Yes. It is a right-angled triangle.
What is a dot-product?The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of numbers of equal length (often coordinate vectors) and outputs a single number. The dot product of two vectors' Cartesian coordinates is frequently used in Euclidean geometry. Although other inner products can be defined in Euclidean space, it is frequently referred to as the inner product (or, less frequently, projection product) of Euclidean space (see Inner product space for more).
The sum of the products of the matching entries of the two number sequences is the dot product, according to algebra. B, it is the result of adding the cosine of the angle between the two vectors and the Euclidean magnitudes of the two vectors.
The vectors that make up the triangle must first be located. The vertices are subtracted to achieve this.
QP=(2,0,-4)-(1,-3,-2)=(1,3,-2)
PR=(1,-3,-2)-(6,-2,-5)=(-5,-1,3)
RQ=(6,-2,-5)-(2,0,-4)=(4,-2,-1)
QP.PR = (1, 3, -2).(-5, -1, 3) = -5-3-6= -14
PR.RQ = (-5, -1, 3).(4, -2, -1) = -20+2-3 = -21
RQ.QP = (4, -2, -1).(1, 3, -2) = 4-6+2 = 0
Calculate the dot products to see if these vectors are perpendicular now.
They are perpendicular if the dot product of two vectors equals zero. As you can see, RQ.QP is zero in your triangle, which supports this. Consequently, a right-angled triangle results.
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Question is below
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The expression, evaluated to the simplest form is -4
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
(9² + 19)/(10² - 5³)
Simplifying the expression
(9² + 19)/(10² - 5³)
9² = 81
10² = 100
5³ = 125
Thus,
The expression becomes
(81 + 19)/(100 - 125)
= 100/-25
= -4
Hence, the expression, evaluated to the simplest form is -4
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the lengths of plate glass parts are measured to the nearest tenth of a millimeter. the lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.9. determine the mean and variance of the lengths. (a) mean round your answer to two decimal places (e.g. 98.76). (b) variance round your answer to three decimal places (e.g. 98.765)
The mean and variance of the lengths are 590. 50 and 0. 075 respectively
How to determine the valuesGiven that the lengths are;
590.1, 590. 2, 590. 3, 590. 4, 590. 5, 590. 6, 590. 7 , 590. 8, 590. 9
Mean = sum of terms/ number of terms
Mean = 590.1 + 590. 2 + 590. 3 + 590. 4 + 590. 5 + 590. 6 + 590. 7 + 590. 8 + 590. 9/ 9
Find the sum of the numerator
Mean = 5314. 5/ 9
Mean = 590. 500
Variance = sum of the distances from the mean/ total number - 1
Variance = (590. 1 - 590. 5)² + (590. 2 - 590. 5)² + (590. 3 - 590. 5)² + (590. 4 - 590. 5)² + (590. 5 - 590. 5)² + (590. 6 - 590. 5)² + (590. 7 - 590. 5)² + (590. 8 - 590. 5)² + (590. 9 - 590. 5)² ÷ 9 - 1
Variance = 0. 16 + 0. 09 + 0. 04 + 0. 01 + 0 + 0. 01 + 0. 04 + 0. 09 + 0. 016 ÷8
Variance = 0. 6/ 8
Variance = 0. 075
Thus, the mean and variance of the lengths are 590. 50 and 0. 075 respectively
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The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 80 centimeters. Find the length and width of the rectangle.
The length and width of the rectangle are 21cm and 19cm.
How to calculate the value?Let the dimensions be represented by x and x+2.
The perimeter of a rectangle is:
= 2(length + width)
= 2(x + x+2) = 80
2x + 2x + 4 = 80
4x + 4 = 80
4x = 80 - 4
4x = 76
Divide
x = 76/4
x = 19
Therefore, the second number will be:
= 19 + 2 = 21
The numbers are 19 and 21.
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f(x)=−x
2
+8x+14
\text{Find }f(-8)
Find f(−8)
The value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
How to evaluate the function?The equation of the function is given as
f(x) = -x^2 +8x + 4
The expression f(-8) means that x = -8
So, we have:
f(-8) = -(-8)^2 + 8(-8) + 4
Evaluate the exponent and the product
f(-8) = -64 - 64 + 4
Evaluate the sum and the difference
f(-8) = -124
Hence, the value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
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Quadrilateral a has side lengths 2,3,5 and 6. quadrilateral b has single length 4,5,8 and 10 could one of the quadrilateral be a scale copy of the other
Quadrilateral b, is not a scaled copy of Quadrilateral a.
The side length of Quadrilateral a=2,3,5, and 6.
The side length of Quadrilateral b=4,5,8 and 10
Now comparing the Ratio of the Corresponding Sides of two quadrilaterals a and b
2/4 ≠ 5/8
3/5 ≠ 6/10
Since the ratio of corresponding opposite sides is not equal. The two Quadrilateral are Not Similar.
So, We can say that Quadrilateral b, is not a scaled copy of Quadrilateral a.
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if 1/3 of a gallon of paint covers 1/8 of a wall, how much paint is needed to cover the entire wall?
Answer:
8/3 or 2 2/3 gallons
Step-by-step explanation:
1/3 of gallon covers 1/8 of a wall, therefore, the amount of pain is needed to cover the entire wall is 1/3 x 8 = 8/3 or 2 2/3 gallons
Vijay's family is leaving for galactic gardens resort once his parents get home from work on friday. their house is 544 miles from the resort. they plan to stop and spend the night at a hotel after 3 hours of driving, then complete the rest of the trip on the second day. if their average speed is 64 miles per hour, how long will they drive on the second day?
The next day they will drive for about 5.5 hours
In given question, Vijay's house is 544 miles from the resort.
after 3 hours of driving, they stop and spend the night at a hotel and then complete the rest of the trip on the second day.
Let in 3 hours of driving, they completed the 'x' miles of distance from their home.
So, they complete the rest of the trip of 544 - x miles on the second day.
Let t be the time in hours they drive on the second day.
Their average speed is 64 miles per hour.
⇒ 64 = [x + (544 - x) ] / [3 + t]
⇒ 64 = 544 / 3 + t
⇒ 64(3 + t) = 544
⇒ 192 + 64t = 544
⇒ 64t = 352
⇒ t = 5.5 hours
Therefore, The next day they will drive for about 5.5 hours
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which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays? fraction 30 over 6
Expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.
As given,
The graph represents
x-axis: Time in minutes
y-axis: Number of sprays
Ordered pairs ( 30,4) ,(60, 8) ,( 90,12), and ( 120, 16)
Consider any two points ( 90,12) ,(120 , 16)
Expression of the rate per minute=( y₂ -y₁)/(x₂ -x₁)
=( 16 - 12)/(120 -90)
= 4/30
Therefore, expression of the rate per minute at which air freshener dispenses sprays is equal to fraction 4 over 30.
The complete question is :
The graph shows the number of sprays an automatic air freshener dispenses, y, in x minutes: A graph is shown. On the x-axis, the values are from 0 till 150 in increments of 30 for each grid line, and on the y-axis, the values are from 0 to 20 in increments of 4 for each grid line. The title of the graph on the x-axis is Time in minutes, and the title on the y-axis is Number of Sprays. A line is shown connecting ordered pairs 30, 4 and 60, 8 and 90, 12 and 120,16. The title for the graph is Dispense Rate. Which expression can be used to calculate the rate per minute at which the air freshener dispenses sprays?
fraction 4 over 30
fraction 30 over 4
fraction 30 over 16
fraction 16 over 30
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a car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) find the number of revolutions per minute the wheels are rotating.
