The distance between pair of parallel lines with the following equation
y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units
Definition of parallel linesParallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.
The fundamental characteristics listed below make it simple to recognize parallel lines.
Straight lines which are always the same distance apart from one another are known as parallel lines.No matter how far apart they are from one another, the parallel lines can never intersect.The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].
Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.
The y-intercept of line y = 2x-7 is (0, -7).
So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is
y = [tex]-\frac{1}{2}x-7[/tex]
The perpendicular intersects or meets the line y = 2x -7 at (0,-7).
Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.
Solve for x:
2x + 3 = [tex]-\frac{1}{2}x-7[/tex]
[tex]\frac{5}{2} x[/tex] = -10 (combine them like terms)
x = -4 (multiply each side by 2\5)
Find y:
y = [tex]-\frac{1}{2}.(-4)-7[/tex]
= -5
so, the point is (-4,-5).
Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).
[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]
[tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]
[tex]={\sqrt {4^2 +(-2)^2}}[/tex]
[tex]=2{\sqrt 5}[/tex]
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Find the value of x for the given values of a and b .
b=3 x+4 a , for a=-9 and b=12
The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16
What are the equations?An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.
Equations can be graphed, just like a function.
We write the given equation
b = 3x + 4a
and we have the values of the coefficients a and b, and these are:
a = -9b = 12We substitute these values in the equation:
b = 3x + 4a
(12) = 3x + 4(-9) :::: We solve the equation
12 = 3x -36
3x = 12 + 36
3x = 48
x = 48/3
x = 16
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The activation energy of a reaction is 133.5 kj, and frequency factor (a) is 8.23 x 1010 sec -1, at what temperature (in celsius) is the rate constant equal to 0.08857 sec-1?
955°C is temperature (in celsius) is the rate constant equal to 0.08857 sec-1.
What is the short definition of activation energy?
The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .
K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]
logk = logA = Eq/RT
log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1 - [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]
= log5.57 + [tex]log 10^{10}[/tex] - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]
= log5.57 + 10log10 - 15.10 * 10³ J/T
-1.5483 = 0.7458 + 10 - 15.10 * 10³/ T
-1.5483 = 10.7458 - 15.10 * 10²/T
- 15.10 * 10³/ T = -1.5483 - 10.7458
15.10 * 10³ /T = 12.2941
T = 15.10 * 10³/ 12.2941
= 1228K
= 955°C
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The Great Pyramid measures 756 feet on each side of the base and the height is 481 feet. Find the volume of the pyramid.
The volume of pyramid is 9.16×10⁷ feet³.
We are given the measure of each side of Great Pyramid, which will be it's length and width. Also, we are given height. The formula for calculation of volume of pyramid is -
Volume = (length×width×height)÷3
Keep the values in formula to find the volume of Great Pyramid
Volume = (756×756×481)÷3
Performing multiplication on Right Hand Side of the equation to find the volume of Great Pyramid-
Volume = 274908816÷3
Solving the Right Hand Side of the equation, by performing division, we get the volume of Great Pyramid -
Volume = 9.16×10⁷ feet³
The volume of Great Pyramid is 9.16×10⁷ feet³.
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m∠3=82.find m ∠4. i need help for my iready question
What is the slope of the function?
pls answer
Answer:
slope = -4
Step-by-step explanation:
slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4
2+2 i know the answer is four
Answer:
5 50bw syfnauw dux fyq euw eywvr6b
Jim buys a watch by making a $25 down payment and paying 15 installments of $12 each. What is the total cost of the watch?
write an equation for the circle
solve 6/7x + 15 - 8 = 31
Answer:
Step-by-step explanation:
simplify
6/7x + 7= 31
6/7x+7-7=31-7
6/7x=24
6/7x=24/6/7
28
6/7(28)+15-8=31
24+15-8=31
39-8=31
Question 5 (2 points)
Natalie wants to make sure she has enough in her account to go out to dinner with her friends. When she views her online bank statement, her
current available balance is not showing. This is what she can see:
Current posted balance: $87.73
Pending withdrawals/debits: $97.68
Pending deposits/credits: $126.02
Available balance:
What is Natalie's current available balance?
Answer: $
Blank 1:
Natalie’s current available balance is $116.07.
To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.
Account Balance = Pending deposits / credits – Pending Withdrawals /debits
= $126.02- $97.68 = $28.34
Available Balance = Account Balance + Current Posted Balance
= $28.34 +$87.73 = $116.07
Current Available Balance = $116.07
The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.
Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.
Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.
Hence Natalie’s current available balance is $116.07.
