1 cm : 25000 cm
Convert 25000cm to km = 1cm : 0.25 km9cm = 9 x 0.25 km9cm = 2.25 kmOn a map with a scale of 1:25,000, 9 cm represents 225,000 km on the ground.
Explanation:To find how many kilometers on the ground is represented by 9 cm on the map, we can use the scale given. The scale is 1:25,000, which means that 1 cm on the map represents 25,000 cm on the ground. Since we want to find the number of kilometers, we need to convert the units. 1 km is equal to 100,000 cm. So we can set up the proportion: 1 cm (on the map) / 25,000 cm (on the ground) = 9 cm (on the map) / x km (on the ground). Cross multiplying, we get 1 * x km = 25,000 * 9 cm. Solving for x, we find that x = 225,000 km.
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Please help me out. :)
Answer:
x = 13.
Step-by-step explanation:
Because it is an isosceles trapezoid the 2 marked angles are equal, so
5x + 15 = 7x - 11
15 + 11 = 7x - 5x
2x = 26
x = 13.
Subtract. Write your answer as a mixed number in simplest form. 5 5 over 11 - 1 3 over11
[tex] \frac{55}{11} - \frac{13}{11} = \frac{42}{11} \: or \:3 \frac{9}{11} [/tex]
A norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. what is the area of the largest possible norman window with a perimeter of 25 feet
Answer:
43.75 ft²
Step-by-step explanation:
Let r = the radius of the semicircle
and h = the height of the rectangle
Then 2r = the width of the window
The formula for the perimeter of a circle is C = 2πr,
so, πr = the perimeter of the semicircle
The perimeter of the window is
P = πr + 2h + 2r = 25
2h + (π +2)r = 25
h = ½[25 - (π + 2)r]
(1) h = 12.5 - (π/2 +1)r
The formula for the area of a circle is A= πr², so
½πr² = the perimeter of the semicircle
The area of the window is
(2) A = ½πr² + 2rh
Substitute (1) into (2).
A = ½πr² + 2r[12.5 - (π/2 +1)r] = ½πr² + 25r - (π +2)r²
A = 25r - (π + 2 - π/2)r²
(3) A = -(π/2 + 2)r² + 25r
This is the equation for a downward opening parabola.
One way to find the vertex is to set the first derivative equal to zero.
dA/dr = -2(π/2 + 2)r + 25 = 0
-(π + 4)r + 25 = 0
-(π + 4)r = -25
r = 25/(π + 4)
(4) r ≈ 3.50 ft
The maximum area occurs when r = 3.50 ft.
Substitute (4) into (1).
h = 12.5 - (π/2 +1)(3.50) = 12.5 - (2.571× 3.50) = 12.5 - 9.00 = 3.50
(4) h = 3.50 ft
Substitute (4) into (2)
A = 1.571(3.50)² + 2×3.50×3.50 = 19.25 + 24.50
A = 43.75 ft²
The area of the largest possible Norman window with a perimeter of 25 ft is 43.75 ft².
The maximum area of a Norman window with a given perimeter of 25 feet can be found by creating an equation for the area, taking its derivative, setting it equal to zero and solving for the window's dimensions. This involves calculus, namely the method for optimization problems.
Explanation:The problem involves maximizing the area of a Norman window given a certain perimeter. The Norman window is composed of a rectangle and a semicircle, where the diameter of the semicircle equals the width of the rectangle. First, let's denote the width of the rectangle or the diameter of the semicircle as x. The radius of the semicircle will then be x/2. The height of the rectangle can be represented as 25 - x (since the perimeter of the window should equal 25 feet).
The area of a rectangle is height multiplied by width. The area of a semicircle is (1/2)πr2. So to find the area A of the Norman window, we add the area of the rectangle and the semicircle: A = x(25-x) + (1/2)π*(x/2)2.
To find the maximum area, we need to take the derivative of A with respect to x, set it equal to zero, and solve for x. We find x approximates to around 7.64 feet (after using calculus concepts). Then substitute x = 7.64 into the area function A and solve for A, which gives us the maximum area of the Norman window.
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One number is 5 less than a second number.twice the second number is 4 less than 4 times the first.find the two numbers
Answer:
9 and 14
Step-by-step explanation:
One number is 5 less than a second number.
a = b - 5
:
Twice the second number is 8 less than 4 times the first.
2b = 4a - 8
replace a with (b-5)
2b = 4(b-5) - 8
2b = 4b - 20 - 8
2b - 4b = -28
-2b = -28
b = 14
then
a = 9
The equation is solved and the two numbers are x = 7 and y = 12
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let's call the first number "x" and the second number "y"
x = y - 5 (the first number is 5 less than the second number)
2y = 4x - 4 (twice the second number is 4 less than 4 times the first)
We can use substitution to solve for one of the variables.
Substituting the first equation into the second equation, we get:
2y = 4 (y - 5) - 4
Simplifying this equation , we get
2y = 4y - 24
2y - 4y = -24
-2y = -24
y = 12
Now that we know that the second number is 12, we can use the first equation to find the first number:
x = y - 5
x = 12 - 5
x = 7
Hence , the two numbers are 7 and 12
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The base of a lampshade is in the shape of a circle and has a diameter of 13 inches. What is the circumference, to the nearest tenth of an inch, of the lampshade? (Use 3.14 for π.)
Question 3 options:
13.3 inches
20.4 inches
26.0 inches
40.8 inches
The circumference is found by multiplying the diameter by PI.
Circumference = 13 inches x 3.14 = 40.82
Rounded to the nearest tenth = 40.8 inches.
Answer:13.3
Step-by-step explanation:
(a) What is the difference between a sequence and a series? A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers. A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. (b) What is a convergent series? What is a divergent series? A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent. A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent. A series is divergent if the sequence of partial sums is a convergent sequence. A series is convergent if it is not divergent. A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.
Answer:
See below.
Step-by-step explanation:
(a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.
(b) A series is convergent if the sequence of partial sums is a convergent sequence (that is tends to a limit). A series is divergent if it is not convergent.
Answer:
(a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. (b) A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.Step-by-step explanation:
A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. In contrast, a series is the sum of the numbers in a sequence. For this multiple choice, choose the best answer that defines what a sequence is.
(a) What is the difference between a sequence and a series?
A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers. A sequence is an ordered list of numbers whereas a series is an unordered list of numbers. A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers.When working with sequences and series, we look at what happens at negative and positive infinity. When a series converges, it approaches a finite number. When a series diverges, it does not approach a finite number but infinity.
(b) What is a convergent series? What is a divergent series?
A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent. A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent. A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent. A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.5 apples cost ?1.45. 3 apples and 2 bananas cost ?1.13. What is the cost of 1 banana
1.45÷5=0.29
0.29×3=0.87
1.13-0.87=0.26
0.26÷2=0.13
One banana costs 0.13
Final answer:
By setting up two equations based on the cost of apples and the combined cost of apples and bananas, we can calculate that the cost of one banana is \'0.13.
Explanation:
To solve the question about the cost of one banana, we need to set up two equations based on the given information. Let's denote the cost of one apple as 'A' and the cost of one banana as 'B'.
We are given that 5 apples cost \'1.45, which can be written as an equation: 5A = 1.45. We are also given that 3 apples and 2 bananas cost \'1.13, which can be expressed as the equation 3A + 2B = 1.13. By solving these two equations simultaneously, we can find the value of 'B', the cost of one banana.
First, we solve the first equation for A: A = 1.45/5. We get A = 0.29. Now, we substitute this value into the second equation: 3(0.29) + 2B = 1.13. This simplifies to: 0.87 + 2B = 1.13. Solving for B, we get: 2B = 1.13 - 0.87, hence B = (1.13 - 0.87)/2. After performing the subtraction and division, we find that B = 0.13.
Therefore, the cost of one banana is \'0.13.
Santos walks 2 kilometers south and then a certain number of kilometers east. He ends 5 kilometers away from his starting position.How many kilometers east did Santos walk?
Answer:
4.6 Or 4.60
Step-by-step explanation:
Like the other person said, 4.56. The question says "round to the nearest tenth" so 4.56 rounds to 4.60
Hope it helps~
To determine how many kilometers east Santos walked, we can use the Pythagorean theorem to find the distance traveled for each leg of the journey.
Explanation:To determine how many kilometers east Santos walked, we need to use the Pythagorean theorem to find the distance traveled for each leg of the journey. Since he ends up 5 kilometers away from his starting position, we can form a right triangle with the hypotenuse representing the total distance walked.
Let's assume Santos walked x kilometers east. The other leg of the triangle represents the 2 kilometers south he walked. Using the Pythagorean theorem, we have x2 + 22 = 52.
This simplifies to x2 + 4 = 25. Subtracting 4 from both sides gives us x2 = 21. Taking the square root of both sides, we find that x ≈ 4.58. Therefore, Santos walked approximately 4.58 kilometers east.
help please 100 points
2 time legal assistant = 900,000 x 2 = 1,800,000
school teacher = 1,850,000
Difference = 1,850,000 - 1,800,000 = $50,000
Master degree for 26 weeks = 1326 x 26 = 34,476
Associates degree for 42 weeks: 792 x 42 = 33,264
Difference = 34,476 - 33,264 = $1,212
For 20 years she earned: $900,000
Twice that would be $1,800,000
So for 30 years the schoolteacher earns the same amount.
Answer:
The difference between the school teacher and the legal assistant is $50,000. The school teacher earns about twice as much in thirty years. The next answer is $1,212.
Step-by-step explanation:
The legal assistant makes $1,800,000 in 40 year. The school teacher in 30 years makes 1,850,000. 1,850,000 - 1,800,000= $50,000.
A person with the masters degree mages $34,476 in 26 weeks.The person with the Associates degree make $33,264 in 42 weeks.
Describe the translation (Picture provided)
Answer:
D
Step-by-step explanation:
We would need to understand 2 rules of translation in order to figure this out.
1. The graph of f(-x) is the graph of f(x) reflect about the y-axis
2. The graph of f(x+a) is the graph of f(x) shifted horizontally a units LEFT and the graph of f(x-a) is the graph of f(x) shifted horizontally a units RIGHT
We are comparing [tex]ln(5-x)[/tex] with the parent graph of [tex]lnx[/tex]. Firstly, there is -x in place of x, this means the graph is reflected about y-axis. Next, there is +5 added with -x, so it means the graph is shifted horizontally 5 units to the LEFT
Looking at the answer choices, D is the correct answer.
Answer:
Option d
Step-by-step explanation:
Let f(x) be a logarithmic function of the form [tex]f(x) = log(x)[/tex]. So:
[tex]y = f(-x)[/tex] represents a reflection of f(x) on the y axis.
[tex]y = f(-x) = log(-x)[/tex]
Then:
[tex]y = f(x + 5)[/tex] represents a displacement of [tex]f(x)[/tex] 5 units to the left.
[tex]y = f(x + 5) = log(x + 5)[/tex]
Therefore, the operation:
[tex]y = f(-x + 5) = log(5-x)[/tex]
Represents a reflection on the y axis and a translation of 5 units to the left
Shelly has a ribbon that is 52 feet long.She wants to cut the ribbon into 8 pieces of equal length.How long should each piece of ribbon be?
Answer:
52/8 = 6.5 feet
A fence in feet is 7 feet 6 inches high 1 foot = 12 inches what is the height of the fence in centimeters?
Answer:
228.6 cm
Step-by-step explanation:
Noah borrows $2000 from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money. The relationship between the amount of money, A, in dollars that Noah owes his father (including interest), and the elapsed time, t, in years, is modeled by the following equation. A=2000e^{0.1t}. How long did it take Noah to pay off his loan if the amount he paid to his father was equal to $2450? Give an exact answer expressed as a natural logarithm.
Answer:
ln(1.225)/0.1
Step-by-step explanation:
The credit all goes to @lucic , but the answer is expressed as a natural log
Uncle Percy and the ratiolas are donating 75% of $84 where does the $84 fit in to proportion
Answer:
The answer in the procedure
Step-by-step explanation:
Let
x-----> amount corresponding to 75%
we know that
using proportion
[tex]\frac{100}{84}\frac{\%}{\$} =\frac{75}{x} \frac{\%}{\$}\\ \\ x=84*75/100\\ \\ x=\$63[/tex]
Brenda earns $1,700 per month after taxes. She is working on her budget and has the first three categories finished.
Housing $612
Food $238
Transportation $370
What is the problem with this budget?
A.
She is budgeting more than the highest recommended for transportation.
B.
She has used the highest recommended percentages for the three categories.
C.
She has allotted more than 36% of her income for housing.
D.
She is budgeting too little for transport
Answer:
B
Step-by-step explanation:
Answer with explanation:
We will use [tex]\frac{28}{36}[/tex], rule here,which states that , 28% of your gross income should be used for housing finances and 36% of your income , should be used for debt purposes.
Total monthly income of Brenda = $ 1700
→28% of 1700
[tex]=\frac{28}{100}\times 1700\\\\=28 \times 17\\\\=476[/tex]
⇒Total Housing finances, which includes , housing, food and transportation = $ 476
→Option C:
She has allotted more than 36% of her income for housing.
A package shipment company recorded the number of packages received at each of two businesses, Aquarium World and Rare Vinyl. The line plots show the number of packages received at each business every day over 2 weeks.
What statement about the two plots’ distributions is true?
(A) The degree of overlap between the two distributions is moderate.
(B) There is no overlap between the two distributions.
(C) The degree of overlap between the two distributions is low.
(D) The degree of overlap between the two distributions is high.
Answer:B:There is no overlap between the two distributions hope this helps
Answer: There is no overlap between the two distributions
Choose the best definitions of parameter and statistic. A statistic is a variable that describes a sample and a parameter is a variable that describes a population. A parameter is an unknown characteristic of a group and a statistic is a known characteristic of a group. A statistic is a number that describes a population and a parameter is a number that describes a sample. A statistic is a number that describes a sample and a parameter is a number that describes a population. A parameter is a number that describes a population. A statistic is a number that is used to estimate a parameter.
Answer:
A statistic is a number that describes a sample and a parameter is a number that describes a population.
Step-by-step explanation:
The definition of "statistic" is:
A piece of data from a portion of a population.
The definition of "parameter" is:
A value that tells you something about a population.
Using these definitions, the correct answer to the question is that a statistic is a number that describes a sample and a parameter is a number that describes a population.
The correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.
What are parameters and statistics?A parameter is a number that describes the entire population (for example, the population mean).
What is a statistic?A statistic is a number that describes a sample (e.g., sample mean).
A few examples of statistics are:
The percentage of 2000 people who support the death penalty, as determined by a random sample.The median salary of 850 Boston and Wellesley college students.Weights of avocados from a single farm's standard deviation.Average screen time of 3000 Indian high school pupils.Hence, the correct option is A statistic is a number that describes a sample and a parameter is a number that describes a population.
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Use the x-intercept method to find all real solutions of the equation.
x^2-9x^2+23x+15=0
Answer:
b.[tex]x=1,3,\:or\:5[/tex]
Step-by-step explanation:
The given equation is;
[tex]x^3-9x^2+23x-15=0[/tex]
To solve by the x-intercept method we need to graph the corresponding function using a graphing tool.
The corresponding function is
[tex]f(x)=x^3-9x^2+23x-15[/tex]
The solution to [tex]f(x)=x^3-9x^2+23x-15=0[/tex] is where the graph touches the x-axis.
We can see from the graph that; the x-intercepts are;
(1,0),(3,0) and (5,0).
Therefore the real solutions are:
[tex]x=1,3,\:or\:5[/tex]
evaluate tangent ^-1 1
Answer:
45° or π/4 radians
Step-by-step explanation:
You want the angle whose tangent is 1.
ArctangentYour calculator can evaluate the inverse tangent function for you.
arctan(1) = 45° = π/4 radians
In a museum there is a sculpture in the shape of a cylinder the cylinder has a diameter of 12 feet and a height of h feet which equation can be used to find v the volume of the cylinder in cubic feet
Answer:
[tex]V=36 \pi h\ ft^{3}[/tex]
Step-by-step explanation:
we know that
The volume of a cylinder (sculpture) is equal to
[tex]V=\pi r^{2}H[/tex]
In this problem we have
[tex]r=12/2=6\ ft[/tex] ----> the radius is half the diameter
[tex]H=h\ ft[/tex]
substitute the values
[tex]V=\pi (6^{2})(h)=36 \pi h\ ft^{3}[/tex]
Answer:
36πh cubic feet
Step-by-step explanation:
To find the volume of a cylinder with a diameter of 12 feet and a height of h feet, we must know the formula for finding the volume of a cylinder.
The volume V of a cylinder with a radius r and a height h is given as
V = πR^2h
where π = 22/7
Given that the radius of the given cylinder is 12 feet, the radius r
= 12/2 feet
= 6 feet
The volume v
= π * 6^2 * h
= 36πh cubic feet
12 points! Pls help.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the circle equations in general form with their corresponding equations in standard form.
Answer:
1) x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
2) x² + y² + 6x - 8y - 10 = 0 ⇒ No choice
3) 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
4) 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ No choice
5) 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
6) x² + y² + 2x - 6y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
Step-by-step explanation:
- The general form of the equation of the circle is:
* x² + y² + Dx + Ey + F = 0
where D , E and F are constant
- The standard form of the equation of the circle is:
* (x - h)² + (y - k)² = r²
where (h , k) is the center of the circle, r is the radius of it
- To chose the circle equations in general form with their
corresponding equations in standard form lets do that
1) x² + y² - 4x + 12y - 20 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-4)/2(1) = 2
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(12)/2(1) = -6
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (2)² + (-6)² - (-20) = 4 + 36 + 20 = 60
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 2)² + (y + 6)² = 60 ⇒ x² + y² - 4x + 12y - 20 = 0
2) x² + y² + 6x - 8y - 10 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(6)/2(1) = -3
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-8)/2(1) = 4
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-3)² + (4)² - (-10) = 9 + 16 + 10 = 35
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 3)² + (y - 4)² = 35 ⇒ there is no choice
3) 3x² + 3y² + 12x + 18y - 15 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(12)/2(3) = -2
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(18)/2(3) = -3
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-2)² + (-3)² - (-15/3) = 4 + 9 + 5 = 18
- We divide F by 3 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 2)² + (y + 3)² = 18 ⇒ 3x² + 3y² + 12x + 18y - 15 = 0
4) 5x² + 5y² - 10x + 20y - 30 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-10)/2(5) = 1
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(20)/2(5) = -2
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (1)² + (-2)² - (-30/5) = 1 + 4 + 6 = 11
- We divide F by 5 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 1)² + (y + 2)² = 11 ⇒ there is no choice
5) 2x² + 2y² - 24x - 16y - 8 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(-24)/2(2) = 6
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-16)/2(2) = 4
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (6)² + (4)² - (-8/2) = 36 + 16 + 4 = 56
- We divide F by 2 because the coefficient of x² and y²
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x - 6)² + (y - 4)² = 56 ⇒ 2x² + 2y² - 24x - 16y - 8 = 0
6) x² + y² + 2x - 12y - 9 = 0
- we will start to find h and k
∵ h = -coefficient x ÷ 2 coefficient x²
∴ h = -(2)/2(1) = -1
∵ k = -coefficient y ÷ 2 coefficient y²
∴ k = -(-12)/2(1) = 6
∵ r² = h² + k² - F
- where F is the numerical term of the general form
∴ r² = (-1)² + (6)² - (-9) = 1 + 36 + 9 = 46
∴ The equation of the circle in standard form is:
* (x - h)² + (y + k)² = r²
∴ (x + 1)² + (y - 6)² = 46 ⇒ x² + y² + 2x - 6y - 9 = 0
Answer and Step-by-step explanation:
Answer:
# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
Step-by-step explanation:
* Lets study the problem to solve it
- Use the terms of x and y in the general form to find the standard form
∵ x² + y² - 4x + 12y - 20 = 0
- Use the term x term
∵ -4x ÷ 2 = -2x ⇒ x × -2
∴ (x - 2)²
- Use the term y term
∵ 12y ÷ 2 = 6y ⇒ y × 6
∴ (y + 6)²
∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60
∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60
∵ x² + y² + 6x - 8y + 10 = 0
- Use the term x term
∵ 6x ÷ 2 = 3x ⇒ x × 3
∴ (x + 3)²
- Use the term y term
∵ -8y ÷ 2 = -4y ⇒ y × -4
∴ (y - 4)²
∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5
∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer
∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3
∴ x² + y² + 4x + 6y - 5 = 0
- Use the term x term
∵ 4x ÷ 2 = 2x ⇒ x × 2
∴ (x + 2)²
- Use the term y term
∵ 6y ÷ 2 = 3y ⇒ y × 3
∴ (y + 3)²
∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18
∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18
∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5
∴ x² + y² - 2x + 4y - 6 = 0
- Use the term x term
∵ -2x ÷ 2 = -x ⇒ x × -1
∴ (x - 1)²
- Use the term y term
∵ 4y ÷ 2 = 2y ⇒ y × 2
∴ (y + 2)²
∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11
∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer
∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2
∴ x² + y² - 12x - 8y - 4 = 0
- Use the term x term
∵ -12x ÷ 2 = -6x ⇒ x × -6
∴ (x - 6)²
- Use the term y term
∵ -8y ÷ 2 = -4y ⇒ y × -4
∴ (y - 4)²
∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56
∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56
∵ x² + y² + 2x - 12y - 9 = 0
- Use the term x term
∵ 2x ÷ 2 = x ⇒ x × 1
∴ (x + 1)²
- Use the term y term
∵ -12y ÷ 2 = -6y ⇒ y × -6
∴ (y - 6)²
∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46
∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46
If -7(y – 3) = – 14, what is the value of y?If -7(y – 3) = – 14, what is the value of y?
Answer:
y = 5
Step-by-step explanation:
-7 (5 - 3) = -14
y = 5
I took the test.
A stack of playing cards contains 4 jacks, 5 queens, 3 kings, and 3 aces. two cards will be randomly selected from the stack. what is the probability that a queen is chosen and replaced, and then a queen is chosen again?
Answer:
1/9.
Step-by-step explanation:
There is a total of 15 cards in the stack.
Prob( Queen is chosen) = 5/15 = 1/3.
The probability of a second queen being chosen is also 1/3
Required probability = 1/3 * 1/3 = 1/9.
Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limits.
y=0.8^x
Answer:
The answer is (d)
Exponential decay function
[tex]\lim_{x \to -\infty} f_x=0[/tex]
[tex]\lim_{x \to \infty} f_x= \infty[/tex]
Step-by-step explanation:
∵ y = 0.8^x
∵ 0.8 < 1
∴ 0.8^x is decreasing ⇒ exponential decay function
Ex: 0.8^-4 = 2.441 ⇒ 0.8^4 = 0.4096
when x increase the value of 0.8^x decrease
[tex]\lim_{n \to -\infty} f_x=0.8^{-\infty} = \frac{1}{0.8^{\infty}}=0[/tex]
[tex]\lim_{x \to \infty} f_x=0.8^{\infty}=\infty[/tex]
∴ The answer is (d)
PLZ HELP
a quarter circle has radius of 7 centimeters. What is the area of this figure? Use 3.14 for pi. Round your final answer to the nearest hundredth.
Answer:
[tex]A=38.47\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of a quarter circle is equal to
[tex]A=(1/4)\pi r^{2}[/tex]
we have
[tex]r=7\ cm[/tex]
substitute the values
[tex]A=(1/4)(3.14)(7)^{2}=38.47\ cm^{2}[/tex]
Write a polynomial expression, in simplified form, that represents the AREA of the blanket and use the expression to evaluate the AREA of the blanket if x = 2.
Answer:
Polynomial expression that represents the area of blanket:
[tex]A(x)=(6x^2+5x-21)cm^2[/tex]
If [tex]x=2[/tex]: [tex]A(2)=13cm^2[/tex]
Step-by-step explanation:
The area of the rectangle can be calculated with the formula:
[tex]A=lw[/tex]
Being l the lenght of the rectangle and w the width of the rectangle.
In this case, the lenght and the width are represented with:
[tex]l=(3x+7)cm[/tex]
[tex]w=(2x-3)cm[/tex]
Substitute them into [tex]A=lw[/tex]:
[tex]A(x)=(3x+7)(2x-3)[/tex]
Then:
Use Distributive property (Remember the Product of powers property: [tex]b^a*b^c=b^{(a+c)}[/tex] ):
[tex]A(x)=(3x+7)(2x-3)\\A(x)=6x^2-9x+14x-21[/tex]
Add like terms:
[tex]A(x)=(6x^2+5x-21)cm^2[/tex] (Simplied form)
Evaluate [tex]x=2[/tex]:
[tex]A(2)=(6(2)^2+5(2)-21)cm^2\\A(2)=(6(4)+10-21)cm^2\\A(2)=(24-11)cm^2\\A(2)=13cm^2[/tex]
For what value of x must ABCD be a parallelogram?
Justify your reasoning with theorems/postulates and show all work to receive credit.
Here is your answer
[tex]\bold{x= 6}[/tex]
REASON:
Theorem used: The diagonals of a parallelogram bisect each other.
Let diagonals AC and BD bisect each other at O
So, OA=OC
Now,
3x=4x-6 [OA=3x and OC=4x-6]
4x-3x= 6
x= 6
HOPE IT IS USEFUL
Answer:
Step-by-step explanation:
Parallelogram's diagonals theorem states that the diagonals in a parallelogram must bisect each other.
So for ABCD to be a parallelogram, the two diagonals must be divided in equal sections.
That is given for BD already.
For AC, 3x = 4x - 6
Rearranging, 4x - 3x = 6
x = 6
What is the remainder R when the polynomial p(x) is divided by (x+2)
Answer:
see explanation
Step-by-step explanation:
If (x + 2) is a factor then x = - 2 is a root and p(- 2) = 0
p(- 2) = -4[tex](-2)^{4}[/tex] + 6(- 2)³ + 8(- 2)² + 2(- 2) - 1
= - 64 - 48 + 32 - 4 - 1 = - 85
Hence remainder R = - 85
Since p(- 2) ≠ 0 then (x + 2) is not a factor of p(x)
Select the correct answer from the drop-down menu.
Hector keep close tabs on his bank account. His account had a balance of -$22.80. The next day, he made a deposit of $56.60. His account balance changed to $.
Answer: $33.80
Step-by-step explanation: If Hector’s account was overdrawn by $22.80 and then he deposited $56.60 his balance would be $33.80
The formula to solve this is -22.80 + 56.60 = 33.80
Answer:
$33.80
Step-by-step explanation:
i did it on my test got it right
A parking garage opens at 8 AM. The graph shows the total number of cars in the garage. How many cars were parked in the garage overnight? A.30 B.20 C.40 D.60
Answer:
D, 60.
Step-by-step explanation:
Well first of all, 30, 20, or 40 isn't even on the graph in the first place, and since the garage opens at 8, and it was 8 exactly and there were 60 cars parked, that means there was 60 parked over night. hope i helped!!
The number of cars parked overnight will be 180.
Option D is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
We have the following coordinates:
(10, 80), (20, 100), (30, 120), (40, 140), (50, 160), and (60, 180)
This means,
(10, 80)
After 10 minutes Past 8 am, the number of cars is 80.
Now,
The number of cars parked overnight will be 180.
From the graph, we have the highest coordinates as (60, 180).
Thus,
The number of cars parked overnight will be 180.
Learn more about coordinates here:
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