cuales de la posibles posibilidades se puede calcular
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
¿Como encontrar las probabilidades?
Sabemos que hay 25 chocolates en total en la caja, tal que:
8 son de mora.5 son de piñalos 12 restantes son de fresa o cereza.La probabilidad de obtener un tipo particular de sabor se obtiene como el cociente entre el número de chocolates de ese sabor y el total de chocolates.
La probabilidad que se pueden calcular es:
c: Probabilidad de que el chocolate no tenga relleno de piña.
Sabemos que 5 chocolates tienen relleno de piña, entonces 20 no tienen relleno de piña. es decir, la probabilidad es:
P = 20/25 = 4/5
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A 12-yard-long pipe is cut into three equal sections. Two of the resulting sections are cut in half, and one of the halves is cut into thirds. If two pipe sections are chosen and combined end to end, what is the difference between the longest possible and shortest possible combinations? (Note: 1 yard = 3 feet)
Answer:
14ft
Step-by-step explanation:
12 yard pipe equals 36ft. Divided equally 3 times gives 3 pipes at 12ft per pipe. 2 of those are divided in half, making 4 6ft pipes. 1 of the 6ft pipes is cut into 3 2ft pipes. you now have 3 pipes at 2ft, 3 pipes at 6ft and 1 pipe at 12ft. the longest 2 pieces are 12ft and 6ft making 18ft. 2 shoetest pieces equal 4ft. 18ft minus 4ft equals 14ft.
A motorist travels from town A to town B, which are 84km apart. If he has completed 7/8 of his journey, what is the distance he has travelled?
The distance that he has traveled exists 73km 500m.
What is the distance?
Distance exists described as the amount of space between two items or the condition of existing far apart. The distance of an object can be described as the complete path traveled by an object.
Given: A motorist travels from town A to town B, which exists 84km apart. He has finished 7/8 of his journey.
To estimate the distance that he has traveled
He covered 7/8 out of 84 km
So, 7/8 × 84 = 73.5 km
The distance he has traveled = 73 km 500 m
Therefore, the distance that he has traveled exists 73km 500m.
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Astrid is looking for a job at a call center. Call center A offers her $15 per hour and call-center B offers her $.25 per minute.
Which place offers a higher wage?
Answer: They are the same
Step-by-step explanation: We convert both to $ per hour. Call center A is $15 per hour. Call center B is $.25 per minute. .25 per minute means $1.00 every 4 minutes. There are 15 4 minutes in an hour so they both offer the same wage.
The coefficient of 8 • 2N is
Answer:
16
Step-by-step explanation:
when we multiply we have 16n so thats is d coefficient
A college class is made up of f freshman and s sophomores. If 5 freshmen drop this class would be 3 times the number of freshman. Which of the following equations represents a in terms of f ?
Answer:
The answer is G.
f-5 drop the class while s class is 3(f-5)
therefore, s=3(f-5)
Find the area of the sector formed by the 60 degree central angle.
503π in2503π in2
103π in2103π in2
100π in2100π in2
None of the Above
The area of the sector of the circle is: A. 50/3π in.².
What is the Area of a Sector of a Circle?The area of a sector that is bounded by two radii of a circle is calculated using the formula, ∅/360 × πr², where we have the following parameters:
r = radius of the circle∅ = central angle formed by the sector.Thus, we are given the following regarding the sector of the circle:
Central angle (∅) = 60 degrees
Radius (r) = 10 inches.
Plug in the values into ∅/360 × πr²:
Area of sector = 60/360 × π(10²)
Area of sector = 1/6 × π(100)
Area of sector = 100/6 × π
Area of sector = 50/3 × π
Area of sector = 50/3π in.²
Thus, the area of the sector of the circle is: A. 50/3π in.².
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A shark begins 172.5 meters below sea level and then swam up 137.1 meters,. Where is the sharks location now in relation to sea level
Answer:
35.4m below sea level
Step-by-step explanation:
172.5 - 137.1 = 35.4
The shark's location is now 35.4m below sea level.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 4 -2 = 2
Using the arithmetic operations of addition and subtraction, the shark's location is now in relation to sea level if the shark begins 172.5 meters below sea level and then swam up 137.1 meters.
Assume that distance below sea level is positive,
⇒ 172.5 - 137.1 = 35.4
Hence, the shark's location is now 35.4m below sea level.
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What is the ratio of my lawn if it is 4 meters by 4.5 meters
Answer:
The 1:n ratio is= 1 : 1.125
The n:1 ratio is= 8/9 : 1
Just the simple ratio is= 4 : 4.5
One number is six more than three times another. If their sum is decreased by four, the result is twenty-two. Find
the numbers.
The smaller of the numbers is
Due Wed 08/10/
and the larger is
Answer: 5 is the smaller number and 21 is the larger number
Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.
A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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