Evaluate the function.f(x) = -3x^2 - 6Find f(-9)
Answers
Given the function
\(f(x)=-3x^2-6\)You have to find f(-9), to do so you have to replace the equation with x=-9 and calculate the value of f(x)
\(\begin{gathered} f(x)=-3x^2-6 \\ f(-9)=-3(-9)^2-6 \\ f(-9)=-3(81)-6 \\ f(-9)=237 \end{gathered}\)When x=-9, the function has a value of 237
Related Questions
Given the graph below, locate the points of the reflection over the x-axis.
Answers
Answer:
Answer:
A: (1,3)
A': (1,-3)
---
B: (5,1)
B': (5,-1)
---
C: (-2,2)
C': (-2,-2)
---
D: (-5,4)
D': (-5,-4)
The reflection of the given points over the x-axis is:
(-5, -4), (-2, -2), (1, -3), (5, -1)
What is Coordinate Geometry?By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given data:
We are given a graph, and we have to find the reflection of the points in the graph over the y-axis.
From the graph given, the points are as as follows:
Let's assume the points as A, B, C and D
A = (-5, 4)
B = (-2, 2)
C = (1, 3)
D = (5, 1)
The reflection over the x-axis are as follows:
A' = (-5, -4)
B' = (-2, -2)
C' = (1, -3)
D' = (5, -1)
Hence, the reflection of the given points over the x-axis is:
(-5, -4), (-2, -2), (1, -3), (5, -1)
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If a = 2+ √5 and b = 1/a find a^2 + b^2
Answers
Hence, The Value of: a^2 + b^2 is 18
Step-by-step explanation: √ Find the RECIPROCAL of: ab = 1/a = 1/ 2 + √5
Rationalize the Denominator:b = 1/2 + √5 * 2 - √5/2 - √5
= 2 - √5/1
Simplify:b = 2 - √5
Square: A and B:a^2 = (2 + √5)^2 = 4 + 4√5 + 5
b^2 = (2 - √5)^2 = 4 - 4√5 + 5
ADD: a^2 and b^2:a^2 + b^2 = 4 + 4√5 + 5 + 4 - 4√5 + 5
= 18 - 3√5
So, Now we solve the Inverse property of addition: ±4 + 5 + 4 + 5
9 + 4 + 5
13 + 5 = 18
Move the expression to the right:a^2 + b^2 = 18
a^2 = 18 - b^2
Now we take the root of both sides/Negative/Positive:a = ± √18 - b^2
a = √18 - b^2
a = -√18 - b^2
Draw a conclusion:Hence, The Value of: a^2 + b^2 is 18
I hope this helps you!
carbon-14 dating wood deposits recovered from an archaeological site contain 19% of the c-14 they originally contained. how long ago did the tree from which the wood was obtained die? (assume the half life of carbon-14 is 5,730 years. round your answer to the nearest whole number.)
Answers
The tree from which the wood was obtained died 13,729 years ago, considering the exponetial function that models the situation.
How to model an exponential function?The standard definition of an exponential function is given by the equation presented as follows:
\(A(t) = A(0)b^{\frac{t}{n}}\)
The parameters of the exponential function with format above are given as follows:
A(0) is the initial value.b is the rate of change of the function.n is the time needed for the rate of change.The half-life of carbon-14 is 5,730 years, hence the parameters b and n have the values given as follows:
b = 0.5, n = 5730.
Then the exponential function for the amount of the substance after t years is given as follows:
\(A(t) = A(0)(0.5)^{\frac{t}{5730}}\)
19% of the substance remained, hence the time is obtained as follows:
\(0.19A(0) = A(0)(0.5)^{\frac{t}{5730}}\)
\((0.5)^{\frac{t}{5730}} = 0.19\)
t = 5730 x log(0.19)/log(0.5)
t = 13,729 years.
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PLS HELP 30 PTS Sue and Kiana each recorded the number of computers they fixed everyday for 15 days. These line plots represent the data recorded.
Classify each statement by selecting true or false.
True False
The centers of the data sets are approximately equal.
True – The centers of the data sets are approximately equal.
False – The centers of the data sets are approximately equal.
The degree overlap is high.
True – The degree overlap is high.
False – The degree overlap is high.
The spreads of the data sets have overlaps.
