Now the given coordinates are,
(-4,10) and (2,-10)
Thus, we have,
x₁ = -4
y₁ = 10
x₂ = 2
y₂ = -10
Given ratio, m₁ : m₂ = 1 : 3
⇒ m₁ = 1; m₂ = 3
Let (x,y) be the coordinates of the point on the directed line segment from (-4,10) to (2,-10) that partitions the segment into a ratio of 1 to 3.
Since the section formula is given as,
So, x = (m₁x₁ + m₂x₂) / (m₁ + m₂)
y = (m₁y₁ + m₂y₂) / (m₁ + m₂)
Put the values,
x = [1(-4) + 3*2)] / (1 + 3) = (-4+6) / 4 = 2/4
⇒ x = 1/2
Similarly y = [1(10) + 3*(-10)] / (1 + 3) = (10-30) / 4 = -20/4
⇒ y = -5
So, the required coordinates are (1/2, -5)
Thus, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 1 to 3 is (1/2, -5).
Answer:(-3,-6)
Step-by-step explanation:
How do I simplify???
1. [tex]i^{23}[/tex] = - i
2. [tex]\sqrt{-128}[/tex] = 8i√2
Explanation:Steps to simplify complex numbers:
Write the division as a fraction when dividing complex numbers. Then multiply both the numerator and the denominator by the denominator's conjugate. Then, use FOIL or the Distributive Property to simplify.Understanding how complex numbers work in their various operations requires simplifying complex numbers.1. To simplify [tex]i^{23}[/tex]
We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]
write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]
[tex](i^{4)^{5} } (i^{2} . i )[/tex] = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]
we know [tex]i^{2}[/tex] = -1
((-1²))⁵ [tex](i^{2} .i)[/tex]
we know that -1² = 1
= 1⁵ [tex](i^{2} .i)[/tex]
= 1 [tex](i^{2} .i)[/tex]
= [tex](i^{2} .i)[/tex]
here [tex]i^{2}[/tex] =-1
-1 . [tex]i^{}[/tex]
= - i
so [tex]i^{23}[/tex] is -i
2. To simplify [tex]\sqrt{-128}[/tex]
= [tex]\sqrt{(- 1) . (128)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]
= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]
here [tex]}\sqrt{-1}[/tex] = i
substituting i we get
= i . 8 √2
= 8i√2
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The amount of gas that a helicopter uses is directly
proportional to the number of hours spent flying. The
helicopter flies for 2 hours and Uses 26 gallons of fuel.
Find the number of gallons of fuel that the helicopter uses
to fly for 5 hours.
Answer:
65
Step-by-step explanation:
2:26
1:x
26/2 = x = 13
The heli uses 13 gallons per hour.
5:y
13x5 = y = 65
Hope that helps
What is the shaded area???
Step-by-step explanation:
[tex]area \: of \: circle = \pi\:r^{2} \\ \pi \times6.5^{2} - \pi \times {2.3}^{2} = 36.96\pi = 116.113... {cm}^{2} [/tex]
Answer:
116.129 cm²
Step-by-step explanation:
Area of circle:[tex]\boxed{\bf Area \ of \ circle = \pi r^2}[/tex]
Area of outer circle:
R = 6.5 cm
Area =3.142 * 6.5 * 6.5
= 132.75 cm²
Area of inner circle:
r = 2.3 cm
Area of inner circle =3.142 * 2.3 *2.3
= 16.621 cm²
Area of shaded area = area of outer circle - area of inner circle
= 132.75 - 16.621
= 116.129 cm²
Members of a lacrosse team raised $2863.50 to go to a tournament. They rented a
bus for $1087.50 and budgeted $74 per player for meals. Which equation or tape
diagram could be used to represent the context if a represents the number of players
the team can bring to the tournament?
Linear equations - The team can bring its 24 players
What do you mean by linear equations with one variable?
A linear equation with one variable is one that can be written as ax+b = 0, where a and b are two integers, and x is a variable. This type of problem only has one solution. For instance, the linear equation 4x+4=8 only has one variable.
We are given that,
the total money raised by the lacrosse team is given to be $2863.50
bus rented at a cost of $1087.50
meal budget per person is calculated to be $74
let us assume the number of players the team can bring to the tournament to be "x".
bus rent + (meal budget * number of players) = total money raised
= 1087.50 + (74*x) = 2863.50
= 1087.50 + 74x = 2863.50
= 74x = 2863.50 - 1087.50
= 74x = 1776
= x = 1776 ÷ 74
= x = 24
Thus the team can bring its 24 players.
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Grace is driving to a concert and needs to pay for parking. There is an automatic fee of $11 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $4 for every hour she had her car in the lot. How much total money would Grace have to pay for parking if she left her car in the lot for 6 hours? How much would Grace have to pay if she left her car in the lot fort hours?
For 6 hours
Grace will pay = $11 + 6 x $4
= $11 + $24
= $35
for t hours
Grace will pay = $11 + t x $4
= $11 + $4t
= $( 11 + 4t )
Mr. Giordano's drove 4.5 miles in 5 minutes. Mr. Baras drove 6.3 miles in 8 minutes. Who drove faster? Explain using unit rates for both teachers.
If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
The distance traveled by Mr. Giordano = 4.5 miles
The time taken = 5 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 4.5/5
= 0.9 miles per minutes
The distance traveled by Mr. Baras = 6.3 miles
The time taken = 8 minutes
Speed = Distance / Time
Substitute the values in the equation
Speed = 6.3/8
= 0.78 miles per minutes
Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove fast because speed of Mr. Giordano is greater than Mr. Baras
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-9- -8x2= -209 Solve this equation by taking square roots
The value of the quadratic equation given as -9- -8x^2= -209 is 5
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to solve the quadratic equation?The quadratic equation is given as
-9- -8x^2= -209
Add 9 to all sides of the equation
So, we have
-8x^2= -200
Divide both sides of the equation by -8
x^2= 25
Take the square roots
x = 5
Hence, the solution of the equation is 5
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Tammy’s take-home pay is $800 a month. She spends 7% on her take-home pay on her cell phone bill. How much is Tammy’s monthly cell phone bill?
Answer:744
Step-by-step explanation:
800-7%=744
Answer:
$56
Step-by-step explanation:
Melanie invests $3,000 at 12% simple interest for 1 year. How much is in the account at the end of the 1 year period?
We have the following:
We must apply the simple interest formula which is the following:
[tex]A=P\cdot(1+rt)[/tex]Where, P is the principal 3000
r is the interest rate 0.12
t is time in years
A is the total value
replacing:
[tex]\begin{gathered} A=3000\cdot(1+0.12\cdot1) \\ A=3000\cdot1.12 \\ A=3360 \end{gathered}[/tex]The answer is $3360 at the end of the 1 year period
You have 900 feet of fencing to enclose a rectangular plot that borders on
a river. If you do not fence the side along the river, find the length and
width of the plot that will maximize the area. What is the largest area that
can be enclosed?
The width, labeled x in the figure, is
(Type an integer or decimal.)
feet.
X
River
900-2x
x
Answer:
A = 101250 meter²
Step-by-step explanation:
Answer:
Maximum area enclosed will be 101250 meter².
Step-by-step explanation:
Let the length of the rectangular plot is x meters and the width is y meters.
900 meters is the length of the fence which represents the length of the three sides of the plot.
Therefore,
x + 2y = 900
y =  meters
Now the area of the rectangular plot will be
A = Length × Width
= (x)(y)
= 
= 450x - 
We know for the maximum area we will differentiate the area and equalize it t the zero.

= 450 - x
For the maximum area, 
Therefore, 450 - x = 0
x = 450
and y = 
y = 
y = 450 - 225
= 225 meters
Now the area enclosed A = 450 × 225
A = 101250 meter²
Provide the name and classification and parent equation for each one.
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Slope of the line graph here is undefined.
When a line is vertical, its slope is ambiguous. A vertical line lacks the horizontal distance required for a positive, negative, or zero slop to exist. Since there is no horizontal change, there is no slope for vertical lines because 0 cannot be divided into any integer.
It is obvious that the x-coordinates are the same if we have a pair of coordinates, (x1, y1) and (x1, y2) through which a line passes. They are the same vertical line's points. As a result, the slope of such a line will be ambiguous.
Examples of undefined slope in real-world situations include elevators that only go up and down, and a mountain cliff that is vertical for a certain amount of height but impossible for climbers to scale.
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Mr. Jonas took out a loan of $12,400. The interest rate is 3% per year, and the interest is not compounded. How much amount will Mr. Jonas have to repay after 4 years?
Jonas have to repay $13888 after 4 years.
Given
Principle amount of loan (P) = $12,400
Rate of interest (R) = 3%
Time period (T) = 4 years
Also the interest is not compounded, hence it is simple interest.
The formula for simple interest is (PTR)/100
Where,
P = Principle amount
T = time period
R = rate of interest
By substituting the values in the formula we get,
Simple interest = (12400 x 4 x 3) / 100
Simple interest = 1488
Hence adding this interest to Principle sum we get
12400 + 1488 = 13888
Jonas has to repay $13888 after 4 years.
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(-8) • 2/3 = I dont know and yea I'm confused lol
a salesperson has found that the probability of a sale on a single contact is approximately .03. if the salesperson contacts 100 prospects, what is the approximate probability of making at least one sale?
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.
So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.
So the probability of making of at least one sale is 1 minus the probability of making no sales.
The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.
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30. A certain test track for new car models is 6,720 meters long. If a car is currently of the way down
the track, how many more kilometers must it travel
to reach the end?
E. 2.24
F. 4.48
met
G. 6.72
H. 10.0
Answer: E. 2.24
Step-by-step explanation:
6720 - 6720 x 2/3
6720 - 4480
= 2,240
1 kilo = 1000 meters
2240 ÷ 1000
= 2.24
is -48=48 have no solution or infinite solutions?
The birth weights ( to the nearest pound) of a sample of 27 newborn babies at a certain hospital are given in the following table, along with the number of babies at each birth weight. Find the mean birth weight of these 27 babies. Round your answer to at least on decimal point
Given
The table,
The sample size is 27.
To find:
The mean weight of these 27 babies.
Explanation:
It is given that,
That implies,
The mean weight of 27 babies is,
[tex]\begin{gathered} Mean=\frac{\sum_^x_if_i}{\sum_^f_i} \\ =\frac{4\times5+6\times10+7\times12}{5+10+12} \\ =\frac{20+60+84}{27} \\ =\frac{164}{27} \\ =6.07 \\ =6.1pounds \end{gathered}[/tex]Hence, the mean weight of 27 babies is 6.1 pounds.
Filling and Emptying Tanks
1) Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters
per minute. How many liters of water remain in the tank after the following amounts of
time?
a) 30 seconds
c) t minutes
b) 7 minutes
c) 18 liters
2) For how many minutes, t, has the water been draining when Tank B contains the
following amounts of water?
a) 75 liters
Period: 6
b) 32.5 liters
d) v liters
Answer:
a) 78.75
b) 62.5
a) 2 minutes
b) 19 minutes
c) 24 minutes and 48 seconds
For what values of b is the difference between the fractions [tex]\frac{2b-1}{2}[/tex] and [tex]\frac{1+5b}{4}[/tex] negative? (for 25 points) i will give you brainlyiest or smthing if u give answer
The value of b for which the difference between the fractions
(2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
What is Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
Two fractions are,
⇒ (2b - 1) / 2 and (1 + 5b) / 4
Since, The difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative.
So, we can formulate;
⇒ (1 + 5b) / 4 - (2b - 1) / 2 < 0
Solve for b, as;
⇒ 1 + 5b - 2 (2b - 1) < 0 x 4
⇒ 1 + 5b - 4b + 2 < 0
⇒ b + 3 < 0
Subtract 3 both side;
⇒ b + 3 - 3 < 0 - 3
⇒ b < -3
Therefore, The value of b for which the difference between the fractions (2b - 1) / 2 and (1 + 5b) / 4 negative will be;
⇒ b < -3
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PLEASE HELP DUE IN 3-5 MINUTES, THANK YOU!!
Answer:
In second week there is percentage limit (-ve sign) of 20% in people traveling examine to first week.
In 0.33 week there is proportion increase of 50% in human beings traveling compare to 2nd week.
In fourth week there is share limit of 75% in humans visiting evaluate to 1/3 week.
Or Lillian bought cupcakes for her sister's birthday party. 12 out of the 40 cupcakes had sprinkles on top. What percentage of the cupcakes had sprinkles?\
Percentage of the cupcakes that had sprinkles = 30 %
Percentage
Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.
Proportion
The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The first step is to divide 12 by 40 to get the answer in decimal form:
12 / 40 = 0.3000
Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:
0.3000 * 100 = 30.00%
Percentage of the cupcakes that had sprinkles = 30 %
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at eaton centre, let us imagine that $60 was spent on four shirts. how could we determine the average cost of each shirt?
Answer: 60 divided by 4
Step-by-step explanation:
Answer:
The average would be $15 for each shirt.
Step-by-step explanation:
divide the amount of money by the amount of shirts.
Find the values of the ratios
(red to blue) of the
perimeters and areas of the
similar figures. Write the
ratios as fractions in
simplest form.
5
8
The ratio of the perimeters is
The ratio of the areas is
Answer:
perimeter: 5/8area: 25/64Step-by-step explanation:
You want the ratios (red to blue), of perimeter and area, given that corresponding sides have the ratio red to blue = 5 to 8.
Perimeter ratioThe ratio of perimeters is the ratio of corresponding side lengths:
red to blue = 5 / 8
Area ratioThe ratio of areas is the square of the ratio of corresponding side lengths:
red to blue = (5 to 8)² = 25 / 64
__
Additional comment
Ratios are customarily expressed in any of three equivalent forms:
5 to 85:85/8 "fraction" formThis question is worth 2 extra credit points. You do not have to complete it if you do notwant to.EXm4 ---> possible beginning ---->2or ------>ma . m2 or ----->(m2)Give a possible beginning to the following expression. (see example above)moHTML EditoreВ
Iris's checking account pays simple interest at 3% per year. She has $185 in
her account. Write a linear function to model the amount of money in her
checking account at any time t.
The linear function to model the amount of money in her checking account at any time t is 185 + 5.55t.
What is an interest?An interest simply means the extra amount that's borrowed when one borrows money or when one saves.
In this case, the checking account pays simple interest at 3% per year. She has $185 in her account.
The amount of money in the account at anytime will be:
= 185 + (PRT/100)
P = principal
R = rate
T = time
= 185 + [(185 × 3 × t)/100]
= 185 + 5.55t
The function is 185 + 5.55t.
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Lana’s Linoleum Luxuries makes rectangular kitchen tiles with an area of t square inches.
The area in square inches of the tile is 9 / 4 t .
How to find the area of a rectangle?She makes rectangular kitchen tiles with an area of t square inches.
Therefore,
area of the rectangular kitchen tiles = lw
t = lw
l = t / w
w = t / l
Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.
Hence,
area of the tile = 3 / 4 t / w × 3(t / l)
area of the tile = 9 / 4 × t² / lw
where
lw = t
Hence,
area of the tile = 9 / 4 × t² / t
area of the tile = 9 / 4 × t
Therefore,
area of the tile = 9 / 4 t
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on a recent holiday weekend, a sample of 500 drivers was stopped by the police. 300 drivers were under 30 years of age. a total of 250 were under the influence of alcohol. of the drivers under 30 years of age, 175 were under the influence of alcohol. what is the probability that a driver selected at random from the sample of 500 is under 30 and not under the influence of alcohol?
P(A). P(Y)= 0.5*0.6=0.3
Probability: - Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Number of cases of A, N(A)= 250,
So,
P(A)=250/500 =0.5
and
N(Y)= 300, so P(Y)=300/500 =0.6
N(A and Y)= 175 so P(A and Y)= 175/500=0.35
A and Y are mutually exclusive implies A and Y donot have any elements in common, but here there are 175 people who are below 30 years and under the influence of alcohol, So they are not mutually exclusive!!
For A and Y to be independent, the Probability of A intersection Y should be equal to the product of their respective probabilities,
in this case P(A). P(Y)= 0.5*0.6=0.3 which is not equal to P( A intersection Y) (0.35)
So, A and Y are not mutually Independent also.
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HELP ME PLEASE!!!!! will give brainlist
Answer:
y=3x+3
Step-by-step explanation:
i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation
Answer:
See below
Step-by-step explanation:
Find two convenient points to calculate the slope:
0,3 and -1,0 slope = m = (3-0) / ( 0 - -1) = 3
and the y axis intercept = 3 (from looking at graph)
line equation is y = mx + b ( where b is the y-axis intercept)
y = 3x + 3
-12/7 = 6w solve for w and simplify your answer as much as possible