The product of 76 and 6.0 × 10² is 45,600, and when expressed in scientific notation, it is 4.56 × 10⁴.
To find the product of 76 and 6.0 × 10², we need to multiply these two numbers together. First, let's rewrite 6.0 × 10² in decimal form. In scientific notation, the number 6.0 × 10² means 6.0 multiplied by 10 raised to the power of 2.
10 raised to the power of 2 means multiplying 10 by itself twice: 10 × 10 = 100. Therefore, 6.0 × 10² can be rewritten as 6.0 × 100.
Now, we can find the product by multiplying 76 and 6.0 × 100:
76 × 6.0 × 100 = 456 × 100
To multiply 456 by 100, we move each digit of 456 two places to the left, which is equivalent to multiplying by 100. This gives us:
456 × 100 = 45,600
So, the product of 76 and 6.0 × 10² is 45,600.
In our case, the product is 45,600. To express this in scientific notation, we need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we move the decimal point four places to the left:
45,600 = 4.56 × 10⁴
Therefore, the product of 76 and 6.0 × 10² expressed in scientific notation is 4.56 × 10⁴.
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Okay can someone explain this?
Answer:
see below
Step-by-step explanation:
90 degree clockwise will change x, y coordinates to y, -x
point D 1,3 becomes 3,-1
point E 4, 4 becomes 4,-4
point F 4, -2 becomes -2,-4
point G 1,-1 becomes -1, -1
This question has two parts. Use the information to answer Part A and Part B.
Part A
Enter a number in the box to create an expression equivalent to 2-5.
Part B
Which expressions represent the distance between the two points on the
number line? Select all that apply.
A 2-5
B. 2+(-5)
c. 1-3-21
D. 12-(-3)
E. 1-3+(-2)|
OF. 1-3-(-2)
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
What is integers on number line?
Integers are represented using a number line. A straight line of numbers is shown visually as a number line. It is made up of positive integers like 1, 2, etc., negative integers like - 1, - 2, etc., and a zero that is neither positive nor negative.
Part A:
2 - 5 = -3
2 + 1 = 3
The distance on the number line between a number and 0 is its absolute value.
a. That distance is never negative.
b. The symbol for Absolute Value is “ | | ”.
Hence, by taking 1 in the box it creates an expression equivalent to 2 - 5.
Part B:
|-3 -2| = 1
This point represent distance from -3 to -2 on the number line is 1 unit.
|2-(-3)| = 5
This point represent distance from 2 to -3 on the number line is 5 units.
|-3 + (-2)| = 5
This point represent distance from -3 to -2 on the number line is 5 units.
|-3 - (-2)| = 1
This point represent distance from -3 to -2 on the number line is 1 units.
Therefore,
Taking 1 in the box it creates an expression equivalent to 2 - 5.
The expressions represent the distance between the two points on the
number line are |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)| etc.
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The inequality |2x - 5 > 8 can be written as which two inequalities?
Answer:
2x - 5 < -8 or 2x - 5 > 8
Step-by-step explanation:
|2x - 5| > 8
2x - 5 < -8 or 2x - 5 > 8
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
We have,
To split the inequality |2x - 5| > 8 into two separate inequalities, we consider both the positive and negative cases for the absolute value expression.
Positive case:
When 2x - 5 is positive, we have:
2x - 5 > 8 _____(1)
Negative case:
When 2x - 5 is negative, we have:
-(2x - 5) > 8
Simplifying the negative case:
-2x + 5 > 8 ______(2)
Now, we have two inequalities:
2x - 5 > 8
-2x + 5 > 8
These are the two inequalities resulting from the given inequality
|2x - 5| > 8.
Thus,
The two inequalities that can be written from the |2x - 5| > 8 are:
2x - 5 > 8
-2x + 5 > 8
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Can someone help me please
Please help I don’t know if I’m doing this correctly
Answers:
Exponential and increasingExponential and decreasingLinear and decreasingLinear and increasingExponential and increasing=========================================================
Explanation:
Problems 1, 2, and 5 are exponential functions of the form [tex]y = a(b)^x[/tex] where b is the base of the exponent and 'a' is the starting term (when x=0).
If 0 < b < 1, then the exponential function decreases or decays. Perhaps a classic example would be to study how a certain element decays into something else. The exponential curve goes downhill when moving to the right.
If b > 1, then we have exponential growth or increase. Population models could be one example; though keep in mind that there is a carrying capacity at some point. The exponential curve goes uphill when moving to the right.
In problems 1 and 5, we have b = 2 and b = 1.1 respectively. We can see b > 1 leads to exponential growth. I recommend making either a graph or table of values to see what's going on.
Meanwhile, problem 2 has b = 0.8 to represent exponential decay of 20%. It loses 20% of its value each time x increases by 1.
---------------------
Problems 3 and 4 are linear functions of the form y = mx+b
m = slope
b = y intercept
This b value is not to be confused with the previously mentioned b value used with exponential functions. They're two different things. Unfortunately letters tend to get reused.
If m is positive, then the linear function is said to be increasing. The line goes uphill when moving to the right.
On the other hand if m is negative, then we go downhill while moving to the right. This line is decreasing.
Problem 3 has a negative slope, so it is decreasing. Problem 4 has a positive slope which is increasing.
Given the function f(x) = -x - 3x², find the value of f(1/2) in simplest form.
Answer:
-5/4
Step-by-step explanation:
To evaluate the function, put the value of the argument where the variable is and do the arithmetic.
Function evaluationf(x) = -x -3x²
f(1/2) = -(1/2) -3(1/2)² = -1/2 -3(1/4) . . . . . use 1/2 in place of x
f(1/2) = -2/4 -3/4 = -5/4
The value in simplest form is ...
f(1/2) = -5/4
A balloon attached to an atmospheric data-gathering device must be at least 1000 m high to begin recording information. Two spotters, Mary and Nathan, walk the same distance from the launch site at an angle of 70° to each other until they are 225 m apart. From these positions, they watch the rise of the balloon with instruments that record the angle of elevation. What angles of elevation must the instruments record in order for the balloon to be at the correct height for atmospheric data gathering?
The angle of elevation that the instruments have to record to be at the correct height is given as 79°
How to solve for the angle of elevationWe have 2x + 70 = 180
We have to find the value of x
2x = 110
x = 55
y/sin x = 225/sin70
This is the use of sine rule
From here we would have
y = 225(sinx/sin70)
Remember x = 55
y = 225(sin55/sin70)
y = 196.1378
tanθ = 1000/y
tan θ = 1000/196.1378
tanθ = 5.098
θ = tan⁻¹5.098
= 78.90°
Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.
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University Data
Receiving
Not Receiving
Total
Financial Aid
Financial Aid
Undergraduates
4222
3898
8120
Graduates
1879
731
2610
Total
6101
4629
10730
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [ ? ]%
Answer:
[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]
help me please please please
The area and circumference of a circle are 12.56square feet and 12.56ft respectively
Area and circumference of a circleThe formula for calculating the area and circumference of a circle is expressed as:
A = πr²
C = πd
where
r is the radius and d is the diameter
Area = 3.14 * (2)²
Area = 12.56ft²
For the circumference
C = 3.14(4)
C = 12.54ft
Hence the area and circumference of a circle are 12.56square feet and 12.56ft respectively
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Which equation can be simplified to find the inverse of y = 2x²?
0-2x²
O
y-1x²
O -y = 2x²
O x = 2y²
O
Answer:
D.) x = 2y²
Step-by-step explanation:
You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.
As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]
When Roberto got a puppy from the shelter, it weighed 10.5Ibs. The puppy gained 40% of its original weight in the first month that Roberto had him. How much did the puppy weight after the first month?
Please help its confusing meeeeee
Answer:
p = 21.4 cm
∠P = 44°
Step-by-step explanation:
Apply the Pythagorean Theorem to solve for the length of p.
p² + 21² = 30²p² = 900 - 441p² = 459p = √459[tex]\fbox {p = 21.4 cm}[/tex]Now, take the inverse sine function to find angle P :
sin⁻¹ (opposite side / hypotenuse)sin⁻¹ (21/30)sin⁻¹ (0.7)[tex]\boxed {44^{o}}[/tex] (approximately)Answer:
a) 21.4 cm
b) 45.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between trig functions and sides of a right triangle. Here, two relevant function are ...
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
b) Angle PThe hypotenuse of the triangle, and the side adjacent to angle P are given, so we have ...
cos(P) = (21 cm)/(30 cm)
The angle value can be found using the inverse cosine function:
P = arccos(21/30)
P ≈ 45.6°
a) Side pNow, we know angle P and the side adjacent to it. We want to find the measure of side p, which is opposite the angle. This can be done using either the sine function or the tangent function. Here, we choose to use the tangent function.
tan(P) = p/21
p = 21×tan(P) = 21·tan(45.573°)
p ≈ 21.4 . . . . cm
__
Additional comment
In the attached, part of the calculator keypad is shown so you can see that the inverse cosine function is the 2ND function of the Cos key. The calculator mode is set to DEG (lower left of display) so that angles are in units appropriate to this problem.
Of course, you can always use the Pythagorean theorem to find the length of side p. More calculations are involved, so we used trig functions instead. Note that the angle P must be found first using the approach here, and its value must be retained with enough significant digits to ensure accuracy in the 'p' calculation.
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle A? Round your answer to the nearest whole number, if necessary.
a = 20 cm
b = 13 cm
C = 139°
Answers:
126°
16°
25°
38°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
What is the measure of angle A?Given that?
side a = 20cmside b = 13cmAngle C = 139°side c = ?Angle A = ?First, we determine the length of side c using the law of cosines.
c = √( a² + b² - 2ab( cosC ) )
We substitute in our values
c = √( 20² + 13² - 2×20×13( cos 139° ) )
c = √( 400 + 169 - 520( cos 139° ) )
c = √( 569 + 392.44898 )
c = √961.44898
c = 31 cm
Next, we find Angle A, using the law of cosines.
A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]
We substitute in our values
A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 ) ]
A = cos⁻¹[ ( 169 + 961 - 400) / 806]
A = cos⁻¹[ 730 / 806]
A = cos⁻¹[ 0.9057 ]
A = 25°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
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There are two numbers. One number is twice the other number. The difference of the smaller number and half the larger number is 20.
An equation created to find the smaller number will have_________
.
Step-by-step explanation:
x, y = 2 numbers
x = 2y
y - x/2 = 20
this is impossible to solve. there is no solution.
because the first equation tells us
y = x/2
and so the second equation is
x/2 - x/2 = 20
0 = 20
so, again, no solution.
OA=
What Is OA=
Help me please!!! Thanksss
The length of side OA in the given rhombus is: 5 units.
What is a Rhombus?A rhombus is a quadrilateral that has four sides that are all of the same length. Therefore, in the image given, the length of AB equals the length of OA.
Given the following:
A(3, 4)B(8, 4)Length of AB = |8 - 3}
Length of AB = 5 units.
AB = OA = 5 units.
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show the height of the pyramid is 9 cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let us assume that the pyramid has a volume of 75 cm³ and square base area of 25 cm², hence:
Volume = (1/3) * area of base * height
75 = (1/3) * 25 * height
height = 9cm
The height of a pyramid with volume of 75 cm³ and square base area of 25 cm², is 9 cm
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There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat.
Probability that a card selected at random is purple = 7/25
Probability of random selectionNumber of red cards, N(red) = 12
Number of blue cards, N(blue) = 17
Number of purple cards, N(purple) = 14
Number of yellow cards, N(yellow) = 7
Total number of cards, N(total) = 12 + 17 + 14 + 7
N(total) = 50
Probability that a card selected at random will be purple
P(purple) = N(purple) / N(total)
P(purple) = 14/50
Reduce to the lowest fraction
P(purple) = 7/25
Therefore, probability that a card selected at random is purple = 7/25
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Complete Question
There are 12 red cards, 17 blue cards, 14 purple cards, and 7 yellow cards in a hat. If a card is selected at random, what is the probability that the card is purple
The graphs of f(x) = 5x and its translation, g(x), are
shown on the graph.
30 Iv
25-
20
15
10 1.5
g(x)
f(x)
65432 15.
10:
-15-
20
-25
-30
(0,
51
(2,25)
(2, 15)
2 3 4 5
(0, -9)
(1,-5)
X
What is the equation of g(x)?
g(x) = 5x-9
g(x) = 5x-10
g(x) = 5-9
Og(x) = 5* - 10
Answer: [tex]g(x)=5^x - 10[/tex]
Step-by-step explanation:
g(x) is the graph of f(x) translated 10 units down.
Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 x + 2 B. y ≥ 2 x + 2 C. y < 2 x + 2 D.
Considering the given linear function, the inequality graphed is:
B. [tex]y \geq 2x + 2[/tex].
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:
m = (4 - 2)/(2 - 1) = 2.
Thus the equation of the line is:
y = 2x + 2.
The left-side of the line is the values above the line, hence the inequality is:
B. [tex]y \geq 2x + 2[/tex].
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Question 15 of 46
Which of the following statements about the polynomial function
F(x) = 2x³ - 2x² +1 is true?
The given polynomial function has 1 relative minimum and 1 relative maximum.
