Answer:
Step-by-step explanation:
x²-8x+16+y²+2y+1=16+1-13
(x-4)²+(y+1)²=2²
general form of a circle's equation is
(x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r= radius
By comparing with A,
(4,-1) is center and radius= 2.
The center of the circle is (-4,2) and the radius is 2
How to determine the center and the radius?The equation is given as:
x^2 + y^2 - 8x + 2y + 13 = 0
Rewrite as:
x^2 - 8x + y^2 + 2y + 13 = 0
Subtract 12 from both sides
x^2 - 8x + y^2 + 2y = -13
Group each variable
[x^2 - 8x] + [y^2 + 2y] = -13
-------------------------------------------------------------------
Take the coefficient of x and y
-8 and 2
Divide by 2
-4 and 1
Square both numbers
16 and 1
-------------------------------------------------------------------
Next, we add 16 and 1 to both sides of the equation
[x^2 - 8x + 16] + [y^2 + 2y + 1] = -13 + 16 + 1
Express as perfect squares and evaluate the sum
(x - 4)^2 + (y + 1)^2 = 4
Express 4 as 2^2
(x - 4)^2 + (y + 1)^2 = 2^2
A circle is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where:
Center = (a,b)
Radius = r
This means that the center of the circle is (-4,2) and the radius is 2
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ab=20 bc=6 cd=8
a. 18.5
b. 11.5
c. 19.5
d. 15
Answer:
A. 18.5
Step-by-step explanation:
If there is a crossword that has four squares that need to be filled, how many possible four-letter arrangements are there (assuming they do not have to make a real word)?
What is the inverse of the function [tex]y=x^{2} +4x+4[/tex]
Answer:
y = 2 ± √x is the inverse but it's not a function. (See note below for additional info)
Step-by-step explanation:
Given the quadratic function:
[tex] \displaystyle{y = {x}^{2} + 4x + 4}[/tex]
We can rewrite the function above using perfect square form:
[tex] \displaystyle{y = {(x + 2)}^{2} }[/tex]
Finding an inverse, we swap the terms of x and y:
[tex] \displaystyle{x = {(y + 2)}^{2} }[/tex]
Square root both sides, solving for y:
[tex] \displaystyle{ \sqrt{x }= \sqrt{ {(y + 2)}^{2}} } \\ \\ \displaystyle{ \sqrt{x }= \left| y+ 2\right| } \\ \\ \displaystyle{ \pm \sqrt{x }= y + 2}[/tex]
Subtract both sides by 2:
[tex] \displaystyle{ \pm \sqrt{x } - 2= y+ 2 - 2} \\ \\ \displaystyle{ \pm \sqrt{x } - 2= y} \\ \\ \displaystyle{y = 2 \pm \sqrt{x} }[/tex]
Therefore the inverse of y = x² + 4x + 4 is y = 2 ± √x.
Note: While it's possible to find the inverse of quadratic function, but the inverse version itself is not really a function. So if you want to go by definition or theorem, you can say there's no inverse function. Otherwise, the answer above is the solution.
help please u^u thank you no links
Answer:
X=14
Step-by-step explanation:
180-58-75=3x+5
3x+5=47
3x=42
X=14
May I have some help?
Answer:
0 ÷ 3 = 0
Step-by-step explanation:
if x = 0 you put it in where the x is
Solve for f
2 + 1.25f = 10 - 2.75f
Answer:
2
Step-by-step explanation:
1. Explain how place-value blocks can
help you with division.
Using place value along with division facts in a division equation, helps in dividing larger numbers easily. Place value counters and tape diagrams are often used to represent division using place value.
What is division?
With the arithmetic operation of division, we can divide a collection of items into equal pieces. Typically, it is represented by the symbol "÷".
The bigger amount that is divided into equal halves is called the dividend.
The number of groups that divide the payout is known as the divisor. Following division, the result is the quotient.
The value of a digit in a number is determined by its place in the number, or place value.
Divide larger numbers simply by applying place value and division facts in a division equation. Place value division is frequently shown using tape diagrams and place value counters.
Example - 4 ÷ 2 = 2
In the first equation, the digits are 4 and 2. We can write it as 4 ones ÷ 2 ones = 2 ones (using the division fact).
Example - 40 ÷ 20 = 2
For the second equation, the digits are the same, but a zero has been added after 4, and the quotient thus has one zero at the end. So, we can write it as 4 tens ÷ 2 ones = 2 tens (using place value and the division fact).
Example - 400 ÷ 200 = 2
Similarly, for the third division equation, the same digits are present, but the number of zeros has increased. We are dividing 4 hundreds ÷ 2 ones = 2 hundreds (using place value and the division fact).
Therefore, place value blocks help in division for making it simpler.
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6. Larry earns $840 per pay period, plus a commission of 8% on his sales. During the last pay period, Larry earned
a total of $2,440.00. What were Larry's total sales during the pay period?
A. $784
B. $22,500
C. $30,500
D. $38,500
7. Tom's bill at a local restaurant was $19.47. If he wants to leave a 15% tip, approximately how much should he
leave?
A. $0.15
B. $3
C. $4
D. $15
6. Larry's total sales during the pay period is $20,000.
7. Tom should leave $3 (approximate)
What is the meaning of total sales?
Total sales revenue usually referred to as gross sales is the sum of the value of the products and services a company provides to its clients over the course of a given reporting period.
Given that Larry earns $840 per pay period, plus a commission of 8% on his sales.
Assume that Larry sale $x during the last pay period.
The total earn is 840 + 8% of x
= 840 + 0.08x
According to the question:
840 + 0.08x = 2,440.00
Subtract 840 from both sides:
0.08x = 2,440 - 840
0.08x = 1600
Divide both sides by 0.08
x = 1600/0.08
x = 20,000
The sales is $20,000.
7. Given that, Tom's bill at a local restaurant was $19.47. He leaves 15% of the total bill as a tip.
15% of $19.47
= 15/100 × $19.47
= 2.920
≈ 3 (approximate)
Tom should leave $3.
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XYZ Company
Balance Sheet
Assets
Cash
$45,000
Inventory $41,000
Property $134,000
Total Assets:
Liabilities
Notes
Wages
Equity
Stock
$55,000
$56,000
$50,000
Investment $59,000
Total Liabilities + Equity:
Using the balance
sheet, calculate XYZ
Company's total
assets - liabilities.
Total Assets - Liabilities = $ [?]
Enter
PH
Skip
Total Liabilities + Equity = $220,000.
Total Assets = $220,000.
What is Ratio Analysis and Balance Sheet?
The relationship between the two separate components is established through ratio analysis. Utilizing figures from the income statement, balance sheet, statement of cash flows, and other financial statements, it is used to assess the company's financial performance.
One of a company's financial statements that is created at the end of the year is the balance sheet. It establishes the balance of a company's assets, liabilities, and stockholder equity at the end of the fiscal year.
Here we are given in the Question,
Assets
Cash = $45,000
Inventory = $41,000
Property = $134,000
Liabilities
Notes = $55,000
Wages = $56,000
and
Equity
Stock = $50,000
Investment = $59,000
Total Liabilities + Equity = ( Notes + wages ) + (stock + Investment)
Total Liabilities + Equity = ( $55,000 + $56,000) + ($50,000 + $59,000)
Total Liabilities + Equity = $220,000.
Total Assets = Cash + Inventory + Property
Total Assets = $45,000 + $41,000 + $134,000
Total Assets = $220,000
Therefore,
Total Liabilities + Equity = Total Assets.
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Help me! I need to get this right! If you do get it right, I will give you Brainlist!
Answer:
d. 1/4
Step-by-step explanation:
comment if u need explanation
Answer:
it's D. 1/4
Step-by-step explanation: hope that helps
Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest, compounded annually. What is the balance after 8 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Balance after 8 years is $2,306.86 at an interest rate of 15 % compounded yearly.
What is compound interest?Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.
given, Melissa opened a savings account and deposited $700.00 as principal. The account earns 15% interest
from the general formula of compound interest
A = [tex]P(1 + r/n)^{nt}[/tex]
where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Given, P = 700$
r = 15%
t = 8 years
A = 700(1 + 15/100)⁸
A = 2306.86$
Therefore, At a 15% annual compounded interest rate, the remaining balance after 8 years is $2,306.86.
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Find the missing length ps. I am going to be sending a lot Bc I need help like fast
Answer:
x = 25
Step-by-step explanation:
This is a similar triangle problem
Therefor two sides of triangle A are in the same proportion as two sides of triangle B
----------------------------
Triangle A
Short leg = x
Long leg = 60
proportion = x/60
Triangle B
Short Leg = 60
Long leg = 144
proportion = 60/144
Therefor
x/60 = 60/144
multiply both sidees by 60
x = 60*60/144
x = 25
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Write the quotient as a mixed number.
26÷3=8 R2
When we divide 26 by 3 we get 8 as a quotient and 2 as a remainder, the Mixed Fraction is [tex]8\frac{2}{3}[/tex]
What is a mixed Number ?A full number plus a legal fraction are combined to form a mixed number. Mixed numbers, commonly referred to as mixed fractions, make it easier for humans to comprehend numbers.
A full number and a legal fraction make up a mixed number. A mixed number like [tex]2\frac{x}{y}[/tex] is one where 1/4 is the correct fraction and 2 is the whole number portion. It should be emphasized that once mixed numbers are transformed into an incorrect fraction, they are simple to add, subtract, multiply, and divide.
Steps to convert Improper fraction to Mixed Fraction :
Divide the numerator by the denominator to obtain the remainder and quotient as the first step. 43 divided by 9 in this situation yields 4 as the quotient and 7 as the remainder.Step 2: This quotient (4) becomes the mixed number's whole number component. While the denominator stays the same, the remainder (7) becomes the numerator portion.Step 3: As a result, 43/9 becomes a mixed number and is written as , meaning that 43/9 = [tex]4\frac{7}{9}[/tex].So when we divide 26 by 3 we get 8 as a quotient and 2 as a remainder so the Mixed Fraction is : [tex]8\frac{2}{3}[/tex]
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Which of the following are solutions to the quadratic equation? Check all that
apply
2x2 + 9x-3 = -x2 + x
Step-by-step explanation:
I don't see options but here's the solution
2x²+9x-3=-x²+x
2x²+x²+9x-x-3=0
3x²+8x-3=0
(3x-1)(x+3)=0
Therefore x=⅓ or-3
Make 4 equal warehouses out of a fence 300 m long. What is the width and length of the sv part if we want them to be the largest possible areas
The width and the length that gives the largest possible areas are 75 meters by 37.5 meters
How to determine the width and the length that gives the largest possible areasFrom the question, we have the following parameters that can be used in our computation:
Number of warehouses = 4
Perimeter of fence = 300 meters
Represent the width with x and the length with y
So, we have the following equations
Area = 4xy
Perimeter = 2(4x + y)
Substitute the known values in the above equation, so, we have the following representation
2(4x + y) = 300
Divide both sides by 2
2x + y = 150
Make y the subject
y = 150 - 2x
Substitute y = 150 - 2x in Area = 4xy
A = 4x(150 - 2x)
This gives
A = 600x - 8x²
Differentiate and set to 0
600 - 16x = 0
So, we have
16x = 600
Divide by 16
x = 37.5
Recall that
y = 150 - 2x
So, we have
y = 150 - 2 x 37.5
Evaluate
y = 75
Hence, the dimensions are 75 meters by 37.5 meters
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The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rate of change of
(i) the perimeter.
(ii) area of rectangle.
Which of the following points is shown in the graph below? Question 5 options:
The point shown on the graph is
(4, -5, 6)
How to find the points shown on the graphAn ordered triplet of lines (the axes) that are pair-wise perpendicular and pass through the same point (the origin) make up a Cartesian coordinate system for a three-dimensional space.
Each axis also has an orientation, and the length of all three axes is equal.
In ordered triplet, the order of the axis is (x, y, z)
z is vertical up positive and down negative
y is horizontal right is positive and left is negative
x is the axis pointing to us which is positive pointing away is negative
Using this information, to trace the point shows that the point marked by a dot is (4, -5, 6).
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MAM I NEED HELP WHAT DO I NEED TO PUT!!!!!
20% of the students in a class are left handed. There are 50 students. How many
of the students are left handed? (Show working)
Answer:
10
Step-by-step explanation:
50 students.
20% = 20/100 = 1/5
50*1/5 = 10
There are 10 left-handers.
answer both for brainliest and 20 pts
Answer:
ed = 3
lm = 30.6
Step-by-step explanation:
Given it was not a strike, what is the probability it was a knuckle
ball? Enter the answer as a percent (%)to the nearest tenth.
On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 1000
obtained = 500
so, 500/1000X100 = 50%
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I need some help, would anyone know?
thank you
Answer:
Step-by-step explanation:
hi!! ;; please help :) 20 points! no links or websites. please .
