[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-5)^2+(y+6)^2=42\implies [x-\stackrel{h}{5}]^2+[y-(\stackrel{k}{-6})]^2=(\stackrel{r}{\sqrt{42}})^2~~ \begin{cases} \stackrel{center}{(5,-6)}\\\\ \stackrel{radius}{\sqrt{42}} \end{cases}[/tex]
Answer:
(5, -6)Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have:
[tex](x-5)^2+(y+6)^2=42\\\\(x-5)^2+(y-(-6))^2=42[/tex]
Therefore
[tex]h=5,\ k=-6,\ r^2=42\to r=\sqrt{42}[/tex]
Flower: Anthony decides to decorate a ballroom with r= 3n + 20 roses, where n is the number of dancers. It occurs to Anthony that the dancers always come in pairs. That is, n=2p, where p is the number of pairs. What is r as a function of p?
Can anyone explain the process of how to answer this problem?
Answer:
r= 6p + 20
Step-by-step explanation:
given:
r= 3n + 20
also given that n = 2p
substituting n=2p into the above equation
r= 3n + 20
r= 3(2p) + 20
r= 6p + 20
How can you solve for x in the proportion 7/8 = x/24?
Set the sum of 7 and 8 equal to the sum of 24 and x, and then solve for x.
Set the sum of 7 and 24 equal to the sum of 8 and x, and then solve for x.
Set the product of 7 and 8 equal to the product of 24 and x, and then solve for x.
Set the product of 7 and 24 equal to the product of 8 and x, and then solve for x.
Answer:
The answer is D
Step-by-step explanation:
What power of 10 can you multiply 0.02 by to get a product of 20?
Answer:
10^{3\\}
Step-by-step explanation:
10x10x10x0.02
=20
Have a nice day!!!!
KA
According to the 2010 census The state with the fewest people is Wyoming with a population of 563,626. Write the number that is 10,000 greater than 563,626
Answer:
573,626
Step-by-step explanation:
563626 + 10000 = 573626
What is the procedure for solving the equation 1/2x = 16?
a) add 1/2 to both sides of the equation
b) subtract 1/2 from both sides of the equation
c) multiply both sides of the equation by 2
d) multiply both sides of the equation by 1/2
Which equation represents a population of 320 animals that decreases at an annual rate of 19%
Population of 320 animals decreases at rate of 19 % = P = 320(0.81)t
What is percentage ?
Percentage means how much per hundredth.
we can write 20% as `1/5 in fraction. when we multiply a fraction by 100 we get the result in percentage.
In the given question
Population (P) = 320
Annual rate or per year decreasing percentage = 19%
As it decreases each year by 19% it retains (100 - 19)%= 81% of 320 animals
So in t years it will be P = 320([tex]\frac{81}{100}[/tex])t animals
Learn more about population increase and decrease here :
https://brainly.com/question/19578262
#SPJ5
Which ordered pair is a solution to the linear system? (2x + y = 5) (x – y = 13)
Answer:
The solution is {6, -7}.
Step-by-step explanation:
2x + y = 5
x – y = 13 Adding these 2 equations eliminates y:
3x + 0 = 18
x = 6.
Substituting for x in equation (1):
2(6) + y = 5
y = 5 - 12 = -7.
The ordered pair that is a solution to the linear system of equations, (2x + y = 5) and (x - y = 13), is (6, -7). The solution was found by using the elimination method.
Explanation:You can solve this linear system by using the substitution or elimination method. Here, I will use the elimination method, which involves adding or subtracting the equations to eliminate one of the variables.
First, add the two equations together. (2x + y) + (x – y) equals 5 + 13. This simplifies to 3x = 18. Second, divide both sides of the equation by 3 to solve for x. This gives x = 6. Substitute this value back into either of the original equations. By substituting into the first equation, it becomes 2*6 + y = 5. Simplifying it, gives y = -7.So the
ordered
pair that is a solution to the linear system is (6, -7).
Learn more about linear system here:
https://brainly.com/question/35683013
#SPJ2
Subtract 2 1/8- 1 7/8
Answer:
2/8 or 1/4
Step-by-step explanation:
2 1/8 - 1 7/8 - Make improper fractions
17/8 - 15/8 - subtract them
2/8 - simplify
1/4 - final
In order to get the answer to this question you will have to change the mixed numbers into improper fractions and then subtract by finding the common denominator and then subtracting the numerators and reduce if needed to get your answer.
[tex]2\frac{1}{8} - 1\frac{7}{8}[/tex]
Convert into improper fractions:
[tex]2\frac{1}{8} =\frac{17}{8}[/tex]
[tex]1\frac{7}{8} = \frac{15}{8}[/tex]
[tex]\frac{17}{8} - \frac{15}{8}[/tex]
Find the common denominator:
[tex]CD=8[/tex]
[tex]17-15=2[/tex]
[tex]=\frac{2}{8}[/tex]
Reduce:
[tex]\frac{2}{8} \div2=\frac{1}{4}[/tex]
[tex]=\frac{1}{4}[/tex]
Therefore your answer is "1/4."
Hope this helps
estimate the square root of 27 over 4 to the nearest 10th
Answer:
1.3
Step-by-step explanation:
Which addition sentence could help solve this problem 3 + 5 + 7 =15
2+3=5
5+5=10
3+7=10
5+2=7
The required sentence are 3 + 7 = 10 could help solve this problem 3 + 5 + 7 =15. Option C is correct.
Given that,
Which additional sentence could help solve this problem 3 + 5 + 7 =15 is to be determined.
The technique in computation to use and analyze the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is arithmetic?In mathematics, it vends on a number of procedures according to the declarations. There are four primary arithmetic operators, addition, subtraction, multiplication, and division,
Here,
The sentence could help solve this problem 3 + 5 + 7 =15
3 + 7 + 5 = 15 - - - - - - -(1)
3 + 7 = 10
Put it in equation 1
10 + 5 = 15
Thus, the required sentence are 3 + 7 = 10 could help solve this problem 3 + 5 + 7 =15. Option C is correct.
Learn more about simplification here:
brainly.com/question/12501526
#SPJ2
I need to know what x is
Preserve
What is this 3 digit number
The given line passes through the points (0, ) and (2, 3). On a coordinate plane, a line goes through (0, negative 3) and (2, 3). A point is at (negative 1, negative 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point ()?
Option 2 is correct.
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
To find the equation of a line that is parallel to the given line and passes through the point (-2, 2), we follow these steps:
1. Determine the slope of the given line. Parallel lines have the same slope.
2. Use the point-slope form of a line equation with the given point and the determined slope to find the equation of the parallel line.
From the graph, we can see that the given line passes through points (0, -3) and (-5, -4). To find the slope (m) of the line, we use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given points, we get:
[tex]\[ m = \frac{-4 - (-3)}{-5 - 0} \][/tex]
[tex]\[ m = \frac{-4 + 3}{-5} \][/tex]
[tex]\[ m = \frac{-1}{-5} \][/tex]
[tex]\[ m = \frac{1}{5} \][/tex]
Now we have the slope of the parallel line, which is[tex]\( \frac{1}{5} \)[/tex]. The point-slope form of the line equation is [tex]\( y - y_1 = m(x - x_1) \)[/tex]. Plugging in the slope and the point (-2, 2), we get:
[tex]\[ y - 2 = \frac{1}{5}(x - (-2)) \][/tex]
[tex]\[ y - 2 = \frac{1}{5}(x + 2) \][/tex]
Now we simplify and solve for y to put it in slope-intercept form ( y = mx + b ):
[tex]\[ y - 2 = \frac{1}{5}x + \frac{2}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + 2 \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{2}{5} + \frac{10}{5} \][/tex]
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
So the equation of the line that is parallel to the given line and passes through the point (-2, 2) is:
[tex]\[ y = \frac{1}{5}x + \frac{12}{5} \][/tex]
123456789
What is the perimeter of a rectangle that has a 3ft hight and 13ft width
Answer:
32 ft
Step-by-step explanation:
3+3+13+13=
32
Perimeter = 32 ft.
Since it is a rectangle, 2 sides measure 13ft, and 2 sides measure 3 ft.
13+13=26
3+3=6
26+6=32.
There are 52 weeks in one year. If cindy drew three pictures each week, for 2 years, how many pictures did cindy draw?
Final answer:
Cindy drew a total of 312 pictures over two years, calculating from three pictures per week for 52 weeks each year, then doubling the result for the two years.
Explanation:
To calculate the total number of pictures Cindy drew over two years, we start by determining the number of pictures she draws each week.
Since Cindy draws three pictures each week, we multiply that number by the number of weeks in one year.
There are 52 weeks in one year.
So, the number of pictures Cindy draws in one year is:
3 pictures/week × 52 weeks/year = 156 pictures/yearSince the question is about a two-year period, we multiply the annual amount of pictures by two:
156 pictures/year × 2 years = 312 picturesTherefore, Cindy drew a total of 312 pictures over two years.
What is 2/28=7/8 cross multiplied
Answer:
see the explanation
Step-by-step explanation:
we have
[tex]\frac{2}{28}=\frac{7}{8}[/tex]
we know that
To cross multiply, start by multiplying the numerator of the left-hand fraction by the denominator of the right-hand fraction.
2(8)
Then, multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.
7(28)
Next, set the 2 products equal to each other.
2(8)=7(28)
-23=5+ 4x what does x equals?
Answer:
x = -7
Step-by-step explanation:
- 23 = 5 + 4x
- 5 = - 5
- 28 = 4x
/4 = /4
- 7 = x
Answer: x= -7
Step-by-step explanation:
you basically add 5 with 5 and they cancel out
You add 5 to -23 and get -28=4x and divide 4x and -28 which gets your answer
For the given true statements, what can you conclude?
If points A, B, and C are collinear, and B is between A and C, then AB + BC = AC.
Points Q, R, and S are collinear and R is between Q and S.
SQ + RS = QR
QR + QS = RS
RS + QS = SR
QR + RS = QS
Answer:
D:QR+RS=QS
Step-by-step explanation:
We are given that
If point A, B and C are collinear, B is between A nd C, then AB+BC=AC
Points Q, R and S are collinear and R is between Q and S.
We have to find the conclusion about given statement.
If R lie between Q and R
Then, QR+RS=QS (segment addition property)
Because point Q, R and S are collinear.
Therefore, option D is true.
Answer:D:QR+RS=QS
A rectangle has an area of 90 square centimeters and a height of 12.5 centimeters. What is the length of the base?
A.
7.2 centimeters
B.
72 centimeters
C.
112.5 centimeters
D.
1125 centimeters
Answer:
A. 7.2 centimeters
Step-by-step explanation:
The length of the base is 7.2 centimeters. The area of a rectangle is length*width
The length is unknown but the area is known. To find the length, all we have to do is divide the area from the height.
The working is as follows :
Area = 90 cm²
Height = 12.5 cm
Length = ?
Length = Area ÷ Height
= 90 ÷ 12.5
= 7.2cm
The length of the base of the rectangle is found by dividing the area by the height, which gives 7.2 centimeters.
Explanation:The subject is about finding the length of the base of a rectangle given its area and height. The formula to find the area of a rectangle is Area = Length x Width. From the question, we know the Area is 90 square centimeters and the height (which can also be considered as the Width) is 12.5 centimeters. Therefore, we can arrange the formula to solve for Length: Length = Area / Width.
Substituting the given numerical values we find: Length = 90 / 12.5 = 7.2 centimeters. So, the correct answer is 7.2 centimeters (Option A).
Learn more about Rectangle Dimensions here:https://brainly.com/question/35474401
#SPJ11
Mary weighs n kg while her sister weighs 15 kg less. How many times is Mary heavier than her sister?
For this case we have to:
n: Represents the weight of Mary in Kg.
If your sister weighs 15 kg less we have:
[tex]y = n-15[/tex]
Where "y" represents the weight of his sister in kg.
To find how many times Mary is heavier than her sister, we must divide Mary's weight by her sister's weight.
We have then:
[tex]N= \frac{n}{n-15}[/tex]
Answer:
Mary is [tex]N= \frac{n}{n-15}[/tex] times heavier than her sister.
Answer:
Mary weighs[tex]\frac{n}{(n-15)}[/tex]heavier than her sister.
Explanation:
As we have given the data in the question that
Weight of marry = n kg
Weight of Marry sister = n-15 kg
Let Marry be ‘K' times heavier than her sister then it means that
K=[tex]\frac{n}{(n-15)}[/tex]
And we can write the above equation as
K(n-15) = n
K=[tex]\frac{n}{(n-15)}[/tex]
which completely explains the above statement that Weight of the marry is K times the weight of her sister.
So the correct answer is K=[tex]\frac{n}{(n-15)}[/tex]
What is 6.02 nearest tenth
Answer:
6
Step-by-step explanation:
The digit in the hundredth place value of 6.02 is 2, so it rounds down.
The number 6.02, when rounded to the nearest tenth, results in 6.0, as '2' in the hundredths place is less than '5' and requires rounding down.
Explanation:Given the number 6.02, rounding to the nearest tenth means identifying what tenth it is closest to. The number in the tenths place is '0'. For rounding, we look at the digit following the tenths place, which is the hundredths place. Here, the number is '2'. If this number is 5 or more, we round up. If it's 4 or less, we round down. So, 6.02 to the nearest tenth, would be 6.0 because 2 is less than 5, so we round down.
Learn more about Rounding Numbers here:https://brainly.com/question/19166897
#SPJ2
After several shares of the company's stock were sold, a profit of $1,320 was earned. The profit was 15% over a 30 day period. How much were the shares worth when they were originally purchased?
Answer:
That's it... Just sum it ul
Answer:
The shares were worth $8800, when they were originally purchased.
Step-by-step explanation:
After several shares of the company's stock were sold, a profit of $1,320 was earned.
The profit was 15% over a 30 day period.
Let the original price of the shares be = x
As there was a profit of 15% on x.
We get the following expression;
[tex]0.15x=1320[/tex]
Then x = 8800
Hence, the shares were worth $8800, when they were originally purchased.
