rate = 12 laps/4 min = 3 laps/min
3 laps ------------------ 1 min
x ------------------ 9 min
x = (9 x 3) / 1
x = 27 laps in 9 min
Result 27 laps in 9 min
Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate A = [ ? ] ft.
The area of the figure = Area of the Triangle + Area of the semi-circle
Area of the Triangle = 1/2 x b x h
Base = 6 feet
Height = 8 feet
Area of the Triangle = 1/2 x 6 x 8 = 48/2 = 24 feet^2
Area of the circle = pi x r ^2 radius = 8/2 = 4 ft
= 3.14 x 4 x 4
= 50.24 feet^2
Total area = 24 + 50.24 = 74. 24 feet ^2
From the given information. Write the recursive and explicit functions for each arithmetic sequence. Use these terms please; recursive f(1) = first term, f(n) = pattern+f(n-1). Explicit: y = pattern*x + 0 term. work backwards to find 0 term
An arithmetic sequence has the form:
[tex]f(n)=f(1)+d(n-1)[/tex]where d is the common difference.
For this sequence the common difference is 3 and the first term is:
[tex]f(1)=3[/tex]Plugging this values in the general expression we have:
[tex]\begin{gathered} f(n)=3+3(n-1) \\ f(n)=3n-3+3 \\ f(n)=3n \end{gathered}[/tex]Therefore the sequence is:
[tex]f(n)=3n[/tex]Now, from this expression we can determine the value of the zeroth term:
[tex]\begin{gathered} f(0)=3(0) \\ f(0)=0 \end{gathered}[/tex]Hence the zeroth term is:
[tex]f(0)=0[/tex]An aircraft factory manufactures airplane engines. The unit cost C (the cost in dollars to make each airplane engine) depends on the number of engines made. Ifx engines are made, then the unit cost is given by the function C(x) = 0.5x ^ 2 - 150x + 26, 777 . How many engines must be made to minimize the unit cost?Do not round your answer.number of airplane engines________
EXPLANATION:
We are given the unit cost to produce x number of airplanes as follows;
[tex]C(x)=0.5x^2-150x+26777[/tex]However, to minimize the unit cost, we need to first take the derivative of the cost function and then find its value at zero.
Thuis is shown below;
[tex]C(x)=0.5x^2-150x+26777[/tex][tex]\frac{d}{dx}=2(0.5)x^{2-1}-1(150)x^{1-1}+0[/tex]Note that for a derivative, the constant term is always equal to zero. We can now simplify what we have above;
[tex]\frac{d}{dx}=1x^1-150[/tex][tex]\frac{d}{dx}=x-150[/tex]We now set this equal to zero and simplify;
[tex]x-150=0[/tex]Add 150 to both sides;
[tex]x=150[/tex]ANSWER:
Therefore, to minimize the unit cost, 150 engines must be made.
Expand and simplify: 3(2a+5) + 5(a-2)
Answer:
11
a
+
5
Step-by-step explanation: you're welcome. Brainlyest?
It takes you 52 seconds to walk from the first (ground) floor of a building to the third floor. How long will it take you to walk from the first floor to the sixth floor (at the same pace, assuming all floors have the same height)?
One brand of cereal sells for $3.15 for 10 ounces. What is the unitprice per pound?a. $.31b. $5.04c. $ 3.49d. $50.40
Answer:
[tex]\begin{gathered} \\ B\colon\text{ \$5.04} \end{gathered}[/tex]Explanation:
Here, we want to get the unit price per pound
From the question, the brand sells for $3.15 per 10 ounces
Mathematically, 1 ounce is 0.0625 pound
Thus $3.15 is the price for 0.625 pounds (10 * 0.0625 pounds)
if $3.15 is for 0.625 pounds
$x will be for 1 pound
Mathematically:
[tex]\begin{gathered} 3.15\times1\text{ = 0.625}\times x \\ x\text{ = }\frac{3.15}{0.625} \\ x\text{ = \$5.04} \end{gathered}[/tex]David buys milk and lemons at the store.
