Ms. Cole has 4 yards of string. She cuts the string into pieces that are each 1/2 yard long. How many pieces of string does Ms. Cole have?

Answer:

$2.00

Step-by-step explanation:

2.50*.20=.5

2.50-.5= $2

The question involves calculating a 20% discount on a head of lettuce normally priced at $2.50. The discount amounts to $0.50, therefore the lettuce would cost $2.00 on Tuesdays.

The subject of this question is mathematics, specifically numerical problem solving involving discounts. Alan's Produce is having a 20% off sale on all produce on Tuesdays. If a head of lettuce normally costs $2.50, we need to calculate how much it would cost with the discount.

The discount can be calculated by multiplying the original price by the percentage reduction. So, $2.50 (the original price) times 20% (the discount) equals $0.50. This means the head of lettuce is $0.50 cheaper on Tuesdays.

Therefore, to find the discounted price, subtract this amount from the original price: $2.50 - $0.50 equals $2.00. So on Tuesdays, a head of lettuce at Alan's Produce would cost $2.00.

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Answer:

negative infinity

Step-by-step explanation:

f(x) = 3 x^7

As x approaches - infinity we do not care about the 3 since it is positive

f(-inf) = (- inf)^7

We can take the negative out since it is to a negative power

f(-inf) = - (inf)^7

inf raised to a power is still infinity

F(-inf) = - inf

It will approach negative infinity

Hello There!

They're in different places the 3 in the ones place couldn't equal as much as the three in the thousands place. It all depends on where the numbers are in relation to the decimal.

Answer:

a. 2 hours

Step-by-step explanation:

All you have to do is find the median between 40 minutes on Saturday, 1 hour 20 minutes on Monday, and 2 hours on Wednesday.

The median is 2. Therefore 2 hours is the answer.

Hope this helps!

Answer:

The correct answer is second option

3π in²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where r is the radius of the circle

To find the area of outer ring

Here radius of large circle = 1 + 1 = 2 in and

radius of small circle = 1 in

Area of outer ring  = Area of large circle - area of small circle

 =  π2² -  π1²

 = 4π - π

 = 3π in²

The correct answer is second option

3π in²

Answer:

3pi

Step-by-step explanation:

To find the area of the outer ring, we must first find the areas of the two circles. The red circle has a diameter of 2 which means the radius is 1. So the area of the red circle is pi.

Finding the area of the whole target, the radius is 2. So the total area is 4 pi.

So the area of the outer ring is 3pi

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) = (6, -2)\\(x_ {2}, y_ {2}) = (- 3,4)[/tex]

Substituting we have:

[tex]d = \sqrt {(- 3-6) ^ 2 + (4 - (- 2)) ^ 2}\\d = \sqrt {(- 3-6) ^ 2 + (4 + 2) ^ 2}[/tex]

Answer:

Option B

The distance between the points (-3, 4) and (6, -2) is calculated using the distance formula from the Pythagorean Theorem, resulting in approximately 10.82 units.

To calculate the distance between two points in a coordinate system, you can use the distance formula derived from the Pythagorean Theorem. This is expressed as:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Given the points (-3, 4) and (6, -2), you can plug these into the formula as follows:

d = √((6 - (-3))² + (-2 - 4)²)

d = √((6 + 3)² + (-6)²)

d = √(9² + (-6)²)

d = √(81 + 36)

d = √(117)

d ≈ 10.82

This result means the distance between the points (-3, 4) and (6, -2) is approximately 10.82 units.

Answer:

The x-coordinate of Q is 5

Step-by-step explanation:

* Lets revise the division of the line segment

- If point (x , y) divides a line segment internally whose endpoints are

 (x1 , y1) and (x2 , y2) at the ratio m1 : m2 from (x1 , y1), then:

# [tex]x=\frac{m_{2}x_{1}+m_{1}x_{2}}{m_{1}+m_{2}}[/tex]

# [tex]y=\frac{m_{2}y_{1}+m_{1}y_{2}}{m_{1}+m_{2}}[/tex]

* Lets solve the problem

∵ Point R divides PQ in the ratio 1 : 3

∴ R is (x , y)

∴ P is (x1 , y1) and Q is (x2 , y2)

∴ m1 = 1 and m2 = 3

∵ x-coordinate of R is -1 and the x-coordinate of P is -3

∴ x = -1

∴ x1 = -3

- Use the rule above

∵ [tex]-1=\frac{(3)(-3)+(1)(x_{2})}{1+3}=\frac{-9+x_{2}}{4}[/tex]

- By cross multiplication

∴ (-1) (4) = -9 + x2

∴ -4 = -9 + x2 ⇒ add 9 to both sides

∴ 5 = x2

* The x-coordinate of Q is 5

the x-coordinate of point O is -2.5.

