The vector PQ is given by the addition of the components of the two vectors i.e. →PQ = →Q + →P
Vector is a quantity having magnitude as well as direction and is used to denote the mathematical and geometrical direction of the given quantity.
For example : Velocity, Displacement etc.
Let us first assume that,
P(x,y,z) and Q(u,v,w)
Now, we need to find the vector PQ
→PQ = →Q + →P
= (ui + vj + wk ) + (xi + yj + zk)
= (ui + xi ) +(vj + yj) + (wk +zk)
= (u+x) i + (v + y) j + (w + z)k
= →PQ
For example : Let P(1,2,1) and Q ( -1, -2,4)
Then, →PQ = →Q + →P
= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)
= (1-1) i + (2 -2) j + (1 + 4)k
= oi+0j +5j
= 5j
Hence, the vector PQ is given by the addition of the components of the two vectors.
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The length of a building is 720 in what is the length of this building in yards?
1ft =12 inches , 3ft =1 yard.
Plsss help dont understand
Divide 7/15 by 3/5
A. 7521
B. 21/75
C.7
D.725
Use the order of operations to simplify each expression.
(8+5 × 2)/ 12
Using the order of operations BODMAS to simplify each expression
( 8+ 5 × 2 ) /12 is equal to 1.5.
As given in the question,
Given expression is ( 8+ 5 × 2 ) /12
Simplify each expression by using the order of operations BODMAS is given by
( 8+ 5 × 2 ) /12
= ( 8 +10 ) /12
= 18 /12
= 3 /2
=1.5
Therefore, using the order of operations BODMAS to simplify each expression ( 8+ 5 × 2 ) /12 is equal to 1.5.
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Explain why three angle measures do not determine a unique triangle. How many triangles are determined by three angles measures?
You can either form no triangles or an endless number of triangles when you are given three angles.
For Example -
How many distinct triangles can you construct using angles of 30, 60, and 90 degrees?
Use a protractor to create one of the angles needed to form a triangle. You can adjust the side lengths to your desired length. Make another angle at the end of one of the sides, then link the sides together. You've constructed a triangle.
You should note that you chose the side lengths. This implies that you might choose differently. This allowed you to create an infinite number of distinct triangles using the same angles.
Hence, we can form infinite number of triangles when only the measurements of three angles is given
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Aadesh joins an science club. it is $ 85 to join for the first month and then $ 125 for each month after that. he stays in the club for 14 months. how much did aadesh pay altogether?
Answer:
$1710
Step-by-step explanation:
multiply 125 by 13 which is 1625 then add 85 which gives you a total $1710
Write a two-column proof for the property reflective property of segment congruence
Miranda uses 15/16 gallon of red paint in an art project. She uses 2/5 as much blue paint as she does red paint. How many gallons of blue paint does Miranda use?
Write the following numbers in scientific notation 250,000 = 0.000035 = 0.00000001 = 324,000,000,000,000,000
Scientific notation exists as a method of writing very large or very small numbers. The expression as a number in scientific notation is 2.5 × [tex]10^5[/tex], 3.5 × [tex]10^{-7[/tex], 1 × [tex]10^{-8[/tex], 3.24 × [tex]10^{17[/tex],
What is meant by scientific notation?
Utilizing scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
To express exceedingly high numbers in a shorter manner, scientists have created a shorthand. Scientific notation is the name of this technique. The foundation of scientific notation is the base-10 powers. The coefficient is defined as the initial number, 1.23.
The guidelines for writing scientific notation.
Always start with a base of 10.
The exponent may have both positive and negative values and must be a non-zero integer.
The absolute value of the coefficient is more than or equal to 1, even though it should be less than 10.
Whole numbers, decimal numbers, positive, negative, or both can all be used as coefficients.
The mantissa represents the remaining significant digits of the number.
The expression as a number in scientific notation is 2.5 × [tex]10^5[/tex], 3.5 × [tex]10^{-7[/tex], 1 × [tex]10^{-8[/tex], 3.24 × [tex]10^{17[/tex],
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The approximate weights of two animals are 5.12 x 102 lbs. and 6.8 x 102 lbs. find the total weight of the two animals. write the final answer in scientific notation with the correct number of significant digits. 1.2 x 103 lbs. 1.19 x 103 lbs. 11 x 102 lbs. 5.8 x 102 lbs.
The correct answer is 1.19×10³ lbs.
The weight of first animal = 5.12×10² lbs
Performing multiplication to get the complete weight of first animal
The weight of first animal = 512 lbs
The weight of second animal = 6.8×10² lbs
Performing multiplication to get the complete weight of second animal
The weight of second animal = 680 lbs
Now, performing addition to find the approximate weights of two animals-
Final answer = 512 + 680
Performing addition to find the approximate weights of two animals
Final answer = 1192 lbs
Now, converting the number in scientific notation -
Final answer = 1.19×10³ lbs
Hence, the final answer in significant digits is 1.19×10³ lbs.
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where RS=3y+3=2y+8 and RT=31 what is the value of y
The value of y in the line segment is 4
How to find the variable in a line segment ?RT is the total line segment.
Therefore,
RS = 3y + 3
ST = 2y + 8
RT = 31
Hence,
RT = RS + ST
31 = 3y + 3 + 2y + 8
31 = 3y + 2y + 3 + 8
31 = 5y + 11
31 - 11 = 5y
20 = 5y
divide both sides by 5
20 / 5 = 5y / 5
y = 4
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Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 50 miles at a speed of 10 mph, while Bob's motorboat traveled 65 miles at a speed of 13 mph. For how long were Niles and Bob traveling?
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If lines p and q are parallel, then angles 3 and 6 are congruent.
The statement "If lines p and q are parallel, then angles 3 and 6 are congruent" is false because "If lines p and q are parallel, then angles 3 and 6 are supplementary".
Given,
The statement "If lines p and q are parallel, then angles 3 and 6 are congruent"
We know,
when two parallel lines are intersect by a transversal then the interior angles on the same side of the transversal is supplementary.
Here, ∠3 and ∠6 are interior angles on the same side of the transversal, So the ∠3 and ∠6 are supplementary
So, the correct statement is "If lines p and q are parallel, then angles 3 and 6 are supplementary"
Hence, the statement "If lines p and q are parallel, then angles 3 and 6 are congruent" is false because "If lines p and q are parallel, then angles 3 and 6 are supplementary".
The complete question is:
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
If lines p and q are parallel, then angles 3 and 6 are congruent.
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Need asap last question on a exam
The zoo needs to replace some of the railroad tracks that support their train ride. The total length of the track is 500 feet, and there are three sections that need to be replaced. These sections measure 62/2 83/8 and 63/4 feet. How much of the zoo railroad track does not need to be replaced?
Based on the calculations, the length of the zoo railroad track which does not need to be replaced is equal to 3543/8 or 442.875.
What is a fraction?A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.
The parts of a fraction.In Mathematics, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorIn order to determine the length of the zoo railroad track which does not need to be replaced, we would add all of the length of the zoo railroad track that need to be replaced and then subtract this value from the total length of the zoo railroad track as follows:
Length of replacement = 62/2 + 83/8 + 63/4
Note: Lowest common denominator (LCM) = 8.
Length of non-replacement = (248 + 83 + 126)/8
Length of non-replacement = 457/8
Length of replacement = 500 - 457/8
Length of replacement = (4000 - 457)/8
Length of replacement = 3543/8 or 442.875.
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Write the equation of the line in slope-intercept form.
-7-y=-3x
The equation of the line in slope-intercept form is y = 3x + (-7) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is -7 -y = -3x .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
-7 -y = -3x
⇒ y = 3x + (-7) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 3
Intercept = c = -7
The equation of the line in slope-intercept form is y = 3x + (-7) .
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Mary's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs mary $5.35 per pound, and type b coffee costs $4.15 per pound. this month, mary made 181 pounds of the blend, for a total cost of $853.15. how many pounds of type b coffee did she use?
Mary used 96 pounds of type b coffee this month.
Using algebraic expression and equation, we can solve how much of each type of coffee did Mary used that month.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that that month, Mary made 181 pounds of the blend that is a mixture of two types of coffee, we can express this as:
181 = a + b
where a = pounds of type a coffee that costs $5.35 per pound
b = pounds of type b coffee that costs $4.15 per pound
Also, the total cost of the blend that month is $853.15, which is the sum of the total cost of the two types of coffee. We can express that as:
$853.15 = $5.35(a) + $4.15(b)
Using substitution method to solve the two equations,
181 = a + b ⇒ a = 181 - b
$853.15 = $5.35(181 - b) + $4.15(b)
853.15 = 968.35 - 5.35b + 4.15b
5.35b - 4.15b = 968.35 - 853.15
1.2b = 115.2
b = 96
a = 181 - b
a = 181 - 96
a = 85
Hence, Mary used 85 pounds of type a coffee and 96 pounds of type b coffee that month.
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PLEASEE HELP I WILL GIVE BRAINLIST PLEASE ITS DUE TONIGHTTTTT!! ILL GIVE EXTRA POINTS PLEASE NO LINKS
Find the distance along Broadway between 37th Street and 36th Street.
The distance between 37th St. and 36th St. is
x= 275ft
What is a similar triangle?Similar triangles are those that share at least one vertex and the angular value between the sides associated to their sides is the same, which makes them proportional in their dimensions (same type of triangle).
To solve this problem we will use the relation of similar triangles, if we raise the equation we have the following way:
x /275 = 220/220
Proportion of the sides
x/275 = 1
x = 275 ft , is the distance x between the lanes N° 37 and 36.
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what are the multiples of 2 from 101 to 200??
The multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.
What are multiples?It should be noted that multiples simply mean the product that can be gotten when a number is multiplied by another number.
It should be noted that the multiples of 2 from 101 to 200 will be all the even numbers starting from 102 to 200.
In this case, the odd numbers aren't multiple of 2.
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Look at the image below.
What is the area of the parallelogram?
square units
The area of the parallelogram is 54 square units.
In this question we have been given a parallelogram
We need to find the area of the parallelogram.
Here, the slant height of the parallelogram is 8 units.
the base of the parallelogram is 9 units.
And the height of the parallelogram is 6 units.
We know that the area of the parallelogram is,
A = base × height
⇒ A = 9 × 6
⇒ A = 54 square units
Therefore, the area of the parallelogram is 54 square units.
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Poppy found a sticker on the sign showing the size of olympic national park. She knows the size is between one million and nine hundred thousand acres. She also knows that the value of the digit in the ten thousand place is 10 times greater than the value of the digit in the thousands place. What is the size of the park?
Answer: Olympic National Park
Established 1938
Size: 922,651 acres
Find the slope of the line that passes through the two points. (4,5) and (1,8)
The slope between the two given points (4,5) as well as (1,8) is -1.
What exactly is the slope of a line?A line's slope is a measure of its steepness & direction.
The slope of a line is defined as a change in y coordinate in relation to a change in x coordinate.
The net change in y coordinates is Δy, while the net change in x coordinates is Δx.As a result, the y coordinate change in relation to the x coordinate change could be composed as,m = Δy/Δx
where,m is the slope
Slope is also written as tan θ = Δy/Δx. Where, tanθ is also called as the line's slope.Now, as per the stated question;
The slope of a line can be calculated using only two points on a straight line. With the coordinates of two points, we can employ the slope of line formula.
Let the coordinates of those 2 points from where the line is passing is;
P1 = (x₁, y₁)
P2 = (x₂, y₂)
The slope of the line is estimated as;
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
The values of the coordinates are given as;
(x₁, y₁) = (4,5) and,
(x₂, y₂) = (1,8)
Substitute the given values of coordinates in the formula to get the slope;
m = (8 - 5)/(1 - 4)
m = 3/(-3)
m = -1
Therefore, given the coordinates of such two points, the slope of a line passing through them is found to be -1.
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Simplify: [tex]\sqrt[3]{135}[/tex]
so i have this problem. Be real cool if you could help e and explain it but if not an answer would be fine
Use your results from Exercises 1-6 to determine whether the given measures define 0 , 1,2, or infinitely many acute triangles. Justify your answers.
a=6, b=9, m
Two sides without an angle measurement, such as a = 6 m and b = 9 m, can be used to create an infinite number of acute triangles.
How many distinct acute triangles can we make, for instance, if our side lengths are 6 m and 9 m and our angle value ranges from 0 to 90 degrees?
Create a triangle with a 45-degree angle, sides that are 10 and 10 meters long, and a third side that can be stretched to the required length. You've constructed a triangle.
We can create a whole different Acute triangle that is identical to this one by altering the length and angle of the third side.
Never overlook picking the side angles and lengths. It's possible that you'll choose to proceed in a different way. There are an infinite amount of distinct triangles that can be created with the same angles.
As a result, we can make an infinite number of acute triangles using a single angle and a single side length.
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Yall pls help me outtt! im having sm trouble with this problem
Step-by-step explanation:
Hello, and thank you for asking your question on Brainly!
This problem is basically telling is to isolate the variable g. But how are we to do so, when it's being sandwiched inside a variety of numbers and letters? The problem looks harder than it seems. But do not fret!
When you're in a trail in the woods and you get lost, the most logical thing is to do the opposite of where you just went in order to try and reach home. We can use this same analogy for math. We just try and use the opposite operation for every action that the function is being acted on!
Let be the original equation,
[tex]u=\sqrt{Ng+Q^3 }[/tex]
Looks pretty complicated right? We want to isolate the variable g, so let's get rid of this 'roof' over their heads.
To get rid of the square root, we can square both sides by two; this negates the square root, and opens up the right section of the equation.
[tex]u=\sqrt{Ng+Q^3 }[/tex]
[tex]u^2 =(\sqrt{Ng+Q^3 })^2[/tex]
[tex]u^2=Ng+Q^3[/tex]
Now, we have to make sure we get the variable g alone. Let's subtract Q cubed to the other side, we can subtract it over to get rid of it on the right hand side.
[tex]u^2=Ng+Q^3\\-Q^3 ~~~~~ -Q^3[/tex]
[tex]u^2-Q^3=Ng[/tex]
We're almost close! Now, all we have to do to isolate the variable g is to divide the whole equation by N, so the right hand side it cancels out. This is the opposite of N multiplied by g.
[tex]\frac{u^2-Q^3}{N} =g[/tex]
It wasn't so bad now, was it? I hope this helped! g is now isolated and this is the end of the problem.
Triangle ABC is mathematically similar to
triangle ADE. Work out the length of DE.
Separate into
two triangles.
D
B
В.
25 cm
E
C
.cm (2
A
30 cm
12cm
cn
Answer:
25 cm
Step-by-step explanation:
triangle abc is Mathematically similar
Which of the following can be added to the number indicated on the number line above to sum to 0?
OA 0.6
OB. 1.4
OC -1.4
OD. -0.6
Answer:
1.4 should be added..................
HELP ASP SHOW UR WORK YOULL GET BRAINILEST
Answer:
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
-15x + 44 = 8x - 12
-8x -8x
-7x + 44 = -12
- 44 - 44
-7x = -56
x = 8
How much would you need to invest in an account paying 16%/a compounded annually if you wanted $3900 after 9 years?
Answer:
$1,025.52
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = Final amount.P = Principal amount invested.r = Interest rate (in decimal form).t = Time (in years).Given:
A = $3,900r = 16% = 0.16t = 9 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies \sf 3900=P(1+0.16)^9[/tex]
[tex]\implies \sf 3900=P(1.16)^9[/tex]
[tex]\implies \sf P=\dfrac{3900}{(1.16)^9}[/tex]
[tex]\implies \sf P=\dfrac{3900}{3.802961...}[/tex]
[tex]\implies \sf P=1025.51662...[/tex]
Therefore, you would need to invest $1,025.52.
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What is the step by step solution to: x^2 -6x +9 =0
Answer:
Step-by-step explanation:
x²-6x+9 = 0
Factor
(x-3)(x-3) = 0
x = 3
Answer:
x = 3
Step-by-step explanation:
We need to find to numbers that sum up to make -6 but their product is +9 :
-3 and -3 will do :
Now we split -6x into -3x and -3x :
x² -3x -3x + 9 = 0
Factorise the first 2 terms:
x(x-3)
Keeping the terms inside the bracket the same as the 1st one factorise the next 2 terms :
x(x-3)-3(x-3) = 0
Keep 1 bracket and make another bracket out of the terms that are outside the brackets :
(x-3)(x-3) = 0
Using the integer rule :
a × 0 = 0
We know that one of these brackets are equal to zero :
x-3= 0
Add 3 to both sides :
x = 3
The other bracket is the same so our final answer is x = 3
Hope this helped and have a good day
It would be nice of you to give brainliest
