Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The data given is -
Assume a, b and c are sides of right-angled triangle.
Then, two adjacent sides of right-angled triangle are -
a^2=29.25 squared units
b^2=13 squared units
The unknown side c is taken to be x.
Find the length of c using Pythagoras Theorem -
c^2=a^2+b^2
where, c is the hypotenuse, a is the perpendicular and b is the base.
Plugging the values in the equation -
x^2=29.25+13
x=√(29.25+13)
x=√42.25
x=6.5
Therefore, the third side measures x=6.5 units.
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A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
There is no sufficient evidence at the 0.05 level to substantiate the publisher's claim
How to determine the substantial claim?The parameters for the claim is more than 47% of their readers own a personal computer0.05 level of significanceNote that the significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant
In conclusion, the advertiser failed to reject the null hypotenuse so this would mean there is not sufficient evidence at the 0.02 level of significance to say that the percentage of people who own a Rolls Royce is higher than 47%
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which answer is this
A.43
B.38
C.61
D.81
Answer:
81
Step-by-step explanation:
by corresponding angles from angle ABC
without computing, decide whether the vaule of each expresstion is much smaller than 1, close to 1, or much greater than 1
Answer: uhm...
Step-by-step explanation:
2...?
A hot air balloon is cruising at an altitude of 120 m above ground when it begins its descent the balloon descends at a rate of 4.5 m per minute explain how you would set up the equation to model when the balloon will reach an altitude of 75 m above ground then solve the equation and check your solution
The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.
The balloon will reach an altitude of 75 meters above the ground.
Now, 120-75 =45 meters
Let t be the time to descends 45 meters
So, 120 - 4.5t= 75
= -4.5 t = 75-120
= -4.5t = -45
= t = -45/(-4.5)
= t = 10 minutes
Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.
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A grocery tore ha 13%-off ale on all bread. You decide to purchae 6 loave of bread. Let b be the original price of a loaf of bread. Expand the expreion 6(b-0. 13b). Once the expreion i expanded, who do the term repreent
6b - 0.78b it will result after expanding the expression.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.
There are three different expression types:
There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.Let, b represent the original price of a loaf of bread.
Given that,
A grocery store has 13%-off sale on all bread.
This means that the amount by which the price of bread was reduced would be
13/100 × b = 0.13 × b = 0.13b
The new price for the loaf of bread would be: b - 0.13b
you decide to purchase 6 loaves of bread. The expression would be:
6(b - 0.13b)
Expanding the expression, it becomes: 6b - 0.78b
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How do you plot a graph step by step?
Plotting a graph step by step is mentioned below.
Define Graph.In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
What is Bar graph?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
There are a few steps to follow when plotting a graph:
Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.To know more about graph visit:
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Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.
Answer:
There is one unique solution (-3, 6)
Step-by-step explanation:
Desmos graphing calculator helps a lot with this stuff
Answer: b) there is only one unique solution (-3, 6)
Step-by-step explanation:
What is the correct equation for a slope of 2 and a y-intercept of -7
Answer:
y=2x-7
Step-by-step explanation:
y=mx+b ==> m is the slope and b is the y-intercept
y=(2)x + (-7) ==> plugin 2 for m=slope and -7 for b = y-intercept
y=2x-7 ==> simplify
The points (p, 6) and (4, 7) fall on a line with a slope of 1/9. What is the value of p?
Please find the missing coordinate using slope.
Step-by-step explanation:
(7 - 6)/(4 - p)= 1/9
4 - p = 9
-p= 5
p = -5
Find the explicit formula for an arithmetic sequence with a common difference of 8 and whose first term is -2.
The explicit formula of the sequence is aₙ = -10 + 8n
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
The first term and the common difference
These values of the first term and the common difference are given as
First term = -2
Common difference = 8
The interpretation of the above sequence is that the 8 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 8
When represented explicitly, we have
aₙ = a + (n - 1) * d
Where
a = -2 and d = 8
Substitute the known values in the above equation, so, we have the following representation
aₙ = -2 + (n - 1) * 8
Evaluate the products
aₙ = -2 + 8n - 8
Evaluate the like terms
aₙ = -10 + 8n
Hence, the explicit formula is aₙ = -10 + 8n
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is a(b)+a(c) the same as a(b+c)
Answer:
Yes, a(b)+a(c) is the same as a(b+c)
Step-by-step explanation:
a(b)+a(c) is the same as a(b+c). We call it distributive property in math.
Would it be possible for 3x2 to equal 1?
Answer:
no
Step-by-step explanation:
3x2=6 ;-;
Is it possible for [tex]3\times2[/tex] to equal 1?
[tex]3\times2=6[/tex]
[tex]6\neq 1[/tex]
Therefore, [tex]3\times2[/tex] DOES NOT equal to 1.
Which expression simplifies to
m-2
—— ?
m-1
I want to know how to get the GCF and LCM of 8,24,48
Answer:
GCF = 8
LCM = 48
Step-by-step explanation:
How do you check if a trinomial is a perfect square trinomial?
The binomial equation can be squared to provide an expression that is a perfect square trinomial.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
The binomial equation can be squared to provide an expression that is a perfect square trinomial.
If and only if a trinomial that takes the form ax 2 + bx + c satisfies the requirement b 2 = 4ac is considered to be a perfect square.
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Customary System Units Metric System Units 1 gallon 3.79 liters 1 quart 0.95 liters 1 pint 0.473 liters 1 cup 0.237 liters Approximately how many centiliters are in 3 quarts
3 quarts is equal to approximately 285 centilitres.
To Calculate this we have:
3 quarts is equal to 3 x 0.95 liters = 2.85 liters.
1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.
Therefore, 3 quarts is equal to approximately 285 centilitres.
In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.
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What is the use of if __ name __ == '__ main __' in Python?
The use of if__name__ == '__main__' in python is to check whether the current script is being run on its own or being imported somewhere else by combining it with if statement.
Here we need to find the use of if __ name __ == '__ main __' in Python.
Basically, in python the term Allows You to Execute Code When the File Runs as a Script, but Not When It’s Imported as a Module
Here for most practical purposes, this is known as the conditional block that you open with if __name__ == "__main__" as a way to store code that should only run when your file is executed as a script.
Therefore, the function is used as a variable defined for each script that defines whether the script is being run as the main module or it is being run as an imported module.
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How do you find the difference between two different numbers?
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.
Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.
Subtracting two integers from each other is a type of subtraction.
The process for determining the difference between two decimals and two whole numbers is the same.
We only add a new step.
Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.
To give them all the same amount of decimal places, we must first convert each decimal.
7.2 becomes 7.200 as a result.
The computation may now be done as before:
8.967 - 7.200 = 1.767
Therefore, there is a 1.767 discrepancy between these figures.
In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.
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what's the equation of a line in slope-intercept form of a line that has a slope of -6 and contains (3,-4)
HELP ME PLEASE!!!!!!
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]
55 pecans put them in 2 buckets where one has 15 more than the other
The number of pecans in each bucket will be 20 and 35.
How to illustrate the expression?From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.
In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.
This will be:
x + x + 15 = 55
2x + 15 = 55.
Collect the like terms
2x = 55 - 15
2x = 40
Divide
x = 20
The other number will be:
x + 15.
= 20 + 15
= 35
The numbers are 20 and 35.
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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.
How to read linear equations?
To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.
A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.
To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.
Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.
Once the constants, variables, and coefficients have been identified, the equation can be solved.
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What is the equation of the function
shown in the graph, given that the
equation of the parent function is
f(x) = (-/-)² ?
(}})
The equation of the function shown in the graph is f(x) = (-2x)^2.
What is function?In mathematics a function is a relation between two states that assigned to each element of the first set exactly one element of the second set in order words it is the rule that is describe how unstead of values is related to another set a values function are used to model real voice scenario and to solve mathematical problems example of function include linear equation polynomials and trigonometric function.
This is based on the equation of the parent function, which is f(x) = (-/-)^2. The graph shows that the function has been shifted two units to the left, which is why the coefficient of x is -2 instead of -1.
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In the triangle below, with right angle R, suppose that m is Angle Q=(5x-13) and m is Angle S=(4x-5) Find the degree measure of each angle in the triangle.
Answer:
Degree measure of each angle is 90⁰, 47⁰ and 43⁰
Step-by-step explanation:
since the triangle is right angled, we assume that Q and S are the other angles of this triangle R
Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰
5x - 13 + 4x - 5 = 90⁰
9x = 108
x = 12
We now replace x in Q and S to get the angles
Q = 5(12) -13
= 47⁰
S = 4(12) - 5
= 43⁰
The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 486 cars traveling east and 189 cars traveling west. What percentage of the cars were traveling east?
The percentage of cars traveling east is 28% of the total number of cars.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The commission counted 486 cars traveling east and 189 cars traveling west.
We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.
From this concept, the percentage of the cars were traveling east would be
The cars traveling east divided by the total numbers of cars time s100%.
= (189/486 + 189)×100%.
= (189/675)×100%.
= 0.28×100%.
= 28%.
So, 28% of the total cars traveling east.
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Find the value of x.
Answer:
x = 32
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
All the indicated angles in the diagram are exterior angles of the polygon.
sum the 5 exterior angles and equate to 360
2x + 71 + 85 + 44 + 3x = 360
5x + 200 = 360 ( subtract 200 from both sides )
5x = 160 ( divide both sides by 5 )
x = 32
It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
Distance between first base to home plate and from home plate to third plate are equal.
Given : It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by the third base to home plate ,and from home plate to third base.
The given situation and distance between first base to home plate and from home plate to third plate are equal.
On Converting the given situation into a geometry problem. So we name the require points.
Let A be the home plate,
B is first base,
C is the second base,
And D is the third base.
Now, we can present a geometrical proof:
Statement and their reasons
(1) BC = CD - ( Given )
(2) AC = AC - ( Reflexive Property )
(3) Δ ACD = Δ ACB - ( SAS Congruence - side angle side)
(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )
Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.
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What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both multiple of 4 and 7 is 2
What are multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.
The multiples of 4
4 8 12 16 20 24 28 32 36 .......
The multiples of 7:
7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....
The smallest common multiple is 28
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help i have 5 mins left
Answer: c = P - a - 5
Step-by-step explanation:
P= a + 5 + c
P - a - 5= c
( r - 8 ) - ( r + 15 )
Find the Sum or Difference! :)
Answer:
-23
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Answer:-23 ITS SUPER EASY:0
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
PLEASE HELPPP
what is the simplified expression for (picture below)
Answer:
[B] 6²
Step-by-step explanation:
Given:
[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]
Solve:
Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]
Now we have - [tex]\frac{6^7}{6^5}[/tex]
Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]
Subtract the exponent - [tex]6^2[/tex]
Hence, the answer is [B] 6²
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