The coordinates of the circumcenter of a triangle with vertices A(0,1),
B(2, 1) , and C(2, 5) is (1,3).
What is circumcenter of triangle?
The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).
Given: A triangle with vertices A(0,1), B(2, 1) , and C(2, 5).
Using distance formula:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
AB = 2 units
BC = 4 units
AC = √20 units
The midpoint of AC:
[tex]= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\\= (\frac{2+0}{2}, \frac{5+1}{2}) \\= (\frac{2}{2} , \frac{6}{2})\\ = (1, 3)[/tex]
The midpoint of AC is (1, 3).
Hence, The coordinates of the circumcenter of a triangle with vertices A(0,1), B(2, 1) , and C(2, 5) is (1,3).
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Which represents the polynomial written in standard form? 8x2y2 – 3x3y 4x4 – 7xy3 4x4 – 3x3y 8x2y2 – 7xy3 4x4 – 7xy3 – 3x3y 8x2y2 4x4 8x2y2 – 3x3y – 7xy3 –7xy3 – 3x3y 8x2y2 4x4
The Standard form of polynomial [tex]8x^2y^-\frac{3x^2y}{2} +4x^4-7xy^3[/tex] will be.[tex]-7xy^3+8x^2y^2-\frac{3x^2y}{2}+4x^3[/tex], Option D is right choice.
We have the polynomial. [tex]8x^2y^-\frac{3x^2y}{2} +4x^4-7xy^3[/tex]
then change it to standard form,
We are aware that in standard form the power of variables should be listed in decreasing order, in this example we have two variables first is x and second is y.
First write, highest degree term of y which has degree 3, next write second term of y which has degree 2 and write third term of y which has degree 1 and last one writes the term which is independent of y.
thus, we write in standard form with respect to y.
hence our required polynomial is. [tex]-7xy^3+8x^2y^2-\frac{3x^2y}{2}+4x^3[/tex].
option D is right choice.
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Jamie is an analyst at an education technology company. she gathered data on the results of a certain type of question. of the 2,000 re
she looked at, 1,092 responded correctly.
what equation could jamie use to calculate the margin of error at a 90% confidence interval?
0.454
2.58
1,092
1.96
2,000
0.546
1.65
(1-1
me=
reset
next
next
The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.
What is margin of error?
The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.
Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.
Here,
Number of samples, N=2000
Probability of responding correctly,
=1092/2000
=0.546
Z-score at 90% confidence level,
=1.645
Margin of Error ME,
=z*√(p*(1-p)/N)
=1.645*√(0.546*(1-0.546)/2000)
=1.645*√(0.546*0.454)/2000
=1.645*√(0.248/2000)
=1.645*√0.000124
=1.645*0.011
=0.0180
With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.
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Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answer:
(x – 3)2 = 49 can be written as (x – 3) = ± √49.
To solve for x, we can square root both sides:
x -3 = ±7
Now we can add 3 to both sides:
x = 3 ±7
So the values of x are:
x = 3 + 7 = 10
x = 3 - 7 = -4
Hence the values of x are -4 and 10.
Step-by-step explanation:
Answer: Did you mean (x - 3)² = 49? If so, the answers are -4 and 10
Step-by-step explanation: This equation is a simple quadratic. We can square root both sides to get:
x - 3 = -7
OR
x - 3 = 7
(Remember 49 has a positive square root and a negative square root)
Now simple rearranging will yield our two answers: 10 and -4.
which of the following expressions is equivalent to -4x^3-12x^3+9x^2
The expression that is equivalent to -4x³ -12x³ + 9x² will be -16x³ + 9x²
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to -4x³ -12x³ + 9x² will be:
= -4x³ -12x³ + 9x²
= -16x³ + 9x²
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The following inequalities form a system. y is less than or equal to two-thirds times x plus 1 y is greater than negative one-fourth times x plus 2 Which ordered pair is included in the solution to this system? (6, −2) (6, 0.5) (6, 5) (6, 8)
Answer:
(6, −2), (6, 0.5)--------------------------------
Given system of inequalities:
y ≤ 2/3x + 1y > - 1/4x + 2Plot the inequality and the given points to determine which of them fall into solution area.
See attached.
As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).
(Answer:
(6, 5)
Step-by-step explanation:
For this question, there are not two correct choices.
Given systems:
y ≤ 2/3x + 1
y > -1/4x + 2
For the first equation, the y-intercept is 1, and the rate of change is 2/3 (rise over run). The inequality symbol is less than or equal to (≤), meaning this will be a solid line and the area shaded will be below the line.
For the second equation, the y-intercept is 2, and the rate of change is -1/4 (this means it is decreasing in number, therefore the line is going down). The inequality symbol is greater than (>), meaning this will be a dashed line and the area shaded will be above the line.
the area overlapped is where the solution will be. The answer is (6, 5) because it lies on the solid line of the first inequality, indicating it does satisfy the first inequality. Any point on the solid line satisfies the inequality. The point also lies above the second inequality, meaning it is a solution to the system.
Also, if you plug it into the system of inequalities, all the outcomes will make sense.
Seven times the first number plus six times the second number equals 31. Three times the first number minus ten times the second number is 29.
Answer:
1st number = 5.5
2nd number = -1.25
Step-by-step explanation:
1) 7x + 6y = 31 (multiply entire equation by 3) → 21x + 18y = 93
2) 3x - 10y + 29 (multiply entire equation by 7) → 21x - 70y = 203
3) 21x + 18y = 93
4) -(21x - 70y = 203) now subtract equation (4) from equation (3) to make the x terms drop out
0 + 88y = -110
y = -110/88 = -1.25 now plug this into equation (1) and solve for x
7x + 6(-1.25) = 31
7x = 38.5
x = 38.5/7 = 5.5
Please help me with this
MATHS GCSE VECTORS
PLS HELP!!!! URGENT
a box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. what is the maximum number of different triangles that can be made using these rods as sides?
On solving the provided question, we can say that we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear.
[tex]2-inch, 3 inch, 4-inch[/tex]
triangle, because 2+3 > 4, 2+4 > 3, and 3+4 > 2
[tex]2-inch, 3 inch, 5-inch[/tex]
This is doesn't make a triangle as [tex]2+5 > 3, and 3+5 > 2,[/tex]
2+3 is not more than 5,, they cannot make triangle.
[tex]2-inch, 4 inch, 5-inch[/tex]
triangle, because 2+4 > 5, 2+5 > 4, and 4+5 > 2
[tex]3-inch, 4 inch, 5-inch[/tex]
a triangle, because 3+4 > 5, 3+5 > 4, and 4+5 > 3
Therefore, since we excluded example 2 above, a maximum of 3 triangles can be created with those rods.
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Use the given graph to determine the limit, if it exists.
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the left of f of x..
The limit of f(x) as x approaches 3 does not exist, as the lateral limits are different.
How to calculate the limit of a function?The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.
On the graph of a function, the limit of f(x) as x approaches a value of a is defined considering it's lateral limits, that is:
Limit as x approaches a to the left.Limit as x approaches a to the right.If the lateral limits are different, then the limit does not exist.
To the left of x = 3, the line ends at point (3,1), hence the lateral limit to the left of x = 3 is given as follows:
1.
To the right of x = 3, the line begins at point (3,3), hence the lateral limit to the right of x = 3 is given as follows:
3.
As the lateral limits as x approaches 3 are different, the limit of f(x) as x approaches x does not exist.
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you ordered a 12 in pizza for a party of five for the pizza to be distributed evenly how should i be cut in triangular pieces
Answer: 2.4 inches per guest
Step-by-step explanation:
2.4 inches per guest
2.4 x 5 = 12
an 8.24 gram sample of a hydrated salt is heated until it has a constant mass of 6.20 grams. what is the percent by mass of water contained in the original sample? group of answer choices 75.2% 24.8% 14.1% 32.9%
The percentage by mass of water contained in the original sample is 24.8%.
Percentage:
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",[1] although the abbreviations "pct.", "pct" and sometimes "pc" is also used.[2] A percentage is a dimensionless number (pure number); it has no unit of measurement.
To find the percent by mass of water in the original sample, we need to find the mass of the water that was lost upon heating. We can do this by subtracting the constant mass (6.20 g) from the initial mass (8.24 g).
mass of water = 8.24 g - 6.20 g = 2.04 g
To find the percentage, we divide the mass of water by the initial mass and multiply by 100:
percent by mass of water = (2.04 g / 8.24 g) x 100 = 24.8%
So the percentage by mass of water contained in the original sample is 24.8%.
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(I WILL GIVE BRAINLIEST) Below is a square picture frame. What is the length of one side of the frame?
The length of one side of the frame is 5.7 inches.
How to find the length of a square?A square is a quadrilateral with 4 sides equal to each other. Opposite sides of a square is parallel to each other.
The picture frame is a square. Therefore, all it's sides are equal to each other.
