Answers
(revenue in year n) = (units sold in year n)*(price per radio in year n)
r(n) = (450 +50n)*(20 +n^2/45) = (10/9)n^3 +10 n^2 +1000n +9000
The cost for the production of all radios sold is given. Profit is then ...
(profit in year n) = (revenue in year n) - (cost in year n)
(profit in year n) = (10/9)n^3 +10n^2 +1000n +9000 -(1000 +10n^2)
(profit in year n) = (10/9)n^3 +1000n +8000
P(n) = (10/9)(n^3 +900n +7200)
b) The sum of numbers 1 to n is given by n(n+1)/2. The sum of numbers 1 to n^3 is given by (n(n+1)/2)^2. The sum of n constants is n*(the constant). Thus the sum T(n) of the terms of P(n) will be the sum of these polynomials multiplied by appropriate factors. It can be written in the form shown in the problem statement.
c) T(20) is computed to be 419,000, so is a little short of predicting the actual value of the contract.
Related Questions
To win at lotto in one state, one must correctly select 5 numbers from a collection of 58 numbers (1 through 58). the order in which the selection is made does not matter. how many different selections are possible?
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Find the total cost of a $619.50 refrigerator if the sales tax rate on the purchase is 2.8?
Answers
What is the solution of square root of-4x=100? x = –2500 x = –50 x = –2.5 no solution
Answers
-4x = 100² = 10,000
x = 10,000/-4 = -2500
The solution is ...
x = -2500
Brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. Determine the angles at which the fences of the three sides will meet.
Rounding each angle to the nearest degree: m<A=___degrees
Answers
The angle measures are ...
∠A = 115°
∠B = 27°
∠C = 38°
_____
You can use the Law of Cosines to solve for angle A, then the Law of Sines for the others.
A = arccos((1.5²+1.1²-2.2²)/(2*1.1*1.5)) = arccos(-1.38/3.3) ≈ 115°
C = arcsin(1.5/2.2*sin(115°)) ≈ 38°
B = 180° -115° -38° = 27°
The angles for Brian's triangular plot of farmland are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C.
To determine the angles of a triangular plot of land with sides measuring 1.1 miles, 1.5 miles, and 2.2 miles, we can use the Law of Cosines. The Law of Cosines states:
⇒ c² = a² + b² - 2ab × cos(C)
Let's label the sides as follows:⇒ a = 1.1 miles
⇒ b = 1.5 miles
⇒ c = 2.2 miles
First, we calculate ∠C (opposite side c):⇒ cos(C) = (a² + b² - c²) ÷ (2ab)
⇒ cos(C) = (1.1² + 1.5² - 2.2²) ÷ (2 × 1.1 × 1.5)
= (1.21 + 2.25 - 4.84) ÷ (3.3)
= (-1.38) ÷ (3.3)
= -0.4182
Then, we find ∠C by taking the inverse cosine (cos-1):⇒ ∠C ≈ 115°
Next, we calculate ∠A (opposite side a) using the same method:⇒ cos(A) = (b² + c² - a²) ÷ (2bc)
⇒ cos(A) = (1.52 + 2.22 - 1.12) ÷ (2 × 1.5 × 2.2)
= (2.25 + 4.84 - 1.21) ÷ (6.6)
= (5.88) ÷ (6.6)
= 0.8909
Then, we find angle A:⇒ ∠A ≈ 27°
Finally, we calculate angle B (opposite side b) using:⇒ ∠B = 180° - ∠A - ∠C
= 180° - 27° - 115°
= 38°
The angles at which the fences of the three sides will meet are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C, when rounded to the nearest degree.
Complete question:
Brian wants to fence in his triangular plot of farm land that measures 1.1 × 1.5 × 2.2 miles.
Determine the angles at which the fences of the three sides will meet.
Rounding each angle to the nearest degree:
If 2 fluid ounces equals 60 milliliters , how many milliliters are in 7 ounces of cough syrup
Answers
How do you solve 6<_2g?
Answers
You're left with 6 / 2 < g which equals 3 < g.
Use any method to solve the equation. If necessary, round to the nearest hundredth.
x^2 + x − 30 = 0
A. –5, 6
B. 10, –12
C. 5, –6
D. 5. 5, –5.5
Answers
Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.
In the method, we will split 30, in such factors, which when added or subtracted gives us 1, and when multiplied gives us -30.
So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.
Now, the equation will be written as -
x² - 5x + 6x - 30 = 0
Taking common, we get
x(x - 5) +6(x-5) = 0
(x-5)(x+6) = 0
So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6
Thus, the correct option is C). x = 5 and -6
Jane multiplied 825 x 22 and got 3,300. Flynn multiplied the same numbers and got 18,150. Which student is correct? What mistake did the other student make?
Answers
Find the equation for the plane through the points upper p 0 left parenthesis negative 2 comma negative 5 comma negative 4 right parenthesis, upper q 0 left parenthesis 5 comma 1 comma negative 4 right parenthesis, and upper r 0 left parenthesis negative 1 comma 2 comma 5 right parenthesis.
Answers
ax +by +cz = 1
By using the given point coordinates for x, y, and z, we end up with three equations in 3 unknowns. These can be described by the augmented matrix ...
[tex] \left[\begin{array}{ccc|c}-2&-5&-4&1\\5&1&-4&1\\-1&2&5&1 \end{array}\right] [/tex]
Putting this in reduced row-echelon form, we find
a = 54/35
b = -63/35
c = 43/35
The equation of the plane through [tex]P_{0}(-2,-5,-4), Q_{0}(5,1,4), R_{0}(-1,2,5)[/tex] is ...
54x -63y +43z = 35
Write the standard form of the number shown. three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven
Answers
The standard form of the given number is 3.89936206767 × 10¹¹
From the question, the given number is
three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven.
First, we will write the number in figures before writing it in standard form.
The number, three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven, written in figure is
389,936,206,767.
Now, to write in standard form,
A number is said to be in standard form, if it is written in form A × 10ⁿ. Where A is a number bigger than or equal to 1 and less than 10 ( That is, A ≥ 1 and A < 10)
and n is any positive or negative whole number
∴ The number, 389,936,206,767, written in standard form is 3.89936206767 × 10¹¹
Hence, the standard form of the given number is 3.89936206767 × 10¹¹
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The following data shows the weight, in pounds, of 6 boxes:
5, 3, 3, 4, 5, 4
What is the value of the mean absolute deviation of the weight of the boxes, and what does it represent about the weight of a box?
Answers
Hope this Helps!!
Write the equation of a circle with center upper c left-parenthesis 4 comma negative 5 right-parenthesis that passes through upper p left-parenthesis 1 comma negative 2 right-parenthesis number .
Answers
(4-1)² +(-5-(-2))² = 18
This is the square of the radius of the circle, so we can use it for r² in the formula
(x -h)² +(y -k)² = r² . . . . . . . circle of radius r and center (h, k)
Your circle has equation ...
(x -4)² +(y +5)² = 18
(n+8)+(n−12) =
what is the answer
Answers
The simplification of ( n + 8) + ( n -12 ) is 2(n -2)
algebraic expression are expression with unknown.
This unknown is represented by letters and in linear algebraic equations , the highest power of the unknown is 1.
Simplifying (n + 8) + (n-12)
n + 8 + n -12
collecting like terms
n + n + 8 -12
2n -4
we can further Factorize
2( n -2)
Therefore, the simplification of ( n + 8) + ( n -12 ) is 2(n -2)
Write 2018 to the power of 2019 + 2018 as the sum of two perfect squares
Answers
According to Brahmagupta-Fibonnaci identity
[tex]( a^{2} + b^{2}) (c^{2}+ d^{2}) = (ac+bd)^{2} + (ad-bc )^{2} [/tex]
Then, we can write that
[tex](13^{2}+ 43^{2})(( 2018^{1009})^{2} + 1^{2})[/tex]
[tex][(13*2008^{1009}+43)^{2} +(13-2008^{1009}*43)^{2}] [/tex]
Q.E.D
Answer: I, III, and IV only
Step-by-step explanation:
a student uses a solution that contains 16 grams of water to conduct an evaporation experiment
Answers
the correct option is:
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
Let's break down the calculations:
Step 1: Calculate the amount of water lost at the end of the first hour.
[tex]\[ \text{Amount lost} = 0.035 \times 16 = 0.56 \][/tex]
Step 2: Subtract the amount lost from the initial amount to find the remaining water at the end of the first hour.
[tex]\[ \text{Remaining water} = 16 - 0.56 = 15.44 \][/tex]
Step 3: Calculate the amount of water lost at the end of the second hour.
[tex]\[ \text{Amount lost} = 0.0425 \times 15.44 = 0.6562 \][/tex]
Step 4: Subtract the amount lost from the remaining water at the end of the first hour to find the remaining water at the end of the second hour.
[tex]\[ \text{Remaining water} = 15.44 - 0.6562 = 14.7838 \][/tex]
So, the correct option is:
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
The complete Question is given below:
A student uses a solution that contains 16 grams of water to conduct an evaporation experiment.
At the end of one hour, the amount of water in the solution has decreased by 3.5% .
At the end of two hours, the amount of water in the solution has decreased by another 4.25% .
Which calculations can be used to determine the amount of water, in grams, remaining in the solution at the end of the second hour?
a.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4:16-0.6562=15.3438
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
c.
Step 1:0.35 xx16=5.6
Step 2: 16-5.6=10.4
Step 3: 0.425 xx10.4=4.42
Step 4:16-4.42=11.58
d.
Step 1: 0.35 xx16=5.6
Step 2: 16-5.6=10.4
Step 3: 0.425 xx10.4=4.42
Step 4:10.4-4.42=5.98
# 11 Q . please solve the diagrama
Answers
The first choice is the correct
The area of a circle is = π r²
Substitute the given,which will give you this : π * 18² = 324 π in²
Hey can you please help me posted picture of question
Answers
So, 2, 2, 2 = B
See attached picture:
One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number of sterile males that mate with fertile females but produce no offspring. let p represent the number of female insects in a population and s the number of sterile males introduced each generation. let r be the per capita rate of production of females by females, provided their chosen mate is not sterile. then the female population is related to time t by t = p + s p[(r − 1)p − s] dp. suppose an insect population with 10,000 females grows at a rate of r = 1.2 and 400 sterile males are added. evaluate the integral to give an equation relating the female population to time. (note that the resulting equation can't be solved explicitly for p. remember to use absolute values where appropriate.)
Answers
[tex]t = \int { \frac{P+S}{P[(r - 1)P - S]} } \, dP [/tex]
Since r = 1.2 and S = 400, we get:
[tex]t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]} } \, dP [/tex]
= [tex] \int { \frac{P+400}{P(0.2P - 400)} } \, dP [/tex]
This is a rational function that we can write as:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} + \frac{B}{(0.2P - 400)} [/tex]
In order to evaluate A and B, let's calculate the LCD:
[tex]\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P - 400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)} [/tex]
which brings to:
P + 400 = 0.2AP - 400A + BP
= P(0.2A + B) - 400A
Since, the left side must be equal to the right side, we get the following system of equations:
[tex] \left \{ {{0.2A + B = 1} \atop {-400A = 400}} \right. [/tex]
Which gives:
[tex] \left \{ {{B=1.2} \atop {A=-1}} \right. [/tex]
Therefore, our integral can be written as:
[tex]t = \int { \frac{P+400}{P(0.2P - 400)} } \, dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP [/tex]
= [tex]- \int { \frac{1}{P} \, dP + 1.2\int { \frac{1}{0.2P-400} } \, dP[/tex]
= [tex]- \int { \frac{1}{P} \, dP + 6\int { \frac{0.2}{0.2P-400} } \, dP[/tex]
= - ln |P| + 6 ln |0.2P - 400| + C
We now have to evaluate the constant C. In order to do so, we consider that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5)
Therefore, the equation relating female population with time is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)
The equation relating females population with time is [tex]\boxed{t = - \ln \left| P \right| + 6\ln \left| {0.2P - 400} \right| - 12\ln \left( 5 \right) + 4\ln \left( {10} \right) - 36\ln \left( 2 \right)}.[/tex]
Further explanation:
Explanation:
The female population is related to time and it is given as follows,
[tex]t = \int {\dfrac{{p + s}}{{p\left[ {\left( {r - 1} \right)p - s} \right]}}dp}[/tex]
The sterile males are 400 and the growth rate is 1.2.
[tex]\begin{aligned}t&= \int {\frac{{p + 400}}{{p\left[ {\left( {1.2 - 1} \right)p - 400} \right]}}dp}\\&= \int {\frac{{p + 400}}{{p\left[ {0.2p - 400} \right]}}dp}\\\end{aligned}[/tex]
The expression [tex]\dfrac{{p + 400}}{{p\left[ {0.2p - 400} \right]}}[/tex] can also be expressed as follows,
[tex]\dfrac{{p + 400}}{{p\left[ {0.2p - 400} \right]}} = \dfrac{A}{p} + \dfrac{B}{{\left( {0.2p - 400} \right)}}[/tex]
Find the least common denominator.
[tex]\dfrac{{p + 400}}{{p\left( {0.2p - 400} \right)}} = \dfrac{{A\left( {0.2p - 400} \right)}}{{p\left( {0.2p - 400} \right)}} + \dfrac{{Bp}}{{p\left( {0.2p - 400} \right)}}[/tex]
[tex]\begin{aligned}p + 400 &= 0.2Ap - 400A + Bp\\p + 400 &= p\left( {0.2A + B} \right) - 400A\\\end{aligned}[/tex]
Equate left and right side of the expression to obtain the value of A and B.
[tex]\begin{aligned}0.2A + B &= 1\\- 400A &= 400\\\end{aligned}[/tex]
The value of A can be obtained as follows,
[tex]\begin{aligned}A&= \dfrac{{400}}{{ - 400}}\\A& =- 1\\\end{aligned}[/tex]
The value of B is 1.2.
Integral can be expressed as follows,
[tex]\begin{aligned}t &= \int {\frac{{p + 400}}{{p\left( {0.2p - 400} \right)}}dp} \\ &= \int {\left( {\frac{{ - 1}}{p} + \frac{{1.2}}{{\left( {0.2p - 400} \right)}}} \right)dp} \\&= - \int {\frac{1}{p}dp} + 6 \times \int {\frac{{0.2}}{{0.2p - 400}}dp}\\&= - \ln \left| p \right| + 6\ln \left| {0.2p - 400} \right| + C\\\end{aligned}[/tex]
At initial time the population is 10000.
[tex]\begin{aligned}- \ln \left| {10000} \right| + 6\ln \left| {0.2 \times 10000 - 400} \right| + C &= 0\\\ln \left| {10000} \right| - 6\ln \left| {1600} \right| &= C\\4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right) &= C\\\end{aligned}[/tex]
Substitute [tex]4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right)[/tex] for [tex]C.[/tex]
[tex]t = - \ln \left| p \right| + 6\ln \left| {0.2p - 400} \right| + 4\ln 10 - 36\ln \left( 2 \right) - 12\ln \left( 5 \right)[/tex]
The equation relating females population with time is [tex]\boxed{t = - \ln \left| P \right| + 6\ln \left| {0.2P - 400} \right| - 12\ln \left( 5 \right) + 4\ln \left( {10} \right) - 36\ln \left( 2 \right)}.[/tex]
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Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponential function
Keywords: exponential growth, growth rate model, pesticides, slowing, insect population, sterile males, mate, fertile, females, explicitly, female grows, integral, female insects, male insects, capita rate, chosen mate, generation.
Q9 Q13.) Find the products AB and BA to determine whether B is the multiplicative inverse of A.
Answers
See pictures below for the answer!
P.S. I think I answered this question already. I still have it on Microsoft Word :)
As always, it is my pleasure to help students like you!
