Yes, all transformations such as translations, reflections, dilations, and rotations preserve parallel lines (parallelism) as well as collinear points (collinearity).
Parallel lines:
Parallel lines are coplanar straight lines that don't intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.Collinear points:
The collinearity of a series of points in geometry is the property of their being on a single line.A set of points with this property is known as a collinear set. In a broader sense, the term has been applied to aligned objects, that is, things that are "in a line" or "in a row."So,
Translation, reflection, dilation, and rotation are all examples of transformation. In all of the preceding cases, parallel lines or collinear points will remain parallel or collinear.Therefore, yes, all transformations such as translations, reflections, dilations, and rotations preserve parallel lines (parallelism) as well as collinear points (collinearity).
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Solve for d.
8d–3=5+9d
Answer:
-8
Step-by-step explanation:
8d-3=5+9d
8d-9d=5+3
-d=8
d=-8
Answer:
d = -8
Step-by-step explanation:
Hello!
Solve for d by isolating the variable.
Solve for d8d - 3 = 5 + 9d-d - 3 = 5-d = 8d = -8The value of d is -8.
During one week, Sheila made
several changes to her bank account.
She made three withdrawals of $30
each from an ATM. She also used
her check card for a $156 purchase.
Then she deposited her paycheck of
$325.
By how much did the amount in her
bank account change during that
week?
$59 increase in her bank account during that week.
What is algebraic operation ?Any of the basic arithmetic operations—addition, subtraction, multiplication, division, raising to the power of a whole number, and taking roots (fractional power)—is considered an algebraic operation. These procedures could be applied to numerical data, in which case they are frequently referred to as arithmetic operations. Similar operations can be carried out on variables, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of a set to the same set.
Given that : Sheila made four withdrawals of each from an ATM. . She also made a $156 purchase with her check card. She then deposited her $375 salary.
It's difficult to determine the solution because we don't know how much money she had in her bank account before making 4 withdrawals, thus a like and rating would be really appreciated. We know she took out $40 four times, which is $160. She also used her card to make a $156 purchase, so when we sum the two amounts, we get $316. She then placed a check for $375 into the bank account, therefore we must deduct $316 from that sum to get at $59; but, since we deducted, Given that we end up with $59 rather than the money we wasted at the beginning, the fact that the price is higher than $316 indicates that there has been an increase.
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Write a coordinate proof of the Distance Formula in Space.
Given: A has coordinates A(x₁, y₁, z₁) , and B has coordinates B(x₂, y₂, z₂) .
Prove: A B = √(x₂-x₁)² + (y₂-y₁)² + (z₂ - z₁)²
Required coordinate proof of distance formula between two points in 3 dimension is:
[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]
As given,
Let points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) be referred to a system of rectangular axes OX , OY, OZ.
Through the points A and B, we draw planes parallel to rectangular coordinate plane as rectangular parallelepiped with AB as diagonal.
Pythagoras Theorem
[tex]AB^2 = AC^2 + CB^2....(1)[/tex]
[tex]AB^2=CD^2+DB^2...(2)[/tex]
From equation (1) and (2) we have,
[tex]AB^2=AC^2+DB^2+CD^2[/tex]
As coordinates of the points, A and B as known,
[tex]AC =y_{2}-y_{1}, CD = x_{2} -x_{1} and DB= z_{2}-z_{1}[/tex]
Distance formula :
[tex]AB^2=(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2[/tex]
Therefore, required coordinate proof of distance formula between two points in 3 dimension is ,
[tex]AB = \sqrt{(x_{2}-x_{1} )^2 +(y_{2}-y_{1} )^2 + (z_{2}-z_{1} )^2}[/tex]
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Evaluate each expression for x=-2,0,1 , and 4.
(1/2)x-8
The value for x = -2,0,1 , and 4 will be -9, -8, -15/2 and -6 respectively.
For x = -2
The value will be -
(1/2)x-8
(1/2)(-2) - 8
= -9
For x = 0
The value will be -
(1/2)x - 8
(1/2)(0) - 8
= -8
For x = 1
The value will be -
1/2(1) - 8
= -15/2
For x = 4
The value will be -
1/2(4) - 8
= -6
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Evaluate the expression for the given values of the variables.
12(3/4)x - (1/2)y) - 6(1/2)x - (3/4)y ; x = 2 and y=-2
The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .
The given expression is 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y.
We have x = 2 and y = -2 as per the question.
To evaluate the expression, first we need to simplify the given expression and then we can substitute the given value of x and y in simplified expression.
The given expression can be simplified as,
12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y
⇒ 9x - (1/2)y - 3x - (3/4)y
⇒ 6x - ((1/2)+(3/4))y
On taking LCM of coefficient of y, we will get
6x - (5/4)y
Now on substituting x = 2 and y = -2, we get
6(2) - (5/4)(-2)
= 12 + (5/2)
= 29/2 = 14.5
The solution of given expression 12(3/4)x - (1/2)y - 6(1/2)x - (3/4)y after evaluation is 14.5 .
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How many significant figures is in 7.357
Answer: 4
Step-by-step explanation: We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.
Solve negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity.
two thirds
18 over 54
negative two ninths
negative two and 42 over 54
Negative one sixth times the quantity 3 minus 15 times the quantity one third squared end quantity end quantity will be C. negative two ninths
How to compute the expression?Based on the information given, the expression will be:
= 1/6 ×( 3 - 15 ) × (1/3)²
= -1/6 × -12 × 1/9
= -2 × 1/9
= -2/9
In conclusion, the correct option is D.
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Find the coordinates of Z if Y is the midpoint of XZ, X(-10, 9), and Y(-4, 8).
The coordinates of Z are (2,7).
What is coordinates in math?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The formula to calculate the midpoint between two points is equal to
[tex]Y = ( \frac{(x_{1} + x_{2}) }{2} , (\frac{y_{1} + y{2} }{2} )[/tex]
we have
X(-10,9),Y(-4,8)
Let
(x2,y2) ----> the coordinates of Z
substitute the values
( -4.8) = ( -10 + x₂ /2 , 9 + y₂/2)
Solve for x2
-4 = ( -10 + x₂/2
-8 = -10 + x₂
x₂ = -8 + 10
x₂ = 2
Solve for y2
8 = (9 + y₂)/2
16 = 9 + y₂
y₂ = 16 - 9
y₂ = 7
therefore, The coordinates of Z are (2,7)
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At the end of December, the Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Type the answer in the box to represent the Cookie Shop's profit at the end of January.
Please dont put random answers
Ill give brainlyist to the correct answer
The Cookie Shop's profit at the end of January due to the decrease was $12000
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The Cookie Shop had a profit of $15,000. At the end of January, their profit had decreased by 20%. Hence:
Decrease in profit = 20% of $15000 = 0.2 * 15000 = $3000
Profit at end of January = $15000 - $3000 = $12000
The Cookie Shop's profit at the end of January due to the decrease was $12000
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Point D(2,4) is rotated 180 degrees about the origin. What are the coordinates of D'?
The coordinates of D' are D' = (-2, -4)
What are the coordinates of D'?The given paramaters are
D = (2, 4)
The rule is given as
180 degrees about the origin.
This is represented as
(x, y) = (-x, -y)
So, we have
D' = (-2, -4)
Hence, the coordinates of D' are D' = (-2, -4)
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Write an equation of the line through the pair of points in slope-intercept form. (Lesson 3-4 )
(4,0) and (-3,-7)
y = x - 4 is an equation of the line in slope-intercept form passing through points (4 , 0) and (-3 , -7)
An equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept.
Given two points passed through by the line, you can use them to write the equation of the line in slope-intercept form.
1. Find the slope of the line using the two given points.
let Point 1(4 , 0) and Point 2(-3 , -7)
slope = m = (y2 - y1) / (x2 -x1)
m = (-7 - 0) / (-3 - 4)
m = -7/-7
m = 1
2. Use the value of the slope and one of the points to find the value of the y-intercept, b. Plug in these values in the formula for slope-intercept form.
y = mx+ b
y = 1x + b
Using Point 1,
0 = 1(4) + b
b = -4
3. Write the equation of the line in slope-intercept form.
y = mx+ b
where m = 1 and b = -4
y = x - 4
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Shilpi deposited some amount in a bank at the rate of 6% per annum which amounts to 8850 for 3 years. find the amount deposited by shilpi. please tell me an answer to me if you have this same question
The amount deposited by Shilpi is 8850
The final answer if I have this same question would be 8850
We are to use simple interest to find out the initial amount deposited
The formula for getting Simple Interest is
SI = (P × R ×T) / 100
Thus,
8850= P * 0.06 * 3
8850= 0.18P
P= 8850 * 0.18
P= 1593
Therefore, the amount deposited by Shilpi is 1593
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6 5/15 in its simiplist form
Answer:
6 1/3
Step-by-step explanation:
Well 5 goes into 15 3 times because 5 * 3 = 15.
So the answer would be 1/3 for the fraction and 6 1/3 for the answer.
Answer:
6 1/3
Step-by-step explanation:
6 is already in its simplest form.
5/15 = 1/3
^ 5/15 is equivalent to 1/3
Describe in words where the square root of 45 minus 9 would be plotted on a number line.
Between −3 and −2, but closer to −3
Between −3 and −2, but closer to −2
Between 6 and 7, but closer to 6
Between 6 and 7, but closer to 7
Answer:
Between -3 and -2, but closer to -2
Step-by-step explanation:
The square root of 45 is approximately 6.708.
Subtract 9 from that and you get -2.292.
-2.292 is between -3 and -2, but is closer to -2.
9,369 divided 53 help
Answer - 9,369 divided 53 = 176.773584906
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
An included side is the side located between two consecutive angles of a polygon.
The given sentence about polygon is true.
A statement is given in the question.
We have to tell whether the statement is true or false.
What is a polygon ?
A polygon is a two-dimensional geometric figure that has a finite number of sides i.e., triangle has three sides.
As per the question ;
The statement given is , "An included side is the side located between two consecutive angles of a polygon."
Let's check whether it is true or false ;
We know that ,
Included side is one which links two angles together.
For example in a right angle triangle ABC ;
Side (base) AC links two angles one a right angle at A and other angle at C.
So ,
We can conclude that the given statement is true i.e., an included side is located between two consecutive angles of a polygon.
Thus , the given statement about polygon is true.
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4 A number generator produces two digits in boxes like this. Each digit is generated randomly. It can be any digit from 0 to 9. Find the probability that: a the first number is 4 b the second number is less than 8 numbered 1 to 4 4 6 c there are no Os.
a. The probability that a first number is 4 is 1/10
b. The probability that the second number is less than 8/10.
c. The probability that there will not be any zero's is 81/100
Given, a number generator produces two digits in a box, each of it is generated randomly from 0 to 9.
a. The probability that the first number is 4 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 1/10
b. The probability that the second number is less than 8 = ?
probability of an event = favourable number of outcomes/ Total number of outcomes.
Total number of outcomes = 10
P(n) = 8/10
c. The probability that there are no zero's = ?
since there are two boxes, there is possibility of getting two zero's.
probability of an event = favourable number of outcomes/ Total number of outcomes.
9/10 × 9/10
= 81/100
Hence we get the required results.
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Please help asap (Show work)
Answer:
See attached image.
Step-by-step explanation:
Substitute 1,2,3, or 4 for [tex]x[/tex]. Then calculate using the order described by PEMDAS.
simplify -6(2+x) i need help
Isaac saves 20% on a hard drive that costs $110 but must pay 6% sales tax. What is the total amount that he must pay at the store?
A. $93.28
B. $88.00
C. $106.00
D. $140.80
E. None of the above
Answer:
A. $93.28
Step-by-step explanation:
The reason why is because 110 - 20% would leave you only paying 88 dollars. but when you add the 6% sales tax you get $93.28
Simplify (-8)^3)6x(1/2)^2x(-8)^-16
After simplifying the expression we get the answer as ₋3x²/8¹³.
Given the expression is (₋8)³ 6x (1/2)²2x(₋8)⁻¹⁶
expand the powers.
(₋8×₋8×₋8) 6x (1/2 × 1/2)2x × 1/8¹⁶
we get:
(₋512) 6x (1/4) 2x × 1/8¹⁶
(₋8)³ 6x (1/4) × 2x × 1/8¹⁶
cancel 8 from numerator and denominator.
₋6x × 1/4 × 2x × 1/8¹³
divide the numbers.
₋3x² × 1/8¹³
₋3x²/8¹³
Hence we get the simplified answer as ₋3x²/8¹³.
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5years ago a woman was 4 times as old as her daughter.in four years time the woman will be two and a half times as old as her daughter.find their present age
At present, the age of the woman is 29 years, while the age of her daughter is 6 years.
In the question, we are given two characters, a woman and her daughter, and told to find their present age. We are also given some clues as to how we will arrive at the answer. Let's consider the first one.
In the first sentence, we are told that 5 years ago, the woman was 4 times as old as her daughter. We don't know the woman's age or her daughter's, so let's call the woman's present age x and her daughter's present age y for now. To know the age of the woman 5 years ago, we will subtract 5 from her current age, which will give us x - 5. Also, the woman was 4 times as old as her daughter 5 years ago, hence:
x - 5 = 4y
If we rearrange that; x = 4y + 5 (let's call this equation 1)
Now, on to the second clue.
In the second sentence, we are told that in four years time, the woman will be two and a half times as old as her daughter. The woman's age in 4 years time is x + 4, hence:
x + 4 = 2[tex]\frac{1}{2}[/tex]y
x + 4 = 5y/2
2x + 8 = 5y (let's call this equation 2)
Next, we will find the value of y (the daughter's present age) by substituting equation 1 into equation 2, that is, putting '4y + 5' in place of x in equation 2, thus:
2(4y + 5) + 8 = 5y
8y + 10 + 8 = 5y
8y - 5y = 18
3y = 18
y = 6
Therefore, at present, the daughter is 6 years old. To find the mother's age, we will substitute the daughter's age in place of y in equation 1:
x = 4y + 5
x = 4(6) + 5 = 29
Hence, the woman is 29 years old, and her daughter is 6 years old.
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Determine the truth value of the following statement for each set of conditions.
If you have a fever, then you are sick. (Lesson 2-3)
You have a fever, and you are not sick.
The truth value of the statement "If you have a f e v e r, then you are s i c k." can be classified as T because it is true.
The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as Fa l s e.
What is the Truth Value?The definition of a truth value is the a t t r i b u t e of a p r o p o s i t i o n as to whether the p r o position is true or false.
For example, the truth value for "3 is odd" is true, which can be denoted as T. The truth value of "2 + 2 = 5" is false.
Now, it is well known that fever is a symptom of a s i c k n e s s. Thus, if you have f e v e r, then you are classified as being s i c k. Thus;
The truth value of the statement "If you have a fever, then you are s i c k." can be classified as T because it is true.
The truth value of the statement "You have a f e v e r, and you are not s i c k." can be classified as False
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what is the absoulte value of 0.75
Answer: 0.75
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) Express the result
in scientific notation
Answer:
1353.4 x 10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) = 770.4 + 583 = 1353.4
Scientific Notation: 1353.4 = 1353.4 x 10^3
Answer: 1.3534x10^3
Step-by-step explanation:
(7.2 x 107) + (5.5 x 106) =6767/5 = 1353.4 = 1.3534x10^3
Use the model to help find the quotient of 6/8 divided by 1/4
The quotient of 6/8 divided by 1/4 is 3.
How to calculate the value?It should be noted that the information is to find the quotient of 6/8 divided by 1/4.
This will be:
= 6/8 ÷ 1/4
= 6/8 × 4/1
= 3
Therefore, the quotient is 3.
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Please help!! Use the graph at right to answer the following questions.
Evaluate f(0)
Answer:
f(0) = 1
Step-by-step explanation:
f(0) means what is the value of y when x = 0
locate x = 0 on the number line, at the origin, go vertically up to meet the graph at (0, 1 ) , then
f(0) = 1
5x/7-3/2+1 then x+1=
Mr. Bell wants to celebrate the class that scores the highest average score on the cycle one exam covering the standard titled, "One Step Equation with Word Problems." His budget for the incentive is $60. For this total, he can purchase "x" amount of boxes of pizza. Each box of pizza cost $9.25. Select the equation that matches the word problem.
Based on the total budget of Mr. Bell for the incentive and the cost of a pizza box, the equation that matches the word problem is 60 ≥ 9.25x
What equation is correct?The amount that Mr. Bell will spend at the most is the budget for the incentive of $60.
He will not spend more than this amount but will spend a maximum of it. This amount of $60 is therefore equal to or greater than the cost of the pizzas:
60 ≥ cost of the pizza
The cost of the pizza is:
= Cost per pizza box x number of boxes
= 9 × x
= 9x
The equation is therefore:
60 ≥ 9.25x
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A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after m months is given by the
following function.
H(m)=51+m
What is the plant's height after 18 months?
M
the plants height would be 69cm
