The stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
What is a sequence?
A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).
To put the given distances in order from the closest one to the farthest one, we need to arrange them in ascending order.
That means we need to start with the smallest value and move toward the largest value.
Looking at the given distances, we see that the smallest value is 0.883, followed by 0.886, then 0.89, and finally 1.25, which is the largest value.
Putting the given distances in ascending order, we get:
0.883, 0.886, 0.89, 1.25
Therefore, the stars in order from the closest one to the farthest one are:
0.883, 0.886, 0.89, 1.25
so, the answer is A.
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6 foot tall adult casts, a shadow that is 15 feet long estimate the height of a child who cast a 10 foot shadow
By similarity of triangle the height of a children will be 4ft.
What is similarity of triangle?Similar triangles are that kind of triangles that have the same shape, but different sizes. examples of similar objects are All equilateral triangles, squares of any side lengths. In another words, if two triangles having their corresponding angles are congruent and corresponding sides are in equal proportion then two triangles are said to be similar. It is denoted by ‘~’ symbol.
We can use the property of similar triangles to estimate the height of the child:
The ratio of the height of the adult to the length of their shadow is the same as the ratio of the height of the child to the length of their shadow:
height of adult / length of adult shadow = height of child / length of child shadow
Plugging in the values we know:
6 / 15 = height of child / 10
Solving for the height of the child:
height of child = (6 / 15) * 10 = 4 feet
Therefore, the estimated height of the child is 4 feet.
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i need the answers pls
Step-by-step explanation:
5. Name the Circle.
Ans. Circle C.
6. Name to radii.
Ans. BH, AD
7. Name two chords.
Ans. AD ,BH
8. Name a diameter
Ans. AD
9. Name a secant .
Ans. KG
10.Name a tangent
Ans. GE
Point of tangency = F
More to Know :
• Radii: The distance from the centre of the circle to the circumference.
• Chord: Chord is a line segment that have two end points on the circle
• Secant: It refers to the line that intersect the circle at two points.
• Diameter: The lines that passes from the centre of the circle and meet at both the ends of the circle.
• Point of tagency: It is referred to the point where the tangent meets the circle.
[tex]\\[/tex]
Carolyn's hair grew 2.45 centimeters since her last haircut. Delia's hair grew 2.03 centimeters since her last haircut. Whose hair grew less since her last haircut? Explain.
Answer:
Delia's hair grew less since her last haircut
Step-by-step explanation:
2.45 centimeters is a higher number then 2.03, making Delia's hair shorter than Carolyn's.
Answer:
Delia's hair grew less.
Step-by-step explanation:
2.45 - 2.03 = 0.42
Deila's hair is 0.42 less than Carolyn's hair.
Explain how you can you prove the Corresponding Angles Theorem using the
Same-Side Interior Angles Postulate and a linear pair of angles.
Answer:
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Converse of the Same-Side Interior Angles Postulate: If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.
एउटा मोटरसाइकलको मूल्य वि.सं 2070 मा रु. 250,000 थियो र वि.सं. 2072 मा रु. 160,000 छ भने वार्षिक मिश्रह्रास दर पत्ता लगाउनुहोस् । The price of a motorcycle was Rs 250,000 in 2070 B.S. and in 2072 B.S., it is Rs 1,60,000. Find the annual rate of compound depreciation.
Step-by-step explanation:
Solution,
P=2,50,000
T=2072-2070
=2 years
Pt=1,60,000
Pt=P(1-D/100)^2
1,60,000=2,50,000{(100-D)}^2
100
1,60,000/2,50,000={(100-D)}^2
100
0.64={(100-D}^2
100
(0.8)^2={(100-D)}
100
80=100-D
100
80=100-D
D=100-80
D=20%
Hence, the deprecation rate is 20% over the period of 2 years
What is the area of this composite figure? Use 3.14 for pi. Round to the nearest hundredth. Show ALL work.
The composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
How to find the area of the composite figureWe can observe from the figure that it is a combination of a sector, a triangle and a trapezoid, so we shall calculate the area of each shape and add their result to get the area of the composite figure as follows:
area of the sector = 135°/360° × 22/7 × 2 × 2
area of the sector = 33/7
area of the sector = 4.7 square units
area of triangle = 2.6 × 1
area of the triangle = 2.6 square units
area of the trapezoid = 1/2 × (2.6 + 6) × 2
area of the trapezoid = 8.6 square units
area of the composite figure = 4.7 + 2.6 + 8.6
area of the composite figure = 15.9 square units
In conclusion, the composite figure compromising of a sector, a triangle and a trapezoid have a total area calculated to be 15.9 square units.
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solve the equation
3(3-2x)=2 x-11
Answer:
x = 2,5
Step-by-step explanation:
[tex]3(3 - 2x) = 2x - 11[/tex]
[tex]9 - 6x = 2x - 11[/tex]
Put numbers with x's to the left, and the plain numbers to the right:
[tex] - 6x - 2x = - 11 - 9[/tex]
[tex] - 8x = - 20[/tex]
[tex]x = 2.5[/tex]
does anyone know how to solve this problem. (image attached)
The rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex] when its length is 10 cm and its width is 6 cm, this is the case.
What is the rate of change?One quantity's rate of change with regard to another quantity is known as the rate of change function. In order to calculate the rate of change, one simply divides the amount of change in one item by the equivalent amount of change in another.
Let L and W represent the length and breadth of the rectangle, respectively, and A represents the area of the rectangle. Next, we have:
A = L * W
When L = 10 cm and W = 6 cm, we are interested in determining the rate of increase of the rectangle's area with regard to time, or dA/dt.
We can begin by finding the derivative of A = L * W with regard to time t for both sides of the equation:
Derivate the equation by both sides with respective t.
[tex]\frac{d}{dt} (L * W) = \frac{dA}{dt}[/tex]
Using the principle of product rule of derivative, we arrive at:
[tex]L * W + L * \frac{dw}{dt} = \frac{dA}{dt}[/tex]
To determine dA/dt when L = 10 cm and W = 6 cm, we are provided that [tex]\frac{dL}{dt}[/tex] = 8 cm/s and [tex]\frac{dw}{dt}[/tex]= 9 cm/s. Therefore, we replace these numbers in the previous equation to obtain:
[tex]\frac{dA}{dt}[/tex] = (8 [tex]\frac{cm}{s}[/tex]) * (6 cm) + (10 cm * 9 [tex]\frac{cm}{s}[/tex]).
[tex]\frac{dA}{dt} = 48 \frac{cm^{2}}{s} + 90 \frac{cm^{2}}{s} \\[/tex]
[tex]138 \frac{cm^{2} }{s} = \frac{dA}{dt}[/tex]
Since the rectangle's area is growing at a pace of 138 [tex]\frac{cm^{2} }{s}[/tex]when its length is 10 cm and its width is 6 cm, this is the case.
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7. The ride length of a roller coaster is 314
minutes. Every ride starts as soon as the
previous ride ends. How many rides take place
in 28 minutes?
Answer: To find out how many rides take place in 28 minutes, we need to divide the total ride length by the length of one side, and then round down to the nearest whole number.
The length of one ride can be calculated by dividing the total ride length by the number of rides. Since we don't know the number of rides, let's call it "n":
length of one ride = total ride length / n
314 minutes / n
Now we can set up an equation to solve for "n":
28 minutes = length of one ride * number of rides
28 minutes = (314 minutes / n) * number of rides
We can simplify this equation by multiplying both sides by "n":
28 minutes * n = 314 minutes * number of rides
Dividing both sides by 314 minutes, we get:
n = (28 minutes * number of rides) / 314 minutes
Multiplying both sides by 314 minutes and dividing by 28 minutes, we get:
number of rides = (n * 314 minutes) / 28 minutes
number of rides = 11.21
Rounding down to the nearest whole number, we get:
number of rides = 11
Therefore, in 28 minutes, 11 rides take place.
Step-by-step explanation:
a jar contains $3.60 in nickels and quarters. there are 28 coins in all. how many of each coin is in the jar?
Drag a statement or reason to each box to complete this proof
Drag the following statement, equation or reason to each box to complete this proof accordingly:
2. Multiplication Property of Equality
3. x-2 = 8
4. Addition Property of Equality
5. x = 10 Simplifying
How to complete the proof of the equation with reason?An equation is a mathematical statement that expresses the equality between two expressions. It contains an equal sign "=" that separates the two expressions.
