To put the given equation of a sphere in standard form, complete the square for x, y, and z, and combine constant terms on the right side. The standard form of the sphere's equation is (x + 2)2 + (y - 3)2 + (z - 3)2 = 28, with a center at (-2, 3, 3) and a radius of √28.
Explanation:To write the equation of the sphere in standard form, we will complete the square for the x, y, and z terms in the given equation x2 + y2 + z2 + 4x − 6y − 6z = −6.
First, we organize the variables and separate the constants:
x2 + 4x + y2 - 6y + z2 - 6z = -6
We then complete the square for each variable by adding and subtracting the square of half the coefficient of the linear term:
x2 + 4x + 4 - 4 + y2 - 6y + 9 - 9 + z2 - 6z + 9 - 9 = -6
Now we can rewrite this as:
(x + 2)2 - 4 + (y - 3)2 - 9 + (z - 3)2 - 9 = -6
Combining the constant terms on the right side we get:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 4 + 9 + 9 + 6
Which simplifies to:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 28
The sphere's center is located at (-2, 3, 3) and has a radius of √28. In standard form, the equation of the sphere is:
(x + 2)2 + (y - 3)2 + (z - 3)2 = 28
Which expression illustrates the associative property of addition?
A. (3 + 19) – 12 = (3 + 12) – 19
B. 3 + (19 – 12) = 3 + (19 + 12) (Not B)
C. (3 + 19) – 12 = 3 + (19 – 12)
D. 3 + (19 –12) = 3 – (19 + 12)
Answer:
C.(3+19)-12=3+(19-12)
Step-by-step explanation:
We have to find an expression which illustrate the associative property.
We know that associative property of addition of three numbers a, b and c
[tex]a+(b+c)=(a+b)+c[/tex]
A.(3+19)-12=(3+12)-19
(3+19)-12=10
(3+12)-19=-4
It is not associative property of addition because both sides are not equal.
B.3+(19-12)=3+(19+12)
3+(19-12)=10
3+(19+12)=34
It is false because both sides are not equal .
C.(3+19)-12=3+(19-12)
(3+19)-12=10
3+(19-12)=10
It is illustrate the associative property of addition.
D.3+(19-12)=3-(19+12)
3+(19-12)=10
3-(19+12)=-28
Both sides are not equal . Hence , it is false.
Lori makes $64,000 each year as an accountant. At Christmas she was given a 12% bonus. What was Lori's total income for the year?
12% = 0.12
64000 x 0.12 = 7680
64000 + 7680 = $71,680
Write an equation for the line, given that m=3 and the y-intercept is (0,2)
Answer:
The equation of required line is y=3x+2.
Step-by-step explanation:
The slope intercept form of a line is
[tex]y=mx+b[/tex] ..... (1)
where, m is slope and b is y-intercept.
We need to find the equation of line whose slope is m=3 and the y-intercept is (0,2).
Substitute m=3 and b=2 in equation (1), to find the equation of required line.
[tex]y=(3)x+(2)[/tex]
[tex]y=3x+2[/tex]
Therefore the equation of required line is y=3x+2.
The equation for the line hose gradient/slope is 3 and a y-intercept of (0, 2) is y = 3x + 2
Further Explanation Equation of a straight line Equation of a straight line is written in the form y=mx+ c, where m and c are numbers. m is the gradient of the line while c is the y-intercept.
Equation of a straight line can be found when given:
A slope of the line and one point where the line is passing through Two points where the line is passing through A slope of the line and the y-intercept Double intercept When an equation of a straight is written in the form of x/a + y/b = 1 Where a is the x-intercept and b is the y-interceptIn this case;
The equation of the straight line with gradient m, passing through a point (x1,y1) is
y-y1 = m(x-x1)
We are given the y-intercept as (0, 2) and the slope is 3
Therefore;
To get the equation, we take another point (x,y)
(y-2)/(x-0) = 3
y-2 = 3x
y= 3x + 2
Keywords: Equation of a straight line, y-intercept,
Learn more about: Equations of a straight line: https://brainly.com/question/11828095 Slope of a straight line: https://brainly.com/question/13060178
Level: High school
Subject: Mathematics
Topic: Equation of a straight line
If p: It is not cold. What is ~ p?
it is cold
it is mildly cold
it depends
none of the above
Answer:
"it is cold"
Step-by-step explanation:
Michelle listed her three children as equal beneficiaries on her life insurance policy. If she has a $400,000 policy, how much will each receive in the event of her death?
The beneficiaries received by each of Michelle children is $133333.3.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Michelle listed her three children as equal beneficiaries on her life insurance policy.
Here, insurance amount received by each is
400000/3
= $133333.3
Therefore, the beneficiaries received by each of Michelle children is $133333.3.
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Final answer:
Each of Michelle's three children would receive $133,333.33 from her $400,000 life insurance policy if they are listed as equal beneficiaries.
Explanation:
Michelle has a $400,000 life insurance policy and has listed her three children as equal beneficiaries. To calculate how much each child will receive in the event of her death, we divide the total policy amount by the number of beneficiaries.
$400,000 ÷ 3 = $133,333.33
Therefore, each child would receive $133,333.33 from the life insurance policy. In this scenario, the division of the life insurance policy ensures an equal distribution among Michelle's three children, with each child entitled to $133,333.33. This approach maintains fairness in the allocation of the financial benefit, aiming to provide an equitable share to each beneficiary.
In ABC, C is a right angle, what is the measure of x?
A. 22.4°
B. 67.6°
C. 20.9°
D. 69.1°
B is the right answer
Answer:
Option B. 67.6°
Step-by-step explanation:
In the given triangle ABC angle C is the right angle, side AB = 21 and side AC = 8.
We have to find the measurement of angle A.
Now from cosine rule we can write
[tex]CosA = \frac{Base}{hypotenuse}[/tex]
Here Base in the corresponding side of the angle A that is 8 and hypotenuse is 21.
Now we put the values
Cos x = 8/21 = 0.3809
[tex]x=cos^{-1}0.3809[/tex]
Or x = 67.61°
Therefore measurement of angle A or x = 67.6° is the answer.
Can you can help me with 6.7 round the decimal the nearest whole number
the number to the right of the deciml point, 7 is greater than 4, so the number would be rounded up
so 6.7 would round to 7.0
How many terms are in the expression shown below?
a2 - ab + 8b + b2 - 1
2
3
4
5
The difference of the squares of twenty and thirteen.
put in numerical form
The difference between the squares of twenty and thirteen will be 234.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
Square of twenty = 20²
20² = 20 × 20 = 400
Square of thirteen = 13²
13² = 13 × 13 = 169
Difference ⇒ 400 - 169 = 231.
Hence "The difference between the squares of twenty and thirteen will be 234".
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I've been trying to solve this, but I have no idea how.
-1/2x + 3 = -x + 7
what is the property of 7(3+4y)=21+28y
One third of a number is three more than one fourth the same number. What is the number.
One moving company charges $800 plus $16 per hour. another moving company charges $720 plus $21 per hour. at what number of hours will the charge be the same and what is the charge?
in the chorus there is 12 more girls than boys there 32 students in the chorus how many boys are there and how many girls are there
Julie is selling candy bars to raise money for new band uniforms. Candy bar x sells for $2 and candy bar y sells for $3. The number of y candy bars Julia sells must be greater than or equal to three times the number of x candy bars she sells. She has at most 36 candy bars to sell. What is the maximum revenue she can make? $36 $99 $108 $216
Correct Answer.
$36
$99 <---
$108
$216
40 POINTS
Which ordered pair is a solution to the system of inequalities?
Check image below.
solve for the 2nd equation with the answers:
A. 1+3 =4 ( not less than 4)
B. 0+4 = 4 ( not less than 4)
C. -3 + 5 = 2 ( less than 4) & y is >-2
D. -2 +-3 = -5 ( less than 4) but -3 is <-2
so answer is C
one serving of granola provides 4% of the protien you need daily. you must get the remaining 48 grans of protien fron other scources. how many grams of protein do you need daily?
Find the coordinates of the missing endpoint if B is the midpoint of AC. C(-5,4), B(-2,5) I need the steps and answer pls and ty
The coordinates of the missing endpoints (1,6) and can be determined by using the midpoint formula.
Given :
B is the midpoint of AC. Points -- C(-5,4), B(-2,5)The following steps can be used in order to determine the coordinates of the missing endpoint:
Step 1 - According to the given data, points C(-5,4) and B(-2,5).
Step 2 - The mid-point formula is given below:
[tex]\rm x = \dfrac{x_1+x_2}{2}[/tex]
[tex]\rm y = \dfrac{y_1+y_2}{2}[/tex]
Step 3 - Let the endpoint be (x,y).
Step 4 - Now, substitute the values of the points in the above formula.
[tex]\rm -2= \dfrac{-5+x}{2}[/tex]
[tex]\rm 5 = \dfrac{4+y}{2}[/tex]
Step 5 - Simplify the above expression.
x = 1
y = 6
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I really need help with #4
How to do the how long will it take two people to paint a room problem?
write an expression to model the following phrase an hourly wage of 13.50 plus a 75 bonus
The tangent of a 45 degree angle is _____.
1
0
1/2
-1
Reduce to simplest form.
3 6/2 × 2 4/5
2 5/6 × 2 7/9
2 2/5 × 4 3/4
1/2 × 3
19/20 × 14
3/8 ×21
3/8 ×12
Shannon wants to buy cupcakes for her friend's birthday party. The bakery she goes to sells cupcakes for $3.50 each. The bakery also sells gift cards for $2.00, and Shannon decides to buy one card. If Shannon buys 10 cupcakes, how much money does she spend at the bakery?
square root of 4x squared times square root of 20x squared
The expression -50 + 100 represents the balance in dollars of a bank account after X months what is the rate of change in dollars per month of the bank account balance
Yup the answer is -50 give the other person brainly they deserve it
Enter the solution to the inequality in the box.
8+4(x−3)+3x≤24
Answer: The required solution is [tex]x\leq4.[/tex]
Step-by-step explanation: We are given to solve the following inequality :
[tex]8+4(x-3)+3x\leq24~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given inequality, we must find the value of the unknown variable x.
From inequality (i), we have
[tex]8+4(x-3)+3x\leq24\\\\\Rightarrow 8+4x-12+3x\leq24\\\\\Rightarrow 7x-4\leq24\\\\\Rightarrow 7x\leq24+4\\\\\Rightarrow 7x\leq28\\\\\Rightarrow x\leq\dfrac{28}{7}\\\\\Rightarrow x\leq4.[/tex]
Thus, the required solution is [tex]x\leq4.[/tex]
If the product of two numbers is zero then at least one of the numbers must be zero
If the coefficient of static friction between the coffee cup and the roof of the car is 0.21, what is the maximum acceleration the car can have without causing the cup to slide? ignore the effects of air resistance.
28Students were surveyed and the results showed that of 18 of them loved to play video games what percentage of the students loved to play video game.