A trapezoid is made of a square with side lengths of 7 feet and an isosceles right triangle whose base and height are both 7 feet.What is the area?
The total area of the trapezoid is 73.5 square feet, calculated by adding the area of the square (49 square feet) to the area of the isosceles right triangle (24.5 square feet).
The area of a trapezoid consists of the area of a square and the area of an isosceles right triangle. Since the square has side lengths of 7 feet, its area is 49 square feet (7 feet x 7 feet). The isosceles right triangle, with both the base and the height being 7 feet, has an area of 24.5 square feet (1/2 x 7 feet x 7 feet). Therefore, the total area of the trapezoid is the sum of the areas of the square and the triangle.
Total area = Area of square + Area of triangle
Total area = 49 square feet + 24.5 square feet = 73.5 square feet.
How much work is needed to stretch this spring from x = 3.0 cm to x = 7.0 cm ?
The work done to stretch a spring is calculated using Hooke's Law, denoted by the formula W = 1/2kx², where 'k' is the spring constant and 'x' the displacement. The displacement is the difference between the final and initial lengths of the spring (7.0 cm - 3.0 cm). However, without the spring constant, a specific numerical answer cannot be provided.
Explanation:The problem requires calculating the work done to stretch a spring. This can be done using Hooke's Law in Physics, which states that the force necessary to extend or compress a spring by a distance 'x' from its equilibrium position is proportional to 'x'. The magnitude of the force applied is represented as F = kx, where 'k' is the spring constant. However, the work done, W, against this force is given by 1/2kx².
To calculate, we need to know the value of the spring constant 'k', and the displacement 'x', which is the difference between the final length (7.0 cm) and the initial length (3.0 cm) of the spring. Without the spring constant, we, unfortunately, cannot provide a numerical answer.
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9+(6-6)x4-(-7-(-2)) solved in order of operations
what number has the same absolute value as 81?
Felicity is placing a rectangle in the coordinate plane. She knows that the longer side of the rectangle is 3 times its shorter side. She places the longer side on the x-axis.
What coordinates should she assign to the top-right vertex of the rectangle?
Answer:
(3a,a)
Step-by-step explanation:
As you know the component on the X vertex is the first that is represented when setting point coordenates, and the second value is in the Y vertex, as you can see the value for Y is a, and in the problem says that the longer side is three times the short side, since the Y vertex is the short side, that means the X vertex will have the longer side, making it 3a. So the coordenates will be (3a,a).
There are 1800 gym members in total. 3\4 are aged 25-59 years. 1/5 are over 60 years old and the remainder are under 25 years old. How many members are under 25 years old
if pictures width 4+w and the length measures 8w+2, how much longer is the picture than it is wide?
The picture is 7w - 2 units longer than it is wide, this is found by subtracting the width (4+w) from the length (8w+2).
To find out how much longer the picture is than it is wide, we must compare the picture's length and width. Given the picture's width is 4+w and the length is 8w+2, we subtract the width from the length to find the difference:
Length - Width = (8w+2) - (4+w) = 8w + 2 - 4 - w = 7w - 2.
Therefore, the picture is 7w - 2 units longer than it is wide.
Part A: Abe rented a bike at $36 for 5 days. If he rents the same bike for 8 days, he has to pay a total rent of $48.
Write an equation in the standard form to represent the total rent (y) that Abe has to pay for renting the bike for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
(10 points)
Janelle has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 7mph and walks back at a speed of 3mph how long should she plan to spend walking back?
Final answer:
Janelle should plan to spend 3 hours walking back.
Explanation:
To find out how long Janelle should plan to spend walking back, we need to calculate the total time it takes her to run and walk. Since she runs at a speed of 7mph, she completes the distance of the race in 1 hour (4 miles / 7mph = 0.57 hours = 1 hour). Therefore, she spends 1 hour running and 3 hours left for walking. To find out the distance she walks back, we use the formula distance = speed x time. Since she walks at a speed of 3mph, the distance she walks back is 3mph x 3 hours = 9 miles.
What is the factorization of g3 – 125?
(g– 5)(g2 + 5g + 10)
(g – 25)(g2 + 25g + 625)
(g – 5)(g2 + 5g + 25)
(g – 25)(g2 + 5g + 125)
Answer: (C) (g – 5)(g2 + 5g + 25)
One angle of a linear pair is 12 less than half the other angle find both angles
The function f(x) is graphed on the coordinate plane.
What is f(−2) ?
Enter your answer in the box.
f(−2) = ?
which would not be a step in solving 3x + 1 + 2x = 2+ 4x?
To solve the equation 3x + 1 + 2x = 2 + 4x, you would first combine like terms, then eliminate variable terms on one side of the equation, and finally solve for x.
Explanation:In solving the equation 3x + 1 + 2x = 2 + 4x, the first step would be to combine like terms on both sides of the equation. This means adding or subtracting the same type of terms together. In this case, you would combine the x terms on the left side and the constant terms on the right side. The equation will then be simplified to 5x + 1 = 2 + 4x.
The next step would be to get rid of the variable terms on one side of the equation. To do this, you can subtract 4x from both sides of the equation. This will result in x + 1 = 2.
Finally, you can solve for x by subtracting 1 from both sides of the equation. This gives us the solution x = 1.
Hannah travels 6 times as many minutes than Raoul does. Together, they travel 63 minutes. How many minutes does Hannah travel? Draw a model and wrote an equation to solve.
(algebra)
Solve for x.
Fx-gx=h
If we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).
What is algebra ?
Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.
An equation is given which is :
(F × x ) - (g × x ) = h
We have to solve this equation to get the value of the variable x.
So, the value of x can be calculated as :
(F × x ) - (g × x ) = h
Taking common x from LHS :
x ( F - g ) = h
Dividing by ( F - g ) on both sides we get :
[ x ( F - g ) / ( F - g )] = h / ( F - g )
or
x = h / ( F - g )
Therefore , if we solve the equation which is (F × x ) - (g × x ) = h , we will get the value of x as x = h / ( F - g ).
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3 1/5 divided by 1 1/7
Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8. How do the estimate and the actual product compare?
A. The actual product is less than the estimate. The numbers differ by less than one.
B. The actual product is greater than the estimate. The numbers differ by less than one.
C. The actual product is less than the estimate. The numbers differ by more than one.
D. The actual product is greater than the estimate. The numbers differ by more than one.
Answer:
b the answer
Step-by-step explanation:
just did it
Final answer:
The actual product is less than the estimate. The numbers differ by less than one.
Explanation:
Javier rounded to the nearest half to estimate the product of 3 2/5 and -3 7/8.
To estimate the product, we can round both numbers to the nearest half, which gives us 3.5 and -3.5. Multiplying these rounded numbers gives an estimate of -12.25.
The actual product of 3 2/5 and -3 7/8 is -3.4. Therefore, the actual product is less than the estimate. The numbers differ by less than one.
What is the unit rate of 15 degrees in 2 hours.
write the phrase as a mathematical expression. 9 more than 4 times a number
what is the greatest common factor of 15 and 27
Final answer:
The greatest common factor of 15 and 27 is 3, which is the largest number that divides both numbers without a remainder.
Explanation:
The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 15 and 27, list the factors of each number:
Factors of 15: 1, 3, 5, 15
Factors of 27: 1, 3, 9, 27
The common factors of 15 and 27 are 1 and 3. The largest of these is 3, therefore the greatest common factor of 15 and 27 is 3.
Could 10.7 cm,3.2 cm,and 5.5 cm be the side lenghts of a triangle
Which of the following statements are equivalent to the statement "price increased by 100%"?
Choose all correct answers.
(A) The price doubled
(B) The price is 150% of the price before
(C) The price was reduced by a quarter
(D) The price became a half of what it was before
(E) The price is now 1.5 of what it was before
(F) The price now is 66 2/3 % of what it was before
(G) The price now is 200% of what it was before
(H) The price is 75% of what it was before
The statements equivalent to a price increase of 100% are that the price doubled and the price is now 200% of the original. These statements mean the new price is twice the original amount.
When analyzing statements that describe a price increase of 100%, it is important to understand that this means the new price is twice the original price. Among the listed statements, the correct ones that are equivalent to a 100% increase in price are:
(A) The price doubled
(G) The price now is 200% of what it was before
These are equivalent because if a price doubles, it is 100% more, making the new price 200% of the original. This can be seen in practical examples, such as if a gumball costs 25 cents and the price doubles, it becomes 50 cents, or 200% of its original cost.
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Yolanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $50 and costs an additional $0.13 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
Round each addend to the nearest ten thousand,and then find the estimated sum.?
337,961 + 482,746
_+_=_
To find the estimated sum, round each addend to the nearest ten thousand by looking at the digit in the ten thousand places. Then add the rounded numbers together.
Explanation:To round each addend to the nearest ten thousand, look at the digit in the ten thousand places. If the digit is 5 or greater, round up by increasing the number in the ten thousand place by 1. If the digit is less than 5, round down by keeping the number in the ten thousand places the same. For 337,961, the digit in the ten thousand places is 9, so it rounds up to 340,000. For 482,746, the digit in the ten thousand places is 7, so it rounds down to 480,000. Now, you can find the estimated sum by adding the rounded numbers, which would be 340,000 + 480,000 = 820,000.
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write a comparison sentence to resent this equation 6 times 7 equals 42
A comparison sentence for the equation '6 times 7 equals 42' using multiplication.
Comparing the given equation '6 times 7 equals 42' using a sentence:
In comparison to the equation 6 times 7 equals 42, the sentence '7 multiplied by 6 results in 42' represents the relationship between the factors and the product.
P(-9,1);m=1 use slope intercept form to write an equation of a line passing through the given point and having the given slope. Express answer in Standord form
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Jimmy is going to pack his backpack for a trip. His backpack is 60 cubic litres. He has a pile of equipment that takes up 43 cubic litres and then he has his sleeping bag that takes up 23 cubic litres. Let r be the amount of room left in his backpack. Which equation could you use to determine if he has enough room in his backpack.
A) r = 23 + 43
B) r = 23 + 43 + 60
C) 23 + 43 + r = 60
D) 23 + r = 60 + 43
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
Given that, Jimmy backpack is 60 cubic liters. He has a pile of equipment that takes up 43 cubic liters and then he has his sleeping bag that takes up 23 cubic liters.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let r be the amount of room left in his backpack.
Total space in backpack = A pile of equipment + Sleeping bag + Room left
So, 60 = 43+23+r
The equation for the given situation is 23 + 43 + r = 60. Therefore, option C is the correct answer.
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The graph shows a line and two similar triangles.
Answer:
Option C. is the correct option.
Step-by-step explanation:
The given line in the graph passes through two points (0, 3) and (3, 7).
We have to find the equation of the line.
Since y = mx + c is the standard equation of a line
where m = slope of the line
c = y - intercept
Slope of a line m = [tex]\frac{(y-y')}{(x-x')}[/tex]
Now we put the values of x and y to find the slope of this line.
m = [tex]\frac{7-3}{3-0}=\frac{4}{3}[/tex]
Since (0, 3) passes through the line
3 = 0 + c
c = 3
Equation of the line will be
[tex]y=\frac{4}{3}x+3[/tex]
Option C. is the answer.
Answer:
me dony know
Step-by-step explanation:
Estimated the difference
645,908 + 335,297
_ - _ = _
The price of a pair of shoes is $45.90. The sales tax rate is 5%. How much sales tax do you need to pay?
Answer:
The sales tax to be paid for the pair of shoes is $2.29.
Step-by-step explanation:
If the price of a pair of shoes is $45.90, and the sales tax rate for it is of 5%, in order to know the sales tax to be paid we have to do the following calculation:
(45.90 x 5) / 100 = X
229.5 / 100 = X
2.295 = X
So, as we can see, the sales tax to be paid is $2.29