Answers
The complete proof to show that ∠HIJ ≅ ∠EFG is:
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Proof of congruent anglesFrom the question, we to prove that the given angles are congruent.
The given angles are ∠HIJ and ∠EFG
To prove that angle HIJ is congruent to angle EFG we will complete the given table.
The given table is
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
Now, we will complete the proof by adding the last statement and its reason
Statement Reason
FG ⊥ EF Given
HI ⊥ IJ Given
m ∠EFG = 90° Definition of perpendicular lines
m ∠HIJ = 90° Definition of perpendicular lines
∠HIJ ≅ ∠EFG Substitution property
Hence,
We have completed the proof by using the substitution property
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Related Questions
Eloise bought 30 pounds of sand to refill 4 sandboxes at a local park. She is going to put the
same amount of sand in each sandbox. Which statement about this situation is true?
Answers
The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).
answer with explanation
Answers
Because the line segment BE bisects angle CBD, that means angle EBD is congruent to angle CBD
To find angle ABC, you can subtract the larger angle (ABD) from the 2 segments (CBD+EBD)
So, 79-24-24=31 degrees ;)
Becky worked part-time at a restaurant. The amount of money she earned for each of six weeks is shown.
$50, $82, $39, $50, $31, $70
Becky earned $23 for working a seventh week. Which statement for these seven weeks is true?
OA. The median decreases and the mean remains the same.
OB. The mean and the median both decrease.
OC. The median and the mean both remain the same.
OD. The mean decreases and the median remains the same.
Answers
Answer:
Step-by-step explanation:
To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.
First, let's calculate the mean of the original data set:
Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67
Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:
31, 39, 50, 50, 70, 82
The median is the middle value, which is 50.
Now, let's add Becky's earnings of $23 to the data set:
31, 39, 50, 50, 70, 82, 23
The new data set has 7 values. Let's calculate the new mean:
Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14
The new mean is less than the original mean, so we can eliminate options A and C.
Now let's calculate the new median. We need to arrange the data set in order:
23, 31, 39, 50, 50, 70, 82
The median is still 50.
Therefore, the answer is option D: The mean decreases and the median remains the same.
A rectangular prism is 38 centimeters long, 18 centimeters wide, and 13 centimeters high. What is the surface area of the rectangular prism?'
Answers
Answer:
53,352 cm
Step-by-step explanation:
1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.
2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.
3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.
If I made a mistake or if have any questions feel free to tell me!
-Mathematics and Science Major for Middle School Students at Harvard University
new car is purchased for 18700 dollars. The value of the car depreciates at
14.25% per year. To the nearest year, how long will it be until the value of the
car is 3000 dollars?
Answers
The minimum time required to depreciate the value of the car is 12 years.
Let us assumed the time to be t. Representing the formula for calculation of time-
Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]
Keeping the values in formula to find the time period
3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]
Solving the expression
[tex] {(0.8575)}^{t} [/tex] = 3000/18700
Cancelling zeroes common in numerator and denominator
3000/18700 = [tex] {(0.8575)}^{t} [/tex]
Taking log on both sides of the equation
t log 0.8575 = 30/187
Keep the value
t = log 0.8575 30/187
t = 12 years
Hence, it will take 12 years for value depreciation.
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An executive for a large company received gross pay of $200,000 for the year 2018. Determine the total amount of FICA tax that was paid on behalf of the employee. Round your answer to the nearest cent. Do NOT round until you calculate the final answer.
Answers
The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.
What is the total amount of FICA tax?The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.
The Social Security tax will be calculated on the maximum taxable earnings of $128,400:
= $128,400 x 6.2%
= $7,961.20
The Medicare tax will be calculated on the entire earnings:
= $200,000 x 1.45%
= $2,900.
The total FICA tax will be:
= Social Security tax + Medicare tax
= $7,960.80 + $2,900
= $10,860.80.
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Describe los Tipos de ángulos que se forman cuando divides un círculo en 4 partes iguales
Answers
The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.
How to describe the angles ?The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.
These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.
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m ANGLE 1 = 3x-5 and m ANGLE 2 = 2x+7 find the values of angle 1 and 2
Answers
Answer: Angle one equals -15, and angle two equals 14, if the +7 equals a positive seven.
Step-by-step explanation:
There are more negatives than positives, so we make the ending answer negative, giving us -15. And the second one is simple multiplication, you double the 7 times two, or vice versa.
Hope this helps!
9. Max's monthly electricity budget only allows him to use 250,50 kWh (kilowatt-hours). The cost for 1 kWh is R2,20. Calculate the cost of his electricity bill.
Answers
Using the given information, the cost of Max's electricity bill is R551.10
Calculating the cost of electricity billFrom the question, we are to calculate the cost of Max's monthly electricity bill
From the given information,
"Max's monthly electricity budget only allows him to use 250.50 kWh"
and
"The cost for 1 kWh is R2.20"
To determine the cost of Max's monthly electricity bill, we will multiply his monthly electricity budget by the cost for 1 KWh
That is,
Max's monthly electricity bill = 250.50 × R2.20
Max's monthly electricity bill = R551.10
Hence,
The cost of Max's monthly electricity bill is R551.10
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I really need help please
Applying the Solution to a 3X3 System
At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?
Show up all steps please
Answers
Using an equation, the number of children, parents, and grandparents in attendance were:
Children = 190Parents = 140Grandparents = 70.What is an equation?An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.
Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.
The total number of people in attendance at the family reunion = 400
Let the number of grandparents = x
Let the number of parents = 2x
Let the number of children = 2x + 50
Equation:x + 2x + 2x + 50 = 400
5x = 350
x = 70
Summary of Attendance:Grandparents = 70
Parents = 140 (2 x 70)
Children = 190 (2 x 70 + 50)
Total = 400 (70 + 140 + 190)
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a) Use the triangle below to answer questions a) and b). B 10 cm A 14 cm Determine which interior angle of the triangle is the largest,
Answers
The largest interior angle of the triangle is the angle A
Determining the largest interior angle of the triangleThe side lengths of the triangles are given as
b = 10 cm
a = 14 cm
The other side length is not given
So, we solve the question using the two side lengths
Having said that:
The general rule is that; the higher the side length, the larger the angle
14 cm is greater than 10 cm
This means that the angle A is greater than the angle B
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graph the following linear inequalities: y < -2+7
Answers
The graph of the inequality is added as an attachment
How to determine the graphFrom the question, we have the following parameters that can be used in our computation:
y < -2 + 7
The above expression is an inequality that implies that
The value of y is less than the sum of -2 and 7
Next, we plot the graph
See attachment for the graph of the inequality
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Find the extrema of the function f(x,y)=x^2+y^2
Answers
Answer:
The function f(x,y) = x^2 + y^2 represents the equation of a paraboloid with its vertex at the origin. Since the function increases as we move away from the origin, there are no maximum points, but there is a minimum point at the origin.
To find this minimum point, we can take the partial derivatives of f(x,y) with respect to x and y, and set them equal to zero:
df/dx = 2x = 0
df/dy = 2y = 0
Solving these equations simultaneously gives us x = 0 and y = 0, which is the only critical point of the function. To determine whether this point is a minimum or maximum, we can use the second partial derivative test.
Taking the second partial derivatives, we have:
d^2f/dx^2 = 2
d^2f/dy^2 = 2
d^2f/dxdy = 0
At the point (0,0), both second partial derivatives are positive, which indicates that the point is a minimum. Therefore, the function f(x,y) = x^2 + y^2 has a minimum value of 0 at the point (0,0).
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0
Which equations can be used to solve for y, the length of the room?From the question, we have the following parameters that can be used in our computation:
Area = 750
Length = y
Width = y - 5
The area is the product of the length and the width
So, we have
y * (y - 5) = 750
When expanded. we have
y^2 - 5y = 750
Lastly, we have
(y + 25)(y – 30) = 0 -- when factored
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Exercise 1: Identify each triangle based on sides. (Equilateral, Isosceles or Scalene).
Answers
The triangles are classified according to their sides as:
1. equilateral 2. Scalene 3. and 4. Isosceles 5. equilateral 6. and 7. scalene triangle. 8. Isosceles 9. and 10. Equilateral
How to Identify Triangles based on their Sides?Recall the following:
A triangle is equilateral if all three sides are equal.
It is isosceles if it has two equal sides.
A triangle is scalene if all three sides are of different lengths.
1. The triangle is equilateral because all sides are equal.
2. Scalene
3. and 4. Isosceles (two sides are equal)
5. All sides are equal, so it is an equilateral triangle.
6. and 7. The three sides have different lengths, therefore, it is a scalene triangle.
8. Isosceles
9. and 10. Equilateral
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mrs. watson is buying vintage records for a friend at a local records shop. Thre price of a record is based on its condition. The table shows the total cost of x number of records for each condition.
Answers
The equation for total cost of buying and shipping the records is
76.4x + 80
We have,
She buys 3 in good condition
So, the cost for 3 good condition
= 3 (10.5x)
= 31.5 x
and, She buys 1 in Fair condition
So, the for 1 fair condition
= 5x
and, She buy 2 new condition then the price is
= 39.9 x
So, the equation for total cost of buying and shipping the records is
= 31.5x + 5x + 39.9x + 8
= 76.4x + 8
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16u-5u+18=3u-14???????
Answers
Answer:
u = -4
Step-by-step explanation:
You want the solution to the equation 16u -5u +18 = 3u -14.
SimplifyThe equation can be simplified by combining like terms:
11u +18 = 3u -14
SolutionAdding (-18-3u) to both sides, we have ...
8u = -32
u = -32/8 = -4 . . . . . . divide by the coefficient of u
The solution is u = -4.
What's the ordered pair so that's a solution for the given linear equation?
6x+4y=8
(-1, __ )
(__,-4)
Thanks!
Answers
The ordered pairs to a solution for the given linear equation are (-1, 3.5) and (4, -4).
To find the ordered pair that is a solution to the equation 6x + 4y = 8, we can substitute the given value of x or y and solve for the other variable.
For the first option, substituting x = -1, we get:
6(-1) + 4y = 8
-6 + 4y = 8
4y = 14
y = 3.5
So, the ordered pair (-1, 3.5) is a solution to the equation.
For the second option, substituting y = -4, we get:
6x + 4(-4) = 8
6x - 16 = 8
6x = 24
x = 4
So, the ordered pair (4, -4) is a solution to the equation.
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What is the square root of ab²?
O ab
Ob√a
Oa²b²
Ob²
Answers
Answer:
b[tex]\sqrt{a}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then
[tex]\sqrt{ab^2}[/tex]
= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]
= [tex]\sqrt{a}[/tex] × b
= b[tex]\sqrt{a}[/tex]
We often use the phrase "to the power of" when talking about exponents. For example, x¹3 is
referred to as x to the power of 13. Why do you think that they would name it like this? How does
increasing the exponent of a number increase its "power"?
Hint: Use a number as an example. (for instance 2) if you keep increasing the power, what happens
to the answer? (i.e. compare 2¹, 2^2, 2^3, 2^4,..., 2^13, 2^14,... until you see the answer you are looking
for!)
Answers
In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.
What is the exponents about?Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.
Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.
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HOW GIAND
4. The circle graph shows the results of a middle
school survey about favorite states to visit on
vacation. If 400 students were surveyed, how
many more students favor visiting Florida than
Colorado? (Example 2)
New York
7%
Favorite State to Visit
Other
16%
North
Carolina
Colorado
Florida
38%
15% California
13%
Answers
92 more students favor visiting Florida than Colorado
How many more students favor visiting Florida than Colorado?From the question, we have the following parameters that can be used in our computation:
Students = 400
Florida = 38%
Colorado = 15%
The percentage difference is
Difference = 38% - 15%
So, we have
Difference = 23%
This means that
Students = 23% * 400
Evaluate
Students = 92
Hence, the number of students is 92
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Express the area of the entire rectangle. Your answer should be a polynomial in standard form. An area model for a rectangle that has a height of x plus two and a width of x plus six. The rectangle is broken into four rectangles to isolate each term in the height and the width. The top left rectangle has a height of x and a width of x. The top right rectangle has a height of x and width of six. The bottom left rectangle has a height of two and a width of x. The bottom right rectangle has a height of two and a width of six.
Answers
The area of the entire rectangle as polynomial is x^2 + 8x + 12
Expressing the area of the entire rectangle as polynomialFrom the question, we have the following parameters that can be used in our computation:
Height = x + 2; Width = x + 6
Broken rectangles
Height = x; Width = xHeight = x; Width = 6Height = 2; Width = xHeight = 2; Width = 6The area of the rectangle is the product of the dimensions
Adding the heights and the width of the individual rectangles, we have
Height = x + 2; Width = x + 6
So, the area is
Area = (x + 2)(x + 6)
Expand
Area = x^2 + 8x + 12
Hence, the area expression is x^2 + 8x + 12
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URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!!!!!
Match the given information with the equation for the line
-5x + 3y = -12
y = 3/2 x - 8
2y-x = -4
Y= -3/4x-2
Answers
A line that contains the point (0,-8) with a slope of 3/2 is y= 3/2x-8
A line that contains the y intercept (0,-2) and a slope of -3/4 is y=-3/4x - 2
A line that contains the points (0,-2) and (4,0) is 2y-x=-4
The radius of a circle is 12 cm. Find its area nearest whole number
Answers
Answer:
452 square centimeters.
Step-by-step explanation:
To find the area of a circle, we use the formula:
A = πr^2
Where A is the area of the circle, r is the radius, and π is a mathematical constant (approx. 3.14).
Given that the radius of the circle is 12 cm, we can substitute r = 12 in the formula:
A = π(12)^2
A = 3.14 x 144
A = 452.16
Therefore, the area of the circle is approximately 452.16 square centimeters. However, we need to round the answer to the nearest whole number.
Since the decimal part of the answer is less than 0.5, we round the answer down to the nearest whole number. Therefore, the area of the circle nearest the whole number is 452 square centimeters.
I need help with this please
Answers
Answer: a. d. f.
Step-by-step explanation:
Find the equation of the line perpendicular to y=1/2x-1 and passes through the point (5,6)
Answers
The equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.
To find the equation of the line perpendicular to y=1/2x-1, we need to determine its slope. We can recall that the slope of a line in slope-intercept form, y = mx + b, is given by m, the coefficient of x. So in the given equation y=1/2x-1, the slope is 1/2.
The slope of a line perpendicular to this line will be the negative reciprocal of the slope, which means it will be -2. To see why this is true, remember that the product of the slopes of two perpendicular lines is always -1. So if the slope of the original line is m, the slope of the perpendicular line will be -1/m.
Now that we know the slope of the perpendicular line is -2, we can use the point-slope form of the equation of a line to find its equation. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
We are given a point on the perpendicular line, (5, 6), so we can substitute that into the equation and also substitute in the slope, -2:
y - 6 = -2(x - 5)
y - 6 = -2x + 10
y = -2x + 16
Hence, the equation of the line perpendicular to y=1/2x-1 and passing through the point (5,6) is y = -2x + 16.
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HELP ME PLEASE ITS DUE TODAY!!! The following data shows the number of times a class of 7th graders ate breakfast over a 30-day period.
{4, 18, 22, 25, 15, 12, 22, 14, 19, 30, 24, 20, 21, 24, 29, 16, 20, 27, 24, 25}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (2 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (2 points)
Answers
Part A: Note that the best graphical representation to use for this kind of data is a Histogram.
Part B : Creating the historgram means you have to first chose the intervals for the data.
What is the reason for the choice above?When it comes to displaying the distribution of a set of continuous data, histograms offer an appropriate visualization method.
This display type divides the data into intervals and plots the number of observations that fall within each interval, hence providing frequency distribution information.
For instance, in creating a histogram for this particular dataset, one can choose intervals or bins with sizes e.g. 5 units covering a range between 0 and 30 before tabulating the count of observed variables in each bin and plotting these counts on the chart's vertical axis.
A histogram illustrates how often students ate breakfast within a 30-day timeframe. This frequency distribution features labeled axes, with the vertical axis representing "Frequency" and the horizontal axis depicting "Number of times students ate breakfast."
Each bar on the horizontal axis corresponds to an interval and shows its frequency on a scaled height basis.
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The equation y=464-8x describes the altitude y in feet of a plane x seconds after it begins its descent how many seconds will it take the plane to land
Answers
In 58 seconds after starting its descent, the aircraft will touch down.
The plane will land when its altitude y is zero.
So we can set y = 0 in the equation:
0 = 464 - 8x
Solving for x:
8x = 464
x = 58
Therefore, the plane will land 58 seconds after it begins its descent.
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In the United States between 1910 and 1994, the amount of currency in circulation M ( in billions of dollars) can be approximated by the function M = 2.08 * (1.06) ^ t where t represents the number of years since 1910. Determine the amount of currency in circulation in the year 1980. (round to the nearest hundredth).
A.3.32
B.122.88
C.220.06
D.2.65
Answers
Answer:
B. 122.88
Step-by-step explanation:
Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:
t = 1980 - 1910 = 70
Now, we can plug in 70 for t to find the amount of currency in 1980:
[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]
Thus, the amount of currency in 1980 according to the model was $122.88 billion
Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.
Answers
The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;
What is the volume of the right circular cone?As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.
Recall, the volume of the cone is;
V = (1/3) × πr²h
V = (1/3) × π × 16.3² × 11.9
V = 3310.9 ft³.
Ultimately, the volume of the right circular cone is; 3310.9 ft³.
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Answer:
3310.9
Step-by-step explanation: