We get the distance between the coordinates of the point S and T as 5 √2 units.
We are given the coordinates of two points as:
S = ( - 2, 4 )
T = ( 3, 9 )
We have to find the distance between the points S and T.
We will use the distance formula for this.
Distance = √(x₂ - x₁)² + ( y₂ - y₁)²
Here, we have:
x₁ = -2
x₂ = 3
y₁ = 4
y₂ = 9
Substituting the values in the formula, we get that:
Distance = √(3 + 2)² + ( 9 - 4)² units
Distance = √(5)² + ( 5)² units
Distance = √25 + 25 units
Distance = √50 units
Distance = 5 √2 units
Therefore, we get the distance between the coordinates of the point S and T as 5 √2 units.
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the difference between two numbers is -1. their sum is -27. find the numbers. let x represent the first number and y represent the second number. solve using system s of equations.
Answer: x = -14, y = -13
Step-by-step explanation:
As stated by the question, we can use a system of equations to help us solve.
First, the difference between two numbers (x and y) is -1. The difference represents subtraction.
x - y = -1
Next, the sum of the numbers (x and y) is -27. The sum represents addition.
x + y = -27
Now, we can solve this system. We will graph both of the equations. The point of intersection is the solution, see attached. This gives us an answer of x = -14 and y = -13.
x - y = -1
x + y = -27
Solve the following equation. 2x/5 + 1 = 7Then place the correct number in the box provided.
Answer:
[tex] \sf \large \: x=15[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
2x/5+1=7
Step 1: Simplify both sides of the equation.
2/5x+1=7
Step 2: Subtract 1 from both sides.
2/5x+1−1=7−1
2/5x=6
Step 3: Multiply both sides by 5/2.
(5/2)*(2/5x)=(5/2)*(6)
x=15
The pie chart describes the distribution of favorite school subject for 300 high school students. How many students reported that “Math” is their favorite subject?
The number of students whose best subject is Maths is 78.
How many students best subject is Maths?A pie chart is a graph that displays information in a circle. The circle is divided into sections which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees. A pie chart is equal to 100%.
The first step is to determine the percentage of the section allocated to mathematics: 100% - (8% + 15% + 8% + 32% + 11%)
100% - 74% = 26%
Number of students whose best subject is Maths = (26/100) x 300 = 78
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The sum of three consecutive even integers is 50 more than the third integer.find the integers
Answer: 24, 26, 28
Step-by-step explanation:
a=even integer one.
b=even integer two.
c=even integer three.
a=b-2
b=c-2
a=c-2-2
a=c-4
a+b+c=50+c
c-4+c-2+c=50+c
c+c+c-4-2=50+c
3c-6=c+50
2c-6=50
2c=56
c=28
b=c-2
b=28-2
b=26
a=26-2
a=24
24, 26, 28
Given the following values, find the perimeter of the figure shown below:
AB = 7 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm.
Do not include "cm" with your response.
Answer:
26
Step-by-step explanation:
First, split the figure into 3 rectangles and label the sides so that it is easier to work with.
Then you have to find the unknown values: HG and AH.
HG: Since AB=7 and AB is the longest horizontal side; we know that HG+EF+CD=AB=7. Plugging in the known values: HG+3+1=7 => HG+4=7. Therefore, HG=3 because 3+4=7.
AH: BC and FG are the corresponding sides to AH so AH+FG=BC. Plugging in the known values: AH+1=3. Therefore, AH is 2 because 2+1=3.
Now you have to use the perimeter of rectangle formula which is P=2(L+w) for the 3 rectangles.
Rectangle 1: 2(3+2)=10
Rectangle 2: 2(3+1)=8
Rectangle 3: 2(3+1)=8
Add them all up to find the total perimeter: 10+8+8=26.
A truck can be rented from Company A for $70 a day plus $0.20 per mile. Company B charges $50 a day plus $0.70 per mile to rent the same truck. Find the number if miles in a day at which the rental costs for Company A and Company B are the same.
At ___ miles, the rental costs are the same from either company.
The computation shows that the number of miles is 40 miles.
How to compute the value?Based on the information, Truck A will be: = $70 + 0.2m
Truck B = 50 + 0.7m
where m = number of miles
Therefore 50 + 0.7m = 70 + 0.2m
Collect like terms
0.7m - 0.2m = 70 - 50
0.5m = 20
m = 20/0.5
m = 40
The number of miles will be 40.
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What is the difference in temperature from 15 degrees C to - 36 degrees C?
a cyclist competing in a race rides past a water station. The graph of the function d(t) - 1/3 |t-60| represents her distance in kilometers from the water station in t minutes. What does the graoh of the function tell you about her race.
From the given absolute value function, we have that:
The cyclist starts 20 kilometers from the station.The cyclist reaches the station in 60 minutes.What is the absolute value function?The absolute function is defined by:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin.
For this problem, the function is:
d(t) = 1/3|t - 60|.
The d-intercept is given by:
d(0) = 1/3|-60| = 20.
Hence: The cyclist starts 20 kilometers from the station.
The t-intercept is found as follows:
1/3|t - 60| = 0
t - 60 = 0
t = 60.
Hence: The cyclist reaches the station in 60 minutes.
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please help
maths midpoint theorem
Step-by-step explanation:
10.
the various sides and line segments have been marked as equal already.
so, SSS proves that both triangles are congruent.
but to reprove things with the midpoint theorem :
remember
the line segment in a triangle connecting the midpoints of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
so,
D, F are the midpoints of BA and BC.
so, AC is parallel to DF and twice as long as DF.
D, E are the midpoints of BA and AC.
so, BC is parallel to DE and twice as long as DE.
E, F are the midpoints of AC and BC.
so, BA is parallel to EF and twice as long as EF.
so, DF = AE = EC
DE = BF = FC
EF = BD = DA
so, the EF of DEF corresponds to DA of ADE.
DF corresponds to AE.
and DE is shared between both triangles.
so, again, all 3 sides correspond 1:1 to sides in the other triangle. and SSS proves they are congruent.
11.
equilateral means all 3 sides are equal :
PS = PT = ST
TSR can only be isoceles (both legs are equal) when
ST = SR
because PM = MQ, M is the midpoint of PQ.
and because of MS || QR, S is the midpoint of PR.
that means PS = SR.
and because PS = ST, ST = SR
therefore, TSR is isoceles.
Write 44.259 in word form
Answer:
Forty-four and two-hundred fifty-nine thousandths.
A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation
C(x)=0.00048(x-200)³ + 311,040
100≤x≤ 1,000
where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by C(x)=
(A) Write the equation for the average cost function C.
The equation for the average cost function C [tex]= \frac{0.00048(x - 200)^{3} + 246840 }{x}[/tex]
When a company creates products or services, it is required to pay production-related expenses. Some of these expenses are cyclical and alter as the output does. Expenditures that alter when production changes include things like raw materials, labor, and utility costs. These are referred to as variables. Other expenses are set, such as rent and insurance payments. These fixed expenses do not alter with changes in output.
The sum of the fixed and variable costs is the total cost.
Total Cost = Variable Cost + Fixed Cost
Now as per the question the cost equation is :
[tex]= \frac{C(x)}{x} = \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]
Therefore, the equation for the average cost function :[tex]= \frac{0.00048(x - 200)^{3} + 246840}{x}[/tex]
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(-4/9) divided by (5/8) = (-4/9) x ?
A. 9/4
B. -8/5
C. 8/5
D. -9/4
Answer:
-4/9 * 8/5 = (- 4/9) x
-32/45= - 4x /9
-288 = 180x
-8/5
Identify the property used in each step of solving the inequality
,,,,step ,,,,,,,,,,,,,,,, justification
3x – 2 > –4. |||||||1. given
3x > -2. |||||||||||||||| 2. _____
x>- 2/3 ||||||||||\|||||3. _____
The algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.
What is the algebraic property used?
We are given the inequality;
3x – 2 > –4
Step 2;
Using Addition Property of Equality, add 2 to both sides;
3x – 2 + 2 > –4 + 2
3x > –2
Step 3;
Using Division Property of Equality, divide both sides by 3 to get;
3x/3 > –2/3
x > –2/3
Thus, we conclude that the algebraic property used in steps 2 and 3 are respectively Addition Property of Equality and Division Property of Equality.
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What number is the opposite of 913?
Answer:
918 , bc it is the answer
Step-by-step explanation:
i used a source
list the factors of 12
Answer:
2·2·3 or {1, 2, 3, 4, 6, 12} depending on what you mean
Step-by-step explanation:
You want the factors of 12.
