Find the area of a triangle bounded by the y-axis, the line
f(x) = 34 − 4 x,
and the line perpendicular to "f" that passes through the origin.
Answers
A drawing of the triangle is attached.
We first plot the y-intercept of the line given to us, f(x)=34-4x. This is in the form f(x)=mx+b, so the y-intercept, b, is 34.
Next we use the slope to find the next points of the line. The slope is -4, which can be written as -4/1 (rise/run). This means from the y-intercept, we go down 4 and over 1 to plot the next point, and continue in this manner. We now have the y-axis and this line drawn.
Next we use the slope of the line to find the slope of the perpendicular line described. Two lines are perpendicular if their slopes are negative reciprocals of each other. The slope of the first line was -4/1; this means the slope of this line must be 1/4. We also know this point goes through the origin, so 0 is the y-intercept, and we have the equation f(x)=1/4x+0.
To graph this, plot a point at 0, the y-intercept. The slope is 1/4, so we go up 1 and over 4 to the next point. This happens to be on the line we previously drew.
To find the area of this triangle, we need to identify the base and height. The height will be perpendicular to the base. The two sides that form a right angle are the bottom and the right hand side, so the bottom is the base and the right hand side is the height.
Now we find the length of each of these sides using the distance formula. For the height:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}=\sqrt{(34-1)^2+(0-4)^2} \\ \\=\sqrt{33^2+(-4)^2}=\sqrt{1089+16}=\sqrt{1105}\approx33.24[/tex]
To find the length of the base:
[tex]d=\sqrt{(0-1)^2+(0-4)^2}=\sqrt{(-1)^2+(-4)^2}=\sqrt{1+16}=\sqrt{17} \\ \\\approx4.12[/tex]
The area of a triangle is given by A=1/2bh:
A=1/2(33.24)(4.12) = 68.4744 ≈ 68.47
Related Questions
Jessica is baking a cake. The recipe says that she has to mix 32 grams of vanilla powder to the flour. Jessica knows that 1 cup of vanilla powder has a mass of 128 grams. She added ¼ cup of vanilla to the flour. Should she add more vanilla powder to make the exact recipe, did she go over, or did she use the perfect amount? How do you know?
Answers
Answer: she used the perfect amount
Jessica added exactly ¼ cup of vanilla powder, weighing 32 grams, to her recipe. This is the perfect amount as stated by the cake recipe.
Explanation:Jessica is tasked with following a cake recipe that requires 32 grams of vanilla powder. She knows that 1 cup of vanilla powder weighs 128 grams. Since she added only ¼ cup of vanilla powder, we need to calculate if this amount is equivalent to the required 32 grams.
First, let's determine how many grams are in ¼ cup of vanilla powder:
Since 1 cup is 128 grams, ¼ of that amount is:128 grams × ¼ = 32 grams.
Therefore, Jessica has added the perfect amount of vanilla powder to her recipe.
The first military strike of the Civil War was at
Bull Run
Lexington
Fort Sumter
Gettysburg
Answers
I’m confused on this question.
Please help.
Answers
The answer is $30,000.00
The way you find this is by using the formula, Percent x Part=Whole
.15 or 15% x $45,000.00= $30,000.00
hopes this helps,
Xeno
Which function is shown in the graph?
Answers
And a three week vacation to Paris Martha's expenses on food gifts and accommodations was $80 less than three times for airfare if the total expenses for the trip was $2660 how much was your airfare?
Answers
if y=q x 5,and if q=10,then what is y?
a.2
b.5
c.30
d.50
Answers
The value of y is 50
Using the expression given:
y = q × 5 q = 10substitute the value of q into the expression
Now we have :
y = 10 × 5
y = 50
Hence, the value of y is 50
Plz Help Meee!!!!! >.<
Answers
how do you convert degrees to radians?
Answers
One degree is equal 0.01745329252 radians:
1° = π/180° = 0.005555556π = 0.01745329252 rad
The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:
α(radians) = α(degrees) × π / 180°
or
radians = degrees × π / 180°
ExampleConvert 30 degrees angle to radians:
α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad
Degrees to radians in terms of piThe angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:
α(radians) = (α(degrees) / 180°) × π
ExampleConvert 30 degrees angle to radians in terms of pi:
α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π
= (1/6) × π = π/6 rad = 0.166667π rad
Final answer:
To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.
Explanation:
To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.
For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:
45 degrees * (π/180) = 45π/180 = π/4 radians.That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.
2 1/4 simplified with 1/4
Answers
2 1/4 +1/4
9/4+1/4=10/4=5/2=1 3/2
1 3/2
A group of people were asked if they enjoy going to concerts or movies.
The table shows the probabilities of the results.
Answers
They are not independent because P(movies|concerts)=0.25 ≠ P(movies)=0.6, and P(concerts|movies)=0.25 ≠ P(concerts)=0.55
Answer:
Option: B is the correct answer.
Enjoying movies and concerts are not independent since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
Step-by-step explanation:
We know that if two events A and B are independent then:
[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]
where P denote the probability of an event.
Now, we know that:
[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]
Similarly:
[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]
If movies and concerts are independent then:
[tex]P(movies|concerts)=P(movies)[/tex]
Similarly:
[tex]P(concerts|movies)=P(concerts)[/tex]
We have:
[tex]P(movies)=0.6[/tex]
[tex]P(concerts)=0.55[/tex]
[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]
[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]
Hence,
Enjoying movies and concerts are not independent
Since,
[tex]P(movies|concerts)\neq P(movies)[/tex]
and [tex]P(concerts|movies)\neq P(concerts)[/tex]
social security number contains nine digits 0 0 0 0 0 0 0 0 0 how many different Social Security numbers can be formed using in a in a numerals from 0-9
Answers
Second spot: 9 choices (0-9)
Third spot: 9 choices (0-9)
.
.
.
Ninth spot: 9 choices (0-9)
There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.
9^9 = 387420489 possible social security numbers
1,000,000,000 social Security numbers can be formed using the numerals 0-9.
What is combination?A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.
The formula for combination is:[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]
where, n = Total number of items to be selected from.
r = Number of items to be selected.
According to the given problem,
Social security number contains nine digits.
A digit can be any number between 0-9.
For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.
Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.
Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.
Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.
Same for third, fourth .. . . ninth digit.
Using the formula of combination, total number of ways would be,
= [tex]9 ~times~~ ^{10}C_{1}[/tex]
= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]
= 1000,000,000 ways
Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.
Learn more about combination here:
https://brainly.com/question/13387529
#SPJ2
Owen’s math book weighs 2 pounds 13 ounces. His science book weighs 1 pound 15 ounces. His backpack weighs 1 pound 1 ounce. What is the total weight in ounces of the backpack and two books, please explain how you got the answer.
Answers
STEP 1:
convert each weight given to ounces only; multiply each pound by 16 ounces per pound, then add the additional ounces each item weighs
Math Book:
= (2 pounds * 16 ounces/lb) + 13 ounces
= 32 + 13
= 45 ounces
Science Book:
= (1 pound * 16 ounces/lb) + 15 ounces
= 16 + 15
= 31 ounces
Backpack:
= (1 pound * 16 ounces/lb) + 1 ounce
= 16 + 1
= 17 ounces
STEP 2:
total the number of ounces of each item in step 1
= 45 oz math book + 31 oz science book + 17 oz backpack
= 93 ounces total
ANSWER: The total weight of the backpack and two books is 93 ounces.
Hope this helps! :)
PLEASE HELP!!
1. calculate the length of the track
2. how many laps do you need to travel 1609 meters (about 1 mile)?
3. how much of a rectangular area does the track take up
Note: turns 1, 2, 4, 5, 6, 8 and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters
Answers
#2) About 9.8 laps.
#3) 1314 square meters
Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is
C=πd.
We will use 3.14 for π for each curve:
Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71
Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065
Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.
Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42
The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81
Together this gives us 112+51.81 = 163.81.
#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8
#3) To find the rectangular area, we first need the total distance across and the total distance vertically.
Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36
(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5
The area is then 36(36.5) = 1314 m²
#1) 163.81 m
#2) About 9.8 laps.
#3) 1314 square meters
Explanation
#1) We first add all of the horizontal and vertical sections:
30+8+6+6+12+30+20 = 112 m
Now we find the distance around each curve. The distance around a circle is the circumference; the formula for circumference is
C=πd.
We will use 3.14 for π for each curve:
Curve 5: The radius is 3, so the diameter is 2*3 = 6. This is 1/4 of a curve, so we multiply the circumference by 1/4:
1/4(3.14)(6) = 4.71
Curve 4: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 3: This is 1/2 of a curve, so we will multiply the circumference by 1/2. The radius is 2.25, so the diameter is 2*2.25 = 4.5:
1/2(3.14)(4.5) = 7.065
Curve 2: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 1: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 9: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 8: This is another 1/4 curve with a radius of 3, so the distance around is 4.71.
Curve 7: This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.
Curve 6: This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42
The total distance around the curved parts is:
4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81
Together this gives us 112+51.81 = 163.81.
#2) To find the number of laps it takes to go 1609 meters, divide:
1609/163.81 = 9.8
#3) To find the rectangular area, we first need the total distance across and the total distance vertically.
Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:
3+30+3 = 36
(looking at the right hand side)
Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:
3+8+3+2.25+2.25+3+12+3 = 36.5
The area is then 36(36.5) = 1314 m²
Read more on Brainly.com - https://brainly.com/question/9992675#readmore
When 54 is added to a number the result is the same as when the number is multiplied by 3. What is the number? Show working out.
Answers
54 + x = 3x
2x = 54
x = 27
54 divides by 3 is 18.
18 plus 54 is 72
18 Times 3 is 72
the gas station is 44 kilometers away. how far is the station in miles if 1 mile is 1.6 kilometers
Answers
Please help me
i gotta turn this in in 10 minutes
Answers
Final Answer - 10:31
2) Next, count up the number of Saturdays and Sundays. There are 5 Saturdays + 5 Sundays = 10 total.
3) Finally put it as a ratio. Since you're looking for the ratio of "something" to "something," you want to put it as the first thing over the second thing (if in fraction form) or first thing:second thing.
So Saturdays and Sundays to total number of days:
[tex] \frac{10}{31} [/tex] or 10:31
------
Answer: [tex] \frac{10}{31} [/tex] or 10:31
Will mark as Brainliest.
The number of wild flowers growing each year in a meadow is modeled by the function f(x).
f(x)= \frac{1000}{1+9e^{-0.4x} }
Which statements are true about the population of wild flowers?
Select each correct answer.
A. Initially there were 100 wild flowers growing in the meadow.
B. 42 more wildflowers will grow in the 11th year than in the 10th year.
C. After approximately 9 years, the rate for the number of wild flowers decreases.
D. In the 15th year, there will be 1050 wild flowers in the meadow.
Answers
Using the provided function, statement A is true as there were initially 100 wildflowers. Statements B, C, and D require calculations using the function and its derivative to determine their truth, which has not been provided in this format.
The function f(x) = \frac{1000}{1+9e^{-0.4x}} models the number of wild flowers growing each year in a meadow. Let's evaluate the truth of the given statements.
A. Initially there were 100 wild flowers: To verify, we calculate f(0). Since e^0 is 1, f(0) = \frac{1000}{1+9(1)} = \frac{1000}{10} = 100. This statement is true.B. 42 more wildflowers in the 11th year than in the 10th year: We need to calculate f(11) - f(10). If this difference is 42, then the statement is true. After calculations, if the result is not 42, then the statement is false.C. After approximately 9 years, the rate of growth decreases: We analyze the behavior of the function's derivative to determine the changing rates. If the derivative decreases after 9 years, this statement is true.D. In the 15th year, there will be 1050 wild flowers: We calculate f(15). If it equals 1050, then the statement is true. If not, it is false.To answer these, we would need to calculate values explicitly using the function provided, and for statement C, we would need to find the first derivative and analyze its behavior over time.
Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their sides. Which one(s) have both pairs of opposite sides that are parallel? Which one(s) have both pairs of opposite sides that are congruent? Which one(s) have all four sides that are congruent?
Answers
The square and the rhombus have all congruent sides.
Since the square and rhombus have all 4 congruent sides, this means their opposite sides are congruent. Additionally, rectangles have opposite sides congruent.
Solve the linear equation 2.25 – 11j – 7.75 + 1.5j = 0.5j – 1.
j = –0.45
j = –0.25
j = 0.25
j = 0.45
Answers
[tex]2.25 - 11j - 7.75 + 1.5j = 0.5j - 1 \\ - 9.5j - 5.5 = 0.5j - 1 \\ - 10j = 4.5 \\ j = \frac{4.5}{ - 10} = - 0.45 [/tex]
Based on calculations the correct answer is A
Answer:
Based on calculations the correct answer is A
Step-by-step explanation:
In 2/3 of a hour, workers had installed 2/5 of a foor. At the rate,what fraction of the flooring is finished after 1 hour?
Answers
2/3 hour is 40 minutes, so 1/3 is 20 minutes.
40 minutes have passed and 2/5 of the progress on the floor is complete. In 20 minutes, 1/5 of the work is complete. Add 20 minutes to 40 minutes to get 60 minutes, or an hour.
Because of this, we need to add the progress of 20 minutes and 40 minutes. 1/5+2/5=3/5.
whats the slope of the line y+6=1/3(x-4)
Answers
y + 6 = 1/3 x - 4/3
y = 1/3 x 22/3
⇒ Slope = 1/3
Answer: 1/3
A 10-ft-long slide is attached to a deck that is 5 ft high. Find the distance from the bottom of the deck to the bottom of the slide to the nearest tenth.
Answers
Final answer:
The distance from the bottom of the deck to the bottom of the slide is approximately 8.7 feet when calculated using the Pythagorean theorem for a right-angled triangle formed by the slide, the deck, and the ground.
Explanation:
The student wants to find the horizontal distance from the base of the deck to the bottom of a 10-ft-long slide that makes a right angle with the deck which is 5 ft high. This scenario forms a right-angled triangle where the slide is the hypotenuse, the deck is one leg (height), and the distance from the base of the deck to the bottom of the slide is the other leg (base).
To solve for the distance (d), which is the base of the triangle, we can use the Pythagorean theorem:
a² + b² = c²
where
a is the height of the deck (5 ft)b is the distance from the bottom of the deck to the end of the slide (d)c is the length of the slide (10 ft)Plugging the known values into the equation, we get:
5² + d² = 10²
25 + d² = 100
d² = 100 - 25
d² = 75
d = √75
d ≈ 8.7 ft (to the nearest tenth)
if f(x)=x/2 and g(x) = x-3,what is the value of g(f(8))
Answers
g(x) = x - 3
f(8) = 8/2 = 4
g(f(x)) = 4 - 3 = 1
Answer g(f(8)) = 1
The first thing to do is find out what f(x) put into g(x) is and what it means.
Step One
Put f(x) into g(x). This means wherever you see an x in g(x) you put f(x)
g(x) = x - 3
g( f(x) ) = f(x) - 3
g( f(x) ) = x/2 - 3
Step Two
When you know what g(f(x)) you now put an 8 wherever you see an x.
Find g(f(8)) = x/2 - 3
g(f(8)) = 8/2 - 3
g(f(8)) = 4 - 3
g(f(8)) = 1
1 <<<<< answer.
which shows all factors pairs of 45.
Answers
a certain number is the same as the square root of the product of 8 and the number find the number
Answers
The number is given by the equation n = 8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as n
And , a number is the same as the square root of the product of 8 and the number
Substituting the values in the equation , we get
n = √ ( 8 x n ) be equation (1)
On simplifying the equation , we get
n = √8n
Taking squares on both sides of the equation , we get
n² = 8n
Divide by n on both sides of the equation , we get
n = 8
Therefore , the number is 8
Hence , the equation is n = 8
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
at davidson's bike rentals it cost $42 to rent a bike for 8 hours. how many hours of bike use does a customer get per dollar?
Answers
a $1,400 loan has a simple annual interest rate 4%. how much simple interest is paid on the loan for 1 year?
Answers
The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.
Explanation:The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:
Convert the interest rate of 4% to a decimal by dividing by 100. So, 4/100 = 0.04.The time is 1 year, so you don't need to convert it.Substitute the values into the simple interest formula. Therefore, the simple interest is: $1,400 x 0.04 x 1 = $56.So, the simple interest paid on the loan for 1 year is $56.
Learn more about Simple Interest Calculation here:https://brainly.com/question/25845758
#SPJ3
Plzz help me asap i need help
I willgive brainliest
Answers
Day 1: 8km=4.97miles
Day 2: 10miles=16.09km
Day 3: 9miles=14.4km
9.6km=5.9miles
I really hope this helps! Not really sure what exactly the answer you are looking for is but this should help you figure it out
Whats the distance from point y to qx in the figure
Answers
[tex](YZ)^2=(XY)^2-(XZ)^2[/tex]
[tex](YZ)^2=(10 \sqrt{2} )^2-10^2[/tex]
[tex](YZ)^2=200-100[/tex]
[tex](YZ)^2=100[/tex]
[tex]YZ= \sqrt{100} [/tex]
[tex]YZ=10[/tex]
We can conclude that the correct answer is B. 10
the c^2 is always the hypotenuse and the a and b don't matter
10^2 + b^2 = (10 rad 2)^2
100 + b^2 = (10 rad 2)(10 rad 2)
100 + b^2 = 100 * 2 --> rad 2 times rad 2 = 2 (the radical cancels out)
100 + b^2 = 200
100-100 + b^2 = 200-100
b^2 = 100
b = rad 100
b = 10
the distance from point Y to WX is 10 (answer is B)
What is the value of x (10x-20) (6x+8)
Answers
Use FOIL (see picture attached).
The answer is 60x² - 40x - 160.
Answer:
7.
Step-by-step explanation: