Answer:
the requisite equation for the given question is y=−5x
Step-by-step explanation:
firstly, select the coordinates (0, 0) through which the perpendicular line will cross (0,0)
then, locate the slope when y=15x+2y=15x+2.
The slope is 1/5 when expressed in the slope-intercept format.
therefore, m=1/5
since, a perpendicular line's equation must have a slope equal to the inverse reciprocal of its initial slope.
therefore, [tex]m_{perpendicular}[/tex]=−1/(1/5)
To determine the slope of the perpendicular line, simplify 1/(1/5).
[tex]m_{perpendicular}[/tex]=−5
By using point-slope method, determine the perpendicular line's equation.
y+0=−5.(x+0)
Solve for y.
y= -5x + 0
y=−5x
hence, the answer for the question is y=-5x
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Approximately how much principal would need to be placed into an account earning 3.575% interest compounded
quarterly so that it has an accumulated value of $68,000 at the end of 30 years?
a. $23,706
b. $23,377
c. $52,069.
d. $58,944
Please select the best answer from the choices provided
The compound interest the answer is b)$23377.
What is compound interest?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
We know that for compound interest, A = [tex]P(1+\frac{r}{n})^n[/tex]
Where,
A = Future amount = $68,000
P = ??
r = 3.575% annual = 0.03575
n = 4 as interest is compounded quarterly
t = time in year = 30 years
Putting the values,
=> 68000 = P [tex](1+\frac{0.03575}{4})^{4*30}[/tex]
=> 68000 = P[tex](1+\frac{0.03575}{4})^{120}[/tex]
=> 68000 = P (1.0089375)[tex]^{120}[/tex]
=> P = $23377.5
Hence the correct option is b)$23377.
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A monopolistic firm's marginal revenue function is
dr 100q+43
dq q² +4q+3
=
where output (=demand) is measured in 100s of units/week and revenue is measured in
$1000s/week. The firm's marginal cost function is constant, de/dq= 3, and cost is also
measured in $1000s/week.
If the demand (= output) for the firm's good increases from 2000 units/week to 2500
units/week, then their weekly revenue increases by [Select]
and their
weekly profit changes by [Select]
Comment: pay attention to the units.
The weekly profit changes by $1000s/week.
What is profit?
The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.
To find the increase in weekly revenue, we need to find the difference in revenue at the two output levels:
2500 units/week: Revenue = 100(2500) + 43 = 2543
2000 units/week: Revenue = 100(2000) + 43 = 2043
So the increase in weekly revenue is 2543 - 2043 = $500s/week.
To find the change in weekly profit, we need to subtract the change in cost from the change in revenue:
Change in cost: 2500 units/week - 2000 units/week = 500 units/week * 3 $1000s/week/unit = 1500 $1000s/week
Change in profit: $500s/week - $1500s/week = -1000
Hence, the weekly profit changes by $1000s/week.
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80% of 40 please help me
Answer:
32
Step-by-step explanation:
0.8 x
Answer:
32
Step-by-step explanation:
Trapezoid ABCD has parallel sides AB and CD, of lengths 12 and 18, respectively. Diagonals AC and BD intersect at E. Draw the line through E that is parallel to AB and CD, and let P and Q be its intersections with DA and BC, respectively. Find PQ.
PQ is the length of the line segment that is parallel to AB and CD, which intersects DA at P and BC at Q. The length of PQ can be found using the Pythagorean Theorem.
Let PQ = x.
Since the line is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles.
Using the Pythagorean Theorem,
12^2 + x^2 = 18^2
x^2 = 18^2 - 12^2
x^2 = 324 - 144
x^2 = 180
x = √180
Therefore, PQ = √180
Since the line through E is parallel to AB and CD, the triangles APE, PQC, and BQD are all right triangles. Using the Pythagorean Theorem, we can calculate the length of PQ. We let PQ = x and set up the equation 12^2 + x^2 = 18^2. After solving for x^2, we get x^2 = 180, and x = √180. Therefore, PQ = √180. This is the length of the line segment that is parallel to AB and CD which intersects DA at P and BC at Q.
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Please answer it asap, it's missing
To find the value of ( f ∘ g ) (4), we need to first substitute 4 into the definition of g(x) and then substitute the result into the definition of f(x).
First we substitute 4 into g(x):
g(4) = -2(4) + 15 = -8 + 15 = 7
Now we substitute 7 into f(x):
f(g(4)) = f(7) = 7^2 - 5(7) - 2 = 49 - 35 - 2 = 12
So the value of ( f ∘ g ) (4) is 12.
