Answers
We are given the function below;
[tex]f(x)=-2x^2-4x[/tex]PART A
We then proceed to find if the function has a minimum or maximum value. To find if the function has a minimum or maximum value. If the x^2 coefficient is positive, the function has a minimum. If it is negative, the function has a maximum.
ANSWER: From the above, we can see that x^2 is negative, hence the function has a maximum
PART B and C
To find the minimum or maximum value, we would plot the graph of the f(x). The graph can be seen below.
From the graph, the black point helps answer part A and part B.
ANSWER: The function's maximum value is f(x)=2.
This is the point where the slope of the graph is equal to zero
ANSWER: The maximum value then occurs at x= -1
We can also solve this by differentiating the function.
[tex]\begin{gathered} f(x)=-2x^2-4x \\ f^{\prime}(x)=-4x-4 \\ At\xi maxmum\text{ }f^{\prime}(x)=0 \\ -4x-4=0 \\ -4x=4 \\ x=-\frac{4}{4} \\ x=-1 \\ \therefore\text{The max}imum\text{ value occurs at x=-1} \\ \text{Inserting the value of x into the function, we have} \\ f(x)=-2(-1)^2-4(-1) \\ f(x)=-2+4 \\ f(x)=2 \\ \therefore\text{The function max}imum\text{ value is 2} \end{gathered}[/tex]
Related Questions
Geometry Match each segment, angle, or arc to its degree measure. segment ADsegment DKsegment AKsegment KLangle BDCangle DAKangle EMAangle FBAarc EJsegment DEsegment AFarc DCE
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The given figure inscribed in the circle is a square.
We know from the properties of a square that all the sides and all the angles of a square are equal.
Also the diagonal bisects each other at 90 degrees.
From the figure we are given;
CD = 14.14
AJ = 10
arc BC = 90 degrees
From the figure and properties of polygons, we can say that;
arc BC = arc CD = arc DE = Arc EB = 90 degree
AJ = AK = AB = AC = AD = AE = 10 = Radius of circle
JL = EC = BD = 20 = diameter of circle (Since, diameter = 2 * radius)
BC = CD = DE = EB = 14.14 = sides of the squares
Thus, the given figure inscribed in the circle is a square.
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please help at the image and answer
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Step-by-step explanation:
the figure is a combination of
1 half-circle with radius 30/2 = 15
1 inner rectangle 13 width, (13+20)= 33 length.
2 right-angled triangles with 20 being one leg, and (30-13)/2 = 17/2 = 8.5 the other leg.
the area of the half-circle is
pi×r²/2 = pi×15²/2 = pi×112.5 = 353.4291735...
the area of the inner rectangle is
13×33 = 429
the area of one triangle (because they are right-angled, their area is leg1 × leg2 / 2)
20 × 8.5 / 2
but we have 2 triangles, and their total area is then
20 × 8.5 = 170
in total the area of the combined figure is the sum of all 3 numbers :
952.4291735...
this should be the cut-off 3rd answer option 952.4.
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
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Answer:
x = 23.04
Step-by-step explanation:
You want to know the value of x such that x/6.4 = 3.6.
One-step equationWe can solve this equation by multiplying by the inverse of the coefficient of x.
The coefficient of x is 1/6.4, so multiplying by 6.4 will give ...
6.4(x/6.4) = 6.4(3.6)
x = 23.04
The value for x in the equation is 23.04.
<95141404393>
Hi, can you answer the second question for me (number 4)?
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Solution
4.
[tex]\begin{gathered} \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{cos\theta(1-sin\theta)+cos\theta(1+sin\theta)}{(1+sin\theta)(1-sin\theta)} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{cos\theta-sin\theta cos\theta+cos\theta+sin\theta cos\theta}{1-sin^2\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{2cos\theta}{cos^2\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=\frac{2}{cos\theta} \\ \\ \frac{cos\theta}{1+sin\theta}+\frac{cos\theta}{1-sin\theta}=2sec\theta \end{gathered}[/tex]i have to find the distance form the swings to fountain. help please
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The first thing we have to do is locate the points where the swings and the fountain are located on the graph.
[tex]\begin{gathered} Fountain\to(-2,-2) \\ Swings\to(5,-2) \end{gathered}[/tex]To calculate the distance between the 2 points we use the following equation:
[tex]\begin{gathered} D(F,S)=\sqrt[]{(x_2-x_1)^2-(y_1-y_1)^2} \\ \end{gathered}[/tex]We replace the values of the points F and S:
[tex]\begin{gathered} D(F,S)=\sqrt[]{(5_{}-(-2)_{})^2-(-2_{}-(-2)_{})^2} \\ D(F,S)=\sqrt[]{(5_{}+2_{})^2-(-2_{}+2_{})^2} \\ D(F,S)=\sqrt[]{(7_{})^2-(0_{})^2} \\ D(F,S)=\sqrt[]{(7)^2} \\ D(F,S)=7 \end{gathered}[/tex]So the distance between the swings and the fountains is 7What is 1/5 divided by 4. (Fraction)
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Given the expression:
[tex]\text{ 1/5 }\div\text{ 4}[/tex]Let's determine the quotient:
Step 1: Transform the whole number into the fractional form.
[tex]\text{ 1/5 }\div\text{ 4 = }\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex]Step 2: Transpose the division into multiplication and reciprocate 4/1.
[tex]\frac{1}{5}\text{ }\div\text{ }\frac{4}{1}[/tex][tex]=\text{ }\frac{1}{5}\text{ x }\frac{1}{4}[/tex][tex]\text{ = }\frac{1}{20}[/tex]Therefore, the answer is 1/20.
The area of a triangle is 40
the length is x+4 and the height is x
what is the value of x
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Answer:
16
Step-by-step explanation:
Area of a triangle = 1/2(b×h)
b or l = x+4
h = x
a = 40
1/2(x+4 × x) = 40
1/2(x+4 × x) = 40x + 4 × x / 2 = 40
4 × x = 4x
4x + x = 5x
5x/2 = 40
cross-multiply
40 × 2 = 5x
40 × 2 = 5x80 = 5x
divide both sides by 5
5x/5 = 80/5
5x/5 = 80/5x = 16
Hi! I just wanted to double check and make sure that I worked the question correctly
Answers
Statement Problem: A boat on the river is 700ft from the base of a dam. The dam is 2460ft above water level. Given that someone standing on the boat stands 5ft above water level, what is the angle of elevation from the individual standing on the boat to the top of the dam? State your answer in radian rounded to 4 decimal places.
Solution:
We would represent the information in a diagram as;
Applying the trigonometry ratio for tangent, we have;
[tex]\tan \theta=\frac{opposite}{adjacent}[/tex]Thus,
[tex]\begin{gathered} \tan \theta=\frac{2460}{700} \\ \theta=\tan ^{-1}(3.5143) \\ \theta=74.1161^o \end{gathered}[/tex]Now, we would convert the angle from degrees to radians. We have;
[tex]\begin{gathered} 74.1161^o\times\frac{\pi}{180}\text{rad} \\ =1.2936rad \end{gathered}[/tex]Reviewrship10These figures are similar. The area ofone is given. Find the area of the other.Help ResourcesArea = 100 in.2ㅁ nSkip8 in.10 in.[? ] in.2Enter
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SOLUTION:
Step 1:
Since the two figures are similar, it means that they have properties in common.
Step 2:
In the bigger figure, the side given is 10in and its area is 100 square inches meaning (10 in x 10 in).
Step 3:
In the smaller figure, the side given is 8in, and from step 1, we can see that the two figures are similar, so the area of the smaller figure will be (8 in x 8 in) = 64 square inches.
