The cost of shipping is the flat rate plus the cost per pound times the number of pounds
c = flat rate + rate* pounds
c = 4 + 0.85*p
The write the second part in the opposite order
c = 0.85p +4
When we add the order doesn't matter
Answer B c = 0.85p + 4
Solve the polynomial equation by factoring and then using the zero product principal
Given: The polynomial below
[tex]x^3+2x^2=9x+18[/tex]To Determine: The factored form of the equation using the zero product principle
Step 1: Put all the terms to the left hand side of the equation
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \end{gathered}[/tex]Step 2: Group the equation into and factorize
[tex]\begin{gathered} (x^3+2x^2)-(9x-18)=0 \\ x^2(x+2)-9(x+2)=0 \\ (x+2)(x^2-9)=0 \end{gathered}[/tex]Step 3: Expand the difference of two squares
[tex]\begin{gathered} a^2-b^2=(a-b)(a+b) \\ x^2-9^2=x^2-3^2=(x-3)(x+3) \end{gathered}[/tex]Step 4: Replace the difference of two squares with its equivalence
[tex]\begin{gathered} x^3+2x^2=9x+18 \\ x^3+2x^2-9x-18=0 \\ (x+2)(x^2-9)=0 \\ (x+2)(x-3)(x+3)=0 \end{gathered}[/tex]Step 5: Use the zero product principle to determine the solution set
[tex]\begin{gathered} (x+2)(x-3)(x+3)=0 \\ x+2=0,or,x-3=0,or,x+3=0 \\ x=-2,or,x=3,or,x=-3 \end{gathered}[/tex]Hence,
The factored form is (x + 2)(x - 3)(x + 3) = 0
The solution set is x = -2, 3, -3
Please look at the picture for accurate description thank you in advance
Given:
Height of person 5.3 ft.
Distance between person and tree is 34 feet
In triangle ABC
BC=34
Angle = 71
[tex]\begin{gathered} \tan \theta=\frac{\text{ perpendicular}}{\text{ base}} \\ \tan \theta=\frac{AB}{BC} \\ \tan 71=\frac{AB}{34} \\ AB=34\times\tan 71 \\ AB=98.7431 \end{gathered}[/tex]So height of tree is person height + AB
[tex]\begin{gathered} =98.7431+5.3 \\ =104.0431 \end{gathered}[/tex]So height of tree is 104
8.The outfield fencing for a Minor League field forms a circular sector with home plate as thecenter. (See the figure at the top of page 681.) The fence is placed at a uniform distance of2130 ft from home plate. The boundaries of the fence, which extends partway into foulterritory, create an angle of 110 degrees with home plate. At $21 per foot, how much willthe fence cost? (Round to the nearest $10.)
The Solution.
Representing the problem in a diagram, we get
To find the length of the boundaries of the fence, we shall use the formula below:
[tex]\begin{gathered} \text{Length}=\frac{\theta}{360}\times2\pi r \\ \text{Where }\theta=110^o \\ \pi=3.14 \\ r=2130\text{ ft} \end{gathered}[/tex]Substituting these values in the formula, we get
[tex]\begin{gathered} \text{Length}=\frac{110}{360}\times2\times3.14\times2130 \\ \\ \text{ =}\frac{11\times3.14\times2130}{18}=4087.23\text{ fe}et \end{gathered}[/tex]We were told that each foot cost $21.
So, the cost of the fence is
[tex]\frac{4087.23}{21}=\text{ \$194.63}\approx\text{ \$190}[/tex]Therefore, the correct answer is $190
1f $300 is invested at a rate of 6% per year and is compounded quarterly, how much will the investment be worth in 12 years?Use the compound interest formula A-P(1+r/n)^ntO $145.23O $358.69O $613.04O $618.41
$613.04
Explanation:Amount invested is the principal
Principal, P = $300
Interest rate, r = 6% = 6/100
r = 0.06
Number of times the interest is compounded per year, n = 4
Time, t = 12
Amount after 12 years, A(12) = ?
Amount formula for compound interest is:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ \\ A(12)=300(1+\frac{0.06}{4})^{4(12)} \\ \\ A(12)=300(1.015)^{48} \\ \\ A(12)=613.04 \end{gathered}[/tex]In 12 years, the investment will be worth $613.04
Identify the property that justifies each step asked about in the answer area below.Line 1:(xz)yLine 2:x(zy)Line 3:x(yz)Line 1 to Line 2:Line 2 to Line 3:
Line 1 to line 2) This property,
[tex](xz)y=x(zy)[/tex]is called associativity.
Line 2 to line 3) The property used here is this:
[tex]xy=yx[/tex]It is called commutativity.
solve each system of equations below by graphing, please use my graphy = 1/2x - 3y= 3/2x - 1
Answer:
(-2, -4)
Explanation:
To solve the system, we need to graph both equations. So, we will find two points for each line.
For y = 1/2x - 3
If x = 0
y = 1/2(0) - 3 = -3
If x = 2
y = 1/2(2) - 3
y = 1 - 3 = -2
For y = 3/2x - 1
If x = 0
y = 3/2(0) - 1 = -1
If x = 2
y = 3/2(2) - 1
y = 3 - 1 = 2
Therefore, we have the points (0, -3) and (2, -2) for the first equation and the points (0, -1) and (2, 2) for the second equation. Now, we can graph the lines as:
The lines intersect at (-2, -4), so the solution of the system is (-2, -4)
Keisha and her friends visit the concession stand at a football game. The stand charges $2 for a hot dog and $1 for a drink. The friends buy a total of 8 items for $11. Tell how many hot dogs and how many drinks they bought. $2.00 HOT DDLC 6100 STEP
EXPLANATION
Let's see the facts:
x= number of hot dogs they buy
y= number of drinks they buy
They buy 8 items, so
x + y = 8
Cost of a hot dog = $2
Cost of x hot dogs = 2x
Cost of a drink = $1
Cost of y drinks = 1y
The total amount they spent is:
2x + y
They spent $11, so
2x + y = 11
Now, we have a system of equations:
(1) x + y = 8
(2) 2x + y = 11
Subtracting (2) from (1):
2x + y = 11
- ( x + y = 8)
------------------
x = 3
Then, to find the number of drinks they bought, substitute x=3 into x + y = 8 and the solve for y:
3 + y = 8
Subtracting -3 to both sides:
3 - 3 + y = 8 -3
Simplifying:
y = 5
Answer:
They bought 3 hot dogs and 5 drinks.
(1 point) Rework problem 4 from section 2.2 of your text, involving the choice of officers for acommittee. For this problem, assume that you have a committee of 10 members, and that youmust choose a parliamentarian, and secretary.msIn how many ways can these selections be made?
There are 90 possible ways the selection can be made
Here, we want to know the number of ways the choice can be made from 10 members
Firstly, we want to select 1 parliamentarian from 10 members; then after the selection we will select a secretary from the remaining nine
As pertaining selections, selecting r items from a total n , can be calculated by the use of the combinatorial formula as follows;
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!_{}} \\ \\ \text{Also, we have;} \\ ^nC_1\text{ = n} \end{gathered}[/tex]So, we have 10 ways to select an item from 10 items, we also have 9 ways to select an item from 9 items
So, the total possible number of ways would be;
[tex]10\times\text{ 9 = 90 ways}[/tex]Triangle ABC has vertices (1,4), (5,6), and (3, 10). It is reflected across the y-axis, forming Triangle A’B’C’. What are the vertices of the new triangle?
Step 1:
First, write the rule for the transformation across the y-axis
The rule for a reflection over the y -axis is (x,y)→(−x,y).
Meaning value of y remains the same and you will multiply the coordinate of x by negative.
Step 2
Coordinates of pre-image
A = (1 , 4)
B = (5 , 6)
C = (3 , 10)
Step 3:
Find the coordinates of the image using the rule.
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
Final answer
The vertices of the new triangle is
A' = (-1, 4)
B' = (-5 , 6)
C' = (-3 , 10)
help students understand how fractions and decimal numbers are related. Her teacher showed her on the ruler that 0.5 is equivalent to circumference of a circle, Whiet number below will give him the approximate value of ? A 300 B. 3.14 0.5 C. 328 liquip D. 3.43 Inches 1 2 11 What decimal number is equivalent to 12 Question 3 Which of the following numbers rational? A 1 78 A 0.31311 B. 1 1875 C 1.875 C v16 D. 1.75 D. 27
The measuring rule shows lines graded between each unit.
Each unit has four lines between them which means each line is a quarter, or 1/4 or 0.25 of each unit.
When the ruler indicates 0.5, that is shown as two quarters, or one half (that is 1/2).
Therefore when the ruler indicates
[tex]\begin{gathered} 1\frac{7}{8} \\ \text{That can be broken down into } \\ 1+\frac{2}{8}+\frac{2}{8}+\frac{2}{8}+\frac{1}{8} \\ \text{Note that }\frac{2}{8}\text{ is equivalent to }\frac{1}{4} \\ \text{Also }\frac{1}{4}\text{ is equivalent to 0.25} \\ \frac{1}{8}\text{ is half of }\frac{1}{4},\text{ and that is equivalent to half of 0.25} \\ \text{Therefore, we now have} \\ 1+0.25+0.25+0.25+0.125 \\ =1.875 \end{gathered}[/tex]The correct answer is 1.875
By how much was the price counted?What was the percentage of the discount?
1.
original price - price with discount = 22-13.26 = 8.74
2.
in order to know the percentage of the discount
first, we need to know the percentage pay
x=percentage pay
(22)(x)=13.26
x=13.26/22= 0.60
the percentage pay 60%
the percentage of the discount is
100%-60%=40%
the percentage of the discount is 40%
The probability of being dealt a club and a diamond is
There are a total of 52 cards in a standard deck.
There are 13 club cards and 13 diamond cards.
The probability of getting a club card is given by
[tex]P(club)=\frac{\text{number of club cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a diamond card is given by
[tex]P(diamond)=\frac{\text{number of diamond cards}}{\text{total number of cards}}=\frac{13}{52}[/tex]The probability of getting a club and diamond is given by
"And" means to multiply the probabilites
[tex]\begin{gathered} P(club\; \; and\; \; diamond)=P(club)\times P(diamond) \\ P(club\; \; and\; \; diamond)=\frac{13}{52}\times\frac{13}{52} \\ P(club\; \; and\; \; diamond)=\frac{169}{2704}=\frac{1}{16} \end{gathered}[/tex]Therefore, the probability of getting a club and diamond is 1/16
A person can join The Fitness Center for $50. A member can rent the tennis ball machine for $10 an hour. Write a linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y).
what is the initial value?
Determine the cost for renting the tennis ball machine for 2 hours? for 5 hours? 0 hours?
How many hours did a member rent the tennis ball machine if the total cost was $130?
The linear function to model the relationship between the number of hours the machine is rented (x) and the total cost (y) is 50 + 10h.
The initial value is $50.
The cost of renting for 2 hours is 70
The hours that a member rent the tennis ball machine if the total cost was $130 is 8 hours.
What is an equation to model the relationship?An equation simply means the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the person can join The Fitness Center for $50 and member can rent the tennis ball machine for $10 an hour. Let the number of hours be h
This will be:
= 50 + (10 × h)
= 50 + 10h
The cost for renting for 2 hours will be:
= 50 + 10(2)
= 50 + 20
= 70
When cost is $130, the hours will be:
50 + 10h = 130
Collect like terms
10h = 130 - 50
10h = 80
Divide
h = 80/10
h = 8 hours.
In conclusion, the number of hours is 8 hours.
Learn more about equations on:
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1. A linear function that models the relationship between the number of hours the machine is rented (x) and the total cost (y) is f(y) = 50 + 10x.
2. The initial value is $50, which refers to the membership cost.
3. The cost of renting the tennis ball machine for 2 hours is $70.
4. The cost of renting the tennis ball machine for 5 hours is $100.
5. The cost of renting the tennis ball machine for 0 hours is $50.
6. A member who rented the tennis ball machine for 8 hours will pay a total cost of $130.
What is a linear function?
A linear function is a mathematical expression in an equation form, like f(y) = a + bx.
The a is a constant (like a fixed cost) just like the b (the slope). The x is the independent variable while y is the dependent variable.
The fixed cost for joining The Fitness Center = $50
The variable cost of renting the tennis ball machine = $10 per hour
To rent the tennis ball machine for 2 hours, the total cost, y = 50 + 10(2)
= $70
To rent the tennis ball machine for 5 hours, the total cost, y = 50 + 10(5)
= $100
To rent the tennis ball machine for 0 hours, the total cost, y = 50 + 10(0)
= $50
To pay a total cost of $130, the member rented the tennis ball machine for 8 hours, given that the total cost of, 130 = 50 + 10x
= 10x = 80
x = 8 hours
Learn more about linear functions at https://brainly.com/question/26934039
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1.y = 6xSolve:(4x + y = 72.y = 3xsolve: { x + 2y + 703Which equation, together with y = -1.5x + 3, makes a system with one solution?Ay = -1.5x + 6B.y = -1.5xC.2y = -3x + 6D.2y + 3x = 6IE.y = -2x + 34.The system x - 6y = 4, 3x - 18y = 4 has no solution.a.Change one constant or coefficient to make a new system with one solution.b.Change one constant or coefficient to make a new system with an infinite number ofsolutions5.Match each graph to its equation.Im
The system of equations:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]This comes from the fact that if we multiply the first equation by 3 then we have:
[tex]3x-18y=12[/tex]But this clearly contradicts the second one. Then the system has no solutions.
a.
To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:
[tex]\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}[/tex]which has one solution.
b.
To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:
[tex]\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}[/tex]then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.
Question:Solve the formula I = Prt to find the principal, P, when I = $272.25, r = 2.2%, and t = 3 years.
Given in the question:
I = $272.25
r = r = 2.2%
t = 3 years
Let's re-equate the formula of Simple Interest to find P in terms of I, r, and t.
[tex]I\text{ = Prt }\rightarrow\text{ P = }\frac{I}{rt}[/tex]Let's plug in the values to find P.
[tex]P\text{ = }\frac{I}{rt}[/tex][tex]P\text{ = }\frac{272.25}{(\frac{2.2}{100})(3)}\text{ = }\frac{272.25}{(0.022)(3)}[/tex][tex]P\text{ = }\frac{272.25}{0.066}[/tex][tex]P\text{ = 4,125 = \$4,125}[/tex]Therefore, the Principal Amount is $4,125.
I need help with this 2Identify the graph with point (0, -8, 5)
Explanation:
Cartesian coordinate system
A point can be defined in the Cartesian coordinate system with 3 real numbers: x, y, z. Each number corresponds to the signed minimal distance along with one of the axis (x, y, or z) between the point and plane, formed by the remaining two axes. The coordinate is negative if the point is behind the coordinate system origin.
The points is given below as
[tex](0,-8,5)[/tex]Hence,
The final answer is
What polynomial must be added to x² - 2x + 6 so that the sum is 3x^2 + 7x ? A. 4x^2 + 5x + 6 B. 3x² + 9x + 6 C. 3x² + 9x - 6 D. 2x² + 9x - 6 E. 2x^2 – 5x + 6
Answer:
The polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Explanation:
Given the polynomial;
[tex]x^2-2x+6[/tex]We want to find the polynomial that must be added to it to give the polynomial;
[tex]3x^2+7x[/tex]To get that we will subtract the polynomial from the sum;
[tex]\begin{gathered} 3x^2+7x-(x^2-2x+6) \\ =3x^2+7x-x^2+2x-6) \\ \text{rearranging;} \\ =3x^2-x^2+7x+2x-6 \\ \text{simplifying;} \\ =2x^2+9x-6 \end{gathered}[/tex]Therefore, the polynomial that must be added is;
[tex]2x^2+9x-6[/tex]Solve for Y2x + = 4a. y = 6x + 12b. y = -6x +12C. y= 6x - 12d. y = -6x - 12
You have the following equation:
2x + y/3 = 4
In order to solve for y, proceed as follow:
2x + y/3 = 4 subtract by 2x both sides
y/3 = 4 - 2x multiply by 3 both sides
y = 3(4 -2x) apply distribution property
y = 3(4) + 3(-2x)
y = 12 - 6x order the expression
y = -6x + 12
Hence the solution for y is:
y = -6x + 12
the fraction 1-4 is blank to the decimal of 0.25
Answer:
equal
Step-by-step explanation:
1/4 = .25
1÷4=.25
Use the composite figures below to mark each statement as true or false. Justify your choices.A.The area of figure A can be found by determining the sum of the area of the rectangle and the area of a semicircle.B. The area of figure b can be found by decomposing the figure into a square and parallelogram.C. Figure b has a total area of 29.75 M2.D.The area of figure a is 45.99 m2 more than the area of figure B.
Answer
A. True
In figure A, there are two semicircles and a rectangle.
Area of the composite figure = Area of a circle + area of a rectangle
Two semicircles give a complete circle, therefore the area of a circle is given by
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius }=\frac{4}{2}=2\text{ m} \\ \Rightarrow A=3.14\times2^2 \\ A=3.14\times4 \\ A=12.56m^2 \end{gathered}[/tex]The area of the rectangle in figure A is given by
A = length x width
A = 7 x 4
A = 28 m²
Therefore, the area of the composite figures = 12.56 m² + 28 m² = 40.56 m²
B. True
Note: label the figure from A - G and join line D to C as shown below.
Area of the composite figure = Area of parallelogram ABCE + Area of square CDFG
Note: Area of parallelogram = base x height
Area of a square = length x length
[tex]\begin{gathered} \text{Area of Composite figure }=(5\times3.5)+(3.5\times3.5) \\ =17.5+12.25 \\ =29.75m^2 \end{gathered}[/tex]C. True
D. False, area of figure A is 40.56 m², and area of figure B is 29.75 m². Therefore, the area of figure A is 10.81 m² NOT 45.99 m². more than the area of figure B
What is the distance between (4, 3) and (9, 15) on the coordinate plane? Select two that apply. 13 units V 169 units V144 units 12 units 5 units
Explanation
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]Step 1
Let
P1=(4,3)
P2=(9,15)
replace
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{distance}=\sqrt[]{(9-4)^2+(15-3)^2} \\ \text{distance}=\sqrt[]{(5)^2+(12)^2} \\ \text{distance}=\sqrt[]{25+144^{}} \\ \text{distance}=\sqrt[]{169} \\ \text{also} \\ \text{distance}=13 \end{gathered}[/tex]I hope this help you
1/2×-8=9 and ×-8=18 are not equivalent because
By definition, you know that two equations are equivalent when they have the same solution. So, solving the first equation you have
[tex]\begin{gathered} \frac{1}{2}x-8=9 \\ \text{ Add 8 }to\text{ both sides of the equation} \\ \frac{1}{2}x-8+8=9+8 \\ \frac{1}{2}x=17 \\ \text{Multiply by 2 }on\text{ both sides of the equation} \\ 2\cdot\frac{1}{2}x=17\cdot2 \\ x=34 \end{gathered}[/tex]Now, solving the second equation you have
[tex]\begin{gathered} x-8=18 \\ \text{ Add 8 to both sides of the equation} \\ x-8+8=18+8 \\ x=26 \end{gathered}[/tex]Since the equations do not have the same solution then these equations are not equivalent.
I need help and I need to right answer please
As you can see, figures ABC and A'B'C' have the same sides and the same orientation about the origin, then the they only differ by their position, a translation is a transformation that let us change the position of a figure without affecting its shape or its size, in this case ABC moved 3 units down and 1 unit left, for this reason the sequence of transformations is:
(x, y) -> (x - 1, y - 3)
Then, the second option is the correct answer
What is the major axis for the equation+= 1? Type h for horizontal or v for vertical.
Consider the given equation,
[tex]\begin{gathered} \frac{x^2}{49}+\frac{y^2}{7}=1 \\ \frac{x^2}{(7)^2}+\frac{y^2}{(\sqrt{7})^2}=1 \end{gathered}[/tex]This is a standard equation of a horizontal ellipse, whose semi-major axisis given as,
[tex]a=7[/tex]So the length of major axis will be,
[tex]2a=2(7)=14[/tex]Thus, the length of major axis of the given equation is 14 units.
Can someone please help me understand algebra.I just want to learn how to understand it because I can not understand it at all.
Algebra
Algebra is a branch of mathematics that uses not only numbers and signs, but also letters to solve operations.
Algebraic term
The algebraic term is a simple expression where letters and numbers are combined, and variables are not added or subtracted. For example:
[tex]-7x^4[/tex]In the previous algebraic term we can identify its parts:
Sign: It can be positive or negative, as in the example.
Coefficient: The number that accompanies the variable, which in this case would be 5.
Variable: It is the unknown represented by the letter x.
Exponent: The power to which the variable is raised, which in the example would be 3. If no exponent appears, it is understood that it is 1.
Algebraic expression
The algebraic expression is a set of variables and numbers that can be combined with different mathematical operations, including addition and subtraction, unlike algebraic terms. An example can be the following:
[tex]-5x^2+4y[/tex]Expressions can be expressed as a function of the number of terms that contain them as
Monomial: Has a term:
[tex]15z[/tex]Binomial: It has two terms:
[tex]2x^2-7y[/tex]Trinomial: It has three terms:
[tex]3x^2+8y+2z[/tex]Polynomial: It has more than three terms:
[tex]5x^3-3y+6z-9[/tex]Algebraic equations
An equation is the association between two algebraic expressions through the equal sign. They can be mainly of two types:
First degree equation: When the variable is raised to the maximum power 1. It is known as an equation.
5x + 5y = 9
Second degree equation: When the variable is raised to the maximum power 2. It is also called a quadratic equation.
5x2-3y + 6z-9 = 3x
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Letmidpoint (2,9), endpoint (1, -3)
Given this is a one of the endpoints of the segment:
[tex](1,-3)[/tex]You know that the midpoint is:
[tex](2,9)[/tex]By definition, the formula for finding the midpoint of a segment is:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
- The coordinates of the midpoint are:
[tex](x_m,y_m)[/tex]- And the coordinates of the endpoints are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_m=2 \\ y_m=9 \\ \\ x_1=1 \\ y_1=-3 \end{gathered}[/tex]Then, you can set up this equation to find the x-coordinate of the other endpoint:
[tex]2=\frac{1+x_2}{2}[/tex]Solving for:
[tex]x_2[/tex]You get:
[tex](2)(2)=1+x_2[/tex][tex]\begin{gathered} 4-1=x_2 \\ x_2=3 \end{gathered}[/tex]Set up the following equation to find the y-coordinate of the other endpoint:
[tex]9=\frac{-3+y_2}{2}[/tex][tex](9)(2)=-3+y_2[/tex][tex]\begin{gathered} 18+3=y_2 \\ y_2=21 \end{gathered}[/tex]Hence, the answer is:
[tex](3,21)[/tex]you want to get rid of the X by elimination in the system below
Hence, the correct option is -3
spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute.Find the rates of change of the radius when r=30 centimeters and r=85 centimeters.Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant.
Answer
Explanation
Given:
A spherical balloon is inflated with gas at the rate of 800 cubic centimeters per minute means
[tex]\frac{dV}{dt}=800\text{ }cm^3\text{/}min[/tex](a) The rates of change of the radius when r = 30 centimeters and r = 85 centimeters is calculated as follows:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \\ \frac{dV}{dr}=\frac{4}{3}\times3\pi r^{3-1} \\ \\ \frac{dV}{dr}=4\pi r^2 \\ \\ But\frac{\text{ }dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \end{gathered}[/tex]So when r = 30, we have
[tex]\begin{gathered} \frac{dV}{dr}=4\pi(30)^2 \\ \\ \frac{dV}{dr}=4\times\pi\times900 \\ \\ \frac{dV}{dr}=3600\pi \\ \\ From\text{ }\frac{dV}{dr}=\frac{dV}{dt}\div\frac{dr}{dt} \\ \\ Putting\text{ }\frac{dV}{dt}=800,\text{ }we\text{ }have \\ \\ 3600\pi=800\div\frac{dr}{dt} \\ \\ \frac{dr}{dt}=\frac{800}{3600\pi}=\frac{800}{3600\times3.14} \\ \\ \frac{dr}{dt}=0.071\text{ }cm\text{/}min \end{gathered}[/tex]Therefore, the rate of change of the radius when r = 30 is dr/dt = 0.071 cm/min.
For when r = 25 cm, the rate of change is:
[tex][/tex]A car that originally cost $3,668 in 1955 is valued at $62,125 if in excellent condition, which is1 times as much as a car in very nice condition—if you can find an owner willing to part with one for any price.What would be the value of the car in very nice condition? (Do not round intermediate calculations.)Value of the car
Let
x ----> value of the car in very nice condition
we know that
1 3/4 x=62,125 ----> linear equation that represent this situation
Solve for x
but first
Convert mixed number to an improper fraction or decimal number
1 3/4=1+3/4=1+0.75=1.75
substitute
1.75x=62,125
x=62,125/1.75
x=35,500
therefore
the answer is $35,500Hi , can you help me please , I did the run and ride the results is y=-4/3x + 4/3. what would the graph look like with ours results?
Given the equation of a straight line below
[tex]y=-\frac{4}{3}x+\frac{4}{3}[/tex]The general equation of a line,
[tex]y=mx+c_{}[/tex]Where
[tex]\begin{gathered} m\text{ is the slope of the line} \\ c\text{ is the y-intercept} \end{gathered}[/tex]The slope, m, of the given line is
[tex]m=-\frac{4}{3}[/tex]The graph of the equation of the line given is shown below
Hence, the slope of the given equation of a line is, m = -4/3