Answer:
u = |u|(cos∝+cosβ+cosγ)
Step-by-step explanation:
Explanation
Proof:-
Given a vector u = x₁ i + y₁j +z₁k
let O X, OY, O Z be the positive co-ordinate axes
P(x₁,y₁,z₁) be any point in the space
Let OP makes angles α,β,γ with co-ordinate axes OX , OY ,OZ .
The angle α,β,γ are known as direction angles and cosine of the angle
l =cosα , m= cosβ , n=cosγ
The perpendicular PA,PB,PC are drawn co-ordinate axes OX,OY,OZ respecctively
InΔOAP , ∠A =90° , cos∝ =[tex]\frac{x}{r}[/tex]
x₁ = rcos∝
InΔOBP , ∠B =90° , cosβ =[tex]\frac{y}{r}[/tex]
y₁ = rcosβ
InΔOCP , ∠C =90° , cosγ =[tex]\frac{z}{r}[/tex]
z₁ = rcosγ
Given u = x₁ i + y₁j +z₁k
|u| = [tex]\sqrt{(x_{1})^{2} +(x_{2} )^{2} +(x_{3} )^{2} }[/tex]
Therefore u = x₁ i + y₁j +z₁k
u = |u|(cos∝+cosβ+cosγ)
Question in picture below Will give brainly
Answer:
J 120
Step-by-step explanation:
6.
Triangles TUV and TWV are congruent triangles.
Angles U and W are corresponding angles, so they are congruent.
m<U = m<W
7x + 15 = 8x
Subtract 7x from both sides.
15 = x
m<U = 7x + 15 = 7(15) + 15 = 8(15) = 120
Answer: J 120
The public debt of a fictional country is 8,127,650,198,774 units of its
currency, while its gross domestic product (GDP) is 23,476,117,934,187 units
of its currency. What is the country's debt-to-GDP ratio?
Step-by-step explanation:
just divide 8,127,650,198,774 by 23,476,117,934,187
by calculator
Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each and the milkshakes cost $5 each. If Mrs. Browning spent a total of $21, how many of each type of treat did she buy?
Please help me please !!!
Answer:
3 milkshakes and 3 sundaes
Step-by-step explanation:
3 * 5 = $15 + 3 * 2 = $21
Any help please I appreciate it thank you on 1 and 2 plzzzz!!!
Answer:
1. angle Y, angle XYZ, and angle ZYX
2. angle PQR, angle SQR, and angle PQS
Step-by-step explanation:
1. The 3 ways to name the given angle are:
✔️The use of an alphabet of the vertex: angle Y
✔️The use of the three alphabets can be named in two ways with the middle alphabet representing the vertex:
angle XYZ
angle ZYX
2. The three different angle in the diagram consist of two adjacent angles that share the same side: angle PQR and angle SQR,
and the bigger angle that sums up the two internal angles, which is angle PQS
Help me I’ll give you stars
Answer:answer choice 2
Step-by-step explanation:
Kung and So Lee offered $87,000
on a home that had been priced
at $96,500. The seller agreed to the
offer. A 20 percent down payment
is required. What is the amount of
the down payment? What is the
amount of the mortgage loan
needed to financethe purchase the purchase
Answer:
Down payment = $17,400
Amount of mortgage loan = $69,600
Step-by-step explanation:
Given that :
Cost of home = $87,000
Down payment = 20%
Amount of down payment :
20% of the cost of home
(20/ 100) * $87,000
0.2 * 87000 = $17,400
The cost of mortgage loan required to finance the purchase :
Cost of home - downpayment
$87,000 - $17,400
= $69,600
A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins If the number chosen appears on the bottom of both of the dice, then the player wins If the number chosen does not appear on the bottom of either of the dice, the player loses What is the expected return to the player, in dollars, for one roll of the dice
Answer: [tex]=\frac{-1}{16}[/tex]
Step-by-step explanation:
given data:
number to be chosen from = 1,2,3,4.
Solution:
ways the number can show
[tex]2*3*1=6[/tex] ways for your number to appear once.
