Answers
Step-by-step explanation:
I can't draw here, but I can tell and explain to you what happens to the points (incl. N).
remember the slope of lines, and what happens when we have to create a perpendicular slope (90°) ?
x and y in the slope ratio y/x go upside down and the sign flips (that means it flips for one of them).
a rotation by 90° follows the same principles.
x and y trade places, and for one of them the sign flips.
the only "difficult" trick is to determine, if the sign of x or of y flips.
let's look at N first.
N = (-5, -4)
the rotation counterclockwise takes it over into the 4th (bottom right) quadrant, where x values are positive.
aha, so the sign of x flips after x and y trade places, and we get
N' = (4, -5)
now for the other points
X = (-3, -2)
the same principle as for N
X' = (2, -3)
B = (-4, 1)
this is now moving from the 2nd (where y values are positive) to the 3rd quadrant (where x and y are negative).
so, again the sign of x flips after x and y trade places
B' = (-1, -4)
with the new coordinates of the points you can now easily draw the new triangle'.
Related Questions
can someone help me find the answer to this??
Answers
The correlation coefficient (r) is 0.9168.
The correlation coefficient can be improved by ignoring the bill for the month of July.
What is the correlation coefficient of the data set?The correlation coefficient for the plotted regression data should be around 0.9168 using the estimated data point taken from the attached graph. This indicates that there is a strong positive correlation between the electricity bill ($) and the amount of time spent at home because the obtained correlation coefficient is very close to 1.How close the R-value is to either -1 or 1 serves as a gauge of the strength of a relationship using the correlation coefficient.The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.
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2(3) 3 as an exponent + 5
Answers
Answer: 13
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
Answers
Answer:
W = 11/8 or 1 3/8
Step-by-step explanation:
The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?
W=(1/4)(L)
width is 1/4 length
if the length is 5 1/2 ft
5 1/2 is equivalent to 11/2
W= (1/4)(11/2)
Multiply across.
W = 11/8 or 1 3/8
8x = 2
Write down the value of x.
(It’s not 2/8 or 0.25)
Answers
Answer:
1/4
Step-by-step explanation:
Get x by itself by dividing both sides by 8
x = 2/8
Reduce
1/4
Answer:
8x=2
/8 /8
Step-by-step explanation:
it is 0.25
8x=2
/8 /8
x=0.25
In the first quadrant, you start at (6, 3)
and move 2 units left
What point will you end up on?
Answers
Answer: the answer is (6,1)
Step-by-step explanation:
Answer:
(4, 3)
Step-by-step explanation:
If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.
A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)
Please help me calculate the value of y with steps
Answers
The value of y in the triangle is 7.5
How to calculate the value of y?The given parameter is the triangle
On the triangle, we have the following equivalent ratio
y : 8 = y + 15 : 20
Express as fraction
y/8 = y + 15/20
Cross multiply
20y = 8y + 90
Collect the like terms
20y - 8y = 90
Evaluate
12y = 90
Divide by 12
y = 7.5
Hence, the value of y in the triangle is 7.5
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$74.95 ladder; 6.5% tax
Answers
Answer:
11.5307692308
Step-by-step explanation:
Answer:
Around $79.88
Jeremiah uses 15 pages out of an exercise book containing 75 pages. What fraction of the exercise book has been used?
Answers
Find the slope of the line that goes through the points (–4, 1) and (8, –5).
Answers
Answer:
[tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
Slope is the change in y over the change in x.
The ordered pair is in the form (x,y). The first number is the x value and the second number is the y value.
for y;
-5 - 1 = -6
for x:
8 - (-4)
8 + 4
12
[tex]\frac{-6}{12}[/tex] Which is the same as [tex]\frac{-1}{2}[/tex] if we divide the top and bottom by 6
-6/12
-1/2
The department store sells logo t-shirts at an original price of $12.50. Every month that a t-shirt doesn’t sell, the store reduces the price by 25%. Brianna calculated the price after two reductions:
12 dollars and 50 cents minus (12 dollars and 50 cents) (0.25) minus (12 dollars and 50 cents) (0.25) = 6 dollars and 25 cents
What is Brianna’s error?
Answers
Answer:
On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.
Step-by-step explanation:
What is each expression written as a single natural logarithm?
(c) 3 ln x+2 ln y+ln 5
Answers
According to the question, to write the solution for the logarithmic function, the concept of indices is also needed.
Therefore, the given expression is [tex]3 ln x+2 ln y = ln5[/tex]
The values get multiplied in addition. Therefore, the above expression can be written as: [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Expression = [tex]ln(x^{3} )+ln(y^{2} )+ln5[/tex]
Using logarithmic definition, we can write:
[tex]ln(x^{3} )+ln(y^{2} )+ln5\\ln(5x^{3} y^{2} )[/tex]
The solution for the given expression is [tex]ln(5x^{3}y^{2} )[/tex]
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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SOLVE FOR BRAINLIEST
Answers
The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse function?The function f(x) is given as
f(x) = x^2 - x - 2
Start by expressing the above function in vertex form
Using a graphing calculator, we have
f(x) = (x - 0.5)^2 - 2.25
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 0.5)^2 - 2.25
The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25
The equation becomes
x = (y - 0.5)^2 - 2.25
Add 2.25 to both sides
So, we have
(y - 0.5)^2 = x + 2.25
Take the square root of both sides
y - 0.5 = √x + 2.25
Add 0.5 to both sides
So, we have
y = 0.5 + √x + 2.25
Express as an inverse function
f'1(x) = 0.5 + √x + 2.25
Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) = 0.5 + √x + 2.25
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Which of the following vertices would minimize the objective function N = 7x + 2y?