True – The spreads of the data sets have overlaps.
False – The spreads of the data sets have overlaps.
Two line plots with the same scale and interval, extending from zero to ten, with tick marks every one unit. The plots are stacked vertically for comparison. Each plot has fourteen data values, which are plotted as follows. In upper plot, one value is plotted at point two on the line, one value at point three, two values at four, four values at five, three values at six, two values at seven, and one value at eight. In lower plot, one value is plotted at point three, two values at four, four values at five, three values at six, three values at seven, and one value at eight
Answers
Answer:
Step-by-step explanation:
1st one false 2 one false the third one true
Rationalise the equation :
\( \frac{y ^{2} }{ \sqrt{x^{2} + y {}^{2} } + x} \)
Answers
Answer:
\(\sqrt{x^2+y^2}-x\)
Step-by-step explanation:
\(\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:\)
\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)
\(\textsf{Cancel the common factor}\:y^2:\)
\(\implies \sqrt{x^2+y^2}-x\)
Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:
\(\;\longrightarrow\dfrac{1}{a+b}\)
Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.
\(\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}\)
Hence, this is what the rationalization means.
Elucidation:We have been given and equation and we have been asked to rationalise the equation.
The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;
\(\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}\)
\(\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}\)
\(\implies \boxed{\sqrt{x^2+y^2}}\)
Hence, this is our required solution for this question.
Last semester, I taught two sections of a same class; Section A with 20 students and Section B with 30. Before grading their final exams, I randomly mixed all the exams I together. I graded 12 exams at the first sitting. (i) Of those 12 exams, the probability that exactly 5 of these are from the Section B is (You do not need to simplify your answers.) . (ii) Of those 12 exams, the probability that they are not all from the same section is (You do not need to simplify your answers.)
Answers
1. The probability is approximately 0.1823.
2. The probability that the 12 exams are not all from the same section is 0.6756
How to calculate the probability1. The probability that exactly 5 of the 12 exams are from Section B is:
P(X = 5) = (12 choose 5) * 0.6 × 0.6⁴ * (1 - 0.6)⁷
= 0.1823
2. The probability that all 12 exams are from the same section is:
P(all from A) + P(all from B) = (20/50)¹² + (30/50)¹²
≈ 0.0132 + 0.3112
≈ 0.3244
Therefore, the probability that the 12 exams are not all from the same section is:
P(not all from same section) = 1 - P(all from same section)
≈ 1 - 0.3244
≈ 0.6756
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\(y=-3x^{2} -6x+8\) the x-interval over which the function is increasing
Answers
The x-interval over which the function is increasing is:x < -1 or x > -1
Given function:\(y=-3x^{2} -6x+8\)
The x-interval over which the function is increasing.
The given function is a quadratic function of the form f(x) = ax² + bx + c. We will determine the intervals for which the function is increasing.
To know the increasing intervals of the given function f(x), we need to determine the intervals for which f'(x) > 0 where f'(x) is the first derivative of the function.
So, Let's find the first derivative of the given function:
\(\begin{aligned}f(x)&=-3x^{2}-6x+8\\\Rightarrow f'(x)&=-6x-6=-6(x+1)\end{aligned}\)
Now, we have to check the sign of f'(x) to find the interval(s) where the function is increasing.
Sign of f'(x) changes at x = -1. If x < -1, f'(x) > 0, so the function is increasing in that interval. Similarly, if x > -1, f'(x) > 0, so the function is increasing in that interval as well.
Therefore, the x-interval over which the function is increasing is:x < -1 or x > -1
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i need help with this please
Answers
Answer:
n= -1.2
Step-by-step explanation:
I think because if you use slope equation to find the slope which is 3/5 and then you use point slop equation to find out what the equation would be. y=3/5x and then you substitue y for 18 and solve/simplify the equation to get -1.2.
assume the prices of cold medicine (per box) are normally distributed with a mean of $17 and a standard deviation of $4.5. find the probability that a randomly selected box of cold medicine will cost more than $15. include a sketch of the density curve in your answer.
Answers
The probability that a randomly selected box of cold medicine will cost more than $15 is approximately 0.8413.
To find the probability, we need to calculate the area under the normal distribution curve to the right of $15. We can use the z-score formula to standardize the value of $15 and then look up the corresponding area in the standard normal distribution table or use statistical software.
