The constant of proportionality for the relationship is p = 75.
How to express proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
In other words, a proportional relationship is one in which two quantities vary directly with each other.
It can be represented as follows:
y = px
where
p = constant of proportionalityx and y are the variablesTherefore, when we are given the variables the constant of proportionality can be found as follows:
where
y = 150
x = 2
p = y / x
p = 150 / 2
Therefore,
p = 75
Complete question: Determine the constant of proportionality for the relationship: y = px where y = 150 and x = 2
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The Manitou Incline, which leads to the top of Pikes Peak in Colorado, climbs from an elevation of 6574 feet to 8585 feet above sea level. The fastest reported time for running up the incline is 16 minutes and 42 seconds, by Mark Fretta. How many vertical feet per second did Mark climb during his record breaking performance? ( Round to 1 decimal digit.)
Answer:
2.0 vertical feet per second
Explanation:
First, determine the vertical distance covered by Mark.
[tex]\begin{gathered} \text{Vertical Distance=}8585-6574 \\ =2011\text{ ft} \end{gathered}[/tex]Next, convert the fastest reported time for running up the incline( 16 minutes and 42 seconds) to seconds.
[tex]\begin{gathered} 16\text{ mins 42 seconds = (}16\times60)+42 \\ =960+42 \\ =1002\text{ seconds} \end{gathered}[/tex]Finally, determine Mark's vertical feet per second:
[tex]\begin{gathered} \text{Mark's vertical sp}eed\text{ per second=}\frac{2011}{1002} \\ =2.007\text{ ft per second} \\ \approx2.0\text{ ft per second (to 1 decimal digit)} \end{gathered}[/tex]Mark climbed at a rate of 2.0 vertical feet per second.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Yesterday a chef used 32 eggs to make 2 chocolate souffles and 6 lemon meringue pies. The day before, he made 2 chocolate souffles and 10 lemon meringue pies, which used 48 eggs. How many eggs does each dessert require? A chocolate souffle requires __ eggs and a lemon meringue pie requires __ eggs.
the system of equations above represent the question, we need to solve the system in order to know the number of eggs necessary for each dessert
x is the number of eggs used to make the chocolate souffle.
y is the number of eggs used to make lemon meringue pies.
First, we need to multiply the second equation with -1 so we have
[tex]-2x-10y=-48[/tex]we will sum the first equation with the equation above
[tex]\begin{gathered} -4y=-16 \\ y=\frac{-16}{-4}=4 \\ y=4 \end{gathered}[/tex]we substitute the value of y in the first equation
[tex]\begin{gathered} 2x+6(4)=32 \\ 2x+24=32 \\ 2x=32-24 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \end{gathered}[/tex]A chocolate souffle requires 4 eggs and a lemon meringue pie requires 4 eggs.
What’s the correct answer answer asap for brainlist
Answer:
Iron
Step-by-step explanation:
Just learned about this
Answer:
C. Hydrogen
Step-by-step explanation:
Carbon, Hydrogen, Oxygen, and Nitrogen are most commonly found in lipids.
if this helps you, pls leave a heart. if it dosent, im so sorry. :(
If one angle in a linear pair is 110 degrees, what is the measureof the other angle?
The other angle = 70°
Explanations:When two angles are form a linear pair , then they are supplementary. That is, they add up to give <180°
The first angle = 110°
Let the second angle be x
110 + x = 180
x = 180 - 110
x = 70°
The measure of the other angle is 70°
Fill in the blanks to correctly complete the sentence.To perform the division x-3)x³ + 6x² + 4x, begin by writing the synthetic division problem shown below.0)1040
The division is given by
x^3+6x^2+4x : (x-3)
therefore
The answer is
3 1 6 4 0
Options for the first box: (0,1), (0,0), (1,0) Options for the second box: increases and decreases Options for the third box: x=-1, x=1, x=0 Options for the fourth box: Decreases to negative infinity and increases to positive infinity
To answer this question we can use the graph of the logarithm:
From this graph we conclude that:
Function f crosses the x-axis at (1,0). As x increases the function increases. As x approaches its vertical asymptote of x=0, the function decreases to negative infinity.
Which of these are equivalent to 11/4 choose all that apply
Answer: -11 ÷ 4; 11 ÷ (-4); [tex]\frac{-11}{4}[/tex]; [tex]\frac{11}{-4}[/tex]
Step-by-step explanation:
A negative divided by a negative is a positive.
A positive divided by a negative or a negative divided by a positive is a negative.
Jackson and his family are driving to his grandmother's house. They have 5 of the trip left to go. Theyplan to complete the remainder of the trip over the next 3 hours. What fraction of the total trip willJackson's family travel each hour, if they drive at a constant rate?
Given:
The number of the trip =5 trips.
The number of hours = 3 hours
Jackson's family travel each hour
[tex]=\frac{The\text{ number of the trips}}{\text{The number of hours}}[/tex][tex]=\frac{5}{3}[/tex]Hence Jackson's family travel 5/3 trip each hour.
Model each rule with a table of values (number 4)
Explanation
Given the function
[tex]y=4x+1[/tex]To model a table of values, we will pick x values from 0 to 5, then use it get the y values. This can be seen below.
[tex]\begin{gathered} when\text{ }x=0 \\ y=4(0)+1=1 \\ when\text{ x=1} \\ y=4(1)+1=5 \\ when\text{ x =2} \\ y=4(2)+1=9 \\ when\text{ x=3} \\ y=4(3)+1=13 \\ when\text{ x= 4} \\ y=4(4)+1=17 \\ when\text{ x=5} \\ y=4(5)+1=21 \end{gathered}[/tex]Therefore, we will have the table of values as
Answer:
What is the correct answer for all? I need help!!
1.
The question requires you to find csc of angle thetha
The formula to apply is;
[tex]co\sec \text{ }\emptyset=\frac{1}{\sin \emptyset}[/tex]So, First find sin of the angle theta, then its reciprocal
Sin theta= opposite side length / hypotenuse
[tex]\sin \emptyset=\frac{8}{8\sqrt[]{2}}[/tex][tex]\sin \emptyset=1.4142[/tex][tex]co\sec \emptyset=\frac{1}{1.4142}=0.70710678118[/tex]Answer
0.7071
Or
Using surds
[tex]\sin \emptyset=\frac{8}{8\sqrt[]{2}}[/tex]Cancel 8 both in the denominator and numerator to remain with
[tex]\sin \emptyset=\frac{1}{1\sqrt[]{2}}=\frac{1}{\sqrt[]{2}}[/tex]T
Find the slope of each line and then determine if the lines are parallel perpendicular or neither.If a value is not an integer type it in as a decimal rounded to the nearest hundredth.
ANSWERS
• Slope of line 1: ,8
,• Slope of line 2: ,-6
,• The lines are ,neither
EXPLANATION
The slope of a line passing through points (x1, y1) and (x2, y2) is,
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The points given for line 1 are (-8, -55) and (10, 89). The slope of this line is,
[tex]m_1=\frac{-55-89}{-8-10}=\frac{-144}{-18}=8[/tex]The points given for line 2 are (9, -44) and (4, -14). The slope of this line is,
[tex]m_2=\frac{-44-(-14)}{9-4}=\frac{-44+14}{5}=\frac{-30}{5}=-6[/tex]• If two lines are ,parallel, then they have the same slope.
,• If two lines are ,perpendicular, then their slopes are opposite and reciprocal.
The slopes of these two lines are 8 and -6. These slopes are different and they are neither opposite nor reciprocal. Hence, these lines are neither parallel nor perpendicular.
(-3, -3) , (-3, -5)find the slope of the line through the given points
Using the slope formula with the points (-3, -3) and (-3, -5), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-5-(-3)}{-3-(-3)}=\frac{-5+3}{-3+3}=\frac{-2}{0}=\propto\text{ (Undefined Slope)}[/tex]We can see that the slope is undefined.
Increase 46 by 13% give your answer as a decimal
For the given question, Increase in 46 by 13% equals 51.98
What is meant by percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.
For the given question,
13% of 46 equals
⇒ 13 / 100 × 46
⇒ 5.98
Now Increasing 13% of 46 =
⇒ 46 + 5.98
⇒ 51.98
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the quotient of 7 subtracted from a number c and 4
The quotient of 7 subtracted from a number c and 4 which is 2 , 4 +3 = 7 and c=3. The quotient is the outcome of splitting two numbers.
What is meant by quotient?In mathematics, the quotient is the result of performing division operations on two numbers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.A quotient in mathematics is the amount created by dividing two numbers. n mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio. The quotient is the outcome of splitting two numbers.To learn more about quotient refer to:
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Kayden walks 4/5 km to a friends house. Then he and friend walk 1 3/5 km more to go fishing at their favorite pond. How far to Kayden walk all together?
PLEASE HELP THIS IS ON KHAN
write equation In standard form
15( y - 1/3 ) =x
The standard form of the linear equation 15( y - 1/3 ) = x is 3x - 45y = -15.
What is the given equation in standard form?The standard form of a linear equation is expressed as;
Ax + By = C
Where A and B are the coefficient of x and y respectively, C is the constant term.
Given the equation in the question;
15( y - 1/3 ) = x
Multiply both sides by 3
3(15( y - 1/3 )) = 3x
First, apply distributive property to remove the parenthesis.
15( 3y - 1 ) = 3x
45y - 15 = 3x
3x = 45y - 15
Now, move all terms containing variables to the left and side of the equation and reorder the equation in form of Ax + By = C
3x - 45y = -15
Therefore, the standard form of the equation is 3x - 45y = -15.
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A roll of gasket material is 16 in wide. What length is needed to obtain 21 sq ft of the material? the answer has to be as a mixed number
The Solution:
Given:
[tex]\begin{gathered} L=length=? \\ \\ W=width=16in \\ \\ A=area=21ft^2 \end{gathered}[/tex]Step 1:
Convert 21 square feet to square inches.
Recall:
[tex]\begin{gathered} 1\text{ foot}=12\text{ inches.} \\ So, \\ 21ft^2=21\times12=252\text{ }inches^2 \end{gathered}[/tex]Step 2:
Apply the formula for area.
[tex]\begin{gathered} A=L\times W \\ \\ 252=L\times16 \end{gathered}[/tex]Divide both sides by 16.
[tex]L=\frac{252}{16}=\frac{63}{4}=15\frac{3}{4}\text{ }inches[/tex]Therefore, the correct answer is:
[tex]15\frac{3}{4}\text{ inches}[/tex]Subtract the two polynomials 3x^2+7x-1 - x^2+6x-1
The polynomial (3x²+7x-1)-(x²+6x-1). The polynomial after subtraction is 2x²+x.
Given that,
The polynomial (3x²+7x-1)-(x²+6x-1)
We have to subtract the polynomial and find the polynomial.
The polynomial is nothing but algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. Mathematical operations like addition, subtraction, multiplication, and positive integer exponents can be performed on polynomial equations, however division by variables cannot.
Take the polynomial,
=(3x²+7x-1)-(x²+6x-1)
We have to subtract the each terms like x² terms and x terms and constant.
=3x²-x²+7x-6x-1+1
=2x²+x
Therefore, the polynomial after subtraction is 2x²+x.
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PLEASE HELP!!! - 55 pts
1.) Mrs. Zech babysits for extra money.
-The job pays $250 for twenty hours of work
-She needs to make $750
How many hours of babysitting would Mrs. Zech need to work to earn the $750?
Answer: Mrs. Zech would need to work 60 hours to earn $750.
Step-by-step explanation: 250 x 3 = 750, Every 20 hours Mrs. Zech makes $250 therefore 20 x 3 = 60 hours of work.
Answer:
60 hours
Step-by-step explanation:
if $250 is for 20hrs, $750 is for x hours (let the number of hours be x)
$250=20hrs
$750=x hrs
then you cross multiply. Which will be represented as
250x= (750x 20)
Divide both sides by 250
X =750x 20/ 250
X = 15000/250
X = 60 hours
What is the solution to the equation below?A.x = B.x = 25C.x = D.x = 9
The given equation is
- 3 + √(3x - 11) = 5
Adding 3 to both sides of the equation, we have
- 3 + 3 + √(3x - 11) = 5 + 3
√(3x - 11) = 8
Square both sides. It becomes
[√(3x - 11)]^2 = 8^2
3x - 11 = 64
Adding 11 to both sides of the equation, we have
3x - 11 + 11 = 64 + 11
3x = 75
Dividing both sides by 3,
3x/3 = 75/3
x = 25
Panama wants to solve the equation 1/3 ( x - 7) = 4To begin , she multipiles both sides of the equation by 3 what should she do next?
Question:
[tex]\frac{1}{3}(x-7)=4[/tex]Step 1: Multiply both sides by 3
[tex]\begin{gathered} \frac{1}{3}(x-7)=4 \\ 3\times\frac{1}{3}(x-7)=4\times3 \\ 1(x-7)=12 \\ x-7=12 \end{gathered}[/tex]Step 2: To find the value of x, Add 7 to both sides
[tex]\begin{gathered} x-7=12 \\ x-7+7=12+7 \\ x=19 \end{gathered}[/tex]Hene,
The final answer is add 7 to both sides
Answer:
Add 7 to each side
Step-by-step explanation:
1/3 ( x - 7) = 4
After multiplying both sides by 3
3*1/3 ( x - 7) = 4*3
( x - 7) = 12
We want to isolate x
Add 7 to each side
x - 7+7 = 12+7
x = 19
D
Question 3
If a car is traveling at 85 mph, how fast is the car traveling in feet per second? Round to 2
decimal places. (Reminder: there are 5280 feet in a mile)
1 pts
Answer:
See below
Step-by-step explanation:
85 mi/hr * 1 hr / 3600s * 5280 ft / mi =
85 * 5280 / 3600 = 124 2/3 ft/s
A ball is dropped from a height of 6 feet. With each bounce, the ball rebounds to a height that is three-quarters as high as the previous bounce. Represent the height to which the ball rises after it hits the floor for the nth time using a recursive formula and an explicit formula. Recursive Formulas: anar.an-1 or an+1 =rean Explicit Formula: an = Q .m-1 Represent (using sigma notation) the total vertical distance the ball has traveled when it hits the floor for the fifth time. Calculate this distance. ? Σ ? k=? Sn 4,(1-r") 1-r
We know that each time the ball bounces it travels a distance of 3/4 the original height, that means that for each bounce the ball will rise:
[tex]a_n=\frac{3}{4}a_{n-1}[/tex]where a_n is the height of the nth bounce and a_(n-1) is the bounce n-1 (the previous one).
Now, from this formula we know that:
[tex]a_1=\frac{3}{4}a_0=\frac{3}{4}\cdot6=\frac{9}{2}[/tex]Therefore the explicit formula for the height of the nth bounce is:
[tex]\begin{gathered} a_n=\frac{9}{2}(\frac{3}{4})^{n-1} \\ =\frac{9}{2}\cdot\frac{4}{3}(\frac{3}{4})^n \\ =6(\frac{3}{4})^n \end{gathered}[/tex]Then:
[tex]a_n=6(\frac{3}{4})^n[/tex]Now, to find the total distance it travels by the fifth bounce we follow:
The first time the ball hits the ground it has traveled a distance of 6 ft.
Now, for the second bounce we have:
[tex]6(\frac{3}{4})+6(\frac{3}{4})=12(\frac{3}{4})[/tex](one distance up and one distance down).
For the third bounce we have:
[tex]6(\frac{3}{4})(\frac{3}{4})+6(\frac{3}{4})(\frac{3}{4})=12(\frac{3}{4})^2[/tex]If we continue this process we notice that the ball will travel a total distance of:
[tex]6+12(\frac{3}{4})+12(\frac{3}{4})^2+12(\frac{3}{4})^4+\ldots\text{..}[/tex]but this can be written (for an infinity number of bounces) as:
[tex]\begin{gathered} 6+12\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^{n+1} \\ =6+12(\frac{3}{4})\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^n \\ =6+9\sum ^{\infty}_{n\mathop=0}(\frac{3}{4})^n \end{gathered}[/tex]As we said this is for an infinity of bounces if we like only five bounces then we have:
[tex]6+9\sum ^5_{n\mathop=0}(\frac{3}{4})^n[/tex]Now to find the distance in this case we do the sum and we get appoximately 35.5928 feet.
