The slope is the change in y divided by the change in x.
The slope is the ratio of rise to run.
so: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)
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.
Is it correct to say that a cube with side lengths 6cm have the same volume and surface area?
Change fraction to decimal: 4/7 and round to the nearest thousandth?
To solve this problem, all we have to remember is that fractions also mean division. Therefore this means that:
4 / 7 = 4 divided by 7
We can use either a calculator to solve for this or do the long division method of division (your choice). Now to solve this simply, I used the calculator and got the answer:
4 / 7 = 0.571428571
However, the problem asked us to round this to the nearest thousandth. We know that the decimal places are:
0.(tenths)(hundredths)(thousandths)
So we are to round this into 3 decimal numbers which gives us:
4 / 7 = 0.571
The profit P after the first month of operation for a new departmental store is $10,605. The profit of the departmental store after x months can be determined by P = 10500(1.01)x. What will the profit of the store be after 6 months?
A) $11,145.96
B) $11,500.00
C) $10,605.67
D) $10,500.00
The profit of the store after six months, using the given growth model, can be calculated by substituting x with 6 in the given equation and calculating the result, leading us to the answer A) $11,145.96.
Explanation:The question relates to an algebraic comprehension of
exponential growth
, using a mathematical model to predict future profit. The profit after x months is given by
P = 10500(1.01)^x
, where 'x' stands for the number of months after the first month. To find the profit after six months, all we have to do is substitute 'x' with '6' in the given equation, like so:
P = 10500(1.01)^6
. When you calculate this, the result is around,
$11,145.96
, so the correct answer to the question 'What will the profit of the store be after 6 months?' is option A) $11,145.96.
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In the given formula, substitute 6 for x, which results in P = 10500(1.01)^6. Upon simplification, it gives the profit after 6 months as $11,145.96.
Explanation:To calculate the profit of the departmental store after 6 months, we need to substitute the value 6 for x in the given formula P = 10500(1.01)^x. This results in P = 10500(1.01)^6.
When we simplify this, it gives the profit as $11,145.96. Therefore, the correct answer is option A) $11,145.96.
This mathematics concept is related to exponential functions in real-world applications like finance and investment, where the principal amount grows at a consistent rate over time.
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How many license plates are possible using three letters followed by three digits if no letter can be repeated?
Write x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers. (1 point)
(x − 4)2 = 3
(x − 3)2 = 2
(x − 2)2 = 1
(x − 1)2 = 4
Answer:
B. [tex](x-3)^2=2[/tex].
Step-by-step explanation:
We have been given an equation [tex]x^2-6x+7=0[/tex]. We are asked to write our given expression in form [tex](x-a)^2=b[/tex].
First of all, we will subtract 7 from both sides of our given equation.
[tex]x^2-6x+7-7=0-7[/tex]
[tex]x^2-6x=-7[/tex]
Now, we will complete the square for left side of equation by adding the half the square of 6.
[tex](\frac{6}{2})^2=(3)^2=9[/tex]
Upon adding 9 on both sides of our equation, we will get:
[tex]x^2-6x+9=-7+9[/tex]
[tex](x-3)^2=2[/tex]
Therefore, our required equation would be [tex](x-3)^2=2[/tex] and option B is the correct choice.
6/7 divided by 1 2/5
The answer to 6/7 divided by 1 2/5 is 30/49 after converting 1 2/5 to an improper fraction and using the rule of multiplying by the reciprocal for division with fractions.
Explanation:To solve the problem of 6/7 divided by 1 2/5, you first need to convert 1 2/5 into an improper fraction. This can be done by multiplying the whole number by the fraction's denominator and then adding the numerator, 1*5+2 = 7, so 1 2/5 becomes 7/5.
Next, when dividing by a fraction, you multiply by its reciprocal. The reciprocal of 7/5 is 5/7. Therefore, 6/7 divided by 1 2/5 equals 6/7 multiplied by 5/7.
When multiplying fractions, you multiply the numerators for the new numerator and the denominators for the new denominator, leading to (6*5)/(7*7) = 30/49.
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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.
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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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.
Find the three arithmetic means in this sequence. 12 __ __ __ 40
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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what is the simplified form of x+7/x+3 + x-4/3
Answer:
[tex]x*(x+2)[/tex]
Step-by-step explanation:
The expression is as follows:
[tex](x+7)/(x+3)+(x-4)/3[/tex]
To simplify we need to get rid of the denominators for each expression. We can see that the denominators are (x+3) and 3. We therefore mutliply the expression with 3(x+3):
[tex]3*(x+7)+(x-4)*(x+3)= 3*x+21+x^2-x-21[/tex]
Simplify the expression
[tex]x^2+2*x=x*(x+2)[/tex]
Write an equation that has a hole at x = 4 and a vertical asymptote at x = -3.
Which of the following words does not indicate multiplication? A. times B. of C. product D. more than
When dividing with polynomials, the goal is to determine how many times the dividend divides evenly into the?
Belkis is pulling a toy by exerting a force of 1.5 newtons on a string attached to the toy.
The string makes an angle of 52 degrees with the floor. What could be the vertical and horizontal components of the force?
You are planning your week-end schedule. You can spend at most 8 hours paying video games and doing homework. You want to spend less than 2 hours playing video games. You must spend at lest 1.5 hours on homework. Which of the following is the system of equations that would represent this situation? Let v= number of hours spent playing video games and let h = the number of hours spent on homework.
A) None of these
B)v<2
h≥ 1.5
v+ h≤ 8
v≥0
h≥0
C) v<1.5
h≥2
v+h≤ 8
v≥0
h≥0
D) v>1.5
h≤2
v+h≥8
v≥0
h≥0
E) v>2
h≤ 1.5
v+h≥8
v≥0
h≥0
A basketball player scored x, y, and z points in 3 games. Express the average number of points scored by the player in terms of x, y, and z.
math???????????.../?
Answer:
Math
Step-by-step explanation:
A ball bearing is shaped like a sphere and has a diameter of 2.5 cm. What is the volume contained inside the ball bearing? Use 3.14 for pi. Round your answer to the nearest hundredth.
8.18 cm3
7.15 cm3
7.08 cm3
6.89 cm3
Answer:
The correct answer is 8.18 cm ^3
Step-by-step explanation:
Formula:
4/3 x pi (3.14) x 1.25 ^3
Pi equals 3.14 and you have to divide 2.5 by 2 because you have to use the radius^3. The other person who answered the question was wrong, so please dont use their answer to help you. Hope this helps you. :)
The volume contained inside the ball bearing is 8.18 cm³
Volume of a sphere:The ball bearing is shaped like a sphere. Therefore, the volume contained inside the ball bearing is the volume of a sphere.
v = 4 / 3 πr³where
r = radius
Therefore,
diameter = 2(radius)
Therefore,
radius = diameter / 2
r = 2.5 / 2 = 1.25 cm
π = 3.14
v = 4 / 3 × 3.14 × 1.25³
v = 24.53125 / 3
v = 8.17708333333
v = 8.18 cm³
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If a coin is tossed twice what is the probability of getting two heads
You are building a rectangular dog pen with an area of 90ft^2.you want the length of the pen to be 3ft longer than twice its width. write an equation that can be used to find the width w of the pen
Given the following functions f(x) and g(x), solve (f/g)(-3) and select the correct answer below:
f(x) = 6x + 8
g(x) = x - 2
A: -2
B: -1/2
C: 1/2
D: 2
We are given the functions:
f(x) = 6x + 8
g(x) = x – 2
The first step in solving this problem is to find for the value of (f / g) (x) given the two functions above. Now finding for (f / g) (x), we can see that if we distribute x inside (f / g) we get f (x) / g(x)
therefore,
(f / g) (x) = f (x) / g (x)
= (6 x + 8) / (x – 2)
Substituting x = -3 will give us:
(f / g) (- 3) = [6 (- 3) + 8] / (- 3 -2)
(f / g) (- 3) = 2
Answer:
D: 2
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.
A chord of a circle is any line segment whose endpoints are on the circle
A.True
B.False
Answer:
True
Step-by-step explanation:
Chord: It is that line segment which connect the two points on the circle.
It is a distance between two boundary points of circle.
Or we can say that
Chord: It is a line segment which connect the two points on circle's circumference.
A chord of a circle is any line segment whose endpoints are on the circle.
Diameter of circle is a largest chord of circle.Diameter is that line segment which divides the circle into two equal halves.
Hence, we can say that given statement is true.
Winning the jackpot in a particular lottery requires that you select the correct fourfour numbers between 1 and 6262 and, in a separate drawing, you must also select the correct single number between 1 and 1616. find the probability of winning the jackpot.
There are 2 drawings, in the 1st one we have to select correct four numbers between 1 and 62 while the 2nd one is to select the one single number between 1 and 16.
In the 1st drawing, the probability of success is 1 divided by the total number of 4 combinations that can be created from 62 numbers.
P1 = 1 / 62C4
P1 = 1 / 557,845
In the 2nd drawing, the probability of success is 1 divided by 16:
P2 = 1 / 16
Since the two drawings must be satisfied before you can win the jackpot, then multiply the two:
P = P1 * P2
P = (1 / 557,845) (1 / 16)
P = 1 / 8,925,520 = 1.12 x 10^-7 = 1.12 x 10^-5 %
Therefore the odd in winning this lottery is 1 in 8,925,520 chances.
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: