keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-\cfrac{4}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 2/3 and that it passes through (-3 , 2) in standard form
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-3)}) \implies y -2= \cfrac{2}{3} (x +3)[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-2)=3\left( \cfrac{2}{3} (x +3) \right)}\implies 3y-6=2(x+3)\implies 3y-6=2x+6 \\\\\\ 3y=2x+12\implies -2x+3y=12\implies {\Large \begin{array}{llll} 2x-3y=-12 \end{array}}[/tex]
In 2012, the population of a city was 5.04 million. The exponential growth rate was 1.65% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 7 million?
d) Find the doubling time.
Answer: It will take 24 years to have 7 million.
Step-by-step explanation:
1.65% of 5.04 million is 83,160.
2018 is 6 years from 2012.
83,160 x 6 = 498,960.
498,960k + 5,040,000mil =5,538,960mil. still not quite 7 million.
498,960k x 4 = 1,995,840mil.
1,995,840mil + 5,040,000mil = 7,035,840mil.
It will take the city 24 years to have 7 million.
I can text 65 words in 10 minutes. At this rate, how many words could I text in 12 minutes?
Solve for x in the equation 2 x squared 3 x minus 7 = x squared 5 x 39.
After solving the equation for x , we get the solution as x = 1 [tex]+[/tex] √47 and x = 1 - √47 .
In the question ,
it is given that ,
the equation in words is written as "2 x squared plus 3 x minus 7 [tex]=[/tex] x squared plus 5 x plus 39 " .
So , the equation in number can be written as
2x² [tex]+[/tex] 3x - 7 = x² [tex]+[/tex] 5x + 39
Making Like terms together ,
we get ,
2x² - x² [tex]+[/tex] 3x - 5x - 7 - 39 [tex]=[/tex] 0
(2 - 1)x² [tex]+[/tex] (3 - 5)x - 46 [tex]=[/tex] 0
x² - 2x - 46 [tex]=[/tex] 0
Applying quadratic formula in the above quadratic Equation ,
we get ,
x = -b ± √(b² - 4ac)/2a
From the given quadratic equation , we get that a = 1 , b = -2 and c = -46 .
So ,
x = -(-2) ± √((-2)² - 4(1)(-46))/2(1)
= 2 ± √(4 [tex]+[/tex] 4(46))/2
= 2 ± √4(1 [tex]+[/tex] 46)/2
= 2 ± 2√47/2
= 2(1 ± √47)/2
= 1 ±√47
x = 1 + √47 and 1 - √47 .
Therefore , After solving the equation for x , we get the solution as x = 1 + √47 and x = 1 - √47 .
The given question is incomplete , the complete question is
Solve for x in the equation , "2 x squared plus 3 x minus 7 = x squared plus 5 x plus 39 " .
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The gold trophy has 27 racers, she will 12 racers on the racetrack that runs.
How many racers did she have runs?
She will have run a total of 2.25 racers in 27 racers
How to determine the number of racers?From the question, we have the following parameters that can be used in our solution:
Total number of racers = 27 racers
Number of racers in a run = 12 racers
From the above parameter, we can calculate the total number of racers using the following equation
The total number of racers is calculated as
Total number of racers in the run = Total number of racers/Number of racers in a run
Substitute the known values in the above equation
So, we have the following equation
Total number of racers in the run = 27/12
Evaluate the quotient
Total number of racers in the run = 2.25
Hence, the total number of racers in the run is 2.25 racers
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-2 = 3x + 8/2 Solve for x.
Simplify your answer as much as possible.
Answer:
x= -2
Step-by-step explanation:
-2 = 3x + 8/2
-2+2=3x+4+2 (add 2 to both sides)
0=3x+6
-6=3x+6-6
3x=-6
x=-6/3
x= -2
Given the equation y=78x+15, what is the value of y when x is 4?
Answer:327
Step-by-step explanation:
Because you already have the equation, all you need to do is plug in the value for X. If X is equal to 4, our equation would look like this:
y = 78 * 4 + 15
Because of order or operations (PEMDAS), we do multiplication first.
y = 312 + 15
y = 327
Hope this helped!
I don't understand this question in my homework
The equation of line passes through the point (-6, -3) will be;
⇒ y = 5/3x + 7
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (-6, -3).
And, The parallel line is,
⇒ 5x - 3y = 9
⇒ y = (5x - 9) / 3
Now,
Since, The equation of line passes through the point (- 6, -3).
So, We need to find the slope of the line.
Since, The slope of the parallel line is same.
Hence, Slope of the line is,
y = 5/3x - 3
m = dy/dx = 5/3
m = 5/3
Thus, The equation of line with slope 5/3 is,
⇒ y - (-3) = 5/3 (x - (-6))
⇒ y + 3 = 5/3 (x + 6)
⇒ y + 3 = 5/3x + 10
⇒ y = 5/3x + 10 - 3
⇒ y = 5/3x + 7
Therefore, The equation of line passes through the point (-6, -3) will be;
⇒ y = 5/3x + 7
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2. Create a graph in the workspace provided to model the relationship that that exists if the school store is selling 5 pens (x) for $2.00 (y). Then find the constant rate of change.
Answer: The constant of variation, k , is 54
Step-by-step explanation: Step 1: Check whether the graph is a straight line. If the graph is not a straight line, it does not represent a proportional relationship. Step 2: Check whether the line goes through the origin. If the graph does not go through the origin, it does not represent a proportional relationship.
P
E
MD
AS
Simplify using
order of operations.
14 + 6 x 2-16+8
Answer: 18
Step-by-step explanation:
There are no parenthesis or exponents, so you use multiplication first.
6 x 2 = 12
That makes your equation 14 + 12 - 16 + 8
Now you only have adding and subtracting left, which you’ll do from left to right.
14 + 12 = 26
26 - 16 + 8
26 - 16 = 10
10 + 8 = 18
Hope this helps!
Determine whether AB and CD are parallel, perpendicular, or neither for A (-1,-1), B (1,5), C (1,2), D (5,4). Graph each line to verify your answer.
Answer:
you can do the favour of marking the answer brainlest pls
HELP MEE
−5g+(−2)−2g −7
Answer:
-7g - 9
Step-by-step explanation:
Subtract the numbers
-5g -2 -2g -7
-5g - 9 - 2g
Combine like terms
-5g - 9 - 2g
-7g - 9
Solution
-7g - 9
Answer:
-7g -9
Step-by-step explanation:
Just subtract and then combine like terms
Solve for w.
10 = |w + 9|
Write your answers as integers or as proper or improper fractions in simplest form.
w =
or w =
Rational zeros of polynomial function
Help!
Zeros of the given polynomial are -2, 2, -3/2, 3/2
What are zeroes of a polynomial?Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole.
Given a polynomial 1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36)
1/4(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0
(4[tex]x^{4}[/tex] - 25[tex]x^{2}[/tex] + 36) = 0
4[tex]x^{4}[/tex] - 16[tex]x^{2}[/tex] - 9[tex]x^{2}[/tex] + 36= 0
4[tex]x^{4}[/tex]([tex]x^{2}[/tex] - 4) - 9([tex]x^{2}[/tex] - 4) = 0
(4[tex]x^{4}[/tex]-9)([tex]x^{2}[/tex] - 4) = 0
(x+2)(x-2)(2x+3)(2x-3) = 0
x = -2, 2, -3/2, 3/2
Hence, Zeros of the given polynomial are -2, 2, -3/2, 3/2
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Which of these statements are true? Choose all answers that apply: (Choice A) Greater width relates to greater area as long as the width is less than 10 (Choice B) Greater width relates to greater area as long as the width is more than 10 (Choice C) To get the greatest area, the width should be 10 (Choice D) To get the greatest area, the width should be 20
The true statement about the function of area of by rectangle and width of rectangle are:
Greater width relates to greater area as long as the width is less than 10 To get the greatest area, the width should be 10The correct answer option is options A and D
Which width gives the maximum area of rectangle?A rectangle is a quadrilateral having opposing sides parallel and four right angles.
At point (x, y) = (10, 100) the area is maximum.
This means that the area of the rectangle is maximum when width is 10m.
If the width of the rectangle is more than 10m, the area reduces or decreases.
Therefore, the statement Greater width relates to greater area as long as the width is more than 10 m is false.
The statement "To get the greatest area, the width should be 20" is false.
Complete question:
Simon has a certain length of fencing to enclose a rectangular area. The function A, models give the rectangles area (in square meters) as a function of its width (in meters).
Wlhich of these statements are true?
A. Greater width relates to greater area as long as the width is less than 10.
B. Greater width relates to greater area as long as the width is more than 10.
C. To get the greatest area, the width should be 10
D. To get the greatest area, the width should be 20
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Use the figure below for the following problems (not drawn to scale).
Given: m/1 = 70,
What is m/4?
O a 125⁰
.Ob
70°
Oc
40°
Od
55°
5
6
The measure of angle 4 is 125° for the given triangle.
According to the question,
We have the following information:
A figure is given of triangle and its exterior angles.
m∠1 = 70°
Now, the two sides (with line on them) of the triangle are equal. So, it means that it is an isosceles triangle.
We know that sum of three angles of a triangle is 180°.
Let's take the two equal angles to be x°.
x+x+70 = 180
2x+70 = 180
2x = 180-70
2x = 110
x = 110/2
x = 55°
We know that angles made on a straight line is 180°.
∠4 and angle x will make a straight line.
∠4 = 180-55
∠4 = 125°
Hence, the correct option is A.
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Express this equation
C The graph
represents the
balance in
Jimena's
checking account
based on the
number of days
since her last
paycheck.
9. The graph can be represented by
y = 450x - 25.
True or False? If false rewrite statement correctly
Answer:
False
Step-by-step explanation:
The correct answer is y = -25x + 450
A population of beetles grows by 25% every month. If the beetle population starts
with 1, 600 beetles, which equation represents the population, P, after t months?
OP= 1,600(0.25)*
OP= 1,600(1.25)
OP 1,600 +0.25t
OP= 1,600 +1.25t
Answer:
Step-by-step explanation:
Morgan got a 42 out of 40 points on her American Government quiz due to an extra credit question. What is her grade as a mixed number in simplest form?
Answer: 1 -1/20
Step-by-step explanation:
Based on the given conditions, formulate: 42 divided by 40
Cross out the common factor: 21/20
Convert to mixed fraction: 1- 1/20
Joseph takes out a loan that gathers compound interest.
The table below shows the value of the loan over time.
a) What is the rate of interest per annum?
Give your answer as a percentage to 1 d.p.
b) Work out the value of the loan 10 years after it starts.
Give your answer in pounds (£) to the nearest 1p.
Start
£7500.00
After 1 year
£7965.00
After 2 years
£8458.83
Answer:
a) 6.2%
b) £13,687
Step-by-step explanation:
a)
To find the rate of interest, we first find the interest itself.
£7965.00 - £7500.00 = £465.00
Using this, we find the rate of interest in percentage as a fraction of the original loan.
(£7500.00 ÷ £465.0) × 100 = 6.2%
Thus, the rate of interest is 6.2%.
b)
Compound interest is found using the formula
[tex]A = P(1 + \frac{r}{100})^{t}[/tex]
Where
A = final amount
P = initial principal balance
r = interest rate
t = number of time periods elapsed
Thus, with an initial balance of £7500, an interest rate of 6.2% and a time period of 10 years, calculated per annum, we can plug the numbers into the formula, giving us
[tex]A = 7500(1 + \frac{6.2}{100})^{10}[/tex]
[tex]=[/tex] £13,686.94
≈ £13,687 (to nearest £1)
Some things to note: number of time periods elapsed mean the amount of times it is compounded; if the question says compounded quarterly for 3 years, t = 12 as it is compounded 4 times a year for 3 years, giving is 12 time periods. This also applies to monthly, bi-weekly etc.
need help with this one
Answer:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Step-by-step explanation:
Point Form:
[tex](\frac{2}{3} ,-\frac{5}{3}) , (-1, -5)[/tex]
Equation Form:
x= [tex](\frac{2}{3}[/tex], [tex]-\frac{5}{3} )\\[/tex] , y= [tex]-\frac{5}{3}[/tex]
x = -1 , y =-5
Hope this answer your question... sorry I couldnt help more, if it didnt.
Find the original price given each total amount and rate of increase. Round to the nearest cent if necessary. 83.82. 10%
The original amount is $92.202.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.
Given:
Total amount = 83.82
rate of increase = 10%
So, the original amount
= 83.82 + 83.82 x 0.1
= 83.82 + 8.382
= $92.202
Hence, the original amount is $92.202.
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solve the equation 15 < b - 4
Answer:
b>19
Step-by-step explanation:
15<b−4
Rewrite so b is on the left side of the inequality.
b−4>15
Move all terms not containing b to the right side of the inequality.
Add 4 to both sides of the inequality.
b>15+4
Add 15 and 4.
b>19
b>19
The result can be shown in multiple forms.
Inequality Form:
b>19
Interval Notation:
(19,∞)
Sarah took a survey asking students if they prefer summer or winter sports. She found that 12 out of 18 students prefer summer sports. Determine what fraction of students prefers winter sports. Write your response in simplest form. Explain how you found your answer.
Answer: 2/3
Step-by-step explanation:
12 out of 18 prefer summer sports so as a fraction it would be 12/18 = 6/9 = 2/3
Answer:
33.3333%
Step-by-step explanation:
EXPLANATION
Based on the given conditions, formulate: (18-12) ÷ 18
Calculate the sum or difference:[tex]\frac{6}{18}[/tex]
Cross out the common factor:[tex]\frac{1}{3}[/tex]
Rewrite a fraction as a decimal: 0.333333
Multiply a number to both the numerator and the denominator: 0.333333x[tex]\frac{100}{100}[/tex]
Write as a single fraction:[tex]\frac{33.33333x100}{100}[/tex]
Calculate the product or quotient:[tex]\frac{33.333}{100}[/tex]
Rewrite a fraction with denominator equals 100 to a percentage: 33.3333%
Answer: 33.3333%
How to solve this mathematical question
Answer:
Part B: (0, -6)
Part C: x = -1
Part D: (-1, -8)
Explanation:
see the attached pdf
Rain fell at a constant rate for 2 hours on Friday. During that time, the total amount of rain that fell was 3/4 inch. what is the rate, in inches per hour, at which rain fell during that time on Friday?
3 1/3
1 7/8
8/15
3/10
The rate, in inches per hour, at which the rain fell during that time on Friday is 3/8 inches per hour.
Time for which the rain fell = 2 hours
The total amount of rain that fell = 3/4 inch
So, in 2 hours, the amount of rain that fell = 3/4
In 1 hour, the amount of rain that fell = 3/8 inches
Hence, The rate, in inches per hour, at which the rain fell during that time on Friday = 3/8 inches per hour.
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Solve the following:-
[tex]\sf \cfrac{x}{11} + 16 = 30[/tex]
Answer:
x = 154
Step-by-step explanation:
[tex]\frac{x}{11}[/tex] + 16 = 30 ( subtract 16 from both sides )
[tex]\frac{x}{11}[/tex] = 14 ( multiply both sides by 11 to clear the fraction )
x = 11 × 14 = 154
Answer:
x = 154
Step-by-step explanation:
Given equation,
→ (x/11) + 16 = 30
Now the value of x will be,
→ (x/11) + 16 = 30
→ x/11 = 30 - 16
→ x = 14 × 11
→ [ x = 154 ]
Hence, value of x is 154.
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket. Use pencil and paper. Draw a graph of the equation and explain why the line should only be in the first quadrant.
The equation where y is the price of the ticket with the coupon, and x is the original price of the ticket.
y= 0.55 x.
Given:
A movie theater sends out a coupon for 45% off the price of a ticket. Write an equation for the situation, where y is the price of the ticket with the coupon, and x is the original price of the ticket.
If x is the price of the ticket without the coupon, and the theater offers a discount if you have a coupon, then having a coupon means that the price a person ultimately pays (y) is the original price (x) minus a 45% of this price:
y= x -0.45 x
By association: y= (1-0.45) x
and then y= 0.55 x.
The line should be in the first quadrant because the first quadrant allows you to represent a situation in which the dependent variable (y) and the independent variable (x) are both positive. This is the case in this exercise, because both prices, the one without discount (x) and the one with discount (y) are necessary positive (you can not pay a negative price!).
Hence we get the required equation.
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determine the sum of the first 8 terms of the geometric sequence if the first term is 5, the common ratio is -2 and the 8th term is -640
Answer:
-425
Step-by-step explanation:
You want the sum of the first 8 terms of the geometric series with first term 5 and common ratio -2.
Series sumThe sum is given by the formula ...
Sn = a1·(r^n -1)/(r -1) . . . . . . a1 = first term, r = common ratio
The sum of 8 terms of the given series is ...
S8 = 5·((-2)^8 -1)/(-2 -1) = 5(255/-3) = -1275/3 = -425
The sum of 8 terms is -425.
A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600
nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of 28° off a direct heading to
Barbados. The captain maintains the 22-knot speed for 15 hours, after which time the path to Barbados becomes clear of
storms.
(a) Through what angle should the captain turn to head directly to Barbados?
(b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained?
(round to one decimal place)
Answer: A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600 nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of
20
∘
off a direct heading to Barbados. The captain maintains the 22-knot speed for 9 hours, after which time the path to Barbados becomes clear of storms. (a) Through what angle should the captain turn to head directly to Barbados? (b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained? (a) The captain should head through an angle of (Do not round until the final answer. Then round to one decimal place as needed.) (b) The time it will take for the ship to reach Barbados is hours (Do not round until the final answer. Then round to one decimal place as needed.)