An electrical heating element produces heat depending on the resistance of the element and the current passed through it. The heat produced can be given by the formula h = I2R where h is the heat generated, I is the current, and R is the resistance. If the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. Determine the formula for the variable resistance.
Answer:
(10x - 40) + 120 / (x+2)
an ostrich that is 78 inches tall is 15 inches taller than 3 times the height of a kiwi. What is the height of a kiwi in inches
Over the weekend, Statton and Tyler drove to Montana to go hunting. Now they're preparing to go home. Tyler needs gas for his jeep, which gets 22 miles per gallon for gas mileage. When he stops at the gas station, he already has 5 gallons of gas in his tank. he buys more gas for $1.25 per gallon if Tyler spends 22 on gas what is the total distance the boys could travel round if necessary to the nearest tenth
he bought : 22/1.25 = 17.6 gallons
17.6 +5 = 22.6 gallons total
22 * 22.6 =497.2 miles total he can drive
Answer:
The answer would be 497.2
Step-by-step explanation:
Proof I hope you do well on the test .
If your front lawn is 24.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1050 new snow flakes every minute, how much snow (in kilograms) accumulates on your lawn per hour? assume an average snow flake has a mass of 1.70 mg.
The sum of two numbers is 70. one number is 8 more than the other. what's the smaller number?
Find all the points, if any, where the graph of 12x-5y=0 intersects (x+12)^2+(y-5)^2=169.
A. There are no points of intersection.
B. (0,0)
C. (4.5, 10.9)
D. (0,0) and (4.5, 10.9)
Answer:
(0,0)
Step-by-step explanation:
If you graph [tex]12x-5y=0[/tex] and [tex](x+12)^2+(y-5)^2=169[/tex] along with the points (0,0) and (4.5, 10,9) you with see that the equations intersect at (0,0)
Simplify the expression sin^2x-1/cos(-x)
is this answer right
When dividing with polynomials, the goal is to determine how many times the dividend divides evenly into the?
Find the quotient of 5+4i/6+8i , and express it in the simplest form
Line K is parallel to line L
What angle is congruent to angle 4.
Answer:
Its A, I took the test..
Is it correct to say that a cube with side lengths 6cm have the same volume and surface area?
The bear population increases at a rated of 2% each year. There are 1573 bears this year. What is the growth factor, b?
To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor.
Explanation:To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor. In this case, the final population is 1573 bears. Let's solve for b: n = ln(1573)/ln(b). To isolate b, we can take the exponential of both sides: b^n = 1573. Now we can solve for b by taking the nth root of 1573. The growth factor, b, is the value that, when raised to the power of the number of years, gives us the final population of bears.
If a coin is tossed twice what is the probability of getting two heads
Find a formula expressing the radius r of a sphere as a function of its surface area
A rope 18 feet long is cut into two pieces. one piece is used to form a circle and the other used to form a square. find a function representing the area of both square and circle as a function of the length of one side of the square.
A car travels 2/5 mile in 1/2 minute. what is the cars speed in miles per hour?
The speed of the car is 48 miles per hour, based on the given information that the car travels 2/5 miles in 1/2 minute.
Explanation:To solve this problem, we first need to recognize that the car has traveled 2/5 miles in 1/2 minute. To calculate the speed in miles per hour (mph), we need to find how far the car would go in 1 hour. In other words, how many 1/2 minutes are there in an hour? An hour has 60 minutes, so there are 2*60=120 half-minutes in an hour. If the car travels 2/5 mile in each half minute, then in one hour (or 120 half-minutes), the car would travel 2/5*120=48 miles. Consequently, the car's speed is 48 miles per hour.
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Two functions are shown in the table below. Function 1 2 3 4 5 6 f(x) = −x2 + 4x + 12 g(x) = −x + 6 Complete the table on your own paper, then select the value that is a solution to f(x) = g(x).
For [tex]\fbox{\begin \\\math{x}=6\\\end{minispace}}[/tex] the function [tex]f(x)=-x^{2} +4x+12[/tex] and [tex]g(x)=-x+6[/tex] has same value.
Step by step explanation:
The given functions are,
[tex]f(x)=-x^{2}+4x+12[/tex]
[tex]g(x)=-x+6[/tex]
Step 1:
Substitute [tex]x=1[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(1)[/tex].
[tex]f(1)=-1^{2} +4(1)+12\\f(1)=-1+4+12\\f(1)=15[/tex]
Substitute [tex]x=1[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(1)[/tex] .
[tex]g(1)=-1+6\\g(1)=5[/tex]
Step 2:
Substitute [tex]x=2[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(2)[/tex].
[tex]f(2)=-2^{2} +4(2)+12\\f(2)=-4+8+12\\f(2)=16[/tex]
Substitute [tex]x=2[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(2)[/tex] .
[tex]g(2)=-2+6\\g(2)=4[/tex]
Step 3:
Substitute [tex]x=3[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(3)[/tex].
[tex]f(3)=-3^{2} +4(3)+12\\f(3)=-9+12+12\\f(3)=15[/tex]
Substitute [tex]x=3[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(3)[/tex] .
[tex]g(3)=-3+6\\g(3)=3[/tex]
Step 4:
Substitute [tex]x=4[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(4)[/tex].
[tex]f(4)=-4^{2} +4(4)+12\\f(4)=-16+16+12\\f(4)=12[/tex]
Substitute [tex]x=4[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(4)[/tex] .
[tex]g(4)=-4+6\\g(4)=2[/tex]
Step 5:
Substitute [tex]x=5[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(5)[/tex].
[tex]f(5)=-5^{2} +4(5)+12\\f(5)=-25+20+12\\f(5)=7[/tex]
Substitute [tex]x=5[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(5)[/tex] .
[tex]g(5)=-5+6\\g(5)=1[/tex]
Step 6:
Substitute [tex]x=6[/tex] in [tex]f(x)=-x^{2} +4x+12[/tex] to obtain the value of [tex]f(6)[/tex].
[tex]f(6)=-6^{2} +4(6)+12\\f(6)=-36+24+12\\f(6)=0[/tex]
Substitute [tex]x=6[/tex] in [tex]g(x)=-x+6[/tex] to obtain the value of [tex]g(6)[/tex] .
[tex]g(6)=-6+6\\g(6)=0[/tex]
Step 7:
As per the given condition [tex]f(x)=g(x)[/tex].
(a). Substitute [tex]f(x)=-x^{2} +4x+12[/tex] and [tex]g(x)=-x+6[/tex] in above equation.
[tex]-x^{2} +4x+12=-x+6[/tex]
(b). Multiply with [tex]-1[/tex] on both sides.
[tex]x^{2} -4x-12=x-6[/tex]
(c). Shift the term [tex]x-6[/tex] to left hand side.
[tex]x^{2} -4x-12-x+6=0\\x^{2} -5x-6=0[/tex]
(d). Split the middle term in such a way that its sum is 5 and multiplication is 6.
[tex]x^{2} -(6-1)x-6=0\\x^{2} -6x+x-6=0\\x(x-6)+1(x-6)=0\\(x+1)(x-6)=0\\x=-1 ,6[/tex]
It is observed from the above solution that for [tex]x=6[/tex] both the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] has same value.
Direct method:
[tex]f(x)=g(x)\\\Leftrightarrow-x^{2} +4x+12=-x+6\\\Leftrightarrow-x^{2} +4x+12+x-6=0\\\Leftrightarrow-x^{2} +5x+6=0\\\Leftrightarrow-x^{2} +6x-x+6=0\\\Leftrightarrow x^{2} -6x+x-6=0\\\Leftrightarrow x(x-6)+1(x-6)=0\\\Leftrightarrow(x+1)(x-6)=0\\\Leftrightarrow x=6,-1[/tex]
The table for the function [tex]f(x)=-x^{2} +4x+12[/tex] and [tex]g(x)=-x+6[/tex] is attached below.
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Answer details:
Grade: Middle school.
Subjects: Mathematics.
Chapter: Function.
Keywords: Function, Middle term split method, Binomial,Quadratic, Polynomial, Factorized, Perfect square, Zeros, Zeros of a function, Expression, Equation, x, x^2, x^3, -x^2+4x+12, -x+6, roots of equation.
Answer:
The answer would be D.
Step-by-step explanation:
Use calculus to find the largest possible area for a rectangular field that can be enclosed with a fence that is 400 meters long.
the largest rectangular area is actually a square.
so the side would be 400/4 = 100 feet
area of a square is S^2
100^2 = 10,000 square feet
Maximum area is 5625m² when the dimensions are 75m × 75m.
To maximize the area of the rectangular field enclosed by a 300-meter-long fence, let's denote the length of one side as x meters and the other side as y meters.
Since the fence length is 300 meters, the perimeter of the rectangle is 2x + 2y = 300, or x + y = 150.
We want to maximize the area, which is given by A = xy.
To find the maximum, we'll use the constraint equation to express one variable in terms of the other, then substitute into the area formula.
1. From the constraint equation, x = 150 - y.
2. Substitute x into the area formula: A = (150 - y)y.
3. Take the derivative of A with respect to y and set it to zero to find the critical points.
4. Solve for y to find the value that maximizes A.
5. Use this value of y to find the corresponding x.
6. Calculate the maximum area using A = xy.
A phone company offers two monthly plans. Plan A costs $16
plus an additional $0.10
for each minute of calls. Plan B has no initial fee but costs $0.14
for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?
Final answer:
The two phone plans cost the same when the user uses 400 minutes. At that point, both Plan A and Plan B will cost $56.
Explanation:
To determine for what amount of calling the two plans cost the same, set up an equation where the cost of Plan A equals the cost of Plan B. For Plan A, the cost is $16 plus $0.10 per minute of calls, and for Plan B, the cost is $0.14 per minute of calls. So, we can write the equation as:
16 + 0.10m = 0.14m
where m represents the number of minutes. Solve for m to find when the two plans are equal in cost:
0.14m - 0.10m = 16
0.04m = 16
m = 16 / 0.04
m = 400
Therefore, the two plans cost the same when the user uses 400 minutes. Now, let's calculate the cost of each plan at 400 minutes:
For Plan A: 16 + (0.10 × 400) = 16 + 40 = $56
For Plan B: 0.14 × 400 = $56
The cost when the two plans cost the same is $56.
Final answer:
The two phone plans cost the same when 400 minutes of calls are used. At that point, the cost for each plan is $56.
Explanation:
To determine when the two plans offered by the phone company cost the same, we need to set up an equation where the two costs are equal. For Plan A, the cost is $16 plus $0.10 per minute. For Plan B, there is no initial fee but it costs $0.14 per minute. We can set up the equation like this:
Plan A: Cost = $16 + $0.10 × (number of minutes)
Plan B: Cost = $0.14 × (number of minutes)
To find out when they cost the same, we set these equal to each other:
$16 + $0.10m = $0.14m
Where m is the number of minutes. Solving for m gives us:
$16 = $0.14m - $0.10m
$16 = $0.04m
m = $16 / $0.04
m = 400 minutes
At 400 minutes, both plans cost the same. Now to find the cost when they are the same:
Cost = $16 + ($0.10 × 400)
Cost = $16 + $40
Cost = $56
Therefore, the two plans cost the same at 400 minutes and the cost at that point is $56.
What is the solution of mc018-1.jpg ? (Picture added)
The solution to the equation [tex]\sqrt{1-3x}= x+3[/tex] is x = -8 or x = -1.
To find the solution of the equation √(1-3x) = x+3, we can use algebraic techniques to isolate the variable x.
First, let's square both sides of the equation to eliminate the square root:
[tex](\sqrt{1-3x})^{2} = (x+3)^2[/tex]
Simplifying, we get:
[tex]1-3x = x^2 + 6x + 9[/tex]
Next, let's gather all the terms on one side of the equation:
[tex]x^2 + 6x + 9 - 1 + 3x = 0[/tex]
Simplifying further, we have:
[tex]x^2 + 9x + 8 = 0[/tex]
Now, we can factor the quadratic equation:
(x+1)(x+8) = 0
Setting each factor equal to zero, we have:
x+1 = 0 or x+8 = 0
Solving these equations, we find:
x = -1 or x = -8
Therefore, the solution to the equation [tex]\sqrt{1-3x}= x+3[/tex] is x = -8 or x = -1.
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A= (4,5) B= (7,-9) what is AB ?
570 people die from smoking related diseases everyday ?
A) how many die form related diseases every hour?
B) how many die form related diseases every week?
C) has many die form related diseases every year?
(570 people/ 1 day)* (1 day/ 24 hours)= 23.75 people/hour.
The rate of people who die from smoking is 23.75 people die per hour.
The rate of people who die from smoking is 3,990 people die per week.
The rate of people who die from smoking is 207,408 people die per year.
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What number must you add to complete the square? X^2 +12x=40
Answer:
36
Step-by-step explanation:
(x+6)^2=76
If you are throwing a dart at the circular target pictured below, and it is equally likely to hit any point on the target, what is the probability that the dart will hit the rectangle?
Use 3.14 for ,and round your answer to the nearest tenth of a percent.
Write an equation that has a hole at x = 4 and a vertical asymptote at x = -3.
Complete the solution of the equation. find the value of y when x equals 11 8x+6y=28
simplify the expression and enter your answer below (19^1/9) ^9
The simplified expression is 19.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
some terms are:
Constant: A constant is a fixed numerical value.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.given:
(1*9^1/9) ^9
Multiply 9 and 1/9
we get
9*1/9 = 1
and 19* 1= 19
Hence, the simplified expression is 19.
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Find the three arithmetic means in this sequence. 12 __ __ __ 40
Write 7x-2-7x+6 in simplest form.