CONCLUSION:
The area of the smaller figure is 8in x 8in = 64 square inches
[tex]8inx8in=64in^2[/tex]determine the sine and cosine of 90 degrees
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Refer to Problems 1-3 to solve Problems 4–6. The first one is done for you. 4. A scale factor between 0 and 1 produces a similar figure that is smaller than the original figure. 5. In Problem 2, YZ = _=4V5, and UV = v=2v5. The ratio of YZ to UV in simplest form is 6. If one polygon can be mapped to another by a series of then the polygons are Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility 218
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The ratio of YZ to UV is 2:1
1) Considering that the distance between YZ is 4√5 and the distance between points U and V is 2√5 the ratio of YZ to UV can be found through this:
[tex]\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}[/tex]2) Let's rationalize it by multiplying both numerator and denominator by √5 to simplify removing the radicals on the denominator.
[tex]\frac{YZ}{UV}=\frac{4\sqrt[]{5}}{2\sqrt[]{5}}\cdot\frac{\sqrt[]{5}}{\sqrt[]{5}}=\frac{4\sqrt[]{5^2}}{2\sqrt[]{5^2}}=\frac{4\cdot5}{2\cdot5}=\frac{2}{1}[/tex]3) So the ratio of YZ to UV is 2:1
A school principal ordered s new electric pencil sharpeners. Each classroom received 2 of them. Write an expression that shows the number of classrooms.
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y = x/2 is the expression that shows the number of classrooms. where y is No. of classrooms and x is the Total No. of sharpener ordered.
What is an Algebraic Expression? an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.Algebraic expressions are used in mathematics to solve various and complex equations. Algebraic expressions can be found in computer programming, where they are utilized for inference tasks. In economics, algebraic expressions are employed to calculate revenue, cost, and so on.The study of algebra improves logical thinking and allows a person to break down an issue first and then solve it. Although theoretical algebraic difficulties may not be encountered on a daily basis, exposure to algebraic equations and problems at some time in life will develop your mind to reason logically.let assume y be the No. of class room,
x be the Total No. of electric sharpeners order
Each classroom received 2 of them
y = x/2
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There are 17 flute players and 15 Clarinet players in Amy’s Music class, For each class the teacher randomly selects a student to hand out the music by Drawing a name from a jar. What is the probability that a player will be selected to hand out the music for the next class
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for this case we have the folloeing information: In a class we have 17 flute players and 15 Clarinet Players for the Amy's Music Class.
The total of students are:
[tex]\text{Total}=17+15=32[/tex]And then if we need to select one player (student) the probability would be given by:
[tex]p=\frac{possible}{total}=\frac{1}{32}[/tex]And the best answer would be A) 1/32
Explain the error Andrew is using vector v to draw a copy of ∆ABC explain his error
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We want to know the mistake is doing Andrew when he tries to draw a copy of ∆ABC using the vector v.
We see that the vector v is directed 3 units to the right, and 3 units down.
For translating the triangle ABC with the vector v, we should make the translation with every point of the triangle.
This means that you move the point A 3 units down and 3 units to the right, but Andrew just moved it 2 units down, and 3 units to the left. Also, we have:
0. The point B was moved two units down and four units to the right.
,1. The point C was moved three units down, and three units to the right
Thus, Andrew didn't move correctly the points A and B.
Please help I am stuck with this problem for homework. I am in the 6th grade.
Answers
Explanation
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints
it is given by
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]then
Step 1
Let
[tex]\begin{gathered} P2=(4,3) \\ M=(4,7) \\ P1=unknown=(x_1,y_1) \end{gathered}[/tex]replace
[tex]\begin{gathered} (4,7)=(\frac{x_1+4}{2},\frac{y_1+3}{2}) \\ \text{hence} \\ 4=\frac{x_1+4}{2} \\ and \\ 7=\frac{y_1+3}{2} \end{gathered}[/tex]Step 2
now, we have to solve for x1 and y1
a)
[tex]\begin{gathered} 4=\frac{x_1+4}{2} \\ \text{Multiply both sides by 2} \\ 4\cdot2=\frac{x_1+4}{2}\cdot2 \\ 8=x_1+4 \\ \text{subtrac 4 in both sides} \\ 8-4=x_1+4-4 \\ 4=x_1 \end{gathered}[/tex]b)
[tex]\begin{gathered} 7=\frac{y_1+3}{2} \\ \text{Multiply both sides by 2} \\ 7\cdot2=\frac{y_1+3}{2}\cdot2 \\ 14=y_1+3 \\ \text{subtract 3 in both sides} \\ 14-3=y_1+3-3 \\ 11=y_1 \end{gathered}[/tex]therefore, the coordinates of the other end point is
[tex](4,11)[/tex]I hope this helps you
Which equation models the line on the graph?
(-1,4)
(3,2)
O A) y-2= -1/2(x-3)
O B) y + 2 = -1/2 (x+3)
O C) y-2=-2(x-3)
OD) y + 2 = -2(x+3)
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Answer:
a i
gussed
Step-by-step explanation:
Rectangle ABCD with vertices A(1, 0),
B(7, 2), C(8, -1), and D(2, -3):
(a) Translation: (x, y) → (x-8, y - 3)
(b) Reflection: in the x-axis
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The vertices after the transformations is A''(-7, 3), B''(-1, 1), C'' (0, 4), and D'' (-6, 6)
How to determine the vertices after the transformations(a) Translation: (x, y) → (x-8, y - 3)
The vertices of the rectangle are given as
A(1, 0), B(7, 2), C(8, -1), and D(2, -3)
The translation rule is given as
(x, y) → (x-8, y - 3)
When this rule is applied, we have
A'(1 - 8, 0 - 3), B'(7 - 8, 2 - 3), C' (8 - 8, -1 - 3), and D' (2 - 8, -3 - 3)
Evaluate
A'(-7, -3), B'(-1, -1), C' (0, -4), and D' (-6, -6)
(b) Reflection: in the x-axis
This rule can be represented as
(x, y) → (x, -y )
When this rule is applied, we have
A''(-7, 3), B''(-1, 1), C'' (0, 4), and D'' (-6, 6)
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EFHNm FG=97m GH=117m EHG= 164GoAngle E:OAngle F:Angle G:Angle H:Blank 1:Blank 2:Blank 3:Blank 4:
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Given a cyclic quadrilateral
As shown:
The measure of the arc FG = 97
The measure of the arc GH = 117
The measure of the arc EHG = 164
The measure of the arc is two times the measure of the inscribed angle opposite to the arc.
So, the measure of the angle E = 1/2 the measure of the arc FGH =
[tex]\frac{1}{2}(\text{arc FG + arc GH ) =}\frac{1}{2}(97+117)=\frac{1}{2}\cdot214=107\degree[/tex]The measure of the angle F = 1/2 the measure of the arc EHG =
[tex]\frac{1}{2}\cdot164=82\degree[/tex]For the cyclic quadrilateral, every two opposite angles are supplementary.
So,
[tex]\begin{gathered} m\angle E+m\angle G=180 \\ m\angle G=180-m\angle E=180-107=73\degree \end{gathered}[/tex]And:
[tex]\begin{gathered} m\angle F+m\angle H=180 \\ m\angle H=180-m\angle F=180-82=98\degree \end{gathered}[/tex]So, the answer will be:
[tex]\begin{gathered} \text{Blank}1\colon107\degree \\ \text{Blank}2\colon82\degree \\ \text{Blank}3\colon73\degree \\ \text{Blank}4\colon98\degree \end{gathered}[/tex]Match the correct slope-internet form of an equation with the standard form of the same equation.
