The ladder reaches approximately 26.11 feet up the wall.
What is trigonometric equations ?
Trigonometric equations are equations that involve trigonometric functions of one or more variables. The most common trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.
We can use trigonometry to solve this problem. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the distance we want to find is one leg, and the angle between the ground and the ladder is the angle opposite the leg we want to find. We can use the sine function to solve for the height h:
sin(65) = h/30
Multiplying both sides by 30, we get:
h = 30 * sin(65)
Using a calculator, we find:
h ≈ 26.11
Therefore, the ladder reaches approximately 26.11 feet up the wall.
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I need help with this please can you help me
The answer of the given question based on the following equations are the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
What is Variable?A variable is symbol or letter used to represent value that can change or vary. Variables are commonly used in the algebra and other branches of mathematics to represent the unknown quantities, as well as in a scientific and engineering applications to represent the physical parameters and measurements.
In algebra, variables are typically represented by the letters such as x, y, z, a, b, c, etc.
To solve this problem, we first need to solve each equation for its respective variable, a, b, and c.
a - 5 = 31
Adding 5 to both sides, we get:
a = 36
1/2b - 5 = 31
Adding 5 to both sides and multiplying by 2, we get:
b = 2(31 + 5) = 72
2c - 5 = 31
Adding 5 to both sides and dividing by 2, we get:
c = (31 + 5)/2 = 18
Therefore, the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
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simplify the square root of 10 divided by square root 8
Use the distributive property to simplify
12 • 3 3/4
Answer:
We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{12\times 3\dfrac{3}{4}}[/tex]
[tex]\mathtt{= 12 \times \dfrac{3\times4+3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{12 + 3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12\times15}{4\times1}}[/tex]
[tex]\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}[/tex]
[tex]\mathtt{= 45}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What happens to the mode of the data set shown below if the number 8 is added to the data set?
A. There is no mode.
B. The mode will not change.
C. There will be two modes.
D. The mode increases by 6.
9. In a recent taste test, 1017 out of 1250 people could not tell the difference between a popular soda's original flavor and the new calorie-fre
difference. Find a test statistic for the proportion.
z = 2.21
z = 1.38
z = 1.20
z = 0.39
Answer:
z=1.20
Step-by-step explanation:
Just Took Test
When you divide a whole number by a fraction how does the quotient compared to the dividend explain
When you divide a whole number by a fraction, the quotient is larger than the dividend.
This is because dividing a whole number by a fraction is the same as multiplying the whole number by the reciprocal (inverse) of the fraction.
For example, if we divide 6 by 1/2, it is equivalent to multiplying 6 by 2, which gives us a quotient of 12. So, the quotient of 12 is larger than the dividend of 6.
This happens because dividing by a fraction means we are dividing the whole into smaller parts, and the more parts we divide it into (i.e., the smaller the fraction), the more of those parts we get. Therefore, the quotient is larger than the dividend as we are getting more of the smaller parts.
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Devon measures and records his height every year. This year, as a fifth grader, his height is 423 feet. He has grown 116 feet since he was in second grade. What was Devon’s height when he was in second grade? Responses 213 feet 2 and 1 third feet 313 feet 3 and 1 third feet 312 feet 3 and 1 half feet 356 feet 3 and 5 sixths feet
Devon's height when he was in second grade was 312 feet 3 and 1 half feet.
The proper explanation of this answer is given below. Devon's height .
To arrive at this answer, we must subtract 116 feet from 423 feet, which is the height that Devon is currently measuring as a fifth grader. 423 feet - 116 feet = 307 feet. However, we know that his height was 312 feet 3 and 1 half feet, which is 5 feet more than 307 feet. Therefore, we can add 5 feet to 307 feet to get the answer, 312 feet 3 and 1 half feet.
The height that Devon is now measuring as a fifth grader is 423 feet, so we must subtract 116 feet from that measurement to get this answer. 307 feet Equals 423 feet minus 116 feet. Yet, we are aware of his height, which was 312 feet 3 and a half feet, or 5 feet taller than 307 feet. In order to obtain the solution, 312 feet 3 and a half feet, we can add 5 feet to 307 feet.
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A large retailer wants to estimate the proportion of Hispanic customers in a particular state. How large a sample size (of the retailer’s customers) do you need to estimate this proportion to within 0.04 accuracy and with 99% confidence? Assume there is no planning value for p* available. The sample size required is:......
To estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you need a sample size of 397 customers.
To accurately estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you will need a sample size of 397 customers. To calculate this, you will need to use the formula:
n = ( 2z × p* × q*) / e2
Where:
- n is the sample size
- z is the Z-score associated with the confidence level (in this case, it is 2.58 for 99%)
- p* is the planning value for the population proportion (in this case, it is not known, so it should be set to 0.5)
- q* is the compliment of p* (in this case, q* = 1 - 0.5 = 0.5)
- e is the desired accuracy (in this case, e = 0.04).
Substituting the values into the formula:
n = (2.582 × 0.5 × 0.5) / 0.042 = 397.
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Find the perimeter of a square if the length of its diagonal is 14.
? square root of ?
Answer:
28√2 units.
Step-by-step explanation:
Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:
√2 s = 14
Solving for "s", we can divide both sides by √2:
s = 14 / √2
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:
s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2
Now we can find the perimeter of the square by adding up the lengths of all four sides:
Perimeter = 4s = 4(7√2) = 28√2
Therefore, the perimeter of the square is 28√2 units.
Tom spent 2/3 of his pocket money to buy apples and spent 1/4 of the remaining money to buy some bananas. It cost Tim 45 dollars to buy the fruits. How many money did he have at first
Tom had 60 dollars as his pocket money initially.
Let's assume that Tom had x dollars as his pocket money.
He spent 2/3 of his pocket money on apples, which means he spent (2/3)x dollars on apples.
He had 1/3 of his pocket money left after buying the apples.
Out of the remaining money, he spent 1/4 on bananas, which means he spent (1/4)(1/3)x = (1/12)x dollars on bananas.
The total amount spent on apples and bananas is given as $45. So, we can write the equation:
(2/3)x + (1/12)x = 45
Multiplying both sides by 12 to get rid of the fractions:
8x + x = 540
Simplifying, we get:
9x = 540
Dividing both sides by 9:
x = $60
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What are the solutions to this equation?
1
-1
√17
-√17
There are no solutions.
Answer:
1 and -1
Step-by-step explanation:
[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]
[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]
[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]
[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]
Cube both sides of the equation:
[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]
[tex] {x}^{2} - 9 = - 8[/tex]
[tex] {x}^{2} = - 8 + 9[/tex]
[tex] {x}^{2} = 1[/tex]
[tex] {x}^{2} - 1 = 0[/tex]
[tex](x - 1)(x + 1) = 0[/tex]
[tex]x = 1 \: \: or \: \: x = - 1[/tex]
[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]
A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. What is the
speed of the plane in still air? What is the speed of the wind?
A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. The speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.
Let's use the following variables:
Let's call the speed of the plane in still air "p"Let's call the speed of the wind "w"When the plane is flying with the wind, its effective speed is p + w. When it is flying against the wind, its effective speed is p - w.
We know that the distance to Toronto and back is 630 km each way, for a total of 1260 km. We also know that the time it took to fly to Toronto with the wind was 7 hours, and the time it took to fly back against the wind was 15 hours.
Using the formula distance = speed x time, we can set up the following equations:
630 = (p + w) x 7 (equation 1)
630 = (p - w) x 15 (equation 2)
We now have two equations with two unknowns. We can solve for either p or w in terms of the other variable. Let's solve for p in terms of w.
From equation 1, we get:
p + w = 90
From equation 2, we get:
p - w = 42
Adding the two equations, we get:
2p = 132
So,
p = 66 km/h
Now we can use either equation 1 or equation 2 to solve for w. Let's use equation 1:
630 = (66 + w) x 7
Simplifying this equation, we get:
90 = 66 + w
w = 24 km/h
Therefore, the speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.
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If you were to have a data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids, this would be a perfect example of a normal distribution. True or false
False. A data set of the heights of 12-year-old boys would not necessarily follow a normal distribution pattern as it may be skewed or not evenly distributed around the mean.
False. A normal distribution is a type of probability distribution that takes the shape of a bell curve. It is characterized by having an equal number of values on either side of the mean, with the values in the middle being more numerous than those on the outside. A data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids would not necessarily fit this pattern. It is possible that the data set may be skewed in one direction or the other, depending on the height of the tallest and shortest boys in the group. It is also likely that the data will not be evenly distributed around the mean, as some boys may be taller or shorter than others.
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8. In a drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of (1 point)
7,000 km, what should be the diameter of the drawing of the planet?
3,500,000 mm
140 mm
14 mm
7,000 mm
Answer: The diameter of the drawing of the planet= 14 mm
Step-by-step explanation:
Given: In a drawing of the solar system the scale is 1 mm = 500 km
which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.
The diameter of planet =7000 kilometers.
Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]
Therefore, the diameter of the drawing of the planet= 14 mm.
Your retail garden store buys 500 plants at $2.49 each from the wholesaler. You plan to sell 75% of the plants to customers for the full retail price of $5.00. Ten percent will be sold to employees at a 20% markdown, and the final 15% will be sold on sale for 25% off at the end of the season. In the end, how much will the store make in net profits?
The store will make a net profit of $1,111.25 from selling the plants.
To find how much will the store make in net profits?
The first step is to calculate the total revenue from selling the plants:
Total revenue = (75% of 500) x $5.00 + (10% of 500) x $4.00 + (15% of 500) x $3.75Total revenue = 375 x $5.00 + 50 x $4.00 + 75 x $3.75Total revenue = $1,875 + $200 + $281.25Total revenue = $2,356.25Next, we need to calculate the cost of buying the plants from the wholesaler:
Cost of plants = 500 x $2.49
Cost of plants = $1,245.00
The net profit is then the difference between the total revenue and the cost of buying the plants:
Net profit = Total revenue - Cost of plants
Net profit = $2,356.25 - $1,245.00
Net profit = $1,111.25
Therefore, the store will make a net profit of $1,111.25 from selling the plants.
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c) when x is divided by 5 the result is 20
Answer:
x= 100
Step-by-step explanation:
x/5 = 20
multiply both the sides by 5 we get
5× x/5 = 20×5
x = 100
If the triangles shown at the right are similar,
what is the value of x?
a - 5in
b - 16.8in
c - 20.4in
d - 30.8
Answer:
b - 16.8in
Step-by-step explanation:
10/x=√34/√96
10/x=5.831/9.798
5.831x=97.98
x=16.803
For rhombus EFGH diagonals eg and fh intersect at k. The diagonals have lengths of EG = 36 and FH=14. What is the measure of
Therefore, the measure of the area of rhombus EFGH is 252 square units.
What is rhombus?A rhombus is a four-sided geometric shape that has the following properties:
All four sides are of equal length.
Opposite sides are parallel to each other.
The angles formed between adjacent sides are equal (i.e., they are all congruent).
The diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle. Additionally, the length of one diagonal is equal to the product of the length of the other diagonal and the sine of one of the angles formed by adjacent sides.
by the question.
[tex]EK^2 = EG^2/4 + KH^2 (where KH is half the length of FH)EK^2 = 36^2/4 + (14/2)^2EK^2 = 324 + 49EK^2 = 373EK = sqrt(373)[/tex]
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x power 4 -8 x power 2 y power 2+ 16 y power 4 -289
The values of x = 17 and y = 0.
Define quadratic equation?
A quadratic equation is a second-degree polynomial equation in one variable of the form a + b + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus", which means square.
Given:
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289[/tex] equals to 0
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289 = 0[/tex]
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} =289[/tex]
We know that [tex](x-b)^{2} =x^{2} -2xy +y^{2}[/tex]
Compare it: [tex](x^{2} -4y^{2} )^{2} = x^{4} - 8x^{2} y^{2} +16y^{4}[/tex]
So, [tex](x^{2} -4y^{2} )^{2} = 289[/tex]
[tex](x^{2} -4y^{2} ) = 17[/tex]
We know that [tex](x^{2} -b^{2} ) = (x+y)(x-y)[/tex]
So, [tex](x +2y)(x-2y) =17[/tex]
If we solve two equations that is:
(x+2y) = 17 and (x-2y) = 17
Simplification, x = 17 and y = 0
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In a state's Pick 3 lottery game, you pay $1.33 to select a sequence of three digits (from 0 to 9), such as 333. If you select the same sequence of three digits that are drawn, you win and collect $477.38. Complete parts (a) through (e). a. How many different selections are possible? b. What is the probability of winning? (Type an integer or a decimal.) c. If you win, what is your net profit? s ] (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.) e. If you bet $1.33 in a certain state's Pick 4 game, the expected value is $0.85. Which bet is better, a $1.33 bet in the Pick 3 game or a $1.33 bet in the Pick 4 game? Explain.
a. There are 1,000 different possible selections. b. The probability of winning is 1/1,000, or 0.001. c. If you win, your net profit is $476.05. d. The expected value is $0.476. e. The Pick 4 game is better.
a. There are 1,000 different possible selections (000 to 999).
b. The probability of winning is 1/1,000, or 0.001.
c. If you win, your net profit is $476.05. This can be calculated by,
$477.38 - $1.33 = $476.05
d. The expected value is $0.476. This can be calculated by,
$476.05 * 0.001 = $0.476
e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.
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The balance in an account earning simple interest varies jointly with principal (the amount invested), the annual interest rate, and time measured in years with a constant of proportionality of 1. If you receive $10,000 from a rich uncle for a graduation gift and invest it in a certificate of deposit that pays 5% simple interest for 50 years (approximately the number of years before you retire), how much will the account then be worth?
After 50 years, the certificate of deposit will be worth
Answer: $100,000
Step-by-step explanation:
$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.
Answer:
$35000
Step-by-step explanation:
account worth = deposit + simple interest
/ 100
intrest = deposit x year x simple interest
10000×50×5/100=25000
account worth = deposit + simple interest
= 10000 + 25000
= $ 35000
could you help me out with this question?
pleaseeeeeeeeeeeeeeeeeeeeeeee help
Answer:
1/5
Step-by-step explanation:
can yall help me again i still don't understand this
Answer:
52.
Step-by-step explanation:
So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.
Answer:
52 members
Step-by-step explanation:
Proportional setup.
(4/11)=(x/143)
A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces? six tops, three pants, two jackets There are a total of □ different outfits.
There are 36 different outfits that can be created using six tops, three pants, and two jackets.
Combinations:Combinations refer to the ways in which a set of objects or items can be arranged or chosen without regard to their order.
In mathematics, a combination is a selection of objects from a larger set, where the order of the selected objects does not matter.
Here we have
A designer has designed different tops, pants, and jackets to create outfits.
Number of options for tops = 6
Number of options for pants = 3
Number of options for jackets = 2
Here,
The total number of different outfits that can be created = (No of options for tops) × (No of options for pants) × (No of options for jackets)
= 6 × 3 × 2
Therefore,
There are 36 different outfits that can be created using six tops, three pants, and two jackets.
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Compare the area of this parallelogram
to the area of a rectangle with a length
of 7 cm and a width of 4.5 cm. Explain.
The area of the parallelogram will equal to Area of the rectangle
Area of parallelogram:
The area of a parallelogram is given by the formula:
A = b × hWhere A is the area of the parallelogram,
b is the length of the base of the parallelogram,
h is the height of the parallelogram.
Area of Rectangle:The area of a rectangle is given by the formula:
A = l × wWhere A is the area of the rectangle
l is the length of the rectangle
w is the width of the rectangle.
Here we have a Parallelogram
Where the height of the parallelogram is 4.5 cm and the length is 7 cm
Using the formula,
Area of parallelogram = 4.5 cm × 7 cm = 31.5 cm²
From the data,
The length of a rectangle is 7 cm and width is 4.5 cm
Using the formula,
Area of the rectangle = 7 cm × 4.5 cm = 31.5 cm²
Therefore,
The area of the parallelogram will equal to Area of the rectangle
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The complete question is given in the picture
work out the maxuim and minuim amount of hickers that could of walked between 8 and 19 miles help
The maximum and minimum amount of hickers that could of walked between 8 and 19 miles is 19 and 7.
What is minimum and maximum value?The minimum and maximum value depend on the context in which they are being used.
In mathematics, the minimum value refers to the smallest value in a set of numbers or a function, while the maximum value refers to the largest value in the same set of numbers or function. For example, in the set of numbers {2, 4, 5, 7}, the minimum value is 2 and the maximum value is 7.According to question:In general, the minimum and maximum values are the limits or boundaries within which a particular quantity or variable can vary.The minimum number of hikers who could have walked between 8 miles and 19 miles is 7 as it lies in the common interval of 10 ≤ x ≤ 15.The maximum number of hikers who could have walked between 8 miles and 17 miles is 19.To know more about minimum and maximum value visit:
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Are these numbers equivalent? 1/3(r^3) and (r^3)/3
1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
What is expression ?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated to produce a value.
Yes, 1/3(r³) and (r³)/3 are equivalent expressions.
This is because division is commutative, meaning that it doesn't matter in which order we divide the numbers. So, we can write (r³)/3 as (1/3)(r³), which is equivalent to 1/3(r³).
In both cases, we are dividing r³ by 3, and the result is the same. Therefore, 1/3(r³) and (r³)/3 are equivalent expressions.
1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
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This shape has been made from two identical isosceles triangles. Work out the size of angle x.
Angles - 25, x
The size of angle x is equal to 100°.
How to determine the value of x?Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:
m∠DAB = 25°
AD = BD = CD
In triangle ΔABD, we have:
AD = BD (Given)
m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)
m∠DBA = 25°.
Next, we would determine the measure of m∠ADB;
m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)
25° + 25° + m∠ADB = 180°
m∠ADB = 180° - 50°
m∠ADB = 130°.
Since ΔABD and ΔACD are two identical isosceles triangles, we have:
m∠DCA = m∠DBA
m∠DCA = 25°
Similarly, we have:
m∠DAC = m∠DAB = 25°
m∠ADC = m∠ADB = 130°
Generally speaking, we know that a complete revolution (circle) is equal to 360°:
m∠ADC + m∠ADB + m∠CDB = 360°
130° + 130° + x = 360°
x = 360° - 260°
x = 100°.
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HELP PLEASE
Determined to fill her water balloons before Diego, Lin fills her balloons at a rate of 1/3 ounce per second. She has already filled balloons with 8 ounces of water
Diego has filled balloons with 6 ounces of water. He continues to fill balloons at a rate of 2/3 an ounce per second.
1. Write an equation for Lin
2. Write and equation for Diego
3. What is the intersection point of the solution tell us about this situation?
1. An equation for Lin is y = 1/3x + 8.
2. An equation for Diego is y = 2/3x + 6.
3. The intersection point of the solution is (6, 10).
Let there have total number of balloons are y.
Lin fills her balloons at a rate of 1/3 ounce per second.
So she filled 1/3 x balloons.
She has already filled balloons with 8 ounces of water.
So the required equation is;
y = 1/3x + 8.................(1)
Diego fills her balloons at a rate of 2/3 ounce per second.
So he filled 2/3 x balloons.
He has already filled balloons with 6 ounces of water.
So the required equation is;
y = 2/3x + 6.................(2)
To determine the intersecting point we solve the both equation.
Subtract equation 1 and 2, we get
1/3x + 8 - 2/3x - 6 = 0
-1/3x + 2 = 0
Subtract 2 on both side, we get
-1/3x = -2
Multiply by -3 on both side, we get
x = 6
Now put the value of x in equation 1
y = 1/3 × 6 + 8
y = 10
To learn more about intersection point link is here
brainly.com/question/14217061
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