Answer:
Step-by-step explanation:
Distance from point N to M can be calculated using the Pythagoras theorem. According to Pythagoras theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, side LN is the hypotenuse, and NM and ML are the other two sides. Therefore, LM can be calculated using the Pythagorean theorem as follows:
NM² + ML² = LN²
7.5² + 8.3² = LM²
56.25 + 69.29 = LM²
125.54 = LM²
LM = √125.54
LM ≈ 11.2
Therefore, the distance from point N to M is equal to the length of the side LM which is approximately 11.2. Hence, the correct option is not available in the given alternatives.
The shape is being enlarged using a scale factor of 2 and centre (6,3).
The coordinates of A' and B' include the following:
A' (4, 7).
B' (10, 9).
What is a dilation?In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (6, 3) by using the following mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate A', we have;
Coordinate A' = (5, 5) → (2(5 - 6) + 6, 2(5 - 3) + 3)
Coordinate A' = (5, 5) → (2(-1) + 6, 2(2) + 3)
Coordinate A' = (5, 5) → (-2 + 6, 4 + 3)
Coordinate A' = (5, 5) → (4, 7)
For coordinate B', we have;
Coordinate B' = (8, 6) → (2(8 - 6) + 6, 2(6 - 3) + 3)
Coordinate B' = (5, 5) → (2(2) + 6, 2(3) + 3)
Coordinate B' = (5, 5) → (4 + 6, 6 + 3)
Coordinate B' = (5, 5) → (10, 9)
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What is your monthly take-home pay if your take-home pay is calculated as 40 hours from Monday to Friday and 8 hours two Saturdays per month; regular
hourly rate is $15.20; pay is double for weekends; 29% is deducted for taxes and insurance? Round intermediate calculations and the final answer to the
nearest cent; use 52 weeks in a year.
Your monthly take-home pay is $?.
Step-by-step explanation:
To calculate your monthly take-home pay, you can use the following formula:
```
Monthly take-home pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2 - Deductions
```
Where:
- Regular hourly rate = $15.20
- Deductions = 29% of gross pay
First, let's calculate the gross pay for one month:
```
Gross pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2
= ($15.20 x 40 x 5) + ($15.20 x 8 x 2 x 4) x 2
= $3,424
```
Next, let's calculate the deductions:
```
Deductions = Gross pay x 29%
= $3,424 x 0.29
= $992.96
```
Finally, let's calculate the monthly take-home pay:
```
Monthly take-home pay = Gross pay - Deductions
= $3,424 - $992.96
= $2,431.04
```
Therefore, your monthly take-home pay is **$2,431.04**.
find f o g and g o f
f(x)= x^3, g(x)=x^2/3
Answer:
f(g(x)) = f((x^2/3)
(x^2/3)^3
continue solving
Find the inverse of the function f(x) = e^(x −3) + 7
The price of an item has risen to $119 today yesterday it was $85 what is the percentage Increase
The price has increased by approximately
40%.How to find the percentage increaseTo calculate the percentage increase, we use the following formula:
Percentage Increase = ((New Value - Old Value) / Old Value) * 100
given data:
New Value = $119
Old Value = $85
Percentage Increase = (($119 - $85) / $85) * 100
= ($34 / $85) * 100
≈ 40%
Therefore, the price has increased by approximately 40%.
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Which of the following expressions does NOT represent 9+9+9+9+9+9+9
The expression that does NOT represent 9+9+9+9+9+9+9 is 9 x 7.
Problem-SolvingThe given expression 9+9+9+9+9+9+9 can be simplified by adding all the numbers together:
9+9+9+9+9+9+9 = 63
Therefore, the expression 63 represents 9+9+9+9+9+9+9.
However, if we multiply 9 by 7, we get:
9 x 7 = 63
Therefore, 9 x 7 represents the product of 9 and 7, not the sum of seven nines.
please help i've been stuck on thissss
SOLVE USING SYSTEMATIC TRIAL!
Answer:
For the second question=7
Step-by-step explanation:
since she drank 8 cups of water on the fourth day29-8
=21
let the volume of first 3 days be xx+x+x=3x
3x=21
x=21/3
x=7
For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 1 minute of play, the game awards one half point, and for every 7 minutes of play, the game awards three and one half points. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many points are awarded for 18 minutes of play? (2 points)
a) The constant of proportionality is given as follows: 0.5.
b) The equation is given as follows: y = 0.5x.
c) The graph would be the graph of a linear function with slope of 0.5 and intercept of 0.
d) 9 points are awarded for 18 minutes of play.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
For every 1 minute of play, the game awards one half point, hence the constant k is given as follows:
k = 0.5.
Thus the equation is given as follows:
y = 0.5x.
Then the number of points for 18 minutes of play is given as follows:
y = 0.5(18)
y = 9.
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i dont know if this is right please help
The total cost of Beatrice dishwasher for the new house including tax is written as D + 0.02D.
What is the total cost of Beatrice dishwasher?Let
price of the dishwasher = D
Tax percentage = 2%
Amount of tax = 2% of D
= 2/100 × D
= 0.02D
Beatrice total cost for the dishwasher = price of the dishwasher + Amount of tax
= D + 0.02D
Hence, the expression which represents the total cost of Beatrice dishwasher is D + 0.02D
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on a biased dice the chance of etting a 1 is 0.3 if rolled 150 times how mnay ones would you get
If the biased dice is rolled 150 times, we can expect to get approximately 45 ones
If the chance of getting a 1 on a biased dice is 0.3, it means that the probability of rolling a 1 on any given roll is 0.3 or 30%.
To determine how many ones you would get if rolled 150 times, we can multiply the probability of rolling a 1 (0.3) by the total number of rolls (150).
Number of ones = Probability of getting a 1 * Total number of rolls
Number of ones = 0.3 * 150 = 45
Therefore, on average, we would expect around 45 instances of rolling a one when using this biased dice over 150 rolls.
It's important to note that the actual number of ones obtained may vary due to the inherent randomness of dice rolls. However, if a biased dice has a 0.3 chance of getting a 1, when rolled 150 times, you would expect to get approximately 45 ones.
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The rectangular tank shown below was 4/5 filled with water. how many more litres of water were needed to fill up the tank?
The volume of water required to fill up the tank is: 540 cm³
How to find the volume of the cuboid?The formula for the volume of a cuboid is:
Volume = Length * Width * Height
Thus:
Volume of bigger tank = 15 * 15 * 12
Volume = 2700 cm³
Now, we are told that it is 4/5 filled with water.
Thus, volume needed to fill up the tank is:
¹/₅ * 2700
= 540 cm³
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what is the volume of the rectangular prism length =9m width = 12m height =5m
The volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.
To find the volume of a rectangular prism, we multiply its length, width, and height.
Given that the length is 9m, the width is 12m, and the height is 5m, we can calculate the volume as follows:
Volume = Length x Width x Height
Substituting the given values:
Volume = 9m x 12m x 5m
To perform the multiplication, we can multiply the numerical values first and then consider the units:
Volume = (9 x 12 x 5) m³
Multiplying the numbers:
Volume = 540 m³
Therefore, the volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Simplify the following expression, and then find its value.
The simplified expression is 6 raised to the power of
.
The value of the simplified expression is
.
The simplified expression is 1,675,616. the value of the expression is 1,675,616.
To find the simplified expression and the value of 6 raised to a power, follow the steps given below:
Step 1: Simplify the expression Firstly, the simplified expression is obtained by using the rule of exponents, which states that if a number raised to a power is multiplied by the same number raised to another power, then the resulting power is the sum of the two powers.
6 raised to the power of 2 is 6 × 6 = 36.6 raised to the power of 3 is 6 × 6 × 6 = 216.6 raised to the power of 4 is 6 × 6 × 6 × 6 = 1296.6 raised to the power of 5 is 6 × 6 × 6 × 6 × 6 = 7776.
Step 2: Find the value of the expression
From these results, it can be seen that when 6 is raised to an even power, the resulting number is even, and when 6 is raised to an odd power, the resulting number is odd. This is because 6 is an even number.
In general, if a number is even, then the result obtained when it is raised to an even power is even, and the result obtained when it is raised to an odd power is odd.
If a number is odd, then the result obtained when it is raised to any power is odd. 6 raised to the power of 8 can be written as 6 raised to the power of 4 raised to the power of 2, as shown below 6 raised to the power of 8 = (6 raised to the power of 4) raised to the power of 2= 1296 raised to the power of 2= 1,675,616
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what is equivalent to 3 radical 6
The equivalent expression to [tex]3\sqrt{6}[/tex] is given as follows:
[tex]\sqrt{54}[/tex]
How to obtain the equivalent expression?Two expressions are defined as equivalent expressions when they have the same result.
The expression for this problem is given as follows:
[tex]3\sqrt{6}[/tex]
For the equivalent expression, we can move the outer term 3 inside the root, with it being squared, as follows:
[tex]3\sqrt{6} = \sqrt{3^2 \times 9} = \sqrt{54}[/tex]
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1(a) Find the centre and radius of a circle whose equation is x² + y² + 2x+8y = 8 (b) Show that the line through p₁ (3, -4) and q₁ (-2, 6) is parallel to the line through p₂ (-3, 6) and 9₂ (9,-18).
The line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.
(a) To find the center and radius of a circle with the equation x² + y² + 2x + 8y = 8, we need to rewrite the equation in the standard form of a circle, which is (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
We start by completing the square for both x and y terms:
x² + 2x + y² + 8y = 8
(x² + 2x) + (y² + 8y) = 8
To complete the square for x terms, we add (2/2)² = 1 to both sides inside the parentheses:
(x² + 2x + 1) + (y² + 8y) = 8 + 1
(x + 1)² + (y² + 8y) = 9
To complete the square for y terms, we add (8/2)² = 16 to both sides inside the parentheses:
(x + 1)² + (y² + 8y + 16) = 9 + 16
(x + 1)² + (y + 4)² = 25
Now the equation is in the standard form. We can see that the center of the circle is (-1, -4) and the radius is the square root of 25, which is 5. Therefore, the center of the circle is (-1, -4) and the radius is 5.
(b) To show that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18), we need to demonstrate that the slopes of the two lines are equal.
The slope of the line passing through p₁ and q₁ is given by:
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (6 - (-4)) / (-2 - 3)
= 10 / -5
= -2
The slope of the line passing through p₂ and q₂ is given by:
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (-18 - 6) / (9 - (-3))
= -24 / 12
= -2
We can see that both slopes are equal to -2. Therefore, the line passing through p₁ and q₁ is parallel to the line passing through p₂ and q₂.
By demonstrating that the slopes of the two lines are equal, we have shown that the line through p₁(3, -4) and q₁(-2, 6) is parallel to the line through p₂(-3, 6) and q₂(9, -18).
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Find the sizes of the three unknown angles in
the image below.
Give your answers in degrees (°).
b
с
a
34°
Answer:
Step-by-step explanation:
See attached for the math problem.
The dimension of the product of the matrices are
The dimension of matrix AB does not existThe dimension of matrix BA is 5 × 3The dimension of matrix AC is 5 × 4What are the dimensions of a matrix?The dimensions of a matrix are the number of rows and columns it has.
Given the matrix A is 5 × 3, Matrix B is 5 × 5 and Matrix C is 3 × 4, to find the dimensions of their products, we proceed as follows.
To find the dimension of the products of a matrix A' with dimension a × b and B' with dimension c x d, to have a product,
the number of columns in the first matrix must equal the number of rows in the second matrix.Also, for the product A' × B' = a x b and c × d, b = c and the dimension of A' × B' are a × d.So, the dimension of AB are 5 × 3 and 5 × 5. Since the number of columns in A is not equal to the number of rows in B, the product does not exist
The dimension of BA are 5 × 5 and 5 × 3. Since the number of columns in B is equal to the number of rows in A, the product exists and the dimension is 5 × 3
The dimensions of AC are 5 × 3 and 3 × 4. Since the number of columns in A is equal to the number of rows in C, the product exists and the dimension is 5 × 4
So,
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2. Which ordered pair is a solution to the following system of nonlinear inequalities?
7-2(x-1)²2 25-y
2 ≤-Y
(1,-2)
No solution.
(1,-3)
O (1,0)
Answer: (1,-2)
Step-by-step explanation:
To check which of the given ordered pairs satisfy the given system of nonlinear inequalities, we will substitute the values of x and y from each ordered pair and then check if the inequalities hold true or not. Let's check one by one.
For the ordered pair (1,-2):
7 - 2(x-1)² ≤ 25 - y
7 - 2(1-1)² ≤ 25 - (-2)
7 ≤ 25 + 2
7 ≤ 27 (This is true)
2 ≤ -y
2 ≤ -(-2)
2 ≤ 2 (This is true)
Therefore, (1,-2) satisfies the given system of nonlinear inequalities.
For the ordered pair (1,-3):
7 - 2(x-1)² ≤ 25 - y
7 - 2(1-1)² ≤ 25 - (-3)
7 ≤ 28 (This is true)
2 ≤ -y
2 ≤ -(-3)
2 ≤ 3 (This is true)
Therefore, (1,-3) does not satisfy the given system of nonlinear inequalities.
For the ordered pair (1,0):
7 - 2(x-1)² ≤ 25 - y
7 - 2(1-1)² ≤ 25 - (0)
7 ≤ 25 (This is true)
2 ≤ -y
2 ≤ -(0)
2 ≤ 0 (This is not true)
Therefore, (1,0) does not satisfy the given system of nonlinear inequalities.
For the ordered pair (0,0):
We do not have the value of x for this ordered pair, so we cannot check whether it satisfies the given system of nonlinear inequalities.
Hence, the ordered pair that satisfies the given system of nonlinear inequalities is (1,-2).
What does the constant term represent?
List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated list.)
T(x) = 9x4 − 3x2 − 7
Answer:
The rational zeros theorem states that all possible rational zeros of a polynomial with integer coefficients are of the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.
In this case, the constant term is -7 and the leading coefficient is 9. Thus, the possible rational zeros are:
p/q = ±1, ±7, ±9
a motorist travels 210 miles in 5 hour n it will take ------ hours to travel 1386 miles
The time needed to travel 1386 miles is given as follows:
t = 33 hours.
What is the relation between velocity, distance and time?Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The motorist travels 210 miles in 5 hours, hence the velocity is given as follows:
v = 210/5
v = 42 miles.
Then the time needed to travel 1386 miles is given as follows:
42 = 1386/t
42t = 1386
t = 1386/42
t = 33 hours.
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Please answer this question
It will take the ball 2.12s to the nearest hundredth to hit the ground.
What is quadratic formula?
Quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0 and that is usually written in the form
x = (-b ± √(b2 − 4ac))/(2a)
From the question, the initial height, h, of the ball is 40 ft
When the ball hits the ground, the height, h, is zero
The equation h = - 16t² + 15t + 40 becomes
0 = - 16t² + 15t + 40
16t² - 15t - 40 = 0
Solving the quadratic equation by formula method for t,
t = (-b ± √(b² - 4ac)) / (2a)
Where, a = 16, b = -15, and c = -49
Substitute these values into the quadratic formula,
t = (15 ± √2785) / 32
Therefore, the possible values of t are:
t = (15 + √2785) / 32
t = (15 - √2785) / 32
Which implies t = 2.12 or t = - 1.18
Since time, t, cannot be negative, t = 2.12s to the nearest hundredth.
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18
X
24
18
These shapes
are similar.
Find X.
8
12
The value of x in the similar shapes is 10
How to calculate the value of x in the similar shapesFrom the question, we have the following parameters that can be used in our computation:
The similar shapes
On the shapes, we have
x/20 = 5/10
Multiply through the equation by 20
So, we have
x = 20 * 5/10
Evaluate
x = 10
Hence, the value of x is 10
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What is the sum of an interior angle and its adjacent exterior angle?
a.30°
b.90°
c.180°
d.360°
Hello!
The sum of an interior angle and its adjacent exterior angle is 180°
The answer is:
C) 180°
Work/explanation:
The sum of an interior angle and its adjacent exterior angle is [tex]\sf{180^o}[/tex], which means that an interior angles and its adjacent exterior angle form a linear pair.
This also means that the angles are supplementary, because they add up to [tex]\sf{180^o}[/tex].
Hence, the right choice is C.If the time is between 8:00 a.m. and 3:00 p.m., then the bank is open.
If the bank is open, then people may make withdrawals or deposits.
Therefore, if …
Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits at the bank.
This conclusion is based on the given premises that the bank is open during the time between 8:00 a.m. and 3:00 p.m. and that when the bank is open, people may make withdrawals or deposits. By combining these premises with modus ponens (a valid form of deductive reasoning), we can infer that if the time is within the bank's operating hours, then people may make withdrawals or deposits at the bank.
02
04
4
O 3
O
8₁
1
How many significant figures does the following number have?
420
The significant numbers in 420 are 4 and 2.
How many significant figures does the following number have?Significant numbers are digits that is nonzero or, when zero, followed either by a nonzero digit or by further zeros and then a nonzero digit.
Significant numbers are digits 1 to 9
All zeros between integers are significant.
Zero’s preceding the first integers are insignificant.
Zero’s after the decimal point are significant.
Zeroes used for spacing the decimal point are not significant.
Therefore, it can be concluded that there are 2 significant numbers in 420 which are 4 and 2.
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If mark bought a plasma TV for $2499 on the installment plan and paid 101.50 for 28 months, how much did he pay in finance charges?
A. 343 B. 400 C. 249 D. 101.50
Answer:
Step-by-step explanation:
101.50 x 28 = 2,842.00
Price of TV = 2,499.00
2,842.00 - 2,499.00 = 343.00
$343.00 was paid in finance charges
PLEASE HELP ME PLEASE PLEASE PLEASE
Initially as x incrases y (increases or decreases)
The slope of the graph is equal to ____ for all x between x= 0 and x=3
Starting at x=3 the function value y (increases or decreases) as x increases
The slope of the graph is equal to _____ for x between x=3 and x=5
For x between x=0 and x=4, the function value of y is (≤ or ≥ or =)
For x between x=4 and x=8 the function of value y is (≤ or ≥ or =)
The slope of the graph is equal to 1 for all x between x= 0 and x=3.
Starting at x=3 the function value y increases as x increases.
The slope of the graph is equal to 3 for x between x=3 and x=5
For x between x=0 and x=4, the function value of y is ≤ 0.
For x between x=4 and x=8 the function of value y is ≥ 0.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (0 - 3)/(3 - 0)
Slope (m) = -3/3
Slope (m) = -1.
For x between x=3 and x=5, the slope is given by;
Slope (m) = (3 + 3)/(5 - 3)
Slope (m) = 6/2
Slope (m) = 3.
By critically observing the graph of this function, we can logically deduce that the function value of y is less than or equal to 0 for x between x=0 and x=4 and greater than or equal to 0 for x between x=4 and x=8.
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According to a study, the probability that an individual will cover his or her mouth when sneezing is 0.29. If 10 random
selected individuals are observed, compute the following probabilites.
Your answers should be rounded to four decimal places.
The probability that five individuals will cover their mouth when sneezing is
The probability that six or less individuals will cover their mouth when sneezing is
The probability that six or fewer individuals will cover their mouth when sneezing is approximately 0.597.
How to find the probability that six or fewer individuals will cover their mouth when sneezingTo calculate the probabilities, we can use the binomial probability formula:
P(X = k) = [tex]C(n, k) * p^k * (1 - p)^{(n - k)}[/tex]
Given:
p = 0.29 (probability of an individual covering their mouth)
n = 10 (number of individuals observed)
(a) The probability that five individuals will cover their mouth when sneezing:
P(X = 5) = C(10, 5) * 0.29^5 * (1 - 0.29)^(10 - 5)
Calculating:
P(X = 5) = 0.0001677
Therefore, the probability that five individuals will cover their mouth when sneezing is approximately 0.0002.
(b) The probability that six or fewer individuals will cover their mouth when sneezing:
P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
Calculating each individual probability and summing them up:
P(X ≤ 6) = 0.0075 + 0.043 + 0.1133 + 0.1954 + 0.2383 + 0.0002 + 0.000007
P(X ≤ 6) = 0.597
Therefore, the probability that six or fewer individuals will cover their mouth when sneezing is approximately 0.597.
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Which of the following statements best explains why the point (2, -2) is not a solution to the system of
inequalities graphed below?
A. The point (2,-2) satisfies the red inequality but not the blue inequality.
B. The point (2,-2) satisfies the blue inequality but not the red inequality.
C. The point (2,-2) doesn't satisfy either the red or the blue inequalities.
D. The point (2, -2) satisfies both the red and the blue inequalities.
Answer: The correct answer is B
Step-by-step explanation:
The point (2, -2) satisfies the blue inequality but not the red inequality. Explanation: To solve this system of inequalities, we need to check if the point (2, -2) is a solution to both of the inequalities. The blue inequality is y > 2x - 6. Plugging in the values of x = 2 and y = -2 gives:-2 > 2(2) - 6 => -2 > -2This is true, so the point (2, -2) satisfies the blue inequality. The red inequality is y < 1/2x + 1. Plugging in the values of x = 2 and y = -2 gives: -2 < 1/2(2) + 1 => -2 < 2This is false, so the point (2, -2) does not satisfy the red inequality. Therefore, the correct answer is B. The point (2, -2) satisfies the blue inequality but not the red inequality.