Coordinates of P is 8
Since 3+2 = 5, we are dividing line segment AB into 5 congruent parts with point P 3/5 of the way from A to B.
x-coordinate of P = x-coordinate of A + (3/5)(change in x from A to B) = -4 + (3/5)(20) = 8
y-coordinate of P = y-coordinate of A + (3/5)(change in y from A to B) = 8 + (3/5)(-10) = 2
P = (8,2)
In each axis, find the distance from A to B, apply the ratio to get the distance from A to P, and add that value to A.
Note the ratio: We are given the ratio of AP to PB as 3/2. This means that the ratio of AP to AB is 3/5
Here is is for the X-axis:
AB = 20
AP = 20 *3/5 = 12
So P = -4 + 12 = 8
It is one of the branches of geometry where the position of a point is defined using coordinates.
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
It is used to divide any line into two parts, in m:n ratio
The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).
The four quadrants along with their respective values are represented in the graph below-
Quadrant 1 : (+x, +y)
Quadrant 2 : (-x, +y)
Quadrant 3 : (-x, -y)
Quadrant 4 : (+x, -y)
The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.
How To Find Coordinates of a Point on Graph With Examples
A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.
Coordinates Definition
A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.
The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:
x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.
y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.
Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).
Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).
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Answer for this please see image attached m
Answer:
angle A=125 angle B= 114 angle C= 121
Step-by-step explanation:
first you have to find x so that you can find each angle
the interior angles of a triangle is equal to 360
add the angles together x+x+7+x+11=360
combine like terms 3x+18=360
subtract 18 on both sides 3x=342
divide by 3 on both sides x=114
to find angles:
plug in X to each side
(114)+7 = angle C
(114)+11= angle A
114= angle B
expressions that have 2\3 as a product.
The expression that have 2\3 as a product are 4/5 × 5/6 and 6/7 × 7/9 which is option (a) and (e) .
An expression in maths could be a sentence with a minimum of 2 numbers/variables and a minimum of one maths operation in it.An expression could be a combination of terms that are combined by victimization mathematical operations like subtraction, addition, multiplication, and division.(a) 4/5 × 5/6 = 20/30
= 2 /3
(b) 7/8 × 9/10 = 63 / 80
(c) 1/3 × 2/3 = 2 /9
(d) 3/4 × 7/12 = 21 / 48
= 7 / 16
(e) 6/7 × 7/9 = 42 /63
= 6 / 9
= 2 / 3
Only the expression (a) and (e) have 2\3 as a product.
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The complete question is given below :
Choose all the expressions that have 2\3 as a product.
(a) 4/5 × 5/6
(b) 7/8 × 9/10
(c) 1/3 × 2/3
(d) 3/4 × 7/12
(e) 6/7 × 7/9
Identify the y-intercept for each function and determine which function has the greater y-intercept. Please help me!
What are the degree and leading coefficient of the polynomial? 18u - 8u^2 -9 + u^7
The leading coefficient and degree of the polynomial 18u - 8u^2 -9 + u^7 are 1 and 7 respectively.
According to the given question.
We have a polynomial 18u - 8u^2 -9 + u^7.
As we know that the leading coefficient of a polynomial is the coefficient of the leading term.
And the highest and the greatest power of a variable in a polynomial equation is called degree of a polynomial.
Here, the leading term of the given polynomial is u^7. Therefore, the leading coefficient of a polynomial is 1.
And the degree of the polynomial is 7.
Hence, the leading coefficient and degree of the polynomial 18u - 8u^2 -9 + u^7 are 1 and 7 respectively.
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The dividen is greater that 1,000, The quotient of 52 with a remainder of 18
The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variable called division.
Let's consider a division problem.
5/2 → 2 + 1
Here 5 is called the dividend,2 is the divisor,2 is the quotient, and 1 is the remainder.
Now,
2 × 2 + 1 = 5
Therefore,divisor × quotient + remainder = dividend
So,
Let's suppose the divisor in the given case is x
Now,
52x + 18 ≥ 1000
52x ≥ 982
x ≥ 18.86
Hence "The minimum divisor such that the dividend is greater than 1000 and a quotient of 52 with a remainder of 18 is 18.86".
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The given question is incomplete complete question is ;
What is the minimum divisor such that The dividend is greater than 1,000, The quotient of 52 with a remainder of 18
It is the end of the budgeting period for John Smith, and he has $500 left in his budget for car rental expenses. He plans to spend this budget on a sales trip throughout the country. He will rent a car that costs $50 per day and $ 0.50per mile, and he can spend no more than 500
The number of miles that John Smith can travel with his budget if he has $500 left in his budget for car rental expenses is 900 miles.
How to calculate the expression?Amount left in the budget = $500
Since he will rent a car that costs $50 per day and $ 0.50per mile, the expression will be:
50 + 0.50m = 500
where m = number of miles
Collect like terms
0.5m = 500 - 50
0.5m = 450
Divide
m = 450/0.5
m = 900
Therefore, the number of miles that John Smith can travel with his budget is 900 miles.
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Construct an angle of measure 45° with the help of a protractor. Bisect it and find the measure of the bisected angles .
Answer:
See attachment
Step-by-step explanation:
Draw a 45o angle
Bisecting means dividing the angle into 2 halves, which is 22.5o each
express the following as percents a)15 girl out of 75 pupils
Zoey needs to order some new supplies for the restaurant where she works. The restaurant needs at least 711 glasses. There are currently 281 glasses. If each set on sale contains 10 glasses, use the drop-down menu below to write an inequality representing
s
s, the number of sets of glasses Zoey should buy
The inequality that represents the number of sets of glasses Zoey should buy is s ≥ 43
What is the inequality?The first step is to determine the number of glasses needed.
The number of glasses needed = 711 - 281 = 430
The second step is to determine the number of sets Zoey needs to buy.
Number of sets needed = 430 / 10 = 43 sets
The third step is to determine the appropriate inequality sign to use
Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe ≥ (greater than or equal to ) would be used since the number of sets can either be equal to or greater.
s ≥ 43
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Alesha went to the movies. A popcorn is $3 more than a soda. She purchased 1 popcorn and 2 sodas. She spent $21. How much is a popcorn?
Answer: a popcorn is $9
Step-by-step explanation:
soda is $6
Vicente is investing money into a savings account that pays 3% simple interest, and plans to leave it there for 10 years. Determine what Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years.
The amount Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years is $15,384.62
What is simple interest?
The simple interest on the savings is determined as the deposit multiplied by the annual interest rate and the number of years that deposit would last in the account
I=PRT
I=simple interest
P=principal=deposit=unknown
R=annual simple interest=3%
T=number of years=10
A(amount in 10 years)=P+PRT
A=P(1+RT)
$20,000=P(1+3%*10)
$20,000=P*1.30
P=$20,000/1.30
P=$15,384.62
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A rental car company charges $71.02 per day to rent a car and $0.12 for every mile
driven. Lily wants to rent a car, knowing that:
She plans to drive 475 miles.
. She has at most $390 to spend.
.
What is the maximum number of days that Lily can rent the car while staying within
her budget?
Answer:
Step-by-step explanation:
4 is the maximum number of days.
Using Inequality, the maximum number of days that Lily can rent the car while staying within her budget is 4 days.
How to find the maximum number of days she can rent the car?The rental car company charges $71.02 per day to rent a car and $0.12 for every mile driven.
Lily wants to rent a car and she plans to drive 475 miles. She has a budget of $390.
Therefore, the maximum number of days that Lily can rent the car while staying within her budget can be calculated as follows:
Using inequality,
total cost = 71.02(x) + 0.12(y)
where
x = number of days
y = number of miles
Therefore,
71.02x + 0.12(475) ≤ 390
71.02x ≤ 390 - 57
71.02x ≤ 333
x ≤ 333 / 71.02
x ≤ 4.68882005069
Therefore,
she can drive maximum of 4 days.
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Buster's dog house is 3 feet long, 2 feet wide, and 2 feet high. how much space would there be if buster's house were twice as long
there woldbe 96 volume
Step-by-step explanation:
to find the volume you have to multiply width x lenghth x height
so set up your equation like this -
3 x 2 x 2
the times everything by 2 so it will now look like this -
6 x 4 x 4
then solve and get the answer 96
In 2002, a school population was 1655. By 2008 the population had grown to 2711.
1) How much did the population grow between the year 2002 and 2008?
In Florida, as of Nov 19, 1,020,000 had people tested positive for corona virus. This was a
0.18% increase from the previous day. If that percent increase continued, how many people
would be infected on Dec 19th?
The number of people that would be infected on Dec 19th, based on the daily growth rate of 0.18% is 1,076,542
What is interval in days between Nov. 19th and Dec.19th?
The interval between November 19th and December 19th is a period of 30 days, since there are 11 more days in November and 19days in December, in essence, using the future value formula, we can compute the number of people tested positive for corona virus on 19th December as shown below:
FV=PV*(1+g)^N
FV=number of people tested positive for corona virus on 19th Dec.=unknown
PV=number of people tested positive for corona virus on Nov. 19th=1,020,000
g=growth rate=0.18%
N=number of days between 19th Nov. and Dec.
FV=1,020,000*(1+0.18%)^30
FV= 1,076,542
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What is f(g(x) of f(x)=9x+2 and g(x)=x-2 over 9
The value of the composite function f(g(x)) is calculated as f(g(x)) = 65.
What is termed as the composite function?Composite functions is one in which one function is placed within another.
A composite function defines one that is reliant on another. A composite function is defined whenever one function is replaced for another. For example, the composite function constituted by substituting g(x) for x in f is f(g(x)) (x).f(g(x)) is spoken as "f оg(x)."For, the given values in the question;
f(x) = 9x+2 and g(x) = x-2
We have to find the value of f(g(x)) for x = 9.
First estimate the value of g(x) by substituting x = 9 in it.
g(x) = x-2
g(9) = 9-2 = 7
Now,
f(x) = 9x+2 and
f(g(x)) = f(7) = 9x+2, (substitute x = 7)
f(g(x)) = 9×7 + 2
f(g(x)) = 65.
Thus, the value of the composite function f(g(x)) = 65.
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QUESTION 8 Nigel received a student loan for $9467. If his tuition was $4997.94, textbook costs $854.84, student fees $702.88, and school supplies $80.41, how much did Nigel have left after paying all his school related expenses? Round your answer to the nearest cent. 3 poin
If angle YXZ measures 90 degrees, which statement is true?
(answers are below)
segment XZ is perpendicular to segment WY
WX =XY
segment XZ is a perpendicular bisector of segment WY
X is the midpoint of segment WY
The true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
What are Perpendicular Segments?Perpendicular segments are line segments that intersect at a point to form right angles which is equal to 90 degrees. The point where perpendicular segments meet have an angle measure of 90 degrees.
In the given diagram, we are told that angle YXZ is equal to 90 degrees. This means that at the point where segment XZ and segment WY meet have an angle measure of 90 degrees.
This means they are perpendicular segments.
Therefore, the true statement about the given diagram is: A. segment XZ is perpendicular to segment WY.
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How long does it take $450 to double at a simple interest rate of 14%? Express your answer in months. Round to the nearest whole number.
The number of months so that the investment gets double will be 86 months.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on. The amount is given as,
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
The principal amount is $450 and if the amount gets doubled, then the value of the amount will be $900. The simple interest rate is 14%. Then the time is given as,
A = P + (PRT)/100
900 = 450 + [450 x 14 x T] / 100
450 = 450 x 14 x T / 100
T = 100 / 14
T = 7.14 years
T = 7.14 x 12
T = 85.7 ≈ 86 months
The number of months so that the investment gets double will be 86 months.
