You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;
How to know the direction of a vector?We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^
Where A is the magnitude of the resultant
x is the value of the x-component
y is the value of the y-component
We are given;
Magnitude of vector = 84 units
Y-component of the vector = -67 units
Thus,
[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]
From A above, let us take the positive value of the x-component and as such our original vector will be;
A = 56.68i^ - 66j^
The direction of the vector V is;
[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]
Since it points entirely to the negative x-axis, then the angle is;
180 - (-27.15) = 207.15°
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Which prism has a volume of 5 cubic units?
Answer:
1 1/4 units by
4 units by
1 unit
Step-by-step explanation:
5=1 1/4*4*1=1.25*4*1
so 1 and one fourth units by 4 units by 1 unit
Gary is looking over his receipts from his trip to europe. when he was in germany, he exchanged us dollars for euros at a rate of 1:0.7716, and when he was in poland, he exchanged euros for polish zloty at a rate of 1:4.0518. to four decimal places, what was the exchange rate of us dollars to polish zloty? a. 1:0.3199 b. 1:3.1264 c. 1:4.8234 d. 1:5.2512
The exchange rate of US dollars to Polish zloty is 1:3.1264. The correct option is b. 1:3.1264
Calculating exchange ratesFrom the question, we are to determine the exchange rate of US dollars to Polish zloty
From the given information,
Gary exchanged US dollars for Euros at a rate of 1:0.7716
That is,
1 US dollar = 0.7716 Euros
Also, he exchanged Euros for Polish zloty at a rate of 1:4.0518
That is,
1 Euro = 4.0518 Polish zloty
Now, we will find the value of 0.7716 Euros in Polish zloty
Since 1 Euro = 4.0518 Polish zloty
Then,
0.7716 Euro = 0.7716 × 4.0518 Polish zloty
∴ 0.7716 Euro = 3.1264 Polish zloty
But
1 US dollar = 0.7716 Euros
Therefore,
1 US dollar = 3.1264 Polish zloty
Hence, the exchange rate of US dollars to Polish zloty is 1:3.1264. The correct option is b. 1:3.1264
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Which value is the closest estimate of this product? 895x7
A. 5,600
B. 5,900
C. 6,300
D. 6,600
The value is the closest estimate of this product is 6,300.
What are the rules for rounding to the nearest hundred?Rules for Rounding Numbers to Nearest 100. Rule 1: While round off to nearest 100, if the digit in the tens place is between 0 to 4 or <5, then the tens place is replaced by 0. Rule 2: If the digit in the unit’s place is equal to 5 or greater than 5, then the tens place is replaced by 0 and the hundreds place is increased by 1.
So 6,265 is between 6,200 and 6,300
6,265 rounded to the nearest hundred is 6,300Therefore, The value is the closest estimate of this product is 6,300.
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what is the difference between -4-(-13)
Answer:
9
Step-by-step explanation:
- 4 - ( - 13 )
= - 4 + 13
= 13 - 4
= 9
Over a period of 12 hours, the temperature dropped 60°F. What was the average change in temperature in one hour?
Answer:
I think 40 I could be wrong
Answer:
5 degrees dropped per hrhour
Step-by-step explanation:
60/12 is equal to 5/1.
This is just a matter of simplifying.
Como puedo encontrar el área de este prisma?
Answer:
To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
W x L
I need this answered please
Answer:
see the attachment!
i hope this can help you!
In one week my brother's daily expense for his lunch are Birr 54, Birr 61, Birr 42, Birr 63, Birr 42, Birr 56, and Birr 58. what
is his mean daily expense?
Answer:
The mean expense is approximately equal to 53.714
Step-by-step explanation:
When you are trying to find the mean of a number set, you are trying to find the average of the stats. As such, use the formula Sum of the Numbers / Total Number of Values.
In this case, we are adding 54 + 61 + 42 + 63 + 42 + 56 + 58, which is equal to 376. We are then dividing this by 7, which is equal to about 53.714.
Laura tried to shade all the multiples of 12 on the hundred chart.
A Laura shaded 12,but multiples are always greater than the number.
B Laura shaded six multiples of 12,but she left out some.
C Laura did not make a mistake.
D Laura shaded the factors instead of the multiples of 12.
Answer:
D Laura shaded the factors instead of the multipls of 12
Step-by-step explanation:
The factors of 12 are 1, 2, 3, 4, 6, and 12, because each of those divides 12 without leaving a remainder
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144
Evaluate the expression 11²
Answer:
121
Step-by-step explanation:
hope it will help you
Which equation represents the line that passes through the points (-4, 4) and (8, -2) ?
Answer:
There fore the answer is y=(-1/2)x +2
Step-by-step explanation:
Find straight line question passing through the points (-4,4) and (8,2)
Use formula (y-y1) (x2-X1) = (y2-V1) (x-x1)
(y-Y1) (x2-X1) = (y2-Y1)(x-x1)
Substitute points in formula
(y-4)(8+4) = (-2-4) (x+4)
(y-4)12=-6(x+4)
y-4=(-1/2) (x)-(2)
y=(-1/2)x-2+4
y=(-1/2)x +2
the product of a number n and 2 is 2 what is the equation
Answer:
n*2=2
Step-by-step explanation:
Product signifies multiplying two or more numbers together. In this instance, it is n and 2. Then it says it is equal to 2, so 2 goes on the other side of the equal sign.
Find the area of this triangle.
6 ft
10 ft
a date in march is chosen at random, then the spinner below is spun once. find the probability of an odd number, then blue?
Answer:
The probability of an odd number is 17/31 and the probabilty of blue is 1/3
Step-by-step explanation:
Triangle x y z is reflected over its hypotenuse to form kite x y z y prime. hypotenuse x z has a length of 13, x y is 5, and y z is 12. triangle xyz is reflected over its hypotenuse to create a kite. what is the approximate distance from y to y’? round to the nearest tenth. 4.6 units 5.4 units 8.0 units 9.2 units
The approximate distance from y to y’ in the given triangle x y z reflected over its hypotenuse to form kite x y z y is 9.2 units.
Value of angle XThe value of angle X in ΔXYZ is calculated as follows;
tanx = 12/5
tanx = 2.4
x = tan⁻¹(.24)
x = 67.38⁰
Vertical heightThe height from vertex Y to horizontal line XZ is calculated as follows;
sinx = h/5
h = 5(sinx)
h = 5(sin67.38)
h = 4.62
Distance between Y and Y'YY' = 4.62 + 4.62 = 9.24 units
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Answer:
A ✔️
Step-by-step explanation:
"4.6"
Maria plans to make a triangular center island along the road. The said plan is illustrated at the image attached. She was able to put a fence around the lot which measures LT = 3m and OL = 3m. The said land area is an example of an oblique triangle which does not contain any right angle. If m∠T = 70 and m∠L = 65, what could be the measurement of ∠O and TO (round off to the nearest whole number)?
WITH SOLUTION!!!
The sum of interior angles of triangle sum up to 180°
Hence,
∠O + 70° + 65° = 180°
∠O = 180° - 65° - 70°
∠O = 45°
∴ The angle ∠O is 45 degrees.
To find length of TOUse cosine rule: a² = b² + c² - 2bc cos(A)
Hence,
TO² = 3² + 3² - 2(3)(3) cos(65)
TO² = 10.39287129
To = √10.4
TO = 3.22 ≈ 3 meters (rounded to nearest whole number)
∴ The length of TO is 3 meters.
i ready 3 5/3 x (-8 1/3)=
Answer:
-350/9 (improper fraction)
-38 8/9 (mixed number)
Step-by-step explanation:
Converting to improper fractions :
3 5/33 x 3/3 + 5/39/3 + 5/314/32. -8 1/3
-(8 x 3/3 + 1/3)-(24/3 + 1/3)-25/3Multiplying them :
14/3 x -25/3-350/9 (improper fraction)-38 8/9 (mixed number)Answer:
[tex]-38 \frac{8}{9}[/tex]
Step-by-step explanation:
[tex]3 \frac{5}{3} \times -8 \frac{1}{3}[/tex]
Convert to improper fractions:
[tex]\implies \dfrac{3 \times 3 +5}{3} \times -\dfrac{8 \times 3 +1}{3}[/tex]
[tex]\implies \dfrac{14}{3} \times -\dfrac{25}{3}[/tex]
Multiply the numerators and denominators:
[tex]\implies \dfrac {14 \times (-25)}{3 \times 3}[/tex]
[tex]\implies -\dfrac{350}{9}[/tex]
Convert back into a mixed number:
[tex]\implies -38 \frac{8}{9}[/tex]
4(4b-8)-3/8
Please help i have no idea what to do
Answer:
[tex]4(4b - 8) - \frac{3}{8} \\ 16b - 32 - \frac{3}{4} \\ \frac{64b - 128 - 3}{8} \\ \frac{64b - 131}{8} [/tex]
hope this will help you
What is a nonagon with a perimeter of 144 inches?
Answer: Regular nonagon
Step-by-step explanation: In image
2. Triangle ABC has side lengths of
5 units, 13 units, and 12 units.
Use the Converse of the Pythagorean
Theorem to prove that ABC is a right
triangle. Write numbers 1-4 to order
the steps.
52 + 122 = 132
a²+ 62=c²
169 = 169
25 + 144 = 169
Therefore, triangle ABC is a right
triangle.
Answer:
1- a²+b²=c²
2- 5²+12²=13²
3- 25+144=169
4- 169=169
How would adding a French class change the tree diagram above? How would that change the number of possible outcomes?
Beginning with the graph of f(x) = x2, what transformations are needed to form g(x) = 3(x + 2)2 – 1?
Answer:
g(x)=(x+3)2 we must find x? so x+3=0 x=-3 we transformation -3 on left
Step-by-step explanation:
can u answer my queston pleas on my acc
The transformations applied to f(x)=x² to form g(x)=3(x+2)² −1 are: Horizontal shift left by 2 units.
Vertical stretch by a factor of 3.
Vertical shift down by 1 unit.
To transform the graph of f(x)=x² into g(x)=3(x+2)² −1, we can identify a series of transformations that have been applied to the original function.
The term (x+2)² inside the function g(x) indicates a horizontal shift to the left by 2 units compared to f(x).
This is a shift in the negative direction on the x-axis.
The coefficient 3 in front of (x+2)² indicates that the graph is vertically stretched by a factor of 3 compared to the graph of f(x).
The term −1 subtracted at the end of the function g(x) indicates a vertical shift downward by 1 unit compared to f(x).
This is a shift in the negative direction on the y-axis.
Hence, the transformations applied to f(x)=x² to obtain g(x)=3(x+2)² −1 are horizontal shift to the left by 2 units, vertical stretch by a factor of 3 and vertical shift downward by 1 unit.
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f(x) = 11x and g(x) = x^2-6x+3 find the function (f•g)(4)
Answer:
-220
Step-by-step explanation:
(11×4)×(4²-6×4+3) (calculate the power)
(11×4)× (16-16×4+3)
44×(16-24+3)
44×(-5)
-44×5
=-220
can you mark me as the brainliest?
please help, much appreciated!!!! (will mark brainliest)
Answer:
16 years
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
A ticket resale service sells sports championship tickets at a markup of 250%. If a ticket originally costs $150, how much does the resale service charge after adding its markup to the price?
Suppose you are running in a marathon for charity, looking to raise at least $1500. People may sponsor you by donating either $15 or $25 for every mile you run. However, you cannot have more than 100 people sponsoring you for this marathon.
Now, create a system of inequalities using the above information (use x and y as the variables).
Answer:
See below ~
Step-by-step explanation:
Let :
x = people donating $15 when you runy = people donating $25 when you runTwo inequalities created are :
15x + 25y ≥ 15003x + 5y ≥ 300 [Simplified] ⇒ Inequality 1x + y ≤ 100 ⇒ Inequality 2Solving
Let the people paying $15 be "x" and $25 be "y"
1st inequality
15(x) + 25(x) ⩾ $1500
2nd inequality
x + y ≤ 100
Trapezoid PQRS is the image of a trapezoid ABCD after a translation right 9 and up 2. They result in congruent figures.
Match the corresponding parts:
AD PS
DC SR
B PSR
D PQR
The correct match for the sides of the trapezoid will be AD=PS, AB=PQ, BC=QR, AD=PS.
What is translation?The process of changing the location of the image on the coordinate system will be known as the translation.
Here we have the Trapezoid ABCD after a translation right 9 and up 2.
They result in congruent figures
The Match of the corresponding parts are given as:
[tex]\rm AD=PS\\\\AB=PQ,\\ \\BC=QR,\\ \\AD=PS.[/tex]
Hence the correct match for the sides of the trapezoid will be AD=PS, AB=PQ, BC=QR, AD=PS.
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Algebra word problem.
Please help I’m really stuck. Will give brainlist!!!
Answer:
George = 10 + 0.5x
Carlee = 13 + 0.25x
Step-by-step explanation:
Let x be the amount they manufacture, each time they make an object, their pay will increase by the set amount meanwhile the 10 and 13 are a set amount of pay that they will receive.
Use circle E to answer the following questions
Based on the circle theorems, the measures in circle E are:
m(AB) = 40°
m∠AEB = 40°
m∠ACB = 40°
m(ADB) = 320°
What are the Circle Theorems?The theorems are:
Measure of the central angle = measure of intercepted arcMeasure of inscribed angle =1/2( measure of intercepted arc)Measure of inscribed angles with same intercepted arcs are congruent.Using the circle theorems, given the inscribed angle, m∠ADB = 20°, we have:
m(AB) = 2(m∠ADB) = 2(20) = 40°
m∠AEB = m(AB) = 40°
m∠ACB = m∠AEB = m(AB) = 40°
m(ADB) = 360° - 40° = 320°
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Answer answer please
Answer:
c
Step-by-step explanation:
dont trust me but it seems like c
