The equation in rectangular coordinates. (x - 1)² + y² = 1
What are different Coordinate Systems ?There are many types of coordinate system depending upon the usage and ease of working , Spherical , Rectangular , Cylindrical , Polar are the examples of Coordinate System.
It is given that the equation in polar coordinates is r = 2 cosθ
To change in rectangular coordinates
The relation between polar and rectangular coordinate is
x = r cosθ and y = r sinθ
x² + y² = r²
r = 2 cosθ
r² = 2r cosθ
r² = x
so the equation in rectangular coordinate system becomes
x² + y² = 2x
x² - 2x + y² = 0
x² - 2x + 1 + y² - 1 = 0
(x - 1)² + y² = 1
This represents the equation in rectangular coordinates.
To know more about Coordinate System
https://brainly.com/question/13498438
#SPJ1
PLEASE HELP (ASAP)
In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.
Angle x of the triangle PQR is 53 degrees.
Angle x is gotten by alternate angle relationship.
How to find an angle in a triangle?Line AB is parallel to line CD
Therefore,
AB║CD
Hence,
62 + x = 115(alternate angles)
62 - 62 + x = 115 - 62
x = 53°
We got the angle x degrees from alternate angle relationship.
learn more on angles here: https://brainly.com/question/13912082
#SPJ1
Answer:
x = 50
Step-by-step explanation:
Angle <BPR and angle <PRD are supplementary angles so their sum is equal to 180
m<BPR + 115 = 180 subtract 115 from both sides
m<BPR = 65
angles:
<APQ, x, and <BPR form a straight line and so their sum is equal to 180
65 + x + 65 = 180 add like terms
130 + x = 180 subtract 130 from both sides
x = 50
help meee please
20 points
Answer:
16 sq. yds
Step-by-step explanation:
1. Split the shape into 2
The small square is 2(2) = 4
The bigger rectangle is 3(4) = 12
4 + 12 = 16 sq. yds
The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
a)0 = –4.9t2 + 19.6t + 24.5
b)0 = –4.9t2 + 24.5t + 19.6
c)19.6 = –4.9t2 + 24.5t
d)24.5 = –4.9t2 + 19.6t
Answer:
s(t) = -4.9t² + 39.2t
Step-by-step explanation:
Given the projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s²
Given
g = -4.9m/s²
v0 = 39.2m/s
s0 = 0m (the initial height)
On substituting into the formula;
s(t) = gt² + v0t + s0
s(t) = -4.9t² + 39.2t + 0
s(t) = -4.9t² + 39.2t
This gives the equation that models the height
Describe fully the single transformation which takes shape A to shape B.
You have the correct answer. Apply a 180 degree rotation around the point (0,2)
Reason:
We'll connect corners between figures A and B.
Draw a line from the upper right corner of figure A to the lower left corner of figure B. This line is in red (see diagram below).
Draw another line from the lower right corner to the upper left corner. This line is in blue.
The red and blue lines intersect at the center of rotation (0,2)
The line segments constructed consist of endpoints of "before" and "after". For instance, the upper right corner in figure A rotates to the lower left corner of figure B. This happens because of the 180 degree rotation.
Note: You can do this rotation either clockwise or counterclockwise, and you would get the same result.
Identify the expression that is equivalent to 6(x2 + y + 2)
6x2 + y + 12
6x2 + 6y + 12
6x2 + 6y + 1
x2 + 6y + 12
Which solution shown below contains an error?
O 3 4
3x 4
O
x+2 x+2
O 2
x+1
8
x-6
=
=
2
x+2
=
=
3x+4
고
1
X+1
2x-12
80x+8
(x+1)(x-6) (x+1)(x-6)
+
=
10x-4
(x+1)(x-6)
PLEASE HURRY!!!!!!!!!!!!!!!!!
what is the length of the diagonal of the square shown below
Answer:
7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
the diagonal d divides the square into 2 right angles.
using Pythagoras' identity in one of the right triangles , then
d² = 7² + 7² = 49 + 49 = 98 ( take square root of both sides )
d = [tex]\sqrt{98}[/tex] = [tex]\sqrt{49(2)}[/tex] = [tex]\sqrt{49}[/tex] × [tex]\sqrt{2}[/tex] = 7[tex]\sqrt{2}[/tex]
Answer:
c =7√2
Step-by-step explanation:
using the Pythagorean theorem we solve the diagonal ,where the two sides are given to find the hypotenuse.
c² =a² + b²
where c is the diagonal (hypotenuse fot thr triangle)
a and b are the legs (sides)
c² =7²+7²
c²= 98
c= √98
c=√49.√2
c=7√2
Already tried simplifying and dividing, but i didn't get the correct answer. Could a step by step explanation be provided so i know how to do this in the future?
Answer:
[tex]\sf \dfrac{x+2}{x}[/tex]
Step-by-step explanation:
Simplifying the expression:
1. Factorize each expression.
x² + 8x + 15
Sum = 8
Product = 15
Factors = 3 , 5 {When we add 3 & 5 we get 8 and when we multiply 3*5, we get 15}
x² + 8x + 15 = x² + 3x + 5x + 15
= x(x + 3) + 5(x + 3)
= (x + 3)(x + 5)
x² - 2x - 15
Sum = -2
Product = -15
Factors = 3 , (-5) {When we add 3 + (-5) =2 and when we multiply, 3*(-5) = -15}
x² - 2x - 15 = x² + 3x - 5x - 15
=x(x + 3) -5(x + 3)
= (x + 3)(x - 5)
x² + 5x = x( x + 5)
x² - 3x - 10
Sum = -3
Product = -10
Factors = 2 , (-5) {When we add 2 +(-5) = -3 and when we multiply 2 *(-5) = -10}
x² - 3x - 10 = x² + 2x - 5x - 10
=x(x + 2) - 5(x + 2)
= (x + 2)(x - 5)
2. Use KCF method and simplify.
K - keep the first fraction
C - change division to multiplication
F - Flip the second fraction.
[tex]\sf \dfrac{x^2 + 8x + 15}{x^2 - 2x - 15} \ \div \ \dfrac{x^2 + 5x}{x^2 - 3x - 10}=\dfrac{x^2 + 8x + 15}{x^2-2x - 12}*\dfrac{x^2 - 3x - 10}{x^2 + 5x}[/tex]
[tex]\sf = \dfrac{(x +3)*(x +5)}{(x+3)(x - 5)}*\dfrac{(x + 2)(x - 5)}{x(x+5)} \\\\= \dfrac{x + 2}{x}[/tex]
What’s the length of three pieces of pipe if they all equal 72m
Answer:
72 × 3 = 216m
216 m is the combined length
what is the side view ? the rest are right like i've tried loads of combinations but they're not right
Answer:
a view from the side.
"the parts are shown in the sectioned side view"
PLEASE HELP!
The measure of angle B = 27 degrees, measure of angle C
= 82 degrees, and b = 12. Then a =
nearest tenth.
to the
Answer: 25,0.
Step-by-step explanation:
∡B=27° ∡C=82° b=12 a=?
∡A=180°-(27°+82°)=180°-109^°=71°.
[tex]\frac{a}{sinA} =\frac{b}{sinB} \\a=\frac{b*sinA}{sinB}=\frac{12*sin71^0}{sin27^0}=\frac{12*0,9455}{0,454} \approx25,0[/tex]
7. Find an equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4.
The equation of the line containing (- 4,5) and perpendicular to the line 5x - 3y = 4 is y = -3 / 5 x + 13 / 5
How to find the equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation passes through (-4, 5) and perpendicular to 5x - 3y = 4
Hence,
perpendicular lines follows the rule below:
m₁m₂ = -1
Hence,
5x - 3y = 4
5x - 4 = 3y
y = 5/ 3 x - 4 / 3
m₁ = 5 / 3
5/3 m₂ = -1
m₂ = - 3 / 5
Hence,
using (-4, 5)
5 = - 3 / 5 (-4) + b
5 = 12 / 5 + b
b = 5 - 12 / 5 = 25 - 12 /5 = 13 / 5
Therefore,
y = -3 / 5 x + 13 / 5
learn more on equation of a line here: https://brainly.com/question/10727767
#SPJ1
Answer:
3x +5y = 13
Step-by-step explanation:
The equation of a perpendicular line through a given point can be obtained by swapping the x- and y-coefficients of the original line's equation, and negating one of them. The constant in the equation needs to be chosen so the equation will be true at the given point.
Form of perpendicular lineSwapping the coefficients of the given equation, we have ...
3x -5y = c . . . . . for some constant c
Negating the y-coefficient gives a perpendicular line:
3x +5y = c
Particular solutionWe want the equation to be true for (x, y) = (-4, 5), so the constant needs to be ...
3x +5y = 3(-4) +5(5) = -12 +25 = 13
The equation of the perpendicular line is ...
3x +5y = 13
__
Additional comment
This process works for equations given in any form. If you start with point-slope form or slope-intercept form, some manipulation of the result may be required to get to the form you want. Standard-form or general-form equations are the easiest to apply this method to.
Note that equations in standard form want to have a positive leading coefficient. That is why we chose to change the sign of the y-coefficient, rather than the x-coefficient.
The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10). On a coordinate plane, a parabola opens up. It goes through (2, 8), has a vertex at (5, negative 11), and goes through (8, 8). On a coordinate plane, a parabola opens up. It goes through (negative 8, 10), has a vertex at (negative 5, 1), and goes through (negative 2, 10). On a coordinate plane, a parabola opens up. It goes through (negative 8, 8), has a vertex at (negative 5, negative 11), and goes through (negative 2, 8).
Using translation concepts, the graph of g(x) is given as follows:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent and translated functions are given, respectively, by:
f(x) = x².g(x) = (x - 5)² + 1.The transformations are as follows:
x -> x - 5, hence the function was shifted right 5 units.y -> y + 1, hence the function was shifted up 1 unit.f(x) has vertex at (0,0), hence g(x) will have the vertex at (5,1). When x = 2, g(x) = (2-5)^2 + 1 = 10, hence the correct statement is:
It goes through (2, 10), has a vertex at (5, 1), and goes through (8, 10).
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Write the equation given the following polynomial graph.
Answer: Option (2)
Step-by-step explanation:
There is a double root at x=-1, so there is a factor of [tex](x+1)^2[/tex].
Eliminate options (1) and (3).Also, as x approaches both positive and negative infinity, the graph approaches negative infinity, so the leading coefficient is negative.
Eliminate (4).Reduce to simplest form
- 9/15 + 5/15
Answer: -4/15
Step-by-step explanation: Since the base denominator is the same, all we have to do is add the numerators (the denominators stay the same.)
-9 + 5 = -4 which is -4/15.
(If my answer was helpful, please mark as Brainliest. I'm trying to get to the Expert rank!)
11. A rectangle is graphed on a coordinate plane. The coordinates for two of the
vertices of the rectangle are (-5,8) and (-5, -6). What is the distance between the
two vertices?
A
2 units
B
C
4 units
10 units
D 14 units
Answer:
D. 14 units
Step-by-step explanation:
d = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-x_{1})^{2} }[/tex]
= [tex]\sqrt{(-5 - (-5))^{2} + (-6 - 8)^{2} }[/tex]
= [tex]\sqrt{0^{2} + -14^{2} }[/tex]
= [tex]\sqrt{0 +196 }[/tex]
= [tex]\sqrt{196}[/tex]
= 14
Which expression is equivalent to this polynomial? 9x² +4 OA. (3x+21)(3x-21) OB. (3x+2)(3x - 2) OC. (3x+21)² OD. (3x + 2)²
Answer:
None of these
Step-by-step explanation:
None of this expressions are equivalent. But if the original polynomial is 9x^2-4, then answer would be (3x+2)(3x-2).
Using formula (a+b)(a-b)=a^2-b^2 , it follows:
(3x+2)(3x-2)=(3x)^2-2^2=9x^2-4
What is the inverse of the following statement? If m is the midpoint of PQ, then PM is congruent to QM
The inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
Inverse of the statement means that explain the condition in reverse way or vice versa.
Since, M is the midpoint of PQ, then PM is congruent to QM.
Proving in reverse way, let m be the point between P and Q the distance M from P is equal to the distance from M to Q. Which implies that M lies as the mid of the P and Q.
Thus, the inverse of the statement is M be the point on PQ since PM is congruent to QM than M is midpoint on the PQ.
Learn more about inverse here:
https://brainly.com/question/5338106
#SPJ1
Daredevil Danny hoop jump Step 4: b) Using your values of a, b, and c, did Daredevil Danny successfully pass through the Flaming Hoop Jump of Awesome? If not, describe what happened. Then, go back to critique your work and revise it. Write about your revision. (5 points) d) Once you have determined the correct values of a, b, and c, verify algebraically that Daredevil Danny will successfully pass through the Flaming Hoop Jump of Awesome. (5 points)
Pleasee Helppp I can't figure it out and I'm running out of time to get it turned in.
The equation of Daredevil Danny's jump in vertex form is y = -0.32(x - 25)^2 + 32
The values of the coefficients a, b and cThe graph of Daredevil Danny's jump is added as an attachment
A quadratic function is represented as:
y = a(x - h)^2 + k
From the graph, we have:
Vertex, (h, k) = (25,32)x-intercepts = 15 and 35So, we have:
y = a(x - 25)^2 + 32
Substitute the value of the x-intercept
0 = a(15 - 25)^2 + 32
Subtract 32 from both sides
a(15 - 25)^2 = -32
Solve for a
a = -0.32
Substitute a = -0.32 in y = a(x - 25)^2 + 32
y = -0.32(x - 25)^2 + 32
Expand the exponent
y = -0.32(x^2 -50x + 625) + 32
Expand the bracket
y = -0.32x^2 + 16x - 200 + 32
This gives
y = -0.32x^2 + 16x - 168
Hence, the values of the coefficients a, b and c are -0.32, 16 and -168
Did he jump successfully?Yes, he jumped successfully
This is so because his maximum height (i.e. the vertex of his jump) is higher than the vertex of the hoop
Read more about quadratic functions at:
https://brainly.com/question/22679014
#SPJ1
From the diagram below, we can say that ___.
Select one:
a.
Δ CED is similar to Δ BEA by AA.
b.
Δ CED is similar to Δ BEA by ASA
c.
the two triangles are not similar
Answer: The correct answer is choice A.
Step-by-step explanation:
This is because the triangles have the same angles, but are scaled differently. Thus because of the scale, there can be no correlation between the sides. Because the triangles share point E you can see that both triangles share the same angle but also notice how lines CD and AB are parallel. This makes all angles identical proving the triangles are the same but different sizes. Concluding that choice A is correct.
A car salesman earn. 2% commission on all of his sales if he needs to make 3,000 a month for his living expenses what total dollar amount must he sell to make his commission each month
The total dollar amount of sales is $150,000
What is the sales amount achieved by the salesman to earn a commission of $3,000?
To compute the portion of total sales earned as commission, we simply multiply the sales amount recorded by the percentage of commission which is 2%
sales commission=sales amount*commission rate
sales commission=$3,000
sales amount=unknown(assume it is X)
commission rate=2%
$3,000=X*2%
X=$3000/2%
X=$150,000
https://brainly.com/question/9090090
#SPJ1
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
555. 0 .041
Answer:
Hence, 0.041 can be expressed as [tex]$4.1 \times 10^{-2}$[/tex].
Step-by-step explanation:
- Given 0.041
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 0.041
[tex]$$\Rightarrow 4.1$$[/tex]
Decimal has moved to 2 places at right.
The power will be negative as original no. is less than 1 .
So, [tex]$4.1 \times 10^{-2}$[/tex]
[tex]$$0.041=4.1 \times 10^{-2} \text {. }$$[/tex]
Find and interpret the slope of the line ca
(10,4) and (2,44)
Answer: -5
Step-by-step explanation:
Slope can be found with change in y over change in x.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Let (10, 4) be point 1 and (2, 44) be point 2.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{44-4}{2-10}[/tex]
[tex]\displaystyle \frac{40}{-8}[/tex]
[tex]\displaystyle \frac{40}{-8}[/tex]
-5
I need help with this geometry question.
1st transformation: A vertical translation of the figure down by 8 units
2nd transformation: Shows a reflection on both axis and vertical translation up the plane by 8 units
Transformation of coordinatesTransformation is a way of changing the position of an object on an xy-plane.
For the translation
(x, y)-> (x, y-8)
It shows a vertical translation of the figure down by 8 units while the translation;
(x, y - 8) -> (-x, -y)
shows a reflection on both axis and vertical translation up the plane by 8 units
Learn more on transformation here: https://brainly.com/question/1462871
#SPJ1
Englewood high school is planning a field trip to everglades national park. on the trip, there must be a minimum of one adult for every 8 students. the buses can carry a maximum of 480 people. define variables and write a system of inequalities to represent this situation.
The system of linear inequalities to represent this situation. is given as-
9p <= 480
a >= 8s
p = a + s
What is linear inequalities?Expressions with linear inequalities compare any two values using inequality symbols like "<," ">," "<=," or ">=." These values could be either numerical, algebraic, or both.
If the linear inequality is larger than or less than but not equal to, a dashed line appears on the graph. On the other hand, a solid line always appears in linear equations. Linear equations lack shaded sections, whereas linear inequalities do.
According to the question,
The buses can carry a maximum of 480 people.
These people include adults as well as students.
Let 'p' represents the total number of people in the bus.
Let 'a' represents the number of adults in the bus.
Let 's' represents the number of students in the bus.
Thus,
p = a + s.
As, there must be a minimum of one adult for every 8 students.
a >= 8s
and,
9p <= 480
Therefore, the system of linear inequalities are found.
To know more about the linear inequality, here
https://brainly.com/question/11897796
#SPJ4
Solve each problem and check your answer using estimates. a. $18.79 + $2.11 + ‐$1.92 + $17.28 b. $7.45 + ‐$24.45 + $74.17 + ‐$76.52 c. $98.45 − $10.63 + $2.82 − $20.26
The solution to the linear expressions are:
a. $36.26b. -$19.35c. $70.38Solving linear expressions:The solution to linear expression is determined by taking into consideration the arithmetic operations used in each linear expression.
From the information given:
a. $18.79 + $2.11 + ‐$1.92 + $17.28
By rearrangement:
= $18.79 + $2.11 + $17.28 ‐$1.92
= $36.26
b. $7.45 + ‐$24.45 + $74.17 + ‐$76.52
By rearrangement:
= $7.45 + $74.17 ‐ $24.45 ‐ $76.52
= -$19.35
c. $98.45 − $10.63 + $2.82 − $20.26
By rearrangement:
= $98.45 + $2.82 − $10.63 − $20.26
= $70.38
Learn more about solving linear expressions here:
https://brainly.com/question/2030026
#SPJ1
Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
With the help of trigonometric function, the above problems have been calculated. See explanation below.
What are Trigonometric functions?The term "trigonometric function" refers to functions that are periodic in nature and that shed light on how a right-angled triangle's angles and sides relate to one another.
The solutions to x in the respective problems is given as follows:
1) x = 5 /Sin(30°)
x = 10
!) Sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°)
= (3√3) / x
x = (3√3) / 3
W) In trigonometry, every right-triangle that is isosceles in nature, the angle made by the legs and the hypotenuse will always equal 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3
= 4√3 / 3
S) Sin(60°) = x / (10/3)
x = (5√3) / 3
Learn more about Trigonometric functions at:
https://brainly.com/question/14421002
#SPJ1
Triangle sqt is isosceles. the measure of angle stq is 48°. what is the measure of angle s t r? 24° 38° 48° 76°
The measure of ∠STR in the isosceles triangle is 24°
What is an isosceles triangle?
A triangle having two sides of equal length is termed as an isosceles triangle. The base angles of an isosceles triangle are also equal in measure. The fact that the perpendicular bisector of the base and the angle bisector of the vertex angle are the same is another crucial characteristic of an isosceles triangle. We refer this as Isosceles Triangle Theorem.
What is the value of angle STR?
It is given that in isosceles triangle SQT,
∠STQ = 48°
Since, the line TR is the angle bisector of angle STQ, we have,
∠STR = ∠RTQ
And, ∠STR + ∠RTQ = ∠STQ
Let ∠STR be x, the, we get,
x + x = ∠STQ
⇒ 2x = 48°
⇒ x = 24°
Learn more about isosceles triangle here:
https://brainly.com/question/2456591
#SPJ4
There are 4 captains of the football team. how many different ways can they line up to receive their championship rings?
24 different ways can they line up to receive their championship rings.
What is a permutation mean in math?
When the order of the arrangements matters, a mathematical technique called a permutation can be used to calculate the number of alternative arrangements in a collection. Common mathematics problems involve choosing only several items from a group of items in a specified sequence.What are permutations used for?
When an arrangement requires an order or a sequence, permutations are used. Combinations are employed when determining merely the number of potential groups is required and neither the order nor the sequence of arrangements is necessary.Given,
No. of captains of the football team = 4
So,
4 ways we can line up their championship rings = (4,4)
4 ×3 ×2 ×1 = 24
Therefore, 24 different ways can they line up to receive their championship rings.
Learn more about permutation
brainly.com/question/1216161
#SPJ4