Solve a Mixture Word Problem
Question
Orlando is mixing nuts and cereal squares to make a party mix. Nuts sell for $7 a pound and cereal squares sell for $4 a
pound. If Orlando wants to make 30 pounds of party mix at a cost of $6.50 a pound, how many pounds of nuts and how
many pounds of cereal squares should he use?
Provide your answer below:
lb cereal squares,
Ib nuts
B FEEDBACK
MORE INSTRUCTION
SUBMIT
Content attribution
Answer: Orlando mixed five pounds of cereal squares and 25 pounds of nuts.
Answer:
5 lbs cereal squares.
25 Ibs nuts.
Step-by-step explanation:
Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.
Total weight of the party mix is 30 pounds.
[tex]x+y=30[/tex] ..... (1)
It is given that,
Cost of nuts = $7 per pound
Cost of cereal = $4 per pound
The cost of mix = $6.50 per pound.
[tex]7x+4y=6.50\times 30[/tex]
[tex]7x+4y=195[/tex] ..... (2)
Substitute the value of x in equation (2) from equation (1).
[tex]7(30-y)+4y=195[/tex]
[tex]210-7y+4y=195[/tex]
[tex]-3y=195-210[/tex]
[tex]-3y=-15[/tex]
Divide both sides by -3.
[tex]y=5[/tex]
Substitute y=5 in equation (1).
[tex]x+5=30[/tex]
Subtract both sides by 5.
[tex]x=30-5[/tex]
[tex]x=25[/tex]
Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.
---
Nathaniel started collecting rocks. He started his collection with two rocks on the first day, then four rocks on the second day, then
elght rocks on the third day, and then sixteen rocks on the fourth day.
Assuming this pattern continues, what will be the total size of Nathaniel's rock collection on the 10th day?
Answer:
Step-by-step explanation:
u keep multiplying see 2*2= 4*4=16*16=256*256=65536*65536= etc
Answer:
plato: 1,024
Step-by-step explanation:
5•(9+4)+362 divided by 2
Answer:
2`13.5
Step-by-step explanation:
5x13=65
65+362=427
427/2=213.5
Step-by-step explanation: everything can be divided by 2 and added together. Or distribute 5. Add them. Then divide by 2
25 000,000/10,000
No calculator
25 000,000/10,000
Cross out equal amounts of 0's from both numbers:
There are 4 0's in 10,000, so remove 4 0's from both numbers to get:
2500/1
Any number over 1 is that number:
2500/1 = 2500
A
B
C
D
Help much appreciate
Answer:
D
Step-by-step explanation:
A is 4, which is rational,
B is just 1/3, which is rational,
C is -8, which is rational,
leaving D, which is 3.1415926535...
A bag contains 22 1/2 cups .A recipe for pancakes uses 1 1/4 cups of flour .how many batches of pancakes can be made with one bag of flour
Answer:
18 batches of pancakes
Step-by-step explanation:
22.5/1.25=18
If f(x) = х2 – 2x and g(x) = 6х +4, for which vаluе оf x does (f + g)(x) = 0?
Answer:
x = - 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4
Equating to zero, that is
x² + 4x + 4 = 0 ← left side is a perfect square
(x + 2)² = 0, thus
x + 2 = 0 ⇒ x = - 2
Answer:
[tex]\boxed{\text{x = -2}}[/tex]
Step-by-step explanation:
ƒ(x) = x² - 2x
g(x) = 6x + 4
(f + g)(x) = x² - 2x + 6x + 4 = x² + 4x + 4
[tex]\begin{array}{rcr}x^{2} + 4x + 4 & = & 0\\(x + 2)^{2} & = & 0\\x+2 & = & 0\\x & = & \mathbf{-2}\\\end{array}[/tex]
[tex](f + g)(x) = 0 \text{ when } \boxed{\textbf{x = -2}}[/tex]
Check:
[tex]\begin{array}{rcl}(-2)^{2} + 4(-2) + 4 & = & 0\\4 - 8 + 4 & = & 0\\0 & = & 0\\\end{array}[/tex]
OK.
What is the solution for the equation 8X – 12 = 4x?
x= 48
x= 30
x=3
X=1
Answer:
C. x = 3
Step-by-step explanation:
8x - 12 = 4x
+12 + 12
8x = 4x + 12
-4x -4x
4x = 12
---- ---
4 4
x = 3
C. x = 3
8x-12= 4x
move -12 to the other side
sign changes from -12 to +12
8x-12+12= 4x+12
8x=4x+12
move 4x to the other side.
sign changes from +4x to -4x
8x-4x= 4x-4x+12
8x-4x= 12
4x=12
divide both sides by 4 to get x by itself
4x/4= 12/4
Answer: x= 3