Answer:The distance between the two points (4, 9) and (7, 5) can be calculated using the distance formula:
√((7 - 4)^2 + (5 - 9)^2) = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Step-by-step explanation:
Two equal ide of a triangle are each 4m le than three time the third ide. Write down the dimenion of the triangle, if it perimeter i 55m
9 m, 23 m, and 23 m are the triangle's measurements.
What is meant by triangle's measurement?The total of a triangle's three inner angles is always 1800. Any two sides of a triangle can have a sum of lengths that is always greater than the length of the third side. Half of a triangle's area is equal to the sum of its base and height. Any triangle's three angles add up to a whole 180 degrees.Wisconsin University's Brian McCall A 45° 45° 90° triangle is a particular kind of isosceles right triangle in which the two legs are congruent and the non-right angles are both 45°. The hypotenuse or missing legs of 45 45 90 triangles can frequently be determined using the Pythagorean theorem.To learn more about triangle's measurement, refer to:
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The surface area of a cone is given by the formula
S = πl + πr2. Solve the formula for l
The surface area of a cone is given by the formula:
S = πl + πr^2
Solving for l, we can start by isolating l on one side of the equation:
S - πr^2 = πl
Dividing both sides by π:
(S - πr^2) / π = l
Therefore, the length l can be found by subtracting the product of π and r^2 from the surface area S, and dividing the result by π.
Work out the area of a rectangle with base,
b
= 14mm and height,
h
= 10mm.
Answer:
70mm
Step-by-step explanation:
(14*10)/2=70
Height and Width multiplied against each other divided by two is the area of a triangle
Shortly after takeoff, an airplane is climbing 250 feet for every 1000 feet it travels. Estimate the airplanes climb angle while this is happening.
Answer: The estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°
Step-by-step explanation:
The climb angle of an airplane can be estimated using the tangent of the rise over the run. To do this, you need to know the rise (the vertical distance the airplane is climbing) and the run (the horizontal distance the airplane is traveling).
In this case, the rise is 250 feet and the run is 1000 feet. The tangent of the angle is the rise divided by the run:
tan(angle) = rise / run = 250 / 1000 = 0.25
To find the angle in degrees, you need to take the inverse tangent (arctan) of 0.25:
angle = arctan(0.25) = 14.0°
So, the estimate of the airplane's climb angle while climbing 250 feet for every 1000 feet it travels is approximately 14°.
Here is a tile game with two colors, say red and blue. On a turn, a person can either take any number of tiles of one color or they can take the same number of red and blue tiles. The last one to take a tile WINS. For example, if you start with 5 red and 7 blue tiles, taking 4 blue tiles is a legal move, taking 2 red tiles is a legal move, and taking 3 red and 3 blue tiles is a legal move, but taking 4 blue and 2 red tiles is not allowed. Describe a strategy for winning this game for all cases with 40 or fewer total tiles. Describe patterns you see in the numbers involved in your solution, and justify what you can
This strategy works for all cases with 40 or fewer total tiles. The pattern observed here is that XORing pattern.
If there are 5 red tiles and 7 blue tiles, the binary representation of these numbers is 101 and 111, respectively. Taking the bitwise XOR of these numbers gives 010, which is 2. Hence, the player should take 2 tiles of either color, leaving 3 tiles of one color and 5 tiles of the other color. This leaves the other player in a losing position.
The pattern observed here is that XORing all the numbers together effectively cancels out all the common bits, leaving only the unique bits. The player should then take a number of tiles such that the unique bits become 0.
Unique bits refer to the concept of binary representation of numbers in mathematics. The binary system is a base-2 numeral system where each digit can either be 0 or 1. Unique bits refers to the distinct and non-repeating number of binary digits used to represent a number. It is a measure of the number of bits needed to represent a unique number.
The unique bits in mathematics is a concept that is widely used in computer science, information theory and cryptography. The more unique bits used, the greater the number of unique combinations that can be produced and hence, the greater the accuracy in representation. For example, using 8 unique bits in binary representation can result in up to 256 unique combinations, compared to using only 7 unique bits, which can only result in 128 unique combinations. Unique bits plays a crucial role in ensuring the accuracy and efficiency of information representation and transmission.
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Can someone PLEASE help? I will give brainliest if possible and lots of points
Click on the image to see questions
Answer:
A) <5 and <6 are commentary
B) 72
C < 4 = 22
<3 = 68
Step-by-step explanation:
A) The square drawn over the 2 angles shows that the angles together measure 90 degrees
B) 90 - 18 = 72
C) 4x -10 + 5x + 28 = 90 Combine like terms
9x + 18 = 90 Subtract 18 from both sides
9x = 72 Divide both sides by 9
x = 8
<4
4x - 10
4(8) - 10
32 - 10
<4 = 22
<3
5x + 28
5(8) + 28
40 + 28
68
<3 = 68
Answer:
Part A: Yes, ∠5 and ∠6 are complementary angles because they add up to 90°.
Part B: If the measure of ∠6 is 18°, then the measure of ∠5 is 72° because ∠6+∠5=90° so 90°-18°=72°.
Part C: ∠4+∠3=90°
(4x-10)°+(5x+28)°=90°
add 10 to both sides
4x+5x+28=100
subtract 28 from both sides
4x+5x=72
combine like terms
9x=72
divide both sides by 9
x=8
now plug 8 in for x
∠4=(4(8)-10)°
∠4=22°
∠3=(5(8)+28)
∠3=68°
22°+68°=90°
Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Explanation:
In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.
Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.
It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.
Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be concluded that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
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In Sandy's experiment, the experimental probability was closest to the theoretical probability in the experiment with 100 flips.
Explanation:
In Sandy's experiment, she used a virtual coin toss app to simulate the results of flipping a coin 100 times, 500 times, and 1,000 times. The experimental probability is the probability obtained from the observed outcomes of the experiment, while the theoretical probability is the probability calculated based on mathematical principles and assumptions.
Based on the information given, it is stated that Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips. This suggests that the observed outcomes of the 100 flips aligned more closely with the expected outcomes based on the theoretical probability.
It is important to note that experimental probability tends to converge towards theoretical probability as the number of trials increases. Therefore, it is expected that the experimental probability would be closer to the theoretical probability in the experiment with 1,000 flips compared to the experiment with 500 flips.
Without further information, it is not possible to determine whether Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments. However, based on the given statement, it can be inferred that the experimental probability was closest to the theoretical probability in the experiment with 100 flips.
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Need help please on this
The line has an equation y = 0.03x + 20, with a slope of $0.03 per GB and the y intercept of $20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let y represent the total cost of buying x gigabyte of data
The line passes through the point (0, 20) and (2000, 80). Hence:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-20=\frac{80-20}{2000-0} (x-0)\\\\y = 0.03x + 20[/tex]
The slope is 0.03 and the y intercept of the line is 20.
The second line passes through the point (0, -2) and (-2, -5). Hence:
[tex]y-y_1=\frac{y_1-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-(-2)=\frac{-5-(-2)}{-2-0} (x - 0)\\\\y=1.5x-2[/tex]
The equation of the line is y = 1.5x + 1 and y = 1.5x - 2
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Teresa was offered two jobs one job pay with $400 a week plus $200 Signing bonus the other job paid 420 week with no signing bonus how many weeks would she have to work orders for the total amount earned from the job to be equal
Teresa would need to work 10 weeks in order to earn the same total amount as the second job.
Assuming Teresa takes the first job, she would need to work for 10 weeks in order to earn the same total amount as the alternate job. The total amount earned from the first job can be calculated by (400 x 10) + 200 = 6000. The total amount earned from the second job can be calculated by (420 x 10) = 4200. Thus, in order to earn the same amount from the total of both jobs, Teresa would need to work 10 weeks at the first job. This can be expressed by the following formula: (400 x n) + 200 = 420 x n, working for n is the number of weeks. Solving for n gives n = 10.
Thus, Teresa would need to work 10 weeks in order to earn the same total amount as the second job.
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Write exponential growth/decay equation and solve for each problem
A savings account balance is compounded annually. If the interest rate is 2% per year and the current balance is $1,460.00, what will the balance be 8 years from now?
Answer:
The equation is y = 1,460e^(2%)x, and the balance will be $2,067.54 in 8 years
The surface area of a sphere is found using the formula SA=4², where r is the radius. If the surface area of a
sphere is 144π square feet, what is the radius, in feet?
A. 6
B. 12
C. 18
D. 36
Answer:
A
Step-by-step explanation:
Surface area of sphere is 4 pi r^2
144 pi = 4 pi r^2
144 pi / (4 pi) = r^2
36 = r^2
r = 6 ft
determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an = n 2 sin(2/n) lim n→[infinity] an = incorrect: your answer is incorrect.
The given sequence is convergent and the limit is 1.
What is a sequence?
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.
Here, we have
Given: aₙ = (n/2) sin(2/n)
First, we will find the limit of a given sequence.
aₙ = [tex]\lim_{n \to \infty} (n/2)sin(2/n)[/tex]
We apply L'hospital's rule here and we get
aₙ = [tex]\lim_{n \to \infty} {cos(2/n)(-2/n^2)}/(-2/n^2)[/tex]
aₙ = [tex]\lim_{n \to \infty} cos(2/n)[/tex]
aₙ = 1
We concluded that the given series is convergent.
Hence, the given sequence is convergent and the limit is 1.
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clay made 4/5 of a pound of a trait mix if he puts 2/5 of a pound into each bag how many bags can clay fill
Answer: 2 bags
Step-by-step explanation:
To determine the number of bags Clay can fill, we need to divide the total amount of the trail mix by the amount of trail mix in each bag.
First, we'll convert the amounts to a common denominator of fifths:
4/5 of a pound of trail mix is 4/5 * 5/5 = 4 fifths
2/5 of a pound is 2/5 * 5/5 = 2 fifths
Now, we can divide the total amount of trail mix by the amount in each bag:
4 fifths ÷ 2 fifths/bag = 2 bags
So, Clay can fill 2 bags with 2/5 of a pound of trail mix each.
a data analyst creates a scatterplot with a lot of data points. it is difficult for the analyst to distinguish the individual points on the plot because they overlap. what function could the analyst use to make the points easier to find? 1 point geom line() geom jitter() geom point() geom bar()
The analyst could use the geom_jitter() function to make the points easier to find.
What is data analyst ?
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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The analyst could use the geom_jitter() function to make the points easier to find.
Analytics is the systematic computational analysis of data or statistics. It is used for the discovery, interpretation, and communication of meaningful patterns in data.
The function geom_jitter() can help to resolve this issue by randomly offsetting the x and y position of each point. By adding a small amount of "jitter" to each point, the overlap is reduced and the individual data points become more visible. In ggplot2 library, which is a popular plotting library in R, geom_jitter() is used as a layer in a plotting pipeline to add jitter to a scatterplot.
To use geom_jitter(), you will first create a scatterplot using the geom_point() function, then add a geom_jitter() layer to it. This will apply the jitter to the points and improve their visibility. For example, in ggplot2 the following code would create a scatterplot with jittered points:
ggplot(data, aes(x=x, y=y)) +
geom_jitter() +
geom_point()
The analyst could use the geom_jitter() function to make the points easier to find.
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what is the value of the expression below when z =4
The solution of the expression ( 10z - 3 ) is equal to 37.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that the expression is 10z - 3. The value of the expression at z = 4 will be calculated below,
Evaluate for z = 4,
E = 10x - 3
E = (10)(4)−3
E = (10)(4)−3
E = 37
Therefore, the solution for the expression is 37.
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The table shows how much a frozen yogurt shop
charges for its yogurt. Write an expression to show
how much it costs to buy a small yogurt with no
toppings and a large yogurt with x toppings. Then
solve for buying a small yogurt with no toppings
and a large yogurt with 3 toppings.
The expression for the cost is cost = 0.35x + 7.5 and the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings is $8.55
To write an expression to show how much it costs to buy a small yogurt with no toppings,
The expression for the costs of a small yogurt with no toppings and a large yogurt with x toppings will be:
Cost = 2.85 + (4.65 + 0.35x)
Cost = 2.85 + 4.65 + 0.35x
Cost = 0.35x + 7.5
To find the total cost for a small yogurt with no toppings and a large yogurt with 3 toppings, substitute x = 3 into the above expression. That is:
Cost = 0.35x + 7.5
Cost = 0.35(3) + 7.5
Cost = $8.55
Thus, the total cost is $8.55
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Profeor Smart i teaching her tudent how the formula for the area of a circle wa derived
The area of circle can be calculated by using the formulas: Area = π x r2, in terms of radius 'r'. Area = (π/4) x d2,
State area of circle?
The area of a circle is pi times the radius squared (A = π r²). Learn how to use this formula to find the area of a circle when given the diameter.Area = length x breadthArea = l × b. Area = π × radius × radiusArea = π × r2(π = 3.14) Using these formulas, area for different quadrilaterals (a special case of polygons with four sides and angles ≠ 90o) is also calculated. Application.We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.To learn more about circle refers to:
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When X has the pdf: f(x) = λe^{-λx}λe^(-λx)λe^-λx for x>0
P(X>x) =
A. 1-λe^{-λx}λe^(-λx)λe^-λx
B. 1-λe^{-λx}λe^(-λx)e^-λx
C. λe^{-λx}λe^(-λx)λe^-λx
D. λe^{-λx}λe^(-λx)e^-λx
The probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex]. Thus, option (A) is correct.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain.
P(X>x) is the probability that X takes on a value greater than x, which means that X is in the tail of the distribution. The cumulative distribution function (CDF) of X, denoted F(x), is defined as F(x) = P(X ≤ x). Since the CDF is a cumulative probability, we can find P(X>x) by subtracting the cumulative probability of X being less than or equal to x from 1:
P(X > x) = 1 - P(X ≤ x) = 1 - F(x)
Now, to find F(x), we can use the cumulative density function (pdf) of X. The pdf of X is given by f(x) = λ [tex]e^{- \lambda x}[/tex] for x > 0. To find the cumulative probability, we need to find the definite integral of the pdf from 0 to x:
F(x) = [tex]\int_0^x \lambda e^{- \lambda x}dx[/tex]
= [tex]-e^{-\lambda x} \int_0^x \lambda de^{\lambda x}[/tex]
= [tex]-e^{-\lambda x}[e^{\lambda x}]_0^x[/tex]
= [tex]-e^{-\lambda x}(e^{\lambda x} - 1)[/tex]
= [tex]1 - e^{-\lambda x}[/tex]
Therefore, the probability that X is greater than x is:
P(X>x) = 1 - F(x) = 1 - (1 - [tex]e^{- \lambda x}[/tex] = [tex]e^{- \lambda x}[/tex]
Hence, the probability that X is greater than x is P(X>x) = 1-λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{- \lambda x}[/tex]λ[tex]e^{-\lambda x}[/tex].
Option (A) is correct.
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For each of the examples below, identify the bearing of D from C.
a)
250°
N
110°
D
b)
145°
D
N
C
215°
Not drawn accurately
a) The bearing of D from C is 250.
b) The bearing of D from C is 145.
What is Bearing in Angle?Angles are measured in bearings clockwise from north. The direction of north must be identified before taking a bearing measurement. The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion.
Given:
a) 250°N, 110°D
As, we know that Bearings are angles, measured clockwise from north. To measure a bearing, we must first know which direction is north.
So, the bearing of D from C is 250.
b) The bearing of D from C in second case is 145.
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The variable whose effect on the response variable is to be assessed by the experimenter.
In an experiment, the variable being measured or tested is known as the dependent variable.
What is dependent variable?Any variable whose value depends on an independent variable is said to be dependent. The thing being measured in an experiment or assessed in a mathematical equation is the dependent variable. Sometimes the dependent variable is referred to as "the result variable." A dependent variable is one that depends on the value of another variable in an expression. As an illustration, if y = 2x, then y relies on x Consequently, y Equals 2 if x = 1. The independent variable is the one whose value is unrelated to the other variables. The dependent variable is the one whose value depends on the independent variable. When the same line is written in two different ways so that there are infinite solutions, an equation system is referred to as dependent.To learn more about dependent variable, refer to:
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find the solution to the initial value problem. dy dt = 8 y t , y(1) = 5
The solution to the initial value problem is y(t) = 5e^8t.
y(t) = 5e^8t
This is a separable differential equation. Separating the variables, we have
dy/dt = 8y
dy = 8y dt
Integrating both sides, we have
∫dy = ∫8ydt
y = 4e^8t + C
To find C, we use the initial condition, y(1) = 5
5 = 4e^8(1) + C
C = 5e^-8
Substituting C into the equation, we have
y(t) = 5e^8t
The solution to the initial value problem is y(t) = 5e^8t.
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Question content area top Part 1 Given the following functions, find the indicated values f(x)=4-9x (a) f(-8) (b) f(0) (c) f(9)
Answer:
Step-by-step explanation:
Given the function f(x) = 4 - 9x, the indicated values are:
(a) f(-8) = 4 - 9(-8) = 4 + 72 = 76
(b) f(0) = 4 - 9(0) = 4
(c) f(9) = 4 - 9(9) = 4 - 81 = -77
So, the values of f(-8), f(0), and f(9) are 76, 4, and -77, respectively.
You drive your Car for 3 hours at an average speed of 130km per hour. How far did you go?
That's my math question I need help on. Thx!!!
This is quite simple. You just need to multiply. 130 × 3 = 390
Therefore, you would have driven 390 km.
A walkway forms one diagonal of a square playground. The walkway is 32m long. How long is a side of the playground
Answer:14 meters
Step-by-step explanation:
An archer is able to hit the bull's-eye 49% of the time. If she shoots 10 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.
a. 0.1267
b. 0.2130
c. 0.7870
d. 0.0010
e. 0.0576
Probability of hitting bull's eye exactly 4 time sin 10 arrows is 0.213
What is Probability ?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Properties of Probability:
Phi or a null set is the probability of an impossibly unlikely event.Its sample space represents an event's highest probable probability.Any occurrence has a probability between 0 and 1. A probability can also be zero (0).An event's probability cannot be negative.The chance of A or B happening is equal to the probability of A plus the probability of B if A and B are two outcomes that cannot both occur simultaneously.The probability of hitting a bull's Eye is 49% = 49/100 = 0.49
The probability of not hitting a bull's Eye is = 1- 0.49 = 0.51
Probability of hitting bull's Eye 4 times = (0.49)⁴
Probability of not hitting Bull's eye 6 times = (0.51)⁶
The total number of combinations possible with 10 sets are ¹⁰C₄.
Probability of hitting bull's eye 4 time sin 10 arrows is
¹⁰C₄*(0.49)⁴*(0.51)⁶ = 0.213
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How to convert psi to atm (atmospheric pressure)?
Take the PSI value and divide it by 14.696 or 14.7 to convert PSI to atm.
What is atmospheric pressure?
The force per unit area that an atmospheric column exerts is known as atmospheric pressure, also known as barometric pressure (that is, the entire body of air above the specified area). A mercury barometer (hence the commonly used synonym barometric pressure) can be used to measure atmospheric pressure because it displays the height of a mercury column that precisely balances the weight of the atmosphere over the barometer. An aneroid barometer, which uses one or more hollow, partially evacuated, corrugated metal discs supported against collapse by an inside or outside spring, can also be used to measure atmospheric pressure. The change in the disk's shape with changing atmospheric pressure can be recorded using a pen arm and a clock-driven revolving drum.
The Imperial system of measurement measures pressures in pounds per square inch (PSI). PSI is frequently used to calculate the pressure of liquids or gases (hydraulic pressure).
The model equation is ATM = PSI/14.7
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Adriana is 8 more than twice the height of her little brother in inches. Adriana is at least 60 inches tall. What is the minimum height of her brother?
Applying inequality, the minimum height of her brother is: 26 inches.
How to Apply Inequality?An inequality is a mathematical statement that shows the relationship between two values or expressions, where one value is either greater than, less than, greater than or equal to, or less than or equal to the other value. It is represented using symbols such as ">", "<", "≥", or "≤".
Let's call the height of Adriana's little brother "x".
So Adriana's height is 2x + 8 inches.
And because Adriana is at least 60 inches tall, we can write the following inequality:
2x + 8 ≥ 60
Subtracting 8 from both sides:
2x ≥ 52
Dividing both sides by 2:
x ≥ 26
So the minimum height of Adriana's little brother is 26 inches.
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Cone A and cone B are mathematically similar. The ratio of the surface area of cone A to the surface area of cone B is 25:4 The volume of cone A is 6000 cm³ Work out the volume of cone B. Optional working
The volume of cone B is calculated as: 384 cm³.
How to Find the Volume of Similar Cones?If the ratio of the surface area of cone A to the surface area of cone B is 25:4, then the ratio of the radii of the cones is 5:2 (since the surface area of a cone is proportional to the square of the radius).
Since the cones are similar, the ratio of their volumes is also the ratio of the cubes of their radii, which is 125:8.
So, if the volume of cone A is 6000 cm³, then the volume of cone B is (6000 * 8) / 125 = 384 cm³.
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If you cannot show the triangles are congruent from the given information leave the triangle's name black and write CNBD for Cannot be Determined in place of the rule.
BOY=???
Step-by-step explanation:
triangle BOY is congruent with triangle MAN by ASA (angle-side-angle) : 2 angles are the same and the side between them has the same length.
that is sufficient to declare the triangles congruent.
Find the equation of the line passing through (-8,3) and (-6, 7). Write your equation in point-slope AND slope-intercept forms. Use the first point in your point-slope form!
point-slope form:
slope-intercept form:
Answer:
point-slope form: y - 3 = 2(x+8)
slope-int form: y = 2x + 19
Step-by-step explanation:
For slope-int form, find the slope of the line.
7-3 / -6-(-8) = 4/2 = 2
This becomes y = 2x + b
To find b: plug in a y-coordinate for the y in the equation and plug in an x-coordinate for the x
7 = 2(-6) + b
7 = -24/2 + b
7 = -12 + b
7 + 12 = -12 + 12 +b
19 = b
The final equation is: y = 2x + 19