Answer:
answer is A
Step-by-step explanation:
because area of a rectangle is L × B
or length × width
since the length is expanded by x
10.5 (12x)
Answer:
Option C
Step-by-step explanation:
The original length of the room = 12 feet
After expansion, the new length = [tex](12 + x)[/tex] feet
Width of the room = 10[tex]\frac{1}{2}[/tex] feet = 10.5 feet
Area of a rectangle = Length × Width
The shape of the living room is a rectangle.
∴Area of living room = [tex](12 + x)[/tex] feet × [tex](10.5)[/tex] feet
[tex]= 10.5(12 + x)[/tex] square feet
Expand the brackets or parenthesis by applying the Distributive Law:
[tex]= (12)(10.5) + (10.5)(x)[/tex] square feet
= [tex](125 + 10x)[/tex] square feet
∴Option C
What is the positive solution to the equation 0= 1/4x^2-4
answers;
4
1
-1
-4
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \pm4[/tex]
[ but since we have been asked for positive solution, it will be 4 ]
Hence, the correct choice is : A.) 4
Please help with triangles
The value of x is given as follows:
x = 131º.
How to obtain the value of x?An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.
Hence the measure of the top angle of the bottom triangle is given as follows:
a = 180 - 98
a = 82.
The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence, considering that the sum of the measures of the internal angles of a triangle is of 180º, their measures are given as follows:
2b + 82 = 180
2b = 98
b = 49.
Considering the vertical angles, the base angles of the top triangle are given as follows:
b = 49.
Hence the value of x is given as follows:
x = 180 - 49
x = 131º.
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HELP..
Which of the following tables represents a linear function?
Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.
What is a linear equation?
A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form
y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Given are three tables in x and y and we have to find which table shows a linear relation.
We know in a linear relation between x and y the graph would be a straight line and also the slope would be constant
i.e. change of y/change of x for any pair in the table would be a constant.
Out of three tables given, only second table ( when we take the order from top to bottom )satisfies this.
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3 Find an equivalent expression to 3(4m2) - 2(m + 5).
Write your answer as an expression with two terms.
Show your work.
Answer:
PLS HELP DUE IN 20 MINS IM ALMOST DONE!!
Answer:
Step-by-step explanation:
its C
Answer:
(12m+10)(2m-2)
hope this helps
an inverse relationship is also called a: select one: a. direct relationship. b. negative relationship. c. proportional relationship. d. positive relationship.
An inverse relationship is also known as a negative relationship, because the correlation coefficient, is negative in an inverse relationship. Correct option is B.
An inverse relationship is a type of relationship between two variables in which they move in opposite directions. As one variable increases, the other variable decreases. In other words, when one variable changes, the other variable changes in the opposite direction.
For example, in the context of physics, the distance between two objects and the gravitational force between them have an inverse relationship. As the distance between the objects increases, the gravitational force between them decreases, and vice versa.
An inverse relationship is also known as a negative relationship. This is because the correlation coefficient, which measures the strength and direction of the relationship between two variables, is negative in an inverse relationship.
A correlation coefficient of -1 indicates a perfect inverse relationship, while a correlation coefficient of 0 indicates no relationship, and a correlation coefficient of 1 indicates a perfect positive relationship.
In contrast, a direct relationship, also known as a positive relationship, is a type of relationship between two variables in which they move in the same direction. As one variable increases, the other variable also increases, and vice versa.
In summary, an inverse relationship is a negative relationship in which two variables move in opposite directions, while a direct relationship is a positive relationship in which two variables move in the same direction.
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marvin the fly starts at $(0,0).$ each step, marvin moves one unit right or one unit up. he is trying to get to his home at $(4,6)$. however, at $(1,4),$ there is a frog that will eat him if he goes through that point. in how many ways can marvin reach his home?
There are 50 ways for Marvin to reach his destination without passing through the forbidden point.
To solve this problem, we can use the unitary method. This method involves breaking the problem down into smaller, simpler units to solve it more easily.
