To find three additional polar representations of the point (2, 3π/4), we can add or subtract 2πk to the angle, where k is an integer. Using this method, we get:
(2, -5π/4) - subtract 2π
(2, 11π/4) - add 2π
(2, -3π/4) - subtract 2π
To find the smallest and largest values of the angle, we need to consider the interval −2π < θ < 2π. The given angle of 3π/4 lies in the second quadrant. Adding or subtracting 2π to this angle will give us angles in the third and fourth quadrants. Therefore, the smallest value of the angle is −3π/4, and the largest value is 5π/4. Thus, the polar representations are:
(2, 3π/4)
(2, -5π/4)
(2, 11π/4)
(2, -3π/4)
(2, 5π/4)
What is the sum of the measures of the interior angles of a 20-sided figure?
Responses
3,240°
360°
3,600°
180°
Answer:
3,240°
Step-by-step explanation:
The sum of the measures of the interior angles of a polygon with n sides can be found using the formula:
(n-2) * 180°
So, for a 20-sided figure, the sum of the interior angles would be:
(20-2) * 180° = 18 * 180° = 3,240°
a store sells cereal for $2.99 and milk for $4.99. a shopper wants to spend at least $12 but no more than $25 on groceries. what is one possible combination of cereal and milk the shopper can buy and still stay in their budget?
The possible combination of cereal and milk the shopper can buy and still stay in their budget is:
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
Inequality:The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.
"Information available from the question"
A store sells cereal for $2.99 and milk for $4.99.
A shopper wants to spend at least $12 but no more than $25 on groceries.
To find the possible combination of cereal and milk the shopper can buy and still stay in their budget.
Now, According to the question:
Let x represents the shopper buy and y represent the milk.
Then represents the inequality according to the information.
A store sells cereal for $2.99
It write 2.99x
And for the milk is 4.99y
So,
12 ≤ 2.99x + 4.99y ≤ 25 (x , y ∈ N)
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Des can choose between two jobs: Job A pays £3.80 per hour for 40 hours per week, Job B pays £4.50 per hour for 32 hours per week. For which job will Des earn the most money per week?
The solution is, For job- A will Des earn the most money per week.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
Job A pays £3.80 per hour for 40 hours per week,
Job B pays £4.50 per hour for 32 hours per week.
for, job A - he earns = £3.80 * 40
= £ 152 pe week
and, for job B - he earns = £4.50 * 32
=£ 144 per week.
Hence, The solution is, For job- A will Des earn the most money per week.
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7)
3)
5)
Determine if the two triangles are congruent. If they are, state how you know.
2)
1)
A
6)
SSS?
SAS?
Some triangle pairs are congruent triangles but some others are not, because:
Congruent; 2 pairs of corresponding angles and 1 corresponding side Congruent; 2 pairs of corresponding sides and 1 corresponding angleCongruent; 2 pairs of corresponding angles and 1 corresponding sideCongruent; 3 pairs of corresponding sidesNot congruent; only 2 pairs of corresponding sidesCongruent; 1 pair of corresponding side and 2 corresponding anglesNot congruent; only 3 pairs of corresponding anglesNot congruent; only 3 pairs of corresponding anglesA pair of triangles is congruent if they have one of these criterias:
SSS (three corresponding sides)SAS (2 pairs of corresponding sides and 1 pair of corresponding angle between those side pairs)ASA (2 pairs of corresponding angles and 1 pair of corresponding side between those angle pairs)AAS (2 pairs of corresponding angles and 1 pair of corresponding side not between the angles)HL (Congruent hypotenuse and 1 pair of corresponding side)Let's explore each triangle pairs we have:
Pair 1
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles .
Pair 1 meet ASA rules --> Congruent triangles
Pair 2
Pair 2 has 1 corresponding angle and 2 pairs of corresponding sides
Pair 2 meets SAS rules --> congruent triangles
Pair 3
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides between the angles.
Pair 3 meet ASA rules --> Congruent triangles
Pair 4
Pair 4 has 3 corresponding sides and meets SSS rules --> congruent triangles
Pair 5
Pair 5 only has 2 corresponding sides --> not congruent triangles
Pair 6
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. They also have another pair of corresponding angles and 1 pair of corresponding sides not between the angles.
