Answer:
Ron: 6+2√5 days ≈ 10.47 days
Lee: 2+2√5 days ≈ 6.47 days
Step-by-step explanation:
Let L represent the number of days it takes Lee to frame a cabin. Then it take L+4 days for Ron to frame it. Working together, they take 4 days. Then their rates, in cabins per day, add up as ...
1/L + 1/(L+4) = 1/4
Multiplying by the product of denominators, we get ...
4(L+4) +4L = L(L+4)
Subtracting the left side gives ...
L^2 -4L -16 = 0
Completing the square, we can write this as ...
L^2 -4L +4 = 20
(L -2)^2 = 20
L = 2 + √20 = 2 +2√5 ≈ 6.47
Lee takes 2+2√5 ≈ 6.47 days to frame a cabin.
Ron takes 6+2√5 ≈ 10.47 days to frame a cabin.
Evaluate the exponential expression: (2x)2−3y2=___, if x = 5 and y = 3.
-125
-73
125
73
Answer:
73
Step-by-step explanation:
Put the values of the variables where the variables are, then do the arithmetic.
(2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73
___
Or, you can let a calculator or spreadsheet evaluate the function for you.
solve
y^2 + 3y = -1
-PlushDNA
Answer:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given: [tex]y^2+3y=-1[/tex]
To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:
[tex]y^2+3y+1=0[/tex]
We can solve for [tex]y[/tex] by using the quadratic formula:
[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]
Let's identify our values:
[tex]a: 1\\b: 3\\c: 1[/tex]
Plug in the values and simplify.
[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]
Your final answers are:
[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]
What is the first step when dividing 3x^2+3x+1 by x-2 using long division?
Answer:
You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.
Answer:
3x^2 / x.
Step-by-step explanation:
The first step is to divide 3x^2 by the first term of x - 2 ( that is x).
What is the correct answer for this?
Answer:
4. maximum: 22; minimum: 1
5. maximum: 24; minimum: -6.25
6. maximum: 49.7; minimum: 39.625
Step-by-step explanation:
I find a graphing calculator to be "appropriate technology" for answering questions of this sort. For the first and last questions, the extremes are the values of the function at the ends of the intervals specified.
For the second question, the parabola opens upward and the vertex is in the given interval, so the vertex is the minimum. The maximum is found at the end of the interval that is farthest from the vertex.
A plumber charges a rate of $65 per hour for his time but gives a discount of $7 per hour to senior citizens. Write an expression which represents a senior citizen’s total cost for the plumber in 2 different ways.
Answer:
t = 58x or t + 7x = 65x
The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)
Explanation:The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:
Method 1: Total Cost = $65 - $7 per hourMethod 2: Total Cost = $65 - ($7 per hour x Number of hours)Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.
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Carrie spent $1 for every $10 she earned. How much did she earn if she spent $7?
Find the quotient 3/4 divided by 1/3 =
Answer:
1/4
Step-by-step explanation:
3 x 1 = 3
4 x 3 = 12
3/12 simplified is 1/4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
What is division?Division means the separation of something into different parts, sharing of something among different people, places, etc.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The numbers are given below.
3/4 and 1/3
The quotient of the numbers 3/4 and 1/3 is given by the number 3/4 divided by 1/3. Then we have
⇒ (3/4) / (1/3)
Simplify the expression, then we have
⇒ (3/4) x (3/1)
⇒ 9 / 4
The quotient of the numbers 3/4 and 1/3 will be 9/4.
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HELP BRAINIEST AND LOTS OF POINTS Two twins, Mason and Jason, play a game in which they have a pile of 99 marbles. They can take anywhere from 1 to 10 marbles each turn. Whoever takes the last marble loses. Mason starts. Both play optimally. Who wins, and how many turns will Mason and Jason take combined? NEED NOW
Answer:
Mason wins after 18 total moves
Step-by-step explanation:
Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.
After each of Mason's 9 turns, the number of remaining marbles will be ...
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.
Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.
After every of Mason's nine turns, the amount of remaining marbles are
89, 78, 67, 56, 45, 34, 23, 12, 1
It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.
mason will win after 18 moves
What is the answer for #7?
Answer:
radius: 1.84 inheight: 3.68 inStep-by-step explanation:
After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...
V = πr²·h = 2πr³ = 39 in³
Then the radius is ...
r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in
h = 2r = 3.67557 in ≈ 3.68 in
_____
The total surface area of a cylinder is ...
S = 2πr² + 2πrh
For a given volume, V, this becomes ...
S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r
The derivative of this with respect to r is ...
S' = 4πr -2V/r²
Setting this to zero and multiplying by r²/2 gives ...
0 = 2πr³ -V
r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r
__
If we substitute the equation for V into the equation just above this last one, we have ...
0 = 2πr³ - πr²·h
Dividing by πr² gives ...
0 = 2r - h
h = 2r . . . . . generic solution for cylinder optimization problems
Which is the rate of change for the interval between 3 and 6 on the x-axis?
–3
–2
2
3
Answer:
The correct answer is 2.
Step-by-step explanation:
To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.
m(slope) = (y2 - y1)/(x2 - x1)
m = (4 - - 2)/(6 - 3)
m = 6/3
m = 2
Answer:
2
Step-by-step explanation:
Rate of change on the given interval a to b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
a=3 and b=6
f(a) and f(b) are the y values on the graph at x=3 and x=6
f(3)= -3 and f(6) is 4
Now plug in the values in the formula
[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]
answer is 2
How many times does the quadratic function below intersect the x-axis? y=x+10x+25
The quadratic function y=x^2+10x+25 intersects the x-axis at a single point (x = -5).
Explanation:A quadratic function intersects the x-axis when the value of y is equal to 0. To find the number of times the function intersects the x-axis, we need to determine the number of solutions for y = 0. The given quadratic function is y = x^2 + 10x + 25. We can solve this equation by factoring or using the quadratic formula.
Factoring: Factoring the quadratic equation, we get (x + 5)(x + 5) = 0.
Since both factors are the same, the function intersects the x-axis at a single point (x = -5).
Quadratic formula: The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
Plugging in the values from the given quadratic function, we get x = (-10 ± √(100 - 4(1)(25))) / 2(1).
Simplifying further, we get x = (-10 ± √(100 - 100)) / 2, which reduces to x = -5. This indicates that the quadratic function intersects the x-axis at a single point (x = -5).
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Need help multiplying -300 to N+M&M=10 for equation (1)
Answer:
3.5 pounds of nuts; 6.5 pounds of M&Ms
Step-by-step explanation:
Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...
6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds
3m +30 = 49.5 . . . . . . simplify
3m = 19.5 . . . . . . . . . . . subtract 30
m = 6.5 . . . . . . . . . . . . . divide by 3
Then 10-m = 10-6.5 = 3.5.
The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.
It’s the second question. 8 friends share twelve candy bars equally. How many does each friend get?
Answer:
Step-by-step explanation:
If we take 1 candy bar and split it between 8 people, each person will get 1/8 of a candy bar. 1/8 for each of those 12 candy bars will give each person 12 × 1/8 = 12/8, or 3/2 = 1 1/2 bars.
You are trying to share 12 candy bars between 8 friends.
Therefore,
12 candy bars ÷ 8 friends = 1.5 bars per person
12 ÷ 8 = 1.5 candy bars
What is B help pleaseeee
Answer:
59.0°
Step-by-step explanation:
Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.
___
You can use the law of cosines to compute the result yourself.
b^2 = a^2 + c^2 - 2ac·cos(B)
cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792
B = arccos(408/792) ≈ 58.9924° ≈ 59.0°
All rectangles are parallelogram. Are all parallelogram rectangles? Explain
Answer:
No
Step-by-step explanation:
A parallelogram may have a right angle (making it a rectangle), but may not.
A party rental company has chairs and tables for rent. The total cost to rent 3
chairs and 8 tables is $55. The total cost to rent 5 chairs and 2 tables is $18. What is the cost to rent each chair and each table
Answer:
chair: $1.00table: $6.50Step-by-step explanation:
When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...
3c+8t = 555c+2t = 18___
I find a graphing calculator easy to use for solving such equations.
___
A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).
You have $2000 to deposit for 7 years and two account options. The first earns you simple interest at a rate of 4% and the second earns you compound interest (compounded annually) at a rate of 2%. Which account earns you more money?
First account (simple interest)
Second account (compound interest)
They earn you the same
Not enough information to say
Answer:
First account (simple interest)
Step-by-step explanation:
The amount of interest earned by the first account is ...
I = Prt = $2000·0.04·7 = $2000·0.28 = $560
The amount in the second account at the end of 7 year is ...
FV = P·(1+r)^t = $2000·1.02^7 = $2297.37
so you have earned $297.37 in interest on the second account.
$560 is more than $297, so the First Account (simple interest) earns more money.
The school yearbook committee surveyed the student body for an article about colleges in which they are pursuing enrollment. The table below shows the number of students in each grade level who are pursuing one or more college.
If there are 170 students in 12th grade, what percentage of the twelfth grade students have more than one college in mind? Round your answer to the nearest percent.
Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.
So 50/170, or 29% is your answer.
Answer:
29%
Step-by-step explanation:
Solve algebraically
y=x^2 + 2x
y=3x+20
Answer:
x = 5 and y = 35
OR
x = -4 and y = 8.
Step-by-step explanation:
Equate the right-hand side of the two equations:
x² + 2 x = y = 3 x + 20.
x² + 2 x - 3 x - 20 = 0.
x² - x - 20 = 0.
Quadratic discriminant
Δ = b² - 4 a · c
= (-1)² - 4 × 1 × (-20)
= 81.
There are two roots:
x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)
= (1 + 9) / 2
= 10 / 2
= 5
and
x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)
= (1 - 9) / 2
= -4.
Find the value of y in both case.
y₁ = 3 × 5 + 20 = 35.
y₂ = 3 × (-4) + 20 = 8.
The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].
To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].
Given equations:
[tex]\[ y = x^2 + 2x \][/tex]
[tex]\[ y = 3x + 20 \][/tex]
Setting them equal to each other:
[tex]\[ x^2 + 2x = 3x + 20 \][/tex]
Now, let's rearrange this equation to solve for \( x \):
[tex]\[ x^2 + 2x = 3x + 20 \[/tex]
[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]
[tex]x^2 - x - 20 = 0[/tex]
This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:
[tex]x^2 - x - 20 = 0[/tex]
[tex](x - 5)(x + 4) = 0[/tex]
Setting each factor equal to zero:
[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]
Solving for [tex]\( x \)[/tex] in each case:
[tex]\[ x = 5 \] or \( x = -4 \)[/tex]
Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:
For [tex]\( x = 5 \)[/tex]:
[tex]y = 5^2 + 2(5)[/tex]
[tex]y = 25 + 10[/tex]
[tex]y = 35[/tex]
For [tex]\( x = -4 \)[/tex]:
[tex]y = (-4)^2 + 2(-4)[/tex]
[tex]y = 16 - 8[/tex]
[tex]y = 8[/tex]
Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].
If f(x)=x^2-5x and g(x)=8-x^3, evaluate the following:
a. (f+g)(3)
b. (g-f)(4)
c. (f*g)(-1)
d.(g/f)(-2)
Answer:
a. -25
b. -52
c. 54
d. 8/7 = 1 1/7
Step-by-step explanation:
Evaluate each of the functions for each of the variable values and compute the composite as defined.
a. (f+g)(3) = f(3) + g(3) = 3^2 -5·3 + 8 -3^3 = -25
___
b. (g -f)(4) = g(4) -f(4) = 8 -4^3 -(4^2 -5·4) = 8 -64 -16 +20 = -52
___
c. (f*g)(-1) = f(-1) · g(-1) = ((-1)^2 -5(-1)) · (8 -(-1)^3) = 6·9 = 54
___
d. (g/f)(-2) = (8 -(-2)^3)/((-2)^2 -5(-2)) = (8+8)/(4+10) = 16/14 = 8/7
_____
Comment on approach to the problem
When there are a number of evaluations of the same function with different values of the variable, it can be convenient to let a calculator or spreadsheet do those for you.
Hi if someone could explain the right answer that would be great i’m totally lost!!
Answer:
A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset
Step-by-step explanation:
A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)
Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.
___
The attached graph shows a function that has characteristics like those of g(x).
___
This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.
How do I answer this question on khan academy.
If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then
present day: [tex]b=4i[/tex]6 years ago: [tex]b-6=6(i-6)[/tex]Rewrite the second equation as
[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]
Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:
[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]
Then
[tex]b=4i\implies b=4\cdot15=60[/tex]
So Ben is 60 years old now.
The function f(x) is shown in this graph. The function g(x)=-2x-6. Compare the slopes
Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).
Hence, the answer is (D).
The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
g(x) = -2x - 6
f(x) is shown in the graph
The slope of g(x), m = -2
From the graph:
(0, 2) and (-1, 1)
M = (1-2)/(-1) = 1
Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.
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Find the area of the Figure.
would love some help, please, and thank you
Answer:
430
Step-by-step explanation:
All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!
A restaurant offers a lunch special for $15 plus a $3 tip for the server. Write an expression that represents the total cost for the special in 2 different ways.
Answer:
s= 15x+3x and s=18x
Step-by-step explanation:
Answer:
The total cost for the special would be $15.45
Step-by-step explanation:
One equation would be 15 x 1.03 = 15.45
Second equation would be (15 x .03) + 15 = $15.45
PLEASE HELP!!!!!! 20 POINTS!!! (BOTH QUESTIONS) VERY EASY!!!!!
The second one is d I’m pretty sure
Answer:
#23, A
#24, D
Hope this helped!!
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9 out of 10 people at a game are rooting for the home team. What is the probability that exactly 6 of 8 people sitting together are rooting for the home team?
A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.
Choosing 6 out of 8 supporters who root for the home team has probability
[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]
HELP ME ASAP!!!! Will somebody please explain to me how to do this. I can't pass Freshman year without getting this done.
Answer:
cot(x) = 3
Step-by-step explanation:
The cotangent is the reciprocal of the tangent.
cot(x) = 1/tan(x) = 1/(1/3) = 3
_____
It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...
secant = 1/cosine . . . . . . so cosine = 1/secant
cosecant = 1/sine . . . . . so sine = 1/cosecant
cotangent = 1/tangent . . . . . so tangent = 1/cotangent
It is also helpful to realize that ...
tan = sin/cos
sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine
sec² = 1 + tan²
csc² = 1 + cot²
Could someone plz help with number 4 ? Thanks
Answer:
255π (cm³).
Step-by-step explanation:
1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;
h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;
d1=1cm., d2=0.7 cm.
2. the final formula of the required volume is
[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]
3. if to substitute the values of d1, d2 and h, then
[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]
A kite is a __________. A. quadrilateral B. parallelogram C. rectangle D. trapezoid
A kite is a quadrilateral.
So the correct answer is A.
Hope this helps,
Davinia.
Final answer:
A kite is a quadrilateral, which is a shape with four sides, but with unique properties that differentiate it from parallelograms, rectangles, and trapezoids.
Explanation:
A kite in geometry is a quadrilateral. A quadrilateral is a kind of shape with four sides, which might not be as commonly discussed in early education as shapes like squares and triangles. A kite is defined by two pairs of adjacent sides that are equal in length, with one pair longer than the other. Unlike a parallelogram, the sides of a kite do not always have to be parallel to each other. In addition, a kite does not necessarily have right angles as a rectangle does, nor does it have only one pair of parallel sides as a trapezoid does. Therefore, when characterizing a kite, the correct answer is A. quadrilateral.