The revolution per minutes of the wheels rotation is 912 rev/ min
How to determine the number of revolutionsGiven the parameters;
Velocity = 65 miles per hourDiameter = 2 feetConvert the velocity
[tex]v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)[/tex]
v = 29. 1 m/s
Let's find the circumference
Circumference = 2 π r
radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters
Circumference= 2 × 3. 142 × 0. 30 = 1. 915
Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec
Let's convert to rev/ min
= 15. 2 × 60
= 912 rev/ min
Thus, the revolution per minutes of the wheels rotation is 912 rev/ min
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A student was asked to evaluate an expression the students work is shown describe any errors and find the correct value of the expression explain your reasoning
30 is the correct value of the expression in linear equation .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.The error starts from here- 36-10 + 4
If we are doing addition or subtraction start from left
=36−10+4
=26+4
= 30
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The vertex of ∠A B C is located at the origin. Point A is located at (5,0) and Point C is located at (0,2). How can ∠A B C be classified?
A. acute
C. right
B. obtuse
D. scalene
As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)
How to determine the features of an angle set on Cartesian plane
Herein we find the locations of the three vertices of the figure, of which we must determine the lengths of the two sides of the angle and determine the value of the angle by trigonometry:
BA = 5, BC = 2
θ = tan⁻¹ (BA / BC)
θ = tan⁻¹ (5 / 2)
θ ≈ 68.199°
As the angle is greater than 0° and less than 90°, then the angle ABC is acute. (Answer: A)
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A gardener is planting flowers and would like for them to be in even rows. he has 24 rose bushes and 28 tulips. what is the greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows?
The required solution is,
1. Gardner can put a maximum of 4 flowers in each row
2. At 150 minutes both the student will meet each other
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
1. For the planting of trees in even rows,
The greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows,
Taking HCF of number of plants 24 and 28
HCF of 24 and 28 is 4
Thus, Gardner can put a maximum of 4 flowers in each row.
2.
Time taken by the first student to complete one lap is 25 minutes,
So,
1 lap = 25 minute
1 minute = 1 / 25 lap
For the second student,
1 lap = 30 minute
1 minute = 1/30 lap
At time x minute both will meet each other,
x/25 -x/30 = 1
5x/750 = 1
x = 750/5
x = 150 minute
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Answer:
4
Step-by-step explanation:
“What is the geometric relationship between the labels angles? What is the relationship of their measures? Then use the relationship to write an equation and solve for x!”
Using complementary and supplementary angles, we have that:
c. The angles are complementary, hence the equation is 4x - 3 + 2x + 1 = 90 and the solution is x = 15.33.
d. The angles are supplementary, hence the equation is 43x + 16 + 110 = 180 and the solution is x = 18.
What are complementary angles?When the measures of two angles add to 90º, the angles are complementary.
This is the case in item c, hence:
4x - 3 + 2x + 1 = 90
6x = 92
x = 92/6
x = 15.33.
What are supplementary angles?When the measures of two angles add to 180º, the angles are supplementary.
This is the case in item d, hence:
3x + 16 + 110 = 180.
3x = 54
x = 54/3
x = 18.
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Complete the statement to describe the expression ab + cdab+cda, b, plus, c, d.
The expression consists of
terms, and each term contains
factors
The expression contains FOUR terms, each with TWO factors.
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one mathematical operation. This math operation can be addition, subtraction, multiplication, or division. An expression has the following structure: The expression is (Number/variable, Math Operator, Number/variable).Expression information: In algebra, the word term defined the single numbers(10), variables(y), and the product of the two (10y).
In the following expression: ab+cd+ef+ghThere are four terms:
abcdefghA factor is a component of a product.
For the given equation, we will have four terms, each with two factors.Therefore, the expression contains FOUR terms, each with TWO factors.
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The correct question is given below:
Complete the statement to describe the expression ab+cd+ef+ghab+cd+ef+gha, b, plus, c, d, plus, e, f, plus, g, h. The expression consists of ----- terms, and each term contains ----- factors. Please fill in the blanks!
Solve equation.
