find a positive and a negative coterminal angle for each given angle.
Answer:
D
Step-by-step explanation:
to find the coterminal angles add/ subtract 360° to the given angle
- 255° + 360° = 105°
- 255° - 360° = - 615°
A community is developing plans for a pool and hot tub. The community plans to form a swim team, so the pool must be built to certain dimensions. Answer the questions to identify possible dimensions of the deck around the pool and hot tub.
Part I: The dimensions of the pool are to be 25 yards by 9 yards. The deck will be the same width on all sides of the pool. Including the deck, the total pool area has a length of (x + 25) yards, and a width of (x + 9) yards.
Write an equation representing the total area of the pool and the pool deck. Use y to represent the total area. Hint: The area of a rectangle is length times width. (1 point)
Rewrite the area equation in standard form. Hint: Use the FOIL method. (1 point)
Rewrite the equation from Part b in vertex form by completing the square. Hint: Move the constant to the other side, add to each side, rewrite the right side as a perfect square trinomial, and finally, isolate y. (4 points: 1 point for each step in the hint)
What is the vertex of the parabola? What are the x- and y-intercepts? Hint: Use your answer from Part a to identify the x-intercepts. Use your answer from Part b to identify the y-intercept. Use your answer from Part c to identify the vertex. (4 points: 1 point for each coordinate point)
Graph the parabola. Use the key features of the graph that you identified in Part d. (3 points)
In this problem, only positive values of x make sense. Why? (1 point)
What point on your graph shows a total area that includes the pool but not the pool deck? (1 point)
The community decided on a pool area that adds 6 yards of pool deck to both the length and the width of the pool. What is the total area of the pool and deck when x = 6 yards? (2 points)
Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has an area of 169 square feet. Find the width of the deck space around the hot tub, x.
Step 1: Write an equation for the area of the enclosed space in the form y = (side length)2. Hint: Don't forget to add x to each side of the hot tub. (1 point)
Step 2: Substitute the area of the enclosed space for y in your equation. (1 point)
Step 3: Solve your equation from Part b for x. (3 points)
Step 4: What is the width of the deck around the hot tub? Hint: One of the answers from Part c is not reasonable. (1 point)
Part I- a) y = (x + 25)(x + 9)
b) y = x^2 + 34x + 225
c) y= (x + 17)^2 - 64
d) The y-intercept is (0, 225), The y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative.
g) y = 465 square yards
Part II- a) y = (6 + 2x)^2
b) 169 = (6 + 2x)^2
c) x = 3.5 feet
Part I:
a) The equation representing the total area of the pool and the pool deck, using y to represent the total area, can be written as:y = (x + 25)(x + 9)
b) To rewrite the equation in standard form using the FOIL method:
y = x^2 + 9x + 25x + 225
= x^2 + 34x + 225
c) To rewrite the equation in vertex form by completing the square:
y = (x^2 + 34x) + 225
= (x^2 + 34x + (34/2)^2) + 225 - (34/2)^2
= (x^2 + 34x + 289) + 225 - 289
= (x + 17)^2 - 64
d) The vertex of the parabola is (-17, -64). The x-intercepts are found by setting y = 0 and solving the equation:
0 = (x + 17)^2 - 64
64 = (x + 17)^2
x + 17 = ±√64
x + 17 = ±8
x = -17 ± 8
x = -25, -9
Therefore, the x-intercepts are (-25, 0) and (-9, 0).
The y-intercept is obtained by setting x = 0 in the equation:
y = (0 + 17)^2 - 64
y = 17^2 - 64
y = 289 - 64
y = 225
Therefore, the y-intercept is (0, 225).
e) The graph of the parabola has the vertex at (-17, -64), x-intercepts at (-25, 0) and (-9, 0), and the y-intercept at (0, 225).
f) Only positive values of x make sense because the dimensions of a pool and deck cannot be negative. In this context, negative values for x would not provide meaningful solutions for the width of the deck.
g) The point on the graph that represents the total area including the pool but not the pool deck is the y-intercept (0, 225).
h) When x = 6 yards, the total area of the pool and deck can be found by substituting the value into the equation from Part b:
y = (6 + 17)^2 - 64
y = 23^2 - 64
y = 529 - 64
y = 465 square yards
Part II:
a) The equation for the area of the enclosed space in the form y = (side length)^2, considering the hot tub and the deck around it, is:
y = (6 + 2x)^2
b) Substituting the area of the enclosed space (169 square feet) for y in the equation:
169 = (6 + 2x)^2
c) Solving the equation for x:
√169 = √((6 + 2x)^2)
13 = 6 + 2x
2x = 13 - 6
2x = 7
x = 7/2
x = 3.5 feet
Therefore, the width of the deck space around the hot tub is 3.5 feet.
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Find the measure of the indicated arc:
55°
110°
O 250°
220°
?
Q
110 °
R
S
Answer:
? = 220°
Step-by-step explanation:
the measure of the inscribed angle QRS is half the measure of its intercepted arc QS , then
QS = ? = 2 × QRS = 2 × 110° = 220°
Select the correct answer. What is the solution to this equation? 9^x - 1 = 2 O A. - 1/1/20 OB. 2 O C. OD. 1/1/20 1 23 Edmentum. All rights reserved. Reset Next
Answer:
D. 1/2
Step-by-step explanation:
9^x - 1 = 2
9^x = 3
x = log{sub}9 (3)
x = 1/2 (9^(1/2)=3)
find the inverse of each function
Answer:
c
Step-by-step explanation:
assume base 10
-logy = x
[tex] \frac{1}{ log(y) } = x[/tex]
log base x y = 5 turns into the format x^ 5 = y
implement that to get c
Let theta be an angle in quadrant two such that cos theta=-3/4. find the exact values of csc theta and cot theta
The exact values of csc(theta) and cot(theta) are: csc(theta) = 4√7/7
cot(theta) = -3√7/7.
To find the exact values of csc(theta) and cot(theta), given that cos(theta) = -3/4 and theta is an angle in quadrant two, we can use the trigonometric identities and the Pythagorean identity.
We know that cos(theta) = adjacent/hypotenuse, and in quadrant two, the adjacent side is negative. Let's assume the adjacent side is -3 and the hypotenuse is 4. Using the Pythagorean identity, we can find the opposite side:
[tex]opposite^2 = hypotenuse^2 - adjacent^2opposite^2 = 4^2 - (-3)^2opposite^2 = 16 - 9opposite^2 = 7[/tex]
opposite = √7
Now we have the values for the adjacent side, opposite side, and hypotenuse. We can use these values to find the values of the other trigonometric functions:
csc(theta) = hypotenuse/opposite
csc(theta) = 4/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
csc(theta) = (4/√7) * (√7/√7)
csc(theta) = 4√7/7
cot(theta) = adjacent/opposite
cot(theta) = -3/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
cot(theta) = (-3/√7) * (√7/√7)
cot(theta) = -3√7/7
Therefore, the exact values of csc(theta) and cot(theta) are:
csc(theta) = 4√7/7
cot(theta) = -3√7/7
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Roger can run one mile in 9 minutes. Jeff can run one mile in 6 minutes. If Jeff gives Roger a 1 minute head start, how
long will it take before Jeff catches up to Roger? How far will each have run?
They each will have run of a mile.
Both Roger and Jeff will have run a distance of 1/3 mile when Jeff catches up to Roger after 2 minutes.
To solve this problem, we can determine the relative speeds of Roger and Jeff.
Since Roger runs one mile in 9 minutes, his speed is 1/9 miles per minute.
Similarly, Jeff runs one mile in 6 minutes, so his speed is 1/6 miles per minutes.
Let's assume that Jeff catches up to Roger after t minutes.
In that time, Roger would have run (1/9) [tex]\times[/tex] t miles, and Jeff would have run (1/6) [tex]\times[/tex] t miles.
Since Jeff gives Roger a 1-minute head start, we can express their distances covered as:
Distance covered by Roger = (1/9) [tex]\times[/tex] (t+1) miles
Distance covered by Jeff = (1/6) [tex]\times[/tex] t miles
For Jeff to catch up to Roger, their distances covered must be equal. So we can set up the equation:
(1/9) [tex]\times[/tex] (t+1) = (1/6) [tex]\times[/tex] t
To solve for t, we can cross-multiply and simplify:
6(t+1) = 9t
6t + 6 = 9t
6 = 9t - 6t
6 = 3t
t = 2
Therefore, it will take 2 minutes for Jeff to catch up to Roger.
Substituting t = 2 back into the equations, we can find the distances covered by each:
Distance covered by Roger = (1/9) [tex]\times[/tex] (2+1) = 1/3 mile
Distance covered by Jeff = (1/6) [tex]\times[/tex] 2 = 1/3 mile
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A ship X sailing with a velocity (21 kmh 052⁰) observes a light fron a lighthuse due North. The bearing of the liglhthouse from the ship 20 minutes later is found to be 312. calcuate correct to thre sigificant figures
i) the orignal distance when the lighthoues is due West of the ship from the time when it is due North of the ship.
ii) the time in minutes, when the lighthouse is due West of the ship from the time when it is due North of the ship.
iii) the distance in km of the ship from the lighthoue when the light.hose is due West of the ship
i) the original distance when the lighthouse is due West of the ship is 7 km
ii) The time in minutes when the lighthouse is due West of the ship is 21 minutes
iii) The distance in km of the ship from the lighthouse when the lighthouse is due West of the ship is 29.97 km
To solve this problem, we'll use the concepts of relative velocity and trigonometry. Let's break down the problem into three parts:
i) Finding the original distance when the lighthouse is due West of the ship:
The ship's velocity is given as 21 km/h at a bearing of 052°. Since the ship observed the lighthouse due North, we know that the angle between the ship's initial heading and the lighthouse is 90°.
To find the distance, we'll consider the ship's velocity in the North direction only. Using trigonometry, we can determine the distance as follows:
Distance = Velocity * Time = 21 km/h * (20 min / 60 min/h) = 7 km (to three significant figures).
ii) Finding the time in minutes when the lighthouse is due West of the ship:
To find the time, we need to consider the change in angle from 052° to 312°. The difference is 260° (312° - 052°), but we need to convert it to radians for calculations. 260° is equal to 260 * π / 180 radians. The ship's velocity in the West direction can be calculated as:
Velocity in West direction = Velocity * cos(angle) = 21 km/h * cos(260 * π / 180) ≈ -19.98 km/h (negative because it's in the opposite direction).
To find the time, we can use the formula:
Time = Distance / Velocity = 7 km / (19.98 km/h) = 0.35 h = 0.35 * 60 min = 21 minutes (to three significant figures).
iii) Finding the distance in km of the ship from the lighthouse when the lighthouse is due West of the ship:
We can use the formula for relative velocity to find the distance:
Relative Velocity = sqrt((Velocity in North direction)² + (Velocity in West direction)²)
Using the values we calculated earlier, we have:
Relative Velocity = sqrt((21 km/h)² + (-19.98 km/h)²) ≈ 29.97 km/h (to three significant figures).
Therefore, the ship is approximately 29.97 km away from the lighthouse when the lighthouse is due West of the ship.
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What is the meaning of "⊂-maximal element"?
A "⊂-maximal element" in set theory refers to an element in a set that cannot be strictly contained within any other element of the set, indicating a maximum extent or boundary within that set.
In the context of set theory and Tarski's notion of finiteness, a "⊂-maximal element" refers to an element within a set that cannot be strictly contained within any other element of the set. Let's break down the meaning of this term.
Consider a set S and a partial order relation ⊆ (subset relation) defined on the power set P(S) of S. A "⊂-maximal element" u of a set A ⊆ S is an element that is not strictly contained within any other element of A with respect to the subset relation. In other words, there is no element v in A such that u is a proper subset of v.
Formally, for any u ∈ A, if there is no v ∈ A such that u ⊂ v, then u is a ⊂-maximal element of A. This means that u is as large as possible within A and cannot be extended by including additional elements.
In the context of T-finite sets, the existence of a ⊂-maximal element in every nonempty subset of the set guarantees that the set has a well-defined structure and does not continue indefinitely without boundaries.
It ensures that there is a definitive maximum element within each subset, which is a key characteristic of finiteness.
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Which expression is equivalent to 3(x+4)
The answer is:
3x + 12
Work/explanation:
To simplify this expression, we will use the distributive property:
[tex]\sf{3(x+4)}[/tex]
Distribute the 3:
[tex]\sf{3\cdot x + 3 \cdot 4}[/tex]
[tex]\sf{3x+12}[/tex]
Therefore, the answer is 3x + 12.
What are the values of x and y?
A) x = 18√3; y = 9√3
B) x = 9; y = 9√3
C) x = 9√3; y = 9
D) x = 9√2; y = 9
The values of x and y are 9√3 and 9. Thus, option C is the answer.
From the figure, we know that angle A = 60°, angle C = 30° and side AC =18 units.
We have to use trigonometric ratios to find the values of x and y.
sin30° = Opposite side/Hypotenuse
But, we also know that sin30° = 1/2
Substituting the value in the above equation, we get
1/2 = y/18
Thus, the value of y = 18/2 = 9.
Now, sin60° = Opposite Side/ Hypotenuse
sin60° = √3/2
Substituting the value, we get
√3/2 = x/18
Thus, x = 9√3.
Therefore, the values of x and y in the given triangle are 9√3 and 9.
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Pls help I am stuck thank you so much
The perimeter of shape C is 30 cm shorter than the total perimeter of A and B.
What is the perimeter of a polygon?The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.
Hence the perimeter of each shape is given as follows:
A = 2 x (5 + 12) = 34 cm.B = 2 x (4 + 9) = 26 cm.C = 12 + 5 + 9 + 4 = 30 cm.Then the difference is given as follows:
34 + 26 - 30 = 30 cm.
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The following pie chart shows the number of rabbits, sheep, cattle, pigs on a farm
sheep
700
cattle
300
Pig
500
a. How many animals are on the farm? b.What represents the number of sheep on the farm
c. what percentage of the total number of animals are rabbits
d. Calculate the angle that represents number of pigs
A box contains 240 lumps of sugar. Five lumps are fitted across the box and there were three layers. How many lumps are fitted along the box?
1. Brandon went to a Formula One car race and used his stopwatch to time how fast his favorite driver, Fernando Alonso, went around the 4.7-kilometer track. Brandon started the timer at the beginning of the second lap, when the cars were already going fast. When he stopped the timer at the beginning of the third lap, one minute and three seconds had passed.
b. If you graphed the distance Fernando had traveled at the beginning of the lap and at the end of the lap, what would the coordinates of these points be? What would the
- and
-axes on this graph represent?
c. Find the equation of the line between these two points. What does this line represent?
d. If Fernando continues to average this speed, about how long do you think it would take him to finish the entire race? The race is 500 km.
Step-by-step explanation:
b. To determine the coordinates of the points on the graph, we need to consider the information given.
At the beginning of the second lap, one minute and three seconds had passed. Since each lap is 4.7 kilometers long, we can calculate the distance traveled at the beginning of the lap using the formula:
Distance = (Number of laps - 1) × Length of each lap
For the beginning of the second lap:
Distance = (2 - 1) × 4.7 km = 4.7 km
At the beginning of the third lap, one minute and three seconds had passed. Therefore, the distance traveled at the beginning of the third lap is:
Distance = (3 - 1) × 4.7 km = 9.4 km
The coordinates of the points on the graph would be:
Point A: (4.7 km, 4.7 km)
Point B: (9.4 km, 9.4 km)
On the graph, the x-axis would represent the distance traveled at the beginning of the lap, and the y-axis would represent the distance traveled at the end of the lap.
c. To find the equation of the line between the two points, we can use the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
Using the coordinates of the two points (4.7 km, 4.7 km) and (9.4 km, 9.4 km), we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (9.4 km - 4.7 km) / (9.4 km - 4.7 km)
= 4.7 km / 4.7 km
= 1
The slope of the line is 1.
Since the line passes through the origin (0, 0), the y-intercept (b) is 0.
Therefore, the equation of the line is:
y = 1x + 0
y = x
This line represents a one-to-one relationship between the distance traveled at the beginning of the lap and the distance traveled at the end of the lap.
d. To estimate how long it would take Fernando to finish the entire race if he continues to average the same speed, we need to find the time it takes for one lap.
In the given scenario, Brandon timed Fernando's lap for one minute and three seconds. Since there are 3 laps in total, we can divide the total time by the number of laps to find the average time per lap:
Average time per lap = Total time / Number of laps
= 1 minute and 3 seconds / 3
= 21 seconds
Since each lap is 4.7 kilometers long, we can calculate the speed:
Speed = Distance / Time
= 4.7 km / (1 minute + 21 seconds)
To estimate the time it would take Fernando to finish the entire race, we divide the total race distance by the speed:
Total race time = Total race distance / Speed
= 500 km / (4.7 km / (1 minute + 21 seconds))
To calculate the time, we need to convert 1 minute and 21 seconds to a decimal form:
1 minute + 21 seconds = 1 minute + (21 seconds / 60 seconds)
= 1 minute + 0.35 minutes
= 1.35 minutes
Substituting the values:
Total race time = 500 km / (4.7 km / 1.35 minutes)
= 500 km × (
1.35 minutes / 4.7 km)
= 500 km × 0.28723...
≈ 143.615 minutes
Therefore, it would take approximately 143.615 minutes for Fernando to finish the entire race if he continues to average the same speed.
Please awnser asap I will brainlist
The solution to the system is (a) (4/5, 5, -4, -4)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The augmented matrix
Where, we have
[tex]\left[\begin{array}{cccc|c}1&0&0&0&4/5\\0&1&0&0&5\\0&0&1&0&-4\\0&0&0&1&-4\end{array}\right][/tex]
From the above, we have the diagonals to be 1
And other elements to be 0
This means that the equation has been solved
So, we have
a = 4/5, b = 5, c = -4 and d =-4
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Rearrange the equation so u is the independent variable
-12u+13=8w-3
w=_______
the answer is
w = -3/2 u + 2
Find the values of x and y.
G
(6y)⁰
X =
(5x)
y =
M
(10x)⁰
K
L
Answer:
be more clear of what u mean edit the question to explain more
Step-by-step explanation:
no explanation
Describe the given translation: T(0, 7)
Answer:
ok t means some thing but zero and seven should be solved
d 1 1 logx tanx
dx x
+ + +
The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.
Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.
The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.
Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.
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Parker has 12 blue marbles. Richard has 34
of the number of blue marbles that Parker has.
Part A
Explain how you know that Parker has more blue marbles than Richard without completing the multiplication.
Enter equal to, greater than, or less than in each box.
Multiplying a whole number by a fraction
less than
1 results in a product that is
the original whole number.
Part B
How many blue marbles does Richard have? Enter your answer in the box.
blue marbles
How many solutions does this system of equations have?
-x+7
= -2x³ + 5x² + x - 2
O A.
0 в.
OC.
D.
no solution
1 solution
2 solutions
3 solutions
Reset
Next
The system of equation: -x + 7 = -2x³ + 5x² + x - 2 has three solutions
The correct answer is option D.
To solve the system of equations:
-x + 7 = -2x³ + 5x² + x - 2
We need to simplify and rearrange the equation to find its solutions. Let's start by combining like terms:
-x + 7 = -2x³ + 5x² + x - 2
Simplifying the left side:
7 = -2x³ + 5x² - x - 2
Next, let's arrange the equation in descending order of the variable's exponent:
-2x³ + 5x² - x - 2 = 7
Now, let's move all terms to one side of the equation to set it equal to zero:
-2x³ + 5x² - x - 2 - 7 = 0
Simplifying further:
-2x³ + 5x² - x - 9 = 0
To determine the number of solutions, we can analyze the degree of the equation. Since it is a cubic equation, it can have a maximum of three real solutions.
The given system of equations is:
-x + 7 = -2x³ + 5x² + x - 2
To find the solutions, we need to set the equation equal to zero. Let's rearrange the terms:
2. -2x³ + 5x² - x - 9 = 0
Now, we can try to factor or use numerical methods to solve the equation. However, factoring a cubic equation can be complex and time-consuming. In this case, we'll use numerical methods to approximate the solutions.
One common numerical method is the Newton-Raphson method, which involves making an initial guess for the solutions and iterating to converge on a more accurate solution.
Using numerical software or calculators, we can find the approximate solutions of the equation as follows:
x ≈ -1.607, x ≈ 1.279, and x ≈ 3.328
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Pamela bought a cat carrier to take her new kitten, Muffinnette, to the vet. The carrier is shaped like a rectangular prism that is 15 inches long, 9 1/2
inches wide, and 10 inches tall.
Which equation can you use to find the volume of the cat carrier, V?
What is the volume of the cat carrier?
A charged particle produces an electric field with a magnitude of 2.0 N/C at a point that is 50 cm away from the particle. a) Without finding the charge of the particle, determine the electric field produced by this charge at a point 25 cm away from it. b) What will happen to the Electric field at the distance 50 cm, if you double the charge? c) What is the magnitude of the particle’s charge?
To solve these problems, we can use Coulomb's Law, which states that the magnitude of the electric field produced by a charged particle is directly proportional to the charge and inversely proportional to the square of the distance from the particle.
a) Without finding the charge of the particle, we can use the inverse square relationship. If the electric field magnitude is 2.0 N/C at a distance of 50 cm, then at half the distance (25 cm), the electric field would be four times stronger. Therefore, the electric field at 25 cm would be 4 * 2.0 N/C = 8.0 N/C.
b) Doubling the charge would result in doubling the electric field magnitude. So, if the electric field at a distance of 50 cm was initially 2.0 N/C, it would become 4.0 N/C after doubling the charge.
c) To determine the magnitude of the particle's charge, we need to use the equation for the electric field:
E = k * (|q| / r^2)
where E is the electric field magnitude, k is the electrostatic constant, |q| is the magnitude of the charge, and r is the distance from the particle.
Using the known values of E = 2.0 N/C and r = 50 cm (or 0.5 m), we can rearrange the equation to solve for |q|:
|q| = E * r^2 / k
Substituting the values and the known value of k, we can calculate the magnitude of the charge.
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In ΔBCD,
B
D
‾
BD
is extended through point D to point E,
m
∠
C
D
E
=
(
9
x
−
12
)
∘
m∠CDE=(9x−12)
∘
,
m
∠
B
C
D
=
(
2
x
+
3
)
∘
m∠BCD=(2x+3)
∘
, and
m
∠
D
B
C
=
(
3
x
+
5
)
∘
m∠DBC=(3x+5)
∘
. Find
m
∠
B
C
D
.
m∠BCD.
m∠BCD = 31.57° (approx). Hence, the answer of the angle is 31.57 degrees.
