Answer:
[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]
Step-by-step explanation:
The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.
5x +3y= 15
3y= -5x +15
Divide both sides by 3:
[tex]y = - \frac{ 5}{3} x + 5[/tex]
Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]
The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.
Slope of perpendicular line= [tex] \frac{3}{5} [/tex]
Substitute the value of the slope into the equation:
[tex]y = \frac{3}{5} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -1, y= 2,
[tex]2 = \frac{3}{5} ( - 1) + c[/tex]
Solve for c:
[tex]c = 2 + \frac{3}{5} [/tex]
[tex]c = \frac{13}{5} [/tex]
Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].
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Drag a statement or reason to each box to complete this proof.
Given: the measure of angle A B D equals 60 degrees. The measure of angle D B C equals 40 degrees. Prove: triangle A B C is an obtuse triangle. Art: triangle A B C with horizontal base B C is drawn. A bisector B D is drawn on A C. The bisector divides A C into two parts A D and D C.
1. m∠ABD = 60°, m∠DBC=40° Given
2. m∠ABD + m∠DBC = m∠ABC ________
3. ______ Substitution Property of Equality
4. ______ Simplifying
5. ∠ABC is an obtuse angle. _________
6. △ABC is an obtuse triangle. Definition of obtuse triangle
Boxes needed to put in _________
100° = m∠ABC
60° + 40° = m∠ABC
Definition of obtuse angle
Angle Addition Postulate
The table to complete the proof is as follows
Equation statement
1. m∠ABD = 60°, m∠DBC=40° Given
2. m∠ABD + m∠DBC = m∠ABC Angle Addition Postulate
3. 60° + 40° = m∠ABC Substitution Property of Equality
4. 100° = m∠ABC Simplifying
5. ∠ABC is an obtuse angle. greater than 90 degrees
6. △ABC is an obtuse triangle. Definition of obtuse triangle
What is obtuse angles?When an angel is greater than 90 degrees the angle is said to be an obtuse angle.
For the question solved here m∠ABC is greater than 90 degrees hence an obtuse angle.
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Write an equation to represent the word problem. Then solve it.
←
Dinh has 3 more patients to care for than Juan. If Dinh has 17 patients to ca
The equation is
(Type an equation using x as the variable. Do not evaluate.)
Juan has to care for
patients.
0
We get that Juan has 14 patients to care for.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Let Juan has x patient to care for.
Therefore according to the question Dinh has x + 3 patients to care for.
Therefore,
The equation is x + 3= 17
=> x = 17 -3
=> x = 14
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Let f(x)=x^2−12 and g(x)=13−x.
Perform the composition or operation indicated. (fg)(4)
Answer:
69
Step-by-step explanation:
Rule:
[tex](fg)(x) = f(g(x))[/tex]
So,
[tex](fg)(4) = f(g(4))[/tex]
First solve g(4).
[tex]g(4) = 13 - 4[/tex]
[tex]g(4) = 9[/tex]
Plug g(4) into f(x).
[tex]f(g(4)) = (g(4))^2-12[/tex]
[tex]f(g(4)) = (9)^2-12[/tex]
[tex]f(g(4)) = 81-12[/tex]
[tex]f(g(4)) = 69[/tex]
Brian is driving on a highway. He uses one gallon of gas every 40 miles he drives. The distance, D (in miles), he travels on g gallons of gas is given by the following function.
D (g) = 40g
How far does Brian drive if he uses 4 gallons of gas?
A cement walkway is to be poured .it is consists of the two rectangles with dimensions and a circle with radius 1.5 yards use 3.14 as an approximate value.how many square yards will the walkway be?If a painter it for 3.75 per square yard,how much will the painting cost?
The area of the walkway in square yards is 22.77 yards²
The cost of painting the walkway will be $85.37.
What is the area of the walkway?The square yards of the walkway can be determined by adding the areas of the two rectangles and the area of the quarter of a circle together.
Area of a rectangle = length x width
Area of the first rectangle = 9.5 x 1.5 = 14.25 yards²
Area of the second rectangle = 4.5 x 1.5 = 6.75 yards²
Area of a circle = πr²
Area of quarter of a circle = 1/4 × πr²
Where:
π = pi = 3.14
r = radius
1/4 x (3.14 x 1.5²) = 1.77 yards²
Area of the walkway = 1.77 yards² + 6.75 yards² + 14.25 yards² = 22.77 yards²
The cost of the painting can be determined by multiplying the area of the walkway by the cost per square yard.
