To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken. The average speed can be calculated as (2D) / (D/3 + D/5), which is approximately 3.53 mi/h.
Explanation:To find Michaela's average speed for the entire trip, we need to calculate the total distance traveled and the total time taken.
Let's assume the distance she climbed up the mountain is D. The distance she climbed down is also D since she retraced her steps. The average speed for climbing up is 3 mi/h and the average speed for climbing down is 5 mi/h.
The total distance is 2D and the total time is D/3 + D/5. Therefore, the average speed can be calculated as (2D) / (D/3 + D/5).
Simplifying this expression gives us the average speed as 3.53 mi/h (rounded to the nearest tenth).
what angle measure forms a linear pair with an angle that measures 125
I am a 2 digit number, add my digits together and you get 5, I am not an odd number, I am greater than 45, what am I?
Victoria is 4 years older than her neighbor. the sum of their ages is no more than 14 years. 1. enter an inequality that can be used to represent this situation in the first box, where x represents victoria's neighbor's age. 2. enter the oldest age victoria's neighbor in the second box.
The equationoflinevis y + 10 = 2 3 ( x – 8 ) . line w , which is parallel to line v , includes the point (6, -5) . what is the equation of line w ?
Which point is the center of the circle?
A.point W
B.point X
C.point Y
D.point Z
Answer:
The center of given circle is X.
Step-by-step explanation:
Given : Circle .
To find: Which point is the center of the circle?
Solution : The diameter of a circle subtends a right angle to any point on the circle is called center of circle .
Therefore, The center of given circle is X.
Answer:
Hence, point X is the center of the circle.
Step-by-step explanation:
We are given a circle.
We have to find the center of a circle.
Circle: It is the set of points in a plane which are equidistant from a particular point called the center of the circle.
As we can see all the points of a circle are equidistant from point X
Hence, point X is the center of the circle.
Hence, correct option is:
B. point X
Simplify the expression. –9z – 13z
A. 4z
B. 4
C. –22z
D. 22z
The amount of money at a gas stations varies directly with the number of gallons purchased. When 14 gallons were purchased the cost was $27.16. Determine the cost for 18 gallons of gas.
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Which statement describes a parallelogram that must be a square?
A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
C. A parallelogram with a right angle and diagonals that are congruent
D. A parallelogram with diagonals that bisect each other.
Answer: B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
Step-by-step explanation:
We know that a parallelogram is a quadrilateral having congruent opposite sides and its diagonals bisect each other.
A square is a kind of parallelogram having all its consecutive sides equal and both diagonals congruent to each other.
Its all 4 angles are right angle.
let's check all the statements :
A. A parallelogram with a pair of congruent consecutive sides and diagonals that bisect each other.
→It can be rhombus ∵ it also has same characteristics.
B. A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
→ It only occurs in square.
C. A parallelogram with a right angle and diagonals that are congruent .
→ it can be a rectangle ∵ it has all its angles right angle and diagonals are congruent.
D. A parallelogram with diagonals that bisect each other.
→ It is the basic property of parallelogram , it can describe a rhombus or rectangle both.
The statement that must be true is (b) A parallelogram with a pair of congruent consecutive sides and diagonals that are congruent.
A parallelogram has parallel and congruent opposite sides
However, the following must be true about parallelograms that can be regarded as squares:
There are congruent consecutive sidesThe diagonals are congruentHence, the true statement is (b)
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What is the value of 3x ( 2x²+6x+3) when x is -3?
a. -27
b. 0
c. 27
d. 54
A business owes $8000 on a loan. Every month, the business pays 12 of the amount remaining on the loan.
How much will the business pay in the sixth month?
The business will pay $506.99 on the loan in the sixth month, after making monthly payments of 12% of the remaining balance on an $8000 loan.
Explanation:To determine how much the business will pay in the sixth month on a loan where they pay off 12% of the remaining balance each month, we need to use a decay formula. This is a type of exponential decay since the amount owed is decreasing by a fixed percentage each month. The formula to find the remaining balance after each payment is:
Balance after n payments = Initial amount * (1 - rate)^n
Starting with an initial loan amount of $8000 and a monthly payment rate of 12% (or 0.12 in decimal form), we calculate the remaining balance each month until the sixth month:
Month 1: 8000 * (1 - 0.12) = 8000 * 0.88 = $7040 remainingMonth 2: 7040 * 0.88 = $6195.20 remainingMonth 3: 6195.20 * 0.88 = $5455.78 remainingMonth 4: 5455.78 * 0.88 = $4801.09 remainingMonth 5: 4801.09 * 0.88 = $4224.96 remainingMonth 6: 4224.96 * 0.88 = $3717.97 remainingNow we can find out how much will be paid in the sixth month by calculating 12% of the balance at the end of the fifth month:
Sixth month payment = 12% of 4224.96
Sixth month payment = 0.12 * 4224.96
Sixth month payment = $506.99
The business will pay $506.99 in the sixth month.
For the equations given above, which statement is true?
It is 4 kilometers from chris's house to the nearest mailbox. how far is it in meters?
I need help with #20 and #21. Show work if possible. Thank You! :)
10. Which transformations result in a preimage and image with opposite orientations?
1 point
Dilations only
Translations and rotations
Rotations and reflections
Reflections and glide reflections
In geometry, reflections and glide reflections are transformations that result in a preimage and an image with opposite orientations. This happens because a reflection flips an object over a line, creating a mirror image with reverse orientation. A glide reflection combines a translation and a reflection, also leading to opposite orientation.
Explanation:In mathematics, particularly in geometry, when we talk about a preimage and an image, we refer to the original shape and the shape after transformation respectively. The transformation that results in a preimage and image with opposite orientations is reflections and glide reflections. A reflection is a transformation that flips a figure over a line, thus turning it into its mirror image. This reverses the orientation of the figure. A glide reflection involves a translation (or glide) followed by a reflection. Again, the result will have an orientation opposite to the original (or preimage).
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What is the value of x?
angle PIR
angle SIM
The first quartile of a data set is 2.5.
Which statement about the data values is true?
One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.
Half of the values are less than or equal to 2.5, and half of the values are more than 2.5.
Three fourths of the values are less than or equal to 2.5, and one fourth of the values are above 2.5.
One fourth of the values are less than or equal to 2.5, and half of the values are above 2.5.
First statement is true.
One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.
The first quartile (Q₁) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower or 25th empirical quartile, as 25% of the data is below this point.The first quartile , is located such that 25 percent of the data lie below first quartile and 75 percent of the data lie above first quartile.Therefore, The first quartile of a data set is 2.5. this statement represent that One fourth of the values are less than or equal to 2.5, and three fourths of the values are above 2.5.
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Which expression equals 1?
a. sin(x) + cos(x)
b. sin^2(x) + cos^2(x)
c. sin^2(x) - cos^2(x)
d. sin(x) - cos(x)
The table below lists the number of floors in the 10 tallest buildings in the world. Note: The buildings are organized by height, not by the number of floors. Skyscraper Number of Floors Taipei 101 Shanghai World Financial Center 101 Petronas Tower 1 88 Petronas Tower 2 88 Greenland Square Zifeng Tower 69 Sears Tower 108 Jin Mao Tower 88 Two International Financial Centre 88 Citic Plaza 80 Shun Hing Square 69 What is the difference between the median and the mode for the number of floors?
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Choose the correct pair !!
Carol earns $8.50 per hour plus 6% commission. She worked 40 hours last week. What is her salary if her total sales were $250
Can you please explain to me what the end behavior of the function f(x)=-2x^4-x^3+3 looks like?
I have trouble putting it into terms of approaching infinities as well.Thank you!
If a car rental costs $35 per day plus $0.79 per mile, and you are traveling for 4 days, 389 miles, how much is the total rental?
Answer:
Total rent costing for traveling for 4 days, 389 miles is $447.31
Step-by-step explanation:
Given : a car rental costs $35 per day plus $0.79 per mile.
We have to find the total rent costing for traveling for 4 days, 389 miles.
Since, Cost of car rent per day is $35
Thus, Cost of car rent for 4 days is $ 35 × 4 = $140
Also, Cost of car rent per miles is $0.79
Thus, Cost of car rent for 389 miles is $ 0.79 × 389 = $307.31
Thus, total car rental cost = Cost of car rent for 4 days + Cost of car rent for 389 miles.
Total car rental cost = $140 + $307.31
Total car rental cost = $447.31
Thus, total rent costing for traveling for 4 days, 389 miles is $447.31
What is the median of 150.8, 149.5, 151.2, 153.1, 150.6, 149.9, 146.5, 151.5, 153.5?
Fran graphs the equations y = 2x2 – 2 and y = –0.5x + 4. Her graph is shown below.
Which value is an approximate solution of 2x2 – 2 = –0.5x + 4?
A. x=-2
B. x=-1
C. x=1
D. x=5
Those are the choices
Answer:
Option A is correct
x= -2 is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex]
Step-by-step explanation:
As per the statement:
Fran graphs the equations
[tex]y=2x^2-2[/tex] and
[tex]y = -0.5x + 4[/tex]
Equate these two equations:
[tex]2x^2-2 = -0.5x+4[/tex]
You can see the graph for these equations as shown.
Since, the line and the parabola intersects at x = -2 and x = 1.5.
From the given options:
x = -2 is the solution for these equations.
Therefore, the value is an approximate solution of [tex]2x^2-2 = -0.5x+4[/tex] is, x = -2
I need help with 1-3 I just don’t understand how to do it at all please help
An architectural drawing of a building shows the elevation of the basement floor to be â12 feet. the elevation of the roof is 32 feet. what is the total distance from the roof to the basement floor?
Work out the value of 6x^2 when x= -2
What is the difference between linear and nonlinear equations