The metro bus travels 5 miles per gallon of gas.
The formula used to calculate the distance traveled per gallon of gas is number of miles traveled divided by number of gallons used. Therefore, to calculate how far the metro bus travels in one gallon, we use the following formula:
Distance per gallon = Miles Traveled / Gallons Used
Distance per gallon = 275 miles / 55 gallons
Distance per gallon = 5 miles
Therefore, the metro bus travels 5 miles per gallon of gas.
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What is the product of (3a 2)(4a2 – 2a 9)?a. 12a3 − 2a + 18b. 12a3 + 6a + 9c. 12a3 − 6a2 + 23a d. 18+ 12a3 + 2a2 + 23a + 18
Answer:
D. 12a^3+2a^2+23a+18
Step-by-step explanation:
In a marathon race of 21 km a runner has been running at a constant speed of 5 by 3 m per second for the last 3 hour. How much distance remain to be run to finish the marathon
the runner still needs to run a distance of 15 km to finish the marathon.
To find out how much distance remains to be run in the marathon, we can first calculate how far the runner has already run in the last 3 hours. We can use the formula:
distance = speed x time
where speed is in meters per second and time is in hours.
The runner has been running at a constant speed of 5/3 m/s for 3 hours, so the distance covered so far is:
distance = (5/3) m/s x 3 hours x 3600 seconds/hour
distance = 6000 meters or 6 km
Therefore, the runner has already completed 6 km of the marathon, which means that the remaining distance to be run is:
remaining distance = total distance - distance already covered
The total distance of the marathon is 21 km, so the remaining distance is:
remaining distance = 21 km - 6 km
remaining distance = 15 km
Therefore, the runner still needs to run 15 km to finish the marathon.
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Peter has hats. He can divide them into equal groups of 2,6 and 8. How many hats does Peter have?
Answer:
24
Step-by-step explanation:
Answer: 24 hats
Step-by-step explanation:
1. Find common multiples: 2: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36 6: 6,12,18,24,30,36 8: 8,16,24,32
2. Find the least common multiple: 24
Use this tax table to find how much tax you need to pay on a taxable income of $25,000.
If taxable income is over-- But not over-- The tax is:
$0 $7,825 10 percent of the amount over $0
$7,825 $31,850 $782. 50 plus 15 percent of the amount over 7,825
$31,850 $77,100 $4,386. 25 plus 25 percent of the amount over 31,850
$77,100 $160,850 $15,698. 75 plus 28 percent of the amount over 77,100
$160,850 $349,700 $39,148. 75 plus 33 percent of the amount over 160,850
$349,700 no limit $101,469. 25 plus 35 percent of the amount over 349,700
Based on the information provided, the total tax this person will need to pay is $2,622,2.
What is the total tax in this case?The amount of money you pay for taxes depends on your income as there are specific percentages to be paid. In the case the income is $25000, this income matches the range $7,825 - $31,850, and therefore you should pay 50 plus 15 percent of the amount over 7,825. Based on this, let's calculate the money to be paid:
$25,000 - $7852 = $17, 148 x 0.15 (15%) = $2,572.2 + $50 = $2622.2
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The members of a school club are selling tickets for a fundraiser. The goal for the fundraiser is to earn $50.00 each day from ticket sales. The list below shows the percent of the goal reached each day. On the first day, the members earned 90% of their daily goal. On the second day, the members earned 6% more than their daily goal. On the third day, the members earned 14% less than their daily goal. How much money, in dollars, did the members earn from ticket sales on all three days?
On the first day, the members earned 90% of their daily goal of $50.00 which is equal to $45.00 (0.9 x $50.00 = $45.00).
On the second day, the members earned 6% more than their daily goal of $50.00 which is equal to $53.00 ($50.00 + 0.06 x $50.00 = $53.00).
On the third day, the members earned 14% less than their daily goal of $50.00 which is equal to $43.00 ($50.00 - 0.14 x $50.00 = $43.00).
Therefore, the members earned a total of $45.00 + $53.00 + $43.00 = $141.00 from ticket sales on all three days.
The members of the school club earned $141.00 from ticket sales over the three days.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find out how much money the members of the school club earned from ticket sales on all three days
Let us calculate the amount of money earned each day and then add them together.
On the first day, the members earned 90% of their daily goal, which is:
0.9 x $50.00 = $45.00
On the second day, they earned 6% more than their daily goal, which is:
$50.00 + 0.06 x $50.00 = $53.00
On the third day, they earned 14% less than their daily goal, which is:
$50.00 - 0.14 x $50.00 = $43.00
To find the total amount of money earned over the three days, we simply add the amounts earned on each day:
$45.00 + $53.00 + $43.00 = $141.00
Therefore, the members of the school club earned $141.00 from ticket sales over the three days.
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please help !! Im having trouble
The length of the line segment between C(-3,3) and D(3,-3) is 6√2 units.
Calculating the length of the distance CDGiven that
C(-3, 3) and D(3, -3)
To find the length of the line segment between points C(-3,3) and D(3,-3), we can use the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the coordinates for C(-3,3) and D(3,-3), we get:
d = √((3 - (-3))^2 + (-3 - 3)^2)
Evaluate
d = √(6^2 + (-6)^2)
d = √72
Simplifying the square root, we can write the length as:
d = 6√(2)
Therefore, the length of the segment CD is 6√2 units.
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Which is the graph of y = −1/2 (x−3)^2−1?
Emergency help needed will mark brainliest
Answer: The first graph
Step-by-step explanation: because the vertex is (3,-1)
Then plug in number like is 1 is x solve for y which will be -3
if x is 2, y is -3/2
x is 3, y is -1
x is 4, y is -3/2
x is 5, y is -3
Answer:
Vertex at (3,-1) and flipped upside down (opening downward)
*looks like the first one of the first attachment*
Step-by-step explanation:
The normal untransformed parabola is a U-ish, V-ish curve that has its vertex at (0,0) and it opens upward. There are "nice" points at (1,1) and (2,4) also at (-1,1) and (-2,4) Your parabola has had four changes made to it:
□The negative sign in front on your equation will FLIP the whole thing upside down so it opens downward.
□The 1/2 in front will "smash" the parabola so it is flatter and wider.
□The - 3 that's in close next to the x will shift (slide, translate) the whole thing to the right 3 units **left and right shifts are kind of the opposite of what you might think: - shifts right and + shifts left**
□The -1 tacked on to the end will shift (slide, translate) the whole thing down one unit. **more intuitive, - shifts down and + shifts up**
Which is the correct substitution for evaluating 10-y2 when y=3
Answer:
6
Step-by-step explanation:
y2= 3x2 = 6.
Determine the average rate of a function
The average rate of change of the quadratic function f(x) on the interval [0, 15] is equal to 23.
How to determine the average rate of change?In Mathematics, the average rate of change of a function f(x) on a closed interval [a, b] can be determined by using this mathematical equation (formula):
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [0, 15]:
a = 0; f(a) = -x² + 8x + 20
f(0) = -0² + 8(0) + 20
f(0) = 20
b = 9; f(b) = 365
f(15) = -15² + 8(15) + 20
f(15) = 365
By substituting the parameters into the average rate of change formula, we have the following;
Average rate of change = (365 - 20)/(15 - 0)
Average rate of change = 345/15
Average rate of change = 23.
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consider parallelogram vwxy below use the information given in the figure to findx m
In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).
Explain about the parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).
A parallelogram with all right angles is known as a rectangle, and a quadrilateral having equal sides is known as a rhombus. Rectangles and squares are both particular varieties of parallelograms since a square is just a degenerate instance of a rectangle.In the given parallelogram vwxy:
Parallel sides are equal.
So, 2x = 6
x = 6/2 = 3
Opposite pair of angles are also equal.
So,
∠W = ∠Y = 65°
Now,
∠YVX = 61° (alternate interior angle).
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Last year the city of Goose Pimple, Vermont, paid an average of $3,261 per employee in health care costs (including insurance and additional claims). This year the city management decided that they will contract with Grimms Health Maintenance Organization. At the end of the year they would like to know if they have saved any money. They take a sample of 50 and find a sample mean of $3,015 with a standard deviation of $1,745. Present a hypothesis, a null hypothesis, and evaluate the hypothesis. Explain in plain English what you have found
The solution to the offered question depends on the hypothesis the response is the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis.
To evaluate the hypothesis, we will play out a one-example t-test. The test measurement is determined as:
t = (test mean - populace mean)/(test standard deviation/sqrt(sample size))
Expecting an importance level of 0.05, we will dismiss the invalid hypothesis if the determined t-esteem is more noteworthy than the basic t-esteem.
Populace mean = $3,261 (given)
Test mean = $3,015
Test standard deviation = $1,745
Test size = 50
t = (3015 - 3261)/(1745/sqrt(50)) = - 2.58
Utilizing a t-table with 49 levels of opportunity (test size - 1) and an importance level of 0.05, the basic t-esteem is ±2.009.
Since the determined t-worth of - 2.58 is not exactly the basic t-worth of - 2.009, we can't dismiss the invalid hypothesis. This really intends that there isn't sufficient proof to recommend that there is a massive distinction in medical services costs per worker between last year and this year with the agreement with Grimms Wellbeing Upkeep Association having no effect.
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Mrs. A grills onions and peppers at a restaurant. She always grills more onions than peppers and always grills some of each. On Sunday, she grilled 38 onions and x peppers. Which pair of inequalities represents the number of peppers, x, she could have grilled on Sunday?
Group of answer choices
x > 0 and x > 38
x > 0 and x < 38
x > 0 and x > 37
x > 0 and x < 37
We can conclude after answering the provided question that As a result, inequality the correct answer is: x > 0 and x < 38
What is inequality?In mathematics, an inequality is a non-equal connection that exists between expressions or values. As a result, imbalance relates to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two points are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are utilized to calculate contrast values. Many simple inequalities can be solved by modifying its two sides until only the variables remain. But a few factors contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.
Mrs. A always grills more onions than peppers, so the number of onions grilled (38) must be greater than the number of peppers grilled (38). (x). As a result, the inequality can be used to represent this relationship:
38 > x
Mrs. A also grills some of each, so the total number of peppers grilled (x) must be greater than zero. As a result, the inequality can be used to represent this relationship:
x > 0
The inequity pair that represents the number of peppers, x, she could have grilled on Sunday is:
x > 0 and 38 > x
This can also be expressed as:
0 < x < 38
As a result, the answer is:
x > 0 and x < 38
As a result, the correct answer is:
x > 0 and x < 38
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PLEASE HELP FAST THIS IS DUE TODAY
Sophia throws a dart at this square-shaped target:
A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3.
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part A: If assuming 0 means the white part, then nο.
Part B: If assuming 0 means the black part, then yes.
What is prοbability?The prοbability οf an οccurrence is a figure that represents hοw likely it is that the event will take place. In terms οf percentage nοtatiοn, it is expressed as a number between 0 and 1, οr between 0% and 100%. The higher the likelihοοd, the mοre likely it is that the event will take place.
Part A: If assuming 0 means the white part, then nο, there is a chance tο hit the black circle but the circle is οnly abοut 1/9th, then the whοle target, sο putting it in numbers, it wοuld be abοut 1/9 cοmpared tο 8/9.
8/ 9 has a higher chance.
Part B: If assuming 0 means the black part, then yes, as I said in Part A, it's basically cοmparing 1/9 tο 8/9.
1/9 being the black part and 8/9 being the white [tex]8/9 > 1/9[/tex] which means the white pοrtiοn has a higher prοbability.
Hence, Part A: If assuming 0 means the white part, then nο.
Part B: If assuming 0 means the black part, then yes.
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A netball team plays three matches. In each match the team is equally likely to win, lose or draw. Draw a tree diagram to show all the possible outcomes over the three matches.
b Calculate the probability that the team:
i wins all three matches,
ii wins more times than loses,
iii loses at least one match,
iv either draws or loses all three matches.
c Explain why it is not very realistic to assume that the outcomes are equally likely in this case.
b. i) The probability of winning all three matches is 1/27.
ii) The probability of winning more times than losing is 3/27.
iii) 7/27
iv) 2/27
c. many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.
What is probability?Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
a. Tree diagram:
Match 1 | Match 2 | Match 3
--------------------------------
Win | Win | Win
Draw | Draw | Draw
Lose | Lose | Lose
b. i) The probability of winning all three matches is P(Win, Win, Win) = (1/3) * (1/3) * (1/3) = 1/27
ii) The probability of winning more times than losing is
P(Win, Win, Draw) + P(Win, Draw, Win) + P(Draw, Win, Win)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 3/27
iii) The probability of losing at least one match is
P(Lose, Win, Win) + P(Win, Lose, Win) + P(Win, Win, Lose) + P(Lose, Lose, Win) + P(Lose, Win, Lose) + P(Win, Lose, Lose) + P(Lose, Lose, Lose)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 7/27
iv) The probability of either drawing or losing all three matches is
P(Draw, Draw, Draw) + P(Lose, Lose, Lose)
= (1/3) * (1/3) * (1/3) + (1/3) * (1/3) * (1/3)
= 2/27
c. It is not very realistic to assume that the outcomes are equally likely in this case because there are many factors that can influence the outcome of a match such as the skill of the players, the tactics used by the teams and the condition of the playing surface.
Therefore, it is unlikely that all outcomes are equally likely as assumed in this case.
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Find the area of a segment of a circle if the central angle of the segment is 50° and the radius is 15
In conclusion the area of the segment is approximately 32.76 square units.
How to find?
To find the area of a segment of a circle, we can use the formula:
Area of segment = (θ/360)πr²2 - (1/2)rsin(θ)
where:
θ is the central angle of the segment in degrees
r is the radius of the circle
π is a constant approximately equal to 3.14
sin is the sine function
In this case, the central angle is 50° and the radius is 15. Substituting these values into the formula, we get:
Area of segment = (50/360)π(15)²2 - (1/2)(15)sin(50)
= (5/36)π(225) - (1/2)(15)(0.766)
= 32.76 square units (rounded to two decimal places)
Therefore, the area of the segment is approximately 32.76 square units.
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a man sets out to travel from A to C via B. from A he travel a distance of 8km on a bearing of north 30°east to B. from B he travel a further 6km due east. calculate how far c is from north of A, east of A.
PLEASE HELP (:
A point on the unit circle has negative x value and a positive y value, select all the possible reference angles it could come from.
SELECT ALL THAT APPLY!
A. 225
B. 150
C. 135
D. 60
E. 300
F. 270
A pοint οn the unit circle having negative x value and a pοsitive y value, has the pοssible reference angles as -
Optiοn B: 150°, Optiοn C: 135°, and Optiοn D: 60°.
What is an angle?An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The Latin wοrd "angulus," which meaning "cοrner," is the sοurce οf the English term "angle." The shared terminus οf twο rays is knοwn as the vertex, and the twο rays are referred tο as sides οf an angle.
The unit circle is a circle with radius 1 centered at the οrigin οf a cοοrdinate plane.
Any pοint οn the unit circle can be represented as (cοs θ, sin θ), where θ is the angle made by the pοint with the pοsitive x-axis.
If a pοint οn the unit circle has negative x value and pοsitive y value, then it must be in the secοnd quadrant οr the fοurth quadrant.
In the secοnd quadrant, the reference angle is the angle between the terminal side and the x-axis, which is always acute.
In the fοurth quadrant, the reference angle is the angle between the terminal side and the x-axis, plus 360 degrees, which is alsο acute.
Therefοre, the pοssible reference angles that the pοint cοuld cοme frοm are -
B. 150°, which is the reference angle fοr an angle οf 210° in the secοnd quadrant.
C. 135°, which is the reference angle fοr an angle οf 225° in the secοnd quadrant.
D. 60°, which is the reference angle fοr an angle οf 300° in the fοurth quadrant.
Therefοre, the angle values are 150°, 135° and 60°.
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1. 2. 4 journal:Algebraic Properties and expressions
The distributive property states that we can distribute a factor across a sum or difference, add or subtract like terms by adding or subtracting their coefficients and The power rule states that when raising a power to another power, we multiply the exponents. and Algebraic Properties explained as
Journal Entry 1:
Today, I learned about the algebraic properties of addition and multiplication. These properties are commutative, associative, and distributive. The commutative property states that the order in which we add or multiply numbers does not affect the result. For example, 2+3 is the same as 3+2, and 2x3 is the same as 3x2. The associative property states that we can group numbers in different ways without changing the result. For example, (2+3)+4 is the same as 2+(3+4), and (2x3)x4 is the same as 2x(3x4). The distributive property states that we can distribute a factor across a sum or difference. For example, 2x(3+4) is the same as 2x3 + 2x4.
Journal Entry 2:
Today, I learned about algebraic expressions and how to simplify them using the properties of addition and multiplication. An algebraic expression is a combination of numbers, variables, and operations. For example, 2x + 3y - 4z is an algebraic expression. To simplify an expression, we use the properties of addition and multiplication to combine like terms and simplify the expression as much as possible. Like terms are terms that have the same variables raised to the same powers. For example, 2x and 5x are like terms, but 2x and 5y are not. We can add or subtract like terms by adding or subtracting their coefficients. For example, 2x + 5x is 7x. We can also multiply terms by using the distributive property. For example, 2(3x + 4y) is 6x + 8y.
Journal Entry 3:
Today, I learned about algebraic expressions with exponents. An exponent is a small number written to the right of a base number that indicates how many times to multiply the base by itself. For example, in 2³, the base is 2 and the exponent is 3. To simplify an expression with exponents, we use the properties of exponents, such as the product rule and the power rule. The product rule states that when multiplying two powers with the same base, we add their exponents. For example, 2³ x 2² is 2^(3+2) or 2^5. The power rule states that when raising a power to another power, we multiply the exponents. For example, (2²)³ is 2^(2x3) or 2^6. We can also simplify expressions with exponents by combining like terms, just like we did with expressions without exponents.
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1.2.4Journal: Algebraic Properties and ExpressionsJournalAlgebra I Sem 1Name:Date:Scenario:The ArcadeInstructions:
•View the video found on page 1 of this journal activity
.•Using the information provided in the video, answer the questions below
.•Show your work for all calculation
Jacob is a construction worker who earns a yearly income given by the expression 2 , 000 x + 6 , 000 , where x is the number of hours he works each week. Carlos works with Jacob and earns a yearly income given by the expression 3 , 500 x - 39 , 000 . A manager predicts that if Carlos and Jacob each work 35 hours, they will earn the same amount of money. Complete the statements. The solution to the equation 2 , 000 x + 6 , 000 = 3 , 500 x - 39 , 000 is Select hours. The manager's prediction is Select the actual number of hours that Carlos and Jacob need to work to earn the same amount of money.
The manager predicts that Carlos and Jacob need to work 35 hours each to earn the same amount of money.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
We can solve the equation 2,000x + 6,000 = 3,500x - 39,000 as follows:
2,000x + 6,000 = 3,500x - 39,000
Subtracting 2,000x from both sides, we get:
6,000 = 1,500x - 39,000
Adding 39,000 to both sides, we get:
45,000 = 1,500x
Dividing both sides by 1,500, we get:
x = 30
Therefore, the solution to the equation 2,000x + 6,000 = 3,500x - 39,000 is x = 30.
To find the actual number of hours that Carlos and Jacob need to work to earn the same amount of money, we can plug in x = 35 into both of their income expressions and set them equal to each other:
2,000(35) + 6,000 = 3,500(35) - 39,000
Simplifying, we get:
76,000 = 76,000
This means they will earn the same amount of money if they each work 35 hours per week.
Therefore, the manager predicts that Carlos and Jacob need to work 35 hours each to earn the same amount of money.
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A new cylindrical can with a diameter of 4 cm is being designed by a local company. The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3.14 for x and
round to the nearest hundredth. Apply the formula for surface area of a cylinder SA-28+ Ph
Answer:
The height is 9.73 cm.
Step-by-step explanation:
We can start by finding the radius of the cylinder:
r = d/2 = 4/2 = 2 cm
Then, we can use the formula for the surface area of a cylinder to solve for the height:
SA = 2πrh + 2πr²
130 = 2π(2)(h) + 2π(2)²
130 = 4πh + 8π
122 = 4πh
h ≈ 9.73 cm (rounded to the nearest hundredth)
So the height of the can is approximately 9.73 cm.
the equation
4x-2y=4
-4x+2y=-3
have the same/different what slopes and the same/different what y-intercept?
Answer:
same slopes: 2. different y-intercepts: (0,-2) and (0,-1.5)
Step-by-step explanation:
First, lets convert both of those to slope intercept form: y = mx + b, where m is the slope and b is the y-intercept.
4x-2y=4 simplifies to -2y=-4x+4, which is y=2x-2
-4x+2y=-3 simplifies to 2y=4x-3, which is y=2x-1.5
this means that they have the same slopes, 2.
they have different y-intercepts. the first one's is (0,-2) and the second one's is (0,-1.5)
‘You must be 1.4m tall or more to ride the rollercoaster’
Which of these expresses the sentence above mathematically?
Answer:
b
Step-by-step explanation:
The symbol in the middle of b means greater than or equal to
What are the x- and y-intercepts of the function f(x) = 2x² + x + 5?
O A. y-intercept: 5, x-intercept: 0
OB. y-intercept: 8; x-intercept: 0
O C. y-intercept: 5; x-intercept: none
OD. y-intercept: 8; x-intercept: none
The x- and y-intercepts of the function f(x) = 2x² + x + 5 is A.
we put x as equal to 0 first and we get y = 5 (y=f(x))
once we get y = 5 we can replace it in the equation and we get 2x^2+x=0 solving the quadratic equation, we get x=0, -1/2
The quadratic equation can be solved by taking x common then we are left with (2x+1).
the x we take common is equal to 0
(2x+1) = 0 gives x=-1/2
hence the x intercept = -1/2, 0 and y intercept =5
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precalculus Question 11.2
a) show that the distance between the two points.
b) describe the positions of the points relative to eachother. simplify the distance formula for this case.
c) simplify the distance formula.
d) choose two points on the polar coordinate system and find the distance between them. then choose different polar representations of the same two points and apply the distance formula again.
I will attach the answer, this work did not come from me but I figured I'd upload it anyways.
A can also be represented as A(2,-11π/6) and B can be represented as B(3,-π/6). Using the distance formula again, we have: distance = sqrt(2^2 + 3^2 - 223*cos(-11π/6 - (-π/6))) = sqrt(13)
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
a) To find the distance between two points in polar coordinates, we can use the Pythagorean theorem to calculate the distance in the radial direction and then use the law of cosines to take into account the angular separation. Thus,
distance = sqrt((r2-r1)^2 + (r1^2 + r2^2 - 2r1r2*cos(θ1 - θ2)))
Simplifying this expression, we get:
distance = sqrt(r1^2 + r2^2 - 2r1r2*cos(θ1 - θ2))
Using the identity cos(a-b) = cos(a)cos(b) + sin(a)sin(b), we can rewrite the expression as:
distance = sqrt(r1^2 + r2^2 - 2r1r2cos(θ1)cos(θ2) - 2r1r2sin(θ1)sin(θ2))
Using the identity cos^2(x) + sin^2(x) = 1, we can simplify the expression further:
distance = sqrt(r1^2 + r2^2 - 2r1r2*cos(θ1-θ2))
b) If θ1 = θ2, then the points lie on the same radial line and are separated only by their radial distances from the origin. In this case, the distance formula simplifies to:
distance = sqrt((r2-r1)^2) = abs(r2-r1)
This is what we would expect, as the distance between two points on the same radial line is simply the absolute difference in their radial distances from the origin.
c) If θ1 - θ2 = 90 degrees, then the points are separated by the maximum angular distance and lie on perpendicular radial lines. In this case, the distance formula simplifies to:
distance = sqrt(r1^2 + r2^2)
This is also what we would expect, as the distance between two points on perpendicular radial lines is simply the Pythagorean sum of their radial distances from the origin.
d) Let's choose two points in polar coordinates: A(2,π/6) and B(3,5π/6). Using the distance formula derived in part (a), we have:
distance = sqrt(2^2 + 3^2 - 223*cos(5π/6 - π/6)) = sqrt(13)
Now let's express these same points in different polar representations.
Therefore, a can also be represented as A(2,-11π/6) and B can be represented as B(3,-π/6). Using the distance formula again, we have:
distance = sqrt(2^2 + 3^2 - 223*cos(-11π/6 - (-π/6))) = sqrt(13)
As expected, the distance between the two points is the same regardless of their polar representations.
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For a certain industry, the mean annual salary rose from $25,200 to $28,960. Calculate the percent of increase. Round to the nearest tenth.
After answering the presented question, we can conclude that equation 0.1492063492063492 * 100% Percentage increase = 14.9% As a result, the average yearly pay has increased by 14.9%.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
To determine the % increase in mean annual wage, find the difference between the new and old salaries, divide it by the old salary, and multiply by 100.
(new salary - previous salary) / old salary * 100% = percentage increase
(28960 - 25200) / 25200 * 100% Percentage increase = 0.1492063492063492 * 100% Percentage increase = 14.9%
As a result, the average yearly pay has increased by 14.9%.
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Find two sets of three positive single digit integers with mmr equal to 4/5'
We find sets of three positive single digit integers with a mean of 4 and a range of 5 is {1, 5, 6} and another possible set is {2, 4, 6}.
Here mmr is mean, median, and range of a set of numbers. The mean of a set of numbers is the sum of all the numbers divided by the total number of numbers in the set. The median of a set of numbers is the middle number when the numbers are arranged in order.
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
To find two sets of three positive single digit integers with a mean of 4 and a range of 5, we can use the formula:
Mean = (sum of numbers) / (number of numbers)
Since we want the mean to be 4, the sum of the three numbers in each set must be 12. Since we want the range to be 5, the largest number in each set must be 5 more than the smallest number.
One possible set of three numbers that satisfies these conditions is {1, 5, 6}. The mean of this set is (1+5+6)/3 = 4, and the range is 6-1 = 5.
Another possible set of three numbers that satisfies these conditions is {2, 4, 6}. The mean of this set is (2+4+6)/3 = 4, and the range is 6-2 = 4.
Therefore, two sets of three positive single digit integers with a mean of 4 and a range of 5 are {1, 5, 6} and {2, 4, 6}.
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please explain and answer very well
According to the information in the table, the bus arrives in Newtown at 11:09. So this trip would take 31 minutes.
How to know what time the bus arrives in Newtown?To find out what time the bus arrives in Newtown we must analyze the table. In this case we can see row 3 that has the information about the bus route that leaves at 11:38.
The fourth city that this bus visits is Newtown, where it arrives at 11:09 after stopping in Milton and Leek. So the arrival time in Newtown would be 11:09.
On the other hand, to find how long the trip took we must compare both times (10:38, 11:09) and find the difference. So, for it to be 11:00, there would be 22 minutes left. Then add 9 minutes, so the total would be 31.
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Please, someone help me. This is geometry, 10th grade level.
Find the areas listed below, round to the nearest
hundredth if necessary. Make sure you use 3.14
for pie
The area of the circle is 200.96 square kilometers, the area of the polygon is 181.02 square kilometers and the shaded region is 19.94 square kilometers.
The area A of a circle with radius r can be found using the formula:
A = πr^2
Plugging in the given value of radius, we get:
A = π(8 km)^2
Simplifying the expression, we get:
A = 64π km^2
So, we have
A ≈ 64 x 3.14 km^2
A ≈ 200.96 km^2
To find the area of an octagon with a radius of 8 km, we can break it up into eight congruent isosceles triangles.
So, we have
Area = 8 * Area of triangle
This gives
Area = 8 * 1/2 * r² sin(central angle)
So, we have
Area = 8 * 1/2 * 8² sin(45)
Evaluate
Area = 181.02
The shaded area is
Shaded = 200.96 - 181.02
Shaded = 19.94
Hence, the shaded area is 19.94 square kilometers.
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??? Help please !!!!!!!
The only option that represents a function is the relation in C.
Which of the following represents a function?We know that a relation maps elements of one set, called the domain, into elements of another set, called the range.
A relation is a function if each of the elements in the domain is mapped into only one element of the range.
Then for example, in option D we can see that the element -3 is mapped into two different values, then it does not represent a function.
Similar thing for the graph in option B, where we can see two points on the same vertical line.
Or the first option where -1 is mapped to two different values.
The only option that represents a function is option C.
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Please help! Solve for y. Round your answer to the nearest tenth and type it as a number
The value of y is 7.5 for the given similar triangle.
Define the Similar triangle?The sides of comparable triangles are relative to one another. For instance, if the proportion of the lengths of two comparing sides of one triangle to another is 2:1, then the other two relating sides will likewise be in the proportion of 2:1.
According to the figure; two triangles are similar because its identities,
So, (2y + 25) = 2 times of (2y + 5)
we can write as,
⇒ (2y + 25) = 2 × (2y + 5)
⇒ 2y + 25 = 4y + 10
⇒ 2y - 4y = 10 - 25
⇒ - 2y = - 15
⇒ y = 15/2 = 7.5
Therefore, the value of y is 7.5 of the given similar triangle.
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