In the given diagram, BD is extended through point D to point E, m∠CDE = (9x - 12)°, m∠BCD = (2x + 3)°, and m∠DBC = (3x + 5)°. We need to find m∠BCD.
Use the Angle Sum Property of a Triangle.The Angle Sum Property of a Triangle states that the sum of all the angles in a triangle is equal to 180°.The angle sum of ΔBCD is:m∠BCD + m∠DBC + m∠CDE = 180°Substituting the given angles, we get:(2x + 3)° + (3x + 5)° + (9x - 12)° = 180°Simplifying the above expression, we get:14x - 4 = 180°14x = 180° + 4x = 184/14x = 92/7Find m∠BCDWe know that m∠BCD = (2x + 3)°
Substituting x = 92/7, we get:
m∠BCD = (2 × 92/7 + 3)° = (184/7 + 3)° = 221/7°
Therefore, m∠BCD = 31.57° (approx). Hence, the answer is 31.57.
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On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction.
The number b varies directly with the number a. For example b = 22 when a = -22. Which equation represents this
direct variation between a and b?
b=-a
0-b=-a
O b-a=0
Ob(-a)=0
Polygon s is a scaled copy of polygon R.
What is the value of t
Using the concept of scale factor, the value of t in polygon s is: 7.2
How to use the scale factor?The amount by which the shape is expanded or contracted is referred to as the scale factor. This is usually utilized when 2D shapes such as circles, triangles, squares and rectangles need to be enlarged. If y = Kx is an equation, K is the scaling factor for x.
From the given image, since Polygon s is a scaled copy of polygon R, then we can say that using the concept of scale factor, we have:
9/t = 12/9.6
t = (9 * 9.6)/12
t = 7.2
Thus, we can be sure that is the value of t of the polygon S using the concept of scale factor
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Please answer ASAP I will brainlist
Answer:
Step-by-step explanation:
The given augmented matrix is already in reduced row echelon form. We can interpret it as a system of equations as follows:
1x + 0y + 0z + (4/5)w = 0
0x + 1y + 0z + 5w = 0
0x + 0y + 1z - 4w = 0
0x + 0y + 0z + w = -4
From the last row, we can see that w = -4. Substituting this value back into the previous rows, we get:
1x + 0y + 0z + (4/5)(-4) = 0
0x + 1y + 0z + 5(-4) = 0
0x + 0y + 1z - 4(-4) = 0
Simplifying these equations, we have:
x - (16/5) = 0
y - 20 = 0
z + 16 = 0
From the second equation, y = 20. From the third equation, z = -16. Substituting these values into the first equation, we get x - (16/5) = 0, which implies x = 16/5.
Therefore, the solution of the system is (16/5, 20, -16, -4).
So, the correct choice is:
A. The system has exactly one solution. The solution is
(16/5, 20, -16, -4)
Determine the equation of the circle graphed below 100pts pls
Answer:
(x + 5)² + (y – 1)² = 25
Step-by-step explanation:
Note that the general equation of a circle is (x – h)² + (y – k)² = r², where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The circle is 10 units in diamater, so the radius is half this: r=10/2=5.
The circle goes from -10 to 0 along the x-axis, so the x-coordinate of its centre is halfway between this: h=(-10+0)/2=-10/2=-5
The circle goes from -4 to 6 along the y-axis, so the y-coordinate of its centre is halfway between this: k=(-4+6)/2=-2/2=1
Now that we know r, h, and k, we can sub these into the general formula to get our equation:
(x - (-5))² + (y – 1)² = 5²
(x + 5)² + (y – 1)² = 25
When parallel lines are intersected by a transversal, which of the following angle pairs are supplementary?
Answer:
if two parallel lines are cut by a transversal,then, exterior angles on the same side of the transversal are supplementary!
Step-by-step explanation:
I don't really know how to explain it but I hope this helped!