We have the following:
The first thing is to simplify the expression as much as possible.
In the case of the vertical asymptote: The values that x cannot take is when it makes the denominator zero, therefore we must set the denominator equal to 0 and thus calculate the value of x that will make the function undefined.
2.
\(\begin{gathered} \frac{4x^6}{2x-6}=\frac{2\cdot2x^6}{2(x-3)}=\frac{2x^6}{(x-3)} \\ x-3=0 \\ x=3 \end{gathered}\)3.
\(\begin{gathered} \frac{6x^2+13x-5}{6x^2-23x+7}=\frac{(3x-1)(2x+5)}{(3x-1)(2x-7)}=\frac{2x+5}{2x-7} \\ 2x-7=0 \\ x=\frac{7}{2} \end{gathered}\)4.
\(\begin{gathered} \frac{x+4}{3x^2+11x-4}=\frac{x+4}{(3x-1)(x+4)}=\frac{1}{3x-1} \\ 3x-1=0 \\ x=\frac{1}{3} \end{gathered}\)5.
\(\begin{gathered} \frac{-x-4}{x^2-x-20}=\frac{-(x+4)}{(x+4)(x-5)}=\frac{-1}{x-5} \\ x-5=0 \\ x=5 \end{gathered}\)6.
\(undefined\)A missionary used his plane to take an injured girl 855 kilometers to the hospital. If he flew at an average speed of 171 kilometers per hour, how long did it take to reach the hospital?
Step-by-step explanation:
171 km/h
travel distance = 855 km
855 / 171 = 5 hours
it took him 5 hours to fly the 855 km (theoretically to the hospital).
normally, with a plane, you can't land on or at a hospital. you would need a helicopter to be able to do that.
so, he could only fly to a nearby airport, and then travel from there to the hospital. but we have no information about that.
One angle on a parallelogram measures 155 what are the measures of the other angle
Answer: 25, 90 ,90
Step-by-step explanation:
One angle on a paralel = 155
=> x+ y + z + 155 = 360
x + y + z = 205 ; x + y ; y + z ; x + z = 180
x + y = 180
=> Z = 205 - 180
Z = 25 Degree
x = y = 90 degree
Mark me as Brainliest pls ! Tysm !
Show your work please help me it’s due tomorrow!!!!
Answer: Consider me the brainiest. The answer is... Decimal form =4.083
Exact form= 49/12
The mixed number form=4 1/12
How do we solve fractions step by step?
Conversion a mixed number 2 1/3 to a improper fraction: 2 1/3 = 2 1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3
To find a new numerator
A; Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.
Two and one-third are seven-thirds.
Conversion a mixed number 1 3/4 to a improper fraction: 1 3/4 = 1 3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4
To find a new numerator:
a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4
b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7
c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.
Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It
is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling. In other words - seven thirds plus seven quarters is forty-nine twelfths.
Q(x)=-3x
r(x) = 4x-1
Find the following.
(r.q)(5) =
(r .q.)(5) =
Answer:
4749
Step-by-step explanation:
because it 36 and 45. it is right, and it is ok
For each equation, choose the statement that describes its solution.
If applicable, give the solution.
