The radius and height that maximize the volume of the cone with a slant height of 12 are both 6√2.
To maximize the volume of a cone with a slant height of 12, we need to find the dimensions (radius and height) that give the maximum volume. Use this formula to get the volume of a cone:
[tex]V = 1/3 * \pi * r^2 * h[/tex]
where r and h represents radius ad height respectively.
From the problem statement, we know that the slant height s of the cone is 12. We can use the Pythagorean theorem to relate the height h, radius r, and slant height s:
[tex]s^2 = r^2 + h^2[/tex]
Substituting s = 12, we get:
[tex]12^2 = r^2 + h^2[/tex]
[tex]144 = r^2 + h^2[/tex]
We want to maximize the volume V, so we need to express it in terms of just one variable. We can use the equation relating r, h, and s:
[tex]s^2 = r^2 + h^2[/tex]
Solving for [tex]h^2[/tex], we get:
[tex]h^2 = s^2 - r^2[/tex]
Substituting s = 12, we get:
[tex]h^2 = 144 - r^2[/tex]
Now we can express the volume V as a function of just one variable, r:
[tex]V = 1/3 * \pi * r^2 * h[/tex]
[tex]V = 1/3 * \pi * r^2 * \sqrt{(144 - r^2)[/tex]
To find the maximum volume, we need to take the derivative of V with respect to r, set it equal to zero, and solve for r:
[tex]dV/dr = 1/3 * \pi * (2r * \sqrt{(144 - r^2)} - 2r^3 / \sqrt{(144 - r^2)})[/tex]
[tex]dV/dr = \pi r / 3 * (2\sqrt{(144 - r^2)} - 2r^2 / \sqrt{(144 - r^2)})[/tex]
Setting dV/dr = 0, we get:
[tex]2\sqrt{(144 - r^2)} - 2r^2 / \sqrt{(144 - r^2)} = 0[/tex]
[tex]2(144 - r^2) - 2r^2 = 0[/tex]
[tex]288 - 4r^2 = 0[/tex]
[tex]r^2 = 72[/tex]
So the radius that maximizes the volume is [tex]r = \sqrt{(72)} = 6\sqrt{(2)[/tex]. To find the height h, we can use the equation [tex]h^2 = 144 - r^2[/tex]:
[tex]h^2 = 144 - (6\sqrt{(2)})^2 = 72[/tex]
[tex]h = \sqrt{(72)} = 6\sqrt{(2)[/tex]
Therefore, the dimensions (radius and height) that maximize the volume of the cone with a slant height of 12 are [tex]r = 6\sqrt{(2)[/tex] and [tex]h = 6\sqrt{(2)[/tex].
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The complete question is:
What are the dimensions (radius and height) of all right circular cones with a slant height of 12 that maximize the cone's volume? The cone's slant height is the distance from the outer edge of the base to the vertex.
ASAP!!! ITS URGENT
What is the difference in perimeters between a rectangle with a length of 9 m and a width of 5 m, and a regular pentagon with a side of 5 m?
Answer:
3cm
Step-by-step explanation:
Perimeter is the boundary or outer line of a shape
Rectangle has 4 sides.
2 sides of top and bottom, being the same size
And 2 sides of left and right sides being the same size.
Perimeter of Rectangle = 9+5+9+5 = 28
Regular Pentagon has 5 equal sides.
So perimeter is: 5+5+5+5+5 = 25
Difference is biggest take away smallest
Therefore 28-25 = 3
Answer = 3cm
Find the measurement of angle B.
By Pythagorean Theorem, Cos⁻¹( 12/√153) is the value of angle B.
What is Pythagorean theorem in math?
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the total of the squares on the legs.
The theorem is named after the Greek mathematician Pythagoras, who is often credited with discovering it, despite the fact that the theorem's existence probably definitely existed before him.
AB² = AC² + BC²
= 12² + 3²
= 144 + 9
= √153
Cosθ = 12/√153
θ = Cos⁻¹( 12/√153)
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Help please!!!!!!!!!!!!!!!!!!!!!!!
Answer:
30°
Step-by-step explanation:
All angles add up to 180°
x + 4x + 30 = 180
Combine like terms
5x + 30 = 180
Isolate the x ( subtract 30 from both sides)
5x = 150
Divide both sides by 5
x = 30°
a certain basketball player makes a foul shot with probability 0.45. what is the probability that (a) his first basket occurs on the sixth shot; (b) his first and second baskets occur on his fourth and eighth shots, respectively?
The probability of making a basket on the sixth shot is 0.075. The probability that the first and second baskets occur on the fourth and eighth shots is 0.031.
For the first shot to be on the sixth trial, five earlier shots must have failed.
The probability of a missed basket is 1 - 0.45 = 0.55.
The probability of five missed baskets in a row is (0.55)5 = 0.166.
The probability of making a basket on the sixth shot is 0.45.
Hence, the probability of making a basket on the sixth shot is 0.45 * 0.166 = 0.075.
There are a few possible ways to get the first and second baskets to happen on the fourth and eighth shots, respectively.
In the end, either of the following two paths will work:
4 failures, then 2 successes, then 2 failures
3 failures, then 1 success, then 1 failure, then 1 success, then 2 failures
Using the multiplication rule, we get the following probabilities for each course:
P(4 failures, 2 successes, 2 failures) = (0.55)4 * (0.45)2 * (0.55)2
= 0.018
P(3 failures, 1 success, 1 failure, 1 success, 2 failures) = (0.55)3 * (0.45) * (0.55) * (0.45) * (0.55)2
= 0.013
The probabilities of the two possible routes must be summed up to arrive at the answer.
Hence, the probability that the first and second baskets occur on the fourth and eighth shots, respectively, is 0.018 + 0.013 = 0.031.
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A 3-yard roll of brown paper costs $0.74. What is the unit price, rounded to the nearest cent?
Answer:
$0.25
Step-by-step explanation:
To find the unit price = total cost ÷ number of . units
So unit price= 0.74 ÷ 3
Unit price = $0.24666666667 per yard
Rounding this to the nearest cent y8ges
Unit price = $0.25 per yard
Therefore the unit price rounded to the nearest tenth is $0.25
When Braxton walks from art class to math class, he usually stops at his locker. The distance from his art classroom to his locker is 95 feet, and the distance from his
locker to his math classroom is 112 feet. What is the range of possible distances from art class to math class if he takes the hallway and goes directly between the
classrooms?
The possible distances from art class to math class range from approximately 161.3 feet to 351.3 feet.
What is Pythagoras Theorem?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
If Braxton walks directly between his art class and math class, then the distance he covers is the shortest distance between the two classrooms, which is the length of the straight line connecting the two points.
We can use the Pythagorean theorem to find this distance:
d = √(95² + 112²) ≈ 144.3 feet
Therefore, the shortest possible distance between the two classrooms is approximately 144.3 feet.
To find the range of possible distances from art class to math class, we need to consider the distance Braxton covers if he stops at his locker.
We can use the triangle inequality to say that the distance between the two classrooms when Braxton stops at his locker must be greater than or equal to the difference between the distance from art class to the locker and the distance from locker to math class:
d ≥ |95 - 112| = 17 feet
So the distance between the two classrooms when Braxton stops at his locker must be at least 17 feet greater than the shortest distance between the two classrooms.
Therefore, the range of possible distances from art class to math class is:
144.3 + 17 ≤ d ≤ 144.3 + (95 + 112) = 351.3 feet
Hence, the possible distances from art class to math class range from approximately 161.3 feet to 351.3 feet.
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8. Find the lower, middle, and higher quartile: 5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19 lower:
middle:
higher:
Answer:
Step-by-step explanation:
To find the lower, middle, and higher quartiles of the given data set, we need to first order the data from lowest to highest:
5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19
The total number of values in the set is 12, so the middle value (or the median) will be the average of the 6th and 7th values:
Median = (9 + 10) / 2 = 9.5
To find the lower quartile (Q1), we take the median of the lower half of the data set, which includes the first six values:
Lower half: 5, 6, 7, 8, 9, 10
Q1 = median of the lower half = (7 + 8) / 2 = 7.5
To find the higher quartile (Q3), we take the median of the upper half of the data set, which includes the last six values:
Upper half: 12, 14, 15, 17, 18, 19
Q3 = median of the upper half = (15 + 17) / 2 = 16
Therefore, the lower quartile is 7.5, the middle quartile is 9.5, and the higher quartile is 16.
