Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
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1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]Related Questions
48. In the parabola, y = 3x ^ 2 + 12x + 11 focus is located at a distance p > 0 from the vertex. Then p=a. 3b. 1/3c. 12d. 1/12e. None of the above
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Given the equation,
[tex]y=3x^2+12x_{}+11[/tex]We are to solve for the vertex first, in order to solve for the vertex.
[tex]3x^2+12x+11=y[/tex]factor all through by 3
[tex]\begin{gathered} \frac{3x^2}{3}+\frac{12x}{3}+\frac{11}{3}=y \\ 3(x^2+4x+\frac{11}{3})=y\ldots\ldots.1 \end{gathered}[/tex][tex]x^2+4x=-\frac{11}{3}\text{ complete the square for the inner expression}[/tex][tex]\begin{gathered} x^2+4x+(\frac{4}{2})^2=-\frac{11}{3}+(\frac{4}{2})^2 \\ (x+2)^2=-\frac{11}{3}+4=\frac{1}{3} \\ =(x+2)^2-\frac{1}{3} \end{gathered}[/tex]Put (x+2)²-1/3 into equation 1
[tex]3((x+2)^2-\frac{1}{3})=y\ldots\ldots2[/tex]The vertex is at (-2,-1)
Note:
[tex]\begin{gathered} \text{vertex}=(h,k) \\ \text{focus}=(h,k+\frac{1}{4a}) \end{gathered}[/tex]P is the distance between the focus and the vertex.
[tex]\begin{gathered} (h-h,k+\frac{1}{4a}-k)=(0,\frac{1}{4a}) \\ \end{gathered}[/tex]where,
[tex]a=3\text{ from equation 2}[/tex]Therefore,
[tex]\begin{gathered} p=(0,\frac{1}{4\times3})=(0,\frac{1}{12}) \\ p=(0,\frac{1}{12}) \end{gathered}[/tex]Hence,
[tex]p=\frac{1}{12}[/tex]The correct answer is 1/12 [option D].
According to the theory of the color yellow + red = orange. If Luisa has x liters of yellow paint and/ 4 liters of red paint. How many liters of orange paint will he get Louise? And if I had 4 liters of yellow paint, could I get exact 5 liters of paint orange?
Answers
Yellow + red = Orange
Yellow paint , x liters
Red paint , 4 liters
a) Because addition applies , adding x liters of Yellow + 4 liters of red and the result is x + 4 liters of orange
b) for second question apply equation
4 • yellow + Red •N = 5
then find N
its possible to obtain 5 liters of paint orange with
2 liters of yellow, 2 liters of red, and adding
0.5 liters of yellow, 0.5 liters of red.
Write using set-builder notation: -2x + 1 < 27
Answers
Instead of describing the constituents of a set, a set-builder notation describes them. The set-builder notation exists A = {x: x is a natural number less than 27}.
What is meant by set-builder notation?A set can be represented by its elements or the properties that each of its members must meet can be described using set-builder notation.
Set-builder notation is a mathematical notation for defining a set by enumerating its elements or by specifying the properties that each of its members must satisfy. It is used in set theory and its applications to logic, mathematics, and computer science.
Let the given inequality be 2x+1 < 27
Subtract 1 from both sides, we get
-2x+1-1 < 27-1
Simplifying the above equation, we get
-2 x < 26
Multiply both sides by - 1 (reverse the inequality)
(-2 x)(-1) > 26(-1)
Simplifying the above equation, we get
2x > -26
Divide both sides by 2
[tex]$\frac{2 x}{2} > \frac{-26}{2}[/tex]
x > -13
Therefore, the set-builder notation exists
A = {x: x is a natural number less than 27}.
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Solve each system of the equation by elimination method. x+3y=-204x+5y=-38
Answers
Given the equation system:
[tex]\begin{gathered} x+3y=-20 \\ 4x+5y=-38 \end{gathered}[/tex]To solve this system using the elimination method, the first step is to multiply the first equation by 4 so that the leading coefficient is the same, i.e., both equations start with "4x"
[tex]\begin{gathered} 4(x+3y=-20) \\ 4\cdot x+4\cdot3y=4\cdot(-20) \\ 4x+12y=-80 \end{gathered}[/tex]Then subtract the second equation from the first one
From the resulting expression, you can calculate the value of y
[tex]\begin{gathered} 7y=-42 \\ \frac{7y}{7}=-\frac{42}{7} \\ y=-6 \end{gathered}[/tex]Next, you have to substitute the value of y in either the first or second equation to find the value of x:
[tex]\begin{gathered} x+3y=-20 \\ x+3\cdot(-6)=-20 \\ x-18=-20 \\ x=-20+18 \\ x=-2 \end{gathered}[/tex]The solution of the system is (-2,-6)
The midpoint of AB is M(4,1). If the coordinates of A are (2,8), what are thecoordinates of B?
Answers
I just need to answer the question number one NOT two .I just need a brief explanation with the answer
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The bedroom of the apartment has 4 walls.
2 of them have the following dimensions: 16ft x 8ft.
2 of them have the following dimensions: 10ft x 8ft.
Find the area of each wall and then add them to find the total area:
[tex]\begin{gathered} Aw1=16ft\cdot8ft=128ft^2 \\ Aw2=10ft\cdot8ft=80ft^2 \end{gathered}[/tex][tex]\begin{gathered} TA=2\cdot Aw1+2\cdot Aw2 \\ TA=2\cdot128ft^2+2\cdot80ft^2 \\ TA=256ft^2+160ft^2 \\ TA=416ft^2 \end{gathered}[/tex]It means that the total area to be covered is 416ft^2.
Now, divide this area by the area that can be covered by one roll of wallpaper to find the number of rolls needed:
[tex]n=\frac{416ft^2}{50ft^2}=8.32[/tex]It means that 8.32 rolls are needed to cover the bedroom. You will have to buy 9 rolls.
5 cm3 cm3 cm5 cm3 cmPrisma5 cmPrism BWhich of the following statements are true about the solids shown above?Check all that apply.A. Prisms A and B have different values for lateral surface area.O B. Prism B has a total surface area of 110 cm?O C. Prism A has a lateral surface area of 60 cm?D D. Prism B has a larger surface area.
Answers
Note that the lateral surface area is the area of the faces of the solid, excluding the cross-sectional faces i.e. faces which are perpendicular to the longitudinal axis.
The lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_A=2(5\times3)+2(5\times3)_{} \\ LSA_A=30+30 \\ LSA_A=60 \end{gathered}[/tex]Similarly, the lateral surface area of prism A is calculated as,
[tex]\begin{gathered} LSA_B=2(3\times5)+2(5\times5)_{} \\ LSA_B=30+50 \\ LSA_B=80 \end{gathered}[/tex]Clearly, prisms A and B have different values of lateral surface area.
So option A is the correct statement.
The total surface area is the sum of all the faces of the solid.
Since we have already calculated the LSA i.e. sum of area of 4 faces of the prism, we can add the area of the two remaining cross sectional faces to get the total area.
The total cross section area of prism B is calculated as,
[tex]\begin{gathered} A_B=2(5\times3) \\ A_B=30 \end{gathered}[/tex]So the total surface area of prism B becomes,
[tex]\begin{gathered} TSA_B=LSA_B+A_B_{} \\ TSA_B=80+30 \\ TSA_B=110 \end{gathered}[/tex]The total surface area of prism B is 110 sq. cm.
So option B is also correct.
Note that we have already found that the lateral surface area of prism A is 60 sq. cm.
Therefore, option C is also correct.
The total cross section area of prism A is calculated as,
[tex]\begin{gathered} A_A=2(3\times5) \\ A_A=30 \end{gathered}[/tex]So the total surface area of prism A becomes,
[tex]\begin{gathered} TSA_A=LSA_A+A_A \\ TSA_A=60+30 \\ TSA_A=90 \end{gathered}[/tex]The total surface area of prism A is 90 sq. cm.
It is oberved that prism B has a larger surface area.
So, option D is also correct.
Hence, we can conclude that all the given statements are correct.
Find the volume of the pyramid. Round your answer to the nearest tenth.16 in.5 in.3 in.The volume of the pyramid isin?
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Recalls that the formula for the volume of a pyramid is given by the product of the area of its base times the height, and all of that divided by 3
Then we start by calculating the area of the base:
Since the base is a rectangle of 3in by 5in, then its area is 15 square inches.
Now this area times the pyramid's height and divided by 3 gives:
Volume = AreaBase x Height / 3
Volume = 15 x 16 / 3 = 80 in^3 (eighty cubic inches)
Then, please just type the number 80 in the provided box (notice that the cubic inches unit is already written on the right of it.
