Find f such that the given conditions are satisfied. f(x)=x2-3x + 12, f(0) = 9 O f(x) = 1x2 - 4x² + 12x +9 O O f(x) - x-x2 + 12x + 1 f(x) = 3x3-4x2 + 12x + 1 O f(x) = 3x - x? + 12x + 9
Answers
To find f(x) we will do an integration
[tex]\begin{gathered} f^{\prime}(x)=x^2-3x+12\text{ } \\ f(x)=\int (x^2-3x+12) \end{gathered}[/tex][tex]\int (x^2-3x+12)=\frac{x^3}{3}-\frac{3x^2}{2}+12x+c[/tex]To find c substitute x by 0 and y by 9 because f(0) = 9
[tex]\begin{gathered} f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+c \\ f(0)=\frac{1}{3}(0)^3-\frac{3}{2}(0)^2+12(0)+c=9 \\ c=9 \end{gathered}[/tex]The function f(x) is
[tex]f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+9[/tex]Answer D
Related Questions
solve for x. z=5x-9y
Answers
ANSWER:
[tex]x=\frac{z+9y}{5}[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]z=5x-9y[/tex]We solve for x as follows:
[tex]\begin{gathered} z+9y=5x \\ 5x=z+9y \\ x=\frac{z+9y}{5} \end{gathered}[/tex]A pair of bikes cost $89.99 and the sales tax is 8%.What is the total cost of the shoes including tax?
Answers
Answer
Total Cost of the bike including tax = $97.1892
Explanation
Cost of the bike = $89.99
Sales Tax = 8% of Cost of bike = 8% (89.99) = 0.08 (89.99) = $7.1992
Total Cost of the bike = (Cost of the bike) + (Sales Tax)
= 89.99 + 7.1992
= $97.1892
Hope this Helps!!!
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
Option is the the. correct answer A
Determine if the following lines are parallel (never intersect), perpendicular (intersect at a 90 degree angle), intersecting (intersect at just one point), or coinciding (intersect at all points)?y = -x + 11, 2y = -2x + 22
Answers
Given
The lines,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]To find:
Whether the lines are perpendicular, coinciding, intersecting or parallel?
Explanation:
It is given that,
[tex]\begin{gathered} y=-x+11\text{ \_\_\_\_\_\lparen1\rparen} \\ 2y=-2x+22\text{ \_\_\_\_\_\_\lparen2\rparen} \end{gathered}[/tex]That implies,
Since the slope of the two lines are,
[tex]\begin{gathered} m_1=-1 \\ m_2=\frac{-2}{2}=-1 \\ \therefore m_1=m_2 \end{gathered}[/tex]Hence, the two lines are parallel.
Animal is a bird Can fly Tiger Penguin ✓ ✓ Robin ✓ Snail Sparrow ✓ ✓ Pelican ✓ ✓ ✓ Bat Let event A = The animal is a bird. Let event B = The animal can fly. Which outcomes are in A and 8? O A. (robin, sparrow.pelican) B. (penguin, robin, sparrow, pelican) c. robin, sparrow, pelican, bat) D. (penguin, robin, sparrow. pelican, bat)
Answers
Outcome that are in A and B simply means both outcome must be achieved.
Therefore,
[tex]\begin{gathered} \text{Animal can fly and Animal is bird both exist in } \\ A\text{. }\mleft\lbrace\text{Robbin, sparrow, pelican}\mright\rbrace \end{gathered}[/tex]Questlon 5 Refer to the figure. HJ I JE. HII IE. HJ HI J H E Complete the explanation to show triangle EJH is congruent to triangle EIH. The two triangles given are _____triangles. The leg and hypotenuse of triangle EJH are congrue hypotenuse of triangle EIH. By the ______ Theorem the third side ma triangles are congruent by the____ Triangle Congruence Theorem.choice 1.acute,obtuse or right angleschoice 2.corresponding parts of congruent triangles, pythagorean,or side-angle-side triangle congruence.choice 3. side-side-side, side-angle-side,or angle-side-angle
Answers
In the given figure, we have two triangles △EJH and △EIH
We are given the following information
[tex]\begin{gathered} \bar{HJ}\perp\bar{JE} \\ \bar{HI}\perp\bar{IE} \\ \bar{HJ}\cong\bar{HI} \end{gathered}[/tex]This means that these two triangles are "Right Triangles"
Therefore.
Choice 1 = right angles
When the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the triangles are congruent.
Therefore,
Choice 2 = side-angle-side triangle congruence
Choice 3 = side-angle-side
Answer: choice 1 -Right Angle
Choice 2 -Pythagorean
Choice 3- Side-Side-Side
Step-by-step explanation:other guy is completely wrong lol
1. Jessica finishes her book in 2 1/3
hours. Eric takes 1 1/2
times longer than
Jessica to finish his book.
This model represents the amount of time Jessica takes to finish her
book. It has a width of 1 and a length of 2 1/3
. The model is 2 1/3 out of 3
Answers
Proportionately, the number of hours it takes Eric to finish the book as Jessica is 3¹/₂ hours.
What is proportion?Proportion refers to the ratio of the quantity contained in a number or value concerning another value's ratio.
Proportions, like ratios, are fractional values, represented using decimals, fractions, or percentages.
In ratio terms, Eric's reading time is 3¹/₂ hours to Jessica's 2¹/₃ hours, giving an absolute ratio of 3: 2 with a constant proportionality of 1.5 hours.
For instance, the product of Eric's reading time, compared to Jessica's reading time, shows that Jessica does a faster reading than Eric.
The total number of hours it takes Jessica to finish her book = 2¹/₃ hours
The total hours it takes Eric to finish the book = 2¹/₃ hours x 1¹/₂
= 3¹/₂ hours (2¹/₃ x 1¹/₂).
Thus, whereas Jessica takes 2¹/₃ hours to finish the book, in proportion, Eric consumes 3¹/₂ hours reading the same book.
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Complete Question:Jessica finishes her book in 2¹/₃ hours. Eric takes 1¹/₂ times longer than Jessica to finish his book. How long did Eric take to finish the book?
if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
Answers
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
A man realizes he lost the detailed receipt from the store and only has the credit card receipt with theafter-tax total. If the after-tax total was $357.06, and the tax rate in the area is 8.2%, what was the pre-tax subtotal?
Answers
Answer: the pre-tax subtotal is $330
Explanation:
Let x represent the pre tax total
If the tax rate in the area is 8.2%, it means that the amount of tax paid is
8.2/100 * x = 0.082x
pretax total + tax = after tax subtotal
Given that after tax subtotal is $357.06, then
x + 0.082x = 357.06
1.082x = 357.06
x = 357.06/1.082
x = 330
the pre-tax subtotal is $330
If the point (-6, 4) is dilated by a scale factor of 1/2, the resulting point is (-3,2).TrueFalse
Answers
(-6,4)
Multiply each coordinate by 1/2
( -6 * 1/2 , 4 * 1/2) = (-3,2)
True
Virginia is going to visit 5 cities this summer. She will choose from 8 different cities and the order in which she visits the cities does not matter. How many different city combinations are possible for the summer travelling?
Answers
Can someone help me with this geometry question? First box has 3 options: 60,96,48Second box has two options: 480 and 552Third box: 180 and 216
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Surface area of a square prism is:
[tex]\begin{gathered} \text{4\lparen ah\rparen= SA square prism} \\ 4(20)(6)\text{= SA square prism} \\ 80(6)\text{= SA square prism} \\ 480=\text{SA square prism} \\ \\ \end{gathered}[/tex]The surface area of the square prism 480.
The surface area for the cube is:
[tex]\begin{gathered} 5a^2=\text{ SA cube} \\ 5(6)^2=\text{ SA cube} \\ 5(36)=\text{ SA cube} \\ 180=\text{ Surface area of the cube} \end{gathered}[/tex]The surface area of the cube is: 180.
The surface area of the pyramid is:
[tex]\begin{gathered} SurfaceAreaPyramid=4bh \\ SAPyramid=\text{4\lparen6\rparen\lparen4\rparen} \\ SAPyramid=\text{ 96} \\ \end{gathered}[/tex]The surface area of the pyramid i 96.
In each geometric figure, we have to remove the inner square faces, since they are not on the surface.
The total surface area is:
[tex]\begin{gathered} SA\text{ cube + SA square prism + SA pyramid= Total SA} \\ 180\text{ + 480 + 96= Total SA} \\ 756=\text{ Total surface area. } \end{gathered}[/tex]The total surface area is 756.
Determine the value of b for which x = 1 is a solution of the equation shown.
2x + 14 = 10x + b
B=
Answers
The linear equation has the solution x = 1 only if the value of b is 6
For which value of b is x = 1 a solution?