Prime factorsThe prime factors of 12 are ...
12 = 2·2·3 = 2²·3
DivisorsThe product of exponents of the prime factors, each increased by 1, is the number of divisors of 12:
(2+1)(1+1) = 3·2 = 6 . . . . number of divisors of 12.
Those are ...
1, 2, 3, 4, 6, 12
__
Additional comment
The word "factors" is often used when "divisors" is intended. An expression is factored when it is expressed as a product of prime factors.
If universal set U = { 1, 2, 3.......10 } A = {factor of 6} B = {factor of 8} and C= {factor of 9} then show (A intersection B intersection C (colon ) in Venn diagram by Shading
hope it help ya..
☘☘☘...
A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points)
Part B:Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)
Part C: In January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?
The inequality that represents the temperatures at which the gas in the truck will remain in liquid form is; -40°F < x < 140°F
How to solve Inequality Word Problems?
A) x is the temperature, and the temperature can't go down to -40°F and so x is greater than -40°F so that the gas doesn't freeze. Finally, x can't go higher than 140°F because the gas will evaporate. Thus, the inequality that represents the temperatures at which the gas in the truck will remain in liquid form is;
-40°F < x < 140°F
B) Open interval of the graph would mean that the interval is from -40°F to < 140°F. However, not equal to means that the gas in the truck can't stay liquid and as such means the coordinate is (-40°F, 140°F)
C) The gas will freeze because it has been said in the question the gas freezes at -40°F and as such if it goes -49°F, then it will freeze because the gas is supposed to stay higher than -40°F.
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At the end of last year, teachers were rated by their students on a 0-10 scale. Two of the teachers' ratings are given. Whose class would you register for? Explain your reasoning.
spellings are incorect
Scaling a Rectangle
A rectangle that is 2 inches by 3 inches has been scaled by a factor of 7.
Scale factor back to original size = 1/7
The transform object is a mathematical mapping from one coordinate system to another. The coordinate system can differ in position (i.e. origin), scale, axis orientation, and relative axis orientation. We are told that the rectangle has been scaled by a factor of 7. This means that if the length and width are x and y respectively, the new scaled measurements will be;7x and 7 years.
Now, to get us back to the original size, all we have to do is divide the new scale measure by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Hence, the scale factor will be 1/7 back to the original size.
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20 POINTS!! Question is in the picture, correct answer= brainest
Answer: 0.1111111111
Find the equation of the tangent line to the graph of the given function at the point with the indicated x-coordinate.
f(x) = 6x²; x = 0
y=
The equation of the tangent line to the graph is equal to y = 0.
What is the equation of the tangent line of a curve at a given location?
A line is tangent to a function if and only if the function meets the curve only in one point. The slope of the tangent line can be found by using the first derivative of the curve and the y-intercept is determined from the slope-intercept form of the equation of the line. First, determine the slope of the tangent line:
f'(x) = 12 · x
f'(0) = 12 · 0
f'(0) = 0
Second, find the intercept of the equation of the line:
y = 6 · 0²
y = 0
b = y - m · x
b = 0 - 0 · 0
b = 0
Then, the equation of the tangent line to the graph is equal to y = 0.
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8/12 divided by 9/12
The area of a
parking lot is 600 square meters. A car requires 6 square
meters. A bus requires 30 square meters. The attendant can handle only
60 vehicles. If a car is charged $2.50 and a bus $7.50, how many of each
should be accepted to maximize income?
The number of cars should be 100 and that of bus be 0.
x is the number of cars and y is the number of buses.
Area: 6x + 30y <= 600 simplifies to x + 5y <= 100
Total money collected: 2.50x + 7.50 y …..this is what you want to maximize
OR you want to maximize 2.50 (x+ 3 y)
OR you want to maximize (x+3y)
Replacing the value of x from the Area equation in the above price, we get
100 - 5y + 3y is the maximum amount you can collect
So you want to maximize 100 - 2y. This happens when y is 0.
When y is 0; x will be 100 and you will collect 250.
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You are borrowing $10840 to buy a car. If you pay the loan off in 6 years (72 months), estimate your monthly payment by ignoring interest and rounding the loan to the nearest hundred dollars.
If we are borrowing $10840 to buy a car and repaying it in 6 years (or 72 months) , our monthly payment will be $150.55 or rounded of $200.
As per the question statement, we are borrowing $10840 to buy a car and repaying it in 6 years (or 72 months) , what will be the estimate monthly payment by rounding off to the nearest hundred dollars
First we are supposed to find the monthly payment then we can round it off to the nearest hundred dollars.
Total loan borrowed = $10840
Time taken to pay it off = 6 years or 72 months,
Payment to be made per month = [tex]\frac{10840}{72} \\ 150.5556[/tex]
Therefore [tex]150.5556[/tex] dollars is to be paid every month for 72 months.
After rounding off to the nearest hundred dollars we will get $200.
Hence we are supposed to pay approximately $200 every month for 72 months.
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Find the circomference of the circle
Answer:
18.84
Step-by-step explanation:
Marty is adding ribbon to the outer edge of the poster shown. How should Marty use estimation to make
sure he buys enough ribbon? How much ribbon should
Marty buy? Explain.
33
22 dimes and 9 nickels
x equals 1
f(4)=f(×)
x=1
3,200x7.253,200 x .0725 = $232 interest monthly
232monthly x 12annual= 2, 784
answer: 33 ( approx)
In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another entity. Interest advance, but rather on a pro-rata basis as a share of the reward received by risk-taking business people when revenue is earned that exceeds all costs.
For Interest, a customer who borrows money from a bank typically pays interest on it, so they pay the bank more than they borrowed; likewise, a customer who earns interest on their savings may withdraw more than they originally put. When it comes to savings, the bank serves as the borrower while the consumer serves as the lender.
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Value of of x such that f(x) = g(x)
The Value of of x such that f(x) = g(x) are -3, 0, 4 and 7
The graph given in the question shows two curves of two different functions f(x) ang g(x)
Here, we need to find the value ox such that f(x) =F g(x)
For this we need to look at the graph of both the function together find the intersection points of both the graph
This is coordinate geometry
We can see that there are 4 points at which the curves are intersecting
We can find the coordinates of these 4 points from the graph
First point ( -3, 4)
Second point (0,3)
Third point (4 , 3)
The fourth and the last point ( 7, 4)
The x coordinates of the intersection points are the values of x such that f(x) = g(x)
Hence, The Value of of x such that f(x) = g(x) are -3, 0, 4 and 7
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1Carla participates in competitive archery. Each competition allows a
maximum of 90 points. Carla's results for the last 8 competitions are (76, 78, 81, 75,
80, 80, 76, 77). Find and interpret the standard deviation of the data.
Answer:
76
Step-by-step explanation:
76 occurs multiple times in the set, thus deviating from it.
Data were collected from a typing class with 45 students. The class had an average of 56 words per minute (WPM)
with a standard deviation of 7 WPM. The teacher realized that the data from one student who typed 55 WPM was
not entered. If this student's results were included in the data set, what effect would it have on the standard
deviation?
O The standard deviation would be noticeably larger.
O The standard deviation would be noticeably smaller.
O The standard deviation would be about the same, perhaps a little larger.
O The standard deviation would be about the same, perhaps a little smaller.
The correct option regarding the standard deviation of the data-set adding observation 55 is:
The standard deviation would be about the same, perhaps a little smaller.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.For this problem, we have that an observation of 55 has a difference squared of 1 with the mean, which is less than the variance of 7² = 49, hence the mean of the differences squared would suffer a small decay(small due to the sample size), and would the standard deviation, hence the correct option is given by:
The standard deviation would be about the same, perhaps a little smaller.
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Answer:
No, its A: The standard deviation would be noticeably larger. I swearrr, these "verified" accounts are so useless bru
In a statistical study what is the difference between an individual and a variable? An individual is a member of the population of interest. A variable is a numerical measurement describing data from a sample. An individual is a member of the population of interest. A variable is a numerical measurement describing data from a population. An individual is the population of interest. A variable is an aspect of an individual subject or object being measured. An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured. An individual is the population of interest. A variable is a numerical measurement describing data from a population.
The correct option regarding individuals and variables is given by:
An individual is the population of interest. A variable is an aspect of an individual subject or object being measured.
What are an individual and a variable in a statistics study?The individuals are the people or the objects in the study, that is, it is the population.The variables are characteristics regarding the individual, that can be numeric or not.Hence the correct option is:
An individual is the population of interest. A variable is an aspect of an individual subject or object being measured.
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