What are the relative minimum and relative maximum?The relative minimum is the point on the graph where the y-coordinate has the minimum value.The relative maximum is the point on the graph where the y-coordinate has the maximum value.To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)Calculation:The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
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EXTRA POINTS HELP ASAP!
x + x/3 = 4/9
solve for x
Answer:
x=1
Step-by-step explanation:
1 + 1/3 = 4/9
1/3 also equals 3/9
hope this helped :)
Answer :
Value of x is 1 / 3Step-by-step explanation :
>> (3 × x + x / 3) = 4 / 9
>> (3x + x / 3) = 4 / 9
>> (4x / 3) = 4 / 9
>> 4x × 9 = 3 × 4
>> 36x = 12
>> x = 12 / 36
>> x = 6 / 18
>> x = 3 / 9
>> x = 1 / 3
Can someone help me please
Answer:
1/9, 3, 27
(A / the first option listed)
Step-by-step explanation:
Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression
first,
x = -2
3ˣ → 3⁻²
when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:
3² = 3 · 3 = 9
so, 3⁻² = [tex]\frac{1}{9}[/tex] (1/9)
next,
x = 1
3ˣ → 3¹
now, here we have something raised to the power of 1, which is always itself, so 3¹ = 3
(think of ^to the power of as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)
and finally,
x = 3
3ˣ → 3³
here, we can multiply 3 by itself 3 times:
3 · 3 · 3 = 27
so, 3³ = 27
[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}
So, our answers in order are:
1/9, 3, 27 (the first option listed)
hope this helps! let me know if I should clarify anything :)
Find the surface area of the composite solid. Round your answer to the nearest hundredth.
A. 424.11 ft²
B. 438.00 ft²
C. 449.00 ft²
D. 549.78 ft²
The surface area of the composite solid is 579.84 square feet
How to determine the surface area of the solid?The composite solid that completes the question is added as an attachment
From the attached figure, we have the following figures:
Rectangular prismCylinderThe surface area of a rectangular prism is
A = 2(lw + lh + wh)
Using the dimensions of the prism, we have:
A = 2(6 * 11 + 6 * 8 + 8 * 11)
This gives
A = 404
The surface area of a cylinder is
A = 2πr^2 + 2πrh
Using the dimensions of the cylinder, we have:
A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5
Evaluate
A = 226.08
The area of the circle between both shapes is
A = πr^2
This gives
A = 3.14 * 4^2
A = 50.24
The surface area of the composite solid is then calculated as:
Surface area = Area of rectangular prism + Area of cylinder - Area of circle
This gives
Surface area = 404 + 226.08 - 50.24
Evaluate
Surface area = 579.84
Hence, the surface area of the composite solid is 579.84 square feet
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The length of each edge of a cube is decreased by $40\%$. By what percent does the volume of the cube decrease
1. What is the value of the 4th iterate of
f(x) = 3x-1/x2 if x0 = -2? Round to three decimal places.
The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
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This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
Select the correct answer. What is the solution to the equation? -2√x+4=-12 A. 4 B. 8 C. 16 D. 64
Answer:
d. 64
Step-by-step explanation:
x^1/2 = 8
Square each side
(x^1/2 )^2=( 8)^2
x = 64
im new to algebra, so most of the stuff im writing here is basic stuff.
8x=24
4x=9
Answer:
x = 3, x = 9/4
Step-by-step explanation:
8x = 24
x = 3 Divide both sides by 8.
4x = 9
x = 9/4 Divide both sides by 4.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1.}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{8x = 24}[/tex]
[tex]\huge\textbf{Divide \boxed{8} to both sides:}[/tex]
[tex]\mathsf{\dfrac{8x}{8} = \dfrac{24}{8}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{24}{8}}[/tex]
[tex]\mathsf{x = 3}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x =}\frak{\ 3}}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{4x = 9}[/tex]
[tex]\huge\textbf{Divide \boxed{9} to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{9}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{9}{4}}[/tex]
[tex]\mathsf{x = 2 \dfrac{1}{4}}[/tex]
[tex]\huge\textbf{Therefore, the answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = }\frak{\ \dfrac{9}{4}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Instructions: Find the missing side. Round your answer to the nearest tenth.
X
-
16
65⁰
X
Answer:
Maybe the answer must be 90°
Now simplify the y-terms to get the equation of the parabolic path. You do not need to expand the x-term. (2 points) Hint: Square both sides to get rid of the square roots
The simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
How to determine the simplified equation?The complete question is added as an attachment
The equation is given as
[tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex]
Subtract (x - 10)^2 from both sides
[tex](y- 6)^2 = 4^2 - (x - 10)^2[/tex]
Evaluate 4^2
[tex](y- 6)^2 =16 - (x - 10)^2[/tex]
Take the square root of both sides
[tex]y- 6= \sqrt{16 - (x - 10)^2}[/tex]
Add 6 to both sides
[tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
Hence, the simplified equation of [tex](x - 10)^2 + (y- 6)^2 = 4^2[/tex] is [tex]y = 6+ \sqrt{16 - (x - 10)^2}[/tex]
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