Dave krug finances a new automobile by paying $6,500 cash and agreeing to make 40 monthly payments of $500 each, the first payment to be made one month after the purchase. the loan bears interest at an annual rate of 12%. what is the cost of the automobile?
Answers
D = [i/12]/[1-(1+i/12)^-12n] = [0.12/12]/[1-(1+0.12/12)^-40] = 0.03046
Therefore,
500 = (C-6,500)*0.03046
C-6,500 = 500/0.03046 = 16,417.34
C = 22,917.34
The cost of the automobile was $22,917.34
The cost of the automobile, excluding the impact of the interest, is $26,500.
Explanation:For this question, we need to determine the total cost of the automobile purchased by Dave Krug. We know that Dave made an upfront payment of $6,500, and also agreed to make 40 monthly payments of $500 each. The total amount paid through monthly payments is $500 * 40 = $20,000.
Here, it is also stated that the loan bears an annual interest rate of 12%. However, no additional data are given for us to calculate the impact of the interest on the overall cost of the car. So, we'll proceed without including the interest.
So, to find the total cost of the car, we combine the upfront payment with the total monthly payments. That is, $6,500 (upfront payment) + $20,000 (total monthly payments) = $26,500. Therefore, the cost of the automobile without taking into account the interest is $26,500.
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Final answer:For every mole of carbon dioxide used, one mole of methane is produced. Therefore, 71.1 moles of carbon dioxide would produce 71.1 moles of methane, assuming hydrogen is in excess.
Explanation:According to the given reaction, we can infer that the stoichiometric ratio between methane (CH4) and carbon dioxide (CO2) is 1:1. This means for each mole of methane produced, one mole of carbon dioxide is consumed. Therefore, if you are starting with 71.1 moles of carbon dioxide and assuming there is excess hydrogen, you would produce 71.1 moles of methane because of this 1:1 mole ratio.
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#SPJ3
write percent as a fraction or in simplest form of 37.5%
Answers
37.5% = 37.5/100 = 375/1000 = 3/8
The simplest form is 3/8, therefore the answer to your question is 3/8.
0.375 = 37.5%
Answer = 3/8
~Hope this helped~
Four pencils are held together with a band.
the figure on the right shows the bottom end of the pencils and the band.
each of the pencils has a diameter of 10mm
find the length of the band in this position.
give your answer in terms of pi.
Answers
Answer: (40+10π) mm.
Step-by-step explanation: Given diameter of the circle = 10mm.
Radius of the circle = 10/2 = 5 mm.
From the figure, we can see that each or the four corners makes a quarter of the circle.
And four corners would make the complete circle with radius 5mm.
Therefore, circumference of the four quarters of a circle = 2 π r
= 2 π (5) = 10 π.
Now, we can see that each side 10 mm of band also there.
So, the length of straight band on all four sides = 4 × 10 = 40 mm.
Total length of the band = (40+10π) mm
The length of the band is the number of units it covers
The actual length of the band is: [tex]\mathbf{40 + 10\pi}[/tex]
The diameter of 1 pencil is given as:
[tex]\mathbf{d = 10}[/tex]
The circumference of 1 pencil is:
[tex]\mathbf{C = \pi d}[/tex]
So, we have:
[tex]\mathbf{C = 10\pi }[/tex]
Multiply by 4, to calculate the circumference of all pencils
[tex]\mathbf{4C =4 \times 10\pi }[/tex]
[tex]\mathbf{4C =40\pi }[/tex]
The rubber band covers a quarter of the 4 pencils.
So, we divide by 4
[tex]\mathbf{C = 10\pi }[/tex]
The length of the band on one pencil is:
[tex]\mathbf{L = 10}[/tex]
Multiply by 4, for the 4 pencils
[tex]\mathbf{L = 40}[/tex]
So, the actual length of the band is:
[tex]\mathbf{Length = 40 + 10\pi}[/tex]
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Simplify.
600(1+0.03)^12
Answers
The above answer will be calculated as -
We are given -
600 ( 1 + 0.03)^12
We will first add - 1 + 0.03 = 1.03
Now, we will multiply 1.03 into 12 times, in order to find the value of ( 1.03)^12
The answer for ( 1.03)^12 = 1.4268
Now, we will multiply 1.4268 with 600
600 × 1.4268 = 856.08 approximately.
Thus, the value of 600*(1.03)^12 has been calculated.
the floor sheerly bedroom is a square with a perimeter of 60 ft what is the area of the floor of sherry bedroom
Answers
In a right rectangles pyramid with base edges a= 18 cm and b= 10 cm the slant height toward a is k= 13 cm while the slant height towards b is l= 15 cm. What is the surface area of the pyramid
Answers
rectangular base:
A = lw
18 x 10
A = 180 square cm
side a triangular lateral faces:
A = 1/2bh
1/2 x 18 x 13
A = 117 square cm x 2= 234 square cm
side b triangular lateral faces:
A = 1/2bh
1/2 x 10 x 15
A = 75 square cm x 2= 150 square cm
Add all the bold areas together:
150 + 234 +180 = 564
The surface area is 564 square cm.
Please help me with this
Answers
The explanation is shown below:
1. By definition, a geometric sequence is a sequence of numbers each number, after the first one, is the result of multiply the previous number by a common ratio.
2. The Option B has the following common ratio:
(2/3) / (4/9)=1.5
1/(2/3)=1.5
r=1.5
3. The Option E has the following common ratio:
-15/3=-5
75/-15=-5
r=-5
Q # 4 Solve the graph please <6. , <1. , <2. ,<4
Answers
∠7 + ∠4 = 180°
the area of a circle is about 254 cm what is the radius
Answers
To find the radius of a circle with an area of 254 cm², you can use the formula for the area of a circle by solving for the radius. We get the radius as 8.99 cm.
The radius of a circle can be found by using the formula for the area of a circle:
Given Area = 254 cm²Formula: A = πr²Solve for r: r = √(A ÷ π)Substitute in Area: r = √(254 cm² ÷ 3.14159)Calculate the radius: r ≈ √(80.865) ≈ 8.99 cmQ2 Q13.) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.
Answers
A (-5,-4) and B (5,10)
Part 1) write an equation for the line in point-slope form
we know that
the equation of a line in point-slope form is
y-y1=m*(x-x1)
step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5
strep 2
with m=7/5 and the point B (5,10)
find the equation of a line
y-y1=m*(x-x1)-----> y-10=(7/5)*(x-5)
the answer Part 1) is
y-10=(7/5)*(x-5)
Part 2) write an equation for the line in slope-intercept form
we know that
the equation of a line in slope-intercept form is
y=mx+b
step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5
step 2
with m=7/5 and the point B (5,10)
find b
y=mx+b
10=(7/5)*5+b-----> 10=7+b-------> b=3
the equation of the line is
y=(7/5)x+3
the answer Part 2) is
y=(7/5)x+3
hey can some one help me with this
Answers
First you have to find the surface area of what he is painting
Finding the areas of all the rectangles he is painting
14 * 8 = 112
14 * 8 = 112
12 * 8 = 96
12 * 8 = 96
12 * 14 = 168
Add all these up
112 + 112 + 96 + 96 + 168 = 584
Divide this by the amount of area a pint of paint covers
584 / 90 = 6.4888...
He needs 7 pints of paint because he needs more than 6
Multiply this by the cost of 1 pint of pint
7 * 7.98 = 55.86
The answer is $55.86
Hope this helps!
A = (8 ft)(14 ft) +(8 ft)(12 ft) +(8 ft)(14 ft) +(8 ft)(12 ft) +(14 ft)(12 ft)
A = (8 ft)*2*(14 ft +12 ft) +(14 ft)(12 ft) . . . . rearranging to simplify a bit
A = 2*(8 ft)(26 ft) +(14 ft)(12 ft)
A = 416 ft² +168 ft²
A = 584 ft²
6 pints of paint will cover 6*(90 ft²) = 540 ft², not quite enough. The next higher multiple of 90 ft² is 7*(90 ft²) = 630 ft², more than adequate.
Jake will need to purchase 7 pints of paint.
The cost of Jake's purchase will be 7*$7.98 = $55.86.