Please answer these two questions:
1. The amount A, in milligrams, of a 10-milligram dose of a drug remaining in the body
reduces at a rate of 20%. Find, to the nearest tenth of an hour, how long it takes for
half of the drug dose to be left in the body.
2. After t years, the rate of depreciation of a car that costs $20,000 is 25%. What is the value of the car 2 years after it was purchased?
show work please!!
so if the inital amount in the body is 10mg, so half that will just be 5mg, so how long will that be?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & 5~mg\\ P=\textit{initial amount}\dotfill &10~mg\\ r=rate\to 20\%\to \frac{20}{100}\dotfill &0.2\\ t=hours\dotfill &t\\ \end{cases}[/tex]
[tex]5 = 10(1 - 0.2)^{t} \implies \cfrac{5}{10}=0.8^t\implies \cfrac{1}{2}=0.8^t\implies \log\left( \cfrac{1}{2} \right)=\log(0.8^t) \\\\\\ \log\left( \cfrac{1}{2} \right)=t\log(0.8)\implies \cfrac{\log\left( \frac{1}{2} \right)}{\log(0.8)}=t\implies \stackrel{ \textit{about 3 hrs and 6 mins} }{3.1\approx t}[/tex]
7. Your meal at a diner costs $24. You use a 20% off coupon. After discount, a 7% sales tax is applied. How much do you pay after tax?
Answer: 20.64 dollars i think.
Step-by-step explanation: 20 percent of 24 is 4.8, so 24-4.8= 19.2
Then, 7 percent of 19.2 is 1.44. The answer is 20.64 dollars I think.
please help! properties of logarithms
Recall a couple properties of logarithms.
log(ab) = log(a) + log(b)
log(a/b) = log(a) - log(b)
So, [tex]log_{12}(\frac{\frac{1}{2}}{8w})=log_{12}(\frac{1}{2})-log_{12}(8w)=log_{12}(\frac{1}{2})-(log_{12}(8)+log_{12}(w))[/tex]
need help asap ill give 100 points simplify the radicals
Answer:
8d[tex]\sqrt{e}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
given
[tex]\sqrt{25d^2e}[/tex] - [tex]\sqrt{d^2e}[/tex] + 2[tex]\sqrt{4d^2e}[/tex]
evaluating each term separately
[tex]\sqrt{25d^2e}[/tex]
= [tex]\sqrt{25}[/tex] × [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]
= 5 × d × [tex]\sqrt{e}[/tex]
= 5d[tex]\sqrt{e}[/tex]
-------------------
[tex]\sqrt{d^2e}[/tex]
= [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]
= d × [tex]\sqrt{e}[/tex]
= d[tex]\sqrt{e}[/tex]
-------------------
[tex]\sqrt{4d^2e}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{d^2}[/tex] × [tex]\sqrt{e}[/tex]
= 2 × d × [tex]\sqrt{e}[/tex]
= 2d[tex]\sqrt{e}[/tex]
-----------------------
then combining them gives
5d[tex]\sqrt{e}[/tex] - d[tex]\sqrt{e}[/tex] + 2(2d[tex]\sqrt{e}[/tex])
= 4d[tex]\sqrt{e}[/tex] + 4d[tex]\sqrt{e}[/tex]
= 8d[tex]\sqrt{e}[/tex]
Find the probability that the spinner lands on a multiple of 3 or a dark green region. Give your
simplest form.
Answer: "A. 3/8"
Step-by-step explanation:
STEP 1: Determine the probability the spinner lands on a multiple of 3. To do this, write out the numbers on the spinner (1-8), and cross out every non-multiple of three (1, 2, 4, 5, 7, 8), this will leave the numbers 3 and 6 unmarked. This being said, 2/8 (1/4) of the numbers on the spinner are multiples of 3.
STEP 2: Determine the probability the spinner lands in a dark green region. In order to do this, write the numbers on the spinner out (1-8), and circle every number representing a dark green region (1, 3, 5, 7). This should leave four numbers (2, 4, 6, 8) un-circled, meaning 4/8 (1/2) of the numbers represent a dark green region.
STEP 3: Add the two answers together (1/4 + 1/2), and you should get the answer 3/8 (A).
NOTE: When adding fractions, make sure they have the same denominators. For example, in this problem, changing 1/2 to 2/4, and doing 1/4 + 2/4, instead of 1/4 + 1/2.
Abc is an isosceles triangle. Ab is the longest side with the length 8x+5. Bc= 4x+4 and ca = 3x+9. Find ab
The length of side AB of the isosceles triangle is 8x + 5.
The formula for finding the length of a isosceles triangle side is given by:
Length of side = √x² + y²
Where x and y are the lengths of the other two sides.
To find the length of the side AB, we need to first calculate x and y. We know that BC = 4x + 4 and CA = 3x + 9.
Therefore, [tex]x = BC - CA = 4x + 4 - 3x - 9 = x + -5[/tex]
And [tex]y = CA - BC = 3x + 9 - 4x - 4 = -x + 5[/tex]
Substituting these values in the formula, we get:
Length of side AB = √((x + -5)² + (-x + 5)²)
= √((x² + 25) + (x² + 25))
= √(2x² + 50)
= √(2(8x + 5)²)
= √(16x2 + 80x + 25)
= 8x + 5
Therefore, the length of side AB is 8x + 5.
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Write the slope-intercept form of the equation of the line that is perpendicular to AB and passes through
Point X. Show all work for full credit.
A
(-10, 8)
-10
-8
X
(-5, 10)
-6
-4 -2
YA
10
8
4
2 B
-2
4
6
-8
-10
(2, 3)
2
4
6 8 10
X
A
Answer:
To find the slope of line AB, we use the slope formula:
slope of AB = (yB - yA) / (xB - xA)
where A = (-10, 8) and B = (2, 3).
slope of AB = (3 - 8) / (2 - (-10)) = -5/12
The slope of a line perpendicular to AB will have a negative reciprocal slope, so its slope will be 12/5.
Using the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept, we can find the equation of the line that passes through point X (-5, 10) and has a slope of 12/5.
10 = (12/5)(-5) + b
10 = -24/5 + b
b = 74/5
Therefore, the equation of the line that is perpendicular to AB and passes through point X is:
y = (12/5)x + 74/5
The grams of fiber from 1,000 different breakfast cereals sold in the United States were collected.
Which graphical representation would be most appropriate for the data, and why?
Bar chart, because the data is categorical
Histogram, because there is a large set of data
Stem-and-leaf plot, because you can see the shape of the data
Line plot, because you can see the mode of the data
Given the variety of morning cereals sold, option B. Histogram is the graphical representation that would be best suitable for the data. This is because there is a large set of data.
Why do histograms get utilised for big data sets?Because they offer a visual depiction of the data distribution, histograms are utilised for big collections of data. They are especially helpful for figuring out how continuous variables, like measurements or time series data, are distributed.
Histograms have a number of benefits, one of which is the simplicity with which massive sets of data may be compared. It is simple to see the overall shape of the distribution and spot trends or outliers when the data are represented as bars. Histograms can also be used to compare many sets of data simultaneously, making it simple to compare various groupings or changes over time.
Histograms also have the advantage of allowing for the identification of a dataset's underlying probability-distribution, which is advantageous for statistical analysis and modelling.
This is why, due to the size of the data and the fact that it includes information from 1,000 distinct grains, a histogram works best to display it.
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Answer:
Histogram, because there is a large set of data
Step-by-step explanation:
Hope this helps :)
Which of the following is divisible by 8? 9731 9641 9632
Answer:
Which of the following is divisible by 8?
9731
9641
96329832 ÷ 8
= 1229
Step-by-step explanation:
You're welcome.
Answer:
The answer to your question is 9632.
Step-by-step explanation:
9731 ÷ 8 = 1216.375 ← Uneven
9641 ÷ 8 = 1205.125 ← Uneven
9632 ÷ 8 = 1204 ← Even
I hope this helps and have a wonderful day!
the city’s sports team asked katie to make 30 larger pennants to hang in the city’s sports dome. if the pennants have a base of 2 meters what is the area of one of the larger pennants
If the pennants have a base of 2 meters, the area of one of the larger pennants is 4m².
What is area of a rectangle?It is determined by multiplying the length of the rectangle by its width. The formula for area of a rectangle is Area = Length × Width (A = L × W).
To calculate this, we can use the formula for area of a rectangle which is length multiplied by width.
In this case, the length and width of the pennant is both 2 meters, so we can calculate the area by multiplying 2m * 2m= 4m².
The sports team asked Katie to make 30 larger pennants, so the total area of all the pennants will be 120m² (4m² * 30).
This means that the total area of the 30 larger pennants is 120m².
The formula for area of a rectangle can be used to calculate the area of any shape that is rectangular in nature.
Therefore, it can be used to calculate the area of a pennant, or any other shape that is rectangular in nature.
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if the variance of a distribution is 16, the mean is 12, and the number of cases is 24, the standard deviation is select one: a. 4 b. 6 c. 8 d. 12
The standard deviation is (a).4
Given that the variance of a distribution is 16, the mean is 12, and the number of cases is 24.
A standard deviation (SD) is a measure of how dispersed the data is in relation to the mean. Whereas, variance is a measure of how data points differ from the mean.
The formula for variance can be expressed as the square of the standard deviation (SD). Therefore, the formula for standard deviation is the square root of the variance.
SD = sqrt(variance)
SD = sqrt(16)
SD = 4
Hence, the standard deviation for the given data is 4.
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Simplify 4-2y + (-8y) + 6.2
Answer:
[tex]\large\boxed{\tt -10y + 10.2 }[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to simplify the given expression.}[/tex]
[tex]\textsf{Note that we can't simplify this expression down to 1 term.}[/tex]
[tex]\large\underline{\textsf{Why?}}[/tex]
[tex]\textsf{This is due to 2 numbers having the variable y, and 2 other numbers without y.}[/tex]
[tex]\textsf{Consider these terms Unlike Terms, as they have a difference in which we can't}}[/tex]
[tex]\textsf{combine them.}[/tex]
[tex]\textsf{Even though there are some Unlike Terms, there is a few Like Terms.}[/tex]
[tex]\textsf{Let's identify the Like Terms, and the Unlike Terms in our expression.}[/tex]
[tex]\large\underline{\textsf{Like Terms;}}[/tex]
[tex]\tt 4 \ and \ 6.2 \ are \ like \ terms. \ (Both \ don't \ have \ any \ variables)[/tex]
[tex]\tt -2y \ and \ -8y \ are \ like \ terms. \ (Both \ have \ the \ same \ variable)[/tex]
[tex]\large\underline{\textsf{Unlike Terms;}}[/tex]
[tex]\tt 4 \ and \ -2y \ are \ Unlike \ Terms.[/tex]
[tex]\tt 6.2 \ and \ -8y \ are \ Unlike \ Terms.[/tex]
[tex]\tt 4 \ and \ -8y \ are \ Unlike \ Terms.[/tex]
[tex]\tt 6.2 \ and \ -2y \ are \ Unlike \ Terms.[/tex]
[tex]\textsf{We know what the Unlike Terms, and Like Terms are for our expression.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Solve by combining Like Terms in the expression.}[/tex]
[tex]\large\underline{\textsf{Combine Like Terms;}}[/tex]
[tex]\tt 4-2y + (-8y) + 6.2[/tex]
[tex]\textsf{When we add a negative term, we are actually subtracting with that term.}[/tex]
[tex]\tt 4-2y -8y + 6.2[/tex]
[tex]\underline{\textsf{Our final answer should be;}}[/tex]
[tex]\large\boxed{\tt -10y + 10.2 }[/tex]
Answer:
[tex] \sf \: -10y + 10.2[/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ 4 - 2y + (-8y) + 6.2
Let's simplify the expression,
→ 4 - 2y + (-8y) + 6.2
→ 4 - 2y - 8y + 6.2
→ -2y - 8y + 6.2 + 4
→ (-2y - 8y) + (6.2 + 4)
→ (-10y) + (10.2)
→ -10y + 10.2
Hence, answer is -10y + 10.2.
Use the same syllable pattern to create an original haiku about the term line
Straight path without bends,
A line connects points in space,
End to end it goes.
A line is a fundamental concept in geometry and is defined as a straight, one-dimensional figure with no thickness or width that extends infinitely in both directions. Lines can be drawn and measured, and they play a crucial role in many geometric and mathematical concepts, including angles, shapes, and equations. In addition to being a key concept in mathematics, lines are also used in art, design, and architecture. In art, lines can be used to create shapes, texture, and movement, while in design and architecture, lines are used to create structure, define space, and create a sense of balance and proportion.
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Complete question:
Use the same syllable pattern to create an original haiku about the term line.
Create a proportion from each set of numbers ONLY use 4 numbers from each set:
1) 66, 99, 8, 11, 6, 88
2) 45, 14, 25, 35, 19, 10
3) 5, 48, 12, 18, 1, 4
4) 9, 45, 13, 75, 25, 5
5) 72, 9, 84, 12, 6, 54
The proportions from each set of numbers are 66:99, 45:14, 5:48.
What is proportion?A proportion is a statement that two ratios are equal. In other words, it is a way to compare two quantities or numbers using a fraction or ratio.
According to question:Here are the proportions using 4 numbers from each set:
1) 66:99 = 8:12
2) 45:14 = 25:7
3) 5:48 = 1:9
4) 9:45 = 1:5
5) 72:9 = 8:1
For example, if we say that the ratio of boys to girls in a classroom is 2:3, we can write the proportion as:
boys/girls = 2/3
Proportions are useful in many different areas, including mathematics, science, and statistics. They can be used to solve problems involving ratios, percentages, and other types of numerical relationships. In statistics, proportions are often used to represent the proportion of individuals in a population who have a certain characteristic or attribute, such as a disease or a trait.
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Using the distance formula √(x₂ - x₁)² + (y₂ - y₁)² , find the distance from the center of your habitat to the point (x, y). Write this equation. Your answer will contain x- and y-terms. (1 point)
The distance from the center of the habitat, located at (10, 4.25), to any point (x,y), is given as follows:
[tex]D = \sqrt{(x - 10)^2+(y - 4.25)^2}[/tex]
How to obtain the distance between two points?Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the distance from any point (x,y) to point (10, 4.25) is given as follows:
[tex]D = \sqrt{(x - 10)^2+(y - 4.25)^2}[/tex]
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h/6 - 1 = -3
what does h equal
Answer:
h=-12
Step-by-step explanation:
h/6 -1 =-3
h/6= -2
h=-12
Answer:
[tex]\tt h=-12[/tex]Step-by-step explanation:
[tex]\tt \cfrac{h}{6}-1=-3[/tex]
Add 1 to both sides:-
[tex]\tt \cfrac{h}{6}-1+1=-3+1[/tex]
[tex]\tt \cfrac{h}{6}=-2[/tex]
Multiply both sides by 6:-
[tex]\tt \cfrac{6h}{6}=6\left(-2\right)[/tex]
[tex]\tt h=-12[/tex]
________________________
Hope this helps!
Can you find the answer please?
The measure of the angle between the two planes is given as follows:
66.1º.
What is the law of cosines?The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:
c^2 = a^2 + b^2 - 2ab cos(C)
The side opposite to the angle is of 241 km, hence the parameters are given as follows:
c = 241, a = 207, b = 233.
Then the angle measure is obtained as follows:
241² = 207² + 233² - 2 x 207 x 233cos(C)
96462cos(C) = 207² + 233² - 241²
96462cos(C) = 39057
cos(C) = 39057/96462
cos(C) = 0.4049
C = arccos(0.4049)
C = 66.1º.
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A set of equations is given below: Equation C: y = 6x + 9 Equation D: y = 6x + 2 Which of the following best describes the number of solutions to the given set of equations? (1 point) One solution No solution Two solutions Many solutions
Answer:
Step-by-step explanation:
No solution.
The two equations represent two different lines with the same slope (6), but different y-intercepts (9 for equation C and 2 for equation D). Since lines with different slopes will intersect at one point, and these two lines have the same slope but different y-intercepts, they are parallel and will never intersect. Therefore, there are no solutions to the system of equations.
help please I’ll mark brainliest!
A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles and they are equal.
B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y.
C. y = 24, ∠7 = 89° and ∠8 = 89°
How to classify the relationship between ∠7 and ∠8?Angle geometry deals with the study of angles, their measurement, and their properties. An angle is formed when two lines or line segments intersect each other at a point.
A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles. Since vertically opposites angles are equal, we can say ∠7 = ∠8.
B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y
C. 5y-29 = 3y+19
5y-3y= 19 + 29
2y = 48
y = 48/2
y = 24
Let's find either the value of 5y-29 or 3y+19:
Put y = 24 in 5y-29
5y-29 = 5(24) - 29 = 91°
∠7 + (5y-29) = 180° (sum of angles on a straight line is 180°)
∠7 + 91° = 180°
∠7 = 180 - 91 = 89°
Since ∠7 = ∠8
∠8 = 89°
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Find the number of sides of a polygon if the sum of the measures of its interior angles is twice the sum of the measures of its exterior angles.
The number of sides of the polygon is equal to the sum of the interior angles divided by the sum of the exterior angles, multiplied by two.
The number of sides of a polygon can be determined by examining the measures of its interior and exterior angles. The sum of the measures of the interior angles of the polygon is twice the sum of the measures of the exterior angles. Therefore, the number of sides of the polygon can be calculated by dividing the sum of the interior angles by the sum of the exterior angles and then multiplying that result by two. This is because the number of interior and exterior angles in a polygon are directly related. The sum of the interior angles is always equal to (n-2) times 180 degrees, where n is the number of sides of the polygon. Likewise, the sum of the exterior angles is always equal to 360 degrees. Therefore, the number of sides of the polygon is equal to (sum of the interior angles divided by the sum of the exterior angles) multiplied by two.
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Please! Help me! What do I graph?
Answer:
look below i promise its the answer
Someone please solve for x
Answer:
x = 154°
Step-by-step explanation:
Given information,
→ The line l & m are parallel to each other.
Now we have to,
→ Find the required value of x.
We know that,
→ Parallel lines are equal to each other.
Forming the equation,
→ x + 26° = 180°
Then the value of x will be,
→ x + 26° = 180°
→ x = 180° - 26°
→ [ x = 154° ]
Hence, the value of x is 154°.
A table of values for an exponential function is
shown.
X
y =
0
1
2
3
4
Y
10
5
2.5
1.25
0.625
Write the equation for the function shown in the table
by typing values in the blank spaces.
) x
One possible equation for the function shown in the table is:
y = 10 * (0.5)^x
This equation represents an exponential function with a base of 0.5 (i.e. each value is half of the previous value) and an initial value of 10 (i.e. y = 10 when x = 0).
To verify this equation, we can plug in the x-values from the table and see if we get the corresponding y-values:
- When x = 0: y = 10 * (0.5)^0 = 10 * 1 = 10 (matches the table)
- When x = 1: y = 10 * (0.5)^1 = 10 * 0.5 = 5 (matches the table)
- When x = 2: y = 10 * (0.5)^2 = 10 * 0.25 = 2.5 (matches the table)
- When x = 3: y = 10 * (0.5)^3 = 10 * 0.125 = 1.25 (matches the table)
- When x = 4: y = 10 * (0.5)^4 = 10 * 0.0625 = 0.625 (matches the table)
Therefore, the equation y = 10 * (0.5)^x represents the function shown in the table.
Hope this helps if can