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we are asked to find the surface area of a prism. To do that, we will find the areas of each lateral rectangle and the areas of the top and bottom triangles.
The areas of the rectangles are:
[tex]\begin{gathered} A_1=(10)(6)=60 \\ A_2=(10)(6)=60 \\ A_3=(10)(50)=50 \end{gathered}[/tex]To determine the ara of the top triangle we will use the following formula:
[tex]undefined[/tex]Related Questions
A quadratic equation is shown below:x^2 + 18x + 76 = 0Which of the following is the first correct step to write the above equation in the form (x-p)^2 = q, when p and q are integers? A. Add 9 to both sides of the equationB. Add 5 to both sides of the equationC. Subtract 5 from both sides of the equationD. Subtract 9 from both sides of the equation.
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SOLUTION:
[tex]\begin{gathered} x^2\text{ + 18x + 76 = 0} \\ To\text{ make left hand p}\operatorname{erf}ect\text{ square, we add 5 to both sides} \\ x^2\text{ + 18x + 76 + 5 = 0 + 5} \\ x^2\text{ + 18x + 81 = 5} \\ x^2\text{ }+18x+9^2\text{ = 5} \\ (x+9)^2\text{ = 5} \end{gathered}[/tex]The correct option B, that is, add 5 to both sides of the equation.
L) Point A bisects CR. CA = 8x + 1 and AR = 6x+13.Find CA.34927
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We will investigate some application of line bisectors.
We have a line segment denoted as ( CR ). A point ( A ) is said to be bisecting the line segment.
Line bisection involves the process of equally dividing the entire line segment in two equal halves! We can also represent this scenario graphically for clearification:
We can also represent line bisection mathematically in terms of two smaller divisions ( CA and AR ) as follows:
[tex]Bi\sec tion\colon\text{ |CA| = |AR| = }\frac{|CR|}{2}[/tex]Where, the quantities are expressed as magnitudes/lengths of each segment indicated.
We are given expressions for bifurcated line segments |CA| and |AR| in terms of variable ( x) as follows:
[tex]\begin{gathered} |CA|\text{ = 8x + 1} \\ |AR|\text{ = 6x + 13} \end{gathered}[/tex]Now we will use the expression given for each smaller division of line |CR| and plug it in the general " Bisection " expression developed above:
[tex]\begin{gathered} |CA|\text{ = |AR|} \\ 8x\text{ + 1 = 6x + 13} \end{gathered}[/tex]We have constructed an equation with a single variable ( x ). We can solve this equation for the variable ( x ) using basic mathematical operations as follows:
[tex]\begin{gathered} 8x\text{ - 6x = 13 - 1} \\ 2x\text{ = 12} \\ x\text{ = 6} \end{gathered}[/tex]Once we have solved for the variable ( x ). We will again use the defined expression for each smaller segments and determine the magnitudes as follows:
[tex]\begin{gathered} |CA|\text{ = 8}\cdot(6)\text{ + 1 } \\ |CA|\text{ = 49 units} \\ \\ |AR|\text{ = 6}\cdot(6)\text{ + 13 } \\ |AR|\text{ = 49 units} \\ \\ |\text{ CR | = 2}\cdot|CA|\text{ = 2}\cdot49 \\ |\text{ CR | = 98 units} \end{gathered}[/tex]Using the drawing find y: MzBDJ = 7y + 2, mZJDR = 2y + 7 * HRT O 25 O 19 O O TY
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2. Line ( has a slope of -7 and a y-intercept of 12. What is the equation for line in slope-intercept form? y =12x-7 y=-7x+12 --7x+12y=0which one of those equations are true
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The general form of a straight line graph is: y = mx + c
where m and c are the slope and slope-intercept respectively.
from the question given, the slope (m) = -7
and the intercept (c) = 12
substituting the values into y = mx + c
then y = -7x + 12
use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $10,000 is deposited in an account at an annual rate of 3% and the interest is compounded quarterly. The amount after ten years will be $_______ (round to the nearest cent as needed). A = P ( 1 + r/m) ^ n
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Given:
P=$10000 : m=4 : r=0.03 : n=40
[tex]A=P(1+\frac{r}{m})^n[/tex][tex]A=10000(1+\frac{0.03}{4})^{40}[/tex][tex]A=10000(1.0075)^{40}[/tex][tex]A=10000(1.3483)[/tex][tex]A=\text{ \$13483}[/tex][tex]1\text{ \$= 100 cent}[/tex][tex]A=13483\times100[/tex][tex]A=\text{ 1348300 cent}[/tex]Therefore,The amount after ten years will be 1348300 cent.
simplifying with like terms; a + 2a -7
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In the expression like terms are a and 2a.
Simplify the expression
[tex]a+2a-7=3a-7[/tex]So answer is 3a - 7.
For each coefficient choose whether it is positive or negative. Choose the coefficient with the greatest value. Choose the coefficient closest to zero.
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First we need to find if the coefficients are negative or positive. The function:
[tex]\lvert x\rvert[/tex]Is always positive which means that its graph must be over the x axis. If this function is multiplied by a positive coefficient then the graph remains over the x axis. On the other hand, if it's multiplied by a negative number then the graph is now under the x axis. A and B graph are over the x axis so they are positive whereas C and D graphs are under the x axis and they are negative and that's the answer for a.
Then we must find the coefficient with the greatest value. Since a positive number is greater than any negative number we can discard C and D. Now we have two options, A and B which we know are different numbers since their graph are different. Both are V shaped but graph B is sharper than graph C. This means that B is greater than C. Then, the answer to part b is coefficient B.
In part c we must choose the coefficient that is closest to 0. Using the same argument as before, the sharper the V shaped graph is the greatest absolute value its coefficient has. This means that the least sharp graph is that of the coefficient that is closer to 0. Looking at the four graphs you can see that the least sharp V is that of coefficient A. Then, the answer to part c is coefficient A.
Find the absolute change and the percentage change for the given situation.120 is decreased to 18
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The absolute change is defined as:
[tex]V_2-V_1[/tex]where V1 and V2 are the initial and final values, respectively.
Plugging the values given we have that:
[tex]18-120=-102[/tex]Therefore the absolute change is -102. (The minues sign indicate a decrease)
The percentage change is given by:
[tex]\frac{V_2-V_1}{\lvert V_1\rvert}\cdot100[/tex]plugging the values given we have:
[tex]\frac{18-120}{\lvert120\rvert}\cdot100=-\frac{102}{120}\cdot100=-0.85\cdot100=85[/tex]Therefore the percentage change is -85% (Once again the minus sign indicate a decrease)
Question 5 of 10 Which of the segments below is a secant? B D O A. CD O B. AB O C. ÃO D. BC
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Diagram
secant = ?
Step 02:
We must analyze the diagra,m to find the solution.
Secant ===> straight line that cuts a curve in two or more parts
Segments:
CD: FALSE
AB: FALSE
AO: FALSE
BC: TRUE
The answer is:
Segment BC is a secant
I need help with number 16 can I please get help?
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We can break apart the figure into 4 separate figures and find the area of each of these individual figures. Then sum to get area of total figure.
We break apart the figure as shown below:
First,
Area of Triangle = 0.5 * base * height
Area of Rectangle = base * height
Now, let's find each of the Areas A through D:
Area of A:
To find the base of this triangle, we have to use pythagorean theorem. By which we can write:
[tex]b^2+4^2=6^2[/tex]Where b is the base. let's solve for b:
[tex]\begin{gathered} b^2+16=36 \\ b^2=36-16 \\ b^2=20 \\ b=\sqrt[]{20} \\ b=\sqrt[]{4}\sqrt[]{5} \\ b=2\sqrt[]{5} \end{gathered}[/tex]Area is
[tex]\begin{gathered} 0.5\cdot\text{base}\cdot\text{height} \\ =\frac{1}{2}\cdot2\sqrt[]{5}\cdot4 \\ =4\sqrt[]{5} \end{gathered}[/tex]Area of B:
This is a rectangle with base = 10 and height 4, so the area is:
Area = 4 * 10 = 40
Area of C:
Area of C is exactly same as area of B, base is 10 and height is 4. So,
Area = 4 * 10 = 40
Area of D:
Like area of A, we have to find the base of the triangle first, using pythagorean theorem. We can write:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ \end{gathered}[/tex]Solving for b:
[tex]\begin{gathered} b^2+4^2=4.5^2 \\ b^2+16=20.25 \\ b^2=\frac{17}{4} \\ b=\frac{\sqrt[]{17}}{\sqrt[]{4}} \\ b=\frac{\sqrt[]{17}}{2} \end{gathered}[/tex]Now, area of triangle is:
[tex]A=\frac{1}{2}(\frac{\sqrt[]{17}}{2})(4)=\sqrt[]{17}[/tex]Area of whole figure:
[tex]\begin{gathered} 4\sqrt[]{5}+40+40+\sqrt[]{17} \\ =80+4\sqrt[]{5}+\sqrt[]{17} \end{gathered}[/tex]Since mulch costs $3 per square feet, we have to multiply the area by "3", so we have:
[tex]3\times(80+4\sqrt[]{5}+\sqrt[]{17})\approx279.202[/tex]It will cost around:
$279.20
A figure is made up of two triangles and a square. The trianglesand the square have the same base length of 9 feet. Thetriangles have a height of 12.3 feet. What is the total area of thefigure?
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if Sarah has 98 baseball cards in her collection for birthday her she's given 78 new cards and she sold 108 cards how many baseball cards does Sarah have left
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68
1) Gathering the data
Sarah has 98 cards
She's given 78 then we can add
98 +78 = 176 cards
2) And right after that Sarah sold 108 cards, so now we can write
176 -108 = 68
3) Finally, Sarah now has 68 baseball cards left.
I need help find the answer to number 10 and 11
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10. We need to identify the value of b in the function:
[tex]f(x)=b^x[/tex]so that it produces the graph given.
Observing the graph, we see that the point (1,2) lies on it. Thus, we have:
[tex]\begin{gathered} 2=b^1 \\ \\ \Rightarrow2=b \end{gathered}[/tex]Therefore, the value of the base b is: 2
The mean life of a television set is 97 months with the variance of 169. If a sample of 59 televisions is randomly selected what is the probability that the sample mean would be less than 100.9 months? Round your answer to four decimal places if necessary
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Given that the mean life of a television set is 97 months, you can set up that:
[tex]\mu=97[/tex]You also know that the variance is:
[tex]\sigma^2=169[/tex]You can find the standard deviation by taking the square root of the variance. Then:
[tex]\sigma=\sqrt{169}=13[/tex]You need to find:
[tex]P(X<100.9)[/tex]You need to find the z-score with this formula:
[tex]z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Knowing that:
[tex]\bar{X}=100.9[/tex]You can substitute values into the formula and evaluate:
[tex]z=\frac{100.9-97}{\frac{13}{\sqrt{59}}}\approx2.30[/tex]You have to find:
[tex]P(z<2.30)[/tex]Using the Standard Normal Distribution Table, you get:
[tex]P(z<2.30)\approx0.9893[/tex]Then:
[tex]P(X<100.9)\approx0.9893[/tex]Hence, the answer is:
[tex]P(X<100.9)\approx0.9893[/tex]Joey buys a home for $205,900. His home is predicted to increase in value 4% each year. What is the predicted value of his home in 22 years? Round answer to thenearest whole number
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Since every year the value of the house increase by 4%, the new value will be the previous value plus 4% of the previous value. To find 4% of a quantity, we just have have to multiply it by 4 and then divide by 100(or, written as a decimal, multiply the number by 0.04).
If we call the previous value of the house as P and the new value as N, the new value after one year will be
[tex]N=P+0.04P=(1+0.04)P=1.04P[/tex]Every year that passes, to get the new value we multiply again by 1.04. The expression for the predicted value after t years is
[tex]N(t)=P_0(1.04)^t[/tex]Where P0 represents the initial value of the house. Evaluating t = 22 on this expression, we have
[tex]N(22)=205,900(1.04)^{22}=487,966.279171\ldots\approx487,966[/tex]The predicted value of his home in 22 years is $487,966.
given triangle CAT is congruent to triangle DOG. Solve for x
Answers
Answer:
The value of x is 2 or -5.5.
Explanation:
Given that triangle CAT is congruent to triangle DOG, then we have that:
[tex]\angle T\cong\angle G[/tex]Step 1: We determine the value of angle T.
[tex]\begin{gathered} \angle T=180^0-(87^0+75^0) \\ =180^0-162^0 \\ =18^0 \end{gathered}[/tex]Step 2: Since angle T is congruent to angle G, then:
[tex](x+4)(2x-1)=18[/tex]Step 3: We solve the equation above for x.
[tex]\begin{gathered} 2x^2-x+8x-4-18=0 \\ 2x^2+7x-22=0 \\ 2x^2-4x+11x-22=0 \\ 2x(x-2)+11(x-2)=0 \\ (2x+11)(x-2)=0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2x+11=0\text{ or x-2=0} \\ 2x=-11\text{ or x=2} \\ x=-5.5\text{ or x=2} \end{gathered}[/tex]The value of x is 2 or -5.5.
is 1,000 feet greater than 300 yards
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hello
to solve this question, we have to know the the dimensions or
There are 221 6th graders in the HPS district that are going on field trip to the Detroit Institute of Arts when we get back to school. If each bus holds 46 students, how many buses should be hierd to transport us?
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Students = 221
Each bus holds 46 students
Divide the total number of students (221) by the capacity of each bus (46 )
221 /46 = 4.8 = 5 buses
Sowen rolled two number cubes with sides numbered 1 through 6, 20 times. Her sums are recorded in the table below.49899462.1012879111087935What is the experimental probability of rolling a sum of 9?4/20Сь5/20Od4/365/36
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The total number of experiment, N=20.
From the given data, 9 is obtained 5 times.
The number of times of getting 9, n=5.
Hence, the probability of getting a sum of 9 is,
[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{5}{20} \end{gathered}[/tex]Hence, option b is correct.
Convert the unit to the specified equivalent unit round your answer to at least1 decimal place if necessary
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Given:
There are given that the 209 ounces to convert into the decigram.
Explanation:
According to the concept:
To convert the ounces into the decigram, we need to multiply the mass values by 283.
That means,
The value of 1 ounce is 283 decigram
So,
[tex]\begin{gathered} 209ounces=209\times283decigram \\ =59147decigram \end{gathered}[/tex]Final answer:
Hence, the value of the 209 ounces is 59147 decigrams.
What is the average rate of change of the equation f(x)^2+3x-5 from x=2 to x=4?Type your numerical answer below. Use the hyphen (-) to represent a negative sign if necessary.
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Given:
The equation is,
[tex]f\mleft(x\mright)=x^2+3x-5,x=2\text{ to x = 4}[/tex]To find: The average rate of change
Explanation:
The average rate of the change formula is,
[tex]A\left(x\right)=\frac{f\mleft(b\mright)-f\mleft(a\mright)}{b-a}[/tex]Here, we have
[tex]\begin{gathered} a=2 \\ b=4 \end{gathered}[/tex]Substituting we get,
[tex]\begin{gathered} A\lparen x)=\frac{f\mleft(4\mright)-f\mleft(2\mright)}{4-2} \\ =\frac{\left\lbrack4^2+3\left(4\right)-5\right?-\left\lbrack2^2+3\left(2\right)-5\right?}{2} \\ =\frac{16+12-5-\left\lbrack4+6-5\right\rbrack}{2} \\ =\frac{23-5}{2} \\ =\frac{18}{2} \\ =9 \end{gathered}[/tex]Final answer:
The average rate of change of the given equation is 9.
Roberto bought a new graduated cylinder for his chemistry class. it holds 650 mililiters of liquid. if the cylinder has a radius of 5 cm, then how tall is the cylinder.
Answers
8.27 cm
Explanation
Step 1
the volume of a cylinder is given by:
[tex]\begin{gathered} \text{Volume}=\text{ area of the circle}\cdot\text{ height} \\ \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \end{gathered}[/tex]then
Let
Heigth=unknown=h
volume=650 ml
radius= 5 cm
also
1 mililiter= 1 cubic centimeter
so,replacing
[tex]\begin{gathered} \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \\ \text{650 }=(\pi\cdot(5cm)^2)\cdot\text{h} \\ 650=25\pi\cdot h \\ \text{divide both sides by 25 }\pi \\ \frac{650}{25\pi}=\frac{25\pi h}{25\pi} \\ h=\frac{650}{25\pi}=8.27\text{ cm} \end{gathered}[/tex]so, the cylinder is 8.27 cm tall.
I hope this helps you
Hay e escalones desde el pedestal hasta la cabeza de la Estatua de la Libertad. La cantidad de escalones que hay en el Monumento a Washington es 27 menos que 6 veces la cantidad de escalones que hay en la Estatua de la Libertad. ¿Qué expresión representa la cantidad de escalones que hay en el Monumento de Washington en función de e? 27 < 6e 6(e-27) 6e-27 They 6e
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Let
e -----> number of steps from the pedestal to the head of the Statue of Liberty
f ----> number of steps on the Washington Monument
we have that
f=6e-27
therefore
teh answer is
6e-27
Do you understand my explanation?escalones que hay en el Monumento a Washington
we have that
f=6e-27
How do I solve for x? Would my answer be 27?
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Given:
[tex]\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o[/tex][tex]We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}[/tex]The sum of the supplementary angles =180 degrees.
[tex]\angle BAC+\angle XAC=180^o[/tex][tex]\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}[/tex][tex]\angle BAC+(5x+13)^o=180^o[/tex][tex]\angle BAC=180^o-\mleft(5x+13\mright)^o[/tex]We know that the sum of all three angles of the triangle is 180 degrees.
[tex]\angle ABC+\angle ACB+\angle BAC=180^o[/tex][tex]\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}[/tex][tex](4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=0[/tex][tex]4x+2+2x-9-5x-13=0[/tex]Adding like terms that have the same variable with the same powers.
[tex]4x+2x-5x+2-9-13=0[/tex][tex]x-20=0[/tex][tex]x=20[/tex]Hence the value of x is 20.
What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark
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To solve this problem, we have to find the zeros of the expression in the denominator, to do it, factor the expression:
[tex]\begin{gathered} x^3-3x^2-26x+48=0 \\ (x-3)(x-4)(x+4)=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x=4 \\ x+4=0 \\ x=-4 \end{gathered}[/tex]The zeros of the function are x=3,4,-4.
Since these values make the expression be zero, they are not included in the domain of the function. This is because the expression in the denominator can not be zero, otherwise, the function would be undefined.
The correct answer is B:
[tex]\mleft\lbrace x\in R\mright|x\ne-4,3,4\}[/tex]I have a pentagon that 8 and 8 and 6 and 6 and 10 whats the perimeter?
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The perimeter of any closed figure is equal to sum of all sides of the figure.
Determine the perimeter of pentagon by addition of measure of sides of pentagon.
[tex]\begin{gathered} P=8+8+6+10+6 \\ =38 \end{gathered}[/tex]So answer is 38 cm.
how do I solve (-2+5i) (4-i) +(2-i)
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Given:
[tex](-2+5i)(4-i)+(2-i)[/tex]Using the distributive property for the multiplication then combine the like terms
so, the given expression will be:
Note: i² = -1
[tex]\begin{gathered} (-2+5i)(4-i)+(2-i) \\ =-2(4-i)+5i(4-i)+(2-i) \\ =-8+2i+20i-5i^2+2-i \\ =-8+2i+20i+5+2-i \\ =(-8+5+2)+(2i+20i-i) \\ =-1+21i \end{gathered}[/tex]So, the answer will be:
[tex]-1+21i[/tex]At a food drive, afood bank has a goal to collect 24,000 cans.If the food bank collects 100 fewer cansthan its goal, how many cans did it collect?
Answers
Given:
• Expected number of cans to collect = 24,000 cans.
,• The food bank collects 100 fewer cans.
Let's find the number of cans it collected.
Since the food bank collected 100 fewer cans, to find the number of cans it collected, let's subtract 100 from the expected goal which is 24000 cans.
Hence, we have:
Number of cans collected = expected goal - 100
Number of cans collected = 24000 - 100 = 23900
Therefore, the number of cans the food bank collected was 23,900 cans.
ANSWER:
23900 cans
1 point 3 John ran 3 les in of an hour Marlon ran s 4 miles in of an hour How lar did Marlon run in one hour?
Answers
Answer:
6.2 miles per hour
Explanation:
Marlon ran 8 1/4 miles in 4/3 of an hour.
So, we first need to transform the mixed number 8 1/4 into a fraction using the following equation:
[tex]\begin{gathered} A\frac{b}{c}=\frac{A\cdot c+b}{c} \\ 8\frac{1}{4}=\frac{8\cdot4+1}{4}=\frac{32+1}{4}=\frac{33}{4} \end{gathered}[/tex]Then, we need to divide 33/4 miles by 4/3 hour as:
[tex]\begin{gathered} \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c} \\ \frac{\frac{33}{4}}{\frac{4}{3}}=\frac{33\cdot3}{4\cdot4}=\frac{99}{16}=6.2\text{ miles per hour} \end{gathered}[/tex]So, Marlon ran 6.2 miles per hour.
A box can be formed by cutting a square out of each corner of a piece of cardboard and folding the sides up. If the piece of cardboard is 78 cm by 78 cm and each side of the square that is cut out has length x cm, the function that gives the volume of the box is V=6084x−312x2+4x3. Complete parts (a) and (b) below.
Answers
a) Notice that:
1)
[tex]6084x-312x^2+4x^3=4x(1521-78x+x^2)=4x(x-39)^2\text{.}[/tex]Therefore V(x)=0 at x=0 and it has a double root at x=39.
2)
[tex]\begin{gathered} V(-1)=6084(-1)-312(-1)^2+4(-1)^3, \\ V(-1)=-6084-312-4<0. \end{gathered}[/tex]Therefore, V(x)<0 when x is in the following interval:
[tex](-\infty,0).[/tex]3)
[tex]V(1)=6084(1)-312(1)^2+4(1)^3>0.[/tex]Therefore, V(x)>0 when x is in the following set:
[tex](0,39)\cup(39,\infty).[/tex]b) Since x is a length, then it must be greater than zero, also 2x must be smaller than 78, therefore the values of x that makes sense in the context are in the interval:
[tex](0,39)\text{.}[/tex]Answer:
a) Option B) The values of x that makes V>0 are in the set:
[tex](0,39)\cup(39,\infty).[/tex]b) Option A) The values of x that give squares that can be cut out to construct a box are the interval:
[tex](0,39)\text{.}[/tex](0,39).