Here we have the linear equation:
2x + 14 = 10x + b
If we replace x by 1 in that equation, we will get:
2*1 + 14 = 10*1 + b
2 + 14 = 10 + b
16 = 10 + b
To find the value of b such that x = 1 is a solution, we need to isolate b, to do so we need to subtract 10 in both sides.
16 - 10 = 10 + b - 10
6 = b
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Linda's medicine bottlesays "If you will be driving, then youshould not take this medicine." What arethe inverse, converse, and thecontrapositive of this statement?
Answers
For two statements p and q, and the compounded statement "If p, then q", we have the following definitions for the inverse, converse, and contrapositive of this compounded statement:
inverse: If not p, then not q.
converse: If q, then p.
contrapositive: If not q, then not p.
So, for the presented statement, i. e., "If you will be driving, then you should not take this medicine" we have:
p: you will be driving
q: you should not take this medicine
Notice that:
not p: you will not be driving
not q: you may take this medicine
Then, using the above definitions, we write:
inverse: If you will not be driving, then you may take this medicine.
converse: If you should not take this medicine, then you will drive.
contrapositive: If you may take this medicine, then you will not be driving.
Point B is located at -2. Points C and D are each 8 units away from point B. Where are C and D located?
Answers
They are located 8 units away, so one has to be away in the left direction and the other one in the right direction
[tex]\begin{gathered} \text{ - 2 - 8 = -10 } \\ \text{ - 2 + 8 = 6} \end{gathered}[/tex]So, C and D are located at -10 and 6
1 4/5 + (2 3/20 + 3/5) use mental math and properties to solve write your answer in simpleist form
Answers
Given data:
The given expression is 1 4/5 + (2 3/20 + 3/5).
The given expression can be written as,
[tex]\begin{gathered} 1\frac{4}{5}+(2\frac{3}{20}+\frac{3}{5}_{})=\frac{9}{5}+(\frac{43}{20}+\frac{3}{5}) \\ =\frac{9}{5}+\frac{43+12}{20} \\ =\frac{9}{5}+\frac{55}{20} \\ =\frac{36+55}{20} \\ =\frac{91}{20} \end{gathered}[/tex]Thus, the value of the given expression is 91/20.
A bridge being designed will crossthe river at a right angle. Theequation of the left bank of theriver is y = 2x + 8. The center ofthe bridge will pass through (0, 2).What is the equation of the linerepresenting the bridge?
Answers
Let's begin by listing out the information given to us:
Left side: y = 2x + 8
Center of the bridge: (0, 2)
[tex]\begin{gathered} y=2x+8 \\ m=2 \\ \text{However, the bridge is perpendicular to }y=2x+8\colon \\ m(perpendicular)=-\frac{1}{m} \\ m(perpendicular)=-\frac{1}{2} \end{gathered}[/tex]Use the point-slope formula to get the equation of the bridge:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(0,2);m=m(perpendicular)=-\frac{1}{2} \\ y-2=-\frac{1}{2}(x-0) \\ y-2=-\frac{1}{2}x \\ y=-\frac{1}{2}x+2 \\ \\ \therefore\text{ equation of the line representing the bridge is }y=-\frac{1}{2}x+2 \end{gathered}[/tex]Consider the right triangle shown below where a=8.09, b=9.4, and c=12.4. Note that θ and ϕ are measured in radians.What is the value of cos(θ)?cos(θ)= What is the value of sin(θ)?sin(θ)=What is the value of tan(θ)?tan(θ)= What is the value of θ?θ=
Answers
By definition
[tex]\cos (angle)=\frac{\text{ adjacent side}}{\text{ hipotenuse}}[/tex]From the picture
[tex]\begin{gathered} \cos (\theta)=\frac{a}{c} \\ \cos (\theta)=\frac{8.09}{12.4} \\ \cos (\theta)=0.65 \end{gathered}[/tex]By definition
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hipotenuse}}[/tex]From the picture:
[tex]\begin{gathered} \sin (\theta)=\frac{b}{c} \\ \sin (\theta)=\frac{9.4}{12.4} \\ \sin (\theta)=0.76 \end{gathered}[/tex]By definition
[tex]\tan (angle)=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]From the picture
[tex]\begin{gathered} \tan (\theta)=\frac{b}{a} \\ \tan (\theta)=\frac{9.4}{8.09} \\ \tan (\theta)=1.16 \end{gathered}[/tex]Isolating θ from the previous equations:
[tex]\begin{gathered} \theta=\arccos (0.65)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arcsin (0.76)=49.46\text{ \degree}\approx49\text{ \degree} \\ \theta=\arctan (1.16)=49.24\text{ \degree}\approx49\text{ \degree} \end{gathered}[/tex](The difference between the values is caused by rounding errors)
A chemist is using 357 milliliters of a solution of acid and water. If 18.6%of the solution is acid, how many milliliters of acid are there? Round your answer to the nearest tenth.
Answers
There are 66.4 milliliters of acid in the solution
Explanation:The amount of the solution of acid and water = 357
Percentage composition of acid in the solution = 18.6%
Amount of acid in the solution = (18.6/100) x 357
Amount of acid in the solution = 66.402 milliliters
Amount of acid in the solution = 66.4 milliliters (to the nearest tenth)
There are 66.4 milliliters of acid in the solution
Jamal is comparingprices of several different brandsof peanuts. Which brand is thebest buy? Explain.
Answers
So we need to figure out which is the best buy. In order to do this we must look at a particular variable: the price per ounce of peanuts. This price is given by dividing the total price of a certain amount of peanuts divided by its weight in ounces. So for the Barrel brand we get:
[tex]\frac{3.39}{10}=0.339[/tex]So the Barrel peanuts cost $0.339 per ounce. For the Mr. Nut peanuts we get:
[tex]\frac{4.54}{14}=0.324[/tex]Then the Mr. Nut peanuts cost $0.324 per ounce. Finally, the price per ounce of the Chip's peanuts is:
[tex]\frac{6.26}{18}=0.348[/tex]Then, the cheapest peanuts are those of the brand Mr. Nut and that is the best buy.
Calculate the degree of the angles in the triangles below.
Answers
the sum of the internal angles of a triangle is equal to 180, then
[tex]\begin{gathered} 2x+7+5x+12=180 \\ 7x+19=180 \\ 7x+19-19=180-19 \\ 7x=161 \\ \frac{7x}{7}=\frac{161}{7} \\ x=23 \end{gathered}[/tex]so
answer:
angle 1 = 2x + 7 = 2(23) + 7 = 46 + 7 = 53°
angle 2 = 5x = 5(23) = 115°
angle 3 = 12°
Use the graph to answer the question.Which statement matches the vector operation shown on the coordinate grid?
Answers
We have the correct statement about the vectors in the graph.
We can already see that it is a sum of vectors like:
[tex]v+w=u[/tex]As v has starting point at (-1,0) and ending point at (3,3), we can describe the vector as:
[tex]v=(3-(-1))\hat{i}+(3-0)\hat{j}=4\hat{i}+3\hat{j}[/tex]As w starts at (3, 3) and ends on (5, 2), we can describe it as:w
[tex]w=(5-3)\hat{i}+(2-3)\hat{j}=2\hat{i}-1\hat{j}[/tex]Finally, u starts at (-1,0) and ends at (5,2), so it can be described as:
[tex]u=(5-(-1))\hat{i}+(2-0)\hat{j}=6\hat{i}+2\hat{j}[/tex]Answer: v + w = u for v = 4i + 3j, u = 2i - j and u = 6i + 2j [Option C].
