Answers
The possible rotation that transforms the image obtained from the reflection of the square ABCD on the line x = -1, with two vertices of the square remaining invariant is as presented as follows;
A rotation of the image of ABCD 270° counterclockwise, about the point (-2, -1) What is a rotation transformation?A rotation transformation is a transformation in which the preimage coordinate points are turned (in a circular manner) about a point.
The vertices of the square ABCD are; A(1, 4), B(3, 4), C(3, 2), D(1, 2)
The coordinates of the square following the reflection across the line x = -1 are; A'(-3, 4), B'(-5, 4), C'(-5, 2), and D'(-3, 2)
The rotation transformation of the image such that two vertices of the square are invariant (such that they remain the same) can be found as follows;
The rotation of a vertices of the image about the point (-2, -1) indicates the relative points are;
A'(-1, 5), B'(-3, 5), C'(-3, 3), and D'(-1, 3)
The image following a rotation of 270° are;
A''(5, 1), B'(5, 3), C'(3, 3), and D'(3, 1)
The above points relative to the origin are;
A''(5 + (-2), 1 - 1) = (3, 0), B''(5 - 2, -1 + 3) = (3, 2), C';(3 - 2, 3 - 1) = (1, 2), and D''(3 - 2, 1 - 1) = (1, 0)
A''(3, 0), B''(3, 2), C''(3, 4), and D''(1, 4)
The points (1, 2), and (3, 2) are therefore, the same as the points in the preimage and are therefore, invariant
The rotation is therefore;
A rotation of the image obtained from the reflection of the square, 270° counterclockwise about the point (-2, -1)Learn more on rotation transformation here: https://brainly.com/question/18392348
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Related Questions
a) Copy and complete the table below for the graph of y = 2x.
21=33 9 1 2
1-4-2 A
b) The lines y = x and y = 2x are shown on the axis below.
Write down one similarity and one difference between these lines.
f y-20 У=2
5-
4-
3-
1-
654-32-18 1 23 45 6*
1-2
--3・
-4・
-5
-6-
Answers
x y
0 0
1 2
2 4
3 6
4 8
5 10
b) One similarity between the lines y = x and y = 2x is that they both pass through the origin (0,0). This means that when x = 0, y = 0 for both lines.
One difference between the lines is their steepness or slope. The slope of y = x is 1, which means that for every 1 unit increase in x, there is a 1 unit increase in y. The slope of y = 2x is 2, which means that for every 1 unit increase in x, there is a 2 unit increase in y. This means that the line y = 2x is steeper than the line y = x.
HELP ASAP PLEASE!!!!!!!!
Answers
The inverse function of f(x) = (x + 5)² on the domain x >= -5 is given as follows:
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
The domain of the inverse function is given as follows:
x >= 0.
How to obtain the inverse function?The function for this problem is defined as follows:
f(x) = (x + 5)² on the domain x >= -5.
The range of the function is y >= 0, as the vertex is at (-5,0) and the function is increasing over it's domain, hence the domain of the inverse function, which is the range of the original function, is given as follows:
x >= 0.
To obtain the inverse function, wee exchange x and y in the definition of the function, and then isolate y, hence:
x = (y + 5)²
[tex]y + 5 = \sqrt{x}[/tex]
[tex]y = \sqrt{x} - 5[/tex]
[tex]f^{-1}(x) = \sqrt{x} - 5[/tex]
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What will be the reminder. When 362*461*2761will be divided by 6
Answers
The remainder when 362 is divided by 6 is 2 (362 ÷ 6 = 60, with a remainder of 2).
The remainder when 461 is divided by 6 is 5 (461 ÷ 6 = 76, with a remainder of 5).
The remainder when 2761 is divided by 6 is 1 (2761 ÷ 6 = 460, with a remainder of 1).
Multiplying these remainders together, we get:
2 x 5 x 1 = 10
Therefore, the remainder when 362 x 461 x 2761 is divided by 6 is 10.