Can you please help with 8 I need to finish 8 more packets by tonight
Given the expression below
[tex]\frac{1}{2}(10.4x-2q)-2.8(x-7q)[/tex]Using distributive property, we have
[tex]\frac{1}{2}(10.4x)-\frac{1}{2}(2q)-2.8(x)-2.8(-7q)[/tex][tex]5.2x-q-2.8x+19.6q[/tex]collect like terms
[tex]\begin{gathered} 5.2x-2.8x+19.6q-q \\ \rightarrow2.4x+18.6q \end{gathered}[/tex]Hence, the simplest form of the fraction is 2.4x + 18.6q
Using the design below, you plan to make a rectangular wall hanging to decorate yourbedroom. Th e green rectangle is 16 ft by 10 ft, the blue square is 7 ft by 7 ft, the orangetriangles have a height of 1.73 ft and a side length of 2 ft, and the yellow circle has adiameter of 3 ft. You plan to glue the pieces together and then outline each piece withblack cord.a. How much black cord does the design use?b. How much fabric of each color does the design show?c. At a craft store, fabric comes in bolts that are a fixed number of inches wide.You can only buy fabric by the whole yard. If each bolt is 48 in. wide, what isthe least amount of each color that you need to buy? Explain.please I try to solve it but I did not understand it please need help thank you so much.
To know the total amount of fabric we need per color, we need to find the area of each color.
The green rectangle.[tex]A_{green}=16\cdot10=160ft^2[/tex]The blue square.[tex]A_{blue}=7\cdot7=49ft^2[/tex]The orange triangles.[tex]A_{orange}=4(\frac{1}{2}\cdot1.75\cdot2)=\frac{14}{2}=7ft^2[/tex]The yellow circle.[tex]A_{circle}=\pi r^2=3.14\cdot(1.5)^2=3.14\cdot2.25=7.065ft^2[/tex]Now, the bolts are sold in fixed yards, we know that 48 inches are equivalent to 1.333... yards, or 4 feet. But, we are using areas so, 48 to the square power in square inches would be equivalent to 16 square feet.
Then, we divide each area by 16 square feet.
[tex]b_{green}=\frac{160}{16}=10[/tex]We need 10 bolts of green fabric.
[tex]b_{blue}=\frac{49}{16}=3.0625[/tex]We need 4 bolts of fabric since if we use 3 we would need a bit more.
[tex]b_{orange}=\frac{7}{16}=0.4375[/tex]We just need 1 bolt of orange fabric.
[tex]b_{yellow}=\frac{7.065}{16}=0.44[/tex]We need 1 bolt of yellow.
The table shows the number of students in the senior class and the number of seniors who have a Yeardriver's license.Number of SeniorsSeniors with a Lice13. What pattern is there between the number of seniors and the seniors who have a driver's license?14. The class of 2018 has 412 seniors. How many seniors in the class of 2018 would be expected to have a driver's license?13. Select the correct choice below and fill in the answer box to complete your choice.(Round to the nearest integer as needed.)O A. Each year, about seniors do not have a driver's license.O B. Each year, about % of the senior class have a driver's license.
Given:
The table containing number of students and number of students who have license.
From the table,
[tex]\begin{gathered} In\text{ the year 2014} \\ 343-232=111\text{ seniors dont have license} \\ In\text{ the year 2015} \\ 360-244=116\text{ seniors dont have license} \\ In\text{ the year 2016,} \\ 310-210=100\text{ seniors dont have license} \\ In\text{ the year 2017,} \\ 378-258=120\text{ seniors dont have license} \\ It\text{ is obsered that there is no relation in the numb}er\text{ of senior with no license} \end{gathered}[/tex]Now,
[tex]\begin{gathered} \frac{a}{100}\times343=232 \\ a=67.64\text{ percent} \\ \frac{a}{100}\times360=244 \\ a=67.78\text{ percent} \\ \frac{a}{100}\times310=210 \\ a=67.74\text{ percent} \\ \frac{a}{100}\times378=258 \\ a=68.25\text{ percent.} \end{gathered}[/tex]It is observed that approximately 68 percent of the senior have license each year.
Fill in the missing angle measures. Given: ab and c d and <1 = 32°
hello
from the image given,
angle 1 = 32
[tex]\begin{gathered} \angle1=\angle8 \\ \text{reaon: alternate angles are equal} \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle3 \\ \text{reason:corresponding angles are equal} \\ \angle3=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle1+\angle5=180^0 \\ \text{reason: angles on a straight line is equal to 180}^0 \\ \angle1=32 \\ 32+\angle5=180 \\ \angle5=180-32 \\ \angle5=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle5+\angle6=180^0 \\ reason;\text{ angles on a straight line = 180} \\ \angle5=148 \\ 148+\angle6=180 \\ \angle6=180-148 \\ \angle6=32^0 \\ or\text{ we can simply say } \\ \angle1=\angle6 \\ \text{reason: opposite angles are equal} \end{gathered}[/tex][tex]\begin{gathered} \angle5=\angle2 \\ \text{reason: opposite angles are equal} \\ \angle2=148^0 \\ or\text{ we can say }\angle1+\angle2=180\text{ since they are on a straight line} \end{gathered}[/tex][tex]\begin{gathered} \angle3+\angle4=180^0 \\ \text{reason: angles on a straight line = 180} \\ 32+\angle4=180 \\ \angle4=180-32 \\ \angle4=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle4=\angle7 \\ \text{reason: opposite angles are equal} \\ \angle7=148 \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle8 \\ \text{reason; alternate angles are equal} \\ \angle8=38^0 \end{gathered}[/tex][tex]\begin{gathered} \angle1=\angle14 \\ \text{alternate angles are equal} \\ \angle14=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle5=\angle13 \\ \text{reason;corresponding angles are equal} \\ \angle13=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle13=\angle10 \\ \text{reason:opposite angles are equal} \\ \angle10=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle9=\angle14 \\ \text{reason:opposite angles are equal} \\ \angle9=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle12=\angle13 \\ \text{reason: alternate angles are equal} \\ \angle12=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle11+\angle12=180 \\ \text{reason:angles on a straight line equal 180}^0 \\ \angle11+148=180 \\ \angle11=180-148 \\ \angle11=32^0 \end{gathered}[/tex][tex]\begin{gathered} \angle12=\angle15 \\ \text{reason : opposite angles are equal} \\ \angle15=148^0 \end{gathered}[/tex][tex]\begin{gathered} \angle11=\angle16 \\ \text{reason: opposite angles are equal} \\ \angle16=32^0 \end{gathered}[/tex]from the calculations above, it's evident we can use several ways to find angles in four parallel lines
Write an equation and solve. A number y divided by 5.5 is equal to 86
y is divided by 5.5 and is equal to 86, so:
[tex]\frac{y}{5.5}=86[/tex]Solve for y:
Multiply both sides by 5.5:
[tex]\begin{gathered} y=86\cdot5.5 \\ y=473 \end{gathered}[/tex]Distribute 4,350$ among John, Maria, and Betsy, so that Maria receives twice as much as John and Betsy recieves 3 times as much as john
To solve this problem we must generate a system of equations that models its behavior.
To make the problem easier, the money distributed to Jhon, Maria and Betsy will be identified by their initials J, M and B.
[tex]\begin{gathered} M+J+B=4350\to(1) \\ M=2J\to(2) \\ B=3J\to(3) \end{gathered}[/tex]The first thing we are going to do is replace the value of equations (2) and (3) in equation (1)
[tex]\begin{gathered} 2J+J+3J=4350 \\ 6J=4350 \\ J=\frac{4350}{6} \\ J=725 \end{gathered}[/tex]Now we know that John will receive $725 now we plug this value into (2) and (3) to find when Maria and Betsy will receive
[tex]\begin{gathered} M=2J \\ M=2(725) \\ M=1450 \end{gathered}[/tex][tex]\begin{gathered} B=3J \\ B=3(725) \\ B=2175 \end{gathered}[/tex]The distribution of the $4350 would be as followsMaria = $1,450John = $725Betsy = $2,175Round to nearest foot
Using the law of sines and relations in a right triangle, the ground distance AB is of:
AB = 3745 ft.
Law of sinesThe ratios between the sine of an angle and the length of the opposite side to the angle are the same in a triangle.
The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is of:
180 - (74 + 49) = 57º.
Then the bottom side of the blue triangle is found as follows:
sin(57º)/3300 = sin(74º)/x
x = 3300sin(74º)/sin(57º)
x = 3782 ft.
Ground distanceThe ground distance can be found considering that:
The adjacent side to the angle of 8º is the ground distance.The hypotenuse is of 3782 ft.Hence the ground distance is calculated as follows:
cos(8º) = AB/3782
AB = 3782 x cos(8º)
AB = 3745 ft.
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