Answer:
Step-by-step explanation:
He used a coupon for 1/2 off the price of the bat which is $69. With the coupon applied, the cost of the bat would be 69 × 1/2 = $34.5
He also used a coupon for 1/2 off the price of the glove which is $75. With the coupon applied, the cost of the bat would be 75 × 1/2 = $37.5
Therefore, a numerical expression to find the total cost of the bat, the glove, and 3 baseballs which are 5.50 each would be
34.5 + 37.5 + 3 × 5.5 = $88.5
The total cost of the bat, the glove, and the baseballs is $88.5 and this can be determined by using the given data and arithmetic operations.
Given :
He used a coupon for 1/2 off the price of the bat which is $69 and the glove which is $75.
The following steps can be used to evaluate the total cost:
Step 1 - Find the cost of the bat after the discount.
[tex]= \dfrac{1}{2}\times 69[/tex]
= $34.5
Step 2 - Find the cost of the glove after the discount.
[tex]=\dfrac{1}{2}\times 75[/tex]
= $37.5
Step 3 - Now, evaluate the cost of the baseballs.
[tex]=3\times 5.5[/tex]
= $16.5
Step 4 - Add all the costs to determine the total cost.
= 16.5 + 37.5 + 34.5
= $88.5
For more information, refer to the link given below:
https://brainly.com/question/20595275
Tiwa spent 1 1/2 hours setting up her computer. It took her 3 times as long to install the software. How long did it take Tiwa to set up the computer and install the software
Answer:
Total time spent by Tiwa to set up the computer and install software = 6 hours
Step-by-step explanation:
Given:
Time spent by Tiwa to set up her computer = [tex]1\frac{1}{2}\ hours[/tex]
Time spent to install the software is 3 times the time she took to set up the computer.
To find the total time Tiwa took to set up her computer and install the software.
Solution:
Time spent by Tiwa to install the software can be given as:
⇒ [tex]3\times 1\frac{1}{2} \ hours[/tex]
In order to multiply mixed numbers we first change them to fractions.
We multiply the denominator to the whole number and add the numerator to it. Then we write the number as numerator of a fraction with the same denominator.
So, [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
So, we have:
⇒ [tex]3\times \frac{3}{2}\ hours[/tex]
⇒ [tex]\frac{9}{2}\ hours[/tex]
Total time spent by Tiwa to set up the computer and install software can be given as:
⇒ [tex]\frac{3}{2}\ hours+\frac{9}{2}\ hours[/tex]
Since denominators are same, so we simply add the numerators.
⇒ [tex]\frac{3+9}{2}\ hours[/tex]
⇒ [tex]\frac{12}{2}\ hours[/tex]
⇒ [tex]6\ hours[/tex]
help in anyway in this ixl
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle shown,
AB represents the hypotenuse of the right angle triangle.
With 45 degrees as the reference angle,
AC represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine QR, we would apply trigonometric ratio
Sin θ = opposite side/hypotenuse side. Therefore,
Sin 45 = BC/6√2
√2/2 = BC/6√2
BC = √2/2 × 6√2
BC = 6
9. Calculate the median 5, 10, 12, 4, 6, 11, 13, 5
Answer:
8.
Step-by-step explanation:
5, 10, 12, 4, 6, 11, 13, 5
Arrange in ascending order:
4, 5, 5, 6, 10, 11, 12, 13.
The median is the mean of the 2 middle numbers:
= (6 + 10) / 2
= 8.
At an election there are 5 candidates and 3 members are to be elected. A voter is entitled to vote for any number of candidates not greater than the number to be elected. In how many ways a voter can vote?
Answer:
Voters can select their members in 10possible ways
Step-by-step explanation:
According to the question, the voters are to elect 3members out of 5 candidates, this means they are to select any 3 candidates of their choice from a pool of 5 candidates. Since "combination" has to do with selection, we use the combination formula.
To select 'r' objects from 'n' pool of objects, we have;
nCr = n!/(n-r)!r!
5C3 = 5!/(5-3)!3!
5C3 = 5!/2!3!
5C3 = 5×4×3×2×1/2×3×2
= 120/12
5C3 = 10
Candidates can therefore vote in 10 possible ways
(Answer asap) Name all of the radii of the circle
Answer:
OT, OU, OR
Step-by-step explanation:
Point O is the center of the circle, so will be one end of any radius. Segments are shown from point O to points T, U, and R on the circle. Each of those segments is a radius:
OT, OU, OR . . . . are radii
_____
OS would also be a radius, but no segment is shown there, and it doesn't show in any answer choice.
Ms Thomas drove at a constant rate for 45. She drove 39 miles during that time. If distance is determined by the equation d=rt where r is the constant rate in miles per hours what was ms Thomas constant rate?
Answer:
Ms. Thomas was driving at constant rate of 52 miles/hour.
Step-by-step explanation:
Given:
Total time to travel (t) = 45 minutes
Distance drove (d) = 39 miles
we need to find the constant rate in miles per hour at which she was driving.
Solution:
Now we know that;
We need to find constant rate at miles per hour;
But time is given in minutes.
So we will convert minutes into hour by dividing by 60 we get;
time [tex]t =\frac{45}{60}= 0.75\ hrs[/tex]
Now we know that;
Distance is equal to rate times time.
framing in equation form we get;
distance [tex]d =rt[/tex]
Or
rate [tex]r= \frac{d}{t} = \frac{39}{0.75}= 52 \ mi/hr[/tex]
Hence Ms. Thomas was driving at constant rate of 52 miles/hour.
Jeff wants to know how many miles it is from his house to school. On a map, the scale is 0.5 inches=2 miles. If his house island school are 3 inches apart on the map, how many miles is it to the school?
It is 12 miles from house to school
Solution:
Given that, Jeff wants to know how many miles it is from his house to school
On a map, the scale is 0.5 inches = 2 miles
His house island school are 3 inches apart on the map
So, from the given scale,
0.5 inches = 2 miles
Distance between school and house in map = 3 inches
Therefore,
0.5 inches = 2 miles
Muliply both sides by 6
[tex]0.5 \times 6\ inches = 6 \times 2\ miles\\\\3\ inches = 12\ miles[/tex]
Thus, it is 12 miles from house to school
For #1-4, graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the Pre-image and image using the correct notation.
See the attached picture:
Edited graph 4. I missed the negative sign in front of the one. The new graph is attached.
A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of 72000$ in one week what was the salesperson paid that week
Answer:
Step-by-step explanation:
A salesperson at a car dealership has a salary of 900 dollars per week plus 3% commission on sales if a salesperson has sales of $72000 in one week, it means that the amount of commission that was received by the salesperson would be
3/100 × 72000 = 0.03 × 72000 = $2160
Therefore, the total amount of pay that the salesperson would receive for the week would be
900 + 2160 = $3060
Evaluate the expression x^3 - (3 + x)^2x 3 −(3+x) 2 x, cubed, minus, left parenthesis, 3, plus, x, right parenthesis, squared for x=4x=4x, equals, 4.
Answer:
15
Step-by-step explanation:
Put the given value of x where x is in the expression and do the arithmetic.
4^3 -(3 +4)^2 = 64 -49 = 15
The value of the expression for x=4 is 15.
Final answer:
The expression x³ - (3 + x)² for x = 4 simplifies to 64 - 49, resulting in a final answer of 15.
Explanation:
The student has asked to evaluate the expression x³ - (3 + x)² for x = 4. To do this, we will substitute x with 4 and simplify the expression step by step. First, calculate the value inside the parentheses: (3 + 4) = 7. Then, we square this value to get 7² = 49. After that, subtract the squared value from 4³ (which is 64), to get the final answer.
The final answer is 15
A scatter plot shows a set of data points that are clustered close to a line that slopes down to the right. Which of the following values would be closest to the correlation for these data? a. -0.40 b. 0.40 c. 0.80 d. -0.80
Answer:
Option D. -0.80
Step-by-step explanation:
A scatter plot that shows a set of data points having two properties
1). If the points are clustered close to the line that reveals the high correlation.
2). Data points are clustered close to the line having slope down to the right or negative slope.
Therefore, Option D. has the highest correlation with negative slope.
The actual volumes of soda in quart-sized bottles can be described by a Normal model with a mean of 32.3 fluid ounces and a standard deviation of 1.2 fluid ounces. What percentage of bottles can we expect to have a volume of less than 32 fluid ounces?
Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%
Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz
b=1.2 oz
Let S be the volume of randomly selected soda bottles
Y-score: S-a/b
For S=32 oz
Substitute the values of S,a and b into the equation
Y=32-32.3/1.2
Y=-0.25
Probability of bottles that have a volume less than 32 oz is
P(S<32)=P(Y<-025)= 0.40129
Percentage of bottles that have volume less than 32 oz will be
0.40127×100%=40.13%
What is the slope of the line through (-9,6)(−9,6)(, minus, 9, comma, 6, )and (-3,9)(−3,9)(, minus, 3, comma, 9, )?
Answer:
0.5
Step-by-step explanation:
The slope m of a linear equation y = mx + b that goes through point (-9,6) and point (-3, 9) would have the following formula
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 6}{-3 - (-9)} = \frac{3}{6}= \frac{1}{2}[/tex] or 0.5
Where [tex](x_1,y_1), (x_2, y_2)[/tex] are the coordinates of the 2 points that this line goes through
When you graph a square root does it curve
Answer:
yes
Step-by-step explanation:
because it is not a whole number so you cant tell
A typical marathon has 26.2 miles. allan makes an average of 12 kilometers per hour when running marathons. Determine how long it would take allan to complete a marathon at the nearest tenth of an hour.
Answer:
3hr 31mins
Step-by-step explanation:
First we convert miles to kilometers
1 miles to km = 1.60934 km
26.2 miles = 26.2 x 1.60934 = 42.164708
A typical marathon approx = 42.165km
If our runner covers 12 km = 1 hr
then he'll cover 42.165km = 42.165/12 = 3.5137 hrs
= 3 hrs + (0.514 * 60 mins) = 3hrs + (30.84mins)
Allan going at that speed would complete the marathon in appox = 3hrs : 31mins.
Answer:
2.34m2
Step-by-step explanation:
boom
Find the piece wise function for the graph
Answer:
See below.
Step-by-step explanation:
x < 2 f(x) = |x|.
x ≥ 2 f(x) = 3.
Plot the points in the coordinate plane. Then find the perimeter and area of the polygon.
A(-3,5), B(1,6), C(3,-2), D(-1,-3)
Perimeter___________
Area__________________
Answer:
The answer to your question is below
Step-by-step explanation:
See the graph below
Process
1.- Find the distance from A to B, B to C, C to D, A to D
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2}}[/tex]
d AB = [tex]\sqrt{(1 + 3)^{2} + (6 - 5)^{2}} = \sqrt{17}[/tex]
dBC = [tex]\sqrt{(-2 -6)^{2} + (3 - 1)^{2}} = \sqrt{68}[/tex]
dCD = [tex]\sqrt{(-1 - 3)^{2} + (-3 +2)^{2}} = \sqrt{17}[/tex]
dAD = [tex]\sqrt{(-1 + 3)^{2} + (-3 - 5)^{2}} = \sqrt{68}[/tex]
2.- Find the perimeter
Perimeter = 2[tex]\sqrt{17} + 2\sqrt{68}[/tex] = [tex]6\sqrt{17}[/tex] u
3.- Find the area
Area = [tex]\sqrt{17} x \sqrt{68}[/tex]
Area = [tex]\sqrt{17x68} = \sqrt{1156} = 34 u^{2}[/tex]
Working together, two people can cut a large lawn in 4 hr. One person can do the job alone in 1 hr less than the other. How long would it take the faster person to do the job? the faster person would do the job alone in hours.
Answer:The faster person will do the job in 7.53hours
Step-by-step explanation:
Let t=faster person
Let t-1= the other person
The job to be done =1
Each person will do a fraction of the job
4/t+4/t-1=1
Multiply both sides wit t(t-1)
4(t+1)+4t=t(t-1)
4t+4+4t=t^2+t
8t+4=t^2+t
0=t^2+t-8t-4
t^2-7t-4=0
Use Almighty formular to solve d quadratic equation
X=-b+- rootb^2-4ac/2a
X=t,a=1,b=-7 c=4
Substituting the values you get:
t=-7 +- root 49+16/2
t=-7 +- root 65/2
t=7 +8.06/2=15.06/2
t=7.53 hours
. Solve the equation. 3/7x + 5 = 8 1 2/7 7 7 2/7 –7
Answer:
x= −5621/201
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
3 /7x+5 = 812/7772/7-7
3 /7x+5= 1/67+−7
3 /7x+5=( 1/67+-7)(Combine Like Terms)
3 /7x+5= −468 /67
3 /7x+5= −468/67
Step 2: Subtract 5 from both sides.
3 /7x+5−5=−468/67−5
3 /7x=−803/67
Step 3: Multiply both sides by 7/3.
( 7/3)*(3/7x)=(7/3)*(−803/67)
x= −5621/201
Malcolm has been watching a roulette-style game at a local charity bazaar. The game has only ten numbers on the wheel, and every number except 8 has come up as a winner during the last 15 minutes. Malcolm decides to bet $10 on number 8, because it eventually has to come up. In this case, Malcolm is showing evidence of…
Answer:
Malcolm is showing evidence of gambler's fallacy.
This is the tendency to think previous results can affect future performance of an event that is fundamentally random.
Step-by-step explanation:
Since each round of the roulette-style game is independent of each other. The probability that 8 will come up at any time remains the same, equal to the probability of each number from 1 to 10 coming up. That it has not come up in the last 15 minutes does not increase or decrease the probability that it would come up afterwards.
A buyer paid $55 comma 68055,680, including the buyer's premium, for a car auction. If the auction adds a 1616% buyer's premium to the sale price of the car, then what was the sale price of the car?
Answer:
The sale price of the car is $48000.
Step-by-step explanation:
i) let the sale price of the car be = $x
ii) the premium is given as 16%
therefore the premium of the car will be equal to = 16% of $x
the premium of the car will be = $0.16x
iii) therefore total price of car in terms of sale price x = $x + $0.16x
therefore total price = $1.16x
iv) total price is given as $55,680
Therefore $55,680 = $1.16x, therefore $x = [tex]\dfrac{55,680}{1.16} = \$\hspace{0.15cm}48000[/tex].
Therefore the sale price of the car is $48000.
Out of 290 racers who started the marathon, 259 completed the race, 27 gave up, and 4 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.
Answer:11.38
Step-by-step explanation:
290-257=33 /290=.11379 x 100=11.37 =11.38
Final answer:
To find the percentage of racers who did not complete the marathon, we add those who gave up and those who were disqualified, a total of 31 racers. The percentage is then calculated using the formula for percentage, resulting in 10.7% of racers not completing the marathon.
Explanation:
To find the percentage of racers who did not complete the marathon, we first need to determine the total number of racers who did not finish. This includes those who gave up and those who were disqualified. In this case, 27 racers gave up, and 4 were disqualified, giving us a total of 31 racers who did not complete the marathon.
To calculate the percentage, we use the formula:
Percentage = (Number of racers who did not complete / Total number of racers) × 100%
Plugging the numbers into the formula gives us:
Percentage = (31 / 290) × 100% = 0.1069 × 100% = 10.69%
Rounding to the nearest tenth of a percent, 10.7% of racers did not complete the marathon.
Suppose that a chemist is mixing two acid solutions, one of 20% concentration and the other of 30% concentration. Which of the following concentrations could not be obtained?
1. 22%,
2. 24%,
3. 28%,
4. 34%
Final answer:
A chemist cannot achieve a 34% concentration by mixing 20% and 30% acid solutions, as it is outside the possible range of concentrations achievable by combining these two solutions, option no 4.
Explanation:
When a chemist is mixing two acid solutions, one with a 20% concentration and the other with a 30% concentration, they can obtain a range of concentrations between the two provided percentages by varying the proportions of each solution mixed. The concentrations that could not be obtained would be any value outside of the 20% to 30% range because the resulting mixture cannot exceed the concentration of the higher concentrated solution or be lower than the concentration of the less concentrated solution. Therefore, a 34% concentration could not be obtained by mixing a 20% solution with a 30% concentration.
Pablo wishes to grow his baseball card collection to at least 3000 cards. He currently has 1200 and his favorite type of cards have 15 cards per package which inequality and solution represent the number of packages of cards that pablo wishes to buy , select all that apply
Answer:
x ≥ 120
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120
answer
x ≥ 120
Step-by-step explanation:
Step-by-step explanation:
i) Let x be the number of packages of cards
ii) we know that Pablo currently has 1200 cards.
iii) Therefore the equation required is
15x + 1200 ≥ 3000 because we know that there are 15 cards in a package and the greater than equal to sign is used because Pablo has to collect at least 3000 cards
iv) Solving the equation we get
15x + 1200 ≥ 3000
⇒ 15x ≥ (3000 - 1200)
⇒ 15x ≥ 1800
⇒ x ≥ (1800 ÷ 15)
∴ x ≥ 120
Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities 0.81, 0.09, 0.08, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?
Answer:
$600
Step-by-step explanation:
Let the random variable [tex]X[/tex] denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of [tex]X[/tex] is given by
[tex]X : \begin{pmatrix}0 & 1000 & 5000 & 10\; 000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by
[tex]F(x) = \left \{ {{X+100, \quad \quad \quad \quad \quad \text{for} \; X = 0 } \atop {X-500+100} , \quad \text{for} \; X = 500,4500,9500} \right.[/tex]
For [tex]X = 0[/tex], we have
[tex]F(X) = 0+100 = 100[/tex]
For [tex]X = 500[/tex],
[tex]F(X) = 500-500+100 = 100[/tex]
For [tex]X = 4500[/tex],
[tex]F(X) = 4500-500+100 = 4100[/tex]
For [tex]X = 9500[/tex],
[tex]F(X) = 9500-500+100 = 9100[/tex]
Therefore, the probability distribution of [tex]F[/tex] is given by
[tex]F : \begin{pmatrix} 100 & 100 & 41000 & 91000\\0.81 & 0.09 & 0.08 & 0.02\end{pmatrix}[/tex]
To determine the premium amount that the company should charge, we need to calculate the expected value of [tex]F.[/tex]
[tex]E(F(X)) = \sum \limits_{i=1}^{4} f(x_i) \cdot p_i = 100 \cdot 0.81 + 100 \cdot 0.09 + 4100 \cdot 0.08 + 9100 \cdot 0.02[/tex]
Therefore,
[tex]E(F) = 81+9+328+182 = 600[/tex]
which means the $600 is the amount the should be charged.
A stadium has 10500 seats and 8 VIP boxes. The stadium is divided into 12 equal sections: 2 premium sections and 10 standard sections. A seat at the premium section costs $48 per game. A seat at the standard section costs $27 per game.
Answer:
1). 875 seats
2). 25 rows in each section
3). $8400
4). Saving of $360
5). 2105 tickets remained unsold
6). x = 16
Step-by-step explanation:
This question is incomplete; here is the complete question.
A stadium has 10,500 seats and 8 VIP boxes. The stadium is divided into 12 equal sections: 2 premium sections and 10 standard sections. A seat at the premium section costs $48 per game. A seat at the standard section costs $27 per game.
1. How many seats are there in each section?
2. If there are 35 seats in each row, how many rows are in each section?
3. If all the seats in the premium section are sold out for a game, how much will the stadium get from those ticket sales?
4. There are 50 games in each season. A season pass costs $2,040. A season pass holder can go to all the games and have a seat in the premium section. How much can a fan save by buying the season pass?
5. For the night game on Tuesday, 8,395 tickets were sold. How many tickets were left?
6. Write an equation using “x” and then solve the equation. Each VIP boxes can seat X people. If all the seats and VIP boxes are filled up, there are 10,628 audience in the stadium.
1). Number of seats in the stadium = 10500
Number of sections = 2 premium + 10 standard = 12
Number of seats in each section = [tex]\frac{10500}{12}=875[/tex]
2). If the number of seats in each row = 35
Then number of rows in each section = [tex]\frac{875}{35}=25[/tex]
3). Number of seats in 2 premium sections = 2×875 = 1750
Cost of 1750 seats at the rate of $48 per game = 1750 × 48 = $84000
4). Cost of one ticket in premium section = $48 per game
If the games planned in one season = 50
Then cost of the tickets = 48×50 = $2400
Cost of the season ticket = $2040
Saving on the purchase of one season ticket = 2400 - 2040 = $360
5). For a night game number of tickets sold = 8395
Total number of seats in the stadium = 10500
Tickets remained unsold = 10500 - 8395 = 2105
6). Number of seats in each VIP box = x
Number of VIP boxes = 8
Number of seats in 8 VIP boxes = 8x
Total number of tickets sold = 10500 + 8x
Total number of audience in the stadium = 10628
Then the equation will be
8x + 10500 = 10628
8x = 10628 - 10500
x = [tex]\frac{128}{8}=16[/tex]
The subject of this question is Mathematics, specifically dealing with seating capacity and pricing in a stadium. To determine the maximum seating capacity of the stadium, add up the number of seats in each section. To calculate the total revenue from a single game, multiply the number of seats in each section by the corresponding ticket price, and then sum up the results.
Explanation:The subject of this question is Mathematics, specifically dealing with the concepts of seating capacity and pricing in a stadium.
To determine the maximum seating capacity of the stadium, we add up the number of seats in each section: 2 premium sections with 48 seats each, 10 standard sections with 900 seats each, and 8 VIP boxes with a capacity of 12 seats each. This gives us a total of 1116 seats.
To calculate the total revenue from a single game, we multiply the number of seats in each section by the corresponding ticket price, and then sum up the results. For the premium sections, the revenue is $48 per seat multiplied by 96 seats, and for the standard sections, the revenue is $27 per seat multiplied by 900 seats. Adding up these two amounts gives us the total revenue from a single game.
Learn more about Mathematics here:https://brainly.com/question/27235369
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Malcom coasted 32 miles from Moonridge to to Mentine and then pedaled back hard. If the round trip took 4 hours, what was Malcombs average speed in mph
Answer:
16 mph
Step-by-step explanation:
The relationship between distance, speed, and time is ...
speed = distance/time . . . . . "miles per hour"
Malcom's distance was 32 miles each way, for a total of 64 miles. Then his average speed was ...
speed = (64 mi)/(4 h) = 16 mi/h
A box with a square base and open top must have a volume of 32,000cm^3. How do you find the dimensions of the box that minimize the amount of material used?
Answer:
Side of 40 and height of 20
Step-by-step explanation:
Let s be the side of the square base and h be the height of the box. Since the box volume is restricted to 32000 cubic centimeters we have the following equation:
[tex]V = hs^2 = 32000[/tex]
[tex]h = 32000/ s^2[/tex]
Assume that we cannot change the thickness, we can minimize the weight by minimizing the surface area of the tank
Base area with open top [tex]s^2[/tex]
Side area 4hs
Total surface area [tex]A = s^2 + 4hs[/tex]
We can substitute [tex]h = 32000/ s^2[/tex]
[tex]A = s^2 + 4s\frac{32000}{s^2}[/tex]
[tex]A = s^2 + 128000/s[/tex]
To find the minimum of this function, we can take the first derivative, and set it to 0
[tex]A' = 2s - 128000/s^2 = 0[/tex]
[tex]2s = 128000/s^2[/tex]
[tex]s^3 = 64000[/tex]
[tex]s = \sqrt[3]{64000} = 40[/tex]
[tex]h = 32000/ s^2 = 32000/ 40^2 = 20[/tex]
1 question 60 points need help now
Solve the equation and show all your work
[tex]\frac{x}{x-2} + \frac{x-1}{x+1} =-1[/tex]
Answer:
The answer to your question is x = 0 and x = 1
Step-by-step explanation:
Equation
[tex]\frac{x}{x - 2} + \frac{x - 1}{x + 1} = -1[/tex]
1)
[tex]\frac{x(x + 1) + (x - 2)(x - 1)}{(x - 2)(x + 1)} = - 1[/tex]
Expand
2) x² + x + x² - x - 2x + 2 = -1(x - 2)(x + 1)
Simplify
3) 2x² -2x + 2 = -1(x² + x - 2x - 2)
4) 2x² - 2x + 2 = -x² + x + 2
Equal to zero
5) 2x² - 2x + 2 + x² - x - 2 = 0
6) 3x² - 3x = 0
Factor
7) 3x(x - 1) = 0
8) 3x₁ = 0 x₂ - 1 = 0
9) x₁ = 0/3 x₂ = 1
10) x₁ = 0 x₂ = 1
If the three angles of a triangle have equal measures, find that measure. The measure of each angle is degrees.
Step-by-step explanation:
the sum of angles in a triangle is 180°. so if a triangle is equivalent, each degree will be 180/3 = 60°