First, we calculate the z-score:
z = (x - μ) / σ
where x is the value ($15), μ is the mean ($17), and σ is the standard deviation ($4.5).
z = (15 - 17) / 4.5 = -0.4444
Using the standard normal distribution table or a calculator, we find that the area to the left of z = -0.4444 is approximately 0.3581. Since we want the area to the right of $15, we subtract this value from 1 to get the probability of the box costing more than $15:
P(X > $15) = 1 - 0.3581 = 0.6419
Therefore, the probability that a randomly selected box of cold medicine will cost more than $15 is approximately 0.6419 or 64.19%.
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What is 6 divided by 2(1+2)
Answers
Answer:
The answer is 1
Step-by-step explanation:
Remember PEMDAS, 1+2 is 3. 2x3 is 6, then 6 divided by 6 is 1.
Answer:
1
Step-by-step explanation:
6 / 2(1 + 2)
6 / 2(3)
6 / 6 = 1
A point charge q
1
=+2.40μC is held stationary at the origin. A second point charge q
2
=−4.30μC moves from the point x=0.155 m,y=0, to the point x=0.250 m. y=0.250 m. Part A What is the change in potential energy of the pair of charges? Express your answer in joules to three significant figures. X Incorrect; Try Again; 5 attempts remaining Part B How much work is done by the electric force on q
2
? Express your answer in joules to three significant figures
Answers
The work done by the electric force on q2 is the same as the change in potential energy, expressed in joules to three significant figures.
Part A:
The change in potential energy (ΔPE) of the pair of charges can be calculated using the formula:
ΔPE = k(q1*q2) / r
where k is the electrostatic constant (k = 8.99 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the separation between the charges.
Given:
q1 = +2.40 μC = +2.40 × 10^-6 C
q2 = -4.30 μC = -4.30 × 10^-6 C
r = distance between the charges = distance between the two points (x2, y2) and (x1, y1)
We can use the distance formula to calculate the separation between the charges:
r = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values:
x2 = 0.250 m
x1 = 0.155 m
y2 = 0.250 m
y1 = 0
r = √((0.250 - 0.155)^2 + (0.250 - 0)^2)
Now, we can calculate the change in potential energy:
ΔPE = (8.99 × 10^9 N m^2/C^2) * [(+2.40 × 10^-6 C) * (-4.30 × 10^-6 C)] / r
Evaluate the expression to get the answer in joules, rounded to three significant figures.
Part B:
The work done by the electric force (W) on q2 can be calculated using the formula:
W = ΔPE
Since the work done is equal to the change in potential energy, the answer for Part B will be the same as the answer calculated in Part A.
Therefore, the work done by the electric force on q2 is the same as the change in potential energy, expressed in joules to three significant figures.
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If y is the altitude in feet and
x is time in minutes,
Use the equation:
y = -2000x + 30,000
to find a plane's altitude at
5 minutes.
PLEASE ANSWER
Answers
Answer: To find the plane's altitude at 5 minutes, we can substitute x = 5 into the equation:
y = -2000x + 30,000
y = -2000 * 5 + 30,000
y = -10,000 + 30,000
y = 20,000
So the plane's altitude at 5 minutes is 20,000 feet.
Step-by-step explanation:
Of the flowers in Rey's yard, 1/3 are tulips and
1/13 are roses. What
fraction of the flowers in Rey's yard are either tulips or roses?
are tulips and
Answers
Answer:
16/39
Step-by-step explanation:
1/3=13/39
1/13=3/39
13/39+3/39=16/39
1. What is 30 percent of 120?
A.30
B.20
C.40
D.36
Answers
Answer:
D 36
Step-by-step explanation:
Answer:
D.36
Step-by-step explanation:
30 ?
--- x ---
100 120
Multiply 30 times 120. You get 3600. Divide that by 100, and you get 36.
help meeee plezzzzzzz
Answers
Use PEMDAS to show your answer
Answer:
-16
Step-by-step explanation:
Or you could use desmos scientific calculator
What is the Algebraic Notation for this reflection?
A (x,y) ---> (y,x)
B (x,y) ---> (-x,y)
C (x,y) ---> (-y,-x)
D (x,y) ---> (x,-y)
Answers
Your y coordinates do not change, but your x coordinates are opposites
What is the common difference/ratio for this sequence 1/6, 1/12, 1/2, 2
Answers
The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio. Sequence refers to a set of numbers in a particular order with a rule governing the manner in which the numbers appear.
The sequence given is {1/6, 1/12, 1/2, 2}. Since this sequence is not consecutive, we cannot use the common difference. We can, however, use the ratio to determine the next terms in the sequence. Let us determine the ratio of successive terms in the sequence: {(1/12) / (1/6)} = 1/2{(1/2) / (1/12)} = 6{(2) / (1/2)} = 4
The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio. Sequence refers to a set of numbers in a particular order with a rule governing the manner in which the numbers appear. A sequence is a group of things, events, or numbers that are arranged in a specific order or following a definite rule. A sequence can be made up of numbers, letters, or any other things that follow a pattern. The ratio of a sequence refers to the quotient of successive terms in the sequence. The ratio of successive terms is constant for a geometric sequence while the difference is constant for an arithmetic sequence.
A common difference is a constant difference between successive terms in an arithmetic sequence. This means that the common difference is the number you add or subtract to get to the next term in the sequence. An example of an arithmetic sequence is {1, 3, 5, 7, 9} where the common difference is 2. This means that you add 2 to the previous term to get to the next term in the sequence. A common ratio, on the other hand, is the quotient of successive terms in a geometric sequence. The common ratio is the number that you multiply or divide by to get to the next term in the sequence. For example, {2, 4, 8, 16, 32} is a geometric sequence with a common ratio of 2. This means that you multiply each term by 2 to get to the next term in the sequence. In the given sequence {1/6, 1/12, 1/2, 2}, since the sequence is not consecutive, we cannot use the common difference. We can, however, use the ratio to determine the next terms in the sequence. The ratio of successive terms in the sequence is 1/2, 6, 4. Hence, this sequence does not have a common difference/ratio.
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The formula to find the perimeter of a rectangle P = 2l + 2w. Solve for w.
Answers
Answer:
w=(P-2l)/2
Step-by-step explanation:
A recipe for 114 dozen cupcakes calls for 123 cups of flour, but Rashida has only 1 cup of flour.
How many cupcakes can she make? Hint: Pay close attention to the units!
[Put your answer as a mixed number. For example, if your answer is 4212, enter 42 1/2]
Answers
Answer:
Rashida can make 9 cupcakes
With 1 cup of flour, you can make 9 cupcakes.
The price of broccoli is $1.25 per pound. Let y be the total cost in dollars of buying x pound of broccoli. Which equation represents the situtation?
Answers
Answer: y=1.25x
Step-by-step explanation:
i got it right
Answer: y=1.25x, which equation represents the situtation.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Here, given that,
The price of broccoli is $1.25 per pound.
Let, y be the total cost in dollars of buying x pound of broccoli.
Hence, equation represents the situtation is y=1.25x.
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8.5675859
rational or irrational ?
Answers
Answer: irrational
Step-by-step explanation:
Answer:
irrational
Step-by-step explanation:
Write the ratio as a fraction in simplest form.
51:9
Answers
Answer:
The ratio of 51:9 in it's simplest form is 17:3.
why is it important to find the area of a circle?
Answers
Answer:it's important to understand the properties of a circle because that's how you understand how it can be used in a problem.
Step-by-step explanation:
The importance of finding out the area of the circle should be explained below.
Area of circle:The radius, diameter, and circumference find the area of the circle. Here the circumference represents the area of the outside of the circle and it could be found by first determining the diameter and the radius of the circle. This measurement should be important for determining the measurement so that it measured the other geometric property of the circle.
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true or false. the x-intercept and the y-intercept for a line will never be the same ordered pair.
Answers
True, the x-intercept and the y-intercept will never be the same ordered pair because they have different x- and y-coordinates
Explanation:The statement is true. The x-intercept and the y-intercept for a line will never be the same ordered pair because they are two distinct points. The x-intercept is the point where a line crosses the x-axis, which means that the y-coordinate of this point is zero.
The y-intercept, on the other hand, is the point where the line crosses the y-axis, which means that the x-coordinate of this point is zero. Therefore, the x-intercept and the y-intercept will never be the same ordered pair because they have different x- and y-coordinates.
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McGraw-Hill Educa...A ALEKS - Michael A...O POLYNOMIAL AND RATIONAL FUNCTIONSThe Factor Theorem
Answers
The factor theorem states that, given a polynomial f(x),
\(\begin{gathered} (x-a)\rightarrow\text{ is a factor of f\lparen x\rparen} \\ \Leftrightarrow \\ f(a)=0 \end{gathered}\)Thus, in our case,
\(\begin{gathered} (x+2)=(x-a) \\ \Rightarrow2=-a \\ \Rightarrow a=-2 \end{gathered}\)Then, we need to evaluate P(-2) to determine whether (x+2) is a factor of P(x),
\(\begin{gathered} P(-2)=(-2)^3+4(-2)^2-3(-2)-14=-8+16+6-14=0 \\ \Rightarrow P(-2)=0 \end{gathered}\)P(-2)=0Therefore, (x+2) is a factor of P(x)Normally a chef uses 13 ounces of chocolate to make chocolate chip cookies. But he started using 16.12 ounces instead. He should advertise the cookies as having _____ percent more chocolate
Group of answer choices
Answers
Answer:
24%
Step-by-step explanation:
\(16.12 - 13 = 3.12\\3.12 * 100 = 312 \\312 / 13 = 24\)
24% more chocolate
1.00 + 0.24 = 1.24
13 * 1.24 = 16.12
When verifying the stability of the potential coexistence points, you calculated the eigenvalues for each requested point. For x = 8.47*10-8 and the point (30568, 386008), choose the eigenvalue with the larger absolute value. What is the value of this eigenvalue, entering it as a negative number if it is negative? Round your answer to 4 decimal places.
Answers
The eigenvalue with the larger absolute value for the Jacobian matrix at the point (30568, 386008) is approximately 5269.407, which is positive. No need to enter it as a negative number.
The system of equations is
f(x,y) = 9x^2 + 3x + y - 30 = 0
g(x,y) = 3x^2 + xy - 10^6 = 0
The Jacobian matrix J is
J(x,y) = [ df/dx df/dy ]
[ dg/dx dg/dy ]
where
df/dx = 18x + 3
df/dy = 1
dg/dx = 6x + y
dg/dy = x
Evaluated at the point (30568, 386008), we have
df/dx = 18(30568) + 3 = 550149
df/dy = 1
dg/dx = 6(30568) + 386008 = 582216
dg/dy = 30568
So, J(30568, 386008) =
[550149 1]
[582216 30568]
The eigenvalues of J(30568, 386008) are the solutions to the characteristic equation
det(J - λI) = 0
where I is the identity matrix and det denotes the determinant.
The characteristic equation is
(550149 - λ)(30568 - λ) - 582216 = 0
Expanding and simplifying this expression, we get
λ^2 - 855717λ + 166573528 = 0
Using the quadratic formula, we get
λ = (855717 ± √(855717^2 - 4(166573528))) / 2
λ ≈ 5269.4073 or λ ≈ 315.5927
The eigenvalue with the larger absolute value is 5269.4073. Since it is positive, we don't need to enter it as a negative number. Rounding to 4 decimal places, we get
5269.4073 ≈ 5269.407
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--The given question is incomplete, the complete question is given
" When verifying the stability of the potential coexistence points, you calculated the eigenvalues for each requested point. For x = 8.47*10-8 and the point (30568, 386008), choose the eigenvalue with the larger absolute value. Here, f(x,y) = 9x^2 + 3x + y - 30 = 0 and g(x,y) = 3x^2 + xy - 10^6 = 0What is the value of this eigenvalue, entering it as a negative number if it is negative? Round your answer to 4 decimal places. Your Answer:"--
I WILL GIVE YOU BRAINLIEST!!!!!
Answers
Answer:
y=x
Step-by-step explanation:
The graph is a line
The only function that is a line is
y=x
which graphs represent functions
A. Graph D only
B. Graph B and Graph D
C. Graph C and Graph D
D. Graph A only
Answers
Answer: C i believe
Step-by-step explanation:
Answer:
the option answer is B
Step-by-step explanation:
the is the answer because it represents functions
Estimate. 110×298
30,000
3,000
40,000
2,000
Answers
Answer:
it's acually 107,800
Answer:
30,000 yes this is correct
Step-by-step explanation: