Answers
Using trigonometric ratios θ = 26.57°
What is a trigonometric ratio?A trigonometric ratio is the ratio of the sides of a triangle.
To find the value of θ, we notice that in the triangle, we have the hypotenuse side and the adjacent side.
Using the trigonometric ratio cosθ = adjacent/hypotenuse
where
adjacent = 6√5 and hypotenuse = 15So, substituting the values of the variables into the equation, we have that
cosθ = adjacent/hypotenuse
= 6√5/15
= 2√5/5
= 2 × 2.236/5
= 4.472
= 0.8944
cosθ = 0.8944
θ = cos⁻¹(0.8944)
= 26.57°
So, θ = 26.57°
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Related Questions
At a large high school, 20% of the students prefer to have a salad for lunch. If you take a random sample of 10 students from this population, what is the average number who will prefer a salad for lunch?
Answers
The first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would choose a salad was 0.64.
What is probability?The idea of probability is used to calculate the possibility or probability of a specific occurrence.
It is a number between 0 and 1, where 0 indicates that the event is inconceivable and 1 indicates that it is guaranteed to happen.
Probabilities can be expressed using fractions, decimals, or percentages.
There is a 0.2 likelihood that any student will choose a salad if their lunch tastes are assumed to be independent of one another's.
If you ask the principal understudy, there is a 0.2 chance that they will answer they prefer a dish of mixed greens. You move on to the next youngster if they don't want a salad.
Because the first student didn't like the salad, there is a 0.2 chance that the second student won't either. The probability that neither of the first two students would prefer a salad was (1-0.2) (1-0.2) = 0.64.
Since none of the n-1 understudies who came before them did, the likelihood that the nth understudy would like a platter of mixed greens is only 0.2. 1-0.2n-1 is the likelihood that none of the first n-1 students will choose a salad.
Therefore, in order to identify a student who prefers salad, you must ask an expected number of students the following questions:
E(x) = 1(0.2) + 2(1-0.2)(0.2) + 3(1-0.2)2(0.2) +...
Even though this is an infinite series, by truncating it after a predetermined amount of words, we can approximate it. Let's imagine we decide to quit after ten terms:
E(x) ≈ 1×(0.2) + 2×(1-0.2)(0.2) + 3(1-0.2)²×(0.2) + ... + 10×(1-0.2)⁹ × (0.2) E(x) ≈ 2.48
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Using R-Studio, load HardyWeinberg package and find the MLE of M
allele in 206th row of Mourant dataset.
Answers
Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:
# Load HardyWeinberg package
library(HardyWeinberg)
# Load Mourant dataset
data(Mourant)
# Extract the genotype counts for the 206th row
counts <- Mourant[206, 2:4]
# Calculate the MLE of M allele frequency
mle <- hw_mle(counts)
# Extract the MLE of M allele frequency
mle_M <- mle$p[2]
Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.
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Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
help me pleaseeee im dying
The parks department held two kite contests. The tables below show the heights of the kites in each contest.
Contest 1
Kite Height (feet)
A 122
B 150
C 170
D 136
E 144
F 112
Contest 2
Kite Height (feet)
A 114
B 160
C 157
D 85
E 152
F 102
What is the difference between the ranges of the heights of the kites in the two contests?
A.
2
B.
17
C.
10
D.
22
Answers
Answer:
The range is the difference between the greatest and least values in a set of data.
For Contest 1, the greatest kite height is 170 feet and the least kite height is 112 feet, so the range is:
170 - 112 = 58 feet
For Contest 2, the greatest kite height is 160 feet and the least kite height is 85 feet, so the range is:
160 - 85 = 75 feet
The difference between the ranges is:
75 - 58 = 17 feet
Therefore, the answer is B. 17.
please help right now pleas
Answers
The area of the shape ABCD and EFGH are 64cm² and 25cm²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
Since the sides of a square are equal. The area of a square is given as;
A = l²
For square ABCD,
one grid square represents 1 square cm
Therefore ,ABCD represents 8 square centimeters.
This means the area of square ABCD is given as;
A = 8²
= 64cm²
For square EFGH,
EFGH has 5 grid squares, therefore the area of the square is given as;
A = 5²
A = 25cm²
therefore the area of squares ABCD and EFGH are 64cm² and 25cm²
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Name: 9) Henry and Jon are painting a fence. If Henry works alone, she can paint the fence in 5 hours. If Jon works alone, she will take 7 hours to paint the fence. How long will it take if they work together to paint the fence?
Answers
Answer:
Step-by-step explanation:
Find X (x=4, need work)
Answers
Based on the angle of two-tangent theorem, the value of x in the image is: x ≈ 4.
What is the Angle of Two-tangent Theorem?The angle of two-tangent theorem states that when two tangent lines intersect outside of a circle, the angle that they form has a measure equal to half the positive difference between the measures of the arcs intercepted by the angle.
Applying the theorem, we have:
70 = 1/2[(360 - 27x + 2) - (27x + 2)]
140 = 360 - 27x + 2 - 27x - 2
140 = 360 - 54x
140 - 360 = -54x
-220 = -54x
-220/-54 = x
x ≈ 4
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If the car passes point A with a speed of 20m/s and begins to increase its speed at a constant rate of At=0.5m/s^2, determine the magnitude of the car's acceleration when s=100m and x=0.path: y=16-(1/625)x^2 s=distance
Answers
The magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2[/tex] evaluated using the kinematic equation of motion.
We can use the kinematic equation of motion to determine the acceleration of the car at the given distance:
[tex]s = ut + (1/2)at^2[/tex]
where s=distance traveled, u = initial velocity, a =acceleration, and t =
time taken.
We can rewrite this equation as:
[tex]t = (2s/u)^(1/2)[/tex]
Substituting the given values, we get:
[tex]t = (2(100)/20)^(1/2)[/tex] = 2.236 seconds
Now, we can use the kinematic equation:
v = u + at
where v is the final velocity.
We know the initial velocity u is 20 m/s, and the car's acceleration At=0.5 [tex]m/s^2[/tex]. To find the final velocity, we can use the kinematic equation again:
[tex]s = ut + (1/2)at^2 + vt[/tex]
Rearranging and substituting the given values, we get:
[tex]v = (s - ut - (1/2)at^2) / t[/tex]
v = (100 - (20)(2.236) - (1/2)(0.5)(2.236)^2) / 2.236
v = 27.839 m/s
Now we can evaluate the acceleration using the equation:
a = (v-u) / t
Substituting the given values, we get:
a = (27.839 - 20) / 2.236
a = 3.49[tex]m/s^2[/tex] (rounded to two decimal places)
Therefore, the magnitude of the car's acceleration when s=100m and x=0 is 3.49 [tex]m/s^2.[/tex]
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Find the missing side lengths for
m and n #18
Answers
Answer:
m = 7√2/2
n = 7√2/2
Step-by-step explanation:
sin45 = m/7
√2/2 = m/7
m = 7√2/2
cos45 = m/7
√2/2 = m/7
m = 7√2/2
The function g(x)=8x-24 has a domain of [-5,5], Find g^-1(x).
Answers
Answer:
g(-5) = 8(-5) - 24 = -40 - 24 = -64
g(5) = 8(5) - 24 = 40 - 24 = 16
y = 8x - 24
8x = y + 24
x = (1/8)(y + 24) = (1/8)y + 3
g^-1(x) = (1/8)x + 3, -64 < x < 16
If the quotient of a number and 8 is added to 1/2, the result is 5/8. Find the number.
Answers
The quotient number is 1.
What is Quotient?
When two quantities are divided by one another, the result is a quotient. The number of times a quantity (the divisor) may be divided into a second amount (the dividend) without a remainder is known as the quotient in the division.
In order to express the given data, let's first set up the equation as follows:
(number/8) + 1/2 = 5/8
(x/8) + 1/2 = 5/8
We need to isolate the number as a variable on one side of the equation so that we can solve it.
Let's start by adding the fractions to simplify the left side of the equation:
(x/8) + 4/8 = 5/8
Next, we can combine the fractions further:
x/8 = 1/8
We can multiply both sides of the equation by 8 to find the number as follows:
number = 1
Therefore, the number is 1.
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given that F(x)=3x^2+10 what is the value of f(-2)?
Answers
F(x) = 3x^2 + 10
F(-2) = 3(-2)^2 + 10
F(-2) = 3(4) + 10
F(-2) = 12 + 10
F(-2) = 22
Therefore, the value of f(-2) is 22.
Evaluate x=50+0.35m to find the amount Mr.parker will pay if he drives 80 miles
Answers
To evaluate x=50+0.35m to find the amount Mr. Parker will pay if he drives 80 miles, we substitute m with 80 and simplify the expression as follows:
[tex]x = 50 + 0.35m[/tex]
[tex]x = 50 + 0.35(80)[/tex]
[tex]x = 50 + 28[/tex]
[tex]x = 78[/tex]
Therefore, Mr. Parker will pay $78 if he drives 80 miles.
I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull
Please help!!!!!!!!!!!
Answers
We have the reasons given as;
<4 + <3 = 180 degrees; supplementary angles
m<1 + m<2 + m<3 = 180; sum of angles in a triangle
m<1 + m<2 = m<4; substitution of equality
Angle n and n are corresponding angles
angle n + <3 are supplementary angles
How to determine the statementFirst, we need to know the following deductions;
The sum of the interior angles of a triangle is 180 degreesComplementary angles are described as pair of angles that sum up to 90 degreesSupplementary angles are described as pair of angles that sum up to 180 degreesAngles on a straight line is equal to 180 degreesLearn about angles at: https://brainly.com/question/25716982
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In rectangle ABCD, A C B D are the diagonals. A C equals 3 x plus 15 and B D equals 4 x minus 5 what is the length of AC
Answers
Upon answering the query we can say that As a result, in rectangle AC is 75 units long.
What is rectangle?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It is also known as an equiangular quadrilateral since each of its angles is equal. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with a rectangle-like form has equal parallel sides and four 90-degree vertices. Due of this, it is occasionally referred to as a "equirectangular rectangle". Due to its opposing sides' equal and parallel lengths, a rectangle is occasionally referred to as a parallelogram.
The diagonals of a rectangle are of equal length. As a result, we have:
[tex]AC = BD\\3x + 15 = 4x - 5\\15 = x - 5\\x = 20\\[/tex]
Now, we can change the equation for AC to use this value of x:
[tex]AC = 3x + 15\\AC = 3(20) + 15\\AC = 60 + 15\\AC = 75\\[/tex]
As a result, AC is 75 units long.
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3(x - 4) + 5x simplify the expression
Answers
Answer:
3(x - 4) + 5x can be simplified to 8x - 12.
Answer: 8x - 12
Step-by-step explanation:
3(x - 4) + 5x
distribute = 3x - 12 + 5x
simplify = 8x - 12
Jimmy is cleaning out his couch when he came across 31 coins. These coins were all nickels and dimes and came out to a total amount of $2.35. How many of each coin did Jimmy find?
Answers
Hence, after finding the solution, Jimmy discovered 16 dimes and 15 nickels. By assuming variables, this problem can be resolved.
Describe variables.In mathematics, a variable is a symbol or letter that designates a value of the variable or amount. Variables are fundamental to many fields of science, technology, and mathematics and are used to formulate and solve equations.
Let's use constants to depict Jimmy's discovery of nickels and dimes.
Let x be the quantity of nickels and y be the quantity of dimes.
We may create the following pair of equations using the data:
Formula 1: x + y = 31
Equation 2 reads: 0.05x + 0.10y = 2.35, which equals the total worth of the coins at $2.35.
The methods of substitution and elimination can be used to calculate the characteristics of x and y. Substitutions made
Equation 1 might be used to convert this x into units of y: x = 31 - y
In Equation 2, replace x with the following expression: 0.05(31 - y) + 0.10y = 2.35
Simplify the equation and find y as follows: 1.55 - 0.05y + 0.10y = 2.35 0.05y = 0.80 y = 16
Jimmy therefore found 16 pennies.
Equation 1 can be changed to y = 16 to determine the amount of nickels: x + 16 = 31 x = 15
Jimmy therefore discovered 15 nickels.
Jimmy discovered 16 dimes and 15 nickels as a result.
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If all nickels and dimes and came out to a total amount of $2.35. Jimmy found 15 nickels and 16 dimes.
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's assume that Jimmy found x number of nickels and y number of dimes. Then we can write two equations based on the given information:
The total number of coins is 31:
x + y = 31
The total value of the coins is $2.35:
0.05x + 0.10y = 2.35
To solve for x and y, we can use the first equation to solve for x in terms of y:
x = 31 - y
Then we can substitute this expression for x into the second equation:
0.05(31 - y) + 0.10y = 2.35
1.55 - 0.05y + 0.10y = 2.35
0.05y = 0.80
y = 16
So Jimmy found 16 dimes. To find the number of nickels, we can substitute this value of y into either of the two equations we started with. Let's use the first equation:
x + y = 31
x + 16 = 31
x = 15
Therefore, Jimmy found 15 nickels and 16 dimes.
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The equation y = 0.5x describes a proportional relationship and is shown in the graph.
graph of a line beginning at point 0 comma 0 and going through 9 comma 3
Which of the following statements is true about the graph shown?
The graph does not show a proportional relationship.
The equation y = 0.5x is correctly represented by the graph.
The graph is incorrect and the line should go through the point (0.5, 0.5).
The graph is incorrect and the line should go through the point (6, 3).
Answers
According to the given data,the equation y = 0.5x is correctly represented by the graph.
What are graphs?Graphs are visual representations of data or mathematical functions. They are useful tools for displaying and analyzing information in a clear and concise way. Graphs can be used to show trends, patterns, and relationships between different variables.
According to the given information:The statement "The equation y = 0.5x is correctly represented by the graph" is true.
The given equation y = 0.5x represents a proportional relationship between the variables x and y, where y is half of x. This means that as x increases, y increases in proportion to x.
The graph shown is a straight line that passes through the points (0,0) and (9,3), and this line represents the proportional relationship between x and y described by the equation y = 0.5x.
Therefore, the equation y = 0.5x is correctly represented by the graph.
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The function f is defined on the real numbers by f(x) = 2 + x − x2
What is the value of f(-3)?
Question 7 options:
A. 14
B. 8
C. -10
D. -4
Answers
Answer:
C
Step-by-step explanation:
f(x) = 2 + x - x²
to obtain f(- 3) substitute x = - 3 into f(x)
f(- 3) = 2 + (- 3) - (- 3)²
= 2 - 3 - 9
= - 10
Answer:
Substituting -3 in the expression for f(x), we get:
f(-3) = 2 + (-3) - (-3)^2 = 2 - 3 - 9 = -10
Step-by-step explanation:
Therefore, the value of f(-3) is -10.
Option C is the correct answer.
Jada has a scale map of Kansas that fits on a page in her book. The page is 5 inches by 8 inches. Kansas is about 210 miles by 410 miles. Select all scales that could be a scale of the map. (There are 2.54 centimeters in an inch.)
Answers
Answer:To determine the possible scales of the map, we need to calculate the ratio of the distance on the map to the corresponding distance on the ground in the actual state. We can do this using the following formula:scale = distance on map ÷ distance on groundFirst, we need to convert the dimensions of Kansas from miles to inches using a common scale factor. Since 1 mile is equal to 63,360 inches, we have:Length of Kansas: 410 miles × 63,360 inches/mile = 25,984,600 inchesWidth of Kansas: 210 miles × 63,360 inches/mile = 13,315,200 inchesNow we can calculate the possible scales of the map based on the dimensions of the page in Jada's book, which is 5 inches by 8 inches:For the length of Kansas:scale = 5 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000484scale = 8 inches ÷ (25,984,600 inches ÷ 2.54 cm/in) = 0.0000774For the width of Kansas:scale = 5 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0000962scale = 8 inches ÷ (13,315,200 inches ÷ 2.54 cm/in) = 0.0001539Therefore, the possible scales of the map are 1:20,655, and 1:10,326.
A species of fish was added to a lake. The population size P (1) of this species can be modeled by the following function, where it is the number of years from the
time the species was added to the lake.
P(t)=2000/1+6e^-0.42t
Find the initial population size of the species and the population size after 7 years.
Round your answers to the nearest whole number as necessary.
Initial population size:
Population size after 7 years:
Answers
Answer:
674
Step-by-step explanation:
Janet wants to purchase a new car. At the car dealership, a salesperson tells her she can choose from 10 car models, 7 exterior
colors, and 9 interior colors.
How many ways can Janet customize a car? Enter your answer as a whole number, like this: 425
evious
Answers
Janet has 630 options to customize a car based on the given features.
How to solve the question?
To determine the number of ways Janet can customize a car, we need to multiply the number of choices she has for each feature. Therefore, the total number of ways Janet can customize a car can be calculated as:
10 car models x 7 exterior colors x 9 interior colors = 630
Thus, Janet has 630 options to customize a car based on the given features.
It's worth noting that this calculation assumes that each feature (car model, exterior color, and interior color) can be combined with any other feature, without any restrictions or dependencies. However, in reality, certain car models may not be available in certain exterior or interior colors, or there may be other restrictions on the customization options.
Additionally, there may be other features that Janet can customize, such as the type of engine, transmission, or other options. Therefore, the total number of customization options may be even greater than what we have calculated here.
In summary, based on the given information, Janet has 630 ways to customize a car, but in reality, the actual number of options may be more limited or varied depending on other factors.
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Which point is located at (4,-2)?
Point J
Point K
Point L
Point M
I READY MATH LEVEL F
PLEASE HELP I NEED FOR TODAY
Answers
Answer:
Step-by-step explanation:
point m
(-37)+(-2) please tell quickly
Answers
Answer:-39
Step-by-step explanation:
The first thing is to open the bracket.
By doing that, the question becomes -37-2.
note that plus×minus=minus.
Hence,-39 as the final answer
Y=4/5x+25 y=4/5x+35 charge then 25$ first day and .80 for every mile the other company 35$ a day at .60 every mile how many miles would make the 2 choices equivalent
Answers
50 miles would make the two choices equivalent in cost.
What is finding the slope?The following formula is used to determine a line's slope:
slope is equal to y2 - y1 / x2 - x1.
where the two points on the line are (x1, y1) and (x2, y2). The steepness or rate of change of the line is indicated by the slope. A line with a positive slope is increasing from left to right, whereas a line with a negative slope is dropping from left to right. An undefined slope denotes a vertical line, while a slope of zero denotes a horizontal line.
To determine the choice where the two miles are equivalent we take x as the number of miles:
For the first company:
Total cost = 25 + 0.8x
For the second company:
Total cost = 35 + 0.6x
Setting the equations as equal:
25 + 0.8x = 35 + 0.6x
0.2x = 10
x = 50
Hence, 50 miles would make the two choices equivalent in cost.
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help!!!! i dont understand =0
Answers
Required value of angle CMG is 53°.
What is supplementary angle?
Supplementary angles are angles whose sum is 180 degrees. For example, an angle of 130° and an angle of 50° are cause the sum of 130° and 50° equals 180°. Similarly, complementary angles add up to 90 degrees. Two supplementary angles, when joined together, form a right and a right angle.
But it should be noted that two complementary angles do not have to be adjacent. Thus, any two angles can be supplementary angles if their sum is 180°.
Geometry is one of the important branches of mathematics that deals with the study of different shapes. This will trigger the exploration of lines and angles. A straight line is a line without curves and is defined as the shortest distance between two points. An angle is formed when line segments meet at a point.
From the figure, it is clear that value of angle DMF is 180°.
Now angle DMF = angle CMD + angle CMG + angle GMF
So, 180° = 63° + angle CMG + 64°
Angle CMG = 180° - 64° - 63° = 180° - 127° = 53°.
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Correct question is "Find the angle CMG from the given picture".
You are making the bottom of a gift box form a piece of cardboard that is 8 inches by 12 inches. To the nearest tenth of a cubic inch, what is the maximum volume of the box?
Answers
The maximum volume of the box is approximately 128.0in³.
Calculating the volume of a gift boxSince the cardboard has dimensions of 8 inches by 12 inches, the largest possible length and width of the box are both 8 inches (since 8 is the smaller of the two dimensions).
Then we can cut two 8-inch by 8-inch squares from the cardboard to make the top and bottom of the box, and then cut out four 8-inch by 2-inch rectangles from the remaining cardboard to make the sides of the box.
The height of the box will be the same as the width of the 8-inch by 2-inch rectangles, which is 2 inches. Therefore, the maximum volume of the box is:
V = l × w × h = 8 in × 8 in × 2 in = 128 in³
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Line A passes through the point (-2, 3) and is parallel to the line given by y = 4x + 9. What is the equation of line A? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
Answers
Answer:
y = 4x + 11
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x + 9 ← is in slope- intercept form
with slope m = 4
• Parallel line have equal slopes , then
y = 4x + c ← is the partial equation of line A
to find c substitute (- 2, 3 ) into the partial equation
3 = 4(- 2) + c = - 8 + c ( add 8 to both sides )
11 = c
y = 4x + 11 ← equation of line A
HEEEEELLLLPPPPP!!!! A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 19 millimeters long, and the height of the equilateral triangle is 16.5 millimeters. The pyramid's slant height is 17 millimeters. What is its surface area?
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Answers
The area of the triangular pyramid is 787.27 mm²
What is the formula for a triangular pyramid?The volume of a right-angled triangular pyramid is given by the formula V = 1 3 × B × h, where B is the area of the base of the triangle and h is the height (the distance from the apex to the base).
To calculate the area of a triangular pyramid, we need to find the area and base of the four triangles.
First, we find the area of the base of an equilateral triangle. The formula for the area of an equilateral triangle is (sqrt(3)/4)*a², where a is the side length. Substituting a=19, we get:
Area of base = (√(3)/4)*19²
= 207.39 mm²
Then we find the area of one triangular surface. We can use the formula for the area of a triangle, which is (1/2) the height of the base. The base of the triangle is the other side of an equilateral triangle with a length of 19 mm. The height of the triangle is the height of the diagonal of the pyramid, which is 17 mm. Using the Pythagorean theorem, we can find the length of the height of the triangle:
h = √ (slope² - (1/2 base)²)
= √(17² - (1/219)²)
= 15.27 mm
Thus, the area of one triangular surface is:
Area of triangle = (1/2)1915.27
= 144.97 mm²
Since there are four triangular faces, the total area of the triangular faces is:
Total area of triangular surfaces = 4 × 144.97
= 579.88 mm²
Finally, the area of the pyramid is the sum of the area of the base and the area of the four triangular sides:
Area = area of base Total area of triangular surfaces
= 207.39 + 579.88
= 787.27 mm²
Therefore the area of the triangular pyramid is 787.27 square millimeters.
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Select the postulate that states a line is determined by two points.
O Postulate 1: A line contains at least two points.
• Postulate 1a: A plane contains at least three points not all on one line.
O Postulate 1b: Space contains at least four points not all on one plane.
• Postulate 2: Through any two different points, exactly one line exists.
O Postulate 3: Through any three points that are not one line, exactly one plane exists
• Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
Postulate 5: If two planes intersect, then their intersection is a line.
Answers
The correct postulate that states a line is determined by two points is:
• Postulate 2: Through any two different points, exactly one line exists.
what is a postulate ?explain.Postulate 2 states that if you have two distinct points, you can uniquely determine a line that passes through both of them. In other words, any two points in space define a line, and there is only one line that can pass through those two points.
This postulate is a fundamental concept in Euclidean geometry, which is the study of geometry based on the work of the ancient Greek mathematician Euclid.
This postulate is often used as a basic assumption or starting point in geometric proofs and constructions. It implies that a line is uniquely defined by just two points, and any additional points on that line can be determined by extending it infinitely in both directions.
It also implies that two distinct points always lie on exactly one line, and no more than one line can pass through them.
Postulate 2 is a fundamental principle in geometry and serves as the basis for many geometric theorems and proofs.
It helps establish the relationship between points and lines in Euclidean space, and it is used to reason about the properties and behavior of lines and points in geometric constructions, proofs, and demonstrations.
therefore, The correct postulate that states a line is determined by two points is:
• Postulate 2: Through any two different points, exactly one line exists.
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