Answer:
The second choice:
[tex]\large\boxed{\large\boxed{1/x\cdot x=1}}[/tex]
Explanation:
The closure property on an operation means that the operation between two elements of a set produce one element of the same set.
In this case, the operation is multiplication and the set is the polynomials.
Then, the closrue property is that the multiplication of two polynomials will always produce a polynomial.
Since, [tex]1/x[/tex] is not a polynomial, the equation [tex]1/x\cdot x=1[/tex] does not support the fact that polynomials are closed under multiplication.
Apply the distributive property and the greatest common factor to write an equivalent expression. Enter your answers in the boxes.
Answer:
12 (5x - 2)
Step-by-step explanation:
First to know if we can get a common factor we have to find a number by which it is divisible on 24 and 60
first we will try with 2
60/2 = 30 both are divisible by 2
24 /2 = 12
then we will take common factor 2
60x - 24
we multiply and divide by 2
2 (60x - 24)/2
we distribute the 2
2(60x/2 - 24/2)
and solve
2(30x - 12)
Now we continue with the same procedure until there is no more number in common to divide
we will try with 2
30/2 = 15 both are divisible by 2
12 /2 = 6
then we will take common factor 2
2(30x - 12)
we multiply and divide by 2
2*2 (30x - 12)/2
we distribute the 2
4(30x/2 - 12/2)
and solve
4(15x - 6)
continue with the same procedure
we will try with 2
15/2 = X only one is divisible by 2
6 /2 = 3
we will try with 3
15/3 = 5 both are divisible by 3
6 /3 = 2
then we will take common factor 3
4(15x - 6)
we multiply and divide by 3
4*3 (15x - 6)/3
we distribute the 3
12(30x/3 - 6/3)
and solve
12(5x - 2)
there is no number other than 1 by which we can divide 5 and 2
12(5x - 2)
5. A survey of student pizza preferences showed that 43 students preferred cheese, 56 preferred sausage, 39 preferred pepperoni, 28 preferred supreme, 31 preferred another kind, and 19 did not like any type of pizza. Make your own probability distribution in order to answer the question. Match the probability of each outcome given to the correct outcome.
Answer:
P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,
P (Supreme) = 0.130, P (Another Kind) = 0.144
and P (Does not like any kind) = 0.088
Step-by-step explanation:
Given:
Number of students who prefer cheese = 43
Number of students who prefer sausage = 56
Number of students who prefer pepperoni = 39
Number of students who prefer supreme = 28
Number of students who prefer another kind = 31
Number of students who did not like any kind = 19
∴ The total number of students surveyed = [tex]43+56+39+28+31+19=216[/tex] The number of students who prefer pizza = [tex]43+56+39+28+31=197[/tex]
The probability that a students likes pizza is,
[tex]P(Student\ likes\ pizza)=\frac{No.\ of\ students\ who\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{197}{216} \\=0.912[/tex]
The probability that a students does not likes pizza is,
[tex]P(Student\ does\ not\ likes\ pizza)=\frac{No.\ of\ students\ who\ does\ not\ prefer\ pizza}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{19}{216} \\=0.088[/tex]
The probability distribution of students who prefer different kinds of pizza is:
The probability that a student likes cheese:[tex]P(A\ Student\ prefers\ cheese)=\frac{No.\ of\ students\ who\ prefer\ cheese}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{43}{216}\\=0.199[/tex]
The probability that a student likes sausage:[tex]P(A\ Student\ prefers\ sausage)=\frac{No.\ of\ students\ who\ prefer\ sausage}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{56}{216}\\=0.259[/tex]
The probability that a student likes pepperoni:[tex]P(A\ Student\ prefers\ pepperoni)=\frac{No.\ of\ students\ who\ prefer\ pepperoni}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{39}{216}\\=0.181[/tex]
The probability that a student likes supreme:[tex]P(A\ Student\ prefers\ supreme)=\frac{No.\ of\ students\ who\ prefer\ supreme}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{28}{216}\\=0.130[/tex]
The probability that a student likes another kind:[tex]P(A\ Student\ prefers\ another\ kind)=\frac{No.\ of\ students\ who\ prefer\ another\ kind}{Total\ no.\ of\ students\ surveyed}[/tex]
[tex]=\frac{31}{216}\\=0.144[/tex]
Thus, the probability distribution table is displayed below:
PLZ HURRY IT'S URGENT!!
