We have the following:
[tex]\begin{gathered} 3x+6=4x+7 \\ 3x=4x+7-6 \\ 3x=4x+1 \\ 3x-1=4x \end{gathered}[/tex]Therefore:
3x+6=4x+7 //// = //// 3x-1=4x
[tex]\begin{gathered} 3\mleft(x+6\mright)=4x+7 \\ 3x+18=4x+7 \end{gathered}[/tex]3(x+6)=4x+7 //// = //// 3x+18=4x+7
[tex]\begin{gathered} 4x+3x=7-6 \\ 7x=1 \end{gathered}[/tex]4x+3x=7-6 //// = //// 7x=1
xx yyy
121212 363636
181818 545454
252525 757575
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
The constant of proportionality for the given set is 3.
Given,
The set;
x y
12 36
18 54
25 75
We have to find the constant of proportionality;
Here,
y = x × r
Where r is the constant of proportionality.
Lets see;
Case 1; 12 and 36
36 = 12 × r
r = 36/12
r = 3
Case 2; 18 and 54
54 = 18 × r
r = 54/18
r = 3
Case 3; 25 and 75
75 = 25 × r
r = 75/25
r = 3
Therefore,
The constant of proportionality for the given set is 3.
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Choose the graph of y = 2 cos x. (2
the expression is
y = 2cos x
when x = 0 degrees
y = 2 x cos0
y = 2 x 1
y = 2
so it is
which of the following fractions is the biggest: 1/6,3/8,1/4,4/9,2/7
Answer:
4/9
Step-by-step explanation:
A map is drawn using a scale of 1 inch : 4 meters. If the length of a paved path on a map is 16 inches, then find the actual length of the paved path.
Nana, this is the solution to the exercise:
Scale 1 inch : 4 meters
For solving this exercise, we will use the Direct Rule of Three, as follows:
Length on the map (inches) - Actual length (meters)
______________________________________________
1 4
16 x
_______________________________________________
1 * x = 16 * 4
x = 64
The actual length of the paved path is 64 meters
For the line y = 1 - 3x, create a table to show the values of x and y where x is from -2 to 2.
For the line y = 1 - 3x the values of x and y are given below:
Given,
y = 1 - 3x
putting x = -2
y = 1 - 3x
y = 1 - 3(-2)
y = 7
Putting x = -1
y = 1 - 3(-1)
y = 4
putting x = 0
y = 1 - 3(0)
y = 1
Now putting x = 1
y = 1 - 3(1)
y = -2
putting x = 2
y = 1 - 3(2)
y = -5
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Which set of sides would make a right triangle? 5,10,12 8,10,12 5,12,13 4,5,6
Our answer are the sides 5,12 and 13 which represent a Pythagoraen triple
The sides of a triangle that would make a right-triangle are collectively called a Pythagorean triple
These measures stem from the Pythagoras theorem which states that the square of the hypotenuse equals the sum of the squares of the two other sides
At any point in time, the hypotenuse refers to the longest side in the triangle
So basically, to get the correct answer from these options, if we square the longest side, and the sum of the squares of the two other sides equal the square of this longest side, the side that provides us with this would be our answer
So let us consider the options individually;
[tex]\begin{gathered} 12^2\text{ }\ne5^2+10^2 \\ \\ 12^2\ne8^2+10^2 \\ \\ 6^2\text{ }\ne4^2+5^2 \\ \\ \text{But;} \\ \\ 13^2=5^2+12^2 \end{gathered}[/tex]Inequality graph the solution x-4<-5
Answer: x < -1
Step-by-step explanation:
So you are starting with x-4<-5
Cancel the -4 on the left side by adding 4 to both sides:
x-4<-5
+4 +4
So you end up with x < -1 which would be your answer.
Hope this helped :)
Colin just travelled across Ontario on a road trip. He bought some skis in Blue Mountain for
$879.95 plus tax, a boom box in Muskoka for $145.58 including taxes, a souvenir in Niagara Falls
for $99.97 plus tax, and some maple syrup in Toronto for $45.14 including tax. Overall, how
much HST did Colin pay on his trip? Answer should be rounded off to whole number.
The Harmonized Sales Tax paid by Colin is $152.
What is Harmonized Sales Tax?Almost all buyers of taxable supplies of goods and services must pay the GST/HST (other than zero-rated supplies). Indians, Indian bands, and entities with band authority, however, are occasionally exempt from having to pay the GST/HST on taxable supplies. In Ontario, the HST (Harmonized Sales Tax) is 13%. Ontario offers a point-of-sale rebate for the 8% provincial HST exemption on a selection of goods.So, the amount of HST Colin pays:
The total amount of items brought:
Skis: $879.95Boom box: $145.58Souvenir: $99.97Maple syrup: $45.14Total amount: $1,170.64
We know that HST is 13% of the amount, then:
$1,170.64/100 × 13 = 152.1832Rounding off: $152Therefore, the Harmonized Sales Tax paid by Colin is $152.
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The price-demand and cost functions for the production of microwaves are given asP= 180 - q/50and C(q) = 72000 + 110g,where q is the number of microwaves that can be sold at a price of p dollars per unit and C(q) is the total cost (in dollars) of producing q units.(C) Find the marginal revenue function in terms of q.R'(q) =(D) Evaluate the marginal revenue function at q=1100.R'(1100) =(E) Find the profit function in terms of q.P(q)(F) Evaluate the marginal proft function at q = 1100.P'(1100)
Answer:
A)
[tex]\begin{equation*} C^{\prime}(q)=110 \end{equation*}[/tex]B)
[tex]\begin{equation*} R(q)=180q-\frac{q^2}{50} \end{equation*}[/tex]C)
[tex]\begin{equation*} R^{\prime}(q)=180-\frac{q}{25} \end{equation*}[/tex]D)
[tex]\begin{equation*} R^{\prime}(1100)=136 \end{equation*}[/tex]E)
[tex]\begin{equation*} P(q)=-\frac{q^2}{50}+70q-72000 \end{equation*}[/tex]F)
[tex]\begin{equation*} P^{\prime}(1100)=26 \end{equation*}[/tex]Explanation:
Given:
[tex]\begin{gathered} p=180-\frac{q}{50} \\ C(q)=72000+110q \end{gathered}[/tex]where q = the number of microwaves that can be sold at a price of p dollars per unit
C(q) = the total cost (in dollars) of producing q units.
A) To find the marginal cost, C'(q), we'll go ahead and take the derivative of the total cost as seen below;
[tex]\begin{gathered} C(q)=72000+110q \\ C^{\prime}(q)=0+110 \\ \therefore C^{\prime}(q)=110 \end{gathered}[/tex]So the marginal cost, C'(q) = 110
B) We'll go ahead and determine the revenue function, R(q), by multiplying the price, p, by the quantity, q, as seen below;
[tex]\begin{gathered} R(q)=p*q=(180-\frac{q}{50})q=180q-\frac{q^2}{50} \\ \therefore R(q)=180q-\frac{q^2}{50} \end{gathered}[/tex]C) We'll go ahead and determine the marginal revenue function, R'(q), by taking the derivative of the revenue function, R(q);
[tex]\begin{gathered} \begin{equation*} R(q)=180q-\frac{q^2}{50} \end{equation*} \\ R^{\prime}(q)=180-\frac{2q^{2-1}}{50}=180-\frac{q}{25} \\ \therefore R^{\prime}(q)=180-\frac{q}{25} \end{gathered}[/tex]D) To evaluate the marginal revenue function at q = 1100, all we need to do is substitute the q with 1100 in R'(q) and simplify;
[tex]\begin{gathered} \begin{equation*} R^{\prime}(q)=180-\frac{q}{25} \end{equation*} \\ R^{\prime}(1100)=180-\frac{1100}{25}=180-44=136 \\ \therefore R^{\prime}(1100)=136 \end{gathered}[/tex]Therefore, R'(1100) is 136
E) To find the profit function, P(q), we have to subtract the total cost, C(q), from the revenue cost, R(q);
[tex]\begin{gathered} P(q)=R(q)-C(q) \\ =(180q-\frac{q^2}{50})-(72,000+110q) \\ =180q-\frac{q^2}{50}-72000-110q \\ =-\frac{q^2}{50}+180q-110q-72000 \\ =-\frac{q^2}{50}+70q-72000 \\ \therefore P(q)=-\frac{q^2}{50}+70q-72000 \end{gathered}[/tex]F) To Evaluate the marginal profit function at q = 1100, we have to first determine the marginal profit, P'(q), by taking the derivative of the profit function, P(x);
[tex]\begin{gathered} \begin{equation*} P(q)=-\frac{q^2}{50}+70q-72000 \end{equation*} \\ P^{\prime}(q)=-\frac{2q^{2-1}}{50}+70(1*q^{1-1})-0=-2q^{50}+70q^0=-\frac{q}{25}+70 \\ \therefore P^{\prime}(q)=-\frac{q}{25}+70 \end{gathered}[/tex]We can now go ahead and find P'(1100) as seen below;
[tex]\begin{gathered} P^{\prime}(1100)=-\frac{1100}{25}+70=-44+70=26 \\ \therefore P^{\prime}(1100)=26 \end{gathered}[/tex]So P'(1100) = 26
The wait time of a line x hours after a store opens is given by the expression:40x-12x+23
What does the value 23 represent?
Question 1 options:
the total rate of change in people per hour
the total number of people in line
the rate at which people join the line
the number of people in line when the store opened
Answer:
Step-by-step explanation:
The wait time of a line x hours after a store opens is given by the expression:40x-12x+23What does the value 23 represent?Question 1 options:the total rate of change in people per hourthe total number of people in linethe rate at which people join the linethe number of people in line when the store opened
how many many eighths are in 8/9
There are 1/9 eighths in 8/9
please Help Asap!!!!
Lexi opened her account with less money and accrues interest at a greater rate.
What is meant by interest?
In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principle amount (the amount borrowed). The charge that the borrower may be required to pay the lender or another entity is not the same as interest. Interest also differs from dividends, which are distributed by businesses to their shareholders from their profits or reserves, but not at a set rate but rather on a pro rata basis as a portion of the rewards received by risk-takers when revenue generated exceeds total expenditures. The amount of interest paid or received during a specific time period divided by the total amount borrowed or lent is the rate of interest.
The correct answer is option (E):
Lexi opened her account with less money and accrues interest at a greater rate.
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Someone please help I don’t understand this at all would really appreciate some help !!!!
The results of the operations of functions evaluated at are listed below:
Addition - (f + g) (- 2) = 9Subtraction - (f - g) (- 2) = 3Multiplication - (f · g) (- 2) = 18Division - (f / g) (- 2) = 2 / 3How to evaluate operations of functions
In this problem we four cases of operations between two functions, a quadratic equation f(x) and a linear equation g(x). There are four operations:
Addition - f (x) + g (x) = (f + g) (x)
Subtraction - f (x) - g(x) = (f - g) (x)
Multiplication - f (x) · g (x) = f · g (x)
Division - f (x) / g (x) = (f / g) (x)
If we know that f(x) = x² - x and g(x) = 3 · x + 9, then the compositions of functions evaluated at x = - 2 are, respectively:
(f + g) (- 2) = (- 2)² - (- 2) + 3 · (- 2) + 9
(f + g) (- 2) = 4 + 2 - 6 + 9
(f + g) (- 2) = 9
(f - g) (- 2) = (- 2)² - (- 2) - 3 · (- 2) - 9
(f - g) (- 2) = 4 + 2 + 6 - 9
(f - g) (- 2) = 3
(f · g) (- 2) = [(- 2)² - (- 2)] · [3 · (- 2) + 9]
(f · g) (- 2) = 6 · 3
(f · g) (- 2) = 18
(f / g) (- 2) = [(- 2)² - 2] / [3 · (- 2) + 9]
(f / g) (- 2) = 2 / 3
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a man paddles his canoe at a rate of 12 kilometers per hour. write this rate as meters per minute
Answer
12 kilometers per hour = 200 meters per minute
Explanation
In order to convert 12 kilometers per hour into meters per minute, we need to note that
1 kilometer = 1000 meters
1 hour = 60 minutes
[tex]\begin{gathered} 12\frac{kilometers}{hour} \\ We\text{ ne}ed\text{ to note that } \\ \frac{1000\text{ meters}}{1\text{ kilometers}}=1 \\ \frac{1\text{ hour}}{60\text{ minutes}}=1 \\ 12\frac{\text{kilometers}}{\text{hour}}\times1\times1 \\ =12\frac{\text{kilometers}}{\text{hour}}\times\frac{1000\text{ meters}}{1\text{ kilometer}}\times\frac{1\text{ hour}}{60\text{ minutes}} \\ =\frac{12\times1000\times1}{1\times60}\frac{meters}{\min ute} \\ =200\frac{\text{meters}}{\text{minute}} \end{gathered}[/tex]Hope this Helps!!!
Use Heron's formula to find the area of the triangle. Round to the nearest square foot.Side a=7 feetSide b=7 feetSide c=5 feet
The area is approximately 16 square feet.
Step - by -Step Explanation
What to find? Area of the triangle using Heron's formula.
Given:
• Side a=7 feet
,• Side b=7 feet
,• Side c=5 feet
The Heron's formula is given below:
[tex]\text{Area}=\sqrt[]{p(p-a)(p-b)(p-c)}[/tex]Where P is the perimeter of the triangle.
a, b and c are the sides of the triangle.
We need to first find the half perimeter of the triangle.
P = a+b+c /2
= 7+7+5 /2=19/2 = 9.5
Substitute the value of p, a, b and c into the formula and simplify.
[tex]\text{Area}=\sqrt[]{9.5(9.5-7)(9.5-7)(9.5-5)}[/tex][tex]=\sqrt[]{9.5\times2.5\times2.5\times4.5}[/tex][tex]=\sqrt[]{267.1875}[/tex][tex]\approx16\text{ square f}eet[/tex]Hence, the area of the triangle is approximately 16 square feet.
I need help on question 10.The solution of the system below is:3x + 2y = 143x – 2y = 10
Given the system of equations:
[tex]\begin{cases}3x+2y=14 \\ 3x-2y=10\end{cases}[/tex]We'll multiply the second equation by -1 and then add both equations up:
[tex]\begin{gathered} \begin{cases}3x+2y=14 \\ 3x-2y=10\end{cases}\rightarrow\begin{cases}3x+2y=14 \\ -3x+2y=-10\end{cases} \\ \\ \rightarrow4y=4 \end{gathered}[/tex]Solving the resulting equation for y ,
[tex]\begin{gathered} 4y=4\rightarrow y=\frac{4}{4} \\ \\ \Rightarrow y=1 \end{gathered}[/tex]We'll plug in this y-value in the first equation and solve for x ,
[tex]\begin{gathered} 3x+2y=14 \\ \rightarrow3x+2(1)=14 \\ \rightarrow3x+2=14\rightarrow3x=12\rightarrow x=\frac{12}{3} \\ \\ \Rightarrow x=4 \end{gathered}[/tex]Therefore, we can conclude that the solution to our system is:
[tex]\begin{gathered} x=4 \\ y=1 \end{gathered}[/tex]1. Given d = 25,01 = 15°, and O2 = 40°. Find x and h. Show work. Round to 2 decimal places.0,
Let's check first this right triangle from the figure:
We have, using tangent on the angle:
[tex]\begin{gathered} \tan (15^o)=\frac{h}{25+x} \\ \Rightarrow h=0.268(25+x) \end{gathered}[/tex]And then, looking at the other right triangle:
Doing the same as before, we have that:
[tex]\begin{gathered} \tan (40)\text{ = }\frac{h}{x} \\ \Rightarrow h=0.839x \end{gathered}[/tex]Now, we can use both equations of h to solve for x:
[tex]\begin{gathered} 0.268(25+x)=0.839x \\ \Rightarrow6.7+0.268x=0.839x \\ \Rightarrow6.7=0.571x\Rightarrow x=\frac{6.7}{0.571}=11.73 \end{gathered}[/tex]Which we can finally use to find h in any equation:
[tex]\begin{gathered} h=0.268(25+11.73)=9.843 \\ or \\ h=0.839\cdot11.73=9.841 \end{gathered}[/tex]Hello, just want to check my answers at Part B. Thanks!
SOLUTION
The given functions are:
[tex]f(x)=(x-2)(x-1)(x-1),g(x)=\sqrt[3]{x}-2[/tex]Notice that when x=0
[tex]\begin{gathered} f(0)=(0-2)(0-1)(0-1) \\ f(0)=-2 \end{gathered}[/tex]Also
[tex]\begin{gathered} g(0)=\sqrt[3]{0}-2 \\ g(0)=-2 \end{gathered}[/tex]This shows that f(0)=g(0)
Hence there are no breakes in the domain of h(x)
Maya is playing golf. On her first two holes she scored one under par then six over par. Find her score after the first two holes.
If Maya is playing golf in which on her first two holes she has one under par then six over par. Her score after the first is 5 over per.
Score after the first two holesFirst is to analyze the given the information given
What she got on the first hole = one under par = -1
What she got on her second hole = six over par = 6
Now let find or determine her score
Score = -1 + 6
Score = 5 over par
Therefore we can conclude that her score is 5 over per.
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A local newspaper charges $13 for each of the first four lines of a classified ad, and $7.50 foreach additional line. Express the cost of a -line ad, c(x), as a piecewise function
The cost is the basic cost increased by the product of the number of extra lines and the price per additional line, then:
Let x be the number of additional lines
c(x)=13+7.50x
Margaret drove to a business appointment at 70 mph. Her average speed on the return trip was 60 mph. The return took ⅓ hr longer because of heavy traffic. How far did she travel to the appointment ?
Let d and t be the distance and the time it takes for Margaret to get the place of the appointment.
d is the product of the speed when she was going to the appointment times the time (t):
[tex]d=70t[/tex]d is also the product of the speed when she was going back home times t+1/3:
[tex]d=60(t+\frac{1}{3})[/tex]Make both d equal and find the value of t:
[tex]\begin{gathered} 70t=60(t+\frac{1}{3}) \\ 70t=60t+20 \\ 10t=20 \\ t=\frac{20}{10} \\ t=2 \end{gathered}[/tex]Use this value of t to find d:
[tex]\begin{gathered} d=70(2) \\ d=140 \end{gathered}[/tex]According to this, she traveled 140 miles to the appointment.
What is the slope of a line perpendicular to the line whose equation is x+3y=-15. Fully simplify your answer.
ANSWER
The slope of the line perpendicular line of the equation is 3
STEP-BY-STEP EXPLANATION:
What to find? The slope of a line perpendicular to the line whose equation is x + 3y = -15
Given the equation
x + 3y = -15
The slope-intercept form of an equation is given as
[tex]y\text{ = mx + b}[/tex]Where m = slope of the line
y = the intercept of the y-axis
The next step is to re-arrange the above equation in the slope-intercept format
[tex]\begin{gathered} \text{Given the equation of a straight line as} \\ x\text{ + 3y = -15} \\ \text{Isolate 3y by substracting x from both sides} \\ x\text{ - x + 3y = -15 - x} \\ 3y\text{ = -x - 15} \\ \text{Divide through by 3} \\ \frac{3y}{3}\text{ = }\frac{-1}{3}x\text{ -}\frac{15}{3} \\ y\text{ = }\frac{-1}{3}x\text{ - 5} \\ \text{Hence, the slope}-\text{intercept form of the above equation is given as} \\ y\text{ = }\frac{-1}{3}x\text{ - 5} \end{gathered}[/tex]NB: That the two lines are perpendicular to each other
From y = mx + b
m = -1/3
The slope of the equation
[tex]\begin{gathered} \text{ For two perpendicular lines, we can calculate the slope as follows} \\ m_1\cdot m_2\text{ =- 1} \\ \text{where m}_1\text{ = }\frac{-1}{3} \\ \frac{-1}{3}\cdot m_2\text{ = -1} \\ \frac{-1\cdot m_2}{3}=\text{ -1} \\ \text{Cross multiply} \\ -m_2\text{ = -1 }\cdot\text{ 3} \\ -m_2\text{ = -3} \\ \text{Divide through by -1} \\ \frac{-m_2}{-1}\text{ = }\frac{-3}{-1} \\ m_2\text{ = }3 \\ \text{Hence, the slope of the perpendicular line to the equation is 3} \end{gathered}[/tex]An animal gained 5 kilograms steadily over 25 years. What is the unit rate of kilograms per year?
Answer:
0.2kg
Step-by-step explanation:
5/25 = 0.2 which is the rate of kg per year
How do I find the correct options for the reasons?
Answer:
Explanation:
Statement: Triangle QRT and Triangle STR are Isosceles Triangles.
Angles QRT is congruent to Angle STR.
Reason: Converse of Alternate Interior Angles
Statement: RQ=RT, TR=TS
Reason: Definition of an Isosceles Triangle
Statement: TR = RT
Reason: Reflexive Property
Statement: RQ=TS
Reason: Transitive Property
Statement: RQ||TS
Reason: Opposite sides are congruent and parallel.
Statement: QRST is a parallelogram.
Reason:
On a flight from Chicago, Illinois, to Denver, Colorado,
the typical cruising altitude of a passenger jet is approximately
38,000 feet. As the flight departs from O'Hare International Airport,
the jet begins to ascend. At 4.3 miles away from the airport, the jet
is at an altitude of 4200 feet. The jet reaches an altitude of 36,700
feet at 167.5 miles away from the airport.
Determine the slope of ascent of the flight given that 5280 feet = 1 mile.
Round your answer to the nearest thousandth.
The slope of ascent of the flight is 0.04
How to calculate the slope of ascent?From the question, we have the following parameters that can be used in our computation:
Typical cruising altitude = 38,000 feetInitial point of ascend = 4.3 miles at 4,200 feetAnother point of ascend = 167.5 miles at 36,700 feetThe above parameters can be represented as
(x, y) = (4.3, 4200) and (167.5, 36,700)
The slope is then calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (36700 - 4200)/(167.5 - 4.3)
Evaluate
Slope = 199.14 feet per mile
Recall that 5280 feet = 1 mile.
So, we have
Slope = 199.14 feet/5280 feet
Evaluate
Slope = 0.04
Hence, the required slope is 0.04
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K
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x)=200x+900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x) = 230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
units.
The cost at the break-even point is $
The revenue at the break-even point is
Answer: 30, 6900, 6900
Step-by-step explanation:
The break-even point is when cost equals revenue.
[tex]230x=200x+900\\\\30x=900\\\\x=30[/tex]
The cost and revenue at x=30 are both $6900.
Mariano is standing at the top of a hill when he kicks a soccer ball up into the air. The height of the hill is h feet,and the ball is kicked with an initial velocity of v feet per second. The height of the ball above the bottom of thehill after t seconds is given by the polynomial -16 + vt + h. Find the height of the ball after 2 seconds if it waskicked from the top of a 20 foot tall hill at 72 feet per second.O 100 ftO 32 ftO 20 ftO 132 ft
we have the equation
[tex]f(t)=-16t^2+vt+h[/tex]given values
t=2 sec
v=72 ft/sec
h=20 ft
substitute given values
[tex]\begin{gathered} f(t)=-16(2)^2+72\cdot2+20 \\ f(t)=100\text{ ft} \end{gathered}[/tex]therefore
the answer is the first optionWhen the engine falls out of Rhonda's old car, it's time to shop for something newer. She is hoping to keep her monthly payment at $140, and a loan will be 5% simple interest for 48 months with a $1000 down payment. Under these conditions, the most expensive car that Rhonda can afford is $6600.00. A salesman tries to convince Rhonda that she would be able to get a much better car if she raises the payment by just $30 per month.
The maximum value increase along with the down payment is $1200.
What is Down Payment?A down payment, sometimes known as a deposit in British English, is an upfront partial payment made when purchasing expensive goods or services like a home or car. At the moment the transaction is completed, it is often paid in cash or an equivalent. The remainder of the payment must then be financed using some kind of loan.
We need to calculate the value by which the price increases if she does raise the payment by $30
So, the total payment made by her = $140 +$30 = $170
This payment is made for 48 months at 5% simple interest
Total payments made= $170 × 48 = $8160
Let P be the total car value
P + SI = 8160
P + PTR = 8160
P(1+TR) = 8160
P = 8160/ (1+0.05 × 48 /12)
P= $6800
The maximum price that can be done is $6800 + down payment
hence the maximum price is $7800
Hence, the maximum value increase =$7800 - $6600= $1200
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Question: When the engine falls out of Rhonda's old car, it's time to shop for something newer. She is hoping to keep her monthly payment at $140, and a loan will be 5% simple interest for 48 months with a $1000 down payment. Under these conditions, the most expensive car that Rhonda can afford is $6600.00. A salesman tries to convince Rhonda that she would be able to get a much better car if she raises the payment by just $30 per month. What is the maximum value increase along with the down payment?
The question is in the ss
An algebraic expression that is equivalent to the given expression
(2c³)⁵(4c⁴) / (8c⁶)² is equal to 2c⁷.
As given in the question,
Given algebraic expression is equal to :
(2c³)⁵(4c⁴) / (8c⁶)²
Law of indices:
mᵃ × mᵇ = mᵃ⁺ᵇ
mᵃ ÷ mᵇ = mᵃ⁻ᵇ
To get equivalent expression simplify the given expression
(2c³)⁵(4c⁴) / (8c⁶)² using law of indices:
(2c³)⁵(4c⁴) / (8c⁶)²
= ( 2⁵c¹⁵) ( 2²c⁴) / ( 2³c⁶)²
=( 2⁵c¹⁵) ( 2²c⁴) / ( 2⁶c¹²)
= 2⁵⁺²⁻⁶ c¹⁵⁺⁴⁻¹²
= 2c⁷
Therefore, an algebraic expression that is equivalent to the given expression (2c³)⁵(4c⁴) / (8c⁶)² is equal to 2c⁷.
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Hello I need help with a question if you are able to assist.
We are given an equation that represents the path of the longest shot put by the women's track team as:
[tex]h(x)=-0.017x^2\text{ + 1.08x + 5.8}[/tex]Where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground.
Solution:
(a) The vertex of the model:
Method 1: We can plot the model on a graph and identify the vertex from the graph. The vertex is the lowest/highest point on the curve.
The graph is shown below:
From the graph, we can see that the vertex of the model is : (31.765, 22.953)
Method 2: The vertex of the model can also be calculated using the formula:
First, we find the x-coordinate using the formula:
[tex]x\text{ = -}\frac{b}{2a}[/tex]Substituting, we have:
[tex]\begin{gathered} x\text{ = -}\frac{1.08}{2\text{ }\times\text{ -0.017}} \\ x\text{ = 31.765} \end{gathered}[/tex]The y-coordinate of the vertex can be obtained by substituting the x-coordinate into the model. So, we have the y-coordinate to be:
[tex]\begin{gathered} y\text{ = h(31.765)} \\ y=-0.017(31.765)^2\text{ + 1.08(31.765) + 5.8} \\ y\text{ = 22.953} \end{gathered}[/tex]Hence, the vertex is : (31.765, 22.953)
(b) The maximum height
The horizontal distance of the maximum height of the shot put from the starting point is :
From the plot, the starting point is -4.98
[tex]\begin{gathered} \text{Horizontal distance = 31.765 + 4.98} \\ =\text{ 36.745 f}eet \end{gathered}[/tex]The maximum height of the shot put is 22.953 feet, 36.745 feet away from the starting point.
(c) The vertical intercept
The vertical intercept is the point where the curve cuts the y-axis.
From the graph, the point is (0, 5.8).
At this point where the horizontal distance is 4.98 feet away from the starting point, the shot put is 5.8 feet above the ground.
(d) The distance from the starting point to when the shot-put stikes the ground is:
From the plot, the intercepts on the x-axis are (-4.98, 0) and (68.509, 0).
Hence, the distance is:
[tex]\begin{gathered} =\text{ 68.509 + 4.98} \\ =\text{ 73.489} \\ \cong\text{ 73.49 f}eet\text{ (2.d.p)} \end{gathered}[/tex]