A. (4,0)
B. (6,3)
C. (3,9)
D. (0,12)
Answers
Check the picture below.
Which relation is a function?
Answers
Using the vertical line test, we conclude that the relation that is a function is the bottom right one.
Which of the graphed relations is a function?
A relation is a function only if all the inputs are mapped into a single output.
If we have the graph of a relation, it only will be a function if it passes the vertical line test.
This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.
With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.
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The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55.
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.
Work out the cost of
a) 1 kg of turnips.
b) 1 kg of mushrooms.
Answers
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.
Let x represent the cost of on kg of mushroom and y represent the cost of one kg of turnips.
The cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55. Hence:
2x + 2.5y = 8.55 (1)
The cost of 3 kg of mushrooms and 4 kg of turnips is £13.10. Hence:
3x + 4y = 13.10 (2)
From both equations:
x = 2.9, y = 1.1
The cost of one kg of mushroom is $2.90 while the cost of 1 kg of turnips is $1.10
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An urn contains 5 tiles, each containing one of the numbers from 1 to 5. An experiment consists of selecting a tile, marking down its number, then replacing it and selecting a second tile and marking down its number. How many outcomes are in the sample space for this experiment?.
Answers
Answer:
wait first of all where did they put grandma?
The number of bags of mulch you need to cover a planting area varies jointly with the area to be mulched a in square feet and the depth of the mulch d in feet. If you need 10 bags to mulch 120ft² to a depth of 3in., how many bags do you need to mulch 200ft² to a depth of 4in ?
Answers
To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
What do we mean by depth?The depth of an object is defined as the distance between its nearest and farthest ends in mathematics. The vertical magnitude of an object is measured by its height. Depth is also a measure of an object's vertical magnitude. These two terms appear to represent the same quantity.So,
When z "varies jointly" with x and y, the following formula can be used to describe it:
z = kxy
Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.
The information provided allows us to calculate the value of k.
n = kad10 = k·(120)(1/4)10/30 = k = 1/3 (divide by the k coefficient)Now we can fill in the blanks with the other values of interest.
n = (1/3)·(200)·(1/3) = 200/9n = 22(2/9)Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.
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Iggy bought the refrigerator on a payment plan.He paid $150 when he bought it and he agreed to pay $28.50 each month for the next 24 months.
Answers
Answer:834$
Step-by-step:150+28.24=834$
if a one time deposit of $1000 in invested at age 25 with 12% annual interest rate, how much will be in the account at age 65 (40 years later)?
Answers
The amount in the account after 40 years will be $5800.
How to illustrate the information?It should be noted that the interest is calculated as:
= (Principal × Rate × Time) / 100
= ($1000 × 12 × 40) / 100
= $480000 / 100
= $4800
Therefore, the amount in the account after 40 years will be:
= Principal + Interest
= $1000 + $4800
= $5800
Therefore, the amount in the account after 40 years will be $5800.
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Question 10: Neil writes down four numbers with a sum of 50.
All the numbers have two decimal places and no two numbers are the same.
Write down four possible numbers Neil could have written down.
Answers
Answer:
15-10-11-14
Step-by-step explanation:
15+10= 25
25+11= 36
36+14= 50
Can someone help me on this question and explain the process?
Answers
Let's call the entire angle between the 10 and 5 sides to be x
Applying to cosine rule:
[tex]9 {}^{2} = 10 {}^{2} + 5 {}^{2} - 2(10)(5)cos(x) \\ 81 = 100 + 25 - 100cos(x) \\ 100cos(x) = 125 - 81 \\ cos(x) = \frac{44}{100} = 0.44 \\ x = arccos(0.44)\approx63.9[/tex]
We can conclude that the angle inside the small triangle is half of x, which i will denote by y
[tex]y = \frac{x}{2} = \frac{63.9}{2} = 31.95[/tex]
Similarly to find the angle which i will denote by z at the right lower corner of the small or large triangle, apply the cosine law again:
[tex]10{}^{2} = 5 {}^{2} + 9 {}^{2} - 2(9)(5)cos(z) \\ 100 = 25 + 81 - 90cos(z) \\ 90cos(z) = 106 - 100\\ cos(z) = \frac{6}{90} = 0.06666 \\ z = arccos(0.06666)\approx86.2[/tex]
The last angle in our small triangle which i will denote by w, will be 180 minus z and y
[tex]w = 180 - (y + z) \\ w = 180 - (31.95 + 86.2) \\ w = 61.85[/tex]
Let t be our missing side,
applying the law of sines:
[tex] \frac{5}{sin(w)} = \frac{t}{sin(y)} \\ t = \frac{5sin(y)}{sin(w)} = \frac{5sin(31.95)}{sin(86.2)} [/tex]
[tex]t \approx2.652[/tex]
Fiona is heating water for a science experiment the temperature of the water increases 4/5 of a degree every 2/5 of a minute how much is the temperature of the water increasing per minute.
Answer needed ASAP
thanks
Answers
The temperature that water is increasing per minute is 2 degrees.
What is the increase in temperature per minute?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.
The first step is to determine what 2/5 of a minute is equivalent to in seconds.
1 minute = 60 seconds
2/5 x 60 = 24 seconds
The formula that can be used to determine the temperature that water is increasing per minute is :
Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute
(4/5 x 60) / 24 = 2 degrees
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The population of a certain animal species decreases at a rate of 3.5% per year. You have counted 80 of the animals in the habitat you are studying.
a. Write a function that models the change in the animal population.
Answers
The function that models the change in the animal population is
[tex]F(x) = x ( 1+ r)^{t}[/tex]
According to the question we have been given that
population decreases = 3.5% per year
Number of animals counted = 80
The formula to be used is
[tex]F(x) = x (1 + r)^{t}[/tex] (1)
where, F(x) = amount of animals counted after t years
x = initial amount of animals
r = decrease or increase rate of animal species.
t = time
Now according to the question,
r = -0.035
x = 80
Putting the required values in equation (1) we get
[tex]F(x) = 80 (1 - 0.035)^{t}\\ F(x) = 80 (0.965)^{t}[/tex]
Thus above is the required function that models the change in the animal population.
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Multiply and simplify. √8 x² . √2 x²
Answers
The simplest form of the expression is 4 x² .
Expressions in science are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by degree operator in between.Simplifying expressions mean editing an analogous math expression with no like terms and through a compact manner.To change expressions, we tend to tend to combine all kind terms and solve all the given brackets, if any, and then inside the simplified expression, we tend to are about to be alone left with not like terms that cannot be reduced any.We have given an expression √8 x² . √2 x² . .....(1)
On multiplying , we get
√8 x² . √2 x² = √16 x⁴
On simplifying , we get
√16 x⁴ = √ 4 × 4 × x² × x²
= 4 x²
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A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $66. A season ski pass costs $400. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes?
Answers
igcse math (quadratic functions)
given the equation: x^2 + 5x - 14
use the discriminant to decide if there are two real and different roots, two equal roots or no real roots
Answers
Answer:
2 real different roots
Step-by-step explanation:
Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:
[tex]\displaystyle{D = b^2-4ac}[/tex]
The formula is derived from a quadratic formula which is:
[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]
The expression inside the square root is discriminant. The discriminant says that:
There are 2 real different roots if the discriminant (D) is greater than 0. (D > 0)There is 2 real double roots (same roots) if the discriminant (D) is equal to 0. (D = 0)There are no real roots (imaginary or complex roots) if the discriminant (D) is less than 0. (D < 0)From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:
a = 1b = 5c = -14Therefore, substitute the coefficients’ values in the discriminant:
[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]
Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.
What is the value of (−12)4?
Answers
Answer:
-48
Step-by-step explanation:
[tex](-12)4\\(-12) \times 4\\= -48[/tex]
Answer: -48
Step-by-step explanation:
negative x negative x negative x negative = negative
12 x 4 = 48
remember the answer needs to be a negative
(-12)4 = -48
what is the domain and the range of the following relation? show work
{(2,-5) , (4,31), (11,-11), (-21,3)}
Answers
The domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}
What is the domain and the range of a function?The domain and the range of a function are the set of input values and output values of the graph
How to determine th domain and range of the function?We have the following ordered pairs of the function
(x, y) = {(2,-5) , (4,31), (11,-11), (-21,3)}
Remove the y values to determine the domain
x = {2, 4, 11, -21}
Remove the x values to determine the range
y = {-5, 31,-11,3}
Hence, the domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}
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Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (h⁰g)(0)
Answers
The value of the expression ( h o g)(0) is 5.
When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.
Consider the two functions,
g(x) = 5x - 2 and h(x) = x² + 1
So,
( h o g)(x) = h(g(x))
( h o g)(x) = ( 5x - 2 )² + 1
( h o g)(x) = 25x² - 20x + 4 + 1
( h o g)(x) = 25x² - 20x + 5
( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1
( h o g)(0) = 0 - 0 + 4 + 1
( h o g)(0) = 5
The value of the expression ( h o g)(0) is 5.
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I need this word problem translated into a inequality expression
One-fourth multiplied by sum of t and 9 is at most 9
Answers
Answer:
[tex]\frac{1}{4}[/tex] (t + 9) ≤ 9
Step-by-step explanation:
One-fourth multiplied by sum of t and 9 is at most 9
One-fourth [tex]\frac{1}{4}[/tex]
sum of t and 9 = t + 9
at most 9 = ≤ 9