Answer: 22
Step-by-step explanation:
(1 × 3) + [2 × 3 [tex]\frac{1}{2}[/tex]] + [1 × 3 [tex]\frac{3}{4}[/tex] [1 × 4 [tex]\frac{1}{4}[/tex]] + [3 × [tex]\frac{3}{4}[/tex]] + [3 × 5 [tex]\frac{1}{4}[/tex]]
= 3 + [2 × [tex]\frac{3}{2}[/tex]] + [1 × [tex]\frac{9}{4}[/tex]] + [1 × [tex]\frac{4}{4}[/tex]] + [3 × [tex]\frac{12}{4}[/tex]] + [3 × [tex]\frac{5}{4}[/tex]]
= 3 + [tex]\frac{6}{2}[/tex] + [tex]\frac{9}{4}[/tex] + [tex]\frac{4}{4}[/tex] (equal to 1) + [tex]\frac{36}{4}[/tex] + [tex]\frac{15}{4}[/tex]
= 3 + 3 + [tex]\frac{9}{4}[/tex] + 1 + 9 + [tex]\frac{15}{4}[/tex]
= 16 + [tex]\frac{9+15}{4}[/tex]
= 16 + [tex]\frac{24}{4}[/tex]
= 16 + 6
= 22
These equations take their y-values from the set (4, 5, 6, 7, 8). Arrange the equations in decreasing order of the values of y that make them true.
4y + (y - 1) = 29
4y = y + 1 = 13
(2y + 3) - 4 = 9
9514 1404 393
Answer:
a, c, b
Step-by-step explanation:
Collect terms, subtract the constant, divide by the y-coefficient.
(a) 4y + (y - 1) = 29 ⇒ y = 6
(c) (2y + 3) - 4 = 9 ⇒ y = 5
(b) 4y - y + 1 = 13 ⇒ y = 4 . . . . . this equation is not what you have written
__
Additional comment
The second equation suffers from a typo, so your answer may vary.
Answer:
in order acb
Step-by-step explanation:
Evaluate p+(n-1) x3 for n=7 and p=9
What is a quadratic function (f) whose zeros are -2 and -11
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have [tex]x1[/tex]=2 [tex]x2[/tex]=-11
then quadratic function will be
(x+2) (x+11)
[tex]x^2+2x+11x+22[/tex]
[tex]x^2+13x +22[/tex]
this is our required quadratic equation.
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Complete question is: Write a quadratic function f whose zeros are 2 and -13.
Hence the required quadratic equation is +13x+22.we can find by multiplying of given factor.
What are quadratic equations explain?Quadratics equation is a polynomial equation of a second degree which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is: ax² + bx + c = 0. where x is an unknown variable and a, b, c are numerical coefficients.
What are the ways to solve a quadratic equation?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula. Quadratic equations have many applications in everyday life. Quadratic equations must be used directly or indirectly in every field that involves calculating speed.
Now we have x¹ = 2 x² = -11
then quadratic function will be
(x+2) (x+11)
x² + 2x + 11x + 22
x² + 13x + 22
This is our required quadratic equation.
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The complete question is-
Write a quadratic function f whose zeros are 2 and -13.
Help me plz have a blessed day
Answer:
b. (2,0)
Step-by-step explanation:
To find which ordered pair is a solution, we have to replace then into the equation, and the result has to be an identity, that is, 0 = 0.
Equation:
[tex]y = -5x + 10[/tex]
Option a:
[tex](-15,5)[/tex], so [tex]x = -15, y = 5[/tex]
[tex]y = -5x + 10[/tex]
[tex]5 = -5(-15) + 10[/tex]
[tex]5 = 75 + 10[/tex]
[tex]5 = 85[/tex]
Not an identity, so this ordered pair is not a solution.
Option b:
[tex](2,0)[/tex], so [tex]x = 2, y = 0[/tex]
[tex]y = -5x + 10[/tex]
[tex]0 = -5(2) + 10[/tex]
[tex]0 = -10 + 10[/tex]
[tex]0 = 0[/tex]
Identity, and thus, the correct answer is given by option b.
How do you simplify 3/4-2/3?
Answer:
1/12
Step-by-step explanation:
3/4 - 2/3 = 9/12 - 8/12 = 1/12
Answer:
The answer is 1/12 good luck with the rest
A normal distribution has a mean 7 of and a standard deviation of 2. Use the 68-95-99.7 rule to find the percentage of values in the distribution between and .
What is the percentage of values in the distribution between 7 and 9?
=================================================
Explanation:
We have 7 at the center. Going 2 units to the left of center gets us to 7-2 = 5. Going 2 units to the right of center gets us to 7+2 = 9.
Since the mean is 7 and the standard deviation is 2, this tells us that the values 5 and 9 are exactly one standard deviation away from the mean.
Due to the empirical rule (aka 68-95-99.7 rule), we just found that roughly 68% of the population is between 5 and 9.
Half of this is 68/2 = 34%, so this is the percent of values between 7 and 9.
please help ASAP I need to do this