The proof of the equation with reason can be completed as follow:
(x-2)/4 = 2 Given
4(x-2)/4 = 4 * 2 Multiplication Property of Equality
x-2 = 8 Simplifying
x - 2+ 2 = 8 + 2 Addition Property of Equality
x = 10 Simplifying
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pick a region of your choice. write out the integrals needed to find the volume of the region using a triple integral with rectangular, cylindrical and spherical coordinates. (you must use all three types coordinates on the same region - choose wisely!). setup but do not evaluate the integrals.
The volume integral for f(x,y,z) = 1 over the region E : x² + y² + z² ≤ 4,
1) In spherical coordinates system is
[tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
2) In cylinderical coordinates system is
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
3) In rectangular coordinates syatm is
[tex]V = \int_{0}^{2}\int_{-\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
We pick a region E : x² + y² + z² ≤ 4 and determine volume over the region E for function, f(x,y,z ) = 1 .
Use of Spherical coordinates (ρ,θ, φ), Volume can be written as[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
In spherical coordinates system we plug,
[tex]x = \rho sin \phi cos \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
[tex]z = \rho cos \phi [/tex]
[tex]dV = dx dy dz = |J| d\rho d\phi d\theta [/tex]
where, [tex]|J| = \rho² sin \phi[/tex]
=> [tex]dx dy dz = \rho² sin \rho d\rho d\phi d\theta[/tex]
So, [tex]V = {\int \int \int}_{x² + y² + z² ≤ 4} 1 \: dxdy dz[/tex]
Now, [tex]V = {\int_{0}^{2π} \int_{0}^{π} \int}_{0}^{2} \rho^{2} \sin( \phi) \: d\rho d\phi d\theta[/tex]
Using Cylindrical coordinates (r,θ,z)Region , E : x² + y² + z² ≤ 4
=> z² ≤ 4 - x² - y²
=> z ≤ ± √4 - x² - y²
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
here, r∈[0, 2], θ∈[0,2π]
[tex]V = \int_{0}^{2π} \int_{0}^{2} (\int_{-\sqrt {4 - x² - y²}}^{\sqrt{ 4 - x² - y²}} dz) rdr d \theta \\ [/tex]
Using rectangular coordinates (x,y,z), Volume integral can be written as :[tex]V = {\int \int \int}_{E} f(x,y,z) dV[/tex]
[tex]V = {\int \int_{ x² + y² ≤ 4} \int}_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } 1 \: dz dx dy \\ [/tex]
Here, y² ≤ 4 - x²
=> y = ± √4 - x² and x∈ [0,2], So,
[tex]V = \int_{0}^{2}\int_{ -\sqrt {4 - x²}}^{\sqrt{4 - x²}} \int_{ - \sqrt{ 4 - x² - y²}}^{ \sqrt{4 - {x}^{2} - {y}^{2} } } \: dz dy dx \\ [/tex]
Hence, in above we determined the volume integral for region, E in all three coordinates systems.
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Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices.
What is the conditional probability that a randomly selected contestant played an acoustic guitar, given they wore leather pants?
A. 9/25
B. 2/5
C. 3/5
D. 6/25
show all steps
The conditional probability that a randomly selected participant wore leather pants and played an acoustic guitar is 6/25. Therefore, the answer is option D. 6/25.
What is conditional probability?Conditional probability is the probability that an event will occur given that another event has already occurred.
It is denoted by P(A|B), where A and B are events, and the vertical line | indicates "given that" or "conditional on".
The conditional probability of an event A given event B is defined as the probability of both A and B happening divided by the probability of B happening:
P(A|B) = P(A and B) / P(B)
In this case, the event A is playing an acoustic guitar and the event B is wearing leather pants.
We can start by finding the probability of wearing leather pants:
P(B) = (6 + 9) + (3 + 7) = 25
This is because there are a total of 6 contestants wearing leather pants and 19 contestants in total.
Next, we need to find the probability of both wearing leather pants and playing an acoustic guitar:
P(A and B) = 6
This is because there are 6 contestants wearing leather pants and playing an acoustic guitar.
Now we can use the formula to find the conditional probability:
P(A|B) = P(A and B) / P(B) = 6 / 25
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find the length of the diagonal of the box below. Round to the nearest hundredth (you have to do pythagorean theorem twice)
Answer:
12.5
Step-by-step explanation:
9.6² + 2.8² = 10²
10² + 7.5² = 12.5²
James starts from point A along the pentagonal path A to B, B to C, C to D,
D to E and finally returns to point A. The distance of side
of pentagon is 8 m .He takes 16
from A to A along the path as said earlier. Write:
Distance covered by him
Displacement
Speed
Answer:
a) Distance is 40m b)0 c)2.5m/min
Step-by-step explanation:
a)8*5=40 b)He went from A to A c)16 min s=d/t 40/16
The sum of the ages of two brothers Kofi and Kwaku is 35. Kofi age is 2/3 of Kwaku's age. find their ages.
2/3 of 35 is 23. Kofi is 23.
help pls show ur work
1. The triangles are not similar because they do not have proportional set of sides.
2. Both triangles are not similar as well.
What is the SSS Similarity Theorem?The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the triangles are similar. "SSS" stands for "side-side-side," which refers to the three corresponding sides that are proportional.
More formally, the SSS similarity theorem can be stated as follows:
If ΔABC ~ ΔDEF, then: AB/DE = BC/EF = AC/DF (the sides are proportional)
1. QP/ML = 90/40 = 2.25
RQ/LK = 81/36 = 2.25
PR/MK = 64/28 = 2.29
Thus, this means that QP/ML = RQ/LK ≠ PR/MK. This implies the three sides are of both triangles are not proportional. Therefore, they are not similar by SSS nor any other theorem.
2. Both triangles do not have any set of corresponding angles that are congruent, therefore, they are not similar.
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Help me please. for 65 points and brainly
Answer:
Answer 3
Step-by-step explanation:
Answer: 3
Step-by-step explanation:
Which expression is equivalent to (7^3)5 ⋅ 7^4?
Answer: [tex]7^3\cdot7^{-5}=7^{-2}=\dfrac{1}{7^2}[/tex]
Step-by-step explanation:
In an Australian netball competition, these teams are tipped to win Round 1 by three experts:
Expert A: NSW, Queensland, WA, Tasmania
Expert B: SA, Victoria, Queensland, WA Expert C: NSW, ACT, WA, Victoria No one tipped the Northern Territory to win. Which team did Victoria play?
Answer:
undetermined or most likely Tasmania
Step-by-step explanation:
Based on the choices of experts in the first round of the Australian netball competition, we can conclude that Victoria played against WA. This is because, out of the common tips, WA was tipped by an expert who also tipped Victoria and didn't tip Queensland. Therefore, WA is the likely team that Victoria played against.
Explanation:To identify which team Victoria played in the Australian netball competition we can reason through our experts' tips. The experts' tips overlap at Queensland and WA as indicated by Expert A and Expert B. However, Expert C tipped Victoria, and they did not tip Queensland which tells us that Victoria did not play against Queensland, leaving us with WA. Hence Victoria must've played against WA.
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6×y^2=240in^2
Solve for Y
Answer:
[tex]y=40\sqrt{\frac{6}{x} }[/tex]
[tex]y=-40\sqrt{\frac{6}{x} } ,x > 0[/tex]
Step-by-step explanation:
pls tell me if wrong have a good night/day
A manufacturer produces 25-pound lifting weights. The lowest actual weight is 24 pounds, and the highest is 26 pounds. Each weight is equally likely so the distribution of weights is uniform. A sample of 100 weights is taken.
Find the probability that the mean actual weight for the 100 weights is greater than 24.9. (Round your answer to four decimal places.)
Thus, the chance according to the equation that the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
What is equation?An equation in mathematics is a declaration of the equivalence of two expressions. Two parts of an equation are divided by the algebraic symbol ([tex]=[/tex]). As an example, the assertion "[tex]2x+3=9[/tex]" is supported by the argument that it is true.
Finding the value or values of the variable(s) needed to make the equation correct is the aim of equation solving. It is possible to create regular or nonlinear, straightforward or complex equations that include one or more variables.
For instance, the variable[tex]x[/tex] is raised to the second degree in the equation "[tex]x^{2} +2x-3[/tex]". In many areas of mathematics, such as algebra, calculus, or geometry, lines are used.
The weights are distributed evenly, with a minimum value of [tex]24[/tex] and a highest value of [tex]26[/tex]. The average of the lowest and maximum values, which is the mean weight of a single weight, is
[tex](mean weight)= (24+26)/2 = 25 pounds[/tex]
The standard deviation of a single weight is the difference between the maximum and minimum values divided by[tex]\sqrt{12}[/tex] (since there are [tex]12[/tex]possible values between [tex]24[/tex] and [tex]26[/tex]), which is
[tex]Standard deviation = (24+26)/\sqrt{12}[/tex]
[tex]We know (standard deviation of mean weight ) = 0.57735/\sqrt{100} =0.057735[/tex]
We must standardise this value by taking the mean weight, subtracting it, and dividing the result by the mean weight's standard deviation in order to determine the likelihood that the mean actual weight for the[tex]100[/tex]weights is higher than [tex]24.9 pounds[/tex]:
[tex]( Z- score )= (24.9-25)/0.057735 = -1.7321[/tex]
Probability is [tex]less than[/tex] [tex]-1.7321 in Z- score approx 0.0418[/tex]
However [tex]mean actual weight > 24.9[/tex] which is the complement of the probability i.e, [tex]\leq 24.9[/tex]
After subtracting the probability we found [tex]1[/tex] [tex](mean weight > 24.9)[/tex]
∴[tex]1 -0.0418 = 0.9582[/tex]
Therefore the the average actual weight for the [tex]100 weights[/tex] is higher than [tex]24.9 pounds[/tex] is roughly [tex]0.9582[/tex]
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A right triangle is drawn on the coordinate plane. Apply a dilation with a scale factor of one over three to this triangle in draw the new triangle on the coordinate plane.
The image of the triangle is attached with coordinates
(0, 0)
(0. 3)
(3, 3)
What is a scale factor?In mathematics, a scale factor is a constant that multiplies every length of an object, changing its size while preserving its shape. In the context of dilation, which is a type of transformation that changes the size of a shape, the scale factor determines the amount by which the shape is enlarged or reduced.
When a shape is dilated with a scale factor greater than 1, the resulting shape is larger than the original. Conversely, when a shape is dilated with a scale factor between 0 and 1, the resulting shape is smaller than the original. If the scale factor is exactly 1, then the shape remains the same size.
In the problem the image is dilated with a scale factor less than one hence the resulting image is lesser
The new coordinates are gotten as follows
(0, 0) * 1/3 = (0, 0)
(0. 9) * 1/3 = (0. 3)
(9, 9) * 1/3 = (3. 3)
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IF I A LIQUID IS AT A TEMPERATURE OF 16.9 AND RISES AT A RATE OF 2.3 AND A SOLID IS AT A TEMPERATURE OF 30.7 AND DECREASES AT A RATE OF 6.9 how long will it take for them to be at the same temperature in minutes
Answer:
The number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Step-by-step explanation:
You know that the temperature of liquid at 16.9°C is decreasing at a rate of 2.3°C per minute. Then, the temperature of the liquid after t minutes, as its value decreases, will be the difference between the initial temperature of 16.9 ° C and the temperature after t minutes. So:
temperature of the liquid= 16.9°C - 2.3 °C/minute * t
On the other side, you know that the temperature of a solid at 30.7°C is decreasing at a rate of 6.9°C per minute. Then, the temperature of the solid after t minutes, as its value decreases, will be the difference between the initial temperature of 30.7°C and the temperature after t minutes. So:
temperature of the solid= 30.7°C - 6.9 °C/minute * t
You want to calculate the number of minutes it will take for a liquid and a solid to reach the same temperature. This is:
temperature of the liquid= temperature of the solid
16.9°C - 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t
Solving:
- 2.3 °C/minute * t= 30.7°C - 6.9 °C/minute * t - 16.9°C
- 2.3 °C/minute * t + 6.9 °C/minute *t= 30.7°C - 16.9°C
4.6 °C/minute * t = 13.8 °C
t=3 minutes
So the number of minutes it will take for a liquid and a solid to reach the same temperature is 3 minutes.
Why is the green triangle not possible given an angle of 30°?
The reason why the green triangle is not possible given an angle of 30° and a side length of 8.73 is due to the fact that the green triangle violates the triangle inequality theorem.
What is triangle inequality theorem?According to the triangle inequality theory, any triangle's lengths of any two sides must add up to more than the length of the third side.
The triangle inequality theorem is broken in the instance of the green triangle if the second side is extended to a very long length, making the triangle's lengths of the two shorter sides (7 and 8.73) less than the length of the longer side (24).
The orange triangle, which has side lengths of 7, 15, and roughly 16.16 (determined using the Pythagorean equation), is the only one that can exist because the green triangle is impossible.
