Tom weighed 122 pounds at the end of the year.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Tom weighed 110 pounds at the beginning of the year.
Pounds gained in June = 13
Pounds lost in August = 5
Pounds gained in November = 4
Now,
Total pounds at the end of the year.
= 110 + 13 - 5 + 4
= 110 + 17 - 5
= 110 + 12
= 122 pounds
Thus,
122 pounds at the end of the year.
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Consider the diagram and the paragraph proof below. Given: Right △ABC as shown where CD is an altitude of the triangle Prove: a2 + b2 = c2 Because △ABC and △CBD both have a right angle, and the same angle B is in both triangles, the triangles must be similar by AA. Likewise, △ABC and △ACD both have a right angle, and the same angle A is in both triangles, so they also must be similar by AA. The proportions and are true because they are ratios of corresponding parts of similar triangles. The two proportions can be rewritten as a2 = cf and b2 = ce. Adding b2 to both sides of first equation, a2 = cf, results in the equation a2 + b2 = cf + b2. Because b2 and ce are equal, ce can be substituted into the right side of the equation for b2, resulting in the equation a2 + b2 = cf + ce. Applying the converse of the distributive property results in the equation a2 + b2 = c(f + e).
Answer:
Because f+e=c
Therefore ,[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
Given A right triangle ABC as shown in figure where CD is an altitude of the triangle.
To prove that [tex]a^2+b^2=c^2[/tex]
Proofe: Given [tex]\triangle ABC\; and\; \triangle CBD[/tex] both are right triangle and both triangles have common angle B si same.
Therefore , two angles of two triangles are equal .
Hence, [tex]\triangle ABC \sim\triangle CBD[/tex] by using AA similarity.
Similarity property: when two triangles are similar then their corresponding angles are equal and their corresponding side are in equal proportion.[tex]\frac{a}{f} =\frac{c}{a}[/tex]Similarly , [tex]\triangle ABC \sim \triangle ACD[/tex] by AA similarity property . Because both triangles are right triangles therefore, one angle of both triangles is equal to 90 degree and both triangles have one common angle A is same .
[tex]\therefore[/tex] [tex]\frac{b}{c} =\frac{e}{b}[/tex]
The corresponding parts of two similar triangles are in equal proportion therefore , two proportion can be rewrite as
[tex]a^2=cf[/tex] (I equation)
and [tex]b^2=ce[/tex] (II equation)
Adding [tex]b^2[/tex] to both sides of firs equation
[tex]a^2+b^2=cf+b^2[/tex]
Because [tex]b^2=ce[/tex] and ce can be substituted into the right side of equation wevcan write as
[tex]a^2+b^2=ce+cf[/tex]
Applying the converse of distributive property we can write
[tex]a^2+b^2=c(f+e)[/tex]
Distributive property: a.(b+c)= a.c+a.b
[tex]a^2+b^2=c^2[/tex]
Because f+e=[tex]c^2[/tex]
Hence proved.
Container A can hold 9 cups of liquid. container B can hold 5 pints of liquid. Container c can hold 2 quarts of liquid. Whice container has the greatest capacity? Explain
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle C?
Enter your answer in the box.
Answer:
92 is correct
Step-by-step explanation:
The boys' basketball team at Washington High School has been doing really well so far this year. In the past six games, they've scored the following points.
84, 67, 74, 87, 67, 73
What is the mean of their scores, rounded to the nearest tenth?
Answer:
(84 +67 +74 +87 +67 +73)/6 = 452/6 = 75.3
Step-by-step explanation:
Exactly what you see :]
an artist painted a 6 foot tall painting, then decide to also create a smaller version. if she uses a scale of 4 inches=1.5 feet, what will be the height of the smaller painting
Final answer:
To determine the height of the smaller version of the painting using the scale of 4 inches = 1.5 feet, we first convert the original height to inches (6 feet = 72 inches) and then use a proportion to find that the height of the smaller painting is 16 inches.
Explanation:
The student's question involves using a scale to determine the height of a smaller version of a painting. The scale given is 4 inches = 1.5 feet. To begin, we convert the original height of the painting from feet to inches since the scale is in inches. The original height of 6 feet is equivalent to 72 inches (because 1 foot is equal to 12 inches).
Next, we set up a proportion using the scale:
4 inches / 1.5 feet = x inches / 6 feet
Now we solve for x, which represents the height of the smaller painting in inches:
4 / 1.5 = x / 6
4 / 1.5 * 6 = x
x = 4 * 6 / 1.5
x = 24 / 1.5
x = 16 inches
Thus, the height of the smaller version of the painting will be 16 inches.
This week laptops are 25 percent off if a laptop cost $340 what is it's sale price
Which equation represents a nonlinear function?
x(y – 5) = 2
y – 2(x + 9) = 0
3y + 6(2 – x) = 5
2(y + x) = 0
Answer:
The correct answer is: A: x(y – 5) = 2
Step-by-step explanation:
edge2021
Please help:
Solve using logarithms. Round the solution to the nearest hundredth. Show your work.
(you will need to use a calculator at some point)
12km is equal to how many meters? (show all work)
convert the following logarithmic equation to the equivalent exponential equation. Use the caret (^) to enter exponents. y=ln x
Answer:
To solve this problem, you need to remember that an exponential function has the following form:
f(x)=a^x
"a" is the base and "x" is the exponent.
2. It is important to know that the logarithmic functions and the exponential functionsare inverse. Then, you have:
y=ln x
e^y=e^(lnx)
e^y=x
3. Therefore, the answer is:
Step-by-step explanation:
You have an equally likely chance of choosing any number from 1 to 10. What is the probability that you choose a number greater than 6?
Answer:
2/5
Step-by-step explanation:
1 to 10, it is 10 numbers
and there are 4 numbers which are 7,8,9,10 are bigger than 6
so P =4/10=2/5
A computer program in Shannon’s computer carries out a single mathematical operation in 1.5 × 10-6 seconds. How much time would the program take to complete 2.5 × 103 mathematical operations?
You forgot A, B, C, and D but the correct answer is option D, 3.75 x 10 ^ -3 seconds
A band that will be the opening act for a concert charges a $500.00 flat fee as well as 10% of all profits from ticket sales. If the band earns $1,200, how much was made in total ticket sales for the show?
Answer:
The answer is 7,000
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Please help me with question 22
The circle is centered at the point (-3,4) and has a radius of length 3. What is its equation?
Keshawn is constructing the inscribed circle for △PQR . He has already used his compass and straightedge to complete the part of the construction shown in the figure. Which construction could be his next step? Construct the angle bisector of ∠XQR . Construct the line through points P and X. Construct the perpendicular bisector of PQ¯¯¯¯¯ . Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Answer:
Construct the perpendicular to QR¯¯¯¯¯ that passes through point X.
Step-by-step explanation:
Reciprocal of 1/10 = ?
Reciprocal of 16 = ?
Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thursday and Friday. How long did Leo paint this week
Leo painted for 2/3 of an hour each day on Monday, Tuesday, Thurday, and friday. Thus, the total time of the week for which he painted is 1.58% of the total time.
What is a fraction?A fraction represents a part of a whole number or, more commonly, any number of equal parts. A fraction can be defined as the parts of a certain size, for example, one-half, eight-fifths, three-quarters, etc.
The time for which Leo painted in this week can be calculated as:
Leo painted 2/3 of an hour each day for monday, tuesday, thursday, and friday
Therefore, the time of painting in an hour = 40 minutes
2/3 × 60 = 120/ 3 = 40 minutes = 40 × 4 = 160 minutes
The number of minutes in a day,
1 day = 60 × 24 = 1,440 minutes
The number of minutes in seven days,
7 days = 1440 × 7 = 10,080 minutes
Therefore, the total time for which Leo painted = time for which he painted in minute divided by total time in minutes
Total time for which Leo painted = 160/ 1440 = 0.0158 or 1.58%
Therefore, total time for which he painted in this week is 0.0158 of total time
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Keisha's boat has a top speed of 9 miles per hour in still water. While traveling on a river at top speed, she went 10 miles upstream in the same amount of time she went 20 miles downstream. Find the rate of the river current.
the second of two numbers is 4 more than the first the sum of the numbers is 56 find the numbers
Answer:
26, 30
Step-by-step explanation:
If you subtract from the sum the excess of the second over the first, you have a sum that is twice the first.
first number = (56 -4)/2 = 26
The second number is 4 more, so is ...
second number = 26 +4 = 30
_____
Check
Their total is 26 +30 = 56, as required.
Use the chain rule to find ∂z/∂s and ∂z/∂t. z = x5y7, x = s cos(t), y = s sin(t)
Using the Chain Rule of differentiation, we can solve for ∂z/∂s and ∂z/∂t given the functions for z, x, and y. The Chain Rule is fundamental for calculus by finding the derivative of composite functions.
Explanation:To solve for ∂z/∂s and ∂z/∂t with z = x5y7, x = s cos(t), and y = s sin(t), we'll employ the use of the Chain Rule of differentiation. First, we consider ∂z/∂s. As z is x raised to the power of 5 then multiplied by y to the power of 7, we can express ∂z/∂x and ∂z/∂y. Proceeding using the chain rule, which in simpler terms could be stated as 'the derivative of the outside times the derivative of the inside', we get the values of ∂z/∂s and ∂z/∂t. The chain rule in calculus is an important tool when differentiating composite functions.
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Jenna has 8 pairs of jeans. Three of them are blue. What percentage of her jeans is blue?
= 37.5%
But my question is this:
Jenna bought two more pairs of jeans.
If both of them are blue, what percentage of her jeans is blue now?
If both of them are not blue, what percentage of her jeans is blue now?
An airplane is flying at an altitude of 10,000 feet when it receives clearance to land at the airport. The angle of depression from the airplane to the airport is 4o. What is the horizontal (ground distance) from the airport to the airplane's position?
2.7 Q9
The functions f and g are defined by the following tables. Use the tables to evaluate the given composite function.
Answer: [tex](gof)(-1)=-2[/tex]
Step-by-step explanation:
By definition, a composite function is a function formed by substituing one function into another function.
Given the composite function:
[tex](gof)(-1)[/tex]
You can rewrite it in the following form:
[tex]g(f(-1))[/tex]
In order to evaluate it, follow these steps:
- Based on the table of the function f(x), the ouput value for [tex]x=-1[/tex] is [tex]y=3[/tex]. Then:
[tex]f(-1)=3[/tex]
- This will be the input of the function g(x).
- Notice in the table of the function g(x) that the output value when [tex]x=3[/tex] is [tex]y=-2[/tex]:
[tex]g(3)=-2[/tex]
Therefore:
[tex]g(f(-1))=-2[/tex] or [tex](gof)(-1)=-2[/tex]
Answer:
The value of [tex]\rm{gof(-1)}[/tex] is -2.
Step-by-step explanation:
Given,
The table contains the functional value of f(x) and g(x).
To find: [tex]\rm{gof(-1)}[/tex]
[tex]\rm{fog(-1)}[/tex] is a composite function of f(x) and g(x).
[tex]\rm{gof(-1)}=\rm{g[f(-1)}][/tex]
Clearly from the table, the value of f(x) when [tex]x=-1[/tex] is 3.
Therefore,
[tex]f(-1)=3[/tex]
Now,
[tex]\rm{gof(-1)}=\rm{g[f(-1)}]\\\rm{fof(-1)}=\rm{g(3)}[/tex]
Clearly from the table, the value of g(x) when [tex]x=3[/tex] is -2.
Thus,
[tex]\rm{gof(-1)}=-2[/tex]
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A roadway repair crew has fixed 42 mi of the roadway. That number of miles is 30% of the total number of miles that need to be repaired
Answer:
The answer is 140 miles 100x42 is 4200 divide that by 30= 140Step-by-step explanation:
Find the longer diagonal of a parallelogram having sides of 10 and 15 and an angle measure of 120° between them. 13.2 18.0 21.8 23.1
Answer:
21.8
Step-by-step explanation:
What is the range of the following set?
28, 45, 12, 34, 36, 45, 19, 20
8
33
45
57
solve the following system using substitution x+4y=21 4x-y=16
during the new year celebration there are orange, green purple, and blue fireworks. In how many different orders can the different colors of fireworks appear?
There are 24 different orders in which the different colors of fireworks can appear.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
If there are four colors of fireworks (orange, green, purple, and blue), then the number of different orders in which they can appear can be found by calculating the number of permutations of four objects, which is:
4! = 4 x 3 x 2 x 1 = 24
Therefore,
There are 24 different orders in which the different colors of fireworks can appear.
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what is the difference of the rational expressions below? 13x/5 - 4x/5
a. 9x/5
b. 17x/5
c. 52x/5
d. 52x/25