We have that the data is: (x₁ =–9.3, y₁=3) and (x₂=– 9.3, y₂=–7.5). The formula to calculate two distance between two points is:
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(x_1-x_2)^2+(y_1-Y_2)^2 } } \end{gathered}$}}[/tex]
When we calculate the distance between two points, we solve what goes inside the parentheses, then it is calculated to the power of 2, and we continue adding the two numbers of the previous results, and finally the square root is calculated.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(-9.3-(-9.3))^2+(-7.5-3)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{(0)^2+(-10.5)^2 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{0+110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=\sqrt{110.25 } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{d[A,B]=10.5 } \end{gathered}$}}}[/tex]
The distance between the points ( – 9.3,3) and ( – 9.3, – 7.5) is 10.5Q8.
(a)
Work out the value of
(√2)^4
[tex]=\sqrt{2} *\sqrt{2} *\sqrt{2} *\sqrt{2} \\=(\sqrt{2} *\sqrt{2})(\sqrt{2} *\sqrt{2})\\=2*2\\=4[/tex]
The answer is 4
The value of [tex](\sqrt2)^4[/tex] is 4.
The number of times a number has been multiplied by itself is referred to as its exponent. The rules of multiplying exponents are of different types. The given equation can be calculated using the Power of a Power rule.
According to this rule, when a base has an exponent, and that entire term has an exponent, the exponents are multiplied together. This is written as
[tex](a^x)^y=a^{xy}[/tex]
Here, both exponents are multiplied together.
Therefore, using the above rule the given square root with an exponent can be written as,
[tex]\begin{aligned}\left(\sqrt2\right)^4&=\left(2^{\frac{1}{2}\right)^4\\&=2^{\frac{1}{2}\times4}\\&=2^2\\&=4\end{aligned}[/tex]
The value is 4.
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write down the temperature which is 5°c below -2°c
Step-by-step explanation:
below -2°
that means
-2 - 5 = -7° C
Answer:
-7 degrees
Step-by-step explanation:
find x, y and z HELPPP
Answer:
x = 30 degrees
y = 15 degrees
z = 150 degrees
Step-by-step explanation:
Finding x:
2x + 90 + x = 180
3x + 90 = 180
3x = 90
x = 30
x and 2y are alternate interior angles, which means that they are congruent:
x = 2y
30 = 2y
15 = y
x and z are same side interior angles, which means that they are supplementary:
x + z = 180
30 + z = 180
z = 180 - 30
z = 150
7x + 2y = 6
-14x - 4y = -12
Answer:
x= 6/7 - 2y/7
y= 3 - 7x/2
Step-by-step explanation:
I said so
i need help, please.
1a) The number of whole servings Susan can make from 4.25 pounds of flour if one serving uses ²/₃ is 6.
1b) The quantity of flour Susan has after making 6 servings is ¹/₄ pounds.
2) Garrison can drink ⁷/₈ gallons of lemonade each of the next six days.
3) The student council sold 122 bags of chips.
4) If a container can hold 3¹/₃ ounces of peanuts, 5 containers will hold 16²/₃ ounces.
5) The number of people at the football game (400) last night who were not wearing orange and black is 240.
6) The number of long sleeves in Jordan's outfits is 45.
How are the numbers determined?The numbers and values can be determined using suitable mathematical operations.
The basic mathematical operations used include division, subtraction, and multiplication.
1) The total quantity of flour available = 4.25 pounds
The amount of flour required per serving = ²/₃ pounds
The number of servings from 4.25 pounds = 6³/₈ servings (4.25 ÷ ²/₃)
= 6 servings.
Quantity of flour left = ¹/₄ pounds [4 - 6(²/₃)]
2) The number of lemonades available = 5.5 gallons
The quantity Garrison took on Monday = ¹/₄ gallons (0.25)
The remaining number of gallons = 5.25 gallons (5.5 - 0.25)
The gallons for the remaining 6 days = ⁷/₈ gallons (5¹/₄ ÷ 6)
3) The total amount realized from sales = $73.20
The unit price per bag of chips = $0.60
The units sold = 122 ($73.20 ÷ $0.60)
4) The ounces of peanuts per container = 3¹/₃
The number of containers = 5
The ounces of peanuts for 5 containers = 16²/₃ ounces (3¹/₃ x 5)
5) The total number of people at the game = 400
The proportion of people wearing orange and black = ²/₅
The proportion of people not wearing orange and black = ³/₅ (1 - ²/₅)
The number of people not wearing orange and black = 240 (400 x ³/₅)
6) The total number of outfits in Jordan's closet = 200
The proportion of shirts = ³/₄
The proportion of long sleeve shirts = ³/₁₀
The number of long sleeve shirts = 45 (200 x ³/₄ x ³/₁₀)
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An artist charges $980 for a portrait but gives 5% discount for cash. Calculate the cash Price of the portrait
Answer:$1031$
Step-by-step explanation: $980 is the worth of the portrait right? That means that 5%-100%=95% of the portrait is 980 so if we multiply by the reciprocal which is 980*100/95=$1031$
(Please help quick!)
Find the area of the triangle.
A=?ft^2
ok I will help you
A=hbb
2
b Base
hb Height
Each day, Julius reads 3 more pages in his novel than he read the day before.
If he read 8 pages on the first day, how many pages will he read on the 11th day?
OA. 33
OB. 35
C. 38
O D. 41
Answer:
He will read C. 38 pages on the 11th day.
Step-by-step explanation:
First day = 8 pages
2nd day = 8+3 = 11 pages
Sequence = (8,11,14.......)
a+(n-1)d
a = first term
nth term = 11
d(difference) = +3 or 3
8+(11-1)3
=38
What is this expression in simplified form?
Answer:
[tex]15\sqrt{5}[/tex]
Step-by-step explanation:
simplify [tex]\sqrt{20}[/tex] and [tex]3\sqrt{50}[/tex]
[tex]\sqrt{20}[/tex] simplifies into [tex]\sqrt{5}[/tex]
so [tex]\sqrt{20}[/tex] = [tex]\sqrt{4} \sqrt{5}[/tex]
we can simplify [tex]\sqrt{4[/tex] into a whole number
[tex]\sqrt{4[/tex] =2
= 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{50[/tex] simplifies into [tex]\sqrt{2[/tex]
so [tex]\sqrt{50[/tex] =3( [tex]\sqrt{25} \sqrt{2}[/tex])
we can simplify [tex]\sqrt{25}[/tex] into a whole number
[tex]\sqrt{25[/tex] = 5
= 15[tex]\sqrt{2[/tex]
then we add these simplified roots back into the question
2[tex]\sqrt{5}[/tex] + [tex]5\sqrt{2[/tex] -[tex]2\sqrt{5[/tex]
we simplify again as [tex]2\sqrt{5[/tex] cancels out
to get a final answer of:
[tex]15\sqrt{5}[/tex]
if x=-7 and y=3, calculate the values of (x+y/x-y)²
If x = -7 and y = 3, the value of the expression (x+y/x-y)² is 4/25 .
In the question ,
it is given that ,
the algebraic expression is given as (x+y/x-y)² ,
we need to find the value of the given expression when the value of x = -7 and y = 3 .
Substituting the values of x = -7 and y = 3 in the expression ,
we get
= (x+y/x-y)²
= ((-7+3)/(-7-3))²
= (-4/(-10))²
= 16/100
cancelling out the common factor 4 , from the numerator and denominator .
= 4/25
Therefore , the value of the given expression at x = -7 and y = 3 is 4/25 .
The given question is incomplete , the complete question is
Calculate the value of the expression (x+y/x-y)² at x = -7 and y = 3 ?
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Peaceful Travel Agency offers vacation packages. Each vacation package includes a city, a month, and an airline. The agency has 3 cities, 1 month, and 3
airlines to choose from. How many different vacation packages do they offer?
If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.
What is the multiplication rule in permutation and combination?
1. Using the multiplication principle, we can count the number of ways to complete a sequence of tasks by multiplying the number of ways to complete each task together.
2. A permutation is a particular arrangement of objects.
Peaceful Travel Agency offers vacation packages.
If the agency has 3 cities, 1 month, and 3 airlines to choose from.
then by using the multiplication rule,
The number of different packages = 3 × 1 × 3
= 9 packages
Hence, If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.
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Ms. Cangiano's class is collecting aluminum cans for a recycling project. George brings in 3 bags with 10 cans in each bag. Ava brings in 6 bags with 11 cans in each bag. how many cans do they have so far?
A: 30
B: 33
C: 96
D: 90
please explain !!
Answer: its c
Step-by-step explanation:
Someone pls help me. i dont understand this at all :c
The equation for the function described, using the translations, is given as follows:
f(x) = 2^(x - 4) + 5.
What are the translations to a function?There are four cases for the translation of a parent function, and they can be represented as follows:
Horizontal translation left a units: f(x + a).Horizontal translation right a units: f(x - a).Vertical translation up a units: f(x) + a.Vertical translation down a units: f(x) - a.In the context of this problem, the parent function is defined as follows:
f(x) = 2^x
The definitions for each translation are given as follows:
Horizontal shift right four units: f(x - 4).Vertical shift up five units, considering the horizontal shift right four units: f(x - 4) + 5.Hence the translated function is defined as follows:
f(x) = 2^(x - 4) + 5.
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9(2x - 6)
A.
9x - 8
B.
9x - 3
C.
18x + 54
D.
18x - 54
Answer:
D.
18x-54
Step-by-step explanation:
9*2x - 9*6
18x - 54
Olivia helps paint a square mural in her classroom. Then she helps paint a mural in the hallway whose length is 5 feet longer and whose width is 2 feet shorter. Let x represent the side length of the mural in Olivia's classroom write an expression that represents the two binomials you would multiply to find the area of the hallway mural. Use that expression to find the area of the hallway mural if each side of the classroom mural is 7 feet long.
Step-by-step explanation:
The square mural in Olivia's classroom has dimensions x by x.
Then she paints a mural of dimensions: x+5 (the length) by x-2 (the width).
Thus the second mural (the hallway mural) has the shape of a rectangle with dimensions (x+5) by (x-2), so the area of the second mural is
(x+5)(x-2).
each side of the classroom mural is 7 feet means that x = 7 ft,
thus the area of the hallway mural is :
(x+5)(x-2)=(7+5)(7-2)=12*5=60 (square feet)
So the answer is 60 square feet.
Students were asked to schedule one from each category: chorus or band; French, Spanish, or German; art, wood shop, or physical education.
Answer:
Have you finished this question? I don't understand.
Step-by-step explanation:
What are the answers to these questions
The input of a function that can be controlled is the independent variable while the output is the dependent variable thus "Number of hours" and "D" are independent while the amount of muscle mass is the dependent variable.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
An input variable that we can control and manage is said to be an independent variable.
For example in function y = f(x) here we can control variable x so it will be an independent variable.
As per the given,
The number of hours we can spend so will be an independent variable.
The input D will be the independent variable.
The amount of mass muscles depends on age so it will be the dependent variable.
Hence "Number of hours" and "D" are independent while the amount of muscle mass is the dependent variable".
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-3x + 4 < 16. Esta difícil
Answer:
x>-4
Step-by-step explanation:
Ruby purchased 3 dozen eggs. She paid $10.00 fo 6 eggs. Ruby decided to resell the 3 dozen eggs for $2.00 per egg. Unfortunately 0.25 of tue egss were broken. She proceeded to sell the remaining unbroken eggs. Did she make a profit or loss?
Answer: A loss of 6 dollars
Step-by-step explanation:
Step 1 is to determine how many eggs she purchased:
3 dozen eggs * 12 eggs per dozen = 36 eggs purchased
Step 2 is to find the cost of the eggs purchased using the information you gave:
(36 eggs / 6) * 10 dollars = $60 purchase price
Step 3 is to find out how many eggs broke which is calculated like this:
36 total eggs * .25 = 9 broken eggs
Step 4 is to find how much money she made from selling the remaining eggs:
(36 total eggs - 9 broken eggs) * $2 per egg = $54 resale
Step 5 is finding the profit or loss:
$54 resale price - $60 purchase price = $ -6 (aka a 6 dollar loss)
true or false stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
It is the true statement.
Given,
In the question:
Stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
To check the above statement is true or false.
Now, According to the question:
Let's know about
Stratified random sampling:Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.
In stratified random sampling, the strata are formed based on member's shared characteristics (e.g. female or male, occupation, education) or attribute (e.g. black or white).
Hence, The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.
It is the true statement.
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Find the sum of the interior angles of the polygon
Answer:
Step-by-step explanation:We can find the sum of interior angles of any polygon using the following formula: where nis the number of sides of the polygon. For example, we use $latex n = 5$ for a pentagon. This formula works regardless of whether the polygon is regular or irregular.
The rate of change for of y = 2x + 6 is __________.
Answer:
2
Step-by-step explanation:
the rate of change is the coefficient of x
been stuck on these last 2 questions. can anybody help? thanks in advance!
The equation that passes through the point (7, -2) and (11, 5) is y = 4/7x - 9
Equation of the line:
The standard form of the equation of the line is written as
y = mx + b
here
x and y represents the coordinates of the equation
m refers the slope of the equation
b refers the y intercept of the equation
Given,
Here we have the points (7, -2) and (11, 5).
Now we have to find the equation that passes through this points.
If you want to find the equation of the line, we have to find the slope and the intercept of the line.
The slope of the line is calculated by using the given point (7, -2) and (11, 5),
=> m = (11 - 7) / ( 5 - (-2))
=> m = 4/7
Now, we have to use the slope and the point (11, 5) to find the value of y intercept of the equation,
=> 5 = (4/7) (11) + b
=> 35 = 44 + b
=> b = -9
Therefore, the equation that passes through the points is y = 4/7x - 9
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent include:
2 + x = 5
x + 1 = 4
-5 + x = -2
What is an equation?It is important to note that an equation is used to illustrate the relationship between the variables that are given.
In this case, the given equation is illustrated as:
2 + x = 5
Collect like terms
x = 5 - 2
x = 3
x + 1 = 4
Collect like terms
x = 4 - 1
x = 3
-5 + x = -2
Collect like terms
x = -2 + 5
x = 3
Therefore, the three equations illustrated are equal.
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58 rooms on 2 floors = ____ rooms per floor
Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.
It pays 2% per annum simple interest.
She puts £1500 into the account.
She does not make any deposits or withdrawals.
How much interest will the charity have received after 3 years?
Interest will the charity have received after 3 years is £60
Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.
It pays 2% per annum simple interest.
She puts £1500 into the account.
interest will the charity have received after 3 years
Interest = PRT/100
Interest = 1500 x 2 x 3/100
Interest = 60
Therefore, interest will the charity have received after 3 years is £60
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Sketch the graph of y = (x + 1)²(x + 3)
Answer:
Step-by-step explanation:
12 - f/4 = 5 please help me fast I have exam
Answer: 12-(28/4)=5
Step-by-step explanation:
12-7=5 I hope it helps :)
Jane solved an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Jane’s mistake and what is the solution to the equation?
-3(4x - 5) = 6(x + 3) + 10
-12x + 15 = 6x + 18 + 10
-12x + 15 = 6x + 18
15 = -6x + 18
-3 = -6x
1/2 = x
Jane made a mistake in her third step. The solution of the equation is x = - 13 / 18
How to solve equations correctly?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
The solve the equation to detect where Jane made the mistake in her solution.
-3(4x - 5) = 6(x + 3) + 10
open the brackets on both sides of the equation
-3(4x - 5) = 6(x + 3) + 10
- 12x + 15 = 6x + 18 + 10
- 12x + 15 = 6x + 28
subtract 6x from both sides of the equation
- 12x + 15 = 6x + 28
- 12x - 6x + 15 = 6x - 6x + 28
-18x + 15 = 28
subtract 15 from both sides of the equation
-18x + 15 = 28
-18x + 15 - 15 = 28 - 15
-18x = 13
divide both sides by - 18
x = 13 / -18
x = - 13 / 18
Therefore, jane made a mistake in her third step. She didn't add 18 and 10 together on the right side of the equation.
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Taki keeps all of her black and white photos in portfolio folders. She
was recently asked to show the photos at an upcoming exhibit. She
notices as she sorts through the photos that, in each folder, two out of
every five photos are landscapes.
1. If Taki has 70 black and white photos in one of her portfolio folders,
how many of them are landscapes?
There are 28 landscapes.
From the question, we have
In five photos = 2 landscapes.
In 70 photos = 2/5*70
=28 landscapes.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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