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Suppose a triangle has sides a, b, and c, and let e be the angle opposite the side of length a. If cose < 0, what must be true? O A. a² + b² = ² O B. b² + c²> a² O c. b² + 2² ²
In the given triangle the statement that holds true is [tex]b^2+c^2 < a^2[/tex]. Therefore, the option (c) is the correct option.
What are cosine formulas?In the cosine formulas, the cosine (cos) function is discussed. Consider a right-angled triangle with one acute angle, x. The cosine formula is cosx = (adjacent side) / (hypotenuse), where "adjacent side" refers to the side adjacent to angle x and "hypotenuse" refers to the longest side of the triangle.
As per cosine rule fore given [tex]$\triangle$[/tex]ABC:
[tex]$\cos \theta=\frac{b^2+c^2-a^2}{2 b c}$$$[/tex]
According to the question;
For a given [tex]$\triangle$[/tex]ABC;
cos e < 0.
Therefore, [tex]\quad \frac{b^2+c^2-a^2}{2 b c} < 0 \\[/tex]
[tex]b^2+c^2 < a^2[/tex]
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Identify the constant of variation. y=(3/2)x
The constant of variation in y = (3/2)x is (3/2)
y = kx (Where k is the constant)
Here, y = (3/2)x
so k = (3/2)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors. 540
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The number is prime.
B. The number is composite. Its prime factors written as a product are ( )
C. The number is neither prime nor composite.
Answer:B. The number is composite. Its prime factors written as a product are (5*3^3*2^2)
Step-by-step explanation:
Since 540 is an even number, that means it can be divided by 2. This means that the number is composite.
You can keep dividing it by 2 until you can't anymore.
Once you divide 540 by 2 twice, then you get 135.
You can divide it by 5 because the ones digit is 5.
Then you get 27, which is 3 times itself 3 times.
You finally multiply the numbers you divided by, and you get 2*2*5*3*3*3, which is 5*3^3*2^2.
show that the value of cos30 degrees x tan60 degrees + sin30 degrees is an integer
Answer:
Step-by-step explanation:
cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2
Determine the slope of the line that contains the given points.
P(-3,-5), Q(-3,-1)
The slope of the line containing (-3,-5) and (-3,-1) is Infinity.
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -1 , [tex]y_{1}[/tex] = -5 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = -3 .
On substituting the values of variables in equation1, we will get
m = ( (-1)-(-5) ) / ( (-3)-(3) ) = (4/0) = Infinity.
As the slope of a line is Infinity, so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-3,-5) and (-3,-1) is Infinity.
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Which equation represents a line which is perpendicular to the line y = 2x - 5?
Step-by-step explanation:
y = 2x + C
we must want to find C
Three friends live in houses with backyards adjacent to a neighborhood bike path. They decide to have a round-robin party using their three homes, inviting their friends to start at one house and then move to each of the other two. If one friend's house is centered at the origin, then the location of the other homes are (5,12) and (13,0) . Write a coordinate proof to prove that the triangle formed by these three homes is isosceles.
The distance of AO and BO are the same so the given triangle will be an isosceles triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
The given vertices are making a triangle as shown below in the figure.
Distance between A(5,12) and O(0,0) is
⇒ [tex]\sqrt{(5 - 0)^2 + (12 - 0)^2}[/tex]
⇒ 13
Distance between B(13,0) and O(0,0) is
⇒ [tex]\sqrt{(13 - 0)^2}[/tex]
⇒ 13
Since the two sides are the same so triangle will be isosceles.
Hence "The distance of AO and BO are the same so the given triangle will be an isosceles triangle".
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Note: enter your answer and show all the steps that you use to solve this problem in the space provided. how you would convert the repeating, nonterminating decimal to a fraction? explain the process as you solve the problem. 0 . 1515 . . .
The fraction for 0.1515... is 5/33
It is possible to convert non terminating decimals to fraction. Because decimals are originally obtained from fractions itself.
If we have a terminating decimal number, by multiplying and dividing with powers of 10 gives a fraction.
For example, for the decimal 0.25, multiply and divide it with 100 which gives, 25/100 = 1/4.
Now we need to find the fraction corresponding to the decimal 0.1515..
Let x = 0.1515...
First we take 100x = 15.1515...
Now we can subtract the decimal part completely from 15.1515... since it is non terminating.
Now, 100x - x = 15.1515..- 0.1515.. = 15
Therefore, 99x = 15
and x = 15/99 = 5/33
So 5/33 is the fraction for the decimal 0.1515...
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what does (x+4)(2x+5) equal?
Step-by-step explanation:
[tex](x+4)(2x+5)\\\\2x^2+5x+8x+20\\\large\boxed{2x^2+13x+20}[/tex]
Directions: If the statement is true, circle true. If the statement is false, circle false.
15. √115 is between the integers 10 and 11.
TRUE
FALSE
HELP PLS which one is least
Answer:
Option B
Step-by-step explanation:
→ Find the option with the smallest power
Option B
Find the value of x
Step-by-step explanation:
or, x + 65° = 180° [ Being Straight line]
or, x = 180° - 65°
or, x = 115°
Therefore the value of x is 115° .
Now,
or, 4x = 4 × 115° = 460° .
A home improvement store sells bags of sand, which are labeled as
weighing 35 pounds. The equipment used to package the sand produces bags
with a weight that is within 8 ounces of the labeled weight.
a. Write an absolute value equation to represent the maximum and minimum
weight for the bags of sand.
b. Solve the equation and interpret the result.
The maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively
Write an absolute value equation to represent the maximum and minimum weight for the bags of sand.Here, we have
Weight = 35 pounds
Labeled weight = within 8 ounces
Convert ounce to pounds
So, we have:
Labeled weight = within 0.5 pound
The equation is then represented as
|x - 35| = 0.5
Where x represents the labeled weight
b. Solve the equation and interpret the result.In (a), we have
|x - 35| = 0.5
Expand
x - 35 = 0.5 and x - 35 = -0.5
Add 35 to both sides
x = 36 and x = 35
Hence, the maximum and the minimum weight for the bags of sand are 36 and 35 pounds respectively
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Question 15 (1 point)
(01.04 MC)
Darnell is planning a trip to Dallas. He knows the hotel costs $155 per night and the round-trip flight is $99. He has a budget of $850 to spend
on his trip. Which of the following inequalities represents his budget to determine how many nights he can stay in Dallas?
OO
Ob
Od
99n+ 155 2 850
99n+155 ≤ 850
155n+99 2 850
155n+ 99 ≤ 850
The inequality that represents the number of nights he can stay in Dallas is 155n+ 99 ≤ 850 (option d).
How many nights can he stay in Dallas?Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toSince his budget is $850, he can spent a total of $850 or less than $850 on the trip. The sign that would be used to represent this is ≤.
(Total hotel stay cost) + cost of flight ≤. budget
(cost per night x number of hotel stays) + $99 ≤ $850
155n + $99 ≤ 850
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Answer:
Answer is D
Step-by-step explanation:
Write the equation for each line. Use slope-intercept form. m = 1/2 and the y -intercept is (0,0) .
The equation of the line in slope-intercept form with a slope of 1/2 and y-intercept of (0 , 0) is y = 1/2 x.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
Given that the slope of the line is 1/2 and the y-intercept is (0 , 0), write the equation of the line by simply plugging in its values.
y = mx + b
y = (1/2)x + 0
y = 1/2 x
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Dan is saving money to buy a game. So far he has saved $12, which is two-thirds of the total cost of the game. How much does the game cost?
Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled. By how much should she increase each dimension?
The dimensions of the decks increased by the 11 feet.
According to the statement
We have to find that the length by which we increase the dimensions.
So, For this purpose, we know that the
The Area is the amount of space occupied by a two-dimensional figure.
From the given information:
Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled.
Then
The shape of the deck is the rectangle then dimensions is 22 feet by 11 feet.
Then
Area of the deck with the given dimensions = Length * Breadth
Area of the deck with the given dimensions = 22* 11
Area of the deck with the given dimensions = 242.
Then the dimensions increased by the x
Then
Area of the deck with the given dimensions = Length * Breadth
Area of the deck with the given dimensions = (22+x)* (11+x)
Area of the deck with the given dimensions = 242 + 22x+11x+x^2
Area of the deck with the given dimensions = 242 + 33x+x^2
Then according to given details:
x^2 + 33x + 242 = 3*242
x^2 + 33x + 242 = 726
x^2 + 33x = 726 - 242
x^2 + 33x = 484
x^2 + 33x - 484 = 0
After solving
The value of the x become
x = 11 and x = -44
Then second option be neglected.
Then the length increased by the 11 feet.
So, The dimensions of the decks increased by the 11 feet.
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need answers quickly pls!!!! :(
Answer:
17
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}9-6\\\end{array}\right]+\left[\begin{array}{ccc}-5-(9)\\\end{array}\right][/tex]
=3+14
=17
What's 3/10 + 8/15? (Brainliest Question)
Answer:
5/6
Step-by-step explanation:
Get LCD of 30 and add
9/30 + 16/30
25/30
Reduce
5/6
What is the square root of 125 in simplest form
Answer:
[tex]5\sqrt{5}[/tex] = ~11.18