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Given:
-x+y=2
x-y=2
x+y=-2
-x-y=-2
To match the correct slope-intercept form of an equation, we follow the process as shown below:
Standard Form: Ax+By=C
Conversion: y= -A/Bx+C/B
So,
For -x+y=2:
A=-1
B=1
C=2
Hence,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{-1}{1}x+\frac{2}{1} \\ Simplify \\ y=x+2 \end{gathered}[/tex]For x-y=2,
A=1
B=-1
C=2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{1}{-1}x+\frac{2}{-1} \\ Simplify \\ y=x-2 \end{gathered}[/tex]For x+y=-2,
A=1
B=1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ y=-\frac{1}{1}x+\frac{-2}{1} \\ y=-x-2 \end{gathered}[/tex]For -x-y=-2,
A=-1
B=-1
C=-2
So,
[tex]\begin{gathered} y=-\frac{A}{B}x+\frac{C}{B} \\ =-\frac{-1}{-1}x+\frac{-2}{-1} \\ Simplify \\ y=-x+2 \end{gathered}[/tex]Therefore, the answers are:
-x+y=2----y=x+2
x-y=2-----y=x-2
x+y=-2----y= -x-2
-x-y=-2----y= -x+2
Suppose the manufacturer multiplied each side of the
original box by 4. What would the new surface area be?
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Answer:
original box wasn't given... atleast send original surface area..
Step-by-step explanation:
^^^^^^!!!!!!!!!!^^^^^^
3. (a) Using a pencil, ruler and a pair of compasses, construct a triangle ABC such d that AB = 5.5 cm, LABC = 90° and ZBAC = 60°. (Marks will be given for clearly drawn construction lines) [4] (b) Using the diagram constructed in part (a), measure the length of AC. [1]
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To solve this question, follow the steps:
1) Draw the segment AB = 5.5 cm using a ruler.
2) Draw the segment BC knowing that the angle ABC is 90º.
3) Draw the segment AC knowing that the angle BAC is 60º.
4) Connect the segments BC and AC.
5) Measure the length of AC using a ruler.
The triangle can be observed below:
Answer: the length of the segment AC is 11 cm.
hello can you help me solve this trigonometry question and in the question use pi to answer it
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The area A of a portion of a circle is:
[tex]A=\pi\cdot r^2\cdot\frac{\alpha}{2\pi}[/tex]Where alpha is the angle of the portion of the circle. So, to find the radius, we clear 'r' from the expression above:
[tex]38=\pi\cdot r^2\cdot\frac{1}{2\pi}\cdot\frac{7}{5}\pi[/tex]We can cancel the pi on the left of 'r' with the one on the right (the one that's dividing):
[tex]38=r^2\cdot\frac{7\pi}{2\cdot5}[/tex]So, now we clear 'r':
[tex]\frac{38\cdot2\cdot5}{7\cdot\pi}=r^2[/tex][tex]\sqrt[]{\frac{380}{7\pi}}=r[/tex]So, the answer is:
[tex]r=\sqrt[]{\frac{380}{7\pi}}km[/tex]Write an equivalent expression by distributing the "−−" sign outside the parentheses:−(−8.4n−1)−(−8.4n−1)
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GIven:
[tex]-(-8.4n-1)[/tex]To Determine: The equivalent of the given expression
Distributing the sign outside as shown below:
[tex]\begin{gathered} -(-8.4n-1) \\ =-\times-8.4n-\times-1 \\ =8.4n+1 \end{gathered}[/tex]Hence, the equivalent expression by distributing the sign outside the given expression is:
8.4n+1
(4.18 x 10-4)(9 x 10-4)Can you please explain how to do step by step?
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Answer:
3.762 x 10^-9
Explanation:
Given the expression:
[tex]\mleft(4.18\times10^{-4}\mright)\mleft(9\times10^{-4}\mright)[/tex]First, we remove the brackets:
[tex]=4.18\times10^{-4}\times9\times10^{-4}[/tex]Next, we bring the powers of 10 together.
[tex]=4.18\times9\times10^{-4}\times10^{-4}[/tex]Next, we combine the powers of 10 by adding the exponents (since they are being multiplied).
[tex]\begin{gathered} =4.18\times9\times10^{-4+(-4)} \\ =37.62\times10^{-8} \end{gathered}[/tex]We then obtain our final result as follows:
[tex]\begin{gathered} =3.762\times10^{-1}\times10^{-8} \\ =3.762\times10^{-9} \end{gathered}[/tex]3. Select all equations that have exactly one solution.
A 5x + 8 = 5x - 15
B. 3x +4= 7x-1
c. 3 (x - 12) = 4x - 36
D. 2 (x-1) + x = 2x - 7
E. 4 (2x - 5) - 3x = 5x-20
Answers
Answer:
Step-by-step explanation:
D the reason is because I said so
Chloe had 200 beads.• She used 15 beads to make a Barrett.• She used all the remaining beads to make 5 bracelets.• She used the same number of beads to make each bracelet.Write an equation that can be used to find B, the number of beads Chloe used to make each bracelet?
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Let B be the number of beads used to make each bracelet. Then the number of beads used to make 5 bracelets is 5B.
Number of beads to make a Barrett = 15
The sum of number of beads used to make 5 bracelets and Barett gives the total number of beads. So,
[tex]5B+15=200[/tex]Solve the system of equations using elimination. −3x + 2y = 9 x + y = 12 (−3, 0) (1, 6) (3, 9) (5, 7)
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The system of equations using elimination. −3x + 2y = 9 x + y = 12 is x = 4/7 and y = 48/7
We need to solve the system of equations using elimination method
-3x + 2y = 12....... equation 1
9x + y = 12...........equation 2
Multiply the 2nd equation with 2
18x + 2y = 24 ............equation 3
Now, subtracting equation 3 from equation 1
- 3x - 18x + 2y - 2y = 12 - 24
-21x = 12
x = 12/21 = 4/7
-3(4/7) + 2y = 12
-12/7 + 2y = 12
2y = 12 + 12/7
2y = 96/7
y = 48/7
Therefore, the system of equations using elimination. −3x + 2y = 9 x + y = 12 is x = 4/7 and y = 48/7
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Answer:
(3, 9)
Step-by-step explanation:
I did the test
This is one that I have a lot of trouble with!
Answers
Given: The function given are
[tex]\begin{gathered} f(x)=4x^3+5x^2-3x-6 \\ g(x)=4x-5 \end{gathered}[/tex]Required: To find the function-
[tex](f-g)(x)[/tex]Explanation: The function can be determined as follows-
[tex](f-g)(x)=f(x)-g(x)[/tex]Putting the values of the function f(x) and g(x)-
[tex]\begin{gathered} (f-g)(x)=(4x^3+5x^2-3x-6)-(4x-5) \\ =4x^3+5x^2-3x-6-4x+5 \\ =4x^3+5x^2-7x-1 \end{gathered}[/tex]Final Answer: Option A is correct.
Hello, I really need help this is from ALEKS and I forgot how to solve this. What is 2/3 + 1/5?
Answers
Answer:
13/15
Step-by-step explanation:
1. Find a common denominator
2. You always multiply the numerator by the same number as the denominator.
3. then add
The linear function y = g(x) Is graphed in the xy-plane. If g(-3) = 4 and g(2) = 19,
what is the slope of line g?
Answers
The slope of the line g is 3.
What is the slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.By calculating the difference between the coordinates of the two points, (x₁,y₁) and (x₂,y₂), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.So, the slope of line g will be:
y₁ = f(x₁)y₂ = f(x₂)Sope formula: y₂ - y₁/x₂ - x₁
Now, calculate as follows:
y₂ - y₁/x₂ - x₁f(x₂) - f(x₁)/x₂ - x₁y = g(x)x₁ = -3x₂ = 2g(x₁) = g(-3) = 4g(x₂) = g(2) = 19Slope:
g(x₂) - g(x₁)/x₂ - x₁19-4/2-(-3)15/53Therefore, the slope of the line g is 3.
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