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given the equations below what is the frist x value where g(x)>f(X)
f(X)=4X=25
g(X)=2(5)x
Answer:There seems to be a typo in the equation for f(x). I will assume that the correct equation is:f(x) = 4x - 25To find the first x value where g(x) > f(x), we can set the two equations equal to each other and solve for x:g(x) = f(x)
2(5)x = 4x - 25
10x = 4x - 25
6x = -25
x = -25/6
Step-by-step explanation:However, we need to check if this value satisfies the condition g(x) > f(x):g(-25/6) = 2(5)(-25/6) = -25
f(-25/6) = 4(-25/6) - 25 = -75/3 - 25/1 = -100/3Therefore, g(x) > f(x) is not true for x = -25/6. We need to keep looking for a larger value of x where g(x) > f(x).To do this, we can graph the two functions and look for the point where the graph of g(x) is above the graph of f(x). Alternatively, we can simply plug in some larger values of x and compare the values of g(x) and f(x) until we find the first x value where g(x) > f(x).Let's try plugging in x = 0:g(0) = 2(5)(0) = 0
f(0) = 4(0) - 25 = -25Since g(0) = 0 and f(0) = -25, we have g(x) > f(x) for x > 0. Therefore, the first x value where g(x) > f(x) is x = 0.
A submarine is passing by a solar station, located al (0,0), that can detect objects that
are as far away as 5km in any direction. A swiss submarine is traveling along a trajectory defined by y= -2/3x +26/3 where x and y represent distances measured in kilometers. Determine algebraically whether the sonar station will detect the submitline.
Answer:
The sonar station will not detect the submarine.
Step-by-step explanation:
The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.
The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:
[tex]\implies (x-0)^2+(y-0)^2=5^2[/tex]
[tex]\implies x^2+y^2=25[/tex]
To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.
[tex]\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25[/tex]
Simplify:
[tex]\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25[/tex]
[tex]\implies 9x^2+4x^2-104x+676=225[/tex]
[tex]\implies 13x^2-104x+451=0[/tex]
Solve the equation for x using the quadratic formula:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}[/tex]
[tex]\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}[/tex]
[tex]\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}[/tex]
[tex]\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i[/tex]
As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.
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-10 -9 -8 -7 -6 -5 -4 -3 -2
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What is the image point of (-9,-5) after the transformation T-5,00 D₂?
attempt 11 out of 20/problem 1 out of ma
C
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
What is transformation ?The term "transformations" refers to the movements or adjustments that can be made to a geometric shape or object, such as turning, reflecting, translating, processes in an organization, or resizing. With these procedures, the original form or object can retain its geometry, angles, and other geometric attributes while changing its position, size, and orientation. Geometry, photography, and other disciplines frequently employ transformations to manipulate and examine patterns and shapes.
given
Applying the translation T-5,00 to the point (-9,-5) first yields (-9-(-5),-5+0) =, which we can use to determine the image point of (-9,-5) following the transformation T-5,00 D2 (-4,-5).
Then, we dilate the point (-4, -5) using the formula (2(-4,2(-5)) = (-8,-10).
Thus, following the transformation T-5,00 D2, the image point of (-9,-5) is (-8,-10). Hence, choice C is the right response.
To know more about transformation visit :-
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Choose the equation that represents the line that passes through the point (6, -3) and has a slope of
1
-İN
2
O
O
y=-x+6
O
y=-x-6
|_y=-x-3
2
|_y=-x+3
Answer:y=-x+6
Step-by-step explanation:
The weight of 4 hummingbirds is recorded below. The weight of each
1
hummingbird has been rounded to the nearest gram.
2
2
2/1/2
3 31/1 4 4/ 5
Weights of birds (grams)
10
What is the weight of all 4 hummingbirds combined?
grams
Answer: The total amount of the hummingbirds' weight is 15 grams.
Step-by-step explanation:
As it is shown in the dot graph, the four hummingbirds' weigh is recorded to the nearest gram.
Hummingbird 1 - 2 1/2
Hummingbird 2 - 3
Hummingbird 3 - 4 1/2
Hummingbird 4 - 5
2 1/2 + 4 1/2 = 7
3 + 5 = 8
Seven plus eight equals to fifteen. Therefore, the total weight of all four hummingbirds is 15.
Hope this helps coralasting123!