Answer:
10
Step-by-step explanation:
362/6 = 60R2
461/6 = 76R5
2761/6 = 460R1
2x5x1 = 10
se the equations shown in the table below to answer the following question.
Equation A -2x -6y=36 -4r
Equation B 2(3x-3y)=36
Equation C 4r-6y+36=-2r
Which two of the three equations create a system of equations with no solution?
Explain how you determined your answer.
Respond in the space provided.
Answers
It costs $1,400 to manufacture 100 designer shoes, and $4,100 to manufacture 400 designer shoes. If x represents the number of shoes, and y is the costs,
find the cost equation
What is the cost to manufacture 150 shoes
If the product sells for $19 per item; find the Revenue Function
Determine the number of items needed to break even.
Answers
Answer:
To find the cost equation, we can use the two data points given:
(100, 1400) and (400, 4100)
We can use the point-slope form of a linear equation, where the slope is the change in cost over the change in quantity:
slope = (4100 - 1400) / (400 - 100) = 2700 / 300 = 9
Using the point-slope form with the first data point:
y - 1400 = 9(x - 100)
y - 1400 = 9x - 900
y = 9x + 500
So the cost equation is y = 9x + 500.
To find the cost to manufacture 150 shoes, we can plug in x = 150 into the cost equation:
y = 9(150) + 500 = 1850
So the cost to manufacture 150 shoes is $1850.
To find the revenue function, we multiply the number of shoes sold by the price per shoe:
Revenue = price x quantity = 19x
To determine the number of items needed to break even, we need to find the quantity where revenue equals cost. Let C(x) be the cost function and R(x) be the revenue function. The break-even point occurs when:
C(x) = R(x)
9x + 500 = 19x
500 = 10x
x = 50
So the company needs to sell 50 designer shoes to break even.
Step-by-step explanation:
Answer:
Cost equation: y = 9x + 500
It costs $1,850 to manufacture 150 shoes.
Revenue function: R(x) = 19x
The number of items that need to be sold to break even is 50.
Step-by-step explanation:
Definition of variables
x is the number of designer shoes manufactured.y is the cost (in dollars) to manufacture the designer shoes.If it costs $1,400 to manufacture 100 designer shoes:
x = 100 when y = 1400.If it costs $4,100 to manufacture 400 designer shoes:
x = 400 when y = 4100.Assuming the relationship between the number of shoes and the cost to manufacture them is linear, the slope of the equation of the line the models the relationship can be found by dividing the change in y-values by the change in x-values of the two data points:
[tex]\implies \sf Slope\;(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4100-1400}{400-100}=9[/tex]
Substitute the found slope and one of the points into the point-slope form of a linear equation to create an equation that gives the total cost to manufacture the shoes in terms of the number of shoes (x):
[tex]\implies \sf y-y_1=m(x-x_1)[/tex]
[tex]\implies \sf y-1400=9(x-100)[/tex]
[tex]\implies \sf y-1400=9x-900[/tex]
[tex]\implies \sf y=9x+500[/tex]
Therefore, the cost equation is y = 9x + 500.
To calculate the cost to manufacture 150 shoes, substitute x = 150 into the cost equation:
[tex]\begin{aligned}\implies \sf y&=\sf 9(150)+500\\&= \sf 1350+500\\&= \sf 1850\end{aligned}[/tex]
Therefore, it costs $1,850 to manufacture 150 shoes.
The revenue is the income a company generates before any expenses are subtracted. Therefore, the revenue function is simply the selling price of the item multiplied by the number of items sold.
Given the product sells for $19 per item, the revenue function is:
[tex]\implies \sf R(x)=19x[/tex]
The break even point is the point at which the total revenue equals the total cost, so there is neither profit nor loss.
To determine the number of items that should be sold to break even, equate the cost equation and the revenue function and solve for x.
[tex]\begin{aligned}\sf R(x)&=\sf y\\\implies \sf19x&=\sf 9x+500\\\sf 10x&=500\\\sf x&=50\end{aligned}[/tex]
Therefore, the number of items that need to be sold to break even is 50.
This graph shows how the time required to complete an online shopping transaction is related to the number of products being purchased.
y
x
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
0
Time (seconds)
Products being purchased
Online shopping
What is the rate of change?
Write your answer as a decimal or integer.
seconds per product
Answers
Answer:
1 product
Step-by-step explanation:
Given the equation that shows how the time required to complete an online shopping transaction is related to the number of products being purchased as;
t = 24p + 27
t represents the time required to complete the transaction
p is the product purchased
If it takes 51 seconds to complete a transaction, to get the amount of product purchased, we will substitute t = 51 into the expression and find p as shown;
51 = 24p + 27
Substract 27 from both sides
51-27 = 24p + 27 - 27
24 = 24p
24p= 24
p = 24/24
p = 1
Hence only 1 product is being purchased
Evaluate the given expression and show the steps, please.
Answers
Answer:
80
Step-by-step explanation:
The variable "n" is not defined, but rather "k" is used in the summation. Assuming that "n" was meant to be "k", the expression should be:
s4 = ∑ k=1 to 4 of 2(3^(k-1))
To evaluate this expression, we need to substitute each value of k from 1 to 4 into the expression 2(3^(k-1)), and then sum up the results.
Starting with k = 1:
2(3^(1-1)) = 2(3^0) = 2(1) = 2
Moving on to k = 2:
2(3^(2-1)) = 2(3^1) = 2(3) = 6
Next, k = 3:
2(3^(3-1)) = 2(3^2) = 2(9) = 18
Finally, k = 4:
2(3^(4-1)) = 2(3^3) = 2(27) = 54
Now we add up these four results:
s4 = 2 + 6 + 18 + 54 = 80
Therefore, the value of s4 is 80.
Philip and Laura want to build a pool in their backyard. The length and width of the pool can be represented by the equation f(x)=(x-3)(5x+2) feet. What is the area of Philip and Laura’s pool? You must show your work and include your units.
Answers
Answer:
5x^2 - 19x + 15
Step-by-step explanation:
We must multiply the pool's length and width to determine its area. We can factor the equation f(x)=(x-3)(5x+2) to determine the length and width:
f(x) = (x-3)(5x+2)
f(x) = 5x^2 - 13x - 6
One of the parameters is the pool's length (x-3), while the other is its breadth (5x+2). We multiply these two elements to determine the area:
Area is length times width (x-3)
(5x+2)
By extending this statement using FOIL (First, Outer, Inner, Last), we may make it simpler:
Area is equal to 5x^2 - 13x - 6x + 15
Area: 5x^2 - 19x + 15
The pool at Philip and Laura's home is therefore 5x^2 - 19x + 15 square feet in size. We are unable to establish the precise square footage of the pool because we were not given a specific figure for x.
Solve g−17≥17 . Graph the solution.
Answers
The inequality expression g - 17 ≥ 17 when solved has a solution of g ≥ 34
How to solve the given inequalityGiven the inequality expression
g - 17 ≥ 17
To solve the inequality g - 17 ≥ 17, we need to isolate the variable g on one side of the inequality.
We can do this by adding 17 to both sides of the inequality:
g - 17 + 17 ≥ 17 + 17
Simplifying, we get:
g ≥ 34
So the solution to the inequality is all values of g that are greater than or equal to 34.
We can graph this solution on a number line by placing a closed circle at 34 and shading to the right, to indicate that any value greater than or equal to 34 satisfies the inequality.
The graph looks like this the attached figure
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In a quadrilateral ABCD, AB is parallel to DC, and AD is parallel to BC. Find the perimeter of △COD if the diagonals of the quadrilateral intersect each other at point O and AC=40 in, BD=50 in, AB=25in.
Answers
Answer:
Step-by-step explanation:
In quadrilateral ABCD, we have:
AB is parallel to DC
AD is parallel to BC
AC = 40 in (given)
BD = 50 in (given)
AB = 25 in (given)
We can use the fact that opposite sides of a parallelogram are equal in length to find the length of CD:
CD = AB = 25 in
Next, we can use the fact that the diagonals of a quadrilateral bisect each other to find the length of AO and OC:
AO = BO = BD/2 = 50/2 = 25 in
OC = OD = AC/2 = 40/2 = 20 in
Now we can use the triangle inequality to find the perimeter of triangle COD:
CO + OD + CD > OC
CO + 20 + 25 > 20
CO + 45 > 20
CO > -25
CO + OC > CO
CO + 20 > 0
CO > -20
CO + CD > OD
CO + 25 > 20
CO > -5
Therefore, the possible range of values for CO is:
-20 < CO < -5
However, since lengths cannot be negative, we can take the absolute value of CO to get:
5 < CO < 20
So the perimeter of triangle COD is:
CO + OD + CD = CO + 20 + 25 = CO + 45
Substituting the possible range of values for CO, we get:
5 + 45 < CO + 45 < 20 + 45
50 < CO + 45 < 65
So the perimeter of triangle COD is between 50 in and 65 in.
Therefore, the perimeter of triangle COD is between 50 in and 65 in, but the exact value depends on the length of CO, which is between 5 in and 20 in.
Which shows the best estimate of the quotient of 523 +67?
O between 7 and 8
O between 8 and 9
O between 70 and 80
O between 80 and 90
Answers
Kareem is considering buying a guitar priced at $179.99 He has $200 cash with him. He uses predict whether he has enough money.
Add 10% and 1%
The current HST rate is 13%
a) Round the price of the guitar to a convenient
amount:
b) What is 10% of the rounded price
c) What is 1% of the rounded price
d) How many 1%s do you need?
e) What is the estimated tax?
f) Add the estimated tax to the rounded price.
Does Kareem have enough money with him? YES OR NO
Answers
Using the concept of percentage, we can deduce that Kareem does not have enough money with him
Does Kareem have enough money with him?To solve the questions given, we need to apply the concept of percentage on some.
a) Rounding the price of the guitar to a convenient amount, we get $180.
b) 10% of the rounded price is: 0.1 x $180 = $18.
c) 1% of the rounded price is: 0.01 x $180 = $1.80.
d) To get the estimated tax, we need to multiply the rounded price by the HST rate: 0.13 x $180 = $23.40. Dividing this by $1.80, we get approximately 13.
e) The estimated tax is $23.40.
f) Adding the estimated tax to the rounded price, we get $180 + $23.40 = $203.40.
Since Kareem has $200 cash with him, he does not have enough money to buy the guitar at the estimated price of $203.40. Therefore, the answer is NO.
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Kyoko has $10,000 that she wants to invest. Her bank has several accounts to choose from. Her goal is to have $20,000 by the time she finishes graduate school in 7 years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal assuming they compound daily? (Hint: solve the compound interest formula for the interest rate. Also, assume there are 365 days in a year)
Answers
The minimum annual interest rate for Kyoko to reach her goal, using daily compounding, is 9.903%.
How is the interest rate determined?The interest rate is computed using an online finance calculator that sets the following parameters.
The compounding period involved is 2,555 days for 7 years, based on the assumption that there are 365 days in a year.
N (# of periods) = 2555 days (7 years x 365 days)
PV (Present Value) = $10,000
PMT (Periodic Payment) = $-0
FV (Future Value) = $-20000
Results:
I/Y = 9.903% if interest compound 365 times per year (APR)
I/Y = 10.409% if interest compound once per year (APY)
I/period = 0.027% interest per period
Total Interest = $10,000.00
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julia needs to make 500 hamburgers for the a school function... hamburger patties are sold in packets of 12
how many packets of patties should she buy ?
Answers
Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:
12x = 500
x = 500/12
x = 41.67
x≅ 42
Julia needs to buy 42 packets
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At Brian’s Bookstore, 0.3 of the shelves hold mysteries, 25% of the shelves hold travel books, and 7/20 of the shelves hold children’s books. Which type of book covers the most shelf space in the store? Explain how you arrived at your answer
Answers
Answer:
Childrens books
Step-by-step explanation:
What is a fraction?A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.
To solve for which type of book covers the most space, we need to first convert 25% from a percentage to a fraction.
What is a percentage?A percentage is a ratio, or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.
If percentages are fractions of 100, then 25% as a fraction would look like this:
25% = [tex]\frac{25}{100}[/tex]We can do the same to 0.3, although it isn't a percentage.
0.3 = 0.30 = [tex]\frac{30}{100}[/tex]Now, we need to convert the fractions ([tex]\frac{25}{100}[/tex], [tex]\frac{30}{100}[/tex], [tex]\frac{7}{20}[/tex]) to have a common denominator.
What is a common denominator?A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.
To make [tex]\frac{7}{20}[/tex] have a denominator of 100, we can multiply the 20 by 5 to get 100.
7 × 5 = 4520 × 5 = 100Now the fraction is [tex]\frac{35}{100}[/tex].
The three fractions given are:
[tex]\frac{30}{100}[/tex] (Mystery books)[tex]\frac{25}{100}[/tex] (Travel books)and [tex]\frac{35}{100}[/tex] (Children books)The larges given fraction is [tex]\frac{35}{100}[/tex] meaning that the children's books cover the most shelf space in the store.
simplify 1/2-1/x-y+2/(x-y)
Answers
Answer: x^2-xy-2x^2y+2xy^2+2x+2y over 2x(x - y)
Step-by-step explanation:
because im that guy
Help please !!
The volume of a fixed amount of a gas varies directly as the temperature 7 and inversely as the pressure P. Suppose that I'-70 cm³ when 7-420 kelvin
kg
kg
and P-18-
Find the temperature when
is 60 cm and P-7
X
Answers
Answer:
First question:
We can start by setting up the formula that relates the volume V, temperature T, and pressure P:
V = k * (T/P)
where k is a constant of proportionality. We can solve for k by plugging in the given values for V, T, and P:
70 = k * (420/18)
Simplifying the right side of the equation, we get:
70 = k * 23.3333
Dividing both sides by 23.3333, we get:
k = 3
Now we can use this value of k to find the temperature T when V is 60 cm and P is 7:
60 = 3 * (T/7)
Simplifying the equation, we get:
T/7 = 20
Multiplying both sides by 7, we get:
T = 140
Therefore, the temperature when V is 60 cm and P is 7 is 140 kelvin.
Second question: We can start by using the formula that relates the time (T), distance (D), and speed (S):
D = S * T
Since the distance between the two cities is constant, we can set the distances for the two cars to be equal:
35 * 9 = 21 * T
Simplifying the right side of the equation, we get:
315 = 21T
Dividing both sides by 21, we get:
T = 15
Therefore, the trip takes 15 hours for a car moving at 21 mph.
Hopefully this helps you! I'm sorry if it wrong. If you need more help, ask me! :]
If sin 0 = -2/3which of the following are possible?
Answers
Is sin (θ) = - 2/ 3, the options that are possible include:
A) sec(θ) = -3/2 and tan(θ) = 2/√5C) cos(θ) = -(√5)/3 and tan(θ) = 2/√5How to find the possible expressions?Since sec(θ) is negative, cos(θ) is also negative (sec(θ) = 1/cos(θ)). This means θ is in the second or third quadrant, but since sin(θ) is negative, θ must be in the third quadrant. Now let's check if the given tan(θ) value is correct:
tan(θ) = sin(θ)/cos(θ)
Since we already know that cos(θ) is negative, we have cos(θ) = -(√5)/3.
Now calculate tan(θ):
tan(θ) = (-2/3) / (-(√5)/3) = 2/√5
The given values in option A are correct.
cos(θ) = -(√5)/3 and tan(θ) = 2/√5
These are the same as in option A. So, this option is also possible.
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complete the table based on the pattern you see
Answers
The figures to complete the table, based on the pattern, would be 6. 20, 7.00.
How to complete the table ?To complete the table, you need to find the common difference between the values in B which is :
= 4. 6 - 3. 8 = 5. 4 - 4. 6
= 0. 80 = 0. 80
The next two values would therefore be :
= 5. 4 + 0. 80 = 6. 20 + 0. 80
= 6. 20 = 7. 00
The complete table then is :
A - 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, 6. 20, 7. 00
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The full question is:
Complete the table based on the pattern you see:
A- 5, 6, 7, 8, 9
B- 3.8, 4.6, 5.4, ____, ____,
Find exact values for the following:
Answers
Answer:
-sqrt(2)
-sqrt(2)
1
1
Step-by-step explanation:
Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
Answers
Assuming that there are no other transactions or fees on the credit card, here's how to calculate the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made:
1.) Unpaid Balance: The unpaid balance is the amount of the credit card balance that remains after making the minimum monthly payment. In this case, the minimum monthly payment is $125, so the unpaid balance would be:
$5000 - $125 = $4875
2.) Interest Charge: The interest charge for unpaid balances is 18% per year. To calculate the monthly interest rate, divide the annual rate by 12:
18% / 12 = 1.5%
3.) To calculate the interest charge for the month, multiply the unpaid balance by the monthly interest rate:
$4875 x 1.5% = $73.13
So the new interest charge for the month is $73.13.
4.) Purchasing Power: Purchasing power refers to the amount of credit that is available on the credit card after making the minimum monthly payment and accounting for any interest charges. To calculate the purchasing power, subtract the unpaid balance and interest charge from the credit limit:
$5000 - $4875 - $73.13 = $51.87
So the purchasing power on the credit card after the minimum monthly payment is made is $51.87.
Factor completely.
9 - 25x2
Answers
Answer:
-41 is the ANS.
Step-by-step explanation:
9-25*2
9-50
-41
Quadrilateral ABCD is shown.
-5
A
3
N
6
2
5-
3-
2-
1-
10
-1-
-24
-3-
-4-
-5-
A
B
(a) Work out the coordinates of C when ABCD is
Rotated 900 clockwise about 0
then
translated by
1 2
3
D
с
4
5
[2 marks]
Answers
Answer:
C'(-5, -2)
Step-by-step explanation:
You want the coordinates of point C(4, 1) after rotation 90° CW about the origin and translation by (-6, 2).
RotationThe transformation accomplished by rotation 90° clockwise is ...
(x, y) ⇒ (y, -x)
TranslationThe translation by (-6, 2) adds those values to the coordinates:
(x, y) ⇒ (x -6, y +2)
Both transformationsCombined, the transformations give you ...
(x, y) ⇒ (y -6, -x +2)
C(4, 1) ⇒ C'(1 -6, -4 +2) = C'(-5, -2)
The coordinates of C after the transformation(s) are (-5, -2).
Consider the equation: x2 18x +72 = 0
A) First, use the "completing the square" process to write this equation in the form (x + D)² =
and enter your results below.
x² 18x+72=0 is equivalent to:
=
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a com
where necessary.
Answer(s): 6,12
Answers
Using square process method, we can get the values of x to be 12 and 6.
Define square process?The formula a (x + m)2 + n = a (x + m)2 + n is the simplest to remember while learning how to complete the square technique.
The following formulas can be used to compute m and n in this situation: m = b/2a and n = c - (b2/4a).
From the question,
x² - 18x + 72= 0
⇒ x² - 18x = -72
Complete the square by adding the half of the square of the coefficient of x to both sides of the expression as shown:
⇒ x² - 18x + (18/2) ² = -72 + (18/2) ²
⇒ x² - 18x + 9² = -72 + 81
⇒ (x-9) ² = 9
⇒ x-9 = ± 3
So, values of x are:
x = 3 + 9
= 12
x = -3 + 9
= 6
Therefore, the values of x are 12 and 6.
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Solve for x to make A||B. A B- 45 x = [?] 6x + 15
Answers
Step-by-step explanation:
45+6x+15=180
60+6x=180
6x=180-60
6x/6=120/6
X=20
The value of x from the same side interior angles in a parallel lines is x = 20
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be represented as A and B
Now , the measures of angles are
p = 45°
And , q = ( 6x + 15 )°
where p and q are same side interior angles
And , the same side interior angles add up to 180°
On simplifying , we get
45 + 6x + 15 = 180
6x + 60 = 180
Subtracting 60 on both sides , we get
6x = 120
Divide by 6 on both sides , we get
x = 20
Hence , the angles in parallel lines are solved and x = 20
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Krish used to take thirty minutes to walk to his office. Recently, he bought a new cycle. Now he takes only seven-tenths of the time he used to take to reach office. How many minutes does he save by cycling to the office?
Answers
Answer:
Krish saves 9 minutes by cycling to his office.
Step-by-step explanation:
Krish used to take 30 minutes to walk to his office. After he bought a new cycle, he takes only 7/10 of the time he used to take to reach the office. Let's call the new time he takes to reach the office "t" (in minutes).
We can set up a proportion to find the value of t:
30 / 1 = t / (7/10)
To solve for t, we can cross-multiply:
30 * 7/10 = t
21 = t
So, Krish now takes 21 minutes to reach his office by cycle.
To find how many minutes he saves by cycling, we can subtract the new time from the old time:
30 - 21 = 9
Krish saves 9 minutes by cycling to his office.
This question asks for the degree, leading coefficient, zeroes, factors, factors with multiplicity, and the final answer
Answers
Answer:
[tex]\textsf{Degree:}\quad 6[/tex]
[tex]\textsf{Leading\;coefficient:}\quad \dfrac{1}{3456}[/tex]
[tex]\textsf{Zeroes:}\quad -6, 2, 5, 8[/tex]
[tex]\textsf{Factors:}\quad (x + 6), (x - 2), (x - 5), (x - 8)[/tex]
[tex]\textsf{Factors\;with\;multiplicity:}\quad (x + 6)^3(x - 2)(x - 5)(x - 8)[/tex]
[tex]\textsf{Equation\;of\;function:}\quad f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
Step-by-step explanation:
ZeroesThe zeroes are the x-values of the points where the function crosses the x-axis, so the x-values when f(x) = 0.
Therefore, the zeroes of the given function are:
x = -6x = 2x = 5x = 8[tex]\hrulefill[/tex]
FactorsAccording to the factor theorem, if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x). Therefore, the factors of the function are the x-values that satisfy f(x) = 0.
Therefore, the factors of the given function are:
(x + 6)(x - 2)(x - 5)(x - 8)[tex]\hrulefill[/tex]
MultiplicitiesThe multiplicity of a factor is the number of times the factor appears in the factored form of the equation of the polynomial.
If the behaviour of the x-intercept is like that of a line, i.e. the curve passes directly through the intercept, its multiplicity is one.
Therefore, the factors (x - 2), (x - 5) and (x - 8) have multiplicity one.
The behaviour of the x-intercept at x = -6 is like that of a cubic function (S-shape). There, this zero has multiplicity 3: (x + 6)³.
[tex]\hrulefill[/tex]
DegreeSo far we have found the zeros, factors and their multiplicities, so we can write a factored form of the function:
[tex]\implies f(x)=a(x+6)^3(x-2)(x-5)(x-8)[/tex]
The degree of the function is the highest exponent value of the variables in the polynomial. Therefore, to find the degree of the function, simply sum the exponents of the factors:
[tex]\implies \textsf{Degree}=3 + 1 + 1 + 1 = 6[/tex]
Therefore, the degree of the function is 6.
[tex]\hrulefill[/tex]
Leading CoefficientFrom inspection of the given graph, the y-intercept is (0, -5).
Therefore, to find the leading coefficient (value of a), substitute (0, -5) into the equation and solve for a:
[tex]\begin{aligned}\implies f(0)=a(0+6)^3(0-2)(0-5)(0-8)&=-5\\a(216)(-2)(-5)(-8)&=-5\\-17280a&=-5\\a&=\dfrac{1}{3456}\end{aligned}[/tex]
Therefore, the leading coefficient of the function is 1/3456.
[tex]\hrulefill[/tex]
Equation of the functionPutting everything together, the function in factored form is:
[tex]f(x)=\dfrac{1}{3456}(x+6)^3(x-2)(x-5)(x-8)[/tex]
In standard form:
[tex]f(x)=\dfrac{1}{3456}x^6+\dfrac{1}{1152}x^5-\dfrac{1}{36}x^4-\dfrac{37}{432}x^3+\dfrac{17}{24}x^2+\dfrac{13}{8}x-5[/tex]
Image shows 2 joined rectangular prisms. One is 10 in. in length, 6 in. in height, and 3 in. in width. The second is 4 in. in length, 3 in. in width, and 6 in. in height. Which expressions can be added to find the volume of the solid figure? A. 10 × 3 and 10 × 6 B. 10 × 3 × 6 and 4 × 3 × 6 C. 10 × 4 and 3 × 6 D. 10 × 3 × 3 and 10 × 3 × 6
Answers
The correct option to determine the value of volume of solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
Explain about the rectangular prisms?One of the three-dimensional shapes that can be created with six pairs with parallel lines is a rectangular prism. Three-dimensional shapes in this category include cubes and cuboids. Prisms come in a variety of classifications based on the base.
Volume of rectangular prism = length * width * height
rectangular prism A:
length = 10 in.
Width = 3 in.
height = 6 in.
rectangular prism B:
length = 4 in.
Width = 3 in.
height = 6 in.
Thus,
volume of the solid = volume of rectangular prism A + volume of rectangular prism A
volume of the solid = 10*3*6 + 4*3*6
Thus, the correct option to determine the value of volume of the solid figure is: B. 10 × 3 × 6 and 4 × 3 × 6.
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Round the decimal number to the nearest tenth: 285.429 can you show steps?
Answers
"To round the decimal number 285.429 to the nearest tenth, we need to look at the digit in the hundredths place, which is 2.
If the digit in the hundredths place is 5 or greater, we round up the digit in the tenths place. If it is less than 5, we leave the digit in the tenths place as it is.
In this case, the digit in the hundredths place is 2, which is less than 5. Therefore, we leave the digit in the tenths place as it is, which is 2.
So, rounding 285.429 to the nearest tenth gives us:
285.4
Therefore, the rounded value of the decimal number 285.429 to the nearest tenth is 285.4." (ChatGPT, 2023)
what is 19/100,also written into decimals
Answers
19/100 into decimals is 0,19
To solve this, we must knowTo write a fraction based on 10/100/1000... you must move the decimal point to the left the number of times equivalent to the number of zeros in the base.
In this case, base 100 has two zeros. Then move two squares to the left.
[tex]\begin{array}{l}\bf 19\\\sf {0}{,}\!\overset{\overset{2}{\curvearrowleft}}{1}\!\overset{\overset{1}{\curvearrowleft}}{9}\\\\\bf \dfrac{19}{100}=0{,}19\end{array}[/tex]
Did you see how easy the conversion was under these circumstances?
If you have any question about this solution, you can ask me in the comments :)