Which angle is coterminal to 128°?A. -52°B. 308C. 232°D. 488°
Answers
The coterminal of angle with measure x is x + 360 degrees
Example:
If x = 30 degrees, then
The coterminal of x is 30 + 360 = 390 degrees
The coterminal of 128 degrees is 128 + 360 = 488 degrees
Then the answer is D
AnimalPossible Locations Relativeto Ocean's Surface25. Reasoning Suppose you plot the locations ofthe animals on a number line. Which animalwould be represented by the point farthest fromO on the number line? Explain. MP2Bloodbelly comb jellyDeep sea anglerfish-0.8 km- km- 2 kmFanfin anglerfishGulper eel-1.1 km26. Which animal is closest to a depth of -0.7 km?Pacific blackdragon- šo kmSlender snipe eel-0.6 km
Answers
Number line
[tex]\ldots-5<-4<-3<-2<\text{ -1< 0<1<2<3<4<5}\ldots[/tex]Let's
[tex]undefined[/tex]Find an equation in standard form of the parabola passing through the points. (2,-20),(-2,-4), (0, -8)
Answers
The equation of a parabola in standard form is
[tex]y\text{ }=ax^2\text{ + bx + c}[/tex]So, we have the following equations,
For ( 2, -20) , -20 = a(2)^2 + b (2) + c,
For (-2, -4), -4 = a( -2)^2 + b (-2) + c,
For (0.-8), -8 = a (0) + b (0) + c
Then solving,
4a + 2b + c = -20 .............. equ 1
4a - 2b + c = -4 ................... equ 2
c= -8
put c= -8 in equ 1,
we have
4a + 2b -8 = -20 = 4a + 2b = -12 ------equ 3
put c= -8 in equ 2,
4a - 2b -8 = -4 = 4a - 2b = 4................... equ 4
Solving equ 3 and equ 4, a= -1 , b= -4
so a =-1, b= -4, c= -8
Then substituting the values in
[tex]y=ax^2\text{ + bx + c}[/tex][tex]y=-1(x^2)\text{ + -4(x) + }(-8)[/tex]
So, y= -x^2 -4x-8
if an above ground graden is the shape of triangular pyramid measuring.the base is a right triangle with adjacent lengths measuring 5feet and 8feet. the height of the pyramid is 1.5feet. the organic soil cost $1.20 per cubic foot. how much will it cost to fill the graden fully
Answers
Solution
The volume for a triangular pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]And the Base is given by:
[tex]B=\frac{1}{2}(5)(8)[/tex]And since h= 1.5 ft we have this:
[tex]V=\frac{1}{6}(5\cdot8)\cdot1.5ft^3=10ft^3[/tex]And then we can find the total cost like this:
[tex]C=10ft^3\cdot\frac{1.2\text{ dollars}}{1ft^3}=12dollars[/tex]Then the final answer would be 12$
complete the equation of the line through (-1,6) and (,7-2)
Answers
The two points given are
A(-1, 6)
B(7, -2)
We shall start by calculating the slope of the line, since we've been given two points.
[tex]\begin{gathered} \text{The slope which is m, is derived as;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{7-\lbrack-1\rbrack} \\ m=\frac{-8}{7+1} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}[/tex]Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}[/tex]Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;
[tex]\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}[/tex]Look at the graphs and their equations below. Then fill in the information about the coefficients A, B, C, and D.
Answers
Given:
Aim:
We need to find the coordinates and The sign of the equation.
Explanation:
[tex]We\text{ know that y=a\mid x\mid is upside and y}\ge\text{0 when a >0 and downside and y}\leq\text{owhen a<0}[/tex]The coefficient of the given functions are
[tex]y=A|x|\text{ is positive}[/tex][tex]y=B|x|\text{ is positive}[/tex][tex]y=C|x|\text{ is negative}[/tex][tex]y=D|x|\text{ is negative}[/tex]The coefficient is closest to zero.
Comparing the graph of y=A|x| and y=B|x|, we get y=A|x| is wider than y=B|x|.
[tex]A
Comparing the graph of y=C|x| and y=D|x|, we get y=D|x| is wider than y=C|x|.
[tex]CComparing the graph of y=A|x| and y=C|x|, we get y=C|x| is wider than y=A|x|.
[tex]C The coefficient is closest to zero y=C|x|.The coefficient with the greatest value.
Comparing the graph of y=B|x| and y=D|x|, we get y=D|x| is wider than y=B|x|.
[tex]D The coefficient with the greatest value is y=B|x|. .Two containers designed to hold water are side by side, both in the shape of acylinder. Container A has a diameter of 8 feet and a height bf 16 feet. Container B hasa diameter of 10 feet and a height of 8 feet. Container A is full of water and the wateris pumped into Container B until Conainter B is completely full.To the nearest tenth, what is the percent of Container A that is empty after thepumping is complete?
Answers
Okay, here we have this:
Considering the provided information, we are going to calculate what is the percent of Container A that is empty after the pumping is complete, so we obtain the following:
First we will calculate the volume of each cylinder using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]Applying:
[tex]\begin{gathered} V_A=\pi\cdot4^2\cdot16 \\ V_A=\pi\cdot16\cdot16 \\ V_A=256\pi \end{gathered}[/tex][tex]\begin{gathered} V_B=\pi\cdot5^2\cdot8 \\ V_B=\pi\cdot25\cdot8 \\ V_B=200\pi \end{gathered}[/tex]After pumping the water from container A to container B, the following amount remains in container A:
Remaining amount of water in A=256π-200π
Remaining amount of water in A=56π
Now, we obtain that the empty percentage that results in A is:
Empty percentage that results in A=200/256*100
Empty percentage that results in A=78.125%
Empty percentage that results in A≈78.1%
Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Answers
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]