Answers
The combined area of the shaded triangles in figure one is 2ab. We have four congruent right triangles given, with legs a and b. The formula to calculate the area of a right triangle is (leg * leg) / 2. So the area of one of the triangles is ab/2. We have four of these triangles, so ab/2 * 4 = 2ab.
The area of the unshaded square in figure one can be represented as c^2. Since the side of the square is given as c, its area must be c^2 (calculate the area of a square by multiplying its side length by itself).
The combined area of the unshaded squares in figure 2 can be represented by a^2 + b^2. Again, we find the areas of each square by multiplying the side lengths togther: (a * a) + (b * b) = a^2 + b^2.
Finally the areas of the squares in figure one and figure two show that a^2 + b^2 = c^2. This is because the shaded triangles in figure one take up the same area as that of figure two. And since the total figure areas are the same, the unshaded parts of each figure must be equal to each other. Therefore, we have a^2 + b^2 = c^2. This is also known as the Pythagorean Theorem.
Related Questions
In the diagram below of triangle BCD, E is the midpoint of BD and F is the midpoint of CD. If EF = 43-4x, and BC = 32-2x, what is the measure of EF?
Answers
The measure of the length EF of the triangle is; 21
How to solve similar triangles?We are given the the triangle BCD and we are told that;
E is the midpoint of BD.
F is the midpoint of CD
Now, since we have those midpoints, it means that by the concept of similar triangles, that;
DF/DC = EF/BC
Since F is the midpoint of DC, then it means that;
2DF = DC
We are given;
EF = 43 - 4x, and BC = 32 - 2x
Thus, we now have;
DF/(2DF) = (43 - 4x)/(32 - 2x)
1/2 = (43 - 4x)/(32 - 2x)
Cross multiply to get;
32 - 2x = 43 - 4x
4x - 2x = 43 - 32
2x = 11
x = 11/2
x = 5.5
Thus;
EF = 43 - 4(5.5)
EF = 43 - 22
EF = 21
Thus, we conclude that the side length EF is 21.
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The general form of a hyperbola is 6x2−5y2+12x+50y−149=0.
What is the standard form of this hyperbola?
Enter your answer by filling in the boxes.
Answers
The quadratic equation (x + 1)² / 46.667 - (y - 5)² / 56 = 1 represents the hyperbola in standard form.
How to derive the standard form of the equation of a hyperbola
In this question we find the equation of a hyperbola in general form, that is, a quadratic equation of the form A · x² + B · y² + C · x + D · y + E = 0, and we need to obtain the standard form of the hyperbola:
(x - h)² / a² - (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a, b - Length of the semiaxes.We can switch from general form into standard form by completing the square, an application of algebra properties:
6 · x² - 5 · y² + 12 · x + 50 · y - 149 = 0
(6 · x² + 12 · x) - (5 · y² - 50 · y) = 149
6 · (x² + 2 · x) - 5 · (y² - 10 · y) = 149
6 · (x² + 2 · x + 1) - 5 · (y² - 10 · y + 25) = 149 + 6 + 125
6 · (x + 1)² - 5 · (y - 5)² = 280
(x + 1)² / 46.667 - (y - 5)² / 56 = 1
The equation of the hyperbola in standard form is (x + 1)² / 46.667 - (y - 5)² / 56 = 1.
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the product of 0.8 and a number is 12represent the statement as an equation determine the solution set using the replacement set 0 8 1 7 15
Answers
Answer:
The product of 0.8 and a number is 12, so the equation representing this statement is: 0.8 * x = 12.
To solve this equation, we need to find the value of x that makes the equation true. We can do this by using the replacement set {0, 8, 1, 7, 15}.
If we substitute 0 for x in the equation, we get: 0.8 * 0 = 12. This equation is not true, so 0 is not a solution.
If we substitute 8 for x in the equation, we get: 0.8 * 8 = 12. This equation is not true, so 8 is not a solution.
If we substitute 1 for x in the equation, we get: 0.8 * 1 = 12. This equation is not true, so 1 is not a solution.
If we substitute 7 for x in the equation, we get: 0.8 * 7 = 12. This equation is not true, so 7 is not a solution.
Finally, if we substitute 15 for x in the equation, we get: 0.8 * 15 = 12. This equation is true, so 15 is a solution.
Therefore, the solution set for this equation is {15}.
Answer: 0.8x=12
x=15
Step-by-step explanation:
0.8x=12
x=15
15*0.8=12
If a triangle has lengths of 11tf and 24ft, check all the possible lengths for the third side
Answers
All the possible lengths for the third side lie between 13 to 35 feet.
What is a triangle Inequality Theorem?
In Euclidean geometry, the theorem is that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.
Therefore, 24 − 11 < x < 24 + 11
13 < x < 35 is the possible length of the third side of a triangle.
13 < x < 35 satisfies the triangle inequality theorem.
Hence, all the possible lengths for the third side lie between 13 to 35 feet.
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Cassidy has 10 feet of thread. She wants to cut the thread into 1 1/6 foot pieces to make necklaces. How many full necklaces can Cassidy make? 
Answers
Answer:8
Step-by-step explanation: 10/ 1 1/6 so the equals to 8 4/7 but the problems says whole necklaces to the answer is 8
If A = {x|x is an odd integer), B = {2, 3, 4, 5), list the elements of the set AUB.
Choose the correct answer below.
O A. {x x is an even integer or x = 2 or x = 4}
O B. {x|x is an even integer or x = 3 or x = 5}
OC. {x|x is an odd integer or x = 3 or x = 5}
OD. {xx is an odd integer or x = 2 or x = 4}
Answers
Answer:
D) {x: | x is an odd integer or x = 2 or x = 4}-----------------------------
Given two sets:
A = {x: | x is an odd integer}, B = {2, 3, 4, 5}Both sets include 3 and 5 so the combination is all the elements of the A and two unique elements of the B:
A∪B = {x: | x is an odd integer or x = 2 or x = 4}The matching choice is D.
Type the correct answer in each box. Use numerals instead of words.
3^1/5
The expression above can also be written in the form (image because I can't type it).
For this expression,
a =
and b =
.
Answers
The value of a is 3.
The value of b is 5.
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,
[tex]3^{1/5}[/tex]
This expression can be written as 5 roots of 3.
[tex]\sqrt[5]{3}[/tex]
Thus,
The value of a and b from the expression [tex]3^{1/5}[/tex]are 3 and 5.
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XYZ has coordinates X(-7, 8), Y(2, 5), Z(0,7). What are the coordinates of the image r(90,0) XYZ
Answers
The new coordinates are X'(8, 7), Y'(5, -2), Z'(7, 0).
How to determine the image of the rotation?The coordinates of the triangle are given as
X(-7, 8), Y(2, 5), Z(0,7).
The rotation is given as r(90,0) XYZ
This means that
We have (x, y) ⇒ (y, -x)
Substitute X(-7, 8), Y(2, 5), Z(0,7) in (x, y) ⇒ (y, -x)
So, we have
X'(8, 7), Y'(5, -2), Z'(7, 0).
Hence, the coordinates of the image are X'(8, 7), Y'(5, -2), Z'(7, 0).
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x (4.4) (1.4)
x=5
Help me solve this question please
Answers
Solve x(4.4)(1.4) given that x = 5
Plug x into equation
5(4.4)(1.4)
Distribute 5 into 4.4
22(1.4)
Distribute 22 into 1.4
30.8
Hope this helps :)
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Cashews cost $63.00 per 5 pound bag. How much would a 2 pound bag of cashews cost?
Answers
1. Which of the following identifies the a, b, c, and d of the absolute value function g(x) = −|2x| + 5?
Answers
The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:
a = -1.b = 2.c = 0.d = 5.How to obtain the parameters of the absolute value function?The standard definition of the absolute value function is given as follows:
f(x) = a|bx + c| + d.
The meaning of each parameter is given as follows:
a is the coefficient of vertical stretch/compression.b is the coefficient of horizontal stretch/compression.c is the coefficient of horizontal shift.d is the coefficient of vertical shift.In this problem, the function is defined as follows:
g(x) = −|2x| + 5.
Compared with the standard absolute value function, the values of these parameters are given as follows:
a = -1, b = 2, c = 0, d = 5.
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Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answers
when me I would say the 1st one but who knows lol
What’s
: -4 (2x + 4) = 5
Please explain step by step to get picked brainliest!
Answers
Answer:
[tex]x=-\frac{21}{8}[/tex]
Step-by-step explanation:
[tex]-4(2x+4)=5 \\ \\ 2x+4=-\frac{5}{4} \\ \\ 2x=-\frac{21}{4} \\ \\ x=-\frac{21}{8}[/tex]
Help plsssssssssssss
Answers
Answer: thanks for the ponts
Step-by-step explanation: ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
A door is 2 feet off the ground and a contractor needs to develop a wheelchair ramp to go on it. Ramps have to be in a ratio of 1:12 slope. How far away from the house would the ramp have to start. Explain
Answers
The slope of the ramp is the ratio of the y and x coordinates thus it will be 24 feet.
What is the slope?A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The situation is making a right-angle triangle as shown below.
The slope of the wheelchair = 2 feet / x
2/x = 1/12
x = 2 x 12 = 24 feet
Hence "The ramp will be 24 feet long since the slope is determined by the ratio of the y and x variables".
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The assets and liabilities of a local surf shop are listed below.
Building Mortgage $109,850
Other Debt $35,988
Accounts Receivable $10,760
Property Value $162,974
Long Term Investments $238,000
Small Business Loan $62,700
Long Term Liabilities $38,000
Owned Inventory $72,980
Cash $215,083
Savings Account $128,721
Owned Equipment $30,971
The surf shop owner receives notice that the property value has increased by $20,000. What is the net worth of the surf shop?
$859,489
$879,489
$612,951
$632,951
PLEASE HELP
Answers
Answer: $879,489
Step-by-step explanation:
When it comes to a business net worth is simple:
assets - liabilities = net worth.
Assets are an expenditure that has utility through multiple future accounting periods. For example, a company pays its electrical bill. This expenditure covers something (electricity) that only had utility during the billing period; therefore, it is recorded as an expense.
Conversely, the company buys a machine, that it expects to use for the next five years. Since this expenditure has utility through multiple future periods, it is recorded as an asset.
Cash, savings, inventory, investments, equipment, and receivables are also assets. Basically, anything that is owned and could be liquidated for cash.
Accounts Receivable $10,760Property Value $162,974Long-Term Investments $238,000Owned Inventory $72,980Cash $215,083Savings $128,721Owned Equipment $30,971In simple terms a liability is something that is owed to someone else:
Building Mortgage $109,850Other Debt $35,988Small Business Loan $62,700Long-Term Liabilities $38,000Find value of x and show work please
Answers
Answer:
D) 4, H) 14
Step-by-step explanation:
D) both angles form a linear pair so 101-5x + 2x+70 = 180
Simplify
171-3x = 180
-3x = 9
x = -3
H) 11x-23 = 41 + 90 because they are opposite angles
Simplify
11x = 154
x = 14
The table shows Adam's age and shoe size. Generate a linear regression equation for the data. Then, use the equation to predict Adam's shoe size when he is 14-years-old.
Answers
The linear regression equation for the data is given as follows:
y = 0.55x + 0.3.
The prediction of Adam's shoe size when he is 14-years-old is given by the following option:
A. 8.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
From the table, the points are given as follows:
(6,3), (8, 4.5), (10,5), (12, 7.5).
Inserting these points into a calculator, the regression equation predicting the shoe size at an age of x is given as follows:
y = 0.55x + 0.3.
Then the estimate for the shoe size at an age of 14 is found when x = 14, hence:
y = 0.55(14) + 0.3 = 8.
Meaning that option A is correct.
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Which of the following numbers are irrational?
-4.8237, π/2, ³√/4, 4+√25
π/2 and ³√4
-4.8237 and 4+√25
-4.8237 and π/2
³√4 and 4+√25
Answers
The irrational numbers are option (A) π/2 and [tex]\sqrt[3]{4}[/tex]
The rational numbers are the numbers that can be expressed in the p/q form
The irrational numbers are the numbers that cannot be expressed in the p/q form.
The first number is -4.8237
This can be expressed in p/q form
It is a rational number
The second number is π/2
This cannot be expressed in p/q form
It is an irrational number
The third number is [tex]\sqrt[3]{4}[/tex]
We cannot express this in p/q form
It is an irrational number
The fourth number is 4 + [tex]\sqrt{25}[/tex]
Find the square root
4 + 5 = 9
This is a rational number
Therefore, the rational numbers are π/2 and [tex]\sqrt[3]{4}[/tex]
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solve this
6/7 × 1/2 = ?
Answers
Answer:
To solve this problem, we need to first perform the multiplication. In mathematics, multiplication is performed before division, so we should calculate the product of 6/7 and 1/2 before dividing it by any other number. To find the product, we simply multiply the numerators together to get 6 and the denominators together to get 14. So the product of 6/7 and 1/2 is 6/14.
Step-by-step explanation:
In the scale used on a blueprint, inch represents 2 feet. On the blueprint what is the length of a room with an actual length of 20 feet?
Answers
On the blueprint what is the length of a room is 5square inch.
What is square?
A square is a quadrilateral because it has four equally sized sides. Our immediate surroundings is filled with many square-shaped things. Equal sides and interior angles of 90 degrees help you identify each square form. A closed form known as a square has four equal sides and two interior angles that are both 90 degrees. A square has a wide range of characteristics.
Given the square bedroom have 3 feet side
The area of the bedroom is = 3² = 9 sq inch
1 inch = 2 feet
1 square inch = 4 square feet
20 square feet = 5square inch
Hence, On the blueprint what is the length of a room 5square inch.
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3. There are five different tables in the class and five students. Each table can be occupied by only onestudent. Their
studying year consists of 200 days. As a small prank on their teacher students would like to sit in a new way every
day, so there are no two days during their studying year such that all students are occupying the same tables.
They would like to see whether this is possible. How many ways are there for them to sit in the class?
Answers
There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five different tables in the class and five students
Each table can be occupied by only one student
There are 200 days of studying years.
As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.
5×4×3×2×1 = 120
There are 120 different places to sit, if they all sit on separate tables.
5×5×5×5×5 = 3,125
There are 3,125 different places to sit if they don't mind sharing s desk sometimes.
Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.
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they figure that the waterfall is at point (3'6). The overlook is at point (0.1). the campsite is at point (3-5). The lake is at point (-4,1). And the parking lot is at point (0.5). Which of these pairs of locations are closest to one another
Answers
Answer:
Step-by-step explanation:
I'm sorry, but I'm not sure what you're asking. It's not clear to me what you mean by "point (3'6)" or "(3-5)." Could you please provide more information or clarify your question
Which expression is equivalent to 2 (x -2 ) -5 (2x -3)
A: 2x - 4 - 10x - 15
B: 2x - 4 - 10x + 15
C: 2x - 2 - 10x - 3
D: 2x - 2 - 10x +15
Answers
The expression equivalent to the given expression 2(x -2)-5(2x -3) is
(2x-4-10x+15)
What is an expression?An expression in maths, a sentence with a minimum of two numbers or variables and at least one maths operation.
Given is an expression, 2(x -2)-5(2x -3)
Using distributive property,
a(b+c) = ab+bc
2(x -2)-5(2x -3) = 2x-4-10x+15
Hence, The expression equivalent to the given expression 2(x -2)-5(2x -3) is (2x-4-10x+15)
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The y-intercept of the line y=-4 x-7 is
a. -7
c. 4
b. -4
d. 7
B
A
D
C
Answers
The y-intercept of a line is where it meets the y-axis.
This y-axis occurs at x = 0.
Simply input x = 0 into the line y = -4x - 7
y = -4(0) - 7
y = -7
y - intercept (we also like to abbreviate that y-int) = -7
Hope this helps :)
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Answer: -7
Step-by-step explanation:
Since the answer is already in slope intercept form x=-4 and y = -7
what is the additive inverse of -17-25
Answers
Answer: 42
Step-by-step explanation: ik additive inverse
A factory made 3 jars of creamy peanut butter and 97 jars of chunky peanut butter. What percentage of the jars of peanut butter were creamy?
Answers
Answer:
3%
Step-by-step explanation:
They made 97+3 total jars, 3 out of 100 is 3 percent.
#19 i
Solve the system of linear equations by elimination.
1.5x - 9y = -21
-1.5x - 3y = 9
The solution is:
Answers
Answer:
to solve a system of linear equations by elimination, we need to eliminate one of the variables, for example, we could add the two equations together to eliminate the variable y. However, we need to make sure that the coefficients of the two equations are the same before we can add them together. We can do this by multiplying the first equation by -1.5 and the second equation by 1.5. This gives us the following system of equations:
-2.25x - 13.5y = -31.5
2.25x - 4.5y = 13.5
We can now add these two equations together to eliminate the variable y, which gives us the following equation:
0 = -18
This equation is not possible, so the system of equations does not have a solution.
Answer:
Math can help you get your answer it has a linear equation by option
Step-by-step explanation:
NO LINKS!! Help me with the 2-Column Proof Part 3aa
Answers
Here is the two column proof:
Statement Reason
RD bisects OS GivenA is the point of intersection Shown on the diagramOA ≅ AS Definition of a segment bisectorProved
18. Which of the following is an equation of the line parallel to y = 5x+8 that passes through the point
(4, -3)?
Answers
Answer:
y=5x-23
Step-by-step explanation:
y=mx+b is the slope intercept form
m is slope
And b is y intercept
We know the line will have a slope of 5 since they are parallel both lines will have the same slope
y=5x+b
To find b we put in the given coordinates (4,-3)
-3=5(4)+b
-3=20+b
-20 -20
-23=b
Now we just plug in b
y=5x-23
Hopes this helps