[tex]1*1=1[/tex] ways for your number to appear twice.
[tex]3*3=9[/tex] ways for your number not to appear at all
[tex]= \frac{6(1) + 1(2) - 9(1)}{16}[/tex]
[tex]= \frac{6+2-9}{16}[/tex]
[tex]=\frac{-1}{16}[/tex]
expected return of the player is [tex]=\frac{-1}{16}[/tex]
two planes travel a constant speed. plane A travels 2.800 miles in 5 hours plane B travels 3.885 miles in 7 hours. which plane is faster?
Martina used 3/4 of a bottle of conditioner in 7/12 of a year. How much conditioner would she use in a full year
Step-by-step explanation:
7 months = 3/4
1 month = 3/4 ÷ 7
= 3/28
12 months / 1 year = 3/28 x 12
= 9/7
not sure if its correct
Answer: 1 2/7
trust me it just worked for me on IXL
sum of 23.5 , 2.1, 6.07 , and 0.893
A map of two cities is plotted on a coordinate grid. One city is centered at (-60,40), while the other is at (40, 20). A rest station lies at the midpoint of a straight road joining the centers of each city. What is the location of the rest station? (1 point)
Answer:
( - 10, 30 )
Step-by-step explanation:
A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
~~~~~~~~~~~~~~~~~~~
A( - 60, 40)
B(40, 20)
The location of the rest station is
( [tex]\frac{-60+40}{2}[/tex] , [tex]\frac{40+20}{2}[/tex] ) = ( - 10, 30 )
Answer:
(-10,30)
Step-by-step explanation:
i just took test
Please make me Brainliest
6) Which expressions are equivalent? Choose ALL that apply.
28
74
1) 7 to the fourth power
) 4 to the seventh power
7.7.7.7
The expressions "7^4", "7 to the fourth power", and "7*7*7*7"are the expressions that are equivalent.
We are given five mathematical expressions.The first expression is "28".The second expression is "7^4", which is equal to 2401.The third expression is "7 to the fourth power", which is equal to 2401.The fourth expression is "4 to the seventh power" which is equal to 16384.The fifth expression is "7*7*7*7", which is equal to 2401.Compare the values of all the expressions above.We can conclude that the second, the third, and the fifth expressions are equivalent as they have equal values.To learn more about expressions, visit :
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A function is initially defined by the set of coordinate pairs ((-3,7), (1,5), (4,13)). Which coordinate pair below, if added to this set, prevents the set from representing a function?
1) (2,5) 2) (5,0) 3) (-1,8) 4) (1,4)
Answer:
(1,4)
Step-by-step explanation:
Given
[tex]\{(-3,7), (1,5), (4,13)\}[/tex]
Required
Which pair makes the relation not a function?
A function is defined as:
[tex]\{(x_1,y_1), (x_2,y_2), (x_3,y_3)..... (x_n,y_n)\}[/tex]
Where each x values (domain) are unique and different from one another.
In the given function, the x values (domain) are: -3, 1 and 4
To get a pair that makes the relation, not a function; we have to select from the given options, any option that has either of -3, 1 and 4 as its x values.
From the list of given options.
4) (1,4) has an x value of 1
Hence, the solution to this question is (1,4)
Which line is perpendicular
to the line passing through
the points (-4, 2) and (4,--4)
Answer:
The line is 4/3x
Step-by-step explanation:
I graphed it
Triangle ABC is formed by the vertices A(1,2,-1), B(-3,-6,2)and C(3,-2,0).
If D is the midpoint of BC, the the length (distance) of AD.
write the midpoint
write the distance
Answer:
Point D: [tex](0,-4, 1 )[/tex]
d = √41
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Midpoint Formula [3D]: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )[/tex]Distance Formula [3D]: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point A(1, 2, -1)
Point B(-3, -6, 2)
Point C(3, -2, 0)
Step 2: Find Point D
Simply plug in your coordinates B and C into the midpoint formula to find midpoint
Substitute [MF]: [tex](\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )[/tex]Divide: [tex](0,-4, 1 )[/tex]Step 3: Find distance d
Simply plug in the 2 coordinates A and D into the distance formula to find distance d
Substitute [DF]: [tex]d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}[/tex]Subtract/Add: [tex]d = \sqrt{(-1)^2+(-6)^2+(2)^2}[/tex]Exponents: [tex]d = \sqrt{1+36+4}[/tex]Add: [tex]d = \sqrt{41}[/tex]Jaron walked 15 blocks north and then 3 blocks west to school. Marisol walked 3 blocks east and then 15 blocks south to school. Write an expression to show that each traveled the same distance.
Answer:
sqrt(15² + 3²) = sqrt(15² + 3²)
Step-by-step explanation:
Using Pythagoras:
15 blocks North = 15 blocks south (direction opposite to each other)
3 blocks west = 3 blocks east (directions opposite to each other)
Hence distance traveled (d) :
JARON
D = sqrt(15² + 3²)
MARISOL:
D = sqrt(15² + 3²)
Hence ;
sqrt(15² + 3²) = sqrt(15² + 3²)
What is the relationship between the ratios?
8/11 and 24/33
Drag and drop to correctly complete the statement.
The ratios are ________.
Enter your answer in the box.
Answer:The ratios are _Equivalent_______.
Step-by-step explanation:
Step 1
Equivalent ratios are ratios that have the same value even though they look different. When we divide or multiply a given ratio by the same number ( in the numerator and denominator )we get anther equivalent ratio.
Step 2
In the given ratios
8/11 and 24/ 33
8/ 11 x 3/ 3 = 24/ 33
also
24/33 ÷ 3/3 = 8/11
This shows that the relationship between the ratios are equivalent.
HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!
What is a control group?
:((((((((((((((((((((((((((((
What is a control group?
A group that changes the variable
The group that applies the variable
The group that tests the variable
A test group where the variable is not changed or applied
Answer:
A scientific control is an experiment or observation designed to minimize the effects of variables other than the independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements.
A regular 12-gon has side length 8 inches. What is its area?
Answer:
RELATED
How to Solve a Hexagon
Updated October 23, 2018
By Chris Deziel
A polygon is any closed two-dimensional figure with 3 or more straight (not curved) sides, and a 12-sided polygon is known as a dodecagon. A regular dodecagon is one with equal sides and angles, and it's possible to derive a formula for calculating its area. An irregular dodecagon has sides of different lengths and different angles. A six-pointed star is an example. There's no easy way to calculate the area of an irregular 12-sided figure unless you happen to have it plotted on a graph and can read the coordinates of each of the vertices. If not, the best strategy is to divide the figure into regular shapes for which you can calculate the area.
Calculating the Area of a Regular 12-Sided Polygon
To calculate the area of a regular dodecagon, you have to find its center, and the best way to do that is to scribe a circle around it that just touches each of its vertices. The center of the circle is the center of the dodecagon, and the distance from the center of the figure to each of its vertices is simply the radius of the circle (r). Each of the 12 sides of the figure is the same length, so denote this by s.
You need one more measurement, and that's the length of a perpendicular line drawn from the midpoint of each side to the center of the 12-sided shape. This line is known as the apothem. Denote its length by m. It divides each section formed by the radius lines into two right-angled triangles. You don't know m, but you can find it using the Pythagorean theorem.
The 12 radius lines divide the circle you scribed around the dodecagon into 12 equal sections, so at the center of the figure, the angle each line makes with the one next to it is 30 degrees. Each of the 12 sections formed by the radius lines is made up of a pair of right-angled triangles with hypotenuse r and one angle of 15 degrees. The side adjacent to the angle is m, so you can find it using r and the sine of the angle.
Step-by-step explanation:
The area of the polygon is 344.18 square inches.
What is the area?The area is the amount of area occupied by an object's flat (2-D) surface or shape.
Given:
A regular 12-gon has a side length of 8 inches.
Apothem of the polygon,
a = {8/2(tan180/8)}
a = 8/2tan22.5
a = 7.17 inches.