In this case, we can break the path from Marvin's starting point to his destination into two smaller paths. The first path is from (0,0) to (1,4), and the second path is from (1,4) to (4,6).
There are five paths from the bottom left corner to the point (1,4) that do not go through the forbidden point.
Once Marvin reaches the point (1,4), he can only go up or to the right to reach his destination. So, we need to count the number of ways to get from (1,4) to (4,6)
We can visualize this by drawing another grid and counting the paths:
In total, there are
=> 5 x 10 = 50
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PLEASE HELP!!
Jenna saves $2,500 per year in an account that earns 10% interest per year, compounded annually. Jenna will have (drop down menu - $411,235, $425,352, or $449,739)
30 years. Her account balance is a result of Jenna's (annuity payments or lump-sum payment)
In 30 years, the amount that Jenna will have is $411, 235
This account balance is as a result of Jenna's annuity payments.
How to find the amount ?The amount that Jenna's account will be worth in 30 years can be found by the future value of annuity formula which is :
= Annuity deposited periodically x Future value of annuity factor, 10 % , 30 years
Annuity deposited periodically = $ 2, 500
Future value of annuity factor = 164.49402268886
The value of the account balance will be:
= 2, 500 x 164.49402268886
= $411, 235
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Answer: $411,235, Annuity Payments
Step-by-step explanation:
I have took the test and know the answer is correct
ABCD is a rectangle with sides 8cm and 6cm PQRS is a rhombus
obtained by joining the midpoints of the sides of the rectangle. find
a)The lengths of the diagonals of PQRS?
b)The area of PQRS?
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
What is the area?Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.
Then the area of the rhombus is given as,
A = (Product of diagonal of rhombus) / 2
A = (8 x 6) / 2
A = 48 / 2
A = 24 square centimeters
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
The diagram is shown below.
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This next question is a little bit tricky, but keep in mind the Disney World / Bush Gardens example from the lectures.
What is the probability that someone uses a cell phone while driving or had no speeding violation?
Find the probability that someone uses a cell phone while driving, add to that the probability that someone did not receive a speeding violation, then subtract the value in the square where those two overlap.
Round your answer to the hundredths place.
The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.
To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.
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A Ferris wheel is 20 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. How many minutes of the ride are spent higher than 19 meters above the ground?
Rounded to the nearest minute, the answer is 12 minutes.
What do you mean by equation?The expressions can contain variables, constants, mathematical operations, and functions. An equation can be used to represent a relationship between two or more variables, and it is often used to solve problems by finding the values of the variables that satisfy the equation.
The radius of the Ferris wheel is half its diameter, which is 20/2 = 10 meters. When the Ferris wheel makes a full revolution, a person riding it will pass the loading platform twice: once on the way up and once on the way down. The highest point reached by the Ferris wheel is at the top, which is 10 + 1 = 11 meters above the ground.
To find out how many minutes of the ride are spent higher than 19 meters above the ground, we need to figure out at which times the rider is at or above this height. Let's call h(t) the height of the rider at time t. We know that h(t) is a sinusoidal function with a period of 10 minutes, an amplitude of 10 meters, and a vertical shift of 11 meters. In other words, we can write:
h(t) = 10 sin(2πt/10) + 11
To find out when h(t) is greater than 19, we solve the inequality:
10 sin(2πt/10) + 11 > 19
Subtracting 11 from both sides, we get:
10 sin(2πt/10) > 8
Dividing by 10, we get:
sin(2πt/10) > 0.8
The sine function is greater than 0.8 at two times in each period: once when it is increasing from 0.8 to 1, and once when it is decreasing from 1 to 0.8. We can find these times by solving the equations:
sin(2πt/10) = 0.8
sin(2πt/10) = -0.8
Using a calculator, we find that these equations have solutions at:
t = 1.167, 8.833, 3.5, 6.5
These times represent the four moments during the 10-minute period when the rider is at or above 19 meters. The first and fourth of these moments occur in the first half of the period, and the second and third occur in the second half.
Therefore, the total time spent higher than 19 meters is:
(8.833 - 1.167) + (6.5 - 3.5) = 11.6667 minutes
Rounded to the nearest minute, the answer is 12 minutes.
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12. If the point (3, -4) is rotated 90°
counterclockwise about the origin, what
are the new coordinates?
A. (-4,-3)
B. (4,3)
C. (-3,4)
D. (3,-4)
Answer:
(4,3)
Step-by-step explanation:
What are the factors of the cubic function f(x) = 64x³ + 27?
Choose each correct answer.
□ (16x² − 12x + 9)
□ (16x² + 12x +9)
□ (4x - 3)
□ (4x + 3)
The factors of the cubic function f(x) = 64x³ + 27 are (4x + 3) and (16x² − 12x + 9). The correct answer would be options (A), and (D).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original.
The cubic function is given in the question, as follows:
f(x) = 64x³ + 27
The above expression can be rewritten as:
f(x) = (4x)³ + (3)³
Compare the sum of cubic formula a³ + b³ = (a + b)(a² - ab + b²) and we get
f(x) = (4x + 3)(16x² − 12x + 9)
Thus, the factors of the cubic function are (4x + 3) and (16x² − 12x + 9).
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Aubrey bought stock in a company two years ago that was worth?
x dollars. During the first year that she owned the stock, it increased by 39%. During the second year the value of the stock increased by 16%. Write an expression in terms of ?
x that represents the value of the stock after the two years have passed
The expression that represents the value of the stock after two years in terms of x is 1.6144x
After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -
x + 0.39x = 1.39x
After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -
1.39x - 0.16(1.39x) = 1.16(1.39x)
Simplifying this expression, we get,
1.16(1.39x) = 1.6144x
Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.
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The complete question is -
Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.
if alpha and beta are the roots of the equation 6x2+x-2 find sum of the product, roots of the product
Answer:
-1/3
Step-by-step explanation:
Yhe equation 6x^2 + x - 2 has two roots, alpha and beta, that can be found by using the quadratic formula or by factoring.
The sum of the roots (alpha and beta) can be found by using the formula:
-b/a
where a = 6, b = 1 and c = -2
-1/6
The product of the roots (alpha and beta) can be found by using the formula:
c/a
where a = 6, b = 1 and c = -2
-2/6 = -1/3
So, the sum of the roots is -1/6 and the product of the roots is -1/3.
4. Astronomers have discovered a new constellation made up of Star A, Star B, and Star C that forms
a right triangle. The angle at Star A is 90 degrees. Star A and Star B are 50 lightyears apart, while
Star A and Star C are 120 lightyears apart. How many lightyears apart are Star B and Star C?
Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).
So, we have:
(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2
(Star B to Star C)^2 = 50^2 + 120^2
(Star B to Star C)^2 = 2500 + 14400
(Star B to Star C)^2 = 16900
Taking the square root of both sides:
Star B to Star C = √16900
Star B to Star C = 129 lightyears
So, Star B and Star C are 129 lightyears apart.
Step-by-step explanation:
A pole leans away from the sun at an angle of 7°
to the vertical, as shown in Figure 27. When the
elevation of the sun is 55°, the pole casts a shadow
42 feet long on the level ground. How long is the
pole? Round the answer to the nearest tenth.
Using trigonometric ratio, the height of the pole is approximately 60 feet
What is angle of elevationThe angle of elevation is the angle between the horizontal and a line from the observer to a point above the horizontal. In other words, it is the angle between the ground and the line of sight to an object above the ground.
Using trigonometric ratio to solve the angle of elevation problem, the height of the pole can be calculated using the tangent of the triangle.
tanθ = opposite / adjacent
tan 55 = x / 42
x = 42 * tan 55
x = 59.98 ft≅ 60 feet
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A scout troop raised money for a camping trip. They made a total of $1,498 at seven bake sales. They earned the same amount at each sale. Miguel thinks they made $215 at each bake sale. Explain why the amount Miguel said is reasonable. 1,498 ÷ 7 is about ÷ = and $215 is close to $
The actual amount of sale for each bake is $214. As Miguel said it is $215 which is very close to the actual amount, it is reasonable.
To determine if Miguel's estimate of $215 per bake sale is reasonable, we can start by calculating the average amount of money the scout troop made per bake sale. We do this by dividing the total amount they earned by the number of sales they had, as follows:
Total amount earned = $1,498
Number of bake sales = 7
Average amount earned per bake sale = Total amount earned ÷ Number of bake sales
= $1,498 ÷ 7
= $214
This calculation shows that the average amount the scout troop made per bake sale was $214. This means that if they had charged a consistent price for all of their baked goods at each sale, they would have made an average of $214 per sale.
Now, we can compare this average to Miguel's estimate of $215 per bake sale. Since his estimate is very close to the actual average, we can conclude that it is reasonable.
It is possible that the scout troop charged slightly different prices for their baked goods at each sale, which could explain the small discrepancy between the actual average and Miguel's estimate. However, given that the difference between the two values is only $1, it is likely that Miguel's estimate is a good approximation of the actual amount.
Moreover, it is reasonable to assume that the scout troop earned the same amount at each bake sale, especially if they had a set price for their baked goods.
If they had charged different prices at each sale, it would have been more difficult to estimate the average amount they earned per sale, and it would have been less likely that Miguel's estimate of $215 per bake sale would have been close to the actual average.
Therefore, based on the calculation and the context of the problem, we can conclude that Miguel's estimate of $215 per bake sale is reasonable.
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One fine day your dog buys 3 rawhide bones, 4 balls, and a squeaky toy at Woofville Mall. The next day he buys another ball and 2 more rawhide bones. Create an expression that represents the total cost.
5. To ship a package, UPS charges $4 for the first pound and $0.50 for each additional
pound. FedEx charges $6 for the first pound and $0.40 for each additional pound. How
many pounds will it take for UPS and FedEx to charge the same?
It will take 20 pounds for both charges to be the same.
What is linear equation?An equation containing variables with its highest power as one is called linear equation.
To ship a package,
UPS charges $4 for the first pound and $0.50 for each additional pound.
FedEx charges $6 for the first pound and $0.40 for each additional pound.
These can be written in the linear equation form as,
Let p be the pound charges by both UPS and FedEx,
then, 4+0.50p-------(1)
6+0.40p-----(2)
When the charges are same, (1)=(2)
4+0.50p = 6+0.40p
⇒0.10p=2
⇒p=20
Hence, this means that, it will take 20 pounds for both charges to be the same.
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Select all the statements that are true about rectangles
The statements that are true about rectangles are mentioned in options
A,B,C,E.
Rectangles -A shape with four sides and internal angles is a rectangle. The lengths of the other two sides are offset by two. The rectangle's diagonal sides are of identical length.
The opposite sides of a rectangle are equal and parallel to one another.
The diagonals cut each other in half, but not exactly.
All diagonals are the same length.
The rectangle's diagonals line up.
The total internal angles add up to the same value
Every internal angle has the same value.
A rectangle has congruent angles on all sides.
A rectangle's opposing angles are congruent.
We may thus infer that the statements about rectangles in the options are accurate based on the aforementioned features.
Q. Select all the statements that are true about rectangles.
A Diagonals are congruent.
B Diagonals bisect angles.
C Opposite angles are congruent.
D Diagonals are perpendicular.
E Diagonals bisect each other.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the function.
Match each transformation of f(x) with its description.
g(x) = 2x
g(x) = 8x
-
10
6
g(x)
f(x) = 2x - 6
= 2x - 2
g(x) = 8x 24
-
compresses f(x) by a factor
of toward the y-axis
shifts f(x) 4 units right
stretches f(x) by a factor
of 4 away from the x-axis
shifts f(x) 4 units down
g(x) = 2x - 14
g(x) = 82 - 4
The transformations are matched accordingly is given below.
What are the matching transformations?A function transformation takes whatever the underlying function f (x) is and "transforms" (or "equates") it, which is a fancy way of saying you alter the equation and shift the graph over.
Parent function is given as f(x) = 2x - 6
The transformations are shifts f(x) 4 units down
f(x) → f(x) - 4
⇒ g(x)= 2x - 6 - 4 = 2x - 10
Then stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x)
⇒ g(x) = 4(2x - 6) = 8x - 24
Now shifts f(x) 4 units right
f(x) → f(x - 4)
⇒ g(x) = 2(x - 4) - 6 = 2x - 14
To compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x)
⇒ g(x) = 2*4x - 6 = 8x - 6.
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Evaluate Ix+yl, for x = 8 and y=-15.
7
23
-7
-23
Answer:
A.7
Step-by-step explanation:
You first have to add 8 and -15
Then, find the absolute value
So, the answer is 7
graph the line. y=-1/5x+5
Answer:
I have graphed it and attached it in the explanation part.
Step-by-step explanation:
A data set has a correlation of -1.00. Explain what this correlation means (strong vs. weak; positive versus negative).
Answer:
A correlation of -1.00 indicates a strong negative correlation. This means that as one variable increases, the other variable decreases at a constant rate. In other words, there is a perfect inverse relationship between the two variables, with one increasing as the other decreases and vice versa. This is the strongest possible negative correlation.
The correlation coefficient ranges from -1 to 1, with -1 indicating a strong negative correlation, 0 indicating no correlation, and 1 indicating a strong positive correlation. Positive correlations indicate that as one variable increases, the other variable also increases. Negative correlations indicate that as one variable increases, the other decreases.
In summary, a correlation of -1.00 indicates a strong negative correlation, meaning that there is a perfect inverse relationship between the two variables.
If 8x+1=64, what is the value of 3²x+1 ?
Answer: 27
Step-by-step explanation:
8^x+1 = 64
8^x+1 = 8²
x+1 =2
x = 2 - 1
x = 1
To Find :
3^2x +1
Substitute the value of x :
3^2(1)+ 1
3^2+1
3^3
27
2 This table shows the relationship between
the total weight, w, in pounds, of a crate
containing t textbooks.
B
t
W
1
2
0
4
8
20
What is the slope of the line that models
this situation?
A 2
16
36
C 4
D
24
52
4
The slope of the line that models this situation is equal to 2.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 8).
Points on y-axis = (4, 20).
Substituting the given data points into the slope formula, we have the following;
Slope, m = (20 - 4)/(8 - 0)
Slope, m = 16/8
Slope, m = 2.
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EL VOLUMEN DE UNA CAJA DE BASE CUADRADA DE LONGITUD X Y ALTUR 10
Find x and y if the sequence 2y, 2xy, 2, xy/2, ... is geometric.
The value of x and y in the geometric sequence are 1/r and 1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
If the first term of the sequence is a ,second term is ar , third term = ar²
r = ar²/ar
In the sequence 2y, 2xy, 2, xy/2, ...
r = 2y/2xy
therefore r = 1/x
r = 2/2xy
r = 1/xy
therefore 1/x = 1/xy
therefore y = 1
x = 1/r
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Write down the percentage multiplier to find 53% of a price
The percentage multiplier to find the 53% of a price is 0.53
The given percentage value = 53%
Percentage of a quantity is defined as the number or the ratio, that can be expressed as the fraction of 100. To find the percentage of a number, divide the number by the whole quantity and multiply by 100. Percentage of a number is usually expressed as by using percentage sign "%"
Here we have to find the percentage multiplier
To find the percentage multiplier divide the given percentage by 100
The percentage value = 53%
The percentage multipler = 53 / 100
Divide the numbers
53 / 100 = 0.53
Therefore, the percentage multiplier is 0.53
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A map of a farm is shown in a coordinate plane in which the coordinates are measured in yards. The map shows the barn at
(-2, 3). A well is dug at (-2, y). What are two values of y such that the barn is 50 yards from the well?
The two values of y such that the barn is 50 yards from the well are given as follows:
y = -47 and y = 53.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the following equation:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For this problem, we have that D = 50, hence the equation is given as follows:
sqrt[(-2 - (-2))² + (y - 3)²] = 50
y - 3 = ±50.
Hence the values of y are given as follows:
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