the distance between Point A (-8,-2) and Point B(6,-1) in Radical form= [tex]\sqrt{197}[/tex]
Distance formula:
The distance between two points formula uses the coordinates of two points in space. In coordinate geometry, the distance between two points can be calculated using the distance formula, present in a two-dimensional or three-dimensional space. The distance formula for two points is also an application of the Pythagoras theorem
the distance formula is used to find the distance between any two points when we already know the coordinates. The points could be present alone on the x-axis or y-axis or on both axes.
Let us consider, that there are two points say A and B in an XY plane. The coordinates of point A are (x1,y1), and of B are (x2,y2). Then the formula to find the distance between two points PQ is given by:
AB=[tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
Note: If the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:
PQ = |x2 – x1|
the distance between point origin O(0,0) and P(x,y) is given by:
OP = √((x2 – 0)² + (y2 – 0)²)
OP = √((x2)² + (y2)²)
or simply,
OP = √(x² + y²)
Solution :
where x and y are coordinates of points other than the origin.
Given :
(x1,y1) = (-8,-2)
(x2,y2)= (6,-1)
Solution:
[tex]d=\sqrt{x^{2} +y^{2} } \\d=\sqrt{(6+8)^{2} +(-1+2)^{2} } \\d=\sqrt{14^{2}+1^{2} } \\[/tex]
[tex]d=\sqrt({197)[/tex]
Radical form= [tex]\sqrt{197}[/tex]
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Find the length of AD. Round the answer to the nearest hundredth.
A. 5
B. 5.1
C. 5.42
D. 6.23
Answer: C 5.42
Step-by-step explanation:
find the distance between the two points in simplest radical form. (8,-1) and (2,-9)
Diane got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 12
cents per yard. If after that purchase there was $22.84 left on the card, how many yards of ribbon did Diane buy?
yards
X
5
Answer:
The number of yards of ribbon that Diane buy in total from the prepaid debit card with $25 on it is 0.18 yards.
Step-by-step explanation:
It is given that, Diane got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 12 cents per yard.
Now, if after that purchase there was $22.84 left on the card, let's calculate how many yards of ribbon did Diane buy in total and for that we need to;
Furthermore, based on the given conditions, we will be formulating the following;
=> (25-22.84) / 12
=> 2.16/12
=> 216/100 × 1/12
=> 9/25 × 1/2
=> 9 / (25×2)
=> 9/50
=> 0.18 yards
Therefore, the number of yards of ribbon that Diane buy in total from the prepaid debit card with $25 on it is 0.18 yards.
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Purchase a home for $160,000 , have a down payment of 25% the bank charges two points at closing, how much are they paying in points
Your customers are investing $160,000 in a house. How much points are they paying in total if they put down a 25% down payment and the bank charges two points at closing? The loan amount after their 25% down payment ($160,000 x.75 = $120,000).
A down payment is a quantity of money that a buyer pays at the beginning of a pricey good or service purchase. A portion of the entire purchase price is covered by the down payment, and the buyer frequently takes out a loan to cover the balance.
This sum is typically expressed as a percentage of the overall cost of buying the house. A typical down payment is 20%, for instance, which means the buyer will pay 20% of the total purchase price up front. During the closing procedure, this sum is typically paid in the form of a cashier's check.
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Translate the sentence into an equation.
Four less than the product of 9 and a number equals 5.
Use the variable c for the unknown number.
Answer:
(9c) - 4=5
Step-by-step explanation:
Product means 'The answer when you multiply' So we are working in multiplication. ( x )
9c is the multiplication.
It says 'less' which means subtracting to our answer. So we subtract 4. So far our equation is: (9c) - 4 (Brackets are needed as we are multiplying 9 by c and not multiplying 9 by c - 4)
Lastly, it says the answer must be 5 so we add that at the end. So the answer is:
(9c) - 4=5
Determine the solutions of the equation:
the absolute value quantity two fifths times x plus 1 end quantity minus 7 equals 0
x = −30 and x = 15
x = −20 and x = 15
x = −20 and x = 20
x = −15 and x = 15
The solutions of the equation are x = 15 and -20
How to determine the solutions of the equation?The equation is given as
the absolute value quantity two fifths times x plus 1 end quantity minus 7 equals 0
Rewrite properly as
|2/5x + 1| - 7 = 0
Add 7 to both sides of the equation
|2/5x + 1| = 7
Remove the absolute bracket
2/5x + 1 = 7 and 2/5x + 1 = -7
This gives
2/5x = 6 and 2/5x = -8
Multiply both sides by 5/2
x = 15 and -20
Hence, the solutions of the equation are x = 15 and -20
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Answer:
x = 15 and -20
Step-by-step explanation:
Please help me simplify
Step-by-step explanation:
3×3^2 is 27 so 27+8÷2 is 31 -(4+3) the answer is 24:)
Pls answer porperlly
Answer: I hope this helps.
Step-by-step explanation:
In the 1800s psychologists established______
behavior and mental processes.
Answer:
the scientific approach led to the birth of modern psychology in the 1800's as psychologists argued that ideas about human behavior and mental processes should be supported by this. In the 1800's, psychologists established these for the (scientific study of human behavior and mental processes).
Step-by-step explanation:
Use the distributive property to remove the parentheses. -3(4v-2y-6)
-12v+6y+18
you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18
i hope this helps :)
consider the line y=9x-8 find the equation that is perpendicular to this line and passes through the point -8,3
The equation of line is y=-9x-69.
To solve this problem we need to know the concept of slope of line and equation of straight line.
Writing the standard form of line is in the form of y= mx+ c where m is the slope of line.
And we also know that the product of slope of a line perpendicular to the line is equal to -1.
Let us assume that the slope of required line is m'
So, m' × 9 = -1
⇒ m'= -9
Now, the equation of line will be;
[tex](y-3)=-9(x+8)[/tex]
⇒ y-3=-9x-72
⇒ y=-9x-69 is the standard equation of line perpendicular to the given line y=9x-8.
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Choose the correct statement.
-2 < -3
1 = -1
5 > -6
The statement 5 > -6 is the correct statement.
In this question, we have been given some mathematical statements.
We need to select the correct statement.
We know that, on the number line , numbers to the right are greater than numbers to the left.
Consider 1st statement
-2 < -3
If we see these numbers on the number line, then -2 is right to -3. This means, -2 is greater than -3.
So, above statement is False.
Consider 2nd statement
1 = -1
If we see these numbers on the number line, then we can observe that both the numbers are not equal.
So, above statement is False.
Consider 3rd statement
5 > -6
If we see these numbers on the number line, then 5 is right to -6. This means, 5 is greater than -6.
So, above statement is True.
Therefore, the statement 5 > -6 is the correct statement.
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Chelsea reduced the size of a triangle to a width of 4 in. What is the new height if it was originally 10 in. tall and 20 in. wide?
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of
Answer:
The LARGEST angle has a measure of 81°
Step-by-step explanation:
Let α be the smallest angle
β be the second angle
θ be the third angle.
• One (second) angle in a triangle has a measure that is three times as large as the smallest angle.
Then
β = 3α
• The measure of thethird angle is 45 degrees more than that of the smallest angle.
Then
θ = α + 45
• We know that the sum of the interior angles of a triangle add up to 180°
Then
α + β + θ = 180
Then
α + (3α) + (α + 45) = 180
Then
5α + 45 = 180
Then
5α = 135
Then
α = 27
_______________
β = 3α = 3 × 27 = 81
θ = α + 45 = 45 + 27 = 72
Conclusion :
The LARGEST angle has a measure of 81°
2.161616 as a fraction
Answer:
16/99
Step-by-step explanation:
i think
-14= -4 + u/5
Solve for u
Answer:
u = -50
Step-by-step explanation:
First let's carry the -4 to the other side and get u/5 by itself
-14 = -4 + u/5
+4 +4
-10 = u/5
The next step is to try and get rid of the u, and in order to do that we have to multiply by 5 on both sides
-10 = u/5
*5 *5
-50 = u
So u should equal -50.
_____
You can also check this answer by plugging it back into the original problem
-14 = -4 -50/5
-14 = -4 -10
-14 = -14
The statement is true, so -50 is our answer for sure.
Hope this helps :)
Help!!!!!!Angle DFG and angleJKL are complementary angles. If the measure if the angle DFG=x+2 and the measure of the angle JKL =x+9 then find x.
∠DFG and ∠JKL are complementary angles
Measure of each angle
Given :
∠DFG and ∠JKL are complementary angles. m∠DFG = x + 5,
and m∠JKL = x − 1
When two angles are complementary then the sum of angles is 90 degrees
∠DFG and ∠JKL are complementary angles.
So,
Now replace the expressions and solve for x
Now replace x with 43 and find out each angle
Divide:
35x³-25x4y³/5x²y²
Answer:
35x³-25x4y³/5x²y² = −5x6y5+35x3
is 4/5 equivalent to 16/20
Answer:
yes
Step-by-step explanation:
you have to divide by the top and bottom to get the answer to the lowest number
Answer:
yes
Step-by-step explanation:
Check by changing to a common denominator
Which equation matches the graph of the greatest integer function given below?
Answer:
A
Step-by-step explanation:
The last number represents where the line meets y-axis
A school district receives a donation of 15,000 pencils. At one of the middle school in the district, there are 4 math classes. At each of the other three middle schools in the district, there are 6 math classes each. Each math class gets the same number of pencils. How many pencils does each math class get?
Hence , the number of pencil's each math class get 1500 .
A numerical expression in arithmetic are often a mixture of numbers, and integers combined mistreatment mathematical operators like addition, subtraction, multiplication, or division.Let the number of pencil's each math class have be "x".
It is given that one middle school have 4 math classes and other three middle school have e 6 math classes .
Then number of pencil's 4 math classes get = 4x
The number of pencil's 6 math classes get = 6x
Total number of pencil's = 15,000
According to question
4x + 6x = 15000
10x = 15000
x = 15000/10
x = 1500
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name a fraction between 6/7 and 1
Answer:7/8, 8/9, 9/10, 10/11, etc.
What is a set of values in math?
Answer:
Step-by-step explanation:
Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4}
Finite And Infinite Sets: Union Of Sets
Power Set: Complement Of A Set
Equivalent Sets: Universal Set
Types Of Sets: Set Theory
how to solve inequality geometrically
Answer:
This article is about the basic inequality {\displaystyle z\leq x+y}{\displaystyle z\leq x+y}. For other inequalities associated with triangles, see List of triangle inequalities.
Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows a case where z is much less than the sum x + y of the other two sides, and the bottom example shows a case where the side z is only slightly less than x + y.
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that
{\displaystyle z\leq x+y,}z\leq x+y,
with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):
{\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}\|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,
Step-by-step explanation:
Answer:
by triangular inequality
Step-by-step explanation:
I need help again please
Answer:
7/10, 12/40, 2/20, -10
If you drive 263 miles and have 11 gallons of gas remaining in your tank. Then you continue driving, and calculate that after driving 314 miles you have 8 gallons left.
What is your rate?
The Fuel efficiency rate in miles per gallon is; 104.67 MPG
How to calculate Fuel efficiency rate?
Let the initial amount of gallons be x
Now, after driving for 263 miles, you have 11 gallons of gas left in your tank.
Now, you continue driving and after driving 314 miles, you have 8 gallons left. This means that number of gallons used to drive 314 miles = 11 - 8 = 3 gallons
Therefore the Fuel efficiency rate which is in miles per gallon is;
MPG = 314/3
MPG = 104.67 MPG
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2x - 3 = -5
What is X?
Answer: x=-1
Step-by-step explanation:
2x - 3 = -5
2x - 3 +3= -5+3
2x=-2
x=-1
Answer:
x = -1
Step-by-step explanation:
To find x, we have to get x by itself.
2x - 3 = -5
Add 3 to both sides
2x - 3 +3 = -5 +3
2x = -2
Divide by 2 to both sides
2x ÷2 = -2 ÷2
x = -1
Have a good rest of your day! :)
Find the earnings for selling the same number of each type of sandwiches. Use x to represent the number of each type of sandwiches sold. Pretzel ham sandwich cost $2.25, pretzel turkey sandwich cost $1.55, bagel ham sandwich cost $2.00, bagel turkey sandwich cost $1.30
Total earnings for selling the same number of each type of sandwiches are $7.10x. This is a simple sum.
Here, the number of each type of sandwiches sold is x.
Pretzel ham sandwich cost $2.25. so, the earnings for selling Pretzel ham sandwich is $2.25x.
Similarly, earnings for selling pretzel turkey sandwich is $1.55x, earnings for selling bagel ham sandwich is $2.00x and earnings for selling bagel turkey sandwich is $1.30x. The total earning can be found by a simple sum of all individual earning of each type of sandwiches.
Therefore, Total earnings for selling the same number of each type of sandwiches are = $2.25x + $1.55x + $2.00x + $1.30x = $7.10x
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Can you please help me solve these math problems questions 49-62
Answer:
The answer to your question is 16
determine whether AB and CD are parallel, perpendicular, or neither.
A(1,5), B(4,4), C(9,-10), D(-6,-5)