.
. He pays a total of $40.01.
• He pays $2.89 for the milk.
• He buys 8 bags of lemons that each cost the same amount.
.
Which equation could be used to determine b, how much each bag of lemons costs?
Can someone tell
Me the equation could be used yo determine b, how much each bag of lemon cost
I'm not sure the right equation that we need to used for this problem.
The solution is, :
8x = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
given that,
David buys milk and lemons at the store.
. He pays a total of $40.01.
• He pays $2.89 for the milk.
• He buys 8 bags of lemons that each cost the same amount.
Cost of 1 bag of lemons = $ x
Cost of 8 bags of lemons = 8 *x = 8x
Cost of 8 bags of lemons = Total cost - cost of the eggs
8x = $40.01 - $2.89
so, 8x = 40.01 -2.89, is the equation.
Hence, The solution is, :
8x = 40.01 -2.89, is the equation could be used to determine b, how much each bag of lemons costs.
To learn more on equation click:
brainly.com/question/24169758
#SPJ2
The slope of this line and the unit rate are the same.Price of Cookies at Bakery141210Find the unit ratefor the number ofcookies per dollar008Number of Cookies464[?] cookies$[ ]22 4 6 8 10 12 146 8Price ($)
SOLUTION
We want to find the unit rate for number of cookies per dollar. This can be done using the diagram below
So the unit rate is calculated thus
[tex]\begin{gathered} \text{Unit rate = }\frac{rise\text{ }}{\text{run}} \\ =\frac{14\text{ cookies }}{7\text{ dollars }} \\ =\frac{14}{7} \\ 2\text{ cookies per dollar} \end{gathered}[/tex]Hence the answer is 2
find the basic feasible solution at this point by setting the non-basic variables equal to 0
To determine wether a variable is a basic variable or not in a simplex tableu we have to look for the variables which have a one in a column and all the other values are zero, the variables that fullfil this condition are the basic ones.
Looking at the tableu we notice that the basis variables are: x2, s5 and Z. Now that we know that, we look at each row where the number one appear and put all the other variables equal to zero, with this in mind we conclude that:
[tex]\begin{gathered} x_1=0 \\ x_2=17 \\ s_3=0 \\ s_4=0 \\ s_5=29 \\ Z=12 \end{gathered}[/tex]How many different permutations can be formed using all the letters in the word COLORADO?
Ok, the number of different permutations are:
8!/3! (Considering the three O's)
The perimeter of the figure is given. Find the length of the indicated side.?4x - 4Perimeter = 16x + 6The length of the indicated side is
Width = 4x + 7
Explanation:The perimeter of the rectangle shown = 16x + 6
The width of the rectangle = 4x - 4
Perimeter of a rectangle = 2(Length + Width )
16x + 6 = 2[ (4x - 4) x Width]
(16x + 6)/2 = (4x - 4) x width
8x + 3 = (4x - 4) x width
Width = 8x + 3 - (4x - 4)
Width = 8x - 4x + 3 + 4
Width = 4x + 7
A roofer earns $22 per hour for regular hours worked and $30per hour for overtime hours worked. If he puts in 40 hours of regular time during a certain week and he wishes to earn $1050, how many hours of overtime should he work?The roofer should work ___ hours of overtime.(Type an integer, proper fraction, or mixed number.)
The roofer should work 5 2/3 hours of overtime.
Explanation:Given:
Earnings for regular hours = $22 per hour
Earnings for overtime = $30 per hour
Time spent on regular hours = 40 hours
Total amount to be earned = $1050
To find:
The number of hours worked overtime
let the number of hours worked overtime = h
Earnings for regular hours (number of hours) + Earnings for overtime (number of hours) = 1050
[tex]\begin{gathered} 22(40)\text{ +}30(h)\text{ = 1050} \\ 880\text{ + 30h = 1050} \end{gathered}[/tex][tex]\begin{gathered} collect\text{ like terms:} \\ 30h\text{ = 1050 - 880} \\ 30h\text{ = 170} \\ \\ divide\text{ both sides by 30:} \\ h\text{ = 170/30} \\ h\text{ = 17/3 = 5}\frac{2}{3}\text{ hours} \end{gathered}[/tex]The Matrix Fishing Company does fishing in Toluca Lake the first year of the company's operation it managed to catch a 190,000 fish due to population decreases the number of fish the company was able to catch decreased by 8% each year how many total fish did the company catch over the first 12 years round to the nearest whole number
Solution
For this case we can model the number of fishes with the following equation:
[tex]A=19000(1-0.08t)[/tex]And for this case we want to find the value for t =12 and replacing we got:
[tex]A=190000\cdot(1-0.08\cdot12)=7600[/tex]And then the number of fishes after 12 years would be 7600
so then they catched 182400
hi please h3lp I have only 10 min to do this because it's due in 10 minutes and I've been trying to figure this out for a while
To graph the system
y ≤ 2x + 1
y < -x - 1
first, you have to graph the lines
y = 2x + 1
y = -x - 1
From the y-intercept and the slope, we know that the first line passes through the points:
(0, 1)
(0+1, 1+2) = (1, 3)
From the y-intercept and the slope, we know that the second line passes through the points:
(0, -1)
(0+1, -1-1) = (1, -2)
Next, we have to find if a point satisfies each equation or not, in order to know which region we have to shade. Taking for example the point (0, 0) and replacing it into the first inequality,
0 ≤ 2(0) + 1
0 ≤ 1
which is true, then we have to shade the region below the line y = 2x + 1
Replacing (0, 0) into the second inequality,
0 < -0 - 1
0 < -1
which is false, then we have to shade the region below the dotted line y = -x - 1
The final result is shown in the next picture.
This corresponds to graph X
6.
A mug is 3/7
full. The mug contains 1/2
of a cup of water. Find
the capacity of the mug. Write the
answer as a fraction or mixed
number in simplest form.
contains
The capacity of the mug is 7/6 cups.
What is the capacity of the mug?
Given,
A mug is 3/7 full.
The mug contains 1/2 of a cup of water.
Solution:
Let x be the water.
Water the mug has = 3/7 of x
= 3/7x
Since the water in the mug is 1/2 cup,
3/7x = 1/2
x = 1/2 ÷ 3/7
= 1/2 × 7/3
= 7/6
Therefore,
The capacity of the mug is 7/6 cups.
To learn more about capacity, refer
https://brainly.com/question/13484626
#SPJ9
M(5,-10) is rotated 270 degrees what is M’?
Problem
M(5,-10) is rotated 270 degrees what is M’?
Solution
For this case we need to remember that is we have any point A =(x,y) when we apply a transformation fo 270° then the new coordinates would be:
M' = (x,-y)
And for this case if we apply this transformation we got:
M'= (5, -(-10))= (5,10)
help meeee please !!
thank you
The answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
What is the point slope form of a line ?
Point slope form is used to represent a straight line using its slope and a point on the line.
a)
We know that the two point -slope form of a line is given by :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
where : m is slope and represented by
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
As per the questions hint is that two points that is (-2 , 11) and (1 , -4).
These points can be represented by :
([tex]x_{1}[/tex] , [tex]y_{1}[/tex]) = (0 , 294000)
([tex]x_{2}[/tex] , [tex]y_{2}[/tex]) = (7 , 288400)
So : the slope will be :
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{288400-294000}{7 - 0}[/tex]
m = -5600 / 7
m = -800
So , the point -slope form of line will be :
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex])
y - 294000 = -800 ( x - 0)
y - 294000 = - 800 x
or
y = -800x + 294000
So , the average price of a new home (y) is given by a linear equation which is :
y = -800x + 294000
b)
As per the question y is the average price of a new home in year x and is given by :
y = -800x + 294000
It is given that x = 0 meant year 2004. So , for year 2014 value of x will be x =10.
Substituting this value to get the value of y or average price of a new home in year 2014 , we get :
y = -800x + 294000
y = - 800 × 10 + 294000
y = -8000 + 294000
or
y = $ 286000
Therefore , the answers are :
a) The average price of a new home (y) is given by a linear equation which is y = -800x + 294000.
b) The average price of a new home in year 2014 will be $286000.
Learn more about point slope form of a line here :
https://brainly.com/question/22250570
#SPJ1
What is anequation of the line that passes through the points (-6,5) and (6,-7)?
The line that passes through the given point may be stated as
y - y1 = m(x - x1)
where (x1, y1) and (x2, y2) = (-6,5) and (6,-7)
m = (y2 - y1)/(x2 - x1)
= (-7 - 5)/(6 - -6)
= -12/12
= -1
Hence the equation of the line that passes through the given points is
(y - 5) = -1(x - -6)
y - 5 = - x - 6
y = -x - 6 + 5
y = -x - 1
The regulation height of a basketball hoop is 10 feet. Let the location of thebasket be represented in the coordinate plane by the point (0, 10). Let the ballbe thrown at a 45° angle with the ground.1. Suppose Nancy is standing a horizontal distance of 10 feet from thebasket at the point (-10, 0), and she shoots a basket from 6 feet in theair with an initial velocity of 22 ft/s.a. Write parametric equations that represent the ball's motion throughthe air.b. Graph the parametric equations on your calculator in an appropriatewindow and sketch the results below.
SOLUTION:
a. The parametric equations that represent the balls motion is;
[tex]\begin{gathered} x(t)=x_0+(v_0cos\theta)t \\ y(t)=y_0+(v_0sin\theta)t+0.5gt^2 \end{gathered}[/tex]Inserting the values;
[tex]\begin{gathered} x(t)=-10+(22cos45)t \\ y(t)=6+(22sin45)t+0.5(-32)t^2 \end{gathered}[/tex]Simplifying, we have;
[tex]\begin{gathered} x(t)=15.56t-10 \\ y(t)=-16t^2+15.56t+6 \end{gathered}[/tex]b. The graph of the parametric equation is given below;
A bird flies downward 2 feet per second for 6 seconds. Then the bird flies up 7 feet. Which equation represents the total distance the bird travels
The equation that represents the total distance the bird travels would be; d = 1/3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.
Given that bird flies downward 2 feet per second for 6 seconds. Therefore, the bird flies up 7 feet.
Since, a bird flies 2 feet = 1 second
Thus, for 6 seconds = 6 x 2 = 12 feet.
for 6 seconds = 12 feet.
Similarly, the bird flies up 7 feet = 6/12 x 7
= 42/12 = 3.5
Hence, the equation that represents the total distance the bird travels would be; d = 2/6 = 1/3.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ1
Makayla bought 1/4 pound of ham and 5/8 pound of turkey. How much more turkey did she buy
The hypotenuse of right triangle is 226 miles long. The difference between the other two sides is 194 miles. Find the missing sides. Use exact values.
Find the value of the short and ling leg.
Answer: short line: 30 miles, ling leg: 224 miles
Step-by-step explanation:
Intro:
We will be using Pythagoras theorm, which states, if we have a 90 degree triangle which has 3 side as H, B and P defined as Hypotenuse, Base and Perpendicular, then H² = B² + P²
In your case, we know that hypotenuse is 226.
We also know that (A + B)² = A² + B² + 2AB
Given:
H = 226
B - P = 194
Solution:
B = 194 + P
So
(226)² = (194 + P)² + P²
51076 = (194)² + P² + (2 x 194 x P) + P²
51076 = 37636 + 2P² + 388P
51076 - 37636 = 2P² + 388P
13440 = 2P² + 388P
6720 = P² + 194P
P² + 194P - 6720 = 0
P² - 30P + 224P - 6720 = 0
P(P - 30) + 224(P - 30) = 0
(P - 30) x (P + 224) = 0
P = 30 or -224
As miles cannot be negative, we will choose answer as 30 miles.
Now we have H = 226 and P = 30
Using Pythagoras theorm:
(226)² = (30)² + B²
51076 = 900 + B²
50176 = B²
B = 224 miles.
So the missing miles are 224 miles and 30 miles
Can you please help me translate the argument into symbolic form?
Let p be: John goes to the beach
Let q be: He will go surfing.
Then in symbolic form, the argument becomes:
[tex]\begin{gathered} p\Rightarrow q \\ p \\ ----------- \\ \therefore q \end{gathered}[/tex]p ⇒ q
p
---------------------
∴ q
An argument is valid if the conjuction of the premises implies the conclusion.
p | q | p ⇒ q | (p ⇒ q) ∧ p | [(p ⇒ q) ∧ p] ⇒ q
---------------------------------------------------------------------\
F | F | T | F | T
F | T | T | F | T
T | F | F | F | T
T | T | T | T | T
The table above shows that the argument is a tautology.
Hence, the argument is valid
Given: 14-2(x + 8) = 5x - (3x - 34); Prove: x = -9
help pls lol
The value of x is -9.
Here the equation is :
14 - 2(x + 8) = 5x -( 3x - 34)
We have to prove that x = -9.
From the above-given equation, we have to find the value of x.
So by evaluating the equation we have:
14 -2(x +8) = 5x - (3x - 34)
= 14 - 2x - 16 = 5x - 3x + 34
= -2 -2x = 2x + 34
= 4x = -34 - 2
= 4x = -36
=x = -9
Therefore the value of the above-given equation x = -9.
To know more about the equation refer to the link given below:
https://brainly.com/question/14107099
#SPJ1
Question 2 of 1010 PointsWhich inequality below satisfies the solution set graphed on the following number line?
ANSWER
C. x² - x ≥ 6
EXPLANATION
Let's analyze the solution set graphed first. We can see that the values -2 and 3 are included in the set, and all values below -2 and above 3. So, the solution set is (-∞, 2] U [3, ∞).
To find which inequality satisfies this solution set we have to solve them. To do so, we will be using the quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]A. To solve this one, first, add x to both sides,
[tex]-x^2+x+6\geqslant0[/tex]Now, apply the quadratic formula to find the zeros. For this inequality, a = -1, b = 1, and c = 6
[tex]\begin{gathered} x=\frac{-1\pm\sqrt{1^2-4(-1)6}}{2(-1)}=\frac{-1\pm\sqrt{1+24}}{-2}=\frac{-1\pm\sqrt{25}}{-2} \\ \\ x_1=\frac{-1-5}{-2}=\frac{-6}{-2}=3 \\ \\ x_2=\frac{-1+5}{-2}=\frac{4}{-2}=-2 \end{gathered}[/tex]But in this case, the solution set is [-2, 3] - note that for any value outside this interval the inequality is false.
B. Similarly, apply the quadratic formula for a = -3, b = 3, c = 18,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{3^2-4(-3)18}}{2(-3)}=\frac{-3\pm\sqrt{9+216}}{2(-3)}=\frac{-3\pm\sqrt{225}}{-6}=\frac{-3\pm15}{-6} \\ \\ x_1=\frac{-3+15}{-6}=\frac{12}{-6}=-2 \\ \\ x_2=\frac{-3-15}{-6}=\frac{-18}{-6}=3 \end{gathered}[/tex]Again, the solution set is [-2, 3] since for any value outside the interval the inequality is not true.
