Answers
Step-by-step explanation:
To prove that two lines are perpendicular, when all we have are those two lines, we can use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
Our diagonals intersect at point O, so we'd need to show the two linear angles formed at that intersection point are equal, and we can do that with triangle congruency.
A rhombus is a parallelogram, so we will use what we already know about parallelograms - that the diagonals bisect each other.
It is then easy to show that the triangles ΔAOD and ΔAOB are congruent using the Side-Side-Side postulate, and from that that ∠AOD ≅ ∠AOB.
And now, since ∠AOD and ∠AOB are a linear pair, we use the Linear Pair Perpendicular Theorem - If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.
PROOF
(1) ABCD is a rhombus //Given
(2) AB=AD //definition of rhombus
(3) AO=AO //Common side, reflexive property of equality
(4) BO=OD // A rhombus is a parallelogram, a parallelogram's diagonals bisect each other
(5) △AOD≅△AOB //Side-Side-Side postulate.
(6) ∠AOD ≅ ∠AOB //Corresponding angles in congruent triangles (CPCTC)
(7) AC⊥DB //Linear Pair Perpendicular Theorem
The converse of this is also true: if a parallelogram's diagonals are perpendicular, it is a rhombus.
Related Questions
If UT and VS biscect each other at W, EHAT method could you use to prove the triangles congruent?
Answers
Answer: Where they bisect each other at W the 2 lines are split in the center by one another which means both of those lines are 180
Step-by-step explanation:
Answer:
SAS
Step-by-step explanation:
You have segments UT and VS bisecting each other at point W, and you want to show triangles UWV and TWS ae congruent.
SASEach half of the segment is congruent to the other half:
UW≅TW and VW≅SW
The angles between them are vertical angles so are congruent:
∠UWV ≅ ∠TWS
So, you have congruent corresponding sides and the angle between. The triangles UWV and TWS are congruent by the SAS congruence postulate.
__
Additional comment
You can use substantially the same argument to say triangles UWS and TWV are congruent. The proof above shows UV≅TS. The congruence of triangles UWS and TWV shows US≅TV. Hence the figure TSUV is a parallelogram.
Given the function defined in the table below, find the average rate of change, in simplest form of the interval 12 < x < 24
Answers
Therefore , as a result the solution of the given problem of expressions comes out to be the typical rate of change is -2/5 in its simplest form.
How is the expression chosen?An algebraic equation must be checked by replacing each variable with a number and performing arithmetic operations. Since 8 plus 6 = 14, the reply variable in the above example is equivalent to 6. In order to test the expression, we can replace the values of the variables with ones we already know.
Here,
Simply said, the median rate of change is -2/5.
The function's gradient or slope is its rate of change.
The slope of a function can be calculated using the formula:
=> D = dy/dx = y2, -y1, and x2, -x1.
Using the coordinates (0, 41) from the table and (15, 35)
Replace the expression with the coordinate:
=>m = 35-41/15-0
=>m = -6 /15
=>m =-2/5
As a result, the typical rate of change is -2/5 in its simplest form.
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26. PICTURE FRAME Aston is making a wooden picture frame
in the shape of a parallelogram. He has two pieces of
wood that are 3 feet long and two that are 4 feet long.
a. If he connects the pieces of wood at their ends to each other, in
what order must he connect them to make a parallelogram?
b. How many different parallelograms could he make with these
four lengths of wood?
c. Explain something Aston might do to specify precisely
the shape of the parallelogram.
Answers
To make a parallelogram, Aston must connect the pieces of wood in the following order: 3 feet, 4 feet, 3 feet, 4 feet.
How many different parallelograms could he make with these
four lengths of wood?He must connect the 3 foot pieces of wood first, and then the 4 foot pieces of wood.There are two different parallelograms he could make with these four lengths of wood.To specify the shape of the parallelogram, Aston could measure the angles of each corner and the lengths of the sides. He could also measure the distance between each corner.Aston could make several different parallelograms with these four lengths of wood. For example, he could arrange the pieces to make a trapezoid, a rectangle, or a rhombus.To specify precisely the shape of the parallelogram, Aston could measure the angles of the four corners to ensure that they are all equal. He could also measure the lengths of each side to make sure that the opposite sides are of equal length.Additionally, he could measure the diagonals of the parallelogram to ensure that they are of equal length. This will guarantee that the shape of the frame is a proper parallelogram.To learn more about parallelogram refer to:
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How do you solve linear inequality step by step?
Answers
Solving a linear inequality step by step involves several steps including isolating the variable on one side of the inequality sign, simplifying the inequality, graphing the inequality, shading the region that include the solutions and representing the solutions in the form of an interval.
1. Isolate the variable on one side of the inequality sign: This can be done by adding or subtracting the same value from both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.
2. Simplify the inequality: This can include combining like terms, or simplifying fractions or decimals.
3. Graph the inequality: This can be done by plotting the inequality on a number line or a coordinate plane, using a solid line for "greater than" or "less than" and a dotted line for "greater than or equal to" or "less than or equal to"
4. Test a point: To test whether a point is a solution of the inequality, substitute the coordinates of the point into the inequality, and check if the statement is true.
5. Shade the region that includes the solutions: The solutions of the inequality are all the points that make the inequality statement true. The solutions of the inequality are all the points that are in the shaded region.
6. Write the solution in interval notation: Write the solution in interval notation, if needed.
Here is an example:
Solve the inequality 2x - 3 > 5.
Step 1: Isolate the variable by adding 3 to both sides: 2x > 8
Step 2: Divide both sides by 2: x > 4
Step 3: Graph the inequality on a number line. Using a solid line, draw a line at x = 4 and shade the region to the right of the line, including 4.
Step 4: Test a point, e.g. x = 5, if 5 > 4 is true.
Step 5: The solution is x > 4.
Step 6: if needed, the solution can be written in interval notation as (4, +inf)
It's important to note that solving inequalities is not always straightforward, and some inequalities may require multiple steps to be solved.
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In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as
Answers
In a scatter diagram, a line that provides an approximation of the relationship between the variables is known as trend line.
Explain what a scatter diagram is?
In a scatter diagram, pairs of numerical data are graphed with one variable on each axis in an effort to find a correlation between them. The points will fall along a line or curve if the variables are correlated. The points will hug the line closer the more highly correlated the data is.
Why are scatter plots employed?
The relationship between two different types of data is displayed using a scatter diagram. The connection between a cause and an effect, between two causes, or even between three causes, could be the subject of the analysis.
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how do I find out if a table is linear or non linear
Answers
Answer:
In the case of the classification problem, the simplest way to find out whether the data is linear or non-linear (linearly separable or not) is to draw 2-dimensional scatter plots representing different classes. Here is a picture that represents the linearly and non-linearly separable dataset and how one can use scatter plots to visualize them.
Step-by-step explanation:
Write a formula to find the number of sides N in a regular polygon given that the measure of one interior angle is x
N= ?
Answers
N = (360/x) - 2
This formula finds the number of sides N in a regular polygon when given the measure of one interior angle x.
The formula is derived from the fact that the sum of all interior angles in a regular polygon is equal to (N-2)*180, where N is the number of sides.
Therefore, it can be rearranged to be N = (360/x) - 2.
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The sum of two numbers is 10 and the difference of those two
numbers is 18. (Usef to represent the first number and s to represent
the second number.)
Answers
| f - s | = 18
-------
This means that:
f = 10 - s
And also that:
| f - s | = 18
(f-s)²=18²
f²- 2sf + s² = 324
But f=10-s
So...
(10-s)² - 2s(10-s) + s² = 324
(10-s)(10-s) - 20s + 2s² + s² = 324
100 - 20s + s² - 20s + 2s² + s² = 324
4s² - 40s + 100 = 324
4s² - 40s + 100 - 324 = 0
4s² - 40s - 224 = 0
1/4 * (4s² - 40s - 224) = 1/4 * 0
s² - 10s - 56 = 0
(s-14)(s+4)=0
So s can be either 14 or -4.
When s = 14, f = -4.
When s = -4, f = 14.
Find the total amount given the original price and tax rate. Round to the nearest hundredth if necessary.
Original price: $123.28
Tax rate: 7.5%
Answers
Answer: 132.526
Step-by-step explanation:
Bong's savings in February was P9,500 and his savings in May was
P7,300. What was the percentage decrease in Bong's savings? Solution:
Answers
Answer: 23.16%
Step-by-step explanation: 7300/9500 can be simplified to 73/95 which gives us 76.84%. subtract that from 100 and you get 23.16
(6x -7) +(-4x - 8) simplified
Answers
Answer:
2x−15
Step-by-step explanation:
6x−7−4x−8
=6x+−7+−4x+−8
Combine Like Terms:
=6x+−7+−4x+−8
=(6x+−4x)+(−7+−8)
=2x+−15
which number is a factor of the prime factorization of 60?
Answers
Answer:
Step-by-step explanation:
So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.
What is quotient formula?
Answers
A quotient is a number created when two numbers are divided. The formula for this is Quotient = Dividend ÷ Divisor.
The division is the process of dividing one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the number that we get as a result.
Then, the quotient formula is given by Quotient = Dividend ÷ Divisor. For example, 50÷5=10. Here, 50 is the dividend, 5 is the divisor, 10 is the quotient, and 0 is the remainder.
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If a₁ = 7 and an = an-1 - 1 then find the value of a5.
Answers
Answer:
a₅ = 3--------------------
Given AP with recursive formula:
a₁ = 7 and aₙ = aₙ₋₁ - 1As per recursive formula the first term is a₁ = 7 and common difference is d = -1.
Use the nth term formula to find the 5th term:
aₙ = a₁ + (n - 1)da₅ = 7 + (5 - 1)*(-1) = 7 - 4 = 3Alex is applying for positions at two different electronic stores in neighboring towns. The first job offer is a $200 weekly salary plus 5% commission on sales. The second job offer is a $75 weekly salary plus 10% commission.
Answers
The amount of sales at which Company A's offer is the same as Company B's is $600
How to calculate the amount?The given parameters that will help us to understand the question are
Company A:
Base = $200
Commission = 10% of sales = .1*S
A = .1S + 200
Company B:
Base = 400
Commission = .05*S
B = .05S + 400
We're looking for the point where they're equal.
200 + .1S = 400 + .05S
Multiply by 100 to get rid of decimals
20000 + 10S = 40000 + 5S
Subtract 20000 from both sides
10S = 20000 + 5S
Subtract 5S from both sides
5S = 20000
Divide both sides by 5
S = 4000
So, at $4000 sales, the two jobs pay the same.
You have to always check your work. This can be done by plugging the values into the basic equations and determining if they check. Or we can graph the two lines and see where they cross.
Company A:
200 + .1(4000) = 200 + 400 = 600
Company B:
400 + .05(4000) = 400 + 200 = 600
Conclusively Alex (A) offers $600 as same as Company B
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Complete question:
A salesperson has two job offers. Company A offers a weekly salary of $200 plus commission of 10% of sales. Company B offers a weekly salary of $400 plus commission of 5% of sales. What is the amount of sales at which Company A's offer is the same as Company B's?
Write an equation in standard form with an x-intercept of 5 and a y-intercept of -4
Answers
An equation in standard form with an x-intercept of 5 and a y-intercept of -4 is,
⇒ 5x + 4y = 20
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The x - intercept = 4 ,
So, ( 4,0) is a point on the line.
And, The y - intercept = 5,
So, ( 0, 5) is a point on the line.
Now, Slope of the line passing through the point (4, 0) and (0, 5) is,
⇒ m = (5 - 0) / (0 - 4)
⇒ m = - 5/4
So, The slope intercept form of an equation is,
⇒ y = mx + b
Where, m = slope and b = y- intercept.
Hence, We get;
⇒ y = - 5/4x + 5
We know that;
An equation in standard form is,
⇒ Ax + By = C
So, We get;
⇒ y = - 5/4x + 5
⇒ 4y = - 5x + 20
⇒ 5x + 4y = 20
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Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
Answers
The triangle can be constructed from sides of triangle measuring 3.5 cm 9.2 cm and 5.3 cm due to side rule of triangle.
The possibility to construct the triangle will be found out through the sum of any two sides of triangle. If the sum is greater than the remaining side of the triangle, the construction is possible. Let us assume the side a, b and c of triangle to be 3.5, 9.2 and 5.3 cm.
Now, using the side-side-side rule of triangle -
Side a + side b > side c
3.5 + 9.2 > 5.3
Add the values
12.7 > 5.3
Side b + side c > side a
9.2 + 5.3 > 3.5
Add the values
14.5 > 3.5
side c + side a > side b
5.3 + 3.5 > 9.2
Add the values
8.8 not greater than 9.2
Based on the results, the construction of triangle from mentioned sides is possible according to length rule of the triangle.
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Writing system of equations (50 points)
-A math quiz has a total of 25 questions. Some questions or worth 1/2 a point and some questions or worth 1/4 point there are a total of 10 points available. Write a system of equations that model the situation
Answers
The required equation is x×1/2+25-x ×1/4=10
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here, A math quiz has a total of 25 questions. Some questions or worth 1/2 a point and some questions or worth 1/4 point there are a total of 10 points available. let there be x 1/2 points question and 25-x 1/4 points question, then
x×1/2+25-x ×1/4=10
Hence, this is the required linear equation
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what is 3x +6.5 and how do you solve it step by step
Answers
Answer: already simplified
Step-by-step explanation:
You cannot solve an equation without an equal sign, you could only solve it if it were like 3x + 6.5 = 0.5
then you would put the x on one side of the equation and the numbers on the other by subtracting 6.5 with 0.5.
3x = -6
divide by 3
x = -2
THIS QUESTION IS ALREADY SIMPLE, THER IS NOTHIGN TO DO ABOUT IT! SORRY!
27x9+57+5 / 9
(psst, lets talk about something lol-)
Answers
Answer:
27x9+57+5 / 9 = 243 + 57 + 5 / 9 = 305 / 9 = 33.89
Step-by-step explanation:
Answer:
33.89
Step-by-step explanation:
(27*9+57+5)/9=33.89
Suppose the x and y vary inversely and x=1 when y=3. wrote a function that models that models the inverse variation. graph the function and find when x=5
Answers
The value of y= 1.6667 when x= 5.
The graph is attached below.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
x= 1 when y=3, if x and y vary inversely.
Then, x = k/y
where is proportionality constant
So, k = x y
k = 3
Using Proportion
x/ y = k
5/y= 3
y= 5/3
y= 1.6667
Hence, y= 1.6667 when x= 5.
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Is 4 6 and 2 3 equivalent?
Answers
So we can write 4/6 as equivalent to 2/3
What is Equivalent ?Equal is not the same as equivalent. While comparable indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is comparable to 2, even if 2 is supposed to be equal to 2.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
So , 4/6 can be written as 2*2/3*2 = 2/3
So we can write 4/6 as equivalent to 2/3
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Explain how to reason with the diagram to find the weight of a piece with a letter.
Answers
The weight of a piece can be found through the letter because the diagram is made up of balanced hangers which means that the weight of one side is equal to the weight of the other side.
How to calculate the weights of the given diagram?For diagram A = X+3 = 8
X = 8-3 = 5
The weight of the letter piece X = 5
For diagram B = 12= 2y
y = 12/2 = 6
The weight of the letter piece y = 6
For diagram C = 11 = 4z
z = 11/4 = 2.75
The weight of the letter piece z = 2.75
For diagram D = 13⅘ = w + 3⅘
w = 13⅘ - 3⅘ = 10
The weight of the letter piece w = 10
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Coach Smith purchases sports equipment.