The area of the polygon,
= 12 x 8 x 7.17 / 2
= 344.18 square inches.
Therefore, the area is 344.18 square inches.
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Heidi is purchasing a frozen yogurt dessert. She must select a flavor, a type of sauce, and a topping from options in
the table.
Frozen Yogurt Dessert Options
Sauce
Pineapple
Blueberry
Strawberry
Topping
Cherry
Rainbow Sprinkles
Chocolate Sprinkles
Nuts
Flavor
Vanilla
Chocolate
How many different combinations are possible?
Answer:
288 combinations.
Step-by-step explanation:
Simply multiply 2! by 3! and 4! which equals to 2 * 6 * 24 = 288 combinations.
Hope this helped!
Answer:
24
Step-by-step explanation:
Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
-1, 2, 4
9514 1404 393
Answer:
f(x) = x³ -5x² +2x +8
Step-by-step explanation:
If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:
f(x) = (x -(-1))(x -2)(x -4)
= (x +1)(x -2)(x -4)
= (x² -x -2)(x -4)
f(x) = x³ -5x² +2x +8
Pls hurry I need the answer
=============================================
Work Shown:
Apply the law of cosines
a^2 = b^2 + c^2 - 2*b*c*cos(A)
10^2 = 13^2 + 11^2 - 2*13*11*cos(A)
100 = 290 - 286*cos(A)
100-290 = -286*cos(A)
-190 = -286*cos(A)
190 = 286*cos(A)
286*cos(A) = 190
cos(A) = 190/286
A = arccos(190/286)
A = 48.368620460647
A = 48
Make sure your calculator is in degree mode.
please help!! if ur not gonna then, dont answer pls
13(9−6m)+14(12m−8) =
Answer:
90m + 5
Step-by-step explanation:
Distribute 13 to (9-6m) and distribute 14 to (12m -8)
13*9 - 13*6m + 14*12m - 14*8 =
117 - 78m + 168m - 112 =
put like terms together
117-112 -78m + 168m =
5 + 90m
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
c
Step-by-step explanation:
Answer:
C) c = 5 ( 3.5b + 10 )
Step-by-step explanation:
This is because the shop will charge a flat rate of $10 per visit. Then it will charge $3.5 per bowl. Hence the equation; (3.5b + 10) is formed. Finally, if one goes there 5 times, they will have to multiply this equation by 5 to find the total cost. Henceforth, C) is the only correct answer.
Select all values that satisfies the inequality 2f >–8
options-
4
4
0
-6
3.5
-2.25
-100
Step-by-step explanation:
2f > -8
f > -4
The values greater than -4 here are 4, 0, 3.5 and -2.25.
Solve this 40 pointsssss
Answer:
2
Step-by-step explanation:
Answer:
6 because the pattern on the 3 rows is remove 1 on each of the starting and end point of the pattern, therefore, 6 for the 4th row, 4 for the 5th row 2 for the last row
Which point is a solution to the linear inequality below:
y - 3x< 1
A (0,0)
B (0, 3)
C (-2, 1)
D (-10, 0)
Answer:
A (0,0)
Step-by-step explanation:
y - 3x < 1
0 - 3(0) < 1
0 < 1
Which equations are equivalent to −4(3d−2)−7minus, 4, left parenthesis, 3, d, minus, 2, right parenthesis, minus, 7 ?
A) −12d−15
B)12d−15
C)None of the above
Please help me !!!
Answer:
She/He is right it's C. Tysm!
The correct answer is:
A) −12d−15 (None of the options provided are equivalent to the given expression.)
How to determine the equivalentTo simplify the expression −4(3d−2)−7, we can apply the distributive property by multiplying -4 to each term inside the parentheses:
−4(3d−2)−7 = -4 * 3d + (-4) * (-2) - 7
This gives us:
-12d + 8 - 7
Combining like terms:
-12d + 1
So the expression is equivalent to -12d + 1.
Therefore, the correct answer is:
A) −12d−15 (None of the options provided are equivalent to the given expression.)
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please help ill give BRAINLIEST
Answer:
B and D
Step-by-step explanation: