By completing squares, we will see that the center of the given circle is at (-3, -2).
How to find the center of the circle?
The general circle equation centered on (a, b) of radius R is:
[tex](x - a)^2 + (y - b)^2 = R^2[/tex]
In this case, our equation is:
[tex]x^2 + y^2 + 6x + 4y - 3 = 0[/tex]
First, we need to complete squares, we will have:
[tex]x^2 + 2*3*x + y^2 + 2*2*y - 3 = 0\\\\x^2 + 2*3*x + (9 - 9) + y^2 + 2*2*y + (4 - 4) - 3 = 0\\\\(x^2 + 2*3*x + 9) - 9 + (y^2 + 2*2*y + 4) - 4 - 3 = 0\\\\(x + 3)^2 + (y + 2)^2 = 3 + 9 + 4 = 16[/tex]
Then, by looking at the left side, we can see that the center of the circle is (-3, -2).
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Answer:
d
Step-by-step explanation:
got it right on edge
If a job has salary of $470 a week, how much would it pay for a year
Answer:
$22560
step 1
$270 × 4month
=$1880 for a month
step 2
$1880×12months
= $22560
An initial deposit of $6300.00 is made into a savings account that compounds 5.2% interest semi-annually. how much is in the account after 10 years?
question 1 options:
$414,740.48
$10,526.59
$10,459.19
$9,289.13
Answer:
$10459.19
Step-by-step explanation:
A forest fire has been burning for several days. The burned area, in acres, is given
the equation y = (4, 800) • 2d, where d is the number of days since the area of the
fire was first measured.
Complete the following table:
Answer:
you gotta show a picture of the table in order for us to know what's missing from it
When d = -1, the value of y is 300 acres means that the area burned in the fire was 300 acres. When d = -3, the value of y is 1.17 acres means that the area burned in the fire was only 1.17 acres three days
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
we can use the given equation y = (4,800)2^d and substitute the values of d in the table to get the complete table.
Now the equation y = (4,800)2d for d when y = 4,800 and then subtract 7 from that value.
(4,800)2d = 4,800
2d = 1
d = 0.5
The fire had burned for 12 hours, before it measured 4,800 acres.
To determine the area the fire had burned a7 days before this measurement, we will then substitute d = -6.5 into the equation:
y = (4,800)2(-6.5) ≈ 0.00025 acres
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pls help this is urgent
aiden’s teacher tells him that the values in the table represent a proportional relationship.
x y
1 5
2. 10
3. 15
Based on the table, Alden claims that in order for a coordinate point to be in the proportional relationship, both the
x-coordinate and y-coordinate must be integers.
Determine a coordinate point that proves that Alden's claim is false.
Enter the x-coordinate in the first response box.
Enter the y-coordinate in the second response box.
Answer:
Step-by-step explanation:
im passing this concept trust me the answer is 12
Which parallelogram has an area of 60 square units?
Answer:
Finding the area of each parallelogram, applying the formula, it is found that the parallelogram D has an area of 60 square units
Step-by-step explanation:
Similarly to a rectangle, the area of a parallelogram is given by height multiplied by base, that is:
In item A, the height is of 15 units and the base is of 10 units, thus, the area, in square units, is of .
In item B, the height is of 6 units and the base is of 10.2 units, thus, the area, in square units, is of .
In item C, the height is of 15 units and the base is of 15 units, thus, the area, in square units, is of .
In item D, the height is of 10 units and the base is of 6 units, thus, the area, in square units, is of , which means that this is the correct option.
2 cm
6 cm
6 cm
What is the surface area of the solid above?
O A. 14 cm2
O B. 120 cm2
O C. 56 cm2
O D. 84 cm2
Answer:
O B. 120 cm2
Step-by-step explanation:
2×(6×6 + 6×2 + 6×2) = 120 centimeters2
The mean shoe size of the students in a math class is 7. 5. Most of the shoe sizes fall within 1 standard deviation, or between a size 6 and a size 9. What is the standard deviation of the shoe size data for the math class? 1. 5 2. 7 3. 0 3. 8.
Answer: 1.5
Step-by-step explanation:Let the standard deviation of the shoe size be represented by ' ' and the mean shoe size be represented by ' = 7.5'. Also, the sizes of the shoe be represented by ' '. So, . Hence, the standard deviation of the shoe size data for the math class is 1.5.
Q5 A and B
Unsure of how to go about this.
Thanks :)
Answer:
Step-by-step explanation:
the given angle measurments are x, (x + 18), and 2(x - 5)
knowing that the angles add up to 180, you can write the equation:
x + (x + 18) + 2(x - 5) = 180
Then you solve the equation
so our equation is:
x + x + 18 + 2(x - 5) = 180
*combine like terms
2x + 18 + 2(x - 5)
*distribute the 2
2x + 18 + 2x - 10
* combine like terms
4x + 8 = 180
* subtract 8 from both sides
4x = 172
* divide both sides by 4
x = 43
so knowing that x is 43, we can plug that in to the original given angle measurements:
the top angle which was x + 18 becomes 43 + 18, or 61
the bottom right angle was 2(x - 5), now it's 2(43 - 5) or 2(38) which is 76
and the other one was x so it's 43 degrees
We can check our work by adding them together.
61 + 76 + 43 = 180
they equal 180 as the angles of a triangle should.
Note: most of these numbers should have degree symbols, but I don't know how to type that.
Find the value of x.
Answer:
x= 20
Step-by-step explanation:
The total amount of degrees in a triangle is 180. The equation we can pull from this is x+x+30+110= 180. Now we can simplify and combine like terms. x+x= 2x. 30+110 is 140. Now move the constant, 140 to the right. 180-140 is 40. Lastly, divide x and 40 by 2 to get the final answer of 20.
If you shift the exponential parent function, f(x) = 2^x , right 2 units, what is the equation of the new function?
Answer:
[tex]g(x)=2^{x-2}[/tex]
Step-by-step explanation:
Translations
For [tex]a > 0[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=2^x[/tex]
Translated 2 units right: [tex]g(x)=f(x-2)=2^{x-2}[/tex]
We know the rule for shifting right(x is changed)
f(x) —» f(x-a)So
here
For a =2
f(x-2)[tex]\sf 2^{x-2}[/tex]Cost of a CD: $23.50
Markup: 63%
Discount: 50%
You and your sister have been saving and decide to buy a Playstation 5 together. You need $500 to
buy the Playstation. Together you have $850 saved up. Since you have more money, you contribute
50% of your savings and your sister contributes 75% of hers toward the $500 cost. How much do each
of you have saved individually?
a. Write a system of equations in standard form to model this situation
b. Solve this system of equations using eliminations
According to the information given, we have that:
a) The system of equations is given by: x + y = 850, 0.5x + 0.75y = 500.
b) You has saved $550 and your sister has saved $300.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: The amount you have saved up.Variable y: The amount your sister has saved up.Item a:
Together you have $850 saved up, hence:
x + y = 850.
You contribute 50% of your savings and your sister contributes 75% of hers toward the $500 cost, hence:
0.5x + 0.75y = 500.
Item b:
From the first equation, we have that:
x = 850 - y
Replacing on the second:
0.5(850 - y) + 0.75y = 500
0.25y = 75
y = 75/0.25
y = 300
x = 850 - y = 550.
You has saved $550 and your sister has saved $300.
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Need help in math ASAP
I need help with number 8….
Pls help
The equation properties are:
The distributive propertyThe associative property.The associative property.How to determine the properties?
The equations are given as:
3 * (6 + 2) = 3 * 6 + 3 * 25 * (7 * 8) = (7 * 5) * 85 * 3 * 7 = 7 * 3 * 5The distributive property of an equation states that:
a * (b + c) = ab + ac
This means that 3 * (6 + 2) = 3 * 6 + 3 * 2 is represented by the distributive property.
The associative property of an equation states that:
a * (b * c) = (a * b) * c
This means that 5 * (7 * 8) = (7 * 5) * 8 and 5 * 3 * 7 = 7 * 3 * 5 are represented by the associative property.
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Find |27|.
27
-27
i don't get it.
Answer:
|27| is 27
Step-by-step explanation:
What are you trying to ask?
Answer:
27
Step-by-step explanation:
Always in absolute value, if the number inside it is negative it will be positive. But if a number is already positive it will stay positive. Absolute value is just another way of making things positive. So always nothing will ever be negative.
Find the product of (x + 3)(x - 3).
x^2 - 6x + 9
x^2 + 6x + 9
x^2 + 9
x^2-9
Step-by-step explanation:
So the question is easy ....the thing that you need to do is just to multiply the expression and organize the like terms....okay so lets solvee..
[tex](x + 3)(x - 3)[/tex]
Solution,
[tex] = x(x - 3) + 3(x - 3)[/tex]
[tex] = {x}^{2} - 3x + 3x - 9[/tex]
[tex] = {x}^{2} - 9[/tex]
Bobby has a party while his parents are away for the weekend. Bobby estimated that if his 9 friends hep him to clean the house, they will finish in time if they start 8 hours before his parents return. But after only two hours of cleaning, Bobby's parents call and say they are just two hours from home. How many more friends does Bobby need to call to help finish cleaning in time.
Bobby will need additional 20 friends to help finish cleaning in time.
Rate at which Bobby and his 9 friends are workingThe rate at which Bobby and his 9 friends are cleaning the house is determined as follows;
10 person ------> 8 hours
1 person -------->?
= 10 x 8 = 80 hours/person
When the parents are 2 hours from the house, Bobby will more friends working at the same rate to complete it in 2 hours time.
During this period Bobby and his friends have worked for 2 hours remaining 6 hours.
New rate;
10 person ------> 6 hours
1 person -------->?
1 person = 10 x 6 hrs = 60 hours per person
Total persons that will do the same work in 2 hours2 = 60/x
x = 60/2
x = 30 persons
Thus, Bobby will need additional 20 friends to help finish cleaning in time.
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PLEASE SOMEONE HURRY I NEED THE ANSWER PLS
7. After washing your hands there are 300 bacteria on your right hand. The amount of bacteria on each of
your hands is doubling each hour. When will the amount of bacteria on your right hand exceed 2000?
A) 2 hours
B) 2½ hours
C) 3 hours
D) 3½ hours
Answer: maybe c?
Step-by-step explanation:
Uh, 300+300 = 600
600+600= 1200
1200+ 1200= 2400
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in a table, shown above. Use technology to find the equation of the least squares regression line. Then use the regression equation to predict the number of cans sold on a day that is 90*F Round your answer to the nearest whole number.
The regression equation to predict the number of cans sold on a day that is 90°F will be 871.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.
Then the regression line will be passing through (55, 340) and (84, 780). Then we have
y - 340 = 15.17(x - 55)
Then the regression equation to predict the number of cans sold on a day that is 90°F will be
y - 340 = 15.17 (90 - 55)
y = 871
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Help please..........................................................
Answer:
A) YXWZ
Step-by-step explanation:
W) 57.4*10^4 = 574 000
X) 5.11*10^5 = 511 000
Y) 0.17*10^6 = 170 000
Z) 7.3*10^5 = 730 000
Y, X, W, Z: A
Four circles, each with a radius of 2 inches, are removed from a square.
Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square?
(16 – 4π) in.2
(16 – π) in.2
(64 – 16π) in.2
(64 – 4π) in.2
Given:
Given that the radius of the circle is 2 inches.
We need to determine the area of the remaining square.
Area of a square:
Given that each circle has a radius of 2 inches.
Then, the diameter of each circle is 4 inches.
Hence, the side length of the square is 2 × 4 = 8 inches.
The area of the square is given by
[tex]A=s^2[/tex]
[tex]A=8^2[/tex]
[tex]A=64[/tex] [tex]in^2[/tex]
Thus, the area of the square is 64 square inches.
Area of the four circles:
The area of one circle is given by
[tex]A=\pi r^2[/tex]
Substituting r = 2, we have;
[tex]A=4\pi[/tex]
Thus, the area of one circle is 4π in²
The area of 4 circles is 4 × 4π =16π in²
Hence, the area of the 4 circles is 16π in²
Area of the remaining square:
The area of the remaining square is given by
Area = Area of the square - Area of four circles.
Substituting the values, we get;
[tex]Area=64-16\pi[/tex]
Thus, the area of the remaining square is (64 - 16π) in²
Hence, Option c is the correct answer.
Answer:
C. (64 – 16π) in.2
Step-by-step explanation:
X is greater than or equal -3 and less than 5
use x only once in your inequality
Answer:
[tex] - 3 \leqslant x \leqslant 5[/tex]
Ruby owns a small business selling bagels. She knows that in the last week 4
customers paid cash, 10 customers used a debit card, and 74 customers used a credit
а
card.
If next week, she is expecting 1600 customers, about how many would you expect to
pay with cash? Round your answer to the nearest whole number.
Answer:
73 people
Step-by-step explanation:
4/10/74=88
1600/88=18.18
18.18 x 4= 73
18.18 x 10= 182
18.18 x 74= 1345
Answer: 73
Step-by-step explanation:
What is the value of x?
99°
35°
81
55
46
134
Answer: 46
Step-by-step explanation:
The angles add to form a straight angle, so x+99+35=180. It follows that x=46.
Find the quotient
5,103 divided by 54
Answer:
94.5 is your answer bc u have to divide to get your answer for your thing
2 + 5^2 / (30 - 5) + 3
2 + 5^2 / (30 - 5) + 3 = 6
---
Hope this helps! :)
Solve the equation. 4y = 12
Answer:
y = 3Step-by-step explanation:
Given equation:
4y = 12To solve the equation, the L.H.S must be equivalent to the R.H.S. To prove that L.H.S is equivalent to R.H.S, we have to know the value of "y".
The value of the y variable can be found by isolating the variable from its coefficient. In this equation, the y-variable can be isolated by dividing both sides by four. This cancels the coefficient, isolating the y-variable on one side of the equation.
⇒ 4y = 12⇒ 4y/4 = 12/4 (Dividing both sides by 4)Once the y-variable has been isolated, we can simplify the other side of the variable. The expression/variable/number obtained, on the other side of the equation, is the value of the y-variable.
⇒ y = 12/4 (Isolating the y-variable)⇒ y = 3 (Simplifying the R.H.S)Therefore, the value of y is 3.
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Hey there!
4y = 12
DIVIDE 4 to BOTH SIDES
4y/4 = 12/4
SIMPLIFY IT!
y = 12/4
y = 3
Therefore, the answer should be: y = 3
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Please help! I asked this question the other day and nobody even looked at it. I need help!!!!
30 points see picture below
Answer:
6912cm³
Step-by-step explanation:
volume is equal to length multiplied by width multiplied by height so if we multiply the three it will give us a volume of 6912cm³
Answer:
a) 6912 cm³
b) 192 cm³
Explanation:
Volume of rectangular prism = Length × Width × Height
Part A
Here Volume: 32 × 72 × 3 = 6912 cm³
∴ The volume of the chocolate slab is 6912 cm³.
Part B
total volume ÷ total students = 6912 ÷ 36 = 192 cm²
Each student receives 192 cm³ of chocolate.
Help me solve the volume for the sphere?
Answer:
38.77 yd³
Step-by-step explanation:
The volume of the sphere can be determined by using the formula 4πr³/3.
[Where "r" is the radius of the circle].
We are given that:
Radius of circle = 2.1 yd
When we substitute the radius in the formula, we get;
⇒ 4 × π × (2.1)³/3
Let π be substituted as 3.14. Then;
⇒ 4 × π × (2.1)³/3
⇒ 4 × (3.14) × (2.1)³/3
When evaulating the cube of 2.1, we get;
⇒ 4 × (3.14) × (2.1)³/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
When simplified, we get;
⇒ 4 × (3.14) × (2.1) × (2.1) × (2.1)/3
⇒ 4 × (3.14) × (2.1) × (2.1) × (0.7)
⇒ 4 × (3.14) × (4.41) × (0.7)
⇒ (12.56) × (4.41) × (0.7)
⇒ 38.77272 ≈ 38.77 yd³ (Rounded to nearest hundredth)
Therefore, the volume of the sphere is 38.77 yd³.
