Factories (a + b)³-3a²b(a + b)
Answer:
(a+b) (a+2ab+b2−3a2b)
Step-by-step explanation:
f(x)=10 x-10 . Find each value.
(f ⁰ f⁻¹)(-10)
The inverse function returns the original value for which the output of a function was given.
The value of f(x) = 10x - 10 is -110.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
An inverse in mathematics is a function that serves to "undo" another function. That is, if f(x) produces y, then putting y into the inverse of f yields x. Invertible functions are those that have an inverse, which is denoted by f1.
Lett the function be F(x) = 10x - 10
To differentiate with respect to X
F⁻¹(x) = 10
F( f⁻¹(x)) = F(10)
F( f⁻¹(x)) = -10x -10
Substitute the value of X = 10, then we get
F( f⁻¹(x)) = -10(10)-10
simplifying the above equation, we get
F( f⁻¹(x)) = -100-10
F( f⁻¹(x)) = -110
Therefore, the value of (f ⁰ f⁻¹)(d) = -110.
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You and your friend decide to get an Uber ride to a concert in downtown Minneapolis to avoid the crazy traffic. Uber charges a flat rate fee of $5.50 just to hop in the vehicle and an additional $2.25 for each mile traveled. Lyft charges a flat rate fee of $3.25 just to hop in the vehicle and an additional $3 for each mile traveled. How many miles (x) does it take for the price to be the same?
Answer:
I deleted my answer bc i accidentally answered the wrong question
The distance between the school and Target is 4.2 miles. On a map the ratio is 0.5 inches is equal to 3 miles. How far would the school and Nokesville be on the map?
The the distance between the school and Nokesville be on the map is 0.7 inches.
What is scaling ?
It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.
It is given that :
The distance between the school and Target is 4.2 miles and on a map the ratio is 0.5 inches is equal to 3 miles that is :
3 miles = 0.5 inches on map
Now to find the distance between the school and Nokesville be on the map we first find for 1 miles on the map and then multiply it by 4.2 miles :
3 miles = 0.5 inches on map
1 miles = 0.5/3 inches on map
4.2 miles = (0.5/3) x 4.2 inches on map
4.2 miles = 0.7 inches inches on map
Therefore, the the distance between the school and Nokesville be on the map is 0.7 inches.
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find the value of 9^-1/2
Applying the negative exponent rule, the value of 9^-1/2 is calculated as: 1/3.
What is the Negative Exponent Rule?If a number has a negative exponent, i.e. a^-1/2, it can be rewritten and expressed as:
a^-1/2 = 1/a^½
1/a^½ can also be rewritten or expressed as:
1/a^½ = 1/√a
Thus, we would apply the negative exponent rule to find the value of the expression, 9^-1/2 as explained below:
9^-1/2 = 1/9^½
Rewrite 1/9^½ as 1/√a
1/9^½ = 1/√9
Take the square root of 9
1/√9 = 1/3
This implies that, the value of the expression, 9^-1/2 is 1/3.
In conclusion, applying the negative exponent rule, the value of 9^-1/2 is determined as: 1/3.
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A retail clothing store offers customers an opportunity to open up a credit card during checkout. one location of the retail clothing store states that the number of credit cards, a, that are opened t months since january can be modeled by the function a(t) = 20 4t. the number of credit cards opened at another location, b, is defined by the function b(t) = 25 − t. what is an expression that can be used to determine the total amount of credit cards opened at the two locations? (a − b)(t) = −5 5t (a − b)(t) = −5 3t (a b)(t) = 45 5t (a b)(t) = 45 3t
An expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
Given,
Number of credit cards opened at location a = a (t) = 20 + 4t
Number of credit cards opened at location b = b (t) = 25 - t
Hence,
Total amount of credit card:
(a + b) (t) = (20 + 4t) + (25 - t)
(a + b) (t) = 20 + 4t + 25 - t
(a + b) (t) = 45 + 3t
Therefore an expression that can be used to determine the total amount of credit cards opened at the two locations is: (a + b) (t) = 45 + 3t.
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Pre-calculus Help please
The inverse of the expression y = 5 · (x - 6)² - 5 is x = √[(y + 5) / 5] + 6. (Correct choice: D)
How to determine the inverse of a function
According to the statement we have a function of the form y = f(x) and we need to find its inverse, that is, finding the equation of x in terms of y. This can be done by using algebra properties:
y = 5 · (x - 6)² - 5 Given
y = 5 · [(x - 6)² - 1] Distributive property
y / 5 + 1 = (x - 6)² Compatibilities with multiplication and addition / Existence of additive and multiplicative inverses / Associative and modulative properties
x - 6 = √(y / 5 + 1) Definition of square root / Symmetric property
x = √(y / 5 + 1) + 6 Compatibility with addition / Existence of additive inverse / Associative, commutative and modulative properties
x = √[(y + 5) / 5] + 6 Addition of fractions with different denominators / Result
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The average distance from Earth to the sun is about 9.3×107 miles. The average distance from Mars to the sun is about 1.4×108 miles. When both planets are at their average distance from the sun, how much farther is Mars from the sun than Earth?
A 79,000,000 mi
B 47,000,000 mi
C 107,000,000 mi
D 233,000,000 mi
plsssssszz answerrrrrr
I think this is one of those trick questions!
I'm going to say the answer is... 90°
because it states within the question that ∠A and ∠B are vertical angles
That is my educated guess. I hope it's helpful!
Pls let me know if my answer is incorrect.
convert 87.65 to base 8
The answer is 127.5146314631
What is 87.65 decimal in octal? 87.65 from decimal to octal is 127.5146314631. Here we show you how to write 87.6510 in octal and how to convert 87.65 from base-10 to base-8.
To convert decimal number 87.65, we convert its integer and fraction part individually and then add them to get the equivalent octal number, as below:
To convert integer 87 to octal, follow these steps:
Divide 87 by 8 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get the equivalent octal number.
87 / 8 = 10 with remainder 7
10 / 8 = 1 with remainder 2
1 / 8 = 0 with remainder 1
Here is the answer to 87 decimal to octal number:
127
For converting decimal fraction 0.65 to octal number, follow these steps:
Multiply 0.65 by 8 keeping notice of the resulting integer and fractional part. Continue multiplying by 8 until you get a resulting fractional part equal to zero (we calcuclate upto ten digits).
Then just write out the integer parts from the results of each multiplication to get equivalent octal number.
0.65 × 8 = 5 + 0.2
0.2 × 8 = 1 + 0.6
0.6 × 8 = 4 + 0.80000000000001
0.80000000000001 × 8 = 6 + 0.40000000000009
0.40000000000009 × 8 = 3 + 0.20000000000073
0.20000000000073 × 8 = 1 + 0.60000000000582
0.60000000000582 × 8 = 4 + 0.80000000004657
0.80000000004657 × 8 = 6 + 0.40000000037253
0.40000000037253 × 8 = 3 + 0.20000000298023
0.20000000298023 × 8 = 1 + 0.60000002384186
Here is the answer to 0.65 decimal to octal number:
0.5146314631
Therefore, decimal number 87.65 converted to octal is equal:127.5146314631
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f(x) = 3x²5x + 20
Find f(-8)
Answer:
f(-8)= -7660
Step-by-step explanation:
f(-8)= 3(-8)^2·5(-8)+20
If an airplane can travel at 20,000 miles per hour, how many meters per second does it travel? Knowing that: 1 mi 1.609 km
Answer: 8,938 [tex]\frac{8}{9}[/tex] or 8,938.8889 meters per second
Step-by-step explanation:
To solve this problem, we will use a process called dimensional analysis (that you have probably done many times without realizing it).
What is dimensional analysis? Let's say you know there are 12 inches in a foot, and you want to know how many inches are in 2 feet. 12 * 2 = 24 inches in a foot, that's dimensional analysis!
Here is the process you would take to solve your problem:
➜ If we have the units [tex]\frac{hour}{hour}[/tex], they "cancel" out to become one. This way, we make sure we end up with the correct units, [tex]\frac{meters}{second}[/tex].
➜ We take units we know, such as 3,600 seconds in an hour, and multiply them by the original value until we end up with the measurement we want.
[tex]\displaystyle 20,000\; \frac{miles}{hour}*\frac{1 \;hour}{3,600\; seconds} *\frac{1,609\;meters}{1\;mile}=\frac{20,000*1*1,609\;meters}{3,600\;seconds} =\frac{32,180,000\;meters}{3,600\;seconds} = 8,938.89\; \frac{meters}{second}[/tex]
In other words;
8,938.89 meters per second
Simplify. √75 + √125
The value of the expression √75 + √125 is 5 (√3 + √5 ).
A number is a fundamental mathematical unit. For counting, measuring, and comparing quantities, we utilize numbers. A set of symbols, or numerals, used to represent numbers is known as a number system.
A square root is a factor of a number that yields the original number when multiplied by itself.
Consider the expression √75 + √125,
Let's assume x = √75 + √125
Now,
75 = 5 × 15 = 5 × 3 × 5
125 = 5 × 25 = 5 × 5 × 5
Therefore,
x = √75 + √125
x = √ [ 5 × 3 × 5] + √ [ 5 × 5 × 5 ]
x = 5√3 + 5√5
x = 5 × [ √3 + √5 ]
x = 5 × [ 1.73 + 2.24 ]
x = 5 × 3.97
x = 19.85
√75 + √125 = 19.85
Hence, the value of √75 + √125 is equal to 19.85.
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Please help me out please please please
The surface area is the sum of the area of the surfaces. The surface area of the box is 360x^2 - 216x
Surface area of a box.
The formula for calculating the surface area of a box is expressed according to the equation:
Surface area = 2(lw + wh +lh)
Given the following parameters
length = 6x
width = 12x - 9
height = 6x
Substitute
Surface area = 2(6x(12x-9) + (12x-9)(6x) +(6x)(6x))
Expand
Surface area = 2(72x^2-54x) + (72x^2-54x) + 36x^2)
Surface area = 2(180x^2-108x)
Surface area = 360x^2 - 216x
Hence the surface area of the box is 360x^2 - 216x
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what is the square of -3
Answer:
The square of -3 is 9
Step-by-step explanation:
(-3)^2=9
During a sale, a store offered a 20% discount on a camera that originally sold for $370. After the sale, the discounted price of the camera was marked up by 20%. What was the price of the camera after the markup? Round to the nearest cent.
Answer:
624
Step-by-step explanation:
650 * .80 = 520520 * 1.20 = 624
Read each question. Then write the letter of the correct answer on your paper.Let g(x)=x-3 and h(x)=x²+6 . What is h(1)xg(1) ?
We get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
We are given the two functions as:
g (x) = x - 3 and h (x) = x² + 6
Now, we will first find h (1)
h (1) = (1)² + 6
h(1) = 1 + 6
Add them, we get:
h (1) = 7
Now, we will find g (1):
g (1) = 1 - 3
g (1) = - 2
Now we will find the expression h(1) × g(1):
h(1) × g(1) = 7 × ( - 2 )
h(1) × g(1) = - 14
Therefore, we get the value of h(1) × g(1) as - 14 for the functions g (x) = x - 3 and h (x) = x² + 6.
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How do you answer and write this out correctly
2.
x^2-4y
/2
4^2- (4*-3)
/2
16+12
/2
28/2
14
14. “-4 times a number plus 29”
Answer:
It depends on what that number is but -4+29 is equal to 29-4; making the answer to -4+29=5.
Step-by-step explanation:
If x= -2, the value of the expression 3x² - 5x +1/x is
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{3x^2 - 5x + 1}{x}}\\\\\mathsf{= \dfrac{3(-2)^2 - 5(-2) + 1}{-2}}\\\\\mathsf{= \dfrac{(3)(4) - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (5)(-2)+1}{-2}}\\\\\mathsf{= \dfrac{12 - (-10) + 1}{-2}}\\\\\mathsf{= \dfrac{12 + 10 + 1}{-2}}\\\\\mathsf{= \dfrac{22 + 1}{-2}}\\\\\mathsf{= \dfrac{23}{-2}}\\\\\mathsf{-11 \dfrac{1}{2}}\\\\\\\\\huge\text{Thus, your answer should be: \boxed{\mathsf{-11\dfrac{1}{2}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Expand each logarithm.
log₃ 7(2 x-3)²
If the expression is log₃ 7(2 x-3)², then the expansion of the expression is [[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]
Given that the expression is log₃ 7(2 x-3)².
We are told to find the expansion of the expression.
Logarithmic function is basically the opposite of the exponential function and is denoted by log or ln.
It says that [tex]log_{a} b[/tex]= [tex]log_{x}b /log_{x}a[/tex].
The expression is log₃ 7(2 x-3)².
We know that log mn=log m +log n.
log₃ 7(2 x-3)²=[[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]
We know that log [tex]a^{b}[/tex]=log b/log a but we are not changing here,So,
log₃ 7(2 x-3)²=[[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]
Hence if the expression is log₃ 7(2 x-3)², then the expansion of the expression is [[tex]log_{3}[/tex] 7+ [tex]log_{3}[/tex] [tex](2x-3)^{2}[/tex]]
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the sum of three is 131 the second of three numbers is seven more than twice the first the third number is 12 less then the first what equation can be used to solos this problem
Answer:
4x - 5 = 131 where x is the first number.
Step-by-step explanation:
Let the first number be x.
Seconder number = 2x + 7.
Third number = x - 12.
So, the equation is :-
x + 2x + 7 + x - 12 = 131
4x - 5 = 131
4x = 136
x = 34
First number = 34, second = 2(34) + 7 = 75 and third number = 34-12 = 22.
PLease help!!!! 3( - 4y - 5) = 8y + 25, Show your work please!!
Answer:
y = -2
Step-by-step explanation:
Given equation:
[tex]3(-4y-5)=8y+25[/tex]
Distribute:
[tex]\implies 3 \cdot -4y - 3 \cdot 5=8y+25[/tex]
[tex]\implies -12y - 15=8y+25[/tex]
Add 15 to both sides:
[tex]\implies -12y - 15+15=8y+25+15[/tex]
[tex]\implies -12y =8y+40[/tex]
Subtract 8y from both sides:
[tex]\implies -12y-8y =8y+40-8y[/tex]
[tex]\implies -20y =40[/tex]
Divide both sides by -20:
[tex]\implies \dfrac{-20y}{-20} =\dfrac{40}{-20}[/tex]
[tex]\implies y =-2[/tex]
Now we have to,
→ solve for the required value of y.
Let's solve the problem,
→ 3(-4y - 5) = 8y + 25
→ -12y - 15 = 8y + 25
→ -12y - 8y = 25 + 15
→ -20y = 40
→ y = -40/20
→ [ y = -2 ]
Hence, the value of y is -2.
X = 2y + 18
5x = -3y - 27
Use the substitution method to solve the system below
Answer:
(0, - 9 )
Step-by-step explanation:
x = 2y + 18 → (1)
5x = - 3y - 27 → (2)
substitute x = 2y + 18 into (2)
5(2y + 18) = - 3y - 27
10y + 90 = - 3y - 27 ( add 3y to both sides )
13y + 90 = - 27 ( subtract 90 from both sides )
13y = - 117 ( divide both sides by 13 )
y = - 9
substitute y = - 9 into (1)
x = 2(- 9) + 18 = - 18 + 18 = 0
solution is (0, - 9 )
Find the center, vertices, and foci of the ellipse with equation x squared divided by 9 plus y squared divided by 25 = 1
Answer:
Center: (0,0)
Vertices: (0,-5), (0,5)
Foci: (0,-3) (0,3)
Step-by-step explanation:
A line passes through the points (6, -3) and (j, -4). If the slope of the line is 1/3 find the value of j.
Answer:
j = 3
Step-by-step explanation:
Recall the slope formula:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now, simply substitute the values from the question.
[tex]\frac{1}{3} =\frac{-4+3}{j-6}[/tex]
Now, use the cross-multiplication method. (remember, when subtracting negatives, the negative becomes a positive)
[tex]1(j-6)=3(-4+3)[/tex] Cross Multiplication
[tex]1(j-6)=3(-1)[/tex] Simplify
[tex]j-6=-3[/tex] Distributive Property
[tex]j=3[/tex] Addition Property
Therefore, j = 3.
What expression is equivalent to -3(2x-4)
The given expression , the value of x is 2.
given,
equivalent expression = -3(2x - 4)
= -6x + 12
x = 2
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x2 + 2y + 1) = 6x2 + 12y + 6.you can write equivalent expressions by combining like terms. Like terms are terms that have the same variables raised to the same powers. For example, the list shows some pairs of like terms. the new coefficient is 9.Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.to know more about equivalent expression;
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Please help is this true or false
the answer for your question is true. I believe.
Suppose you invest $ 500 in a savings account that pays 3.5 % annual interest. How much will be in the account after five years?
Amount $593.84 will be in the account after five years.
According to the question we have been given that the
amount invested initially = $500
annual interest rate = 0.035
Time = 5 years.
The formula for the future value is given as
[tex]FV = a(1 + r)^{t}[/tex] (1)
where , FV = future value
a = amount invested initially
r = annual interest rate
t = time
putting the required values in equation (1) we get
[tex]FV = 500 (1 + 0.035)^{5} \\FV = 500 ( 1.035)^{5}[/tex]
FV = 500*1.188
FV = $ 593.84
Thus, $593.84 will be the amount in the account after five years.
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Simplify each expression.
ln e¹⁰
We will get lne¹⁰ itself after simplifying the given expression lne¹⁰.
What is an expression?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.So,
Given expression: ln e¹⁰Then,
lne¹⁰⇒ lne¹⁰Therefore, we will get lne¹⁰ itself after simplifying the given expression lne¹⁰.
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