The sum of three numbers is140 . The first number is 8 more than the third. The second number is 4 times the third. What are the numbers? First number: Second number: Third number:
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Answer:
x= 30
y= 88
z= 22
Step-by-step explanation:
x= z+8
y= 4z
x + y + z = 140
we substitute to the third equation (z+8) + (4z) + z= 140 so we obtain 6z+8= 140. Z is then equal to 140-8/6= 22.
Then x= 22+8= 30, y=22(4)= 88
30+88+22= 140
Help on math question precalculus ChoicesVertical shift Period DomainRange Phase shift Amplitude
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All the x-values that satisfy the function - Domain
Translating the sine or cosine curve up or down - Vertical shift
How long a given function takes to repeat itself - Period.
A horizontal shift of a sine or cosine function- Phase shift
All the y-values that satisfy the function- Range
Distance from the horizontal axis or midline to the maximum and minimum points - Amplitude
What are the coordinates of the point on the directed line segment from (−8,−4)(−8,−4) to (−5,8)(−5,8) that partitions the segment into a ratio of 5 to 1?
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-Given that f(x) = 6(x - 1). Choose the correct statement. A. f-1(12) = 3.5 B. f-1(3) = 1 c. f-16) = 3 D. f-1(9) = 2.5
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Given that function is f(x) = 6(x - 1).
Let y = 6(x - 1). Replace x with y and then solve for y.
[tex]\begin{gathered} x=6(y-1) \\ \Rightarrow x=6y-6 \\ \Rightarrow6y=x+6 \\ \Rightarrow y=\frac{x+6}{6} \end{gathered}[/tex]Thus, f^-1(x) = (x + 6)/6.
[tex]f^{-1}(12)=\frac{12+6}{6}=3[/tex][tex]f^{-1}(3)=\frac{3+6}{6}=1.5[/tex][tex]f^{-1}(6)=\frac{6+6}{6}=2[/tex][tex]f^{-1}(9)=\frac{9+6}{6}=2.5[/tex]Thus, option D is correct.
Write a explicit formula for the given recursive formulas for each arithmetic sequence
9,15,21,27 and 7,0,-7,-14
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In arithmetic progression, 9,15,21,27,33,39 is a₅ and a₆ .
What is arithmetic progression?
A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. It also goes by the name Arithmetic Sequence.a₁ = 9
a₂ = 15
a₃ = 21
Notice that a₂ - a₁ = 6 and a₃ - a₂ = 6
We can deduce that aₙ₊₁ = aₙ + 6
We can test this on the 4th term : a₄ should equal 21 + 6 = 27
Since this checks out we can say that the sequence is an arithmetic progression with a common difference of 6.
a₅ = 27 + 5 = 33
and
a₆ = 33 + 6 = 39
7,0,-7,-14
find the common difference by substracting any term in the sequence from the term that comes after it.
a₂ - a₁ = 0 - 7 = -7
a₃ - a₂ = -7 - 0 = -7
a₄ - a₃ = -14 - -7 = -7
the difference of the sequence is constant and equals the difference between two consecutive terms.
d = -7
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Here is a system of equations.y=-3x+3y=-x-1Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many solutions.-6
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From the given system, we can observe that the y intercepts of the equations are 3 and -1 respectively.
Also we can find the x intercepts by replacing y for 0 and solving for x:
[tex]\begin{gathered} 0=-3x+3 \\ -3=-3x \\ x=\frac{-3}{-3} \\ x=1 \end{gathered}[/tex][tex]\begin{gathered} 0=-x-1 \\ 1=-x \\ x=-1 \end{gathered}[/tex]It means that the x intercepts of the lines are 1 and -1 respectively.
Using these points we can graph both lines, this way:
According to this graph, the intersection of these lines is at (2, -3). This represent the solution of the system, therefore, the solution of the system is x=2 and y=-3.
Please help me I need this done fast I will give brainliest to whoever answers first
Answers
Consider that a standard quadratic equation is given by,
[tex]y=ax^2+bx+c[/tex]The curve passes through the point (-5,0),
[tex]\begin{gathered} 0=a(-5)^2+(-5)b+c \\ 0=25a-5b+c \\ c=-25a+5b\ldots\ldots\ldots(1) \end{gathered}[/tex]The curve passes through the point (3,0),
[tex]\begin{gathered} 0=a(3)^2+(3)b+c \\ 0=9a+3b+c \end{gathered}[/tex]Substitute value from equation (1),
[tex]\begin{gathered} 0=9a+3b+(-25a+5b) \\ 0=-16a+8b \\ b=2a\ldots\ldots\ldots(2) \end{gathered}[/tex]The curve passes through the point (4,9),
[tex]\begin{gathered} 9=a(4)^2+(4)b+c \\ 9=16a+4b+c \end{gathered}[/tex]Substitute tha values from (1) and (2),
[tex]\begin{gathered} 9=16a+4(2a)+(-25a+5(2a)) \\ 9=16a+8a-25a+10a \\ 9=9a \\ a=1 \end{gathered}[/tex]Substitute in equation (2),
[tex]\begin{gathered} b=2(1) \\ b=2 \end{gathered}[/tex]Substitute the values in equation (1),
[tex]\begin{gathered} c=-25(1)+5(2) \\ c=-25+10 \\ c=-15 \end{gathered}[/tex]Substitute the values of a, b, and c, in the standard equation,
[tex]\begin{gathered} y=(1)x^2+(2)x+(-15) \\ y=x^2+2x-15 \end{gathered}[/tex]This is the equation of the given parabola.
Therefore, option B is the correct choice.
Given that line S and line T are parallel, and line R is a transversal that cuts through lines S and T, which angles are alternate interior anglesZА A
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The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.
In this case:
9 to the power of -3 as a fraction or number without exponents (simplified fractions).
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Answer:
1/729
Step-by-step explanation:
A number raised to a negative exponent is the same as 1 divided by the number raised the the exponent
9⁻³
1/9³
1/729
Consider the function f (x) = x2 – 3x + 10. Find f (6).
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The given function is f(x) = x^2 - 3x + 10
this means that the expression is a function of x
f(6) means replace x with 6
f(6) = (6)^2 - 3(6) + 10
f(6) = 36 - 18 + 10
f(6) = 18 + 10
f(6) = 28
The answer is 28
Finding the time given an exponential function with base e that models a real-world situation
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We are solving for the value of t if C(t) = 19. We can rewrite the equation into
[tex]19=5+17e^{-0.038t}[/tex]Solving for t, we have
[tex]\begin{gathered} 17e^{-0.038t}=19-5 \\ 17e^{-0.038t}=14 \\ e^{-0.038t}=\frac{14}{17} \\ -0.038t=\ln \frac{14}{17} \\ -0.038t=-0.1941 \\ t=\frac{-0.1941}{-0.038} \\ t\approx5.1 \end{gathered}[/tex]The bottled water will achieve a temperature of 19 degrees C after 5.1 minutes.
Answer: 5.1 min
Blossom's Computer Repair Shop started the year with total assets of $318000 and total liabilities of $211000. During the year, the
business recorded $505000 in computer repair revenues, $311000 in expenses, and Blossom paid dividends of $50200. Stockholders'
equity at the end of the year was
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Ur welcome
Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
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Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
Part A
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
so
In this problem
we have that
QS/TV=QR/TU=RS/UV
that means, that the scale factor is
scale factor=TV/QS
substitute the given values
scale factor=2.8/7=0.4
scale factor=0.4Part B
Find the the length of RS
we have that
The length of RS is equal to the length of UV divided by the scale factor
so
RS=5.7/0.4
RS=14.25Part 2
Keeshonbought Packages of pens represented by P there were four pence in each package Keyshawn gave six to his friends which expression shows this situation
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The expression that shows when Keeshon bought Packages of pens represented by P is 24p.
What is an expression?An expression is used to illustrate the information that's given regarding a data.
Let the pens be represented by p.
In this case, there there were four pend in each package and Keyshawn gave six to his friends. This will be:
= 6(4 × p)
= 6(4p)
= 24p
This shows the expression.
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Simplify (sqrt)98m^12Using factor tree. Please draw. Quick answer = amazing review. Not a graded or timed assessment. Please use factor tree or split up using perfect squares
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The simplified expression is 7m⁶ √2
STEP - BY - STEP EXPLANATION
What to find?
Simplify the given expression.
Given:
[tex]\sqrt[]{98m^{12}}[/tex]To simplify the above, we will follow the steps below:
Step 1
Apply radical rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\text{ . }\sqrt[]{b}[/tex]That is;
[tex]\sqrt[]{98m^{12}}=\sqrt[]{98}\times\sqrt[]{m^{12}}[/tex]Step 2
Simplify each value under the square root.
[tex]\sqrt[]{98}=\sqrt[]{49\times2}=\sqrt[]{49}\times\sqrt[]{2}=7\sqrt[]{2}[/tex][tex]\sqrt[]{m^{12}}=(m^{12})^{\frac{1}{2}}=m^{\frac{12}{2}}=m^6[/tex]Therefore, the simplified expression is:
[tex]\sqrt[]{98m^{12}}=7m^6\text{ }\sqrt[]{2}[/tex]Determine whether the statement is true or false, and explain why.
If a function is positive at x = a, then its derivative is also positive at x = a.
Choose the correct answer below.
OA. The statement is true because the sign of the rate of change of a function is the same as the sign of its value.
OB. The statement is false because the derivative gives the rate of change of a function. It expresses slope, not
value.
OC. The statement is false because the sign of the rate of change of a function is opposite the sign of its value.
OD. The statement is true because the derivatives of increasing functions are always positive.
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Answer: B. The statement is false because the derivative gives the rate of change of a function. It expresses slope, not value.
find the distance between the given points. if the answer is not exact, use a calculator and give an approximation to the nearest tenth (-7,-2), (5,3)
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The distance is:
[tex]d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]By replacing x and y
[tex]d=\sqrt[]{(5-(-7))^2+(3-(-2))^2}[/tex]Then solve
[tex]\begin{gathered} d=\sqrt[]{(5+7)^2+(3+2)^2} \\ d=\sqrt[]{12^2+5^2} \\ d=\sqrt[]{144+25}^{} \\ d=\sqrt[]{169} \\ d=13 \end{gathered}[/tex]Answer: 13
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed. Balan, who lives on this planet, does a survey and finds that her colony of 500 contains 100 green, one-headed Jolos; 125 purple, two-headed Jolos; and 270 one headed-jolos.How many green Jolos are there in Balan's colony?A. 105B. 170C. 205D. 230
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According to the table, there are 270 one-headed in total, and there are 500 Jolos, we just have to subtract to find the total of two-headed Jolos
[tex]500-270=230[/tex]There are 230 two-headed Jolos.
Now, we subtract the total of two-headed Jolos and the two-headed purple Jolos to find the total green.
[tex]230-125=105[/tex]There are 105 two-headed green Jolos.
At last, we have to sum the number of one-headed green Jolos and the two-headed green Jolos,
[tex]100+105=205[/tex]Hence, there are 205 green Jolos in total.Sarina throws a ball up into the air, and it falls on the ground nearby. The ball's height, in feet, is modeled by the function ƒ(x) = –x2 – x + 3, where x represents time in seconds. What's the height of the ball when Sarina throws it?Question 12 options:A) 1 footB) 3 feetC) 4 feetD) 2 feet
Answers
Answer:
3 feet
Explanation:
We are told from the question that the ball's height, in feet, is modeled by the below function;
[tex]f(x)=-x^2-x+3[/tex]where x = time in seconds
To determine the height of the ball when Sarina throws the ball, all we need to do is solve for the initial height of the ball, i.e, the height when x = 0. So we'll have;
[tex]\begin{gathered} f(0)=-(0)^2-(0)+3 \\ f(0)=3\text{ f}eet \end{gathered}[/tex]Julian is decorating the outside of a box in the shape of a right rectangular prism. Thefigure below shows a net for the box.
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The surface area of the box equals the sum of the surface area of each of its parts.
And the area of each rectangle that form the box is found by multiplying the width by the height of that rectangle.
We have two ractangles with sides 7 ft and 10 ft. So the area of each one is:
7 ft * 10 ft = 7 * 10 * ft * ft = 70 ft²
Since there's two of this rectangle, their areas sum up to
2 * 70 ft² = 140 ft²
Now, we also have two rectangles with sides 7 ft and 14 ft (the second and the fourth rectangles from left to right in the image). So, their areas sum up to:
2 * (7 ft * 14 ft) = 2 * (98 ft²) = 196 ft²
Finally, we also have two rectangles with sides 10 ft and 14 ft. Then, their area together is:
2 * (10 ft * 14 ft) = 2 * (140 ft²) = 280 ft²
Therefore the total surface area of the box is the sum:
140 ft² + 196 ft² + 280 ft² = 616 ft²
Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
Answers
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
find the minimum value of the function f(x)=2x2-22x+68 to the nearest hundredth
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Minimum value of the function
[tex]f(x)=2x^2-22x+68[/tex]To calculate the minimum value we will use the derivative.
[tex]\begin{gathered} f^{\prime}(x)=4x-22 \\ 4x-22=0 \\ 4x=22 \\ x=\frac{22}{4} \\ x=5.5 \end{gathered}[/tex]The answer would be 5.5