The vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j).
How to determine a vector in polar form
Let be a vector in rectangular form, that is, a vector of the form (x, y). A vector in polar (trigonometric) form is defined by the following expression: (r, θ)
And the magnitude (r) and direction of the vector (θ), in degrees, are, respectively:
Magnitude[tex]r = \sqrt{x^{2}+y^{2}}[/tex] (1)
Direction[tex]\theta = \tan^{-1}\frac{y}{x}[/tex]
And the vector in rectangular form is described below:
(x,y) = (-7, 9) - (-5, 2)
(x,y) = (-2, 7)
And its polar form is determined below:
[tex]r = \sqrt{(-2)^{2}+7^{2}}[/tex]
[tex]r = \sqrt{53}[/tex]
r ≈ 7.280
θ = tan⁻¹ (-7/2)
θ ≈ 105.945°
And the vector between (-5, 2) and (-7, 9) represented in trigonometric form is described by the expression 7.280 · (cos 105.945° i + sin 105.945° j). [tex]\blacksquare[/tex]
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An item is regularly priced at $76. It is now priced at a discount of 80% off the regular price.
Answer:
Sale price:
The price after the original price has been discounted.Our goal is to find the sale price.
We could use either of the two methods shown below:
Find what the discount price is, and reduce that off the original price.
Or
Simply find the sale price by finding the leftover percentage of the discount and multiplying it by the original price.
Let's use the second technique.
The leftover percentage of 80% is 20%, because;
100 - 80 = 20%.
Now multiply this percentage with the original price:
20%(can be considered 20/100), so
20/100 × $76
= 15.2, the sale price of this item is $15.20!
what type of bias can occur
survey question “how many words per minute can you read?”
People may have a bias towards whether they read fast or slower on purpose because they believe they will retain more information that way (each person is different). If your taking a wpm test, for example, you won't pay attention to comprehension, only speed. Another bias is the type of book your reading and whether you enjoy it. Studies prove that you tend to soak in more information and read faster when you are enjoying the book.
Which statement correctly describes the scatter plot?
Answer:
b
Step-by-step explanation:
a. Multiplication Property of Equality
b. Division Property of Equality
c. Addition Property of Equality
d. Subtraction Property of Equality
1) the base of the rectangular prism is shaded what is the lateral surface area
ignore number 5
Answer:
the lateral surface area is11ftStep-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧Find the value of x. Segments that appear to be tangent are tangent. Round your answer to the nearest tenth.
Answer: 6.3
Step-by-step explanation:
Which graph represents y as a function of X?
A
B
C
D
Answer:
A
Step-by-step explanation:
Vertical line test. Draw vertical lines (you don't have to actually draw them, imagine them) across the relation. If any line intersects two portions of the relation, it is not a function.
Find the equation of the perpendicular bisector of line MN
Answer:
Y=(-1/2)x+9/2
Step-by-step explanation:
For straight lines y=mx+c
m=gradient
Find the gradient first-m=(y2-y1) /(x2-x1)
Take the points M and N and substitute in the equation
m=(5-2)/(-1-5)
m=-1/2
Gradient of line MN×gradient of perp line =-1
There fore gradient of perp line =2
Evaluate the expression
Answer:
36
Step-by-step explanation:
Given expression:
[tex](10 - 3 + 5)^{2}} \times \dfrac{1}{4}[/tex]
Simplify the expression in the parenthesis
[tex]\implies (12)^{2} \times \dfrac{1}{4}[/tex]
Simplify the exponents in the expression:
[tex]\implies (12) \times (12) \times \dfrac{1}{4}[/tex]
[tex]\implies 144 \times \dfrac{1}{4}[/tex]
∴ Recall that: (a × 1/b = a ÷ b)
[tex]\implies 144 \div 4[/tex]
Simplify the expression:
[tex]\implies 144 \div 4[/tex]
[tex]\implies \boxed{36}[/tex]
Answer:
C) 36
Step-by-step explanation:
Given expression:
[tex]\dfrac14(10-3+5)^2[/tex]
Following the order of operations, carry out the operations inside the bracket first:
[tex]\implies \dfrac14(7+5)^2[/tex]
[tex]\implies \dfrac14(12)^2[/tex]
Now carry out the exponent:
[tex]\implies \dfrac14(144)[/tex]
Finally:
[tex]\implies \dfrac{144}{4}=36[/tex]
Fill in the missing values for the factored expression.
2x2 + 4x
=________(x+2)
*hint: find the GCF
Answer:
2x(x+2)
Step-by-step explanation:
What is the measure of the missing angle?
