The change in elevation of the scuba diver after 8 minutes is -24.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.
The expression (8)(2)(-1.5) represents the change in the scuba diver's elevation after 8 minutes.
To determine the change in elevation, we need to evaluate the expression.
(8)(2)(-1.5) = (16)(-1.5) = -24
Thus, the change in elevation is -24.
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Multiple Choice. 4. A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. Which of the following would result in the smallest margin of error in estimating the mean salt content, u? A. 90% confidence, n = 25 B. 90% confidence, n = 50 C. 95% confidence, n = 25 D. 95% confidence, n = 50 E. n = 100 at any confidence level 1 =
The right response is E. n = 100 at whatever degree of confidence.
We are aware that the sample size's square root and the margin of error are inversely proportional. The margin of error therefore decreases as n increases, but we also know that margin of error is proportional to the critical value, which increases as confidence level increases. However, for t and z, and for a relevant confidence level, the critical value lies between 1-3, so the sample size has the greatest impact.Because of this, choice E is the right one.
Therefore, The right response is E. n = 100 at whatever degree of confidence.
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711
Put the measures of the angles in order from least to greatest
Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]
Step-by-step explanation:
[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]
convert 549999549999 to a decimal. responses a .549.5 49 b .549.549 c 5.4955. 495 d .549
In decimal form, 549/999 is expressed as.549, which repeats.
Why do we use decimals?
One of the number types in algebra that has a whole integer and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.
Divide 549 by 999 to get the decimal equivalent of 549/999.
The solution is.549549.
Over the repeated numerals is a bar.
In decimal form, 549/999 is expressed as.549, which repeats.
In decimal form, 549/999 is expressed as.549, which repeats.
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Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).
What is the parabola?
The parabola is a smooth curve without any sharp points. It has a minimum value of a turning point called the vertex. As we can see the minimum value of this parabola is at zero, zero. That is this parabola exists only above the origin. The parabola is symmetrical about a central line called the axis of symmetry.
To represent the parabola shown in the form y = a(x-r)(x-s), we need to first identify the vertex and the axis of symmetry of the parabola.
The vertex of the parabola is (4,-4) and the axis of symmetry is x = 4.
Given that the vertex form of the parabola is y = a(x-h)² + k where (h,k) is the vertex.
Therefore, substituting the values we get:
y = a(x-4)² -4
Now, we need to find the value of a which will give us the same parabola.
If we look at the parabola, we can see that the y-coordinate of the vertex is -4 and the x-coordinate is 4.
So we substitute these values into the equation to get:
-4 = a(4-4)² -4
Solving this equation gives us a = -1
So the equation that represents the parabola is:
y = -1(x-4)² -4
which is the same as y = -1(x-4)(x-4)
thus the correct answer is d. y=-4(x-2)(x-2)
Hence, The equation in the form y = a(x-r)(x-s) to represent the parabola is d. y = -4(x-2)(x-2).
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What amounts of 35% pure silver and 40% pure silver should be mixed to obtain 14 grams of 37% pure silver? (either give EXACT answers, which are fractions, or give 5 decimal places) number of grams of 35% silver is number of grams of 40% silver is
5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37% amount of pure silver.
Let x be the number of grams of 35% silver and y be the number of grams of 40% silver.
We know that the total amount of silver is 14 grams, which is the sum of x and y. Therefore,
x + y = 14
We also know that the total amount of pure silver is 37%, which is the sum of 35% pure silver and 40% pure silver. Therefore,
0.35x + 0.40y = 0.37(x+y)
Substituting the first equation in the second equation,
0.35x + 0.40y = 0.37(14)
Solving for x and y,
x = 5.12 and y = 8.88
5.12 grams of 35% silver and 8.88 grams of 40% silver should be mixed to obtain 14 grams of 37% pure silver.
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problem 10: the various lines represent paths taken by different people walking in a city. all blocks are square and 140 m on a side. randomized variables l
The lines represent different routes taken by people walking in a city, where each block is 140m by 140m in size. The routes are determined by randomized variables, such as starting point, destination, and available pathways.
For a route that is 140m by 140m:
1. Calculate the diagonal length of the route: √2 x 140 = 196.4 m
2. Calculate the perimeter of the route: 4 x 140 = 560 m
3. Calculate the area of the route: 140 x 140 = 19600 m2
When calculating a route that is 140m by 140m, the first step is to calculate the diagonal length of the route. This is done by using the Pythagorean Theorem, which is written as √2 x 140. The result of this calculation is 196.4m. The second step is to calculate the perimeter of the route. This is done by multiplying the length of each side of the route by 4, which gives a total of 560m. The final step is to calculate the area of the route. This is done by multiplying the length and width of the route (140m x 140m), which gives a total of 19600m2. By using these calculations, one can easily measure the length, width, and area of a route that is 140m by 140m.
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declare a 2-dimensional array, , of empty arrays. all arrays are zero indexed. declare an integer, , and initialize it to . there are types of queries, given as an array of strings for you to parse: query: 1 x y let . append the integer to . query: 2 x y let . assign the value to . store the new value of to an answers array.
A dynamic array is an array with a big improvement: automatic resizing.
How does dynamic array works?A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.Explanation :
Initial Values:
n = 2
arr[0] = [ ]
arr[1] = [ ]
Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5]
arr[1] = [ ]
Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]
arr[0] = [5]
arr[1] = [7 ]
Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5, 3]
arr[1] = [7 ]
Query 3: Assign the value at index 0 to arr [( 1 ⊕ 0 ) % 2 )] = arr[1] to
Last Answer, print Last Answer.
last answer = 7
arr[0] = [5, 3]
arr[1] = [7 ]
Query 4: Assign the value at index 1 to arr [( 1 ⊕ 7 ) % 2 )] = arr[0] to
Last Answer, print Last Answer.
last answer = 3
arr[0] = [5, 3]
arr[1] = [7 ]
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this question involves the implementation of the point class which is used to represetn a single (x, y0 point
The Python program above defines the class Cse20, which is used to generate a subject.
What is meant by python program?The class Cse20, which is used to generate a subject, is defined in the preceding Python program ( instance of the Cse20 object). The getter methods, such as get length, get title, and get length in days, return a topic's length, title, and length in days, respectively, but the __str__ and __add__ methods override the topic's string object and addition of length, respectively.
class Cse20_topic:
def __init__(self, title, length):
self.title = title
self.length = length
def get_length(self):
return self.length
def get_title(self):
return self.title
def get_length_in_days(self):
return self.length*7
def __str__(self):
return f'Title: {self.title}, length: {self.length}'
def __add__(self, other):
return self.length+other.length
The complete question is:
Write the implementation of a class Cse20 Topic that represents a topic in the cse20 class. The class should implement the init function, getters, and override the str and add functions.
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Select the correct answer.
Solve the equation for x in terms of c.
(cx + 1) == //
O A.
OB.
O C.
O D.
x =
X=
x =
x =
4c
27
8c
29
18c
29
8c
The equation for x in terms of c is x = 29/8c (D).
From the case we have the equation of:
[tex]\frac{2}{3}(cx + \frac{1}{2})-\frac{1}{4}=\frac{5}{2}[/tex]
We will use distribution to isolate x on the left side and all terms of c from others on the right side.
2cx + 2 - 1 = 5
3 6 4 2
We will use the lowest common multiple to eliminate the numerator:
2cx + 2 - 1 = 5
3 6 4 2
--------------------------- x 12 --> lowest common multiple
8cx + 4 - 3 = 30
8cx + 1 = 30
8cx = 29
x = 29/8c
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evaluate f(-x)=x/x2+1
To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.
So f(-x) = (-x)/((-x)^2 + 1)
Simplifying the denominator we get:
f(-x) = (-x)/(x^2 + 1)
The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.
It's important to note that we can also express this as f(-x) = -f(x)
So the value of f(-x) is x/(x^2 + 1) with the x-value negated.
List all of the factors for each number 28
the factors for 28 are 1,2,4,7,14 and 28
What number when multipled by 1 1/4 has a product of 1?
Answer:
if we multiply 11/4 to 4/11 it gives product as 1
The length of a rectangle is represented by the expression 10.5g - 3.4k, and the width is represented by the expression
5.7k+2.4g.
Which expression represents the perimeter of the rectangle?
Remember, the perimeter of a rectangle is the sum of all four sides of the rectangle.
A. 16.2g + (-k)
B.12.9g + 2.3k
C.25.8g + 4.6k
D. 32.4g + (-2k)
The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L. The same wire can be reused to make a square, considering that all the sides are equal in length. Look at the image below showing the perimeter of a rectangular park.
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The perimeter of a rectangle is the sum of all four sides of the rectangle is 32.4g + (-2k).
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.The perimeter of a shape is defined as the total distance around the shape.
It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions. For example, imagine a triangle made of a wire of length L. The same wire can be reused to make a square, considering that all the sides are equal in length. Look at the image below showing the perimeter of a rectangular park.
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A 1.25” diameter shaft is being stretched by a load of 39,000 lb. Calculate the stress on the part.
I got 31784.84108 psi
is this correct?
It has a diameter of 1.25 inches and yield stress of 63,000 psi. Find the variable component stress.
Calculate the stress at the component?alternative the fee of weight for pressure in the formula for stress, σ = F/A, wherein F is the force and A is the vicinity of go-phase.
In easy phrases we can define pressure because the pressure of resistance per unit area, provided by means of a frame against deformation. strain is the ratio of force over area (S =R/A, in which S is the strain, R is the inner resisting force and A is the move-sectional location).
while the forces acting on the frame are trying to squash it's far compression. The method underneath is used to calculate the pressure: strain =force/ cross-sectional location. σ= F/A.
If we are about to layout a beam or a member. We need strain fee to evaluate with extraordinary pass-sectional shapes and distinct material homes to reach at a feasible section.”
Therefore, It has a diameter of 1.25 inches and yield stress of 63,000 psi.
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If it took Rachel and David 10 minutes to play a game of checkers, and they started playing at 2:25 P.M., at what time did they finish playing the game?
Answer:
2:35
Step-by-step explanation:
you are gust adding so 25 +10 = 35
need help with my math I want to make sure is correct
The value of 3.8 in mixed number and improper fraction are 3 8 / 10 and 38 / 10.
How to convert decimals to fractions?Fractions are numbers that are written in 2 parts: a numerator and a denominator. The numerator is the top value while the denominator is the bottom value.
A mixed fraction is a combination of fractions and whole number.
Let's write the decimal 3.8 as a mixed fraction and improper fraction.
Hence, as a improper fraction,
3.8 = 38 / 10
In mixed fraction,
3.8 = 38 / 10 = 3 8 / 10
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Prove that the union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other
The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other.
Let [tex]$V_1, V_2$[/tex] be two subspaces of V.
Suppose is a subspace of V.
Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and [tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]x_1+x_2 \in V_1 \cup V_2$.[/tex]
But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex].
Only the elements that are already present in the two subspaces are combined.
A subspace is formed by the union of two subspaces of a vector space, and each subspace contains the other.
Either way, by the existence of additive inverses and closure properties for subspaces we have:
[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]
Or
[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]
By associative/commutative properties we have:
[tex]x_2 \in V_1[/tex] or [tex]x_2 \in V_1[/tex]
Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex].
If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex].
If [tex]$x_2 \in V_1$[/tex] for all [tex]x_2 \in V_2[/tex] then [tex]$V_2 \subseteq V_1$[/tex].
In either case, we see one subspace is a subset of the other.
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It takes a hose 5 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 12 inches tall. How long will it take the same hose to fill an aquarium measuring 22 inches by 27 inches by 29 inches?
minutes
To find out how long it will take the hose to fill the larger aquarium, we need to compare the volume of water in each aquarium. The volume of the first aquarium is 8 x 9 x 12 = 864 cubic inches, and the volume of the second aquarium is 22 x 27 x 29 = 14,938 cubic inches. The second aquarium is 14,938 / 864 = 17.2 times larger than the first aquarium.
The time it takes to fill the first aquarium is 5 minutes, so it will take 5 x 17.2 = 86 minutes to fill the second aquarium with the same hose.
It will take 86 minutes to fill the second aquarium.
A television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off. If he paid 8% sales tax on the sale price, how much did he pay in total?
$281.88 is the total amount sam paid for television.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that television was originally priced at $522, but Sam waited to buy it until the television was on sale for 50% off.
Let us find the 50% of 522
50/100×522
0.5×522
$261
8% sales tax on the sale price
8/100×261
0.08×261
$20.88
The total he paid is $261+$20.88 is $281.88.
Hence, $281.88 is the total amount sam paid for television.
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About how fast was the car traveling at t = 10 seconds? At t = 20? At t = 30?
Answer:
Step-by-step explanation:
I'm sorry, I am missing more information to calculate the speed of the car at t = 10 seconds, t = 20 and t = 30. The speed of the car depends on the mathematical function that describes the position of the car in time. Without the knowledge of that function, I'm not able to determine the car's speed at different points in time.
A podcast host is curious how her listeners like the show. She decides to poll the next 100 listeners who send her fan emails. 80 out of 90 listeners polled said they liked it. The result may lead to
-volunteer vias
-response bias
-selection bias -non response bias
The probability result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners.
The podcast host is polling the next 100 listeners who send her fan emails in order to find out how they like the show. The results of the poll show that 80 out of 90 listeners polled said they liked it. This result may lead to selection bias, as the podcast host is only polling her next 100 fans who send emails, and not all of her listeners. This means that the results of the poll may not be reflective of the opinion of all of the podcast host's listeners. Furthermore, the results may be influenced by the volunteer bias, as the respondents may have volunteered to take part in the poll because they already liked the show and wanted to show their support. Additionally, the results may be affected by non-response bias, as those who chose not to take part in the poll may have different opinions than those who did.
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determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following: (a) 20 to 85 (b) 30 to 190 (c) 140 to 500
The appropriate interval width for a random sample of 110 observations.
a) w=1
b) w=2
c) w=2
and d) w=4
The interval width is a value that is used to divide the usage distribution into usage rate intervals.
we shall determine an appropriate interval width for a random sample of 110 observations that fall between and include each of the following.
let's start.
we are aware the formula to calculate class width.
[tex]w=\frac{L.O-S.O}{N.C}[/tex],
where,
w for width, L.O is stand for largest observation and S.O for smallest observation and N.C is number of classes.
We solve it by options.
so first come on option (a)
given interval is 20 to 85.
[tex]w=\frac{85-20}{110} \\w=\frac{65}{110} \\w=0.59[/tex]
since we need to round upward the class width, w=1
for option (b)
[tex]w=\frac{190-30}{110} \\\\w=\frac{160}{110} =1.45[/tex]
since we need to round upward the class width, w=2
for option (c)
[tex]w=\frac{230-40}{110} \\\\w=\frac{190}{110}=1.73[/tex]
since we need to round upward the class width, w=2
for option (d)
[tex]w=\frac{360}{110} =3.27[/tex]
since we need to round upward the class width, w=4,
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find four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term g
Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are [tex]7 , -28 , 112,-448[/tex].
Geometric sequence is type of sequence in which ratio of two consecutive term is equal.
Let the geometric sequence be [tex]G_{1} , G_{2} , G_{3} , G_{4}[/tex] and common ratio be [tex]r[/tex]
According to the question,
[tex]G_{1} = G_{2} + 35[/tex] (eq 1)
⇒ [tex]G_{1} = rG_{1} +35[/tex] ∵ [tex]G_{2}= rG_{1}[/tex]
⇒ [tex]G_{1} (1-r) = 35[/tex]
⇒ [tex]1-r = \frac{35}{G_{1} }[/tex]
⇒ [tex]r = 1 -\frac{35}{G_{1} }[/tex] (eq 2)
Also according to the question,
[tex]G_{3} = G_{4} + 560[/tex]
⇒ [tex]G_{3} = rG_{3} + 560[/tex]
⇒ [tex]G_{3} (1-r) = 560[/tex]
⇒ [tex]r^{2} G_{1} (\frac{35}{G_{1} } ) = 560[/tex]
⇒ [tex]35r^{2} = 560[/tex]
⇒ [tex]r^{2} = 16[/tex]
⇒ [tex]r=[/tex] ±[tex]4[/tex]
∴ [tex]r = -4[/tex] as we can see that value is decreasing at even term and at even term the power of common ration is odd.
Now putting [tex]r= -4[/tex] in eq 2 we get :
[tex]G_{1} =7[/tex]
Hence , Geometric sequence will be [tex]7 , -28 , 112,-448[/tex].
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A club has 18 girls and 12 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups the president can make?
By finding the greatest common factor between the given numbers, we conclude that the maximum number of groups will be 6.
How to find the greatest number of groups that the president can make?To find it, we just need to find the greatest common factor between the numbers of boys and girls, to find it, we will decompose these numbers as a product of prime factors.
We will get:
18 = 2*3*3
12 = 2*2*3
The greatest common factor is 2*3 = 6
That is the maximum number of groups alowed, such tthat each group will have:
18/6 = 3 girls.
12/6 = 2 boys.
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A 10 foot vertical post cast a 2 foot shadow at the same time a nearby cellphone tower cast a 116 foot shadow. How tall is the cell phone
Answer:23.2
Step-by-step explanation:
10/2=5
10/5=2
116/5=23.2
Answer:
580 ft.
Step-by-step explanation:
The height of the cellphone tower can be found using the following proportion:
(shadow of cellphone tower) / (shadow of 10 foot post) = (height of cellphone tower) / (10 feet)
Solving for the height of the cellphone tower:
(116 feet) / (2 feet) = (height of cellphone tower) / (10 feet)
Which brings us to:
116 ÷ 2 = x ÷ 10
58 = x ÷ 10
580 = x
The cell phone tower is 580 ft.
17 less than a number is at least -1
In the word problem 17 less than a number is at least -1 the number in reference is 16
What is word problem?In place of mathematical symbols, word problems are mathematical problems that are presented in everyday language. The fact that word problems must first be converted into mathematical equations and then those equations must be solved is a problem when dealing with word problems.
Word problems are mathematical problems that are presented in everyday language rather than using mathematical symbols. When dealing with word problems, it is a problem that word problems must first be transformed into mathematical equations, and then those equations must be solved.
Given
17 less than a number is at least -1, i.e.
x - 17 = -1
x = - 1 + 17
x = 16
Thus, in the word problem 17 less than a number is at least -1 the number in reference is 16.
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given the triangle below, find the length of side x. triangle is not drawn to scale. round your final answer to 4 decimal places.
The length of the x is 12 units .
What is Pythagorean theorem?The Pythagorean theorem states that in a right-angled 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. It can be written as c² = a²+ b², where c is the hypotenuse and a,b are the other two sides.
Since the given triangle is a right anlgled triangle so we will use Pythagorean theorem:
using Pythagorean theorem :
H² = P² + B²
where H is hypotenuse , P is perpendicular and B is base of the triangle
H = 13
P = 12
B = x
=> 13² = 12² + x²
=> 169 = 144 + x²
=> x² = 169- 144
=> x² =25
=> x = 5
so the value of x = 5 units
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Complete question:
given the triangle below, find the length of side x.
Please help me figure this out.
To make b the subject of the equation, we have: b = 2a + c
What is subject of formula?Subject of formula is the process expressing a required alphabet in the terms of others in a given expression. It involves the applications of arithmetic operations so as to arrive at the required answer.
Thus, rearranging the equation and make b the subject in the question, we have;
a = 1/2 (b - c)
a = (b - c)/ 2
multiply through by 2
2a = b - c
express b in terms of a and c to have;
b = 2a + c
Therefore, after rearranging the equation, b as a subject is:
b = 2a + c
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pairs in the form (h,g), where h is the
number of hours driven and g is the gallons of
gas left.
Katie after 1 hour of driving, he had 6.75 gallons of gas. Also, after 6 hours of driving, she had 1.5 gallons left.
What is linear equation?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Ax+By=C represents a two-variable linear equation in its standard form. As an illustration, the conventional form of the linear equation 2x+3y=5 It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
We can write these values as coordinate points, on the form:
As a result, the sentence: "After an hour of driving, Katie had $6.75 worth of gas." can be seen as the following:
(1,6.75)
And: "After 6 hours of driving, there was only 1.5 gallons left" will have the point:
(6,1.5)$
Part B
With this in mind, we can find the slope of a linear function that passes through those two points. Then,
[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1.5-6.75}{6-1}=\frac{-5.25}{5}=-1.05$[/tex]
Thus, the slope is -1.05.
Part C
Now, we will write a linear equation that relates[tex]$\mathrm{g}$[/tex] and[tex]$\mathrm{h}$[/tex]. As we already have the slope, we can use it to find the y-intercept as:
[tex]$$y=m x+b$$[/tex]
[tex]$g=m h+b$[/tex]Writing it with the variable[tex]s $\mathrm{g}$[/tex]and [tex]$\mathrm{h}$[/tex].
[tex]$$1.5=(-1.05)(6)+b$$[/tex]
[tex]1.5+6.3=b \\[/tex]
7.8=b
This means that an equation for g in terms of h is given by:
[tex]$$g=-1.05 h+7.8$$[/tex]
Part D
For this portion, we will apply the linear equation we discovered for calculating how much gas she will still have after a three-hour drive. Thus, h will have a value of 3, and we replace on the function to get the following result:
[tex]g=-1.05(3)+7.8 \\[/tex]
=-3.15+7.8
=4.65
This means that Katie will have 4.65 gallons left after driving for 3 hours.
The complete question is,
Katie noticed that after 1 hour of driving, she had 6.75 gallons of gas. After 6 hours of driving, there was only 1.5 gallons left. (Hint: Leave your answers as decimals). A.) Represent the information as two coordinate pairs in the form of (h, g), where h is the number of hours driven and g is the gallon of gas left. B.) Calculate the slope between the two coordinates. C.) Assuming the relationship between h and g is linear, create an equation for g in terms of h. D.) How much gas would she have left after dving for 3 hours?
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g) h) i) 2x. x w/f X + < 5 3 2 a+20 3a + 2 3 3x+2 12 2 3 4x-1 1/4-x)
The answer to the equation X + 5 3 2 a + 20 3 a + 2 3 3x + 2 12 2 3 4x-1 1/4-x is [tex]33 x-\frac{1}{4}$$[/tex] .
What is the basic rule for solving any equation?Simplify [tex]$34 x-1 \cdot \frac{1}{4}-x: \quad 33 x-\frac{1}{4}$[/tex]
[tex]$$34 x-1 \cdot \frac{1}{4}-x$$[/tex]
like phrases together
[tex]$$=34 x-x-1 \cdot \frac{1}{4}$$[/tex]
Add comparable elements: [tex]34 x-x=33 x$[/tex]
[tex]$$=33 x-1 \cdot \frac{1}{4}$$[/tex]
Multiply: [tex]$1 \cdot \frac{1}{4}=\frac{1}{4}$[/tex]
[tex]=33 x-\frac{1}{4}$$[/tex]
Both the addition rule and the multiplication/division rule are introduced to us in algebra 1 as the two rules for solving equations. According to the equation addition rule, an equation's solution set can be changed by adding the same amount to either side of an equation without doing so.
Identification, prioritisation, and selection of potential solutions are all steps in the process of problem solving, which also involves characterising the issue at hand, figuring out its root cause, and putting a plan of action into action. Algebraic Golden Rule: "Do unto one side of the equal sign as you will unto the other."
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