Which equation can be used to find the two numbers whose ratio is 4 to 3 and that have a sum of 42?
4x + 3x = 42
34x=42
43x=42
4x−3x=42
Answer:
4x + 3x = 42
Step-by-step explanation:
if the number of students at a particular High School who participate in after-school drama programs increases at a rate of 8% per year, how long will it take for the number of students participating in the after-school programs to double?
a. about 25 years
b. about 12.5 years
c. about 3.6 years
d. about 9 years
Answer:
d. about 9 years
Step-by-step explanation:
There is a "rule of thumb" for doubling time* that says the product of the percentage rate of change per year and the doubling time in years is about 72. Here, that means the doubling time is about ...
72/8 = 9 . . . . years
_____
You can write the exponential equation ...
multiplier = (1 +.08)^n
and solve for multiplier = 2:
2 = 1.08^n
log(2) = n·log(1.08) . . . . . take logs
log(2)/log(1.08) = n . . . . . divide by the coefficient of n
9.00647 ≈ n
It will take about 9 years for the participation to double.
_____
* The farther away from 8% the rate of change is, or the more times per year it is compounded, the less accurate is the "rule of 72." When compounding is continuous, the "rule of 72" becomes the "rule of 69.4". For this problem, answer choices are sufficiently far apart that the rule of thumb is adequate for making a correct choice.
A researcher is gathering data on the 50 states. She wants to actually enter the name of the state into the data matrix as one of the variables in her data set. What type of SPSS variable should that be?
Answer: String variables
Step-by-step explanation:
SPSS means Statistical Package for Social Sciences.
The SPSS has only two variables namely:
1. String variables which includes numbers,letters and other characters.
The string variables cannot perform calculations. It is basically used to type names of people, age,occupation,home addresses,email addresses e.t.c Which is what is what the researcher was trying to do.
2. Numeric variables which include only numbers. It can perform calculations too using mathematical operations like addition,multiplication,division and subtraction.
Why shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency distribution?
Answer:
Step-by-step explanation:
Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!
Point A(-7, - 2) is rotated 270 counterclockwise and then shifted down 3 units.
What are the coordinates of A'?
A. (2,4)
B. (-2,-7)
C. (-2,4)
D. (7,-5)
The coordinates of A' after rotation of 270 counterclockwise and then shifted down 3 units are (2, 4).
To find the coordinates of point A' after a 270-degree counterclockwise rotation around the origin and then shifting down 3 units, we first perform the rotation.
A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. So, when we rotate point A(-7, -2) 90 degrees clockwise, we swap the coordinates and change the sign of the former x-coordinate, which gives us the new point A''(2, 7). Next, we shift A'' down 3 units, which means we subtract 3 from the y-coordinate, resulting in A'(2, 4).
what equivalent expression was used
3y+4y
Answer:
7y²
Step-by-step explanation:
First u group them like 4+3+y+y=7y²
Jenny plans to invest $9,000. America's Bank offers a 10 year CD at an annual interest rate of 3.8% compounding interest semi-annually. How much is her investment worth at the end of the 10 years?
Group of answer choices
$9,000
$13,114
$15,840
$18,000
Answer: $13,114
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 9000
r = 3.8% = 3.8/100 = 0.038
n = 2 because it was compounded 2 times in a year.
t = 10 years
Therefore,.
