Answer:
The correct option is;
A dilation by a scale factor of Two-fifths and then a translation of 3 units up
Step-by-step explanation:
Given that the coordinates of the vertices of square S are
(0, 0), (5, 0), (5, -5), (0, -5)
Given that the coordinates of the vertices of square S' are
(0, 1), (0, 3), (2, 3), (2, 1)
We have;
Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)
Where;
(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices
When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;
s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5
For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)
Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2
Therefore;
The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5
The after the dilation (about the origin), the coordinates of S becomes;
(0, 0) transformed to (remains at) (0, 0) ....center of dilation
(5, 0) transformed to (5×2/5, 0) = (2, 0)
(5, -5) transformed to (2, -2)
(0, -5) transformed to (0, -2)
Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;
For (0, 0), (2, 0), (2, -2), (0, -2) we have;
(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)
(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)
For (0, 1), (0, 3), (2, 3), (2, 1) we have;
(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)
(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)
Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)
That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up
The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.
Answer:
a
Step-by-step explanation:
Which list is in order from least to greatest
The correct answer to this question is A. 9.4 x [tex]10^{-8}[/tex], 9.25 x [tex]10^{-6}[/tex], 2.5 x [tex]10^{3}[/tex], 7 x
Explanation:
These numbers are written in scientific notation. In this system, the exponent shows the number of spaces the period has been moved to make the number shorter. Additionally, a positive exponent shows the number has a certain number of digits to the right, while a negative exponent shows the number has digits to the left. In this way, the numbers presented can be converted as:
9.4 x [tex]10^{-8}[/tex] = 0.000000094 (Exponent indicates eight spaces to the left)
9.25 x [tex]10^{-6}[/tex] = 0.00000925 (Exponent indicates six spaces to the left)
2.5 x [tex]10^{3}[/tex] = 2500 (Exponent indicates three spaces to the right)
7 x [tex]10^{3}[/tex] = 7000 (Exponent indicates three spaces to the right)
Assume that a procedure yields a binomial distribution with a trial repeated n=18 times. Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of k=5 successes given the probability p=0.51 of success on a single trial.
(Report answer accurate to 4 decimal places.)
Answer:
0.0278 is the probability
Step-by-step explanation:
Okay, here we want to find the probability of 5 successes
The best way to go about this is by using the Bernoulli trial
So is p = probability of success = 0.51
Then q = probability of failure = 1-0.51 = 0.49
Mathematically, the Bernoulli approximation for k = 5 out of n = 18 is set up as follows;
P(k = 5) = nCk • p^k • q^(n-k)
P(k = 5) = 18C5 * 0.51^5 * 0.49^13
P(k = 5) = 0.027751047366 which is 0.0278 to 4 decimal places
What is the answer to 85% of 62
Answer:
52.7
Step-by-step explanation:
Of means multiply
85% * 62
.85 * 62
52.7
Turn the percentage into a decimal.
85% = 0.85
Multiply.
62 * 0.85 = 52.7
So, 52.7 is 85% of 62.
Best of Luck!
Which graph represents the solution to this system of inequalities? y 2x-4
Answer:
where's the graph??? .......
Use the Binomial Theorem to expand (3+2x)4
Answer:
(3+2x)4 = 16x4+96x3+216x2+216x+81
Step-by-step explanation:
Answer:
(3+2x)^4
(3)^4+4(3)³(2x)¹+6(3)²(2x)²+4(3)¹(2x)³+(2x)⁴
81+216x¹+216x²+96x³+16x⁴
Pls help (probability)
The table below provides the drinking and smoking habits of 1200 college students surveyed. What is the
probability that someone in this group drinks, if you already know that that
person smokes?
Answer:
315/1200 = 63/240 = 21/80 = 0.2625 = 26.25%
Step-by-step explanation:
rotate the triangle below: A(5,3) B(8,10) C(11,3) angle of rotation is 180 centre origin direction is anti- clock wise
Answer:
see explanation
Step-by-step explanation:
Under a rotation ( clockwise or anticlockwise ) about the origin of 180°
a point (x, y ) → (- y, - x ), thus
A(5, 3 ) → A'(- 3, - 5 )
B(8, 10 ) → B'(- 10, - 8 )
C(11, 3 ) → C'(- 3, - 11 )
Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?
A. Removing the outlier will not change the spread of the graph of the data set.
B. Removing the outlier will not change the variance of the data set.
C. Removing the outlier will increase the variance of the data set.
D. Removing the outlier will decrease the spread of the graph of the data set.
Answer:
D.
Step-by-step explanation:
if you remove the low value outlier, the variation from the mean will decrease therefore decreasing the varianc.
Answer:
D. Removing the outlier will decrease the spread of the graph of the data set.
Step-by-step explanation:
Outliers increase the spread of the data set.
So removing an outlier will generally decrease the spread or variance or standard deviation of a data set.
The answer is
D. Removing the outlier will decrease the spread of the graph of the data set.
Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of a
apples
Answer:
40 apples
Step-by-step explanation:
2 apples= [tex]\frac{1}{5}[/tex] grams
x apples= 4 grams
8/[tex]\frac{1}{5}[/tex] = 8 x 5/1=40
Answer:
40
Step-by-step explanation:
edu instruction correct
Michael is on page 28 of a 315-page book. He must finish the book within the next 14 days. He solved the inequality 28+ 14p = 315 He did not use the correct value as the coefficient of p and should have solved 14 + 28p <= 315
Answer:
yes you're right it is 14 + 28p = 315
Answer:
C
Step-by-step explanation:
I had this question edge 2021
Suppose that Mike invests $5000 into an account that pays 12% interest compounded
continuously. He wants to know how many years it will take for his investment to double and be worth
$10,000. Can Mike solve the following equation to find his answer? Why or why not?
2 = e 120. Solve the equation listed in the question above for t. First find the exact answer. Then
approximate your answer to three decimal places
Answer:
t = log(2)/0.12 years (exact value)
= 5.776 years (to three decimal places)
Step-by-step explanation:
The future value of an amount P at continuous interest rate i% for t years can be calculated using the continuous interest formula:
FV = Pe^((i)t)
where e is the Euler's constant = 2.7182818284....
We're given
10000 = 5000 e^((0.12)t)
simplify
2 = e^(0.12t) ........................ see below
[ please compare if this is the same as the one shown in the original question, the formula posted as "2 = e 120" does not look right, probably because of typographical difficulties, then answer if the equation given in the question can be used to solve the problem]
take (natural) log using the power property of logarithms
log(2) = 0.12t log(e)
using natural log, log(e) = 1
log(2) = 0.12t
simplify
t = log(2)/0.12 years (exact value)
To obtain the time (in years)
t = log(2)/0.12 = 0.6931/0.12 = 5.7762 years
Check using the rule of 72 (approximate)
72/12(%) = 6,
Since continuous interest accumulates interest faster, so 5.8 years sound reasonable.
help plz its math and i will give brainlest if u answer
Answer:
not a right triangle
Step-by-step explanation:
We can use the Pythagorean theorem to see if it is a right triangle
a^2 + b^2 = c^2
15^2 + 12^2 = 21^2
225 + 144 = 441
369 = 441
This is not true so it is not a right triangle
Answer:
Step-by-step explanation:
A triangle is a right angled triangle if sum of squares of two sides is equal to the square of third side.
12²+15²=144+225=369
21²=441
so a²+b²≠c²
it is not a right angled triangle.
Sandra y Roberto, cada uno de ellos con una copia del libro, deciden que ellos pueden ganar tiempo "leyendo en equipo" la novela. En este esquema, Sandra leerá desde la página 1 hasta una cierta página y Roberto leerá desde la página siguiente hasta la pagina 760. Cuando ellos hayan terminado cada uno contará la parte que leyó al otro. ¿Cuál es la última página que Sandra debería leer de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?
Answer:
La última página que Sandra deberá leer es la página 380.
Step-by-step explanation:
Sandra y Roberto tienen un libro de 760 páginas y se lo dividen, la pregunta es ¿Cuál es la última página que debería leer Sandra de tal manera que ella y Roberto pasen la misma cantidad de tiempo leyendo la novela?
Para que ambos pasen la misma cantidad de tiempo leyendo la novela, tendrían que dividirse el libro a la mitad, por lo que cada uno debería leer 760 ÷ 2 = 380 páginas.
Por lo que Sandra deberá leer de la página 1 a la 380 y Roberto leerá de la 381 a la 760.
Por lo tanto, la última página que Sandra deberá leer es la página 380.
Using the order of operations, what should be done first to evaluate 6 squared + 10 divided by (negative 5) (3) minus 5?
A.Subtract 5 from 3.
B.Divide 10 by –5.
C.Add 6 and 10.
D.Evaluate 6 squared.
Answer:
apply the BODMAS concept
brackets, off, division, multiplication, addition, subtraction
Step-by-step explanation:
(6²+10)÷(-5×3)-5
in this case the answer is D
The population of a certain type of seahorse grew by 13% from year to year.
Should the be modeled linear function or Exponential function ?
Answer: Exponential function
Step-by-step explanation:
A linear function is the form[tex]f(x)=mx+c[/tex] , where m is the constant rate of change of y with respect to x and c is the y-intercept.
An exponential growth function is in the form [tex]f(x)=A(1+r)^x[/tex], where r is the rate of growth (generally in percent) and A is initial value.
If the population of a certain type of seahorse grew by 13% from year to year, then the rate of growth is 13% .
Hence it is an exponential equation.
How would 7/2 be written as a complex number
Answer:
We could rewrite 7/2 as 7a + 2
Step-by-step explanation:
Complex numbers is when real numbers [i.e: 1, 1/2, 200, 5/7, etc..) and an imaginary numbers [numbers that give a negative result when squared] are combine together.
Please answer this in two minutes
Answer:
G = 66.0
Step-by-step explanation:
Since this is a right angle, we can use trig functions
tan theta = opp/ adj
tan G = 9/4
take the inverse tan of each side
tan ^ -1 ( tan G) = tan^-1( 9/4)
G = 66.03751103
To the nearest tenth
G = 66.0
write the expression in radical form. (88c)^2/3
Answer:
[tex]\sqrt[3]{88c^{2} }[/tex]
Step-by-step explanation:
If we have a term to a fractional power, that’s the same as finding the denominator root of the number - if the numerator of the fraction isn’t 1, then the term itself inside the root sign becomes the term to the numerator power.
So - since the denominator of this fraction is 3, we find the cube root of 88c. Since the numerator is 2, we square 88c.
[tex]\sqrt[3]{88c^{2} }[/tex].
Hope this helped! (By the way, this was my 100th answer!)
help needed! I'll mark brainiest to the right anwser thank you!
Answer:
B. Better measure of spread: the standard deviation
D. Better measure of center: the median
Step-by-step explanation:
The mean is the average of a data set.
The median value is best for measuring the center value because median measures the middle value of a set of data.
The IQR only measures the inner range of a data set.
The standard deviation is best for measuring the spread because standard deviation measures the spread of data distribution.
the probability of spinning an even number is 1/2 if you spin 600 times how many times would you predict getting an even number
Answer:
300
Step-by-step explanation:
1/2 * 600 = 300
There are 300 times would you predict getting an even number.
We have to given that,
The probability of spinning an even number is 1/2.
And, you spin 600 times.
Hence, Number of times would you predict getting an even number is,
⇒ 1/2 of 600
⇒ 1/2 × 600
⇒ 600 / 2
⇒ 300
Therefore, There are 300 times would you predict getting an even number.
Learn more about the probability visit:
https://brainly.com/question/13604758
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Consider the function f (x) = StartRoot 5 x minus 5 EndRoot + 1. Which inequality is used to find the domain?
Answer: [tex]5x-5 \ge 0[/tex]
This is the same as [tex]x-1 \ge 0[/tex]
========================================================
Explanation:
We have [tex]f(x) = \sqrt{5x-5}+1[/tex]
The stuff under the square root (this stuff is called the radicand) is what we'll focus on (the +1 at the end does not affect the domain at all). We want this to be 0 or larger. This is to avoid applying the square root to negative values, which leads to complications.
So 5x-5 must be 0 or larger meaning we write [tex]5x-5 \ge 0[/tex]
Optionally we can divide all three terms (5x, -5 and 0) by 5 to go from [tex]5x-5 \ge 0[/tex] to [tex]x-1 \ge 0[/tex]
If you wanted to solve for x, you would get [tex]x \ge 1[/tex] to set up the domain. Meaning that x = 1 is the smallest x value you can plug into the function. The x value can be anything larger than 1 as well.
Royston's car had gallons of gas at the start of the trip. During the trip, he stopped at a gas station and refueled the car with gallons. If the car consumed gallons of gas during the trip, there are still gallons of gas remaining in the tank.
Answer:
3 gallons of gas are still remaining in the tank
Step-by-step explanation:
Royston's car had 15 1/5 gallons of gas at the start of the trip. During the trip, he stopped at a gas station and he refueled the car with 5 3/5 gallons. If the car consumed 17 4/5 gallons of gas during the trip, there are still ____________ gallons of gas remaining in the tank?
Given:
Initial gallons of gas=15 1/5
Refueled gallons of gas= 5 3/5
Used gallons of gas=17 4/5=89/5
Total gallons of gas available=
Initial + Refueled
=15 1/5 + 5 3/5
=76/5 + 28/5
=76+28/5
=104/5 gallons
Equivalent to
=20 4/5 gallons
Total remaining gallons of gas= Total gallons of gas available - Total gallons of gas used
=104/5 -89/5
= 104-89/5
=15/5
=3 gallons
Answer:
3 gallons
Step-by-step explanation:
Two fair dices, X and Y , are tossed separately. Let A, B and C represent the following three events. A: You got an odd number from die X. B: You got an even number from die Y . C: The sum of two dice is an odd number. Whether A, B, C are independent
Answer:
Events A and B are independent but Event C is dependent on both Event A and Event B.
Step-by-step explanation:
Find whether events A, B and C are independent.
- Events A and B are independent of each other, because the appearance of an odd number on die X does not effect or influence the appearance of an even number on die Y.
- Event C, on the other hand, is dependent on both event A and event B. How?
For Event C to take place, one die will have to show an odd number while the other shows an even number.
NOTE: The odd number must not show up on die X and the even number show up on die Y. Both number types can appear on any die.
The key is just that one number must be odd and the other even; in order for their sum to be an odd number.
A school librarian can buy books at a 20% discount from the list price. One month she spent $72 for books. What was the list price value of the books? Is the answer $90?
Answer:
[tex]\boxed{\sf \ \ YES \ \ }[/tex]
Step-by-step explanation:
Hello
let's say that the price of the book was x
the price after a 20% discount is x - 20%*x = x*(1-20%)=x*(1-.20)=0.8*x
and this is $72 so we can write that
0.8*x=72
and then divide by 0.8 both parts
x = 72/0.8=90
So the list price value of the book is $90
and we can verify as 90 - 20%*90 = 90 - 18 = 72
Hope this helps
X²+Y²=250 and XY=117
What are the values of X and Y?
Answer:
x = -9, y = -13 or x = 13, y = 9 or x = -13, y = -9 or x = 9, y = 13Step-by-step explanation:
[tex]x^2+y^2=250\\\\x^2-2xy+y^2+2xy=250\\\\(x-y)^2=250-2xy\\\\(x-y)^2=250-2\cdot117\\\\ (x-y)^2=16\\\\x-y=4\qquad\qquad\vee\qquad \qquad x-y=-4\\\\x=4+y \qquad\qquad \vee\qquad\qquad x=-4+y\\\\(y+4)y=117\qquad\vee\qquad\quad (y-4)y=117\\\\y^2+4y-117=0\qquad\vee\qquad y^2-4y-117=0\\\\y=\dfrac{-4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\qquad\vee\qquad y=\dfrac{4\pm\sqrt{4^2-4(-117)}}{2\cdot1}\\\\y=\dfrac{-4\pm\sqrt{16+468}}{2}\qquad\ \ \vee\qquad y=\dfrac{4\pm\sqrt{16+468}}{2}[/tex]
[tex]y_1=\dfrac{-4-22}{2}\ ,\quad y_2=\dfrac{-4+22}{2}\ ,\quad y_3=\dfrac{4-22}{2}\ ,\quad y_4=\dfrac{4+22}{2}\\\\y_1=-13\ ,\qquad y_2=9\ ,\qquad\quad\qquad\ y_3=-9\ ,\qquad y_4=13\\\\x_{1,2}=4+y_{1,2}\qquad\qquad\qquad\qquad\qquad x_{3,4}=-4+y_{3,4}\\\\x_1=-9\ ,\qquad x_2=13\ ,\qquad\quad\qquad x_3=-13\ ,\qquad x_4=9[/tex]
The ratio of George's money and Tia's
money was 9 : 4. After George spent
$24 and Tia collected $11, the amounts
money they had are the same. How
much
money
did Tia have at first?
===================================================
Explanation:
G = amount of money George starts with
T = amount of money Tia starts with
Initially the ratio of their money is 9:4 so G/T = 9/4. Solve for G to get G = (9/4)T.
--------
After George spends 24 dollars he's left with (G-24) dollars. Tia gains 11 dollars so she has (T+11) dollars. They have the same amount of money after these two events occur, so G-24 = T+11.
Plug in G = (9/4)T and solve for T
G-24 = T+11
(9/4)T-24 = T+11 ... replace G with (9/4)T
4*[ (9/4)T-24 ] = 4*[ T+11 ] ... multiply both sides by 4 to clear out fraction
9T - 96 = 4T + 44 ... distribute
9T - 4T = 44 + 96
5T = 140
T = 140/5
T = 28
Tia started off with 28 dollars. We could stop here because your teacher is only asking about Tia's initial amount.
----------
If you want to find how much George started with, then plug T = 28 into G = (9/4)T to get...
G = (9/4)T
G = (9/4)*28
G = 2.25*28
G = 63
George started off with 63 dollars
The ratio of 63:28 reduces to 9:4 after dividing both parts by the GCF 7. This confirms the first fact we're given.
Notice how 63 drops to 63-24 = 39 after George spends $24. At the same time, Tia's amount increases to 28+11 = 39, which is the same as George's updated amount. Both facts match the description, so we have confirmed the answer.
Answer:
$28
Step-by-step explanation:
Boris is selling pirate hats. If he sells the hats for $50 he will sell 135 hats.
For each increase in price of $2 he will sell 3 fewer hats.
Determine the possible prices he could charge to earn $6486 or more.
Answer:
Current price $50eax135hats= $6750
Step-by-step explanation:
If he sells the hats at $52 he sells 3 less hats so $52x132=$6864
if he sells the hats at $54 he has 6 less hats= 54x129=6966 etc
$56 x 126=$7056
i need help with this equation 20 points help quick
Answer:
[tex]\boxed{y=|\frac{1}{2}x - \frac{3}{2}|+3}[/tex]
Step-by-step explanation:
The translation is a horizontal translation.
The graph is translated 1 unit to the left. So the value of x is added by 1.
[tex]f(x+1)[/tex]
[tex]y=|\frac{1}{2} (x+1)-2|+3[/tex]
[tex]y=|\frac{1}{2}x + \frac{1}{2} -2|+3[/tex]
[tex]y=|\frac{1}{2}x + - \frac{3}{2}|+3[/tex]
What is the quotient (2x^3 + 3x - 22) / (x-2)
Answer:
The quotient is 2x^2+4x+11
Step-by-step explanation:
Solve using the quadratic formula.
2x2=8x-7
Answer:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]
Step-by-step explanation:
Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)
The given equation is not written in quadratic form. To rewrite the equation:
All values need to be on the left side of the equation and set equal to zero.To overcome this difficulty, follow these mathematical steps:
[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]
Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.
Part 2: Using the quadratic formula
The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].
Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]
Substitute these values into the quadratic formula and solve for x.
[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]
Part 3: Solving for x with the values from the quadratic formula
Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.
This equation will have two zeros/roots to solve for by setting x equal to zero.
Operation 1: Addition
[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]
Operation 2: Subtraction
[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]
Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:
[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]