Pair 6 meet AAS rules --> Congruent triangles
Pair 7
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 7 also has another 2 corresponding angles. In total, pair 7 has 3 corresponding angles.
Pair 7 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
Pair 8
We know that both triangle have a vertical angle on its connection, hence both angles are congruent. Pair 8 also has another 2 corresponding angles. In total, pair 8 has 3 corresponding angles.
Pair 8 is not congruent triangles because three corresponding angles might have different size of sides. A pair of triangles can be congruent only if there is at least one pair of corresponding side between them.
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Draw a rectangle on graph paper with vertices whose coordinates are (-1, 2), (-1, -4), (3, -
4), and (3, 2).
(Graph paper provided in the jamboard in Q1).
Part A: Find the perimeter and area of the rectangle. Show your work.
Part B: Multiply the coordinates of the vertices of the rectangle by 3. State the new vertices.
Part C: Draw the rectangle whose vertices are those you found in Part B. Find the perimeter and area of this new rectangle.
Show your work.
Part D: Compare the perimeter of the rectangle in Part C to the perimeter of the original rectangle. (list each and then compare).
Part E: Compare the area of the rectangle in Part C to the area of the original rectangle. (list each and then compare).
The area of the new rectangle is 9 times the previous area and the perimeter of the new rectangle is 3 times the previous area
Part A: Find the perimeter and area of the rectangle.From the question, we have the following parameters that can be used in our computation:
(-1, 2), (-1, -4), (3, -4), and (3, 2).
See attachment for the points, where we have
Length = 4 and width = 6
Using area and perimeter formulas, we have
Area = 4 * 6 = 24
Perimeter = 2 * (4 + 6) = 20
Part B: Multiply the coordinates by 3Here, we have
New = (-3, 6), (-3, -12), (9, -12), and (9, 6).
Part C: Find the new perimeter and area of the rectangle.See attachment for the points, where we have
Length = 12 and width = 18
Using area and perimeter formulas, we have
Area = 12 * 18 = 216
Perimeter = 2 * (12 + 18) = 60
Part D: Comparison of the areasThe area of the new rectangle is 9 times the previous area
i.e. 216/24 = 9
Part E: Comparison of the perimetersThe perimeter of the new rectangle is 3 times the previous area
i.e. 60/20 = 3
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please help
thank you!!
Step-by-step explanation:
Hi joolin
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A new refrigerator has a price of $480.00. The store will discount the price by 15% if the purchaser pays in cash. What is the cash price of the refrigerator?
The cash price of the refrigerator is $408.
What is discount?A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.
Given that, a new refrigerator has a price of $480.00.
The store will discount the price by 15% if the purchaser pays in cash.
Now, the discount is
15% of 480
= 15/100 ×480
= 0.15×480
= 72
Now, 480-72
= $408
Therefore, the cash price of the refrigerator is $408.
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Camden just accepted a job at a new company where he will make an annual salary of $43000. Camden was told that for each year he stays with the company, he will be given a salary raise of $2000. How much would Camden make as a salary after 7 years working for the company? What would be his salary after tt years?
The solution is, the salary of the Luke after 10 years is 98000 dollars & the salary of the Luke after t years is 53000+4500t .
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
Given data:
* The starting salary of the Luke in the new company was,
S1 = 53000
* The salary raise given to Luke each year is,
R = 4500
(a). The salary of the Luke after 10 years is,
S = S1 +R*10
S = 53000 + ( 4500* 10)
S = 98000
Thus, the salary of the Luke after 10 years is 98000 dollars.
(b). After the t years,
S = S1 +R*t
S = 53000 + ( 4500* t)
S = 53000+4500t
Thus, the salary of the Luke after t years is 53000+4500t .
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a box contains 6 blue blocks, 13 yellow blocks, 15 blue spheres, and 17 yellow spheres. what is the probability you draw a sphere given it is blue?
The probability that you draw a sphere given that it is blue is given as follows:
5/7.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The total outcomes in this problem are the blue shapes, hence the number is given as follows:
6 + 15 = 21 shapes.
The desired outcomes are the blue spheres, hence the number is given as follows:
15.
Hence the probability that you draw a sphere given that it is blue is given as follows:
p = 15/21
p = 5/7. (simplify numerator and denominator by 3).
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Help please (will mark as brainlest)
[tex] - a {x}^{2} + 2x + a - 5[/tex]
The value:[tex] - 183[/tex]
Using a standard deck of 52 cards, Lisa drew a card, recorded the suit of the card picked, then replaced it back in the deck. She continued this for a total of 40 draws. The table shows the frequency of each type of card drawn.
The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%
How to find the experimental probability ?The experimental probability that a heart is selected is:
= Number of times hearts was selected / Number of times Lisa drew a card
= 9 / 40
This then means that the experimental probability of not selecting a heart is:
= 1 - experimental probability of selecting a heart
= 1 - 9 / 40
= 31 / 40
= 0. 775
= 77. 5 %
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The question is:
Determine the experimental probability of not selecting a heart.
(A) P(not heart) = 9%
(B) P(not heart) = 10%
(C) P(not heart) = 67.5%
(D)P(not heart) = 77.5%
Match the exponent expression to it's correct solution.
The matching is as follow:
x²³ / x³ --> [tex]x^{20[/tex]
[tex]x^{14}/ x^{17}[/tex] --> 1/x³
[tex]x^{19}/ x^{33}[/tex] --> 1/[tex]x^{14[/tex]
[tex]x^{16}/ x^7[/tex] --> [tex]x^9[/tex]
What are exponent and Power?Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.
Given:
We will use the Property of exponent and power
[tex]x^m/ x^n[/tex] = [tex]x^{m-n[/tex]
1. x²³ / x³
Using the property
x²³ - ³ = [tex]x^{20[/tex]
2. [tex]x^{14}/ x^{17}[/tex]
Using the property
= [tex]x^{14- 17}[/tex]
= [tex]x^{-3[/tex]
= 1/x³
3. [tex]x^{19}/ x^{33}[/tex]
Using the property
= [tex]x^{19-33}[/tex]
= [tex]x^{-14}[/tex]
= 1/[tex]x^{14[/tex]
4. [tex]x^{16}/ x^7[/tex]
Using the property
= [tex]x^{16-7}[/tex]
= [tex]x^9[/tex]
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Hi,what is 9/10 divided by 3/5
The value of 9/10 divided by 3/5 is 3/2.
How to multiply two fractions?
When multiplying fractions, you first start with the two fractions you want to multiply. You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.
Firstly , let's find the reciprocal of the divisor
Reciprocal of
3/5 is 5/3
Now, multiply it with the dividend
So,
9/10 ÷ 3/5
= 9/10 × 5/3
= 45/30
After reducing the fraction, the answer is
3/2
Hence , the value of 9/10 divided by 3/5 is 3/2.
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it is known that a certain drug causes side effects in 12 12 % of patients. if we consider a random sampling of 12 12 patients, what is the probability less than two have the side effect?
By applying binomial distribution formula, it can be concluded that the probability less than two have a side effect is 56.86%.
Binomial distribution is the discrete probability distribution of the number of successes or failures in n independent trials, where each trial result has a probability p.
P(x) = C(n,x) · pˣ · qⁿ⁻ˣ where:
C = number of combinations
p = probability of success
q = probability of failure
x = number of times for a specific outcome within n trials
n = number of trials
We have the following information:
p = 12% = 0.12, thus:
q = 1 - p
= 1 - 0.12
= 0.88
n = 12
We want to find the probability less than two have the side effect, P(x<2):
P(x<2) = P(0) + P(1)
= (C(12,0) · 0.12⁰ · 0.88¹²) + (C(12,1) · 0.12¹ · 0.88¹¹)
= (1 · 1 · 0.2157) + (12 · 0.12 · 0.2451)
= 0.2157 + 0.3529
= 0.5686 ≈ 56.86%
Thus, the probability less than two have the side effect is 56.86%.
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A back-to-school sale offered a laptop for $379. This sale price reflected a 15% discount.
Use the equation to find the cost of the computer before the reduction in price.
(Round to the nearest cent as needed.)
If a back-to-school sale offered a laptop for $379 and this sale price reflected a 15% discount, after using the equation the cost of the computer before the reduction in price is, $446.47.
What is percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Let's call the original cost of the laptop "x".
The equation to find the cost after a discount is:
x - x * (discount rate) = sale price
In this case, the discount rate is 15%, or 0.15. Plugging in the given values:
x - x * 0.15 = 379
Expanding the equation:
x - 0.15x = 379
0.85x = 379
Dividing both sides by 0.85:
x = 379 / 0.85
x = 446.47
So, the cost of the laptop before the reduction in price was $446.47.
