Answers
Answer:
150
Step-by-step explanation:
the formula for this is 2a squared + 4 a h
when we plug everything in we end up getting 2*3 squared + 4*3*11
and when solved it gets toy 150
Related Questions
Write the equation of the line, in slope-intercept form, with the
following information:
rate of change: undefined
point: (-3,2)
Answers
y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
Thus, The most "popular" type of a straight line is one with a slope-intercept. Due of its simplicity, this is helpful to a lot of kids.
The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
You may learn how to determine the equation of a line from any two points that this line passes through using the slope intercept form calculator.
Continue reading to find out what a linear equation's slope intercept form is, how to calculate a line's equation, and the significance of the slope intercept form equation in practical applications.
Thus, y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
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A health store sells two different sized square granola bars. the side length of the smaller granola bar, C(x), is modeled by the function C(x)=1/4 square root x +2, where x is the area of the larger granola bar in square inches. which graph shows C(x)
Answers
The graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Option C
The function C(x) = (1/4)√x + 2 represents the side length of the smaller granola bar, where x is the area of the larger granola bar in square inches. To determine which graph shows C(x), we need to analyze the characteristics of the function.
First, let's consider the behavior of the function C(x) = (1/4)√x + 2:
Square Root Function: The term √x indicates that the function involves the square root of x. This means that as x increases, C(x) will also increase, but at a decreasing rate.
Scaling Factor: The coefficient (1/4) scales the square root of x. It affects the steepness of the function and causes C(x) to increase more slowly compared to a simple square root function.
Vertical Shift: The constant term (+2) shifts the entire function vertically upward by 2 units. This means that the graph will be raised by 2 units compared to a standard square root function.
Based on these characteristics, we can conclude that the graph of C(x) will be an increasing curve with a flattened slope compared to a simple square root function, and it will be shifted upward by 2 units.
Among the answer choices, the graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Without the actual graphs provided, it is difficult to specify the exact choice, but it should exhibit these features described above.
It is essential to refer to the available graphs or visually analyze the functions to determine the correct graph that shows C(x). Option C is correct.
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The additional growth of plants in one week are recorded for 11 plants with a
sample standard deviation of 3 inches and sample mean of 10 inches.
t at the 0.05 significance level = Ex: 1.234
Margin of error = Ex: 1.234
Confidence interval = [ Ex: 12.345 Ex: 12.345 ]
[smaller value, larger value]
Answers
1. The t-value of the data is 1.833
2. The margin of error is 1.66
3. The confidence interval is between 11.66 to 8.34
What is the margin of error?From the question given;
sample size = 11
sample mean = 10 inches
standard deviation = 3 inches
1.The t-value of the data with a degree of freedom equal to 10 at 0.05 significance level = 1.833
2. Using the formula below, the margin of error is;
[tex]ME = t * \frac{SD}{\sqrt{n} }[/tex]
ME = margin of errort = t-valueSD = standard deviationn = sample sizeSubstituting the values into the formula above;
ME = 1.833 * 3/√11
ME = 1.66
3. The confidence interval of the data is;
CI = mean ± ME
where CI is the confidence interval, mean is the sample mean, and ME is the margin of error. In this case, the confidence interval is calculated as follows:
CI = 10 +/- 0.96 = 9.04 to 10.96 inches
CI = 10 ± 1.66 = 11.66 to 8.34
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
ABC forms a right-angled triangle
Let the distance between AB = x
Using Pythagoras theorem
Sin 30 = Opposite / Hypoteneuse
Sin 30 = 12 in/ x
However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.
Using Pythagoras' theorem, Sin 30 = 1/ 2
Substituting back into the equation, we get:
1/ 2 = 12 in / x
Cross multiplying, we get:
x = 24 in
Recall x = AB
AB = 24 inches
To remember the angles and their respective formula, use SOHCAHTOA
Where sin x = Opposite / Hypoteneuse
Cos x = Adjacent / Hypoteneuse
Tan x = Opposite / Adjacent
The support beams of truss bridges are triangles. James made a model of a truss bridge with a scale of 1 inch = 4 feet. If the height of the tallest triangle on the model is 9 inches, what is the height of the tallest triangle on the actual bridge?
Answers
The height of the tallest triangle on the actual bridge is 12 feet.
If James made a model of a truss bridge with a scale of 1 inch = 4 feet, we can use this information to find the height of the tallest triangle on the actual bridge.
Let x be the height of the tallest triangle on the actual bridge. Since the scale of the model is 1 inch = 4 feet, the height of the tallest triangle on the model can be converted to feet by multiplying by 4. Therefore, the height of the tallest triangle on the model is:
9 inches * (1 foot / 12 inches) * 4 = 3 feet
We can use the similarity of triangles to set up a proportion to find x. The corresponding sides of similar triangles are proportional. In this case, the height of the triangle on the model corresponds to the height of the triangle on the actual bridge, and the scale factor from the model to the actual bridge is 1/4 (since 1 inch on the model represents 4 feet on the actual bridge). Therefore, we have:
height of triangle on model / height of triangle on actual bridge = scale factor
3 feet / x = 1/4
Multiplying both sides by x, we have:
3 feet = (1/4) x
Multiplying both sides by 4, we have:
12 feet = x
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(-20,13) (16,15)
Can some find the slop for this question
Answers
Slope (m) = (y2 - y1) / (x2 - x1)
Given the points (-20, 13) and (16, 15), we can assign the coordinates as follows:
x1 = -20, y1 = 13
x2 = 16, y2 = 15
Now, we can substitute these values into the slope formula:
Slope (m) = (15 - 13) / (16 - (-20))
= 2 / 36
= 1 / 18
Therefore, the slope of the line passing through the points (-20, 13) and (16, 15) is 1/18.
A rectangular room is tiled with tiles 1
2
inches long and 1
2
inches wide. If the room is L tiles long and W tiles
wide, find the room’s area, in square inches.
Answers
The room’s area, in square inches is,
⇒ A = 144LW square inches.
We have to given that,
A rectangular room is tiled with tiles 12 inches long and 12 inches wide.
And, The room is L tiles long and W tiles wide.
Hence, Lenght of L tiles,
= 12L
And, Length of W tiles,
= 12W
Since, We know that,
Area of rectangle is,
⇒ A = Length x width
Substitute given values, we get;
⇒ A = 12L x 12W
⇒ A = 144LW square inches.
Therefore, The room’s area, in square inches is,
⇒ A = 144LW square inches.
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Find the probability of not rolling factors of 5 on both dice
Answers
The probability of not rolling factors of 5 on both dice is 25/36
Calculating the probability of not rolling factors of 5 on both diceFrom the question, we have the following parameters that can be used in our computation:
Rolling two number cubes
Using the above as a guide, we have the following:
Sample space, S = {1, 2, 3, 4, 5, 6}
In the above sample space, we have
Not factors of 5 = {1, 2, 3, 4, 6}
So, we have
P(Not rolling factor of 5) = 5/6 * 5/6
Evaluate
P(Not rolling factor of 5) = 25/36
Hence, the probability is 25/36
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Question
Two six sided dice are rolled.
Find the probability of not rolling factors of 5 on both dice
If you are traveling 14 miles per hour, how many inches would you travel in 3 seconds? (1 mile = 5280 feet; 1 foot = 12 inches) (Convert 3 seconds to inches)
Answers
1 mile = 5280 feet
1 foot = 12 inches
First, let's convert the speed from miles per hour to inches per hour:
14 miles/hour * 5280 feet/mile * 12 inches/foot = 14 * 5280 * 12 inches/hour
Next, we need to convert hours to seconds since we want the distance traveled in 3 seconds:
(14 * 5280 * 12 inches/hour) * (1 hour/3600 seconds) = 14 * 5280 * 12 * 1/3600 inches/second
Now, we can calculate the distance traveled in 3 seconds:
Distance = Speed * Time = (14 * 5280 * 12 * 1/3600 inches/second) * 3 seconds
Simplifying the expression:
Distance = (14 * 5280 * 12 * 3) / (3600) inches
Calculating the value:
Distance = 7392 inches
Therefore, if you are traveling at a speed of 14 miles per hour, you would travel 7392 inches in 3 seconds.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
a^2 = b^2 + c^2 - 2(b)(c)cosx
In this case we need to find the angle of f, so for a we use the length f is. It’s set up like this:
30^2 = 20^2 + 25^2 -2(20)(25)cosx
Next multiple and simply everything
900 = 1025 -1000cosx
Now subtract 1025
-125 = -1000cosx
Divide by -1000 to get cosx by itself
.125 = cosx
Now take the inverse of cos
Cos^-1 (.125)
And you get 82.8 or 83
So the answer should be A
Hope that helps. Lmk if there are questions.
a triangle has angle measurements of 51 89 and 40 what kind of triangle is it?
(20 points, please answer quick)
Answers
The correct classification for this triangle is an acute triangle.
How to solveThe angle measures given are 51, 89, and 40 degrees.
There are no angles that are either equal to or greater than 90 degrees among those mentioned. Consequently, the triangle does not contain any angles that are either right or obtuse.
To categorize a triangle according to its angles, the total of the angles within the triangle, which is invariably 180 degrees, is taken into account.
51 + 89 + 40 = 180
Given that the total of the angles is 180 degrees, we can deduce that this particular triangle is acute in nature. An acute-angled triangle is a type of triangle that has three angles which are each smaller than 90 degrees.
Therefore, the correct classification for this triangle is an acute triangle.
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The following number is a BASE-7 NUMBER. Convert this to a base 10 number and enter your answer in the box.
463421
(Remember, the above number is in Base 7!)
Number in base 10:
Answers
The base 10 equivalent of the base 7 number 463421 is 83174.
To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum up the results.
For the number 463421 in base 7:
= 4 x 7⁵ + 6 x 7⁴ + 3 x 7³ + 4 x 7² + 2 x 7¹ + 1 x 7⁰
= 4 x 16807 + 6 x 2401 + 3 x 343 + 4 x 49 + 2 x 7 + 1 x 1
= 67228 + 14406 + 1029 + 196 + 14 + 1
= 83174
Therefore, the base 10 equivalent of the base 7 number 463421 is 83174.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer: D
Step-by-step explanation: -135
1. What will the coordinates of Triangle RST be after it is translated 4 units down and 3 units left?
--5-5
R
Da
4
64
5-
4
3-
bo
24
4
10
=arpy 5
-3
--5-
1 2 3 4 5 6 x
O Re(-7,-2), Sc(2, -1), Tc(-1,-9)
ORE(-1,-2), Sc(8,-1), Tc (5,-9)
ORE(-1,6), Sc(8,7), TC(5, -1)
O Re(-7,-2), Sc(8,-1), Tc(-1,-1)
Answers
The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;
R¢(-7, -2), S¢(2, -1), T¢(-1, -9)
What is a translation transformation?A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.
The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)
The translation transformation that is applied on the triangle RST includes;
A vertical translation 4 units downwards
An horizontal translation 3 units to the left
The translation transformation is therefore; T₍₋₃, ₋₄₎
Therefore, applying each transformation, we get;
R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)
S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)
T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)
The correct option is therefore, the first option
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These shapes are similar.
Find X.
X
5
9
27
15
21
Answers
The value of X is 7.
Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.
To find the value of X such that given numbers are in pattern.
The next three number are three times of first three numbers respectively.
Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.
Consider the given set of numbers, X, 5, 9, 9 × 3, 5 × 3, 21.
By using the data and the pattern set gives,
3X = 21.
Divide by 7 on both sides,
X = 7.
Hence, the value of X is 3
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The side lengths of ABC are AB = 12, BC= 19, and AC = 11. List the
angles of the triangle in order from smallest to largest.
Answers
The angles of the triangle are ordered as follows:
<B, <C and <A.
What is the law of sines?We consider a triangle with side lengths and angles related as follows:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
By the law of sines, we have that the greater angle measures are opposite to the greater side lengths.
Hence the angle measures for this problem are ordered as follows:
<B -> opposite to AC = 11.<C -> opposite to AB = 12.<A -> opposite to BC = 19.More can be learned about the law of sines at https://brainly.com/question/4372174
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The angles of triangle ABC is arranged below
angle b - smallest
angle c
angle a - largest
How to arrange the measure of the anglesTo determine the angles of triangle ABC in order from smallest to largest, we can use use the knowledge that the side with higest length will face the largest angle.
Let the angles be
angle c is opposite AB = 12
angle b is opposite AC = 11
angle a is opposite BC = 19
Using the knowledge as introduced we have that
angle a > angle c > angle b
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What is the meaning of "we call a class R an n-ary relation if all its elements are n-tuples"?
Answers
The statement is saying that a class R is considered an n-ary relation if all its elements are n-tuples.
The symbol R⊂Vⁿ represents that the class R is a subset of Vⁿ, which is the class of all n-tuples.
Here, Vⁿ represents the set of all possible n-tuples, and R is a subset of that set.
The notation Cⁿ is used to denote the set of n-tuples with elements from the set C, and C×D represents the Cartesian product of sets C and D.
The statement defines an n-ary relation as a class where all its elements are n-tuples, and it establishes a connection between the class R and the set of all n-tuples (Vⁿ).
The notation Cⁿ and C×D are used to describe sets of n-tuples and Cartesian products, respectively, in a mathematical context.
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Enter the number that belongs in the green box. 4 51° 109°
Answers
The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.
What is the length of the longest side?It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.
Consequently, it follows from the sine law that;
4 / sin 20° = x / sin 109°
x = 4 sin 109° / sin 20°
x = 11.06.
Ultimately, the number that belongs in the green box is; 11.06.
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Which graph shows the solution set for -4.421.6x-3.6?
←++
-3
←++
-3
-2 -1 0
←+++
-7
-2
-1 0
-7 -6 -5 -4
-6 -5 -4
1
1
-3
♡
2
2
3
-2
3
-2 -1
-1
Answers
The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:
Add 3.6 to both sides of the inequality to isolate the term with x:
-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6
-0.8 ≥ 1.6x
Divide both sides of the inequality by 1.6
-0.8 / 1.6 ≥ 1.6x / 1.6
-0.5 ≥ x
So, the solution to the inequality is x ≤ -0.5.
Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....
Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
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For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle.
Answers
The angles in the triangle are as follows:
∠X = 58°
Exterior angle of ∠X = 122°
How to find the angle of a triangle?The sum of angles in a triangle is 180 degrees. The sum of the exterior angle and the interior angle of a triangle is 180 degrees.
Therefore, let's find the measure of ∠X in the triangle XYZ.
Hence,
m∠X = (2g + 16)°
The exterior angle of m∠X measures 4g + 38 degrees.
Hence,
2g + 16 + 4g + 38 = 180
6g + 54 = 180
6g = 180 - 54
6g = 126
g = 126 / 6
g = 21
Therefore,
∠X = (2(21) + 16)° = 42 + 16 = 58 degrees
Exterior angle of ∠X = 4(21) + 38 = 84 + 38 = 122
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Show your work HELPPPP DUE TOMORROW!!
Answers
Answer:
10
Step-by-step explanation:
[tex]2\frac{3}{8}[/tex]+[tex]1\frac{3}{4}[/tex]+[tex]5\frac{7}{8}[/tex]=
[tex]2\frac{3}{8} +1\frac{6}{8} +5\frac{7}{8}[/tex]=
[tex]8\frac{16}{8} =10[/tex]
Need some help on this question!!!!!
Answers
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
We have,
To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.
The volume of a cube-shaped package:
The side length of the cube-shaped package is 1/4 feet.
The volume of a cube is given by V = s³, where s is the side length.
Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.
The volume of the part of the truck being filled:
The dimensions of the rectangular prism-shaped part of the truck are:
Length = 8 feet
Width = 6(1/4) feet = 6.25 feet
Height = 7(1/2) feet = 7.5 feet
The volume of a rectangular prism is given by V = length × width × height.
Therefore, the volume of the part of the truck being filled is:
8 × 6.25 × 7.5
= 375 cubic feet.
To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:
= 375 cubic feet / (1/64 cubic feet)
= 375 × 64
= 24000 packages.
Therefore,
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
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help please show work
Answers
The slope of line AD will be 4/3
Given,
ABCD is a square.
AB ⇒ y = -3/4 x + 7
Now,
AB is straight line.
Straight line equation ⇒ y =mx + c
m = slope of line
c = y intercept
Here,
m = -3/4 ( slope of line AB )
Now for slope of line AD,
ABCD is a square. Thus AB and AD are perpendicular to each other.
According the relation,
[tex]m_{1} m_{2} = -1[/tex]
[tex]m_{1}[/tex] = slope of line 1
[tex]m_{2}[/tex] = slope of line 2
So,
-3/4 [tex]m_{2}[/tex] = -1
[tex]m_{2}[/tex] = 4/3.
Hence slope of AD is 4/3 .
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(3a - 5b)(, + 5b)(a ^ 2 + ab - b ^ 2)
Answers
The solution after resolving into factors are,
⇒ 8 (a - 3b) (a - b)
We have to given that,
Resolve into factors the expression,
⇒ (3a - 5b)² - (a + b)²
Now, We can simplify for resolving the factors as,
⇒ (3a - 5b)² - (a + b)²
Since, WE know that,
⇒ x² - y² = (x - y) (x + y)
Hence,
⇒ (3a - 5b)² - (a + b)²
⇒ [(3a - 5b) - (a + b)] [ (3a - 5b) + (a + b)]
⇒ [3a - 5b - a - b] [4a - 4b]
⇒ (2a - 6b) (4a - 4b)
⇒ 2 (a - 3b) × 4 (a - b)
⇒ 8 (a - 3b) (a - b)
Thus, The solution after resolving into factors are,
⇒ 8 (a - 3b) (a - b)
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A set of twins purchase a small, oddly shaped plot of land for their retirement. They want to divide the parcel along the grid lines into two identical plots. Can they do it and how?
Answers
The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.
To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.
For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.
If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.
However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.
To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.
If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.
the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.
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Note the full question may be :
To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.
Define the variables
Answers
a. The variables are x and y which represents 2 shots and 3 shots respectively.
b. The system of equations are;
x + y = 11
2x + 3y = 29
What are the variables to this problem?a. Let's define the variables to write the system of equations:
Let x be the number of two-point shots Noah made.
Let y be the number of three-point shots Noah made.
b. We can write a system of equations that model this problem.
Equation 1: x + y = 11
This equation represents the total number of shots Noah made, which is 11.
Equation 2: 2x + 3y = 29
This equation represents the total number of points Noah scored, which is 29. Since each two-point shot is worth 2 points and each three-point shot is worth 3 points, we can multiply the number of two-point shots (x) by 2 and the number of three-point shots (y) by 3 and sum them up to get the total score of 29.
The system of equations that can be used to determine the number of two-point shots Noah made and the number of three-point shots he made is:
x + y = 11
2x + 3y = 29
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Un atleta parte desde el reposo en una competencia al cabo de 30 segundos su velocidad es de 2m/s ¿cuál es la aceleración del atleta?
Answers
The required acceleration is 0.0666 [tex]m^{2}[/tex]/s.
Given that the velocity of the object is 2m/s and time is 30s.
Acceleration is the rate of change of velocity with respect to time.
To find the acceleration by using the formula.
acceleration (a) = velocity (v) / time (t).
By using data and formula gives,
acceleration (a) = velocity (v) / time (t).
acceleration (a) = 2 / 30
acceleration (a) = 0.0666 [tex]m^{2}[/tex]/s.
Hence, the required acceleration is 0.0666 [tex]m^{2}[/tex]/s.
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What is the equation for this line?
Answers
y=2/3x-4 is the equation of the line where 2/3 is the slope.
We have to find the equation of line which is passing through points (0, -4) and (3, -2).
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁.
Slope = -2+4/3-0
=2/3
Now let us find the y intercept.
-4=2/3(0)+b
b=-4
The equation of line is y=2/3x-4.
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P(-1; -1) S(-3; -7) Q(4; 2) R(7; -5) Determine (correct to one decimal place): 3.2 3.1 the acute angle between QR and the x-axis the angle of inclination of PQ POR 3.3 3.4 the angle of inclination of SP 3.5 SPR 3.6 PSR.
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1. Acute angle between QR and the x-axis:
The angle between QR and the x-axis can be found by calculating the arctan of the slope of QR. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1).
Given points Q(4, 2) and R(7, -5):
m(QR) = (-5 - 2) / (7 - 4) = -7/3
Using the arctan function, we can find the acute angle (A1):
A1 = arctan(-7/3) ≈ -68.2 degrees
2. Angle of inclination of PQ:
The angle of inclination of PQ can be found using the same method as above with points P(-1, -1) and Q(4, 2):
m(PQ) = (2 - (-1)) / (4 - (-1)) = 3/5
The angle of inclination (A2) can be found by taking the arctan of the slope:
A2 = arctan(3/5) ≈ 30.96 degrees
3. Angle of inclination of POR:
The angle of inclination of POR can be found using points P(-1, -1) and R(7, -5):
m(POR) = (-5 - (-1)) / (7 - (-1)) = -6/8 = -3/4 = -0.75
The angle of inclination (A3) can be found using the arctan function:
A3 = arctan(-0.75) ≈ -36.87 degrees
4. Angle of inclination of SP:
To find the angle of inclination of SP, we can use points S(-3, -7) and P(-1, -1):
m(SP) = (-1 - (-7)) / (-1 - (-3)) = 6/2 = 3
The angle of inclination (A4) can be found using the arctan function:
A4 = arctan(3) ≈ 71.57 degrees
5. Angle SPR:
To find angle SPR, we can use the Law of Cosines. Using the distance formula, we can find the lengths of sides SP, SR, and PR. Let's denote SP as a, SR as b, and PR as c:
a = sqrt((-3 - (-1))^2 + (-7 - (-1))^2) = sqrt(4^2 + 6^2) = sqrt(52) ≈ 7.21
b = sqrt((-3 - 7)^2 + (-7 - (-5))^2) = sqrt(10^2 + 2^2) = sqrt(104) ≈ 10.2
c = sqrt((-1 - 7)^2 + (-1 - (-5))^2) = sqrt((-8)^2 + 4^2) = sqrt(80) ≈ 8.94
Now we can apply the Law of Cosines to find the angle SPR (A5):
cos(A5) = (a^2 + b^2 - c^2) / (2ab)
A5 = arccos((7.21^2 + 10.2^2 - 8.94^2) / (2 * 7.21 * 10.2)) ≈ 42.1 degrees
6. Angle PSR:
To find angle PSR, we can subtract the angle SPR (A5) from the angle of inclination of SP (A
100 Points! Multiple choice geometry. Photo attached. Thank you!
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8. Option (A) is correct as line XB is a radius
9. Option (D) is correct as line BD is a tangent line
What is the radius and tangent of the circleThe radius is the straight line from the center of the circle to the circumference and according to the tangent to a circle theorem, a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
8. The only option that represents a radius is the line from the center X to the point B on the circle circumference.
9. The line from the point B to the point D is called is a tangent to the circle
Therefore, line XB is a radius and line BD is a tangent line.
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