The question deals with dividing a line segment in a given ratio and finding the coordinates of a point. We are told that point R divides line segment PO in the ratio 1:3, the x-coordinate of R is -1, and the x-coordinate of P is -3. We are asked to find the x-coordinate of point Q, presumably typo for O.

Using the section formula, which states that the coordinates of a point dividing a line segment in the ratio m:n can be calculated using the formula (mx2 + nx1) / (m + n) for x-coordinate, here we have m = 1, n = 3, x1 (P's x-coordinate) = -3, and R's x-coordinate = -1. So, we can calculate the x-coordinate of point O (Q seems to be a typo in the question) as follows:

(1×(-1) + 3×(-3)) / (1 + 3) = (-1 - 9) / 4 = -10 / 4 = -2.5

Therefore, the x-coordinate of point O is -2.5.

Answer:

b. it is not a function. it's not a function because I'm does not pass the horizontal lines test

Answer:

The correct option is B.

Step-by-step explanation:

Vertical line test: A vertical line intersects a function's graph at most once.

Horizontal line test: A horizontal line intersects a function's graph at most once.

If a graph passes the vertical line test, then it represents a function.

If a graph passes the horizontal line test, then its inverse is a function.

Check whether the given graph passes horizontal line test or not.

Let x-axis or y=0 be a horizontal line. The curve intersect x-axis at (-2,0) and (2,0).

Since the graph of the function intersect a horizontal line more than one time, therefore it does not passes the horizontal line test and inverse of the given function is not a function.

Hence the correct option is B.

Answer:

480 mm³

Step-by-step explanation:

The volume (V) of a pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × height, hence

V = [tex]\frac{1}{3}[/tex] × 96 × 15 = 32 × 15 = 480

Answer: C 1/3

Step-by-step explanation:

The +1/3 is the y-intercept and the -2/9 is the slope.

It is the same as y=mx+b, just that f(x) means function of x and is usually referred to as y.

Hello There!

Answer Attached In Image Below.

Have A Great Day!

Answer:

5/8

Step-by-step explanation:

0.625 as a fraction is equal to 5/8

When you place 625 over 1000 you get 5/8 when simplified:

625/1000 = 5/8

Answer: The m∠A is 55° and m∠B is 35°. Hope this helps

Step-by-step explanation:

Step 1: m∠A + m∠B = 90°

Step 2: m∠A + (m∠A − 20°) = 90°

Step 3: m∠A + (m∠A − 20°) = 90°

+20° = +20° Add 20° to both sides.

m∠A + m∠A = 110°

2(m∠A) = 110° Divide both sides by 2.

m∠A = 55°

Step 4: m∠A + m∠B = 90°

55° + m∠B = 90° Substitute 55° for m∠A.

m∠B = 35°

The measures of two complementary angles where one is 20° greater than the other, we set up equations based on the sum of their measures being 90°. Solving these equations, we find that the measure of angle A is 55° and the measure of angle B is 35°.

The measures of two complementary angles, where the measure of angle A is 20° greater than the measure of angle B. To find these measures, we can set up the following equations based on the properties of complementary angles:

Let m B be the measure of angle B.

Therefore, m A will be m B + 20° because it's given that angle A is 20° greater than angle B.

Since angles A and B are complementary, their measures must add up to 90°, hence m A + m B = 90°.

Substitute m A = m B + 20° into the equation m A + m B = 90° to get (m B + 20°) + m B = 90°.

Combine like terms to form 2m B + 20° = 90°.

Solve for m B by subtracting 20° from both sides to get 2m B = 70°.

Divide both sides by 2 to find m B = 35°.

Substitute m B = 35° into m A = m B + 20° to find m A = 35° + 20° = 55°.

Therefore, the measure of angle A is 55° and the measure of angle B is 35°.

Answer:

15 months needed

Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

We are required to simplify the following expression;

[tex]\frac{\sqrt{8y} }{\sqrt{y} }[/tex]

Using the properties of radicals;

[tex]\frac{\sqrt{a} }{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]

The expression can be re-written as;

[tex]\sqrt{\frac{8y}{y}}=\sqrt{8}[/tex]

Now;

[tex]\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}\\ \\2\sqrt{2}[/tex]

Answer:

yes it is possible for two different numbers to eventually have the same result

Step-by-step explanation:

its basically like saying five times 2 which is 10 and 2 times 5 which is also 10 its different numbers but same outcome

Answer:

Yes. Squared variables usually have two solutions, unless they are 0 (1 solution) or negative (no solution).

Step-by-step explanation:

Solving the generic x² = c has two solutions when c>0, one solution when c=0, and no (real) solutions for c<0.

When c>0, the solutions are x = √c and x= -√c.

Answer:

Cone

Step-by-step explanation:

Answer:

The answer is cone.

Step-by-step explanation:

Which of the following is a solid consisting of a disc, a point not in the same plane as the disc, and all the points between them?

The correct answer is a cone.

A cone is a solid consisting of a disc, a point not in the same plane as the disc, and all the points between them.

The disc specification is ruled out in cube and pyramid The point is ruled out in prism.

So, the answer is cone.

Answer:

B. Pairs

Step-by-step explanation:

A P E X

Answer:

Triplets

Step-by-step explanation:

just did it on pex learning

Answer:

B. 0.4

Step-by-step explanation:

Use the definition of the probability

[tex]Pr=\dfrac{\text{Number of all favorable outcomes}}{\text{Number of all possible outcomes}}[/tex]

You have to find the probability that a randomly selected reference book is hard cover. Hence, from the table

So, the probability is

[tex]Pr=\dfrac{10}{25}=\dfrac{40}{100}=0.4[/tex]

Hence, the probability that a randomly selected reference book is a hardcover is:

                             0.4

Let A denote the event that the book selected is a reference book.

and B denote the event that the book  is hardcover.

Let P denote the probability of an event.

We are asked to find:

                  P(B|A)

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

From the table we have:

[tex]P(A)=\dfrac{25}{60}=\dfrac{5}{12}[/tex]

and

[tex]P(A\bigcap B)=\dfrac{10}{60}=\dfrac{1}{6}[/tex]

Hence, we have:

[tex]P(B|A)=\dfrac{\dfrac{1}{6}}{\dfrac{5}{12}}\\\\\\P(B|A)=\dfrac{2}{5}\\\\\\P(B|A)=0.4[/tex]

           Hence, the answer is:

                 0.4

Answer:

D. y=-2x-6

Step-by-step explanation:

First start with what we know....

y = -2x + 3 (Slope Intercept Form)

Because of this we can eliminate B.  

Parallel means that the lines wouldn't be touching which means they should have the same slope and the only one with the same slope is D.

For this case we have that an equation of a line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

They give us the following information:

[tex]m = -2\\b = 3[/tex]

Then the line is:

[tex]y = -2x + 3[/tex]

They ask us to find a parallel line. By definition, if two lines are parallel then they have the same slope. Thus, the line sought is of the form:

[tex]y = -2x + b[/tex]

We look for the cut point "b" substituting the point where the line passes: [tex](2,2)[/tex]

[tex]2 = -2 (2) + b\\2 = -4 + b\\2 + 4 = b\\b = 6[/tex]

Finally, the line is:

[tex]y = -2x + 6\\y + 2x = 6[/tex]

Answer:

Option A

Answer:

Graph g(x) = 2x - 3

Step-by-step explanation:

Plug in (x+1) to f(x) = 2x - 5:

g(x) = 2(x+1) - 5 = 2x + 2 - 5

g(x) = 2x - 3

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Functions [tex]f(x)=2x-5[/tex] and [tex]g(x)=f(x+1)[/tex]

To find : Graph g(x)?

Solution :

First we find the function g(x),

As  [tex]g(x)=f(x+1)[/tex]

Finding f(x+1) by substituting x=x+1 in f(x)

[tex]f(x+1)=2(x+1)-5[/tex]      

[tex]f(x+1)=2x+2-5[/tex]  

[tex]f(x+1)=2x-3[/tex]          

Substitute in g(x),

[tex]g(x)=2x-3[/tex]

Now, To plot the g(x) we find the x-intercept and y-intercept

x-intercept, g(x)=0

[tex]2x-3=0[/tex]

[tex]x=\frac{3}{2}[/tex]

y-intercept, x=0

[tex]g(x)=2(0)-3[/tex]

[tex]g(x)=-3[/tex]

Plotting these two points draw the graph,

Refer the attached figure below.

Answer:

Only option C: The shortest side can equal 7 cm.

Step-by-step explanation:

Let the length of the shortest side be x cm, then the length of the longest side is 4x cm. Let the length of the middle side be y cm. Note that

[tex]x<y<4x[/tex]

The perimeter is

[tex]x+y+4x=60\\ \\5x+y=60[/tex]

A. The value x cannot be 40 cm, because then y is negative

B. If the longest side is 30 cm long, then

[tex]4x=30\\ \\x=7.5\\ \\y=60-5\cdot 7.5=22.5[/tex]

But

[tex]x+y=7.5+22.5=30\ cm[/tex]

This means that such triangle does not exist

C. If x=7 cm, then 4x=28 cm,

[tex]y=60-5\cdot 7=25\ cm[/tex]

Since,

[tex]7+25=32>28\\ \\7+28=35>25\\ \\25+28=53>7,[/tex]

such triangle exists and this option is possible

D. If x=25 cm, then y is negative

E. If x=5 cm, then 4x=20 cm and

[tex]y=60-5\cdot 5=35\ cm[/tex]

But this triangle does not exist, because [tex]5+20<35[/tex]

The longest side of this scalene triangle with a perimeter of 60 cm can equal 30 cm or the shortest side can equal 7 cm.

We can use the variables x, y and z to represent the shortest (x), medium (y) and longest (z) sides.  The perimeter of a triangle is found by adding together all of the sides; this gives us the equation

x + y + z = 60

We know that the longest side, z, is equal to 4 times the length of the shortest side, x.  This means that z = 4x; we can now write our equation as

x + y + 4x = 60

Combining like terms, we have

5x + y = 60

1.  Checking all of the possible options, we first determine if x can equal 40:

This would give us a negative side length, which is impossible.

2.  Let the longest side be 30 cm.  This means that the shortest side is 1/4 of that; 30÷4 = 7.5.  Using 7.5 for x,

This is within the range of acceptable side lengths, since it is between the smallest (7.5) and the largest (30).

3.  Let the shortest side be 7 cm.  This means x = 7:

This is between the longest side, 7 cm, and the longest side, 4(7) = 28 cm.  This is acceptable.

4.  Let the value of x be 25:

This will give us a negative value for the medium side, which is impossible.

5.  Let the shortest side be 5 cm.  This means x = 5:

This means the medium value, 35, would be greater than the longest side, 20; this is incorrect.

This means the correct options are that the longest side can be 30 cm and the shortest side can be 7 cm.

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Keywords:  perimeter of scalene triangle, finding side lengths of scalene triangles, finding perimeter

It can go into 100 feet 4 times. After you add four times you should have 97 and 4/8 or 97 and 1/2

Answer:  She can cut 49 pieces from the ball of string that’s is 100 feet.

Step-by-step explanation:  Given that Carla is cutting pieces of string that are exactly [tex]24\dfrac{3}{8}[/tex] inches long.

We are to find the number of pieces that she can cut from a ball of string with weight 100 feet.

We know that

1 feet = 12 inches.

So, 100 feet = 1200 inches.

Also, [tex]24\dfrac{3}{8}=\dfrac{195}{8}.[/tex]

Now, the number of pieces with length [tex]\dfrac{195}{8}[/tex] inches = 1.

So, the number of pieces with length 1 inch will be

[tex]\dfrac{1}{\frac{195}{8}}=\dfrac{8}{195}.[/tex]

Therefore, the number of pieces that can be cut from 1200 inches is given by

[tex]\dfrac{8}{195}\times1200=49.23.[/tex]

Thus, she can cut 49 pieces from the ball of string that’s is 100 feet.

The combination that represents less money than Miriam has (963 cents) is option C, which has a total of 956 cents.

First, let's remember the conversion of dollars, dimes, and pennies into cents. One dollar is equivalent to 100 cents, a dime is equal to 10 cents and a penny is one cent. So to solve the problem, we convert all the options into cents and find out which combination is less than 963 cents.

1. Option A: (9*100 cents) + (50*10 cents) + (1*1 cent) = 900 + 500 + 1 = 1401 cents

2. Option B: (900*100 cents) + (3*10 cents) + (8*1 cent) = 90000 + 30 + 8 = 90038 cents

3. Option C: (9*100 cents) + (5*10 cents) + (6*1 cent) = 900 + 50 + 6 = 956 cents

4. Option D: (900*100 cents) + (60*10 cents) + (2*1 cent) = 90000 + 600 + 2 = 90602 cents

Among all the options, option C is the only combination that is less than 963 cents.

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Answer:

27

Step-by-step explanation:

Evaluate the [tex]\sqrt[4]{81}[/tex] = 3

Since [tex]3^{4}[/tex] = 81

We are noe left to evaluate (3)³ = 27

Answer:

Option 2 is correct.

Step-by-step explanation:

Actual price = $500

After 2 years the worth of item is increased to = $551.25

We need to find the equation that represents y, the value of the item after x years.

According to given information the equation can be of form

[tex]y=500(r)^x[/tex]

where r represents the growth and x represents the number of yeras.

We need to find the value of r that represents the growth

The value of y = 551.25, and value of x = 2

Putting values and solving:

[tex]y=500(r)^x\\551.25 = 500(r)^2\\551.25/500 =(r)^2\\1.1025 = (r)^2\\Taking square root on both sides\\\\\sqrt{1.1025}=\sqrt{(r)^2}\\  => (r) = 1.05\\[/tex]

Putting value of r in the equation

[tex]y=500(r)^x[/tex]

[tex]y=500(1.05)^x[/tex]

So Option 2 is correct.

To solve the equation 10 ln(100x) - 3 = 117, first isolate the ln(100x) by adding 3 to both sides and then divide by 10. Exponentiate both sides with base e to remove the ln, and finally divide by 100 to solve for x.

We are given the equation 10 ln(100x) – 3 = 117. To solve for x, follow these steps:

10 ln(100x) = 120

ln(100x) = 12

100x = e^12

x = (e^12) / 100

Now, by using a calculator we can find the value of e^12 and then divide it by 100 to find the value of x.

Final answer is:  x = 1627.54

Answer:

Step-by-step explanation:

The largest number is 5. Therefore x ≥ 6.

Convert numbers from x system to decimal system:

[tex]42_x=4x+2\\\\53_x=5x+3\\\\125_x=1x^2+2x+5[/tex]

Solve the equation for x:

[tex]42_x+53_x=125_x\Rightarrow4x+2+5x+3=x^2+2x+5\qquad\text{combine like terms}\\\\(4x+5x)+(2+3)=x^2+2x+5\\\\9x+5=x^2+2x+5\qquad\text{subtract 5 from both sides}\\\\9x=x^2+2x\qquad\text{subtract}\ 9x\ \text{from both sides}\\\\0=x^2-7x\\\\x^2-7x=0\qquad\text{distributive}\\\\x(x-7)=0\iff x=0\ \vee\ x-7=0\\\\x=0<7\qquad\bold{it's\ not\ a\ solution}\\\\x-7=0\qquad\text{add 7 to both sides}\\\\x=7\qquad\bold{it's\ a\ solution}[/tex]

The answer is:

The last equation,

[tex]y+3=-6(x+9)[/tex]

To find which of the given equations represents a line that passes through the point (-9,-3) and has a slope of -6, we need to find an equation that can be satisfied by evaluating the given point.

We can see that the only equation that can be satisfied evaluating the point (-9,-3) is the last equation:

[tex]y+3=-6(x+9)[/tex]

Evaluating the point, we have:

[tex]-3+3=-6*(-9+9)[/tex]

[tex]0=-6*(0)[/tex]

[tex]0=0[/tex]

We can see that the equation is satisfied!

Also, we can see that evaluating the point into the other equations, they will not be satisfied.

Let's prove that:

Evaluating:

First equation:

[tex]y-9=-6(x-3)\\-3-9=-6*(-9-3)\\-12=-6*(-12)=72[/tex]

The equation is not satisfied.

Second equation:

[tex]y+9=-6(x+3)\\-3+9=-6*(-9+3)\\6=-6*(-6)=36[/tex]

The equation is not satisfied.

Third equation:

[tex]y-3=-6(x-9)[/tex]

[tex]-3-3=-6(-9-9)[/tex]

[tex]-6=-6(-18)=108[/tex]

The equation is not satisfied.

Hence, the correct option is the last option, the equation that represents a line that passes through (–9, –3) and has a slope of –6 is the last equation:

[tex]y+3=-6(x+9)[/tex]

Have a nice day!

Note: I have attached a picture for better understanding.

Answer: D. y + 3 = –6(x + 9)

​

Step-by-step explanation:

Answer:

150 yards.

Step-by-step explanation:

1 yard = 3 feet

To find how many yards 450 feet is, divide 450 by 3.

450/3 = 150

So, 150 yards. :)

The air that can circulate per​ minute will be 150 cubic yards.

The term “volume” refers to the amount of three-dimensional space taken up by an item or a closed surface. It is denoted by V and its SI unit is in cubic cm.

A typical air conditioner can move 450 cubic feet of air per minute. It can circulate 150 cubic yards of air per minute.

Unit conversion;

1 yard = 3 feet

1 feet = 1/3  yard

Volume in the cubic yard is calculated as;

450 feet = 450/3

450 feet = 150 cubic yard

Hence, the air that can circulate per​ minute will be 150 yards.

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Answer:

x = 75 and y = -72

Step-by-step explanation:

It is given that,

1/5 x + 1/8 y = 1   ------(1)

1/2 x − 1/3 y = 1  -------(2)

To find the solutions of the system of equations

Step 1: eq(1) * 5 ⇒

x + 5/8y = 5  ----(3)

Step 2:  eq(2) * 2 ⇒

x - 2/3y = 2  -----(4)

Step 3: eq(3) - eq(4) ⇒

x + 5/8y = 5  ----(3)

x - 2/3y = 2  -----(4)

0 +(5/8 - 2/3)y = 3

 -1/24 y = 3

y = -24*3 = -72

Step 4: Substitute the value of y in eq(1)

1/5 x + 1/8 y = 1   ------(1)

1/5 x + 1/8 (-72) = 1   ------(1)

1/5 x  - 24 = 1

1/5 x = 25

x = 5*25 = 75

Therefor x = 75 and y = -72

Answer:

[tex]x = \dfrac{110}{31}; \qquad y = \dfrac{72 }{31}[/tex]

Step-by-step explanation:

I am guessing that your two equations are

(1) ⅕x + ⅛y = 1

(2) ½x - ⅓ y = 1

To get rid of fractions, I would multiply each equation by the least common multiple of its denominators.

[tex]\begin{array}{rcrl}(3) \qquad 8x + 5y & = & 40 & \text{Multiplied (1) by 40}\\(4) \qquad 3x - 2y & = & 6 & \text{Multiplied (2) by 6}\\\end{array}[/tex]

We can solve this system of equations by the method of elimination.

[tex]\begin{array}{rcrl}(5) \qquad \, \, 16x + 10y & = & 80 & \text{Multiplied (3) by 2}\\(6) \qquad \, \: 15x - 10 y & = & 30 & \text{Multiplied (4) by 5}\\31x & = & 110 & \text{Added (5) and (6)}\\\\(7)\qquad\qquad \qquad x & = & \dfrac{110 }{31} & \text{Divided each side by 31}\\\end{array}[/tex]

[tex]\begin{array}{rcrl}3 \left (\dfrac{110}{31} \right) - 2y & = & 6 & \text{Substituted (7) into (4)}\\\\ (5) \qquad16x + 10y & = & 80 & \text{Multiplied (3) by 2}\\\\(6)\qquad 15x - 10 y & = & 30 & \text{Multiplied (4) by 5}\\\\31x & = & 110 & \text{Added (5) and (6)}\\\\(7)\qquad \qquad \qquad x & = & \dfrac{110 }{31} & \text{Divided each side by 31}\\\\3 \left(\dfrac{110}{31} \right ) - 2y & = & 6 & \text{Substituted (7) into (4)}\\\\\end{array}\\\\[/tex]

[tex]\begin{array}{rcll}\dfrac{330}{31} - 2y & = & 6 &\\\\-2y & = & 6 - \dfrac{330}{31} &\\\\y & = & \dfrac{165}{31} -3 & \text{Divided each side by -2}\\\\ & = & \dfrac{165 - 93}{31} &\\\\ & = & \dfrac{72}{31} &\\\\\end{array}\\\\\therefore x = \dfrac{110}{31}; \qquad y = \dfrac{72 }{31}[/tex]

The diagram below shows the graphs of your two functions intersecting at (3.548, 2.323). These are the decimal equivalents of your fractional coordinates.