Hence, using Pythagoras's theorem, the side length of the square can be found as follows:
c² = a² + b²
where
c = hypotenusea and b are the other legsTherefore,
x² + x² = 8²
2x² = 64
divide both sides by 2
x² = 64 /2
x = √32
x = 5.65685424949
x = 5.7 inches
Therefore,
length of side frame = 5.7 inches
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Solve the following compound inequality: 3 less-than negative 2 x minus 1 less-than-or-equal-to 7. a. Negative 2 less-than x less-than-or-equal-to negative 4 c. Negative 1 less-than x less-than-or-equal-to negative 3 b. Negative 2 greater-than x greater-than-or-equal-to negative 4 d. Negative 1 greater-than x greater-than-or-equal-to negative 3 Please select the best answer from the choices provided A B C D
The solution for the compound inequality is -2>x≥-4. Therefore, option C is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is 3<-2x-1≤7.
Here, 3<-2x-1
Add 1 on both the sides of an inequality, we get
4<-2x
Divide -2 on both the sides of an inequality, we get
-2>x
Here, -2x-1≤7
Add 1 on both the sides of an inequality, we get
-2x≤8
Divide -2 on both the sides of an inequality, we get
x≥-4
The solution is -2>x≥-4
Therefore, option C is the correct answer.
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let f be the function given by . what are all values of c that satisfy the conclusion of the mean value theorem of differential calculus on the closed interval [0,3]?
The only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b], then there exists some c in the interval such that
f'(c) = (f(b) - f(a)) / (b - a).
In the case of f(x) = x(x-3) , on the closed interval [0,3], we can solve for c using the equation above.
We begin by calculating f'(c), which is equal to 2c - 3. Then, we set the equation equal to (f(3) - f(0)) / (3 - 0), which is equal to -3 / 3.
Substituting this into our equation for f'(c), we get 2c - 3 = -1, which simplifies to c = 2.
Therefore, the only value of c that satisfies the conclusion of the Mean Value Theorem on the closed interval [0,3] is c = 2.
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Jeremy borrowed money from his dad for a car repair. The graph represents the amount
remaining that Jeremy owes his dad.
a. Write an equation to represent the situation.
b. What does the slope mean in the context of
the situation?
c. What does the y-intercept mean in the context
of the situation?
a. The linear equation is -75x+700 which represents the situation.
b. The slope represents the rate of change in the amount owed.
c. The y-intercept represents the amount that Jeremy borrowed from his dad.
What is a linear equation?
Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. The general form is y=ax+b, where a is the slope and b is the y-intercept.
a. We know that general form of an equation is y=ax+b.
So, after substituting (0,700) and (8, 100) into y=ax+b, we get,
700= 0+b
b=700
100=8a+700
a=-75
Hence, the linear equation is -75x+700 which represents the situation.
b. The slope represents the rate of change in the amount owed.
c. The y-intercept represents the amount that Jeremy borrowed from his dad.
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Can you have a triangle with 2cm 3cm 5cm Class 7?
No , we cannot have a triangle with 2cm , 3cm and 5cm , because the sum of two sides is not greater than the other sides .
What is a Triangle ?
A triangle can be defined as the closed figure , that is made up of three line segments .
The Condition for any three sides to form a triangle : the sum of any two sides of triangle should be greater than the third side .
The sides of triangle are given to be : 2cm , 3cm and 5cm ;
on adding the two sides ,
we get ;
⇒ 2 + 3 = 5 > 5 ; False
⇒ 3 + 5 = 8 > 2 ; True
⇒ 2 + 5 = 7 > 3 ; True
All the conditions are not met ,
Therefore , the given sides cannot form a triangle .
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Based on these formulas, which scenario would not have been possible?
Answer:
answer: D
Step-by-step explanation:
Three cylinders and one cone of the same height and diameter.
Here, the volume of a cylinder is [tex]\pi r^{2} h[/tex]
So, the same of 3 cylinders is [tex]3\pi r^{2} h[/tex]
The same as a cone is [tex]\frac{\pi r^{2}h}{3}[/tex]
here [tex]3\pi r^{2} h[/tex] > [tex]\frac{\pi r^{2}h}{3}[/tex]
so D is not possible
find a cartesian equation for the curve and identify it. r2 cos(2θ) = 1
For the given polar equation the cartesian form of the equation is x² - y² = 1
The term polar equation in math is defined as another way to represent a complex number.
The general form the complex number is written as
=> z = a + bi
It is also known as the rectangular coordinate form of a complex number. And the horizontal axis is the real axis and the vertical axis is the imaginary axis.
Here we have given an equation r²2cos(2θ) = 1.
It can be rewritten as,
=> r²cos2θ − r²sin2θ = 1
Then here we substitute x as rcosθ and y as rsinθ, we get the cartesian equation as,
=> x² − y² = 1.
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given the summary statistics below for the size of a sample of automobile engines, show how we can tell there are no outliers in the data set.?
There are a few ways to tell if a dataset contains outliers, one of which is by using summary statistics.
Outliers are data points that fall far outside of the main body of a dataset. They can have a significant impact on the overall summary statistics of a dataset, such as the mean and standard deviation.
Given the summary statistics below for the size of a sample of automobile engines:
Mean: 2.5
Median: 2.5
Mode: 2.5
Standard deviation: 0.5
We can tell that there are no outliers in the data set because the mean, median, and mode are all equal. This indicates that the values in the dataset are tightly clustered around a central value, which is a good indication that there are no outliers. Additionally, the standard deviation is relatively small, which also suggests that the values in the dataset are not spread out very much, again indicating that there are no outliers.
Another approach is using the interquartile range (IQR). This can be calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3) of a dataset. Values that fall outside of the range of 1.5*IQR below the first quartile (Q1) or above the 3rd quartile (Q3) are considered outliers.
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Help Solve the system of equations 2x+3y=02x+3y=0 and -4x-y=30−4x−y=30 by combining the equations. Look at screen shot im 14 thanks
The solution for the system of equations:
2x + 3y = 0
-4x - y = 30
is y = 7 and x = -10.5
How to solve the system of equations?
Here we want to solve the following system of equations:
2x + 3y = 0
-4x - y = 30
By combining the equations.
If we add two times the first equation and the second equation, we will get:
2*(2x + 3y) + (-4x - y) = 0 + 30
We can simplify that to get:
4x + 6y - 4x - y = 30
5y = 30
Now we can solve that for y.
y = 30/5
y = 7
Now to find the value of x, we can replace y by 7 in one of the equations of the system.
2x + 3*7 = 0
2x = -21
x = -21/2
x = -10.5
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what is a visual representation of data where numbers on the left side of a chart show one part of each value, while numbers on the right side of the chart show the other?
A visual representation of data where numbers on the left side of a chart show one part of each value and numbers on the right side of the chart show the other is called a bar chart. A bar chart is a chart that uses rectangular bars to represent different values or categories. Each bar has a length that represents a value or a category. The left side of the chart is called the y-axis, or the vertical axis, and the right side of the chart is called the x-axis, or the horizontal axis. The x-axis typically shows the categories, and the y-axis shows the values of those categories. The height of each bar represents the value of the data point, with the height on the y-axis and the categories on the x-axis. This type of graph is useful for comparing the relative sizes of different groups or categories, as well as spotting trends and patterns.
a large company states in their promotional literature that 80% of their employees have college degrees. if 5 employees are selected at random from this company, what is the probability that all 5 will have college degrees? 0.0003 0.3277 0.6723 0.9997
There is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.
The probability of all 5 employees selected at random from the company having college degrees is calculated by using the following formula: P = (0.8)^5. Substituting 0.8 for the probability of having a college degree, this equation simplifies to P = 0.32768.
Therefore, P = (0.8)^5 = 0.32768.
This implies that there is a 0.32768 or 32.77% probability that all 5 employees selected at random from the company have college degrees.
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is there end behavior for square root function? like for example: [tex]\sqrt{6x}[/tex] or [tex]\sqrt{x-5}-6[/tex]
Answer:
Step-by-step explanation:
Yes, there is an end behavior for a square root function. The end behavior of a square root function is determined by the sign of the leading coefficient of the equation. For example, if the leading coefficient is positive, then the end behavior will be asymptotic to the positive x-axis as x increases, and asymptotic to the negative x-axis as x decreases. Conversely, if the leading coefficient is negative, then the end behavior will be asymptotic to the negative x-axis as x increases, and asymptotic to the positive x-axis as x decreases.
find the x for 4+3x=x+6 linear equation
here is your Answer.
hope it is helpful,
Please mark me brainiest
Answer:
x =1
Step-by-step explanation:
4 + 3x = x + 6
minus 4 from both side
6-4 = 2
3x = x + 2
then minus x from both side
3x-x=2
(pretend there's a 1 beside the x)
2x = 2
then divide 2 from both side and 2/2 =1
s0 x=1
that doesn't make sense but ye
I need to find X AND Y HELPPP
The values of variables in the kite is - x = 35°, y = 12.5°. The angles measures of the kite are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.
What is a kite?
A kite is a quadrilateral having reflection symmetry across a diagonal in Euclidean geometry. A kite has two equal angles and two pairs of adjacent equal-length sides as a result of its symmetry. Another name for kites is deltoids.
The given angles of the kite are -
∠a = (3x+5)°
∠b = y°
∠c = (2y-20)°
∠d = (4x-30)°
According to the properties of kite -
The two angles are equal where the unequal sides meet.
So, ∠a = ∠d
(3x+5)° = (4x-30)°
3x - 4x = -30 - 5
-x = -35
x = 35°
Substituting to find the value of ∠a -
∠a = (3x+5)°
∠a = [3(35)+5]°
∠a = (105+5)°
∠a = 110°
Substituting to find the value of ∠d -
∠d = (4x-30)°
∠d = [4(35)-30]°
∠d = (140-30)°
∠d = 110°
According to the properties of the kite ∠ADC = 90°.
So, ∠c = 90°/2 as line BD is a bisector.
(2y-20)° = 90°/2
2(2y-20)° = 90°
(4y - 40)° = 90°
4y = 90° - 40°
4y = 50°
y = 12.5°
Substituting to find the value of ∠b -
∠b = y°
∠b = 12.5°
Substituting to find the value of ∠c -
∠c = (2y-20)°
∠c = [2(12.5)-20]°
∠c = (25-20)°
∠c = 5°
Therefore, the value of angles are ∠a = 110°, ∠b = 12.5°, ∠c = 5° and ∠d = 110°.
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3 semicircles are connected to 3 sides of a square. Each side of the square measures 4 centimeters. What is the area of the composite figure?
The area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
What is the area of the semicircle?The area of the semicircle is the space occupied by it. It can be given as,
[tex]A_{s} = \frac{d^{2} }{8} \pi[/tex]
Here, (d) is the diameter of the semicircle.
Each side of the square measures 4 centimeters. The area of the square is square of its side. Thus,
Area of the square, [tex]A_{s}[/tex] = 4² = 16cm²
3 semicircles are connected to 3 sides of a square. Thus, the diameter of the semicircle is equal to 4 cm. The area of 3 semicircles is,
[tex]A_{sc} = 3 *\frac{4^{2} }{8} \pi\\A_{sc} = 6\pi[/tex]
The area of the composite figure is,
[tex]A = A_{s} + A_{sc} \\A = (6\pi + 16) cm^{2}[/tex]
Thus, the area of the composite figure which consist 3 semicircles and a square with 4 centimeters is (6π+16) cm².
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7. When it is 9:00A.M. eastern standard time (EST)
in Pittsburgh, it is 6:00A.M. pacific standard time
(PST) in Los Angeles. A plane takes off from
Pittsburgh at 9:00 A.M. EST and arrives in Los
Angeles at 11:00 A.M. PST. If a second plane
were to leave Los Angeles at 10:00 A.M. PST and
take exactly the same amount of time for the trip,
what would be the plane's arrival time (EST) in
Pittsburgh?
A. 6:00 P.M. EST
B. 5:00 P.M. EST
C. 4:00 P.M. EST
D. 3:00 P.M. EST
Please guys I need this tomorrow help tysm I rlly appreciate it
Answer:
A, 6:00 P.M. EST
Step-by-step explanation:
The time difference between EST and PST is -3 hours
11 am - 9am = 2 hours
2 - (-3) = 2+3 = 5 hours
The flight time is 5 hours
Then:
The time difference between PST and EST is +3 hours
5 + 3 = 8
If the fly leaves Los Angeles at 10:00 AM PST
10 + 8 = 18
The plane will arrive at 6:00PM EST
Questions 2-5. Simplify each of the following.
2. (-1/3)(12)(-3/4)
3. 1/4(-8a + 4b)
4. (24x - 12y)(-1/6)
5. 1/2(4c - 6d) - 1/3(6c-9d)
Find the value of fx) = 3x + 7 for x = 8.
Answer:
the value of f(8) is 31
Step-by-step explanation:
To find the value of f(x) = 3x + 7 for x = 8, we need to substitute 8 in for x in the equation and perform the arithmetic.
f(x) = 3x + 7
f(8) = 3(8) + 7
f(8) = 24 + 7
f(8) = 31
[tex]f(x)=3x+7[/tex] x = 8
Substitute 8 with x:
[tex]f(8)=3(8)+7[/tex]
[tex]f(8)=24+7[/tex]
[tex]\fbox{f(8) = 31}[/tex]