Write an equation (any form) for the quadratic graphed below:
I added the photo of the graph
Check the picture below.
so we are really looking for the equation of a parabola whose vertex is at (2 , 3) and it passes through (4 , 1)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=2\\ k=3\\ \end{cases}\implies y=a(~~x-2~~)^2 + 3\hspace{4em}\textit{we also know that} \begin{cases} x=4\\ y=1 \end{cases}[/tex]
[tex]1=a(4-2)^2+3\implies -2=a(2)^2\implies -2=4a \\\\\\ \cfrac{-2}{4}=a\implies -\cfrac{1}{2}=a~\hfill \boxed{y=-\cfrac{1}{2}(x-2)^2 + 3}[/tex]
Find the area of the figure.
Answer:
1) 143 square inches
2) 32 square inches
3)152 square yards
4) 150 square inches
Step-by-step explanation:
Finding the area:1) Parallelogram:base= 11 in ;height = 13 in
[tex]\sf \boxed{\text{Area of parallelogram = base * height}}[/tex]
= 11 * 13
= 143 square inches
2) Triangle:base = 8 cm ; height = 8 cm
[tex]\sf \boxed{\text {Area of triangle = } \dfrac{1}{2}*base * height}[/tex]
[tex]\sf =\dfrac{1}{2}*8 * 8\\\\= 4 * 8\\\\= 32 \ in^2[/tex]
3) Kite:diagonal = p = 7 + 12 = 19 yd
diagonal 2 = q = 8 + 8 = 16 yd
[tex]\sf \boxed{\text{Area of kite =} \dfrac{pq}{2}}[/tex]
[tex]\sf =\dfrac{19*16}{2}\\\\= 19*8\\\\= 152 \ yd^2[/tex]
4)Trapezium:a = 13 in ; b = 12 ; h = 12 in
a,b are the parallel sides of the trapezium.
[tex]\sf \boxed{\text{Area of trapezium = }\dfrac{(a + b)*h}{2}}[/tex]
[tex]\sf = \dfrac{(13+12)*12}{2}\\\\\\=\dfrac{25*12}{2}\\\\=25*6\\\\= 150 \ in^2[/tex]
Determine the longest interval in which the given initial value problem is certain to have a unique twice differentiable solution. Do not attempt to find the solution.
the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
Initial value problem:
y'' + 4y' + 4y = 0, y(0)=1, y'(0)=2
The longest interval in which the initial value problem is certain to have a unique twice differentiable solution is the interval (-∞, ∞).
The given initial value problem is a second order linear homogeneous differential equation. This type of equation is known to have a unique twice differentiable solution on the interval (-∞, ∞). Therefore, the longest interval in which the initial value problem is certain to have a unique twice differentiable solution is (-∞, ∞).
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The area of a circle is 27 square meters. Determine the radius. Use 3 for pi
The radius of a circle with area of 27 square meters is 3 meters.
What is area of a circle?
The area of a circle is the space encircled or encompassed by its circumference. It is represented in the form of square units.
Area of circle(A)= πr^2
where 'r' represents the radius of the circle
We are given that area of a circle is 27 square meters i.e.
⇒πr^2 = 27
The value of π is 3
So, we get
⇒3r^2 = 27
⇒r^2 = 9
⇒r = 3
Hence, the radius of a circle with area of 27 square meters is 3 meters.
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What happens to the value of the expression m-10 as m decreases
1. Formulate a series and show a proof by PMI to validate.
2. Give at least one example each on the operations of functions.
3. In at least 50 words; What have you learned in GE4?
Series: 1 + 3 + 5 + 7 + 9 + ...
Proof by PMI:
P: The series starts with 1 and increases by 2 for each consecutive term.
M: The nth term of the series is 2n - 1.
I: The series is an arithmetic series with a common difference of 2.
Operations of functions:
Addition: (f + g)(x) = f(x) + g(x)
Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f + g)(x) = (2x + 1) + (3x - 2) = 5x - 1
Multiplication: (f * g)(x) = f(x) * g(x)
Example: f(x) = 2x + 1 and g(x) = 3x - 2, then (f * g)(x) = (2x + 1) * (3x - 2) = 6x^2 - 2x + 3x - 2 = 6x^2 + x - 2
GE4 is a mathematical modeling course, in which I have learned how to use mathematical methods and models to analyze and solve real-world problems. I learned how to use statistical analysis, optimization, and simulation to make predictions and decisions. I also learned how to use various tools and software to create and analyze models. I learned to use mathematical tools to solve problems in different fields such as finance, engineering, and science.
the quotient of 2 and 9
Answer: The quotient of 2 and 9 is 0.2222 (approximately) or 2/9
Step-by-step explanation:
Quotient is a mathematical term that refers to the result of dividing one number by another. In this case, the quotient of 2 and 9 is found by dividing 2 by 9, which results in 0.2222 (approximately) or 2/9.
It's important to note that the quotient is a decimal number because 9 doesn't divide into 2 exactly, so there is a remainder of 0.2222. The quotient represents the number of times 9 can be divided into 2, which is a fraction of a time. In this case, 9 can be divided into 2 only 0.2222 times.
I hope this helps :)
The quotient of 2 and 9 is the result of the division of 2 by 9 which is approximately 0.2222.
Explanation:The question is asking for the quotient of 2 and 9. The quotient is the result of division. So, to find the quotient of 2 and 9, you need to divide two by nine.
The calculation is as follows: 2 ÷ 9 = 0.2222 (rounded to the fourth decimal place).
So, the quotient of 2 and 9 is approximately 0.2222.
Always remember, that when the divider (the number we divide by) is larger than the dividend (the number to be divided), we get a quotient less than one.
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Fred is a weightlifter who can lift 800 pounds on 45% of his attempts. Which of these expressions represents the probability Fred will make 30 lifts out of 60? A. B(30,.45,60)B. B(30,800,60)C. N(30, 800,60) D. N(60, 45, 30)E. B(60, 45, 30)
Expression represents the probability of the given number of attempts and the success rate is given by option E. B( 60 , 45 , 30 ).
As given in the question,
In the given situation,
Let us consider 'n' represents the number of trials attempt by the weightlifter.
'p' represents the probability of success in his number of trials.
And 'r' represents the number of success out of his total number of attempts.
Here n = 60
p = 45%
r = 30
Using binomial distribution method we can represents the expression of the probability for the given condition :
B( n , p , r )
Substitute the values we get,
= B( 60, 45, 30 )
Therefore, for the given total number of lifts , success rate the expression represents the probability is given by option E . B ( 60, 45 , 30 ).
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Julie is rolling two trick number cubes she got with a magic set she purchased. Both of her number cubes have the number 5 on three of the faces, 10 on two of the faces, and 15 on one of the faces. Which of the following tables is a probability model for the sum of the two number cubes?
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-third, one-third, one-third.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 20, 30. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fourth, one-third, StartFraction 5 Over 18 EndFraction.
A 2-column table with 3 rows. Column 1 is labeled Sum with entries 10, 15, 20. Column 2 is labeled probability with entries one-fifth, one-fifth, one-fifth.
The probability of rolling two trick number cubes with the numbers 5, 10, and 15 on them can be calculated using the formula P(A) = n(A) / n(S), where P(A) is the probability of event A, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.
In this case, the total number of possible outcomes is 6, since there are six possible combinations of two number cubes. The number of favorable outcomes for a sum of 10 is 2, since there are two possible combinations (5 and 5, and 10 and 15). Therefore, the probability of rolling a sum of 10 is 2/6, or one-third. The probability of rolling a sum of 15 is also one-third, since there is only one possible combination (10 and 5). The probability of rolling a sum of 20 is one-sixth, since there is only one possible combination (10 and 10). Therefore, the probability model for the sum of the two number cubes is a 2-column table with 3 rows. Column 1 is labeled Sum with entries 5, 10, 15. Column 2 is labeled probability with entries one-half, one-third, one-sixth.
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Could someone help me
Answer: g = 3 sqrt n/ n
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
pamela decided to start a donut company that will focus on savory donuts. the cost of ingredients for each donut is $0.67. Pamela will sell each donut for $2.99. her goal by the ebd of the year is to make at least 4000. how many donuts will she need to sell in order to reach her goal
4000 donuts will Pamela need to sell in order to reach her goal.
What is the profit?
Profit is when the selling price is more than the cost price or revenue is more than the cost while loss is the opposite of profit.
To calculate the number of donuts Pamela needs to sell to reach her goal, you need to divide her desired profit by the profit per donut.
If the cost of ingredients for each donut is $0.67 and she plans to sell each donut for $2.99, the profit per donut would be $2.99 - $0.67 = $2.32.
To reach her goal of making at least 4000, she needs to make a profit of $2.32 x 4000 = $9280.
So she needs to sell $9280/$2.32 = 4000 donuts.
Hence, 4000 donuts will Pamela need to sell in order to reach her goal.
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find the values of x and y.
Answer:
how if there are no numbers or anything to find
Step-by-step explanation:
Determine the amount of semi-annual coupon paid for a 3% bond with a
face value of P100,000 which matures after 8 years. How many coupons
A semi-annual coupon bond is a bond that pays interest twice a year at a fixed rate.
To determine the amount of semi-annual coupon paid, you can use the following formula:
C = (r * FV) / n
Where:
C = coupon payment (semi-annual)
r = annual coupon rate (3% in this case)
FV = face value (100,000 in this case)
n = number of coupon payments per year (2 for semi-annual)
So, the semi-annual coupon payment for the bond is:
C = (0.03 * 100,000) / 2
C = 1500
The bond matures after 8 years, so the bond will pay 8*2 = 16 semi-annual coupons.
(PLEASE ANSWER BY TODAY) A car service charges $2.50 to pick you up and charges c cents for each mile of your trip.
Write an equation in the form y=mc+b that could represent the cost of a car based on the number of miles driven.
The linear equation for the given situation is y= cx + 2.50.
What is a linear equation?
A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. Such an equation on the graph, forms a straight line.
We are given that a car service charges $2.50 to pick us up and charges c cents for each mile of our trip.
So, the equation that represent the cost of a car based on the number of miles driven is given by:
y= cx + 2.50
Hence, the linear equation for the given situation is y= cx + 2.50.
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a heat source is applied to a metal surface, causing the temperature of the metal to increase with respect to time at a rate that is proportional to the sum of the metal's instantaneous temperature, t, and the metal's original temperature, to. select the differential equation that represents the relationship.
Answer:
the answer is d t d T = c ( T + T 0 )
Step-by-step explanation:
140/297 write as simplest Fraction form
Answer:
is already in the simplest form. It can be written as 0.47138 in decimal form (rounded to 6 decimal places).
Find the GCD of numerator and denominator
GCD of 140 and 297 is 1
When you divide both the numerator and denominator by 1
The answer will remain the same
In 2010, the population of a city was 144,000. From 2010 to 2015, the population grew by 8%. From 2015 to 2020, it fell by 7%. How much did the population decrease from 2015 to 2020, to the nearest 100 people?
Answer:
144600
Step-by-step explanation:
In 2010, pop'n 144,000.
From 2010 to 2015, the population grew by 8%.
so by 2015 = 144000*1.08 = 155520
From 2015 to 2020, it fell by 7%.
so 155520 * (1-7%) = 155520 * 0.93 = 144634
round to the nearest 100 = 144600
the perimeter of an athletic field is 352 m. if the width is 68 m, find the length. write your answer as an integer or simplified fraction
Answer:
108
Step-by-step explanation:
p=2(l+w)
352=2(l+68)
352=2l+136
2l=352-136
2l=216
l=108
Formula of Perimeter of rectangle( P ) = 2 ( l + b )
Perimeter = 352m
Width = 68m
Length = ?
Now
Perimeter ( P ) = 2 ( l + b )
352m = 2 ( l + 68m )
352m = 2l + 136m
352m - 136m = 2l
216m = 2l
[tex]l \: = \frac{216m}{2} \\ [/tex]
l = 108m
hence the length is 108m...
Ellie had 15 candies , after opening it she found out that 13 were not green, if she opens 3 or more packs , how many green candies should she expect
Answer:
She should expect 8 candies
Step-by-step explanation:
If 13 were not green that would leave 2 that were green which means that ( hoping that the same amount is in each one) if you count by 2's 3 more times you would get 8 and if there is more just continue counting by 2's
Maria clothing store sold $5230 worth of items last week. She invested half of her income
from the week in new items to sell. Then she paid herself $300 salary for the week. A
manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was
her ending balance?
Write the expression and find the balance.
(5230-300+500)/2; $2715
(5230/2)-300 + 500; $2815.
(5230/2) +500 - 300; $2815
Answer:
Step-by-step explanation:
Maria clothing store sold $5230 worth of items last week. She invested half of her income from the week in new items to sell.Then she paid herself $300 salary for the week. A manufacturer gave her a rebate of $500 for items that were reduced at the factory. What was her ending balance? Write the expression and find the balance.
you run an experiment in which you flip 3 coins, and each one lands heads or tails. your sample space can be written: {hhh, hht, hth, htt, thh, tht, tth, ttt}. assume all outcomes have equal probability.
The sample space consists of 8 possible outcomes, each with an equal probability of 1/8. The outcomes are the combinations of heads (h) and tails (t) when flipping 3 coins.
1. Determine how many possible outcomes there are in the sample space.
There are 8 possible outcomes in the sample space: hhh, hht, hth, htt, thh, tht, tth, and ttt.
2. Determine the likelihood of each result.
Since all outcomes have equal probability, the probability of each outcome is 1/8.
In this experiment, we are flipping three coins, and each one lands either heads (h) or tails (t). Our sample space consists of all the possible combinations of heads and tails that can occur when flipping the coins. Therefore, our sample space is {hhh, hht, hth, htt, thh, tht, tth, ttt}. Since all outcomes have equal probability, the probability of each outcome is 1/8. This means that the probability of each combination of heads and tails is the same. For example, the probability of getting 3 heads is 1/8 and the probability of getting 2 heads and 1 tail is also 1/8.
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Differentiate the given function.
y=x² √4x-3
Answer: I hope this helps you
Step-by-step explanation:
[tex]y=x^2\sqrt{4x-3}\implies \cfrac{dy}{dx}=\stackrel{\textit{\LARGE product rule}}{2x\sqrt{4x-3}~~ + ~~x^2\cdot \stackrel{\textit{chain rule}}{\cfrac{1}{2}(4x-3)^{-\frac{1}{2}}(4)}} \\\\\\ \cfrac{dy}{dx}=2x\sqrt{4x-3}~~ + ~~\cfrac{2x^2}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{8x^2-6x+2x^2}{\sqrt{4x-3}} \\\\\\ \cfrac{dy}{dx}=\cfrac{6x^2-6x}{\sqrt{4x-3}}\implies \cfrac{dy}{dx}=\cfrac{6x(x-6)}{\sqrt{4x-3}}[/tex]
Write an equation of the line that passes through point P and is
perpendicular to the line with the given equation.
P(1, 3), y = 2x - 1
Y is 1/3x +5 an equation of the line that passes through point P.
How the perpendicular lines calculated?The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=ab, then m=ba. Use the provided information to calculate the slope before attempting to discover a line's equation.The need for determining the perpendicular line is coordinates and a line equation. Think about a line with the equation axe + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. The slopes should add up to -1 if one line is perpendicular to this one.The slope of the new line will be equal to (1/3) = 1/3because perpendicular lines have slopes that are the negative reciprocals of one another.
X and Y are represented by X and Y, (x,y) is the pair of coordinates for the point, and m is the slope in this equation, which reads: Y - y = m(X-x).
Y-4 = 1/3(X-1), which leads to Y = 1/3X +1 +4 and Y = 1/3X +5.
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The following equations define a system.
2x + y = 10
−x + 2y = 5
Which graph represents the system?
The graph shows a line that passes through negative 5 comma 0 and 0 comma 2.5. There is a second line that passes through 0 comma 10 and 5 comma 0. The lines intersect at 3 comma 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma 10. There is a second line that passes through 0 comma 2.5 and 5 comma 0. The lines intersect at negative 3 comma 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 2.5. There is a second line that passes through 0 comma negative 10 and 5 comma 0. The lines intersect at 3 comma negative 4.
The graph shows a line that passes through negative 5 comma 0 and 0 comma negative 10. There is a second line that passes through 0 comma negative 2.5 and 5 comma 0. The lines intersect at negative 3 comma negative 4.
Option (a) is the correct answer i.e. the graph that shows a line that passes through negative 5 comma 0 and 0 comma 2.5, there is a second line that passes through 0 comma 10 and 5 comma 0 and the lines intersect at 3 comma 4, represents the system of given equations.
What is a system of equations?
A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations.
Given equations : 2x + y = 10 .......equation 1
−x + 2y = 5 ......equation 2
Let's take the equation : 2x + y = 10
when x=0, y = 10 and when y=0, x=5
So, the first line passes through (0,10) and (5,0).
Now, If we look at second equation : −x + 2y = 5
when x=0, y = 2.5 and when y=0, x= -5
So, the second line passes through (0,2.5) and (-5,0).
Now, we've −x + 2y = 5
we'll use substitution method to find out the intersection point.
multiplying it by 2, we get -2x + 4y = 10 ......equation 3
Adding equation 1 and 3,
we get, 5y = 20
y = 4
Putting y = 4 in equation 3,
we get, x= 3.
Hence, The intersection point is (3,4).
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The student government snack shop sold 32 items this week.
For each snack type, what percentage of all snacks sold were of that type? Do not round your answers.
The percentages of each snack type that were sold are given as follows:
Fruit cup: 25%.Veggie sticks: 18.75%.Chips: 43.75%.Water: 12.5%.How to obtain the percentage?A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.
Hence the percentages for each type are obtained as follows:
Fruit cup: 8/32 x 100% = 25%.Veggie sticks: 6/32 = 18.75%.Chips: 14/32 = 43.75%.Water: 4/32 = 12.5%.More can be learned about proportions at https://brainly.com/question/24372153
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