A = 9000(1+0.038/2)^2 × 10
A = 9000(1+0.019)^20
A = 9000(1.019)^20
A = $13114
The final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P(1 +\dfrac{R}{100})^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P(1 +\dfrac{R}{100})^T[/tex]
For this case, we are given that:
Initial amount Jenny invested = $9,000 = PThe rate of interest = 3.8% semi annually (0.5 years) = 3.8/2 = 1.9% per 0.5 years = R Thus, unit of time = half yearTime for which investment was made= 10 years = 20 half years =TThus, the final amount at the end of 10 years is given by:
[tex]A = P(1 +\dfrac{1.9}{100})^T\\\\A = 9000(1 + \dfrac{1.9}{100})^{20} = 9000(1.019)^{20} \approx 13114 \text{\: \: (in dollars)}[/tex]
Thus, the final amount that Jenny's investment would be worth of at the end of 10 years is given by: Option B: $13114 approx.
Learn more about compound interest here:
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Two particles are moving in straight lines. The displacement (in meters) of particle 1 is given by the function e^(4cos(t)) , where t is in seconds. The displacement (in meters) of particle 2 is given by the function -(t^3)/(3) - (t^2)/(2) + 2 , where t is in seconds. Find the first positive time at which the particles have(approximately) the same velocity.
A.) t = 1.569 seconds
B.) t = 0 seconds
C.) t = 2.366 seconds
D.) t = 0.588 seconds
E.) t = 1.011 seconds
The velocities of particles are given by the derivatives of their displacement functions. Equating the velocity functions of the two particles and solving numerically, we find that they have the same velocity for the first time at about t = 1.569 seconds.
Explanation:The velocity of an object is given by the derivative of its displacement function. So, we need to first find the derivatives of the given displacement functions to find the velocities of the particles.
The derivative of e^(4cos(t)) is [tex]-4e^{(4cos(t))sin(t)[/tex]. The derivative of [tex]-(t^3)/(3) - (t^2)/(2) + 2 is -t^2 - t.[/tex] Now, we equate the two velocities and solve for t[tex].-4e^(4cos(t))sin(t) = -t^2 - t[/tex]
Unfortunately, this equation does not have a simple algebraic solution. However, it can be solved numerically using, for example, a graphing calculator or numerical software. By using these tools, we find the first positive time at which the particles have approximately the same velocity to be about t = 1.569 seconds. Therefore, the correct answer is A.) t = 1.569 seconds.
Learn more about Velocity of Particles here:https://brainly.com/question/14326156
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I'm shipping and handling fee of $35 is charged to all furniture orders over $250. If the order is $437.50 what percent is the shipping and handling fee
Answer: the shipping and handling fee is 8 percent of the cost of the order.
Step-by-step explanation:
Shipping and handling fee of $35 is charged to all furniture orders over $250.
If the order is $437.50, it means that there would be a handing and shipping fee of $35 because the price of the order is above $250.
The percentage of the original price of the order that is the shipping and handling fee would be
35/437.5 × 100 = 0.08 × 100
= 8%
Final answer:
To find the percent that the shipping and handling fee is of the total order, divide the fee by the order amount and multiply by 100. For an order of $437.50 with a fee of $35, the shipping fee is 8% of the total order.
Explanation:
The question asks us to determine what percent the shipping and handling fee is of the total furniture order.
To calculate this percentage, we can use the formula:
Percentage = (Part / Whole) imes 100
In this case:
Part = $35 shipping and handling feeWhole = $437.50 total furniture orderNow, we insert the values into the formula:
Percentage = ($35 / $437.50) imes 100
Percentage = 0.08 imes 100
Percentage = 8%
Therefore, the shipping and handling fee is 8% of the total order.
PLEASE HELP a basketball player shoots a basketball with an initial velocity of 15 ft/sec. The ball is released from an initial height of 6.5 feet. PLEASE HELP
Part 1:
Replace "v0" in the given equation with the given velocity of 15 ft/sec:
y = -16t^2 + 15t +6.5
Part 2:
Now set the equation to 0 which would be when the basketball hits the ground:
-16t^2 +15t +6.5 = 0
A quadratic equation is solved using the formula:
t = -b +/- sqrt(b^2-4ac)/2a
Using the given equation: a = -16, b = 15 and c = 6.5
Replace the values and solve:
t = -(15)+/- sqrt(15^2 -4(-16)(6.5))/2(-16)
This solves to get both -0.32 and 1.26 seconds.