Answer:
The missing angle = 113°
Step-by-step explanation:
Let the missing angle be x
Sum all angles in a triangle = 108°
34° + 33° + x° = 108°
x° = 108° - 34° - 33°
x° = 113°
!!PLEASE PLEASE PLEASE PLEASE PLEASE MARK ME THE BRAINLIEST!!
Answer:
[tex]\tt x=113^o[/tex]
Step-by-step explanation:
We know that the sum of angles in a triangle is always 180°.
So the sum of the three angles must be 180°.The two angles you know measure 34° and 33°.
Now, let's write an equation and find the measure of the unknown angle:-
[tex]\tt 34^o+33^o+ x=180^o[/tex]
[tex]\tt 67^o+x=180^o[/tex]
[tex]\tt x=180^o-67^o[/tex]
[tex]\tt x=113^o[/tex]
Therefore, the measure of the missing angle is 113°.
What is the mean of this data set? 3, 5, 10, 11, 15
Answer:
8.8.
Step-by-step explanation:
There are 5 values so:
mean = (3+5+10+11+15)/ 5
= 44/5
= 8.8.
Which of the following describes an example of mutually exclusive outcomes A and B for throwing a single 6-sided
die?
A = the outcome is odd, B = the outcome is 3
A = the outcome is in {1,2,3,4}, B = the outcome is in {4,5,6)
A = the outcome is odd, B = the outcome is even
A = the outcome is less than 6, B = the outcome is more than 1
You have 976 grams of a radioactive kind of rhodium. How much will be left after 120 seconds if its half-life is 30 seconds?
grams
there will be approximately 61 grams of the radioactive rhodium remaining after 120 seconds.
What are exponential growth and decay?A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.
Given, You have 976 grams of a radioactive kind of rhodium.
The formula for the amount of a substance remaining after a certain amount of time given its half-life is:
N = N₀ *[tex](1/2)^{t / t_{1/2} }[/tex]
where:
N₀ is the initial amount of the substance
N is the amount of the substance remaining after time t
t₁/₂ is the half-life of the substance
In this problem, N₀ = 976 grams, t = 120 seconds, and t₁/₂ = 30 seconds. We can plug these values into the formula and solve for N:
N = 976 * (1/2)⁽¹²⁰/³⁰⁾
N = 976 * (1/2)⁴
N = 976 * 0.0625
N ≈ 61
Therefore, after 120 seconds, there will be approximately 61 grams of the radioactive rhodium remaining.
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What mistake did Lindsay make?
Answer:
Step-by-step explanation:
Discussion and Correction
The algrebra itself is fine. The exclusions are not so good. The difficulty comes in the denominator. It factors into (2x)(x - 3). x cannot take on a value of 0 (that was pointed out and that is correct). The problem comes in the plus/minus 3. Plus 3 is correct. x - 3 will come 0 if x = 3. Nothing bad will happen if x = - 3
Answer: So the exclusions in the denominator should be modified to x = 3.
Answer:
The excluded values are x-values that make the denominator of the original expression zero, since [tex]\dfrac{a}{0}[/tex] is undefined.
[tex]x = -3[/tex] is not an excluded value since this x-value does not make the denominator zero.
[tex]x = -3[/tex] makes the numerator zero, but as [tex]\dfrac{0}{a}=0[/tex] it is not an excluded value.
Therefore, step 3 of her work should read:
[tex]\textsf{Finding excluded values}:x\neq 0\:\textsf{and}\:x\neq 3[/tex]
You start driving west for 3 miles, turn right, and drive north for another 13 miles. At the end of driving, what is your straight line distance from your starting point? Round to the nearest tenth of a mile.
Answer:
13.3 miles to nearest 1/10.
Step-by-step explanation:
The journey forms a right triangle so by Pythagoras:
d^2 = 3^2 + 13^2
d^2 = 9 + 169
d^2 = 178
d = 13.34 miles.
An orchard sells 4 pounds of apples for one dollar how much would 5 pounds of apples cost
Answer:
1.25
Step-by-step explanation:4 pounds equal to 1 dollar so that means that each pound equals to 0.25 cents. SO, now you multiply 0.25 x 5= 1.25
What is the unit rate for headphones if eight headphones cost $390.92
Help me pls I need the unit rate too !
$48.865 per headphone
unit rate : total cost/total items
unit rate:
390.92/8
48.865
Each headphone costs $48.865
I need it quickly
which graph could represent the system of equations 4x+2y=8 and 3x-y=1?
Answer:
E
I use Desmos graphing to solve this
^● ●^
How does graphing two sets of data on one graph help you see patterns?
Answer:
~Shoto todoroki here~
The Mathematical tables and graphs are a good way to represent patterns. It helps to organize data and can reveal the relationships, making it easier to write equations that describe the patterns.
(Hope this helps!)
please help, thank you guys
Step-by-step explanation:
1) 165⁰
2) 180⁰
Note:FOR initial temperature check the temperature at t=0
I hope it helped you
What is true when a system of equations has no solution?
The lines intersect in one place.
The lines are parallel and do not intersect.
The lines coincide (are the same line).
This is impossible
Answer:
D. This is impossible
Step-by-step explanation:
In math, when you solve an answer and you’re given no solution, it means that whatever equation you just did cannot be solved, and is therefore, impossible; there is no answer.
Side note: If you have any further questions feel free to let me know.
Answer:
B. The lines are parallel and do not intersect.
Step-by-step explanation:
What number, when divided by 6, is equivalent to 15?
n=90
n=5/2
n=4
n=15
Answer:
90
Step-by-step explanation:
15+15=30
3x30=90
Therefore, the answer to what divided by 6 equals 15 is 90. You can prove this by taking 90 and dividing it by 6, and you will see that the answer is 15. Tip: For future reference, when you are presented with a problem like "What divided by 6 equals 15?", all you have to do is multiply the two known numbers together.
Therefore, n=90 is your correct answer
A cylinder is sliced by a plane that is not parallel to the base and intersects only the lateral surface. the resulting cross section is .
The cylinder that is sliced by the plane which is not parallel to the base of the cylinder and intersects only at the lateral surface is called an ellipse.
What is the formation of an Ellipse in a Cylinder?When a cylinder with a longitudinal axis (z) is sliced at an angle to the xy plane, an elliptical shape is created.
In a circle, every plane crosses a circular cylinder perpendicularly to its axis. A plane that is neither at right angles to the axis nor parallel to it, crosses the cylinder in an elliptical shape.
Learn more about an ellipse here:
https://brainly.com/question/26679189
Answer:
It is an ellipse.
Step-by-step explanation:
Plato/Edmentum
Which expression is equal to:
4b + 4c / z
a. 4(b + c) / z
b. 4b(4c / z)
c. 8bc / z
d. (b + c) ● (4+z)
(marking brainliest)
4(b + c) / z
Reason:
We factor 4 from 4b+4c to get 4(b+c). The z in the denominator stays where it is. This factoring is possible because of the distributive property.
This is why [tex]\frac{4b+4c}{z}[/tex] is the same as [tex]\frac{4(b+c)}{z}[/tex]
Side note: you should use parenthesis to write (4b+4c)/z, which indicates all of 4b+4c is over top the z. This is because 4b+4c/z might get mistaken for [tex]4b+\frac{4c}{z}[/tex]
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The figure pictured below is made of a cylinder and a hemisphere. Its volume can be determined using the following formula, in which r is the radius and h is the height
of the cylinder. Determine the volume of the figure. Show your work
Answer:
395.64 m³
Step-by-step explanation:
Volume (figure)
Volume (hemisphere) + Volume (cylinder)2/3πr³ + πr²hπr² (2/3r + h)3.14 x 9 (2 + 12)3.14 x 9 x 143.14 x 126395.64 m³Answer:
The answer is 396m^3.
Step-by-step explanation:
The solution is in the attached file
6/25 simplest form explain please on how to do ittt
Answer:
0.24
Step-by-step explanation:
6 divided by 25 = 0.24
The cafeteria at San Isidro Elementary has 18 tables. Fourteen of the tables seat 14 students each and the rest of the tables seat 16 students each. What is the maximum number of students that can sit at the tables in the cafeteria at one time?
Answer:
You have to use the cafeteria-style formula where you multiply all the numbers
Step-by-step explanation:
First u multiply
18 by 14 and then by 16
Which of the three situations given below is best modeled by an exponential function?
I. A bacteria culture doubles in size every day.
II. A plant grows by 1 inch every 4 days.
III. The population of a town declines by 5% every 3 years.
I. The bacteria culture doubles in size every. day
lara makes salad dressing by mixing 8
spoonfuls of oil and some vinegar. The tape
diagram shows the ratio of oil to vinegar.
Answer:
3:6
Step-by-step explanation:
8 ÷ 4 = 2
2 ÷ 1 = 2
6 ÷ 3 = 2
Answer:
1. 2:8
2. 1:4
3. 3:12
Step-by-step explanation:
There are 2 parts of oil for every one part of vinegar.
2+1=3
The ratio is made up of 3 total parts.
The part to whole ratio of oil to total is 2:1.
We are looking for an equivalent ratio that has 8 spoonfuls of oil.
If we have 4 times as much oil, we also need 4 times as much vinegar.
Also, we will have 4 times as much total dressing.
2x4=8
1x4=4
3x4=12