Golf balls cost $25 per pack and lacrosse balls
cost $10. He has $250 dollars in the budget for
golf balls and lacrosse balls.
Part A. Write an inequality where g is the number
of golf balls purchased and I is the number of
lacrosse balls.
Part B. Given the coaches budget, which of the
following is a viable option for the equipment he
can purchase?
Answers
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
Inequality: What is it?In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.
Here,
Given:
Lacrosse balls cost $10 per pack
while golf balls price $25 per pack.
Total funds equal $250.
In order to create an inequality,
we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.
So, the inequality is:
25g + 10l ≤ 250
Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.
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What is the residual for five?
Answers
-1.6 is the residual value of 5 for given regression table.
What is residual?A residual value is the difference between the observed and expected y-values (as determined by the regression equation).
Here,
In this case, the given regression equation for the line,
y = 5.2 x - 0.4
As a result, for x = 5, the anticipated value is y = 5.2 5 - 0.4 = 26.0 - 0.4 = 25.6.
Now, according to the table,
The observed value of y = 24 for x = 5.
As a result, the residual for 5 = Observed y for 5 - Predicted y for 5
= 24 - 25.6 = - 1.6
The first option is the correct one.
The residual value of 5 for the provided regression table is -1.6.
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The complete question:
The line of best fit to model the data in the table is y = 5.2x – 0.4.
What is the residual for 5?
–1.6
–0.6
0.6
1.6
How do you find the center and radius of an endpoint?
Answers
To find the center and radius of a circle given the endpoints of its diameter, you can use the following steps:
Find the midpoint of the diameter: The midpoint of the diameter is the center of the circle. To find the midpoint, you can use the midpoint formula: (x,y) = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the diameter.Find the radius: The radius of a circle is half the length of its diameter. To find the radius, you can use the distance formula to find the distance between the two endpoints of the diameter: d = √((x2 - x1)^2 + (y2 - y1)^2) and divide the result by 2.For example, if the endpoints of a diameter are (-3, 4) and (7, -6), you can use the midpoint formula to find the center:
(x,y) = ((-3 + 7)/2 , (4 + -6)/2)
(x,y) = (2,-1)
The center of the circle is (2,-1)
To find the radius, you can use the distance formula:
d = √((7-(-3))^2 + (-6-4)^2)
d = √((10)^2 + (-10)^2)
d = √(100+100)
d = √200
d = 10√2
The radius of the circle is 10√2/2 units.
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3. 53°C below zero
write an integer for each situation
Answers
Answer:
See below
Step-by-step explanation:
52 degrees C below 0 ° C is just - 53 °C
What are the types of substitutions?
Answers
Answer:
"Substitution comes in three flavors: nominal, verbal, or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
What should be added to 2x2 xy 2y2 to obtain 3x2 5xy?
Answers
To obtain 3x² + 5xy from 2x² + 2xy², you would need to add the polynomial x² + 5xy to the original expression.
In order to add two polynomials together, the terms must have the same degree and variable. In this case, we see that 2x^2 and 2xy^2 have different degrees and variables. So, we need to find a polynomial that when added to 2x² + 2xy² will give us 3x² + 5xy.
To do this, we can start by looking at the x² term in 3x² + 5xy. We can see that we need to add x² to our original polynomial. Next, we can look at the xy term in 3x² + 5xy. We can see that we need to add 5xy to our original polynomial.
So by adding x² + 5xy to 2x² + 2xy², we get the desired polynomial of 3x² + 5xy.
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What value of x will make the triangles similar by the sss similarity theorem brainly.
Answers
The value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the two triangles are similar. This applies to all triangles, regardless of their size or shape.
To use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Once you have this information, you can use the theorem to determine if the two triangles are similar.
It's important to note that to use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Without this information, it's not possible to determine if the two triangles are similar.
Therefore the value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem only states that the two triangles are similar, it doesn't tell anything about the angles of the triangles.
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