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
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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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]
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.
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
You have a 1
-gallon paint can in the shape of a cylinder. One gallon is 231
cubic inches. The radius of the can is 3
inches. What is the approximate height of the paint can? Use 3. 14
for pi
The formula [tex]V = \pi r^2h[/tex] is used to find the height of a 1-gallon paint can with radius 3 inches, which is approximately 7.81 inches.
The formula for volume of a cylinder:
[tex]V = \pi r^2h[/tex]
where V,r and h are the volume, radius, and height respectively.
In this problem, we are given that the can has a volume of 231 cubic inches, which means:
[tex]231 = \pi r^2h[/tex]
We are also given that the radius of the can is 3 inches, so we can substitute this value into the equation:
[tex]231 = \pi (3^2)h[/tex]
Simplifying, we get:
231 = 9πh
Dividing both sides by 9π, we get:
h = 231 / (9π)
We can simplify this expression by using the approximation π ≈ 3.14:
h = 231 / (9 × 3.14)
h ≈ 7.81
Therefore, the approximate height of the paint can is 7.81 inches.
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The sum of the probabilities in the distribution is .
The sum of probabilities in a distribution always equals 1, as it ensures all possible outcomes have a certainty of 100%. It is a fundamental rule in probability, and deviations suggest issues with the distribution.
The sum of probabilities in a probability distribution always equals 1 because probabilities represent the likelihood of an event occurring, and it is certain that some event will occur. In other words, the total probability of all possible outcomes must add up to 100% or 1.
For example, if we flip a coin, the probability of getting heads is 0.5 and the probability of getting tails is also 0.5. The sum of these probabilities is 1, which means that one of these events is certain to happen when the coin is flipped.
If the sum of probabilities is not equal to 1, then it means that there is something wrong with the distribution, such as a missing outcome or an incorrect probability assignment. Therefore, it is a fundamental rule of probability that the sum of probabilities in a distribution always equals 1.
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Complete question: Why should the sum of the probabilities in a probability distribution always equal to 1?
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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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.
for continuous random variables, the probability of any specific value of the random variable is one. true or false
The given statement "for continuous random variables, the probability of any specific value of the random variable is one." is false because the random variable taking on any specific value is then given by the area under the PDF curve at that value, which is zero.
In fact, for continuous random variables, the probability of any specific value is zero. This may seem counterintuitive at first, but it is a fundamental property of continuous random variables.
The PDF is a function that describes the relative likelihood of the random variable taking on a particular value within its range. The probability of the random variable taking on a specific value is then given by the area under the PDF curve at that value.
Since the PDF is a continuous function, the probability of the random variable taking on any specific value is zero. This is because the area under a continuous curve at any single point is zero.
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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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Two lines intersect to form a linear pair of congruent angles. The measure of one angle is (8x+10) and the measure of the other angle is (15y/2). Find the values of x and y.
The values of the variable x and y are x = 10 and y = 12.
What is intersection?In mathematics, the intersection of two or more lines refers to the point or points at which the lines meet or cross each other.
When two lines intersect, they form two pairs of opposite angles that add up to 180 degrees. If one pair of opposite angles is congruent, then their measures are equal.
Let's call the measure of the congruent angles a. Then we have:
a = 8x + 10 (the measure of one angle)
a = 15y/2 (the measure of the other angle)
Since these angles are congruent, their measures must be equal. So we can set the two expressions for a equal to each other:
8x + 10 = 15y/2
8x = 15y/2 - 10
x = ( 15y/2 - 10) / 8 ................. equation 1
To solve for x and y, we need another equation. We know that the sum of the measures of the two angles in a linear pair is 180 degrees. So we can write:
a + a = 180
Substituting the expressions for a, we get:
8x + 10 + 15y/2 = 180
Substituting x = ( 15y/2 - 10) / 8 into the expression we found for y, we get:
8( 15y/2 - 10) ÷ 8 + 10 + 15y/2 = 180
15y/2 - 10 + 10 + 15y/2 = 180
15y/2 + 15y/2 = 180
30y = 360
y = 12
Substituting y = 12 into the expression we found for x,
x = ( 15y/2 - 10) / 8
= ( 15 × 12 /2 - 10) / 8
= (15 × 6 - 10)/8
= 80/8
= 10.
Therefore, the values of x and y are x = 10 and y = 12.
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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]
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°.
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°
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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The line plot displays the cost of used books in dollars.
Cost of Used Books
5
Cost in Dollars
Which measure of center is most appropriate to represent the data in the graph, and why?
O The median is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are no outliers present.
O The median is the best measure of center because there are outliers present.
O The mean is the best measure of center because there are outliers present.
Based on the line plot display, A, the most appropriate measure of center to represent the data in the graph is the median because there are no clear outliers present.
Why is median an appropriate measure?Median is an appropriate measure of center when there are outliers present in the data. Outliers are extreme values that are much larger or smaller than the rest of the data, and they can greatly affect the mean. In such cases, the median is a better measure of center because it is not affected by outliers.
Outliers can skew the mean, making it an unreliable measure of center in this case. The median, on the other hand, is less affected by outliers and provides a more representative measure of the central tendency of the data.
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Complete question:
The line plot displays the cost of used books in dollars.
Which measure of center is most appropriate to represent the data in the graph, and why?
O The median is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are no outliers present.
O The median is the best measure of center because there are outliers present.
O The mean is the best measure of center because there are outliers present.
What is the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2
Answer:
x^2 - x - 6 = 0
Step-by-step explanation:
If the quadratic equation has solutions 3 and -2, then it can be factored as:
(x - 3)(x + 2) = 0
Expanding the left side of the equation, we get:
x^2 - x - 6 = 0
This is the quadratic equation that has a leading coefficient of 1 and solutions 3 and -2.
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]
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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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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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
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!
a rectangular field is to have an area of 900 and is to be surrounded by a fence. the cost of the fence is 14 dollars per meter of length. what is the minimum cost this can be done for?
The minimum cost of fencing the rectangular field with an area of 900 square meters is approximately $2,375.15.
Let's solve for one variable in terms of the other using the area equation:
l x w = 900
l = 900/w (by dividing both sides by w)
Now we can substitute this expression for "l" into the perimeter equation:
P = 2l + 2w
P = 2(900/w) + 2w
P = (1800/w) + 2w
To minimize P, we can take the derivative with respect to w and set it equal to zero:
dP/dw = -1800/w² + 2 = 0
Solving for w, we get:
w = √(1800/2) = 30√(2)
We can now use this value of w to find the corresponding value of l from the area equation:
l = 900/w = 900/(30√(2)) = 30√(2)
Therefore, the dimensions of the rectangular field that require the least amount of fencing while still having an area of 900 square meters are l = 30√(2) meters and w = 30√(2) meters.
The total length of fencing required is:
P = 2l + 2w
P = 2(30√(2)) + 2(30√(2))
P = 120√(2)
The minimum cost of the fence can be found by multiplying the total length of fencing by the cost per meter of fencing:
Cost = 14 x P = 14 x 120√(2) = 1680√(2) dollars = $2,375.15.
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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.
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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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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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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6. If m R = 28°, find m O. The figure is not drawn to scale. (1 point)
152°
28°
62°
56°
The measure of ∠O is 56°. The solution has been obtained by using properties of circles.
What is a circle?
A circle is a round-shaped figure that has no sides or edges. A circle is a closed shape, a two-dimensional shape, and a curved shape in geometry.
We are given that m∠R = 28°.
Now, we take a point P on the circumference of the circle.
We know that in a circle, the angles that the same arc subtends on the circumference have equal measurements.
So, both the angles i.e. ∠P and ∠R are same as they are subtended by the same arc.
Therefore, we get
m∠P = m∠R = 28°
Moreover, an arc's angle at the circle's centre is twice as large as its angle at the circle's edge.
So, from this we get
⇒ m∠O = 2 * m∠P
⇒ m∠O = 2 * 28°
⇒ m∠O = 56°
Hence, the measure of ∠O is 56°.
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