Total cost = 22.77 yards² x 3.75 = $85.37
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Movie theaters keep track of how many tickets they sell. For the 5:30 showing, the theater
sold a total of 272 adult and student tickets and took in a total of 1694 dollars. If adults
tickets sold or 7 dollars and students sold for 4 dollars each how many of each type were sold
for the 5:30 show.
As a result, we deduce that 101 tickets were sold to adults and 171 to students after solving the algebraic equations.
What are Algebraic equations ?The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation.
So on the information provided to us:
we know that the total amount of the tickets sold =1694$
total no. of people = 272
Lets assume the no. of kids to be y and the adults to be x
So the first equation we get for the total no. of people is:
x+y=272...(i)
the next equation we get for the total amount of tickets sold will be equal to the no. of adults and children multiplied by the cost of each adult and child respectively :
7x+4y=1694....(ii)
Two solve both equations simultaneously , we multiply equation i with 4
we get:
4x+4y=1088
7x+4y=1694
on solving both the equations simultaneously we get
3x=606
x=101
putting value of x in equation (i) we get
y=171
Therefore, we conclude that the no. of tickets sold to adults were 101 and to students were 171.
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the cities A B C in respective order lie approximately in a straight line. the distance from city a ti b is 100miles. the distance from city A to city C is 110miles. find the distance from city b to city c
Based on the distance between Cities A and B and also cities A and C, and the fact that the cities are on a straight line, the distance between City B and City C can be found to be 10 miles
How to find the distance?The distance between cities A and B and cities A and C are related because they are on a straight line.
This means that the distance between cities A and B and cities A and C can be used to find the distance between cities B and C and also the distance between cities A and B and cities B and C can be used to find the distance between A and C.
To find the distance between cities B and C, formula is:
= Distance between cities A and C - Distance between cities A and B
= 110 - 100
= 10 miles
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help meeeeee
8 Answer:
Evaluate the expression (2y)3 when y = 3.
9 Answer:
Evaluate the expression x2 + y when x = 4 and y = 3.
10 Answer:
Evaluate the expression (a + b)3 when a = 3 and b = 5.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation \#1.}[/tex]
[tex]\mathsf{(2y)^3}\\\mathsf{= (2(3)^3}\\\mathsf{= (6)^3}\\\mathsf{= 6^3}\\\mathsf{= 6\times6\times6}\\\mathsf{= 36\times6}\\\mathsf{= 216}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{216}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + y}\\\mathsf{= 4^2 + 3}\\\mathsf{= 4\times 4 + 3}\\\mathsf{= 16 + 3}\\\mathsf{= 19}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{19}}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Equation \#3.}[/tex]
[tex]\mathsf{(a + b)^3}\\\mathsf{= (3 + 5)^3}\\\mathsf{= (8)^3}\\\mathsf{= 8^3}\\\mathsf{= 8\times 8 \times 8}\\\mathsf{= 64\times8}\\\mathsf{= 512}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{512}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Two shops rent pairs of skis for a rental fee plus a fee per hour. Write and solve an equation to
find how many hours must a pair of skis be rented for the total costs to be the same?
Shop A Equation:
Shop B Equation:
Solution:
Rental Fee
Hourly Fee
Shop A
$3
$9
Shop B
$9
$6
For the total costs to be the same a pair of skis must be rented for 3 hours.
Two shops rent pairs of skis for a rental fee plus a fee per hour.
Let, the number of hours must a pair of skis be rented = x
Equation for Shop A,
3 + 9x equation 1
Equation for Shop B,
9 + 6x equation 2
Total cost for Shop A and Shop B is same so we can equate equation 1 and equation 2 as mentioned below:
3 + 9x = 9 + 6x
3x = 6
x = 3
Thus we can write, for the total costs to be the same a pair of skis be rented for 3 hours.
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Help please…..?
Number 3 and 4 only
Answer:
3. You determine the sign of a number when you add a negative number and a positive number by taking the signn of the bigger number. For example -4+3 is -1 because the negative number is bigger than the positive so it takes its sign
4. you can make the number possible by making the number negative
50÷2 and 5÷3solve the question and tell the remainder
Step-by-step explanation:
the perimeter of a triangle is 84 cm and its area is 36 CM square if one its side is 30 cm find the length of remaining two side
7. Let A=(8,9,10,11,12,13).
n=
a. How many subsets does A have?
b. How many proper subsets does A have?
subsets.
a. A has
(Type a whole number.)
b. A has
(Type a whole number.)
proper subsets.
a. A has 64 subsets.
b. A has 63 proper subsets.
What are subsets and proper subsets?If all of the items of Set A are also present in Set B, Set A is said to be a subset of Set B. Set A is, in other words, contained within Set B.
If Set B has at least one element that is not present in Set A, Set A is considered a proper subset of Set B.
If a set has "n" members, the number of subsets of that set is 2ⁿ, and the number of proper subsets of that subset is 2ⁿ-1.
Given:
Set A=(8,9,10,11,12,13)
Number of elements in the given set,n = 6
a. Number of subsets of A = 2ⁿ = 2⁶ = 64
b. Number of proper subsets of A = 2ⁿ-1 = 2⁶-1 =63
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What is the length of XY
SolutionSoltuion:
From the question, the given value id
[tex]\begin{gathered} XQ=3 \\ XR=RW \\ XR+RW=XW \\ XQ=QY \\ XQ+QY=XY \end{gathered}[/tex]By applying the theorem above, we will have the value of XY be
[tex]\begin{gathered} XQ+QY=XY \\ XQ=3 \\ QY=3 \\ XY=3+3 \\ XY=6 \end{gathered}[/tex]Hence,
The final answer = 6
I need help please
Step-by-step explanation:
To help, but not give the answer so you can learn to do this:
To find the slope, choose any two points on the graph (no really IT DOESN'T MATTER WHICH ONE). Use the equation y-y/x-x to get the slope.
Ex. 8-3/5-1=4/3
(NOTE: Always write your answer as either an improper fraction or a whole number!)
To find the distance, go across the x-axis, however many units away the closest point is to your chosen point. Then, go across the y-axis for the required # of units. Next, find the total number of the x and y units. You can also subtract the smallest coordinate from the greatest if the two ordered pairs are in the same quadrant. If not in the same quadrant, add the coordinates together. If the value of x or y happens to be the same as your chosen coordinate, find the sum of the two numbers that are equal, or subtract if in the same quadrant.
Also, in case you have another question relating to the same line, the given line is NOT proportional. Just in case, though!
I hope this helps you with your question!
(Happy Halloween! )
The wholesale price for a shirt is 6.50. A certain department store marks up the wholesale price by 80%. Find the price of the shirt in the department store.
Round your answer to the nearest cent, as necessary.
The new price of the shirt is $11.70
How to determine the price of the shirt in the store?The given parameters are
Price = 6.50
Make up percentage = 80%
The price of the shirt in the store is calculated as
New price = Old price + Old price * Make up percentage
Substitute the known values in the above equation
So, we have the following equation
New price = 6.50 + 6.50 * 80%
Evaluate the product
So, we have the following equation
New price = 6.50 + 5.20
Evaluate the sum
So, we have the following equation
New price = 11.70
Hence, the price of the shirt in the store is $11.70
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How do we get our voice?
Answer: The lungs provide the airstream which powers human voice. As air is pushed up the windpipe from the lungs, the larynx, which is made up of two vocal folds, opens and closes to produce vibrations. These vibrations are carried through to the throat, nose, and mouth, which act as resonators- morphing the vibrations into distinct human sounds.
Step-by-step explanation:
Answer:
Our vocal cords gve us our voice.
Step-by-step explanation:
The vocal folds (cords) produce sound when they come together and then vibrate as air passes through them during exhalation of air from the lungs. This vibration produces the sound wave for your voice.
First person to answer this will get brainilest
Find the area of each figure.
Assume the average test score from the last year's class was 85 points with a standard deviation of 9. By sketching a normal curve, which value below is the best estimate for the proportion of students earned a 70 points or higher?
The given information is:
- The average test score is 85 points
- The standard deviation is 9
- It is a normal distribution
We need to find the best estimate for the proportion of students earned a 70 points or higher.
First, we need to find the z-score for 70, by applying the following formula:
[tex]z=\frac{x-\mu}{\sigma},\text{ where }\mu=average,\sigma=standard\text{ }deviation,x=value[/tex]Then, as x=70, we replace the given values and find z:
[tex]z=\frac{70-85}{9}=\frac{-15}{9}=-1.67[/tex]Then, we can find the estimate as follows:
[tex]P(X\ge70)=P(z\ge-1.67)=1-P(z<-1.67)[/tex]Now, in a standard normal table, we search the cumulative probability of z<-1.67, and it is 0.0475:
Thus, replace this value to find P(X>=70):
[tex]P(X\ge70)=1-0.0475=0.9525[/tex]The probability is 0.9525, if we multiply it by 100%, we obtain: 95.25%
The best estimate is 95%.
What’s the correct answer answer asap for brainlist
The skeletal muscle can fatigue with too much movement or exercise.
what is skeletal muscles?Skeletal muscle, in contrast to smooth muscle and cardiac muscle, is controlled voluntarily. Skeletal muscle is striated, similar to cardiac muscle; it has long, thin, multinucleated fibers that are crossed in a regular manner by fine red and white lines that give the muscle its unique look. Myofibrils, which are made up of sarcomeres joined in series, make up muscle fibers. The arrangement of actin and myosin filaments, which results in the banding pattern of myofibrils, produces the striations of skeletal muscle. The ability of muscular tissue to contract is special. Only the skeletal muscle can be controlled voluntarily out of the three types of muscles (skeletal, smooth, and cardiac).To more learn about skeletal muscle refers to:
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25. To make an enclosure for chickens, a rectangular
area will be fenced next to a house. Only three sides
will need to be fenced. There is 120 ft of fencing
material.
X
a. What quadratic function represents the area of the
rectangular enclosure, where x is the distance from the house?
Answer:
y = x(120 -2x)
Step-by-step explanation:
You want the quadratic function representing the area of a rectangular enclosure such that three sides of it have a total length of 120 feet.
AreaThe dimension perpendicular to the house is given as x. There are two length of fence with that dimension, so the remaining fence is (120 -2x). This is the length that can be used parallel to the house.
The area (y) is the product of the dimensions of the enclosure:
y = x(120 -2x)
__
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i need help will give points
x = -16
Explanation:The given equation is:
[tex]3+\frac{x}{-8}=5[/tex]Multiply through by -8 (Equality property of multiplication)
[tex]\begin{gathered} -8(3)+(-8)\frac{x}{-8}=-8(5) \\ -24+x=-40 \end{gathered}[/tex]Add 24 to both sides of the equation (Equality property of addition)
-24 + 24 + x = -40 + 24
x = -40 + 24
x = -16
Therefore, the solution to the equation is x = -16
Identify Linear Function from Points Which table of Values REPRESENTS a linear Functions?draw the problems on the table Please.
Linear functions from tables
I'll draw the calculations directly on the tables as required. The table that has the same slope represents a linear function.
Table A has different values for the slope, this table is not a linear function.
Table C is not a linear function since the slope is not constant
Table B does not have a constant slope, so it's not a linear function
Table D has a constant slope of 1/3, thus this table represents a linear function
mrs green wants to use wood to make a fence around her circular garden. Her garden has a radius of 16 feet How much wood will she need to enclose her garden?.
ANSWER
100.5 feet
EXPLANATION
The radius of the circular garden is 16 feet.
To find how much wood she would need to make a fence around the garden, we need to find the circumference of the garden.
Circumference can be found using the formula:
[tex]C\text{ = 2}\pi r[/tex]where r = radius
Therefore:
[tex]\begin{gathered} C\text{ = 2 }\cdot\text{ }\pi\cdot\text{ 16} \\ C\text{ = 100.5 ft} \end{gathered}[/tex]She would need 100.5 ft length of wood to enclose the garden.
3) A clock is set correctly at 1pm. If it loses 3 minutes every hour, what will the clock show
when the correct time is 10 am the next day?
Based on the time the clock is set to, and the minutes lost every hour, the time the clock would show the next day at 10 am is 8:57 am
How to find the time shown?To find the time that the clock would show the next day, first find the difference between the 1 pm and 10 am the next day:
This difference is:
= 10 am the next day - 1 pm
= 10 + (12 - 1)
= 10 + 11
= 21 hours
The number of minutes lost is:
= 21 x 3 minutes per hour
= 63 minutes
The time the clock would be showing is:
= 10 am - 63 minutes
= 8:57 am
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(5+6) + what = 5 + (6+2)
Answer:
total is 13. so 5+6 = 11 and total is 13 so 13 - 11 = 2
At American High School, there is a 25.5% probability a randomlyselected student is an honor roll student, while there is a 37%probability that a randomly selected student is a varsity athlete.The probability that a student is an honor roll student and avarsity athlete is 6%.
Given,
probability of randomly selected student is an honor roll student,
[tex]\frac{25\cdot5}{100}=0\cdot255[/tex]probability of randomly selected student is a varsity athlete,
[tex]\frac{37}{100}=0\cdot37[/tex]The probability of the student is an honor roll student and a
varsity athlete,
[tex]\frac{6}{100}=0\cdot06[/tex]The probability of multiple events is,
[tex]0.255\times0.37\times0.06=0.005661[/tex]0.005661
Sara bought 7 red peppers for $5.60.
Find the unit rate. Then use the unit rate to write an equation relating the cost in dollars c to the number of red peppers p.
The unit rate of what Sarah bought is 0.8 dollars per pepper.
The equation relating cost in dollars, c to the number of red peppers is c = 0.8p
How to find unit rate?A unit rate describes the ratio of two different units for the quantity of one.
In other words, the unit rate can be defined as the ratio between two measurements with the second term as 1.
Therefore, the unit rate when Sara buys 7 red peppers for $5.60 can be calculated as follows
unit rate = cost of pepper / number of pepper
unit rate = 5.60 / 7
unit rate = 0.8 dollars per pepper
Let's use the unit rate to write an equation relating the cost in dollars c to the number of red peppers, p.
Therefore,
c = 0.8p
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Jeff found that one third bag of popcorn weighed 1/4 lb how many pounds will one full bag of popcorn weigh
Based on the weight of one third bag of popcorn, one bag of popcorn weighs 3/4 lb
How to determine the weight of one bag?The statement is given as
One third bag of popcorn weighed 1/4 lb
This means that
1/3 bag = 1/4 lb
Multiply both sides of the equation by 3
So, we have the following equation
3 * 1/3 bag = 1/4 lb * 3
Evaluate the products
So, we have
3/3 bag = 3/4 lb
Evaluate the quotient
So, we have
1 bag = 3/4 lb
Hence, the conclusion is that the weight of one bag is 3/4 lb
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Arielle is hiking down into the canyon. She starts at the rim and hikes down 55 feet in 2 3/4 minutes. If she continues at this rate, where will Arielle be in relation to the rim after 15 minutes
First, determine the speed of Arielle by calculating the quotient in between 55 ft and 2 3/4 minutes. To find the quotient, convert the mixed number to a normal fraction before:
[tex]2\frac{3}{4}=2+\frac{3}{4}=\frac{8+3}{4}=\frac{11}{3}[/tex]then, calculate the speed:
[tex]v=\frac{55}{\frac{11}{3}}=\frac{\frac{55}{1}}{\frac{11}{3}}=\frac{55\cdot3}{11\cdot1}=\frac{165}{11}=15[/tex]then, the Arielle's speed is 15 ft/min
next, find the distance traveled by Arielle in 15 min, by using the previous result:
[tex]d=v\cdot t=(15ft/\min )(15\min )=225ft[/tex]Hence, in relation to the rim, Arielle will be at 225 ft
please help !!!!!!!!! THANK YOU
For the give question;
The given line is; -2x + 3y = 6
Write the equation in slope intercept form; y = mx + c.
-2x + 3y = 6
3y = 2x + 6
y = (2/3)x + 2
Slope m₁ = 2/3 and y intercept is 2.
For the relation of slope;
Parallel line : m₁ = m₂Perpendicular line: m₁×m₂ = -1Part a: -3x - 2y = 4
Write the equation in slope intercept form;
-2y = 3x + 4
y = (-3/2)x - 2
m₂ = -3/2
m₁ ≠ m₂ as 2/3 ≠ -3/2
m₁×m₂ = 2/3 × -3/2 = -1
Thus, the both lines are perpendicular.
Part b: -2x + 3 y = -6
Write the equation in slope intercept form;
3y = 2x - 6
y = (2/3)x - 2
m₂ = (2/3)
m₁ = m₂
Thus, both lines are parallel.
Part c: 2x + 3y = 6
Write the equation in slope intercept form;
3y = -2x + 6
y = (-2/3)x + 2
m₂ = -2/3
m₁ ≠ m₂ as 2/3 ≠ -2/3
And, m₁×m₂ = 2/3 × -2/3 ≠ 1
Thus, lines are neither parallel not perpendicular.
Part d: -2x + 3y = 0
Write the equation in slope intercept form;
3y = 2x
y = 2/3 x
m₂ = 2/3
m₁ = m₂
Thus, both lines are parallel.
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