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The marketing club school is openings student store. They randomly survey 50 students who how much money they spend
onunch each day. What is the expected value for a student to spend on lunch each day?
Student Lunch Survey
Number of Dollars spent on
Students
Lunch Eschwy
510
SSS
05. 18
5. 07
See
signou
us
247
The Expected value is the long-term average position of any variable. The anticipated value will be$5.18
The predicted value is the long-run average of all variables. It also shows the loaded normal probabilities for all possible values. Investors use expected value to estimate an investment's return, often in relation to its risk.
Given the data in detail
Pupil Lunch check Bones spent Probability
2$10 20/50.
1$8 8/50.
12$6 72/50.
23$5 115/50.
8$4 32/50.
4$3 12/50
The sum will be
aggregate = 20+ 8 +72 +115 +32 +12
50
= 259/50
= $5.18
The anticipated value a pupil would spend on lunch each day will be $5.18
Question
From the following data, calculate the expected value a pupil can spend on lunch each day?
Students & Amount spent
2$ 10
1$ 8
12$ 6
23$ 5
8$ 4
4$ 3
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Write 13/12 as a mised number
Answer:
[tex]\frac{13}{12}=1\frac{1}{12}[/tex]
Step-by-step explanation:
You have 12/12 + 1/12 so it would end up being 13/12 so you can simplify the 12/12 to 1 and have [tex]1\frac{1}{12}[/tex]
Practice 9. Expressing the future in time clauses. (Chart d-3)
Complete the sentences with the correct form of the verb.
1. Grandma and Grandpa are planning to travel often when they (retire)
2. I'll wake up tomorrow morning when the alarm clock (ring)
3. The students will relax after they (finish)
4. You'll feel a lot better after you (take)
this medicine.
5. The residents of the coastal areas will prepare for the hurricane before it
(arrive)
6. Mark will work in a law firm as soon as he (graduate)
school.
7. We'll have dinner as soon as the rice (be)
8. I'll tell you as soon I (hear)
9. Before we (leave)
10. We'll start our newspaper delivery again after we (get)
their final exams.
ready.
from law
any news.
on vacation, we'll stop our newspaper delivery.
back from vacation.
The chance at least one of the alarms will wake her up is 0.96.
What is the probability of both independent events?If the probability of one event does not affect the probability of another event, the events are independent.
Given
Probability that Alarm clock 1 is reliable = 60% = 0.60
Probability that Alarm clock 2 is reliable = 90% = 0.90
P of alarm clock 1 not reliable = 0.40
P of alarm clock 2 not reliable = 0.10
Therefore,
The chance at least one of the alarms will wake her up is;
=p1.p2' + p1'. p2 + p1.p2
so, calculating we get,
= 0.96
Hence, the chance at least one of the alarms will wake her up is 0.96.
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today the temperature is 75 degrees. yesterday was 65 degrees. what is the percentage of increase from yesterday to today?
The high temperature increased by 15.38% from yesterday to today.
First, you must find the actual increase in temperature. by using this formula:
Percentage increase = (Today's temperature - Yesterday's temperature) / Yesterday's temperature * 100
Percentage increase = (75 - 65) / 65 * 100 = 15.38%
Temperature is a physical quantity that indicates hot and cold. It is the manifestation of thermal energy, present in all matter, which is the inception of the occurrence of heat, a flow of energy when a body is in contact with another that is colder or hotter.
Temperature is measured with a thermometer.
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33. Solve the equation and check your solution: -2(x - 1) = 2 - 2x
Answer:
this equation is always true
Step-by-step explanation:
Solve the equation and check your solution: -2(x - 1) = 2 - 2x
-2(x - 1) = 2 - 2x
-2x + 2 = 2 - 2x
-2x + 2x = 2 - 2
0 = 0
(this equation is always true)
------------------------------
check
whatever value you give to x the equation is always true, let's take 2 as an example
-2(2-1) = 2 - 2 * 2
-4 + 2 = 2 - 4
-2 = -2
# 25 i
You buy 6 balloons and 3 banners for $15. Your friend buys 4 balloons and 1 banner for $9. What is the cost of each balloon? of each
banner?