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In the word grapefruit , the ratio of vowels to consonants is 2 : 3
Answer:
pineapple: 4:5strawberry: 3:7Step-by-step explanation:
You want the ratio of vowels to consonants in each of the words "pineapple" and "strawberry."
RatioTo form the reduced ratio vowels:consonants, we need to identify the type of letter each is. Here we use bold to identify the vowels.
pineapple ⇒ 4:5
strawberry ⇒ 3:7 . . . . counting "y" as a vowel
The city of Raleigh has 10,300 registered voters. There are two candidates for City Council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 300 randomly selected registered voters was conducted. 9595 said they'd vote for Brown, 182 said they'd vote for Feliz, and 23 were undecided.
Answer:
What do I solve for?
Step-by-step explanation:
1. The price of one kg grapes is 60p, find the total price of 30 kg grapes in pounds.
2. The price of one kg carrots is 35p, find the total price of 40-kg carrots in pounds.
3. The price of one kg grapes is 60p and the price of one kg bananas is 40p per kg, find the total price of 30 kg grapes and 40kg bananas in pounds.
4. The price of one kg oranges is 90p and the price of bananas is 30p per kg, find the total price of 30 kg oranges and 40kg bananas in pounds
Maths:
Round 1
1) Grapes cost £1.50 per kg and carrots cost £1.00 per kg. How much would it costs for 3kg of
grapes and half a kilogram of carrots? £5
2) Jenny decides to share her sweets between herself and her 3 friends. She has 212 green
sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jenny and her friends
get each? 256
3) Large chocolate bars come with 32 pieces. Medium chocolate bars come with 24 pieces.
Barry buys 8 large bars of chocolate and 6 medium bars. How many pieces of chocolate will he
have altogether? 400
4) A flower shop sells roses for £1.79, carnations for £1.25 and buttercups for £1.30. Holly
decides to buy 3 roses and a buttercup. How much does she spend? £6.67
5) Pencils come in packs of 12 and each pack costs £1.19. Mr Green needs to buy a pencil for
each of the 50 children in his class. How much will he spend on pencils? £5.95
Round 2
1) Mrs Orange decides to share her savings between her six grandchildren. She has £350 in
her savings tin and £1450 in her savings account. How much will each of her grandchildren get?
£300
2) Green lollipops come in packs of 5, yellow lollipops come in packs of 6 and blue lollipops
come in packs of 4. A school buys 32 packs of blue lollipops and 18 packs of green lollipops.
How many lollipops will they buy altogether? 218
3) The baker’s oven can bake 28 loaves of bread at a time. In a day, it can go through 30 full
bakes. How many loaves of bread would be baked after 1 week? 5880
4) Ms Purple sells cars for a living. In one day, she sells 2 blue cars (at £4500 each), 7 yellow
cars (at £6000 each) and 12 black cars (at £8000 each). How much money does she take in car
sales in that one day? £147,000
5) Coaches carry 58 people. A school decides to take its 300 pupils and 38 staff on a visit to the
beach. A single coach costs £128. How much will the total cost of the coaches come to? £768
Topic:
Fruit Veg
Quince
raspberry
Lettuce
garlic
tomato
strawberry
grape
pumpkin
blackberries
nashi
kiwi
chilli
pear
passion fruit
cantaloupe
fig
eggplant/aubergine
cucumber
lemon
peach
lime
watermelon
pineapple
Zucchini/courgette
grapefruit
persimmons
mango
plum
cauliflower
Broccoli
Leeks
Fennel
Carrots
Coriander
Silverbeet
Snow peas
Beans
Celery
Beetroot
Peas
Artichoke
Sweet potato
Please help solve number 24
How long does it take to ride a bicycle 100 miles at each of the following speeds: 5 mph, 10 mph, 15 mph, 20 mph, 25 mpb? What is always true about the product speed x time?
The times associated with each speed are:
20 h10 h6.667 h5 h4 hIt is always true that the speed is inversely proportional to time.
How to analyze the motion of a bicycle at constant speed
In this case we find the situation of bicycle moving at constant speed, where the traveled distance (s), in miles, is equal to the following expression:
s = v · t (1)
Where:
v - Speed, in miles per hour.t - Time, in hourNow we proceed to calculate time needed for each speed:
t = s / v
Case 1
t = 100 mi / 5 mi / h
t = 20 h
Case 2
t = 100 mi / 10 mi / h
t = 10 h
Case 3
t = 100 mi / 15 mi / h
t = 6.667 h
Case 4
t = 100 mi / 20 mi / h
t = 5 h
Case 5
t = 100 mi / 25 mi / h
t = 4 h
According to the model for rectilinear uniform motion, the speed is inversely proportional to time.
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how many days will it take to finish a 20 pound bag of rice when you use 0.4 pounds each day
Answer:
50
Step-by-step explanation:
divide 20 by 0.4
= 20/0.4 = 20 * (1/0.4)
= 20*2.5
= 50
Write the expression. Then, check all that apply.
twice the difference of a number and six
The algebraic expression for the given statement is: 2(n - 6).
How to Write an Algebraic Expression?To translate the statement, "twice the difference of a number and six", follow the steps below:
The two operations we would use are multiplication and subtraction.
The constants are 2 and 6.
Twice is translated as 2 ×, (-) is "difference".
Let the number be "n" .
The difference of a number, n, and 6, would be: n - 6.
Therefore, we would have the following algebraic expression: 2(n - 6).
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Ronnie is playing a card game where the goal is to get the lowest possible score. In
the first round, Ronnie scored -6 points. In the second round, he scored -12 points.
What is Ronnie's total score
Find the difference. 5 1/9 - 3 4/9
A.
B.
C.
D.
Answer: 1 6/9, or 1 2/3
Step-by-step explanation:
Regroup the 5 and 1/9 to get 4 10/9. Subtract the 3 4/9 from the 4 10/9, getting 1 6/9. Simplified, this is 1 2/3. Hope this helps!
At the movie theatre, child admission is $5.90 and adult admission is $9.00. On Saturday, 137 tickets were sold for a total sales of $1003.60. How many adult tickets were sold that day?
The number of adult tickets, that were sold that day at the movie theatre was 62
What are simultaneous equations?
Simultaneous equations are two or more equations that must be solved concurrently in order to derive the values of the unknown, the total sales, as well as the total number of tickets sold, can be modeled into equations as below:
let x be the number of adult tickets
let y be the number of children's tickets
9x+5.90y=1000.60....... equation 1
x+y=137.................. equation 2
solve for y in equation 2
y=137-x
substitute for y in equation 1
9x+5.90(137-x)=1000.60
9x+808.30-5.90x=1000.60
9x-5.90x=1000.60-808.30
3.10x=192.30
x=192.30/3.10
x=adult tickets=62
children tickets=137-62
children tickets=75
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100 POINTS!!! Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Multiply or divide as indicated. Leave your answer with no factors in the denominator.
p^-4 q^5 r^6 / p^-3 qr^-2
Answer:
[tex]\dfrac{q^{4} r^8}{p}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]
Separate the variables:
[tex]\implies\dfrac{p^{-4}}{p^{-3}} \times \dfrac{q^5}{q} \times \dfrac{r^6}{r^{-2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies p^{(-4-(-3)} \times q^{(5-1)} \times r^{(6-(-2)}[/tex]
[tex]\implies p^{(-4+3)} \times q^{(5-1)} \times r^{(6+2)}[/tex]
[tex]\implies p^{-1} \times q^{4} \times r^8[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies \dfrac{1}{p} \times q^{4} \times r^8[/tex]
Simplify:
[tex]\implies \dfrac{q^{4} \times r^8}{p}[/tex]
[tex]\implies \dfrac{q^{4} r^8}{p}[/tex]