6 t-18=30
To solve the equation, add 18 to both sides, then divide by 6. The solution is t = 8.
A linear equation is an equation of which the highest degree of its variables is 1.
Steps to solve linear equations:
Simplify the expressions. If there are parentheses, remove them by multiplying the corresponding terms.Combine the same terms.Isolate the variable on one side by using subtraction of addition.Use division or multiplication to find the value of the variable.Recall that if we subtract or add the same number to both sides of an equation, it does not change the equality.
The given problem:
Solve 6t-18 = 30
The variable is t. Isolate the variable by adding 18 to both sides:
6t -18 +18 = 30 +18
6t = 48
Divide both sides by 6
6t : 6 = 48 : 6
t = 8 (solved)
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Solve the following inequality X-5 > 25
1. -20
Answer: x>10
Step-by-step explanation:
X-5 > 25-20
x-5+5>5+5
x>5+5
x>10
on a number line, suppose point e has a coordinate of , and eg. what are the possible coordinates of point g? question content area bottom part 1 the possible coordinates for g are
The possible coordinates of point G on this number line are either -10 or 14.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
Given the following data:
E = 2.
EG = 12.
On this number line, the coordinate of EG is given by this mathematical expression:
EG = |E - G|
Substituting the given parameters into the expression, we have;
12 = |2 - G|
2 - G = ±12
G = 2 ± 12
Simplifying and evaluating the above expression, we have:
G = 2 + 12
G = 14.
OR
G = 2 - 12
G = -10
Therefore, the possible coordinates of point G on this number line are either -10 or 14.
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Complete Question:
On a number line, suppose point E has a coordinate of 2, and EG= 12. what are the possible coordinates of point G?
How did the values compare the greatest 1/4 -1 1/4 -2 1/4 -1 3/4 -2 1/4
The values compared to the greatest :
-2 1/4,-1 1/4,-1 3/4, 1/4
Comparing and ordering fractions is an essential part of developing a sense of numbers. This is also an essential skill to have when facing practical questions, such as:
"Would you like to have {\displaystyle {\frac{3}{4}}}{\frac{3}{4 }} d 'a pizza does not, or {\displaystyle {\frac{6}{7}}}{\frac{6}{7}} of a pizza?" There are several ways to compare and order fractions. If you have a calculator, the fastest way is to convert fractions to decimals. If you don't have a calculator, you can make comparisons easily by finding a common denominator or simply using your reasoning skills and what you already know about fractions.
In this way, the given fractions are compared from largest to smallest
-2 1/4,-1 1/4,-1 3/4, 1/4
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What is the slope of segment AB?
answer:
3/8
explanation:
(m/n)
count units from point a and b vertically, that is m.
count units from point a and b horizontally, that is n.
Which sum or difference is modeled by the algebra tiles
Answer:
The answer is C
Step-by-step explanation:
First there are 2x first then there are other x's then two 1 equals 2
-4 1/3 divided by 2 1/5
Answer: -1.9696969696969696969696
Step-by-step explanation:
Answer:
Exact form: -65/33
Decimal form: -1.96
Mixed number: - 1 32/33
Step-by-step explanation:
HELP ASAP I DON'T UNDERSTAND
Answer:
-2
Step-by-step explanation:
I did the math, trust me. Just input -2 into the x's and solve.
Answer:
D. x = -6
( 3x-6² - 30x-6 - 72 = 0 )
Step-by-step explanation:
So first you work out:
3x² = ( 3 x -6²) = -108
Then work out 30x = ( 30 x -6 ) = -180
-108 - -180 => 72
Then just do 72 - 72 =
Which would be 0! ☆*:.｡.o(≧▽≦)o.｡.:*☆
hope this helped! xx
x+1= 10
Please step by step
Pre algebra
Answer: x=9
Step-by-step explanation:
x+1= 10
x-1+1=10-1
x=10-1
x=9
Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus. How old is Tanya now?
Answer: 36 years old
Step-by-step explanation:
T=Tanya. M=Marcus
T=M+28
T+6=3(M+6)
T+6-6=3(M+6)-6
T=3(M+6)-6
M+28=3(M+6)-6
M+34=3M+18
34=2M+18
2M=16
M=8
T=M+28
T=8+28
T=36 years old
The current age of Tanya is equivalent to 45 years old.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that Tanya is 28 years older than Marcus. In 6 years, Tanya will be three times as old as Marcus
Assume the initial age of Tanya is {x} years and that of Marcus is {y} years old. So, we can write -
x = y + 28 ....... Eq[1]
x + 6 = 3y ........ Eq[2]
Using Eq[1] in Eq[2], we get -
y + 28 + 6 = 3y
y + 34 = 3y
2y = 34
y = 17
Than, we can write [x] as -
x = 17 + 28
x = 45
Therefore, the current age of Tanya is equivalent to 45 years old.
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I need help bc I got this one wrong twice lol.
The answer is H, B and C; And Z, K and R
Step-by-step explanation:
H, B and C; And Z, K and R form a straight line
QUESTION 11:
Consider the graphed function. Based on its end behavior, which of the following could be its equation? (photo attached below):
A) f (x)= x^3 + 6x^2-5x
B) f (x)= -x^4 +6x^3 - 5x^2
C) f (x)= x^4 +6x^3-5x^2
D) f (x)= -x^3+ 6x^2-5x
QUESTION 12:
Divide x2 by x – 1. What is the value of the remainder?
A) 0
B) 1
C) -1
D) 2
this is very important... its for alegbra.. please help
Answer in decimal form = -0.2
Answer as a fraction = -1/5
=========================================================
Explanation:
The term "rate of change" is the same as "slope" for linear equations.
Use the slope formula to get the steps shown below.
[tex](x_1, y_1) = (-3, 3.6) \text{ and } (x_2, y_2) = (5, 2)\\\\m = \frac{y_2 - y_1}{x_2 - x_1}\\\\m = \frac{2-3.6}{5-(-3)}\\\\m = \frac{2-3.6}{5+3}\\\\m = \frac{-1.6}{8}\\\\m = \frac{-16}{80}\\\\m = -\frac{1}{5}\\\\m = -0.2\\\\[/tex]
The decimal value is exact without any rounding done to it.
A slope of -1/5 means we go down 1 unit and to the right 5 units.
slope = rise/run = -1/5
rise = -1 = go down 1
run = 5 = go to the right 5
The length of each side of the base of a regular octagonal prism is 6 inches, and the height is 11 inches. Find the lateral area.
The lateral area of the regular octogonal prism is 528 square inches.
How to determine the lateral area of a regular octogonal prism
Regular octogonal prisms has two regular octogonal base sides and eight rectangular lateral sides. In this problem we must look for the sum of the areas of the eight rectangular lateral sides, where each area is equal to the product of base side (l) and height (h), both in inches. Then,
A = l · h
A = (6 in) · (11 in)
A = 66 in²
A' = 8 · A
A' = 8 · (66 in²)
A' = 528 in²
The lateral area of the regular octogonal prism is 528 square inches.
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Perform the following operation
and express the answer in
scientific notation.
4.3x1027.0×10²
[?]×10]
Answer:
[tex]4.4161 \times 10 ^{2} [/tex]
[tex]4.3 \times 1027 \times 10 { \\ \\ }^{2} [/tex]
[tex]4416.1 \times 10^{2} [/tex]
[tex]4.4161 \times 10 ^{2} [/tex]
5×62+6×33-68 (help pls I need it
Answer:
440
Step-by-step explanation:
To do this problem, you have to follow the PEMDAS order.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
We have to do 5x62 first, which is 310. Next, we multiply 6 and 33, which gets us 198. Then, we add 310 to 198, which is 508. Finally, we subtract 68 from 508 to get 440.
Hope this helps!
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