Each balloon costs $
Save / Exit
and each banner costs $
The cost of each balloon and each banner is $2 and $1 respectively.
What is the cost of each balloon and banner?Let
cost of balloon= x
cost of banner= y
6x + 3y = 15
4x + y = 9
Multiply equation (2) by 3
12x + 3y = 27
6x + 3y = 15
12x + 3y = 27
Subtract the equations to eliminate y
12x - 6x = 27 - 15
6x = 12
divide both sides by 6
x = 12/6
x = $2
Substitute into
4x + y = 9
4(2) + y = 9
8 + y = 9
y = 9 - 8
y = $1
Therefore, each balloon cost $2 and each banner cost $1
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The bearing of a fishing boat from a lighthouse is 118°.
Work out the bearing of the lighthouse from the fishing boat.
The bearing of the lighthouse from the fishing boat is 242
Hwo to determine the bearingFrom the question, we have the following parameters that can be used in our computation:
The bearing of a fishing boat from a lighthouse is 118°.
The bearing of the lighthouse from the fishing boat is calculated as
The bearing of the lighthouse from the fishing boat = 360 - The bearing of a fishing boat from a lighthouse
Substitute the known values in the above equation, so, we have the following representation
The bearing of the lighthouse from the fishing boat = 360 - 118
Evaluate
The bearing of the lighthouse from the fishing boat = 242
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what is the volume of the triangle ?
Answer: 720
Step-by-step explanation:
Volume = l x w x h, so 9 x 10 = 90, 90 x 8 = 720.
Hope this helps.
Please help me with this
The table that represents a linear relationship is the one in option 3.
Which table represents a linear relationship?A linear relationship can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we add 1 to the input we get:
y = a*(x + 1) + b
y = (a*x + b) + a
So for each increase of 1 unit on the input we have a constant increase on the value of y.
The table that represents a line is the number 3, where you can see that the increases in the f(x) values are constants.
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the points of this 3-by-3 grid are equally spaced horizontally and vertically. how many different sets of three points of this grid can be the three vertices of an isosceles triangle?
The number of different sets of three points of this grid can be the three vertices of an isosceles triangle is 36.
An isosceles triangle is one with two equal sides. The two angles that face the two equal sides are also equal. An isosceles triangle, in other words, is a triangle whose two sides are equal in length.
By using the Permutation formula,
Number of isosceles triangle to be formed is,
9!/(7!x2!) = 9x8x7!/7!x2!
= 9x8/2
= 36
So number of isosceles triangle that can be formed of this 3-by-3 grid is 36.
When a square is described as a 3 x 3 Magic square, it has three rows and three columns. An illustration of a 3 by 3 magic square with the magic constant.
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(Projectile Motion) Mary is outside her apartment building. She needs to pass her key to John, who is 6 m above the ground floor of the building. Mary has no time to run upstairs, so she throws the key towards John. Suppose the height, h m, of the key above the ground floor at time t seconds is given by h = -11t² + 20t + 1. Is it possible for John to catch the key? Justify your answer.
5. Sam has $9.10, but all of it is nickels. If one nickel is worth $0.05, how many nickels does Sam
have? If all of the $9.10 were pennies, how many pennies would Same have?
$9.10 in all nickels is how many nickels
9.10 / 0.05
how many 5 cent pieces add up to that
182 nickels
a penny is one cent
just move the decimal place over twice
9.10
910.0
910 pennies
Hope this helps
- Jeron :- )
Emily buys 6 cans of beans for $1.50 each. She also buys a pineapple, The total cost of the item is $12.30. HURRY PLS :) THANK YOU BTW! :)
Answer:
$3.30
Step-by-step explanation:
6 x 1.50 = 9
12.30 - 9 = $3.30
A triangle has side lengths 4 inches 5 inches and 7 inches Is the triangle a right triangle?
Answer:
Step-by-step explanation:
To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the sides of the triangle as follows:
a = 4 inches
b = 5 inches
c = 7 inches
Using the Pythagorean theorem, we can calculate:
c^2 = a^2 + b^2
7^2 = 4^2 + 5^2
49 = 16 + 25
49 = 41
Since 49 does not equal 41, this means that the triangle is not a right triangle.
Therefore, the answer is no, the triangle is not a right triangle.
What is the answer to this problem solving for X? (12x-8=10x+6)