The time has to be a positive value so t = 1.26 seconds.
Part3:
Using the quadratic form at^2 + bt + c
The maximum is found using t = -b/2a = -15/2(-16) = = 0.47 seconds
The maximum height would be at 0.47 seconds
Part 4:
Replace t with 0.47 and solve for maximum height:
y = -16(0.47)^2 + 15(0.47) +6.5
Maximum height would be 3.52 feet
Suppose you want to determine the distance d that light travels in h hours. The speed of light is approximately 670,616,629 miles per hour. Which direct variation equation represents this situation? d = 670,616,629h h = 670,616,629d
Answer:
[tex]d = 670,616,629h \ mi[/tex]
Step-by-step explanation:
Given:
Speed of the light = 670,616,629 mi\hr
We need to find the direct variation equation represents given situation.
Solution:
Speed is defined as the ratio of distance and time. So, the equation of the speed is as follows:
[tex]Speed = \frac{Distance}{Time}[/tex]
And also written as.
[tex]S = \frac{d}{h}[/tex]
Now, we write the above equation for distance.
[tex]d = S\times h[/tex] ------------(1)
Where:
d = distance travel by object.
S = speed of the object.
h = Total time taken
Substitute S = 670,616,629 mi\hr in equation 1.
[tex]d = 670,616,629h \ mi[/tex]
Therefore, direct variation equation to represents the given situation
[tex]d = 670,616,629h \ mi[/tex]
Which equation can be used to solve for x, the side length of the original square? x2 − 2x − 120 = 0 x2 + 2x − 120 = 0 x2 − 2x + 120 = 0 x2 + 2x + 120 = 0
Question:
A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.
Which equation can be used to solve for x, the side length of the original square?
x2 − 2x − 120 = 0
x2 + 2x − 120 = 0
x2 − 2x + 120 = 0
x2 + 2x + 120 = 0
Answer:
Option a: [tex]x^{2} -2x-120=0[/tex] is the equation
Explanation:
It is given that the area of the square paper is [tex]x^{2}[/tex] square units.
The area of the remaining piece of paper is 120 square units.
It is also given that the area of the remaining piece of paper is [tex]x^{2}-2 x[/tex]
Thus, equating the area of the remaining piece of paper, we have,
[tex]x^{2} -2x=120[/tex]
Subtracting 120 from both sides of the equation, we have,
[tex]x^{2} -2x-120=0[/tex]
Thus, the equation [tex]x^{2} -2x-120=0[/tex] can be used to solve for x.
Hence, Option a is the correct answer.
Angle C is an inscribed angle of circle P. Angle C measures (x + 5)° and arc AB measures (4x)° . Find x.
3
5
7
9
Step-by-step explanation:
[tex]m \angle \: C = \frac{1}{2} (m \: arc \: AB)\\(By\:inscribed \:\angle\:theorem) \\ \\ \therefore \: (x + 5) \degree =\frac{1}{2} (4x)\degree \\ \\ \therefore \: x + 5=\frac{1}{2} \times 4x \\ \\ \therefore \: x + 5=2x \\ \\ \therefore \: x - 2x = - 5 \\ \\ \therefore \: - x = - 5 \\ \\ \: \: \: \: \: \huge \purple{ \boxed{\therefore \: x = 5}}[/tex]
At a car dealership, there are three times as many sedans as SUVs. If there are a combined 24 sedans and SUVs, how many sedans are there at the dealership?
Answer:
There are 18 Sedans in the dealership shop.
Step-by-step explanation:
Let x represent the number of Sedans in the dealership shop.
Let y represent the number of SUV's in the dealership shop.
If there are a combined 24 sedans and SUVs, it means that
x + y = 24 - - - - - - - - - - - -1
At a car dealership, there are three times as many sedans as SUVs. This means that
x = 3y
Substituting x = 3y into equation 1, it becomes
3y + y = 24
4y = 24
y = 24/4 = 6
x = 3y = 6 × 3
x = 18
At And Easter egg hunt there were a total of 4680 eggs hidden the number of real eggs what's 2/3 the number of chocolate eggs how many eggs were chocolate
Answer:
There are 3120 chocolate eggs.
Step-by-step explanation:
We are given the following in the question:
Total number of eggs = 4680
Number f chocolate eggs =
[tex]\dfrac{2}{3}[/tex] the number of real eggs
We have to find the number of chocolate eggs.
Number of chocolate eggs =
[tex]\dfrac{2}{3}\times \text{Total number of eggs}[/tex]
[tex]=\dfrac{2}{3}\times 4680\\\\=3120[/tex]
Thus, there are 3120 chocolate eggs.
Sahil got 28 questions right on the math test. Angelina got 7 more wrong answers than Sahil. There where 40 questions on the test. How many answers did Angelina get wrong on the math test? Which equation represents this situation
Answer:
19 wrong answers.
Step-by-step explanation:
Given:
Sahil got 28 questions right.
Angelina got 7 more wrong answers than Sahil.
There where 40 questions on the test.
Question asked:
How many answers did Angelina get wrong on the math test ?
Solution:
Total questions on the test = 40
Number of right answers, Sahil got = 28
Number of wrong answers, Sahil got = 40 - 28 = 12
As Angelina got 7 more wrong answers than Sahil,
Number of wrong answers, Sahil got = 12
Then, number of wrong answers, Angelina got = 12 + 7 = 19
Therefore, 19 answers did Angelina get wrong on the math test out of 40.
Angelina got 35 wrong answers on the math test.
Explanation:To find the number of wrong answers Angelina got on the math test, we need to know how many questions she got right. Since Sahil got 28 questions right and there were 40 questions on the test, we can subtract Sahil's score from the total number of questions to find Angelina's score. Sahil got 28 questions right, so Angelina would have gotten 40 - 28 = 12 questions right. And since Angelina got 7 more wrong answers than Sahil, we can subtract Sahil's wrong answers from Angelina's total wrong answers to find the specific number. If Sahil got 12 questions right, then he must have gotten 40 - 12 = 28 questions wrong. And since Angelina got 7 more wrong answers than Sahil, we can add 7 to Sahil's wrong answers to find Angelina's total wrong answers. Therefore, Angelina got 28 + 7 = 35 wrong answers on the math test.
Define like terms. Give an example of like terms and then combine them
Answer:
Like terms are numbers with or without variables that have the same variables.
Step-by-step explanation:
5x and 3x are like terms because they have the same variable.
5x and 3y are not like terms because the variables are different.
To combine them, just add or subtract them. You cannot combine non-like terms!
Answer:
Definition: Like terms - Term in math that have the same variables or powers.
Ex. 2x, -5x, and 7x.
Combine Them: 2x + 7x = 9x - 5x = 4x
Step-by-step explanation:
According to the 2016 study by the Pew research 74 percent of adults American have read at least one book in the past 12 months a sample of 10 adult americans is randomly selected le t x be the randem variable representing the number of people who have read at least on book explain why x is a binomial random variable by filling the blanks below in this problem a trial is------------- the number of trials n=--------------
Answer:
x is a binomial random variable because a trial is independent and number of trials, n = 10.
Step-by-step explanation:
We are given the following information:
We treat adult reading at least one book in the past 12 months as a success.
P(Adult reading atleast one book) = 74% = 0.74
Then the number of adults follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
If x is a random variable representing the number of people who have read at least on book, then x follows a binomial distribution because:
There are n independent trials. Here, n = 10.Each trial have two possible outcome either a success(read atleast one book) or a failure(not read atleast one book)The probability of success is same for each trial. Here p = 0.74Thus,
x is a binomial random variable because a trial is independent and number of trials, n = 10.
Jorge soccer team is having its annual fundraiser. The team hopes to earn three times as much as it did last year. The team earned $87. What is the team's goal for this year
Answer:
$261
Step-by-step explanation:
The team hopes to earn three times more than it did last year
Last year the team earned $ 87
We are required to determine the team's goal this year.
Therefore;
Since they hope to raise three times than last year;
Then;
Goal this year = 3 × last year's earnings
= 3 × $ 87
= $261
Therefore, the team's goal this year is $261
Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages. Which best describes the population?
Answer:
Hurricanes
Step-by-step explanation:
We are given the following in the question:
Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages.
Population:
It is the collection of all possible values of the variable of interest or individual of interest.The population is always greater than sample.A sample is a subset of population.Thus, for the given scenario
Population of interest:
Hurricanes
From this population a sample of hurricanes that have caused greater than $1 million in damages is taken.
Answer:
A)Hurricanes
Step-by-step explanation:
Liam opened a savings account with a $400
deposit and a simple interest rate of 7.5%. If
the balance of the account is now $670 and
there were no deposits or withdrawls, how
long ago did he open the account
Answer: he open the account 9 years ago.
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the amount deposited.
P represents the principal or amount deposited.
R represents interest rate
T represents the time for which the amount deposited was left in the account.
From the information given,
P = 400
R = 7.5%
I = 670 - 400 = $270
Therefore,
270 = (400 × 7.5 × T)/100 = 30T
T = 270/30
T = 9 years
Step-by-step explanation:
9 years thank you yw bubye
Give the equation that you would use to solve for exterior angles. Solve for x.
Answer:
X = 93
Step-by-step explanation:
Angles of a polygon = (n - 1)180
The above polygon is heptagon (with 6 sides)
(6-1) × 180
5×180 = 900
Add the given Angles and equate it to 900 (as gotten above)
4x + 3x + 47 + 93 + 46 + 62 = 900
7x + 248 = 900
Collect like term of the number
7x = 900-248
7x = 652
Divide both side by the coefficient of x
7x/7 =652/7
X = 93.1429
Two of the vertices of a rectangle are (1, -6) and ( -8, -6 ) if the rectangle has a perimeter of 26 units what are the coordinates of it's other vertices?
Answer:
(1, -2)
(-8, -2)
Step-by-step explanation:
(1 , -6) and (-8 , -6)
1 - (-8) = 9
we know that the length of the side that we know the vertices is 9
from there we make an equation with the sum of the sides equal to the perimeter
we will have 2 times 9 and 2 times x beacause it is a rectangle
x + x + 9 +9 = 26
2x + 18 = 26
2x = 26 - 18
2x = 8
x = 8/2
x = 4
Now that we know the missing side we just have to add or subtract this value to the coordinate in and of the vertices we have and we will obtain the missing vertices
(1, -6 + 4)
(1, -2)
( -8, -6+4 )
(-8, -2)
The coordinates of the other two vertices of the rectangle are (1, -2) and (-8, -2), found by calculating the length of one side using the given vertices and then applying the rectangle's perimeter to find the length of the adjacent sides.
Explanation:The subject of the question is to find the other two vertices of a rectangle given two of its vertices and the perimeter. We know that the opposite sides of a rectangle are equal in length. So, to solve this, we can use the distance formula to find the length of one side with the two given points (1, -6) and (-8, -6). The length of this side is the absolute value of the difference in the x-coordinates, which is 9 units. Since the perimeter is 26, and this length is 9, the sum of the lengths of the other two sides is 26 - 2*9 = 8 units. Therefore, each of these sides is 4 units long. Because the given points have the same y-coordinate, they lie on a horizontal side of the rectangle, so the other two vertices will have the same x-coordinates as the given ones and will be 4 units vertically away. If we add and subtract 4 units from the y-coordinate of the given points, we get the other two vertices: (1, -6 +4) and (-8, -6 +4). So the coordinates of the other two vertices are: (1, -2) and (-8, -2).
Travel Ez sells dollars at a rate of ($1.40)/(1 euro) and buys dollars at a rate of ($1.80)/(1 euro). At the beginning of a trip, Sophie exchanged $540 to get 300 euros. At the end of the trip she is left with 40 euros, so she exchanges the 40 euros back to dollars. How many dollars will Sophie get in exchange?
a. $72.
b. $22.
c. $56.
d. $28.
Answer:
C
Step-by-step explanation:
In the first instance, he wanted buying euros in exchange for his dollars. He had $540 and wanted to buy euros. The conversion factor here is that for every 1 euro, he pays $1.80
Now at the second instance, he wanted buying dollars with his left over euros. This means for every 1 euro, he gets $1.4
Since, he is having 40 euros, the total amount in dollars he would get will be 40 * $1.4 = $56
Circles M and K are congruent, segment QR is congruent to arc LN . Find the length of segment QR .
Answer:
26/3 or 8.67
Step-by-step explanation:
Arc lengths are congruent and the radii are the same implies angle at the centre is also equal,
Hence length of the chords are equal too
4x+2 = x+7
3x = 5
x = 5/3 or 1.67
Length of QR = 4x+2
= 4(5/3) +2
= 20/3 + 2
= 26/3 = 8.67
Answer:
8.67
Step-by-step explanation:
Hi, does anyone know how to solve this. If so, please show the working out too. Thanks.
See the explanation
Explanation:I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:
The triangle at the bottom is right, so by Pythagorean theorem is true that:
[tex]w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}[/tex]
By law of sines:
[tex]\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta[/tex]
By law of sines again:
[tex]\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}[/tex]
Learn more:Classification of triangles: https://brainly.com/question/10379190
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Write the equation of the function.
is it y = x2 / 6 - 3x /2 + 13/3 ?
Yo sup??
Since there is an x^2 term therefore this equation is of a parabola
By taking LCM and then cross multiplying it.
6y=x^2-9x+26
6y=x^2-9x+(9/2)^2+23/4
6y-23/4=(x-9/2)^2
we see that this is of the form
X^2=4AY
(x-9/2)^2=4(3y/2-23/16)
Hope this helps.
Answer:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
Step-by-step explanation:
This looks like a square root function [tex]f(x) = \sqrt{x}[/tex] but symmetric with respect to the x axis and shifted to the right for 1 and up for 3:
Lets take [tex]f(x) = \sqrt{x}[/tex] . The function symmetric with respect to the x axis would be [tex]-f(x)[/tex], so now we have:
[tex]f(x) = -\sqrt{x}[/tex]
Lets take [tex]f(x) = -\sqrt{x}[/tex] and shift it up for y = 3. Now we have:
[tex]f(x) =- \sqrt{x}+3[/tex]
Lets take [tex]f(x) = -\sqrt{x}+3[/tex] and shift it right for x = 1. That means that instead of x we will have x-1:
[tex]f(x) =- \sqrt{x-1}+3[/tex]
Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the voters were for blue 5/9 of the remaining voters were for green. And the remaining 48 voters were for red. How many voters were for blue?
Answer:
There were 180 voters for blue color.
Step-by-step explanation:
Let the total number of voters be 'x'.
Given:
Number of Voters for blue color = [tex]\frac{5}{8}x[/tex]
Number of Voters for green color = [tex]\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)[/tex]
Now we will use LCM to make the denominator common we get;
Number of Voters for green color = [tex]\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}[/tex]
Number of Voters for red color = 48
We need to find the number of voters for blue color.
Solution:
Now we can say that;
total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.
framing in equation form we get;
[tex]x=\frac58x+\frac{15x}{72}+48[/tex]
Combining like terms we get;
[tex]x-\frac58x-\frac{15x}{72} = 48[/tex]
Now we will make denominators common using LCM we get;
[tex]\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48[/tex]
Now denominators are common so we will solve the numerators we get;
[tex]\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48[/tex]
Now multiplying both side by 6 we get;
[tex]\frac{1}{6}x\times6=48\times6\\\\x = 288[/tex]
Number of voters for blue color = [tex]\frac{5}{8}x=\frac{5}{8}\times 288= 180[/tex]
Hence There were 180 voters for blue color.