C. Subtract 6 from both sides,
[tex]x^2-x-6\geqslant0[/tex]Apply the quadratic formula, with a = 1, b = -1, and c = -6,
[tex]\begin{gathered} x=\frac{-(-1)\pm\sqrt{(-1)^2-4\cdot1(-6)}}{2\cdot1}=\frac{1\pm\sqrt{1+24}}{2}=\frac{1\pm\sqrt{25}}{2}=\frac{1\pm5}{2} \\ \\ x_1=\frac{1+5}{2}=\frac{6}{2}=3 \\ \\ x_2=\frac{1-5}{2}=\frac{-4}{2}=-2 \end{gathered}[/tex]In this case, if we take any value between -2 and 3, for example 1,
[tex]\begin{gathered} 1^2-1\ge6 \\ \\ 0\ge6 \end{gathered}[/tex]We can see that the inequality is false, while if we take a value greater than 3 or less than -2, for example, -5,
[tex]\begin{gathered} (-5)^2-(-5)\ge6 \\ \\ 25+5\ge6 \\ \\ 30\ge6 \end{gathered}[/tex]We can see that the inequality is true.
Hence, we can conclude that inequality C satisfies the solution set graphed.
There are 3 consecutive even integers that have a sum of 30. What are the integers?
Answer:
8, 10, 12
Step-by-step explanation:
x+x+2+x+4=30
3x+6=30
3x=30-6
3x=24
x=8
please answer by correcting the math equation asap
The error in the subtraction of the given fraction is that the LCM was not used before subtraction of numerators and as such if correctly answered the final fraction is; -15/4
How to subtract fractions?
We are given the subtraction of fraction expression as;
3/4 - 9/2
Now, the first step in this subtraction is to find the L.C.M of both denominators.
Factors of 2 ; 1, 2
Factors of 4; 1, 2, 4
Thus, the L.C.M of both denominators is; 2 * 2 = 4
Now, the next step is to divide the LCM by the denominator and multiply by the numerator while retaining the LCM as common denominator to get;
[(3 * 4/4) - (9 * 4/2)]/4
= (3 - 18)/4
= -15/4
The method used in the question to subtract the fraction did not take into account finding the LCM.
Read more about Fraction Subtraction at; https://brainly.com/question/18175484
#SPJ1
3 years ago I was 2/3 as old as I will be 8 years from now. How old am I?
Considering the definition of an equation and the way to solve it, if 3 years ago I was 2/3 as old as I will be 8 years from now, I am 25 years old.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign. One or more unknown values appear in it, in addition to certain known data.
Solving an equation is determining the value or values of the unknowns that transform the equation into an identity. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.My ageBeing "x" the my age today, and knowing that 3 years ago I was 2/3 as old as I will be 8 years from now, the equation in this case is:
x -3= 2/3×(x +8)
Solving:
x -3= 2/3x +2/3×8
x -3= 2/3x +16/3
x - 2/3x= 16/3 + 3
1/3x= 25/3
x= 25/3 ÷ 1/3
x= 25
Finally, I am 25 years old.
Learn more about equations:
brainly.com/question/4983716
brainly.com/question/13314678
#SPJ1
Order the sides of the triangle from shortest to longest. (HINT: You need to find the missing angle first!) 85 40° X V
To find the missing angle we use that the sum of the inner angles of a triangle must add up 180º:
[tex]\angle W+\angle V+\angle X=180º[/tex]We know W and V, so we clear X:
[tex]\angle X=180º-\angle W-\angle V=180º-80º-40º=60º[/tex]To order the sides, you don't need the size of them. Let's take a look at the angles:
So, since the angle with vertex on W is the widest, the opposite side to it (the segment XV) will be the longest. Then, the second angle is the one in X, so the second largest side will be it's opposite side (segment WV).
And finally but not last, the shortest side will be the oposite one to the narrowest angle, the one in V.
In summary, the sides ordered from shortest to longest are: c-a-b
Solve -3(x+2) > 10+5x