3(y+2)+y=4(y-1)+9
5(u+1)-u=4(u-1)+9
ANSWER
The first equation has no solution
The second equation has infinitely many solutions
STEP-BY-STEP EXPLANATION:
From the question provided, you are given the following equations
3(y + 2) + y = 4(y - 1) + 9
5(u + 1) - u = 4(u - 1) + 9
To find the values of y and u, we need to solve the equations independently
\(\begin{gathered} 3(y\text{ + 2) + y = 4(y - 1) + 9} \\ \text{open the parentheses} \\ 3\cdot\text{ y + 3 }\cdot\text{ 2 + y = 4}\cdot y\text{ - 4 }\cdot1\text{ + 9} \\ 3y\text{ + 6 + y = 4y - 4 + 9} \\ \text{Collect the like terms} \\ 3y\text{ + y + 6 = 4y + 5} \\ 4y\text{ + 6 = 4y + 5} \\ 6\text{ = 5} \\ \text{Hence, the equation has no solution} \end{gathered}\)\(\begin{gathered} 5(u\text{ + 1) - u = 4(u - 1) + 9} \\ \text{Open the parentheses} \\ 5\cdot\text{ u + 5}\cdot1\text{ - u = 4}\cdot u\text{ - 4}\cdot1\text{ + 9} \\ 5u\text{ + 5 - u = 4u - 4 + 9} \\ \text{Collect the like terms} \\ 5u\text{ - u + 5 = 4u + 5} \\ 4u\text{ + 5 = 4u + 5} \\ 5=\text{ 5} \\ \text{Hence, this equation has infinite }solutions \end{gathered}\)Calculate the gradient of the line 2y =8x+4
Answer:
m=4
2y/2=y
8x/2=4x
4/2=2
so
y=4x+4
A cylinder has a height of 12 inches. A similar cylinder has a height of 15 inches. What is the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder?
The ratio is 15+\(r_2\) : \(12+r_1\).
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here surface area of the cylinder = \(2\pi rh+2\pi r^2\) square unit
=> A = \(2\pi r(h+r)\) square unit.
Now Height = 12 in , radius = r1 then,
=> \(A_1 = 2\pi r_1(12+r_1)\) -----> 1
Now Height = 15 in , radius = r2 then,
=>\(A_2=2\pi r_2(15+r_2)\)-------> 2
Now the ratio of the surface area of the larger cylinder to the surface area of the smaller cylinder then,
=>\(2\pi r_2(15+r_2) : 2\pi r_1(12+r_1)\)
=>\(15+r_2:12+r_1\)
Hence the ratio is \(15+r_2:12+r_1\).
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Answer:
25:16
Step-by-step explanation:
I took the
hyla paid 37.88 for 3 prizzas and a order of garlic rolls if the garlic rolls cost 3.50 how much did each pizza cost
Answer: The answer is $11.46 per pizza
Step-by-step explanation:
First subtract 3.50 from 37.88 since we know how much the garlic roles are. after that you should get 34.38. Then just divide 34.38 by 3, you'll then get the price for each pizza.
HELP, ILL GIVE BRAINLIEST BUT HELP ASAP WITH THIS!!
Answer:
proportional
Step-by-step explanation:
Devon and Kylie each makr a cheese sauce. Devon uses 8 oz of cheese for every 9 oz of cream. Kylie uses 11 oz of cheese for every 12 oz cream. Whose cheese sauce will have a stronger cheese flavor? Show your work.
Answer:
Kylie's sauce has a greater proportion of cheese.
Step-by-step explanation:
The cheese sauce which have a stronger cheese flavor is Kyle's cheese sauce
Devon:Cream = 9 oz
Cheese = 8 oz
Ratio of cheese to cream = 8 : 9
= 8/9
= 0.89
Kyle:Cream = 12 oz
Cheese = 11 oz
Ratio of cheese to cream = 11 : 12
= 11/12
= 0.92
Therefore, the cheese sauce which have a stronger cheese flavor is Kyle's cheese sauce
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Use the symbols <,> or = to compare the decimals 56.72 and 5.672
Answer:
>
Step-by-step explanation:
its because 56.72 is greater than 5.672
Answer:
56.72 > 5.672
Step-by-step explanation:
> means greater than
< means less than
so 56.72 is greater than (>) 5.672
The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.
The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.
Let's assume the width of the rectangle is "b" cm.
According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (length + width)
Substituting the given perimeter value, we have:
7 1/3 cm = 2 * (2b + b)
To simplify the calculation, let's convert 7 1/3 to an improper fraction:
7 1/3 = (3*7 + 1)/3 = 22/3
Rewriting the equation:
22/3 = 2 * (3b)
Simplifying further:
22/3 = 6b
To solve for "b," we can divide both sides by 6:
b = (22/3) / 6 = 22/18 = 11/9 cm
Therefore, the width of the rectangle is 11/9 cm.
To find the length, we can substitute the width back into the equation:
Length = 2b = 2 * (11/9) = 22/9 cm
So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.
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I really need help with my question
answer :
z=11
y=13
will be ur answers
A high-end interior designer charges an hourly rate for his services plus a consultation fee. As a courtesy to his clients, after working on a job for over 20 hours, his hourly rate drops and the consultation fee is waived. The fees for the interior designer's services can be modeled with the following piecewise equation, where x represents the number of hours. f(x)={150x+300, x≤20100x, x>20 How much would it cost for 18 hours of interior design services? Enter your answer in the box. $
Answer:
3000
Step-by-step explanation:
Evaluate (1.28 × 105) + (1. 13 × 10³). Express the result in scientific notation.
The value of the expression in scientific notation is 1.2913 * 10^5
How to evaluate the expression?The expression is given as:
(1.28 × 105) + (1. 13 × 10³)
Rewrite properly as
(1.28 × 10^5) + (1. 13 × 10^3)
Express 10^3 as 10^-2 * 10^5
So, we have
(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 × 10^5) + (1. 13 × 10^-2 * 10^5)
Factor out 10^5
So, we have:
(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 + 1. 13 × 10^-2) * 10^5
This gives
(1.28 × 10^5) + (1. 13 × 10^3) = (1.28 + 0.0113) * 10^5
Evaluate the sum
(1.28 × 10^5) + (1. 13 × 10^3) = 1.2913 * 10^5
Hence, the value of the expression in scientific notation is 1.2913 * 10^5
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The scientific notation of (1.28 × 105) + (1. 13 × 10³) is 1.2913 × 10⁵
How to express numbers in scientific notation?Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.
The proper format for scientific notation is a × 10ᵇ
where
a = number or decimal.b = integerTherefore, let's evaluate (1.28 × 10⁵) + (1. 13 × 10³)
(1.28 × 10⁵) = 128000
(1. 13 × 10³) = 1130
Hence,
(1.28 × 10⁵) + (1. 13 × 10³) = 128000 + 1130 = 129130
In scientific notation,
(1.28 × 10⁵) + (1. 13 × 10³) = 129130 = 1.2913 × 10⁵
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Which value below is included in the solution set for the inequality statement? -3(x-4) > 6(x-1) 0-1 02 07 0 3 NEXT QUESTION ASK FOR HELP
The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.
To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.
Starting with the given inequality:
-3(x - 4) > 6(x - 1)
First, distribute -3 and 6 to the terms inside the parentheses:
-3x + 12 > 6x - 6
Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:
-3x - 6x > -6 - 12
-9x > -18
To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:
x < (-18) / (-9)
x < 2
Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.
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Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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HELP WITH THIS EASY MATH AUESTION DOWN HELOW!! WILL MARK AS BRANLIEST AND I NEED AN EXPLANTION TOO
Answer:
A. 36, -36
Step-by-step explanation:
y = x^2 - 12x - 5
steps to complete the square
add a 5 to both sides to move the constant
x^2 - 12x = 5
Then take -12, the coefficient of the variable and divide by 2 and square.
12/2 = 6, 6^2 = 36
Then add 36 to both sides.
x^2 - 12x + 36 = 5 + 36
Then subtract the 5 and 36 from both sides.
x^2 - 12x + 36 - 36 - 5
Matrix M has x-rows and (11-x) columns. Matrix N has y-rows and (y+5) columns. If MN and NM both are defined, find the values of x and y
Answer:
\(x=8, y=3\)
Step-by-step explanation:
Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.
Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:
\(y=11-x----(1)\)
Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:
\(y+5=x----(2)\)
Substitute (1) into (2):
\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)
Substitute (3) into (1):
\(y=11-8=3\)
Let (-3, 7) be a point on the terminal side of 0.
Find the exact values of sin 0, sec 0, and tan 0.
Answer:
\(\sin O \approx 0.919\), \(\sec O \approx -2.539\) and \(\tan O = -\frac{7}{3}\).
Step-by-step explanation:
Given a point (x, y) with respect to origin and in rectangular coordinates, the exact value of sine, secant and tangent functions are, respectively:
\(\sin O = \frac{y}{\sqrt{x^{2}+y^{2}}}\)
\(\sec O = \frac{1}{\cos O} = \frac{\sqrt{x^{2}+y^{2}}}{x}\)
\(\tan O = \frac{\sin O}{\cos O} = \frac{y}{x}\)
Given that \(x = -3\) and \(y = 7\), the exact values of sine, secant and tangent are:
\(\sin O = \frac{7}{\sqrt{(-3)^{2}+7^{2}}}\)
\(\sin O \approx 0.919\)
\(\sec O = \frac{\sqrt{(-3)^{2}+7^{2}}}{-3}\)
\(\sec O \approx -2.539\)
\(\tan O = \frac{7}{-3}\)
\(\tan O = -\frac{7}{3}\)
find f^n(x) if f(x)=1/(2-x)
This is the Answer
I hope it's helps
-10a-4b-1 5a-2b8 how
Answer:
-25a - 2b^8 - 4b
Step-by-step explanation:
-10a - 4b - 15a - 2b^8
combine like terms,
-10a - 15a = -25a
Answer them all please
Answer:
see the attachment
i hope it helps u ✌️✌️✌️☠️a) The highest common factor and the least common multiple are 12 and 48, respectively.
b) The highest common factor and the least common multiple are 12 and 72, respectively.
c) The highest common factor and the least common multiple are 8 and 160, respectively.
d) The highest common factor and the least common multiple are 12 and 48, respectively.
e) The highest common factor and the least common multiple are 14 and 840, respectively.
Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integersIn this question we must determine the highest common factor and the least common multiple of two integers.
The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.
Now, we proceed to determine the numbers for each case:
a) 12 and 48First, we factorize each integer:
\(12 = 2^{2}\times 3\), \(48 = 2^{4}\times 3\)
Then the highest common factor and the least common multiple are, respectively:
\(LCM = 2^{4}\times 3 = 48\), \(HCF = 2^{2}\times 3 = 12\)
The highest common factor and the least common multiple are 12 and 48, respectively. \(\blacksquare\)
b) 24 and 36First, we factorize each integer:
\(24 = 2^{3}\times 3\), \(36 = 2^{2}\times 3^{2}\)
Then, the highest common factor and the least common multiple are, respectively:
\(LCM = 2^{3}\times 3^{2} = 72\), \(HCF = 2^{2}\times 3 = 12\)
The highest common factor and the least common multiple are 12 and 72, respectively. \(\blacksquare\)
c) 32 and 40First, we factorize each integer:
\(32 = 2^{5}\), \(40 = 2^{3}\times 5\)
Then, the highest common factor and the least common multiple are, respectively:
\(LCM = 2^{5}\times 5 = 160\), \(HCF = 2^{3} = 8\)
The highest common factor and the least common multiple are 8 and 160, respectively. \(\blacksquare\)
d) 24, 48 and 60First, we factorize each integer:
\(24 = 2^{3}\times 3\), \(48 = 2^{4}\times 3\), \(60 = 2^{2}\times 3 \times 5\)
Then, the highest common factor and the least common multiple are, respectively:
\(LCM = 2^{4}\times 3 \times 5 = 48\), \(HCF = 2^{2}\times 3 = 12\)
The highest common factor and the least common multiple are 12 and 48, respectively. \(\blacksquare\)
e) 42, 56 and 70First, we factorize each integer:
\(42 = 2\times 3 \times 7\), \(56 = 2^{3}\times 7\), \(70 = 2\times 5\times 7\)
Then, the highest common factor and the least common multiple are, respectively:
\(LCM = 2^{3} \times 3 \times 5 \times 7 = 840\), \(HCF = 2\times 7 = 14\)
The highest common factor and the least common multiple are 14 and 840, respectively. \(\blacksquare\)
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while eating your yummy pizza, you observe that the number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour. on average, how many customers arrive in each 10 minutes interval?
In every 10 minutes an average of 3 customers will arrive to the pizza station
Given,
The number of customers arriving to the pizza station follows a poisson distribution with a rate of 18 customers per hour.
We have to find the average number of customers arrives in each 10 minutes.
Here,
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P (X = x) = (e^-μ × μ^x) / x!
Where,
The number of successes is x.
The Euler number is e = 2.71828.
μ is the average over the specified range.
Now,
Rate of 18 customers per hour;
μ = 18 n
n is the number of hours.
Number of customers arrive in each 10 minutes
10 minutes = 10/60 = 1/6
Then,
μ = 18 x 1/6 = 3
That is,
In every 10 minutes an average of 3 customers will arrive to the pizza station.
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show that the set of vectors in is orthogonal and (b)normalize the set to produce an orthonormal set.
An orthonormal set is a set of orthogonal unit vectors.
Normalization is the process of making unit vectors.
Orthonormal VectorsA set of vectors in which each vector is orthogonal to every other vector in the set is called an orthogonal set of vectors.
Two vectors are orthogonal when their dot product equals zero.
An orthonormal set is one in which each vector has length 1 and is orthogonal.
The process of creating a vector of length 1 in the same direction of the original vector is called "normalization".
An orthonormal set of vectors that is a basis of a vector space is quite useful. We can use the Gram-Schmidt process to transform a basis of a vector space (which may not be orthogonal) into an orthonormal basis.
To normalize vectors to produce an orthonormal set of vectors, we calculate the length of the vector and divide the vector by its length, to obtain a unit vector.
Since the question asked about "how to normalize vectors to produce an orthonormal set" that implies that the vectors already form an orthogonal set.
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The given question is incomplete,
So , I take another question, The question is:
How to normalize vectors to produce an orthonormal set?
how many inconsiderate people take up space in this world?
Answer:
Too many :(
Step-by-step explanation:
Its life u know
can i pls have brainliest
Answer:
that number is probably too high to count, don't ya think
Please help find the answer. Thank You!
Answer:
Step-by-step explanation:
208
Which value of c is in the domain of f(x)
The value of c in the domain of f(x) depends on the specific function f(x) and its domain.
In order to determine which value of c is in the domain of f(x), we need to know the function f(x) and its domain. A domain is the set of all possible input values of a function.
If a value of c is in the domain of f(x), then we can plug it into the function and get a valid output.
In general, a function f(x) can have a restricted domain due to certain conditions or limitations. For example, a square root function cannot have negative values under the radical because that would result in an imaginary number.
Thus, the domain of a square root function is restricted to non-negative values.
In order to find the domain of a function, we need to consider any restrictions on the input values. For example, if we have the function f(x) = 1/x, we cannot plug in x = 0 because that would result in division by zero, which is undefined.
Therefore, the domain of f(x) is all real numbers except 0. We can write this as D(f) = {x : x ≠ 0}.Once we know the domain of f(x), we can check which value of c is in the domain by seeing if it satisfies the condition.
For example, if the domain of f(x) is D(f) = {x : x > 2}, then c = 3 is in the domain because 3 is greater than 2. On the other hand, c = 1 is not in the domain because 1 is less than 2.
Therefore, the value of c in the domain of f(x) depends on the specific function f(x) and its domain.
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. To buy a car, Mitchell borrowed $17,000 for 3 years at an annual simple interest rate of 9%. If it takes him 3 full years to pay off the loan, how much interest will he will pay for the car? * O $9,045 O $9,009,000 O $ $4590 O $459,000 2. Jaelyn deposits $750 into an account that yields 6.5% simple interest. How much will he in her account in 30 months if she door no 10 points
Answer:
45
Step-by-step explanation:
I just took test and got 100%A FRANK RA
FRANK
FRANK
riddle
what do you mean.. is this some other things not about math?