Q. 10. Prove that the sum of the (interior) angles of a pentagon is 540°.
using geometry**
- Like line segments, ray XY, angles etc
please don't answer with (n-2)180 formula.
answer related to proving by lines and angles
like - <ABC + <BCA + <CAB = 180° etc...
Answers
Answer:
Step-by-step explanation:
The answer is that yes it is because a pentagon has three triangles inside it and a triangle is equal to 180 degrees so you times 180 times three and you get 540 degrees so yes that is correct!
Related Questions
Paing through (3, 4) and perpendicular to the line whoe equation i y=1/9x8; lope-intercept form
Answers
The equation of the line passing through (3, 4) and perpendicular to the line y=1/9x + 8 in slope-intercept form is y = -9x + 31
Suppose we have two lines with slope m₁ and m₂ respectively, then those lines are perpendicular to each other if
m₁ x m₂ = -1
In the given problem, the line is perpendicular to a line whose equation is:
y = 1/9 x + 8
Hence,
m₁ x m₂ = -1
1/9 x m₂ = -1
m₂ = -9
Therefore, the equation of the second line is:
y = -9x + b
To find the value of b, we use the fact that the line passing through (3,4)
Substitute x = 3, and y = 4
4 = -9 (3) + b
b = 4 + 27 = 31
Thus, the equation of the line is:
y = -9x + 31
Your question is incomplete, but most probably your question was:
Find the equation of the line passing through (3, 4) and perpendicular to the line whose equation is y=1/9x + 8 in slope-intercept form.
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One week, 100 tudent purchaed item from the tudent tore and the tore made a profit of $500. The next week, when 80 tudent purchaed item, the profit wa $460. Write a linear equation relating profit, to the number of tudent,
Answers
A linear equation relating profit, to the number of student is shown below.
y = 2x + 500
Linear equation is used to present the elements in mathematic. A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.
To write a linear equation relating profit to the number of students, we need to find the slope and the y-intercept of the line.
The slope of the line can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
In this case, we can use the two data points given to find the slope:
slope = (460 - 500) / (80 - 100) = -40/ -20 = 2
The y-intercept of the line is the point where the line crosses the y-axis, which is the profit when the number of students is 0. In this case, the y-intercept is 500, since that is the profit when 100 students purchase items.
Using these values, we can write the linear equation in slope-intercept form:
y = 2x + 500
This equation can be interpreted as follows: the profit (y) is equal to 2 times the number of students (x) plus 500.
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Work out the base of a square with area,
A
= 64cm2.
Answers
Answer: 8cm
Step-by-step explanation:
Square root 64 to get 8
Answer:
8cm
Step-by-step explanation:
A base is either the length or the width of the square (doesn't matter because square has 4 equal lengthed sides). To find the area from the base, square it. To find the base from the area, square root it (inverse operations.)
[tex]\sqrt{64cm^2}[/tex]
8cm
4
The volume of a spherical balloon (V=4/3pir^3) is increasing at a constant rate of 0.78 inches per minute. At the instant when the radius is 3.20 inches, the radius is
increasing at a rate of…
Answers
The rate at which the radius is increasing is; 0.006 in/min
How to find the rate of increase of radius?We are given that the formula for the volume of a spherical balloon is;
V = ⁴/₃πr³
where r is the radius
The volume is increasing at the constant rate of 0.78 inches per minute. Thus;
dV/dt = 0.78
Now, differentiating with respect to t gives;
dV/dt = ⁴/₃(3πr²)(dr/dt)
At radius of 3.2 inches, we have;
0.78 = 4π * 3.2² * dr/dt
dr/dt = 0.78/(4π * 3.2²)
dr/dt = 0.006 in/min
This is therefore the rate at which the radius is increasing.
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Use the long division method to find the result when 8x³ +26x² + 25x + 6 is divided by 2x + 3.
Answers
Answer:
(4x^2 +7x + 2)
Step-by-step explanation:
(8x³ +26x² + 25x + 6)/( 2x + 3)
(8x³ +26x² + 25x + 6) = (4x^2 +7x + 2)(2x + 3)
(4x^2 +7x + 2)(2x + 3)/(2x+3) = (4x^2 +7x + 2)
Winter coat are marked 70% off on February 1t if a coat cot 57. 75 on January 31t how much will it cot on February 1t
Answers
The price of the winter coats is going to be $17.325.
what is marked price?The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price.
given,
Marked Price of winter coats = $57.75 and discount = 70%
Discount = 70%
57.75 × 70/100
5.775 × 7
40.425
Selling Price = M.P - Discount
57.750 - 40.425
17.325
therefore ,
The price of the winter coats is going to be $17.325.
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sketch the curve with equation x2/3 + y2/3 = 4 and use symmetry to find its length.
Answers
The equation x²/3 + y²/3 = 4 represents an ellipse in the shown graph below and the length of the given ellipse is 8 units.
The equation x²/3 + y²/3 = 4 represents an ellipse centered at the origin with a major axis along the x-axis and a minor axis along the y-axis.
The equation can be rewritten as x²/4 + y²/12 = 1 to highlight the lengths of the semi-major and semi-minor axes.
The semi-major axis length is given by the square root of the denominator of the x-term, which is 4, so the semi-major axis length is 2.
The semi-minor axis length is given by the square root of the denominator of the y-term, which is 12, so the semi-minor axis length is 2√3.
Based on the symmetry of the ellipse, we can determine that it is symmetric with respect to both the x-axis and the y-axis.
This means that the length of the entire ellipse can be found by multiplying the semi-major axis length by 4, since there are 4 identical sections due to symmetry.
Length of the ellipse = 4 * semi-major axis length
= 4 * 2
= 8.
Therefore, the length of the given ellipse is 8 units.
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The correct question is as follows:
Sketch the curve with the equation x²/3 + y²/3 = 4 and use symmetry to find its length.
Use the image below to answer the identify the following: One pair of vertical angles: One pair of adjacent angles: One pair of supplementary angles:
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A pair of vertical angles is; Angle 1 and Angle 4
A pair of supplementary angles are; Angle 2 and angle 1
How to identify angle properties?Vertical Angles are defined as the angles that are opposite each other when two lines cross each other.
Two angles are defined as adjacent angles when they share the common vertex and side.
Two angles are defined as supplementary angles if they sum up to 180 degrees.
By those definitions above, we can say that;
Angle 1 & 2 as well as angle 3 & 4 are pairs of supplementary angles.
We can also say that;
Angle 4 and 1 are vertical angles while angle 2 and 3 are vertical angles as well.
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Helppp pleaseeeeeeeeeeeeeeee…………
Answers
The expression that represents the number of football cards that Frankie has is given as follows:
F = J + 65.
How to model the situation?The situation can be modeled by a system of equations, in which the variables are given as follows:
Variable F: number of football cards that Frankie has.Variable J: number of football cards that John has.Frankie has sixty-five more football cards than his friend John, hence the expression that represents the number of football cards that Frankie has is given as follows:
F = J + 65.
As the term sixty-five more means that the number 65 is added to the amount of cards that John has, which is symbolized by J, to obtain the amount F, which is the number of football cards that Frankie has.
Missing InformationThe problem asks for the expression of the number of cards that Frankie has.
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Jeremy's mother deposited $1,200 into a
savings account as a college fund when he
was born. How much will Jeremy have in
this account after 18 years at a yearly
simple interest rate of 4.25%?
A) $51.00
C) $918.00
B) $10,380.00
D) $2,118.00
Answers
Answer: D) $2,118.00
Step-by-step explanation:
1 year = 4.25% interest rate
18 years = 76.5% interest rate
76.5% = 0.765
Take 1200 times 0.765 = $918.00
$918.00 is the interest money he will receive after 18 years. We have to add both numbers to find the total.
$1,200 + $918.00 = $2118.00
i need help on this question
Answers
dose the following relation represen a function {(-21,-4),(-4,-17),(-12,-21),(4,-12),(23,-17)}
Answers
Answer:
yes
Step-by-step explanation:
for a relation to be a function then each value of x can only map to one unique value of y.
This is the case here, then the relation is a function
Need help with this question
Answers
The figure S is translatation and then followed by rotation to map it into
figure T.
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The figure S is translated (moved a fixed amount from the preimage)
and then followed by rotation(the preimage is rotated to create the final image) to map it into figure T.
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A parabola is the set of all points in the plane that are equidistant from a fixed point called the ____ and a fixed line called the ____ of the parabola.
Answers
Find an equation of the parabola with focus (-5, -2) and directrix y = 2.
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Check the picture below, so the parabola looks more or less like so.
keeping in mind the vertex is half-way between the focus point and the directrix, this one lands as you see it in the picture, with a negative "p" distance.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-5\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=( ~~ x-(-5) ~~ )^2\implies -8y=(x+5)^2 \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{8}(x+5)^2 \end{array}} ~\hfill[/tex]
which of the following is most likely a continuous quantitative variable? the number of gallons of paint purchased. the number of quarts of milk purchased. the population of egypt. the number of miles of interstate highways. the number of times you sharpen your pencil working statistics problems.
Answers
A continuous quantitative variable is a measure of a quantity that can take any value within a certain range. An example of this is the number of gallons of paint purchased.
A continuous quantitative variable is a type of data that is measured on a continuous scale. This type of data is typically used to measure quantities that can take any value within a certain range. Examples of continuous quantitative variables include the number of gallons of paint purchased, the number of miles of interstate highways, or the population of a city. Continuous quantitative variables differ from discrete quantitative variables, which are used to measure counts of items or events. For example, the number of quarts of milk purchased or the number of times you sharpen your pencil while working on statistics problems would be discrete quantitative variables. Continuous quantitative variables can be measured with precise accuracy, while discrete quantitative variables can only be measured in whole numbers, since they are counts of items or events.
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(4.8)/(2z+15)=(0.2)/(5) PLS HELP! SHOW STEPS TOO IF POSSIBLE!
Answers
Answer:
z = 52.5
Step-by-step explanation:
You want the solution for (4.8)/(2z+15)=(0.2)/(5).
Cross multiplyMultiplying by 5(2z +15) we have ...
5(4.8) = 0.2(2z +15)
24 = 0.4z +3 . . . . . . . . . . simplify
21 = 0.4z . . . . . . . . . . . . subtract 3
z = 21/0.4 = 52.5 . . . . divide by the coefficient of z
The value of z is 52.5.
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write the expression using exponents. 2.1⋅x⋅z⋅z⋅z⋅z
Answers
The expression is - 2xz⁴
An exponent is a method of expressing large numbers in terms of power. So, exponent means how many times a number is multiplied by itself. For example, 5 is multiplied by itself 3 times i,e 5 *5*5. It can be written as 5³.
Here, 3 is the exponent, and 5 is the base. We can read it as 5 is raised to power 3. The symbol '^' is used to represent the exponents. It is called a carrot.
Based on the power there are different laws of exponents, such as :
Multiplication law Division lawSo, The expression is - 2xz⁴
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8.
For which set of data is the median greater than the mean?
A.
B.
C.
D.
{8, 12, 14, 14, 20}
{8, 12, 14, 14, 22}
{9, 13, 14, 15, 19}
(9, 13, 14, 15, 20}
Answers
Answer:
B
Step-by-step explanation:
For a set of data to have a median that is greater than the mean, it must have an odd number of values and be skewed to the right. This means that the majority of the values in the set must be smaller than the median, with a few larger values on the right side of the distribution.
Out of the given options, the only set of data that satisfies these conditions is (B) {8, 12, 14, 14, 22}. This set has an odd number of values, and the median of 14 is greater than the mean of 14.4. The other options have either an even number of values, or are not skewed to the right.
Therefore, the correct answer is (B) {8, 12, 14, 14, 22}.
the three perpendicular bisectors of a triangle intersect in one point called the
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when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same
Answers
Answer:
normal force decreases
Step-by-step explanation:
N=mgcosθ, and cosine decreases as theta increases
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Answer:
A) decreases
Step-by-step explanation:
As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.
7(3x+5)-11x simply the expression
Answers
Answer:
10x + 35
Step-by-step explanation:
7(3x+5)-11x
21x + 35 - 11x
10x + 35
Lee i packing a truck with mall and large filing cabinet. The large cabinet weigh 30 pound, and the mall cabinet weight 20 pound. To optimize the load, the total load weight hould be 1550 pound from a total of 65 cabinet. How many of each ize of cabinet hould Lee pack in the truck?
Answers
The number of cabinets of large size Lee should pack is equal to 40 and that of small size is equal to 25.
To determine how many of each size of cabinet Lee should pack in the truck, you can set up a system of equations. Let X be the number of large cabinets and Y be the number of small cabinets.
The total weight of the large cabinets is 30X pounds, and the total weight of the small cabinets is 20Y pounds. The total weight of all the cabinets is 1550 pounds, so the equation to represent this is:
30X + 20Y = 1550
The total number of cabinets is the sum of the number of large cabinets and the number of small cabinets, so the equation to represent this is:
X + Y = 65
To solve this system of equations, you can use the substitution method. First, solve for X in the second equation by substituting 65 - Y for X:
X = 65 - Y
Then, substitute 65 - Y for X in the first equation:
30(65 - Y) + 20Y = 1550
Solving this equation for Y, you get:
Y = 25
Substituting this value for Y in the second equation, you get:
X = 65 - 25 = 40
So, Lee should pack 40 large cabinets and 25 small cabinets in the truck.
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Ticket to a baketball game can be ordered online for a et price per ticket plu a $5. 50 ervice fee. The total cot in dollar for ordering 5 ticket i $108. 0. Which linear function repreent c, the total cot, when x ticket are ordered? (A ervice fee i a ingle fee applied to the total, no matter the number of ticket purchaed). C(x) = 5. 50 20. 50x
c(x) = 5. 50x 20. 50
c(x) = 5. 50 21. 60x
c(x) = 5. 50x 21. 60
Answers
The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
The total cost for ordering 5 tickets is $108.00. This means that each ticket costs $20.50 plus a service fee of $5.50.
Therefore, we can create a linear function that represents the total cost when x tickets are ordered. The function is: c(x) = 5.50 + 21.60x. This means that for each ticket purchased, an additional $21.60 will be added to the service fee of $5.50.
When x = 5, then c(x) = 5.50 + 21.60x = 5.50 + 21.60(5) = 108.00, which matches the given total cost.
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Given that the measurement is in inches find the circumference of the circle to the nearest tenth use 3.14 for
Answers
The circumference of the circle is 25.12 inches
How to determine the circumference?From the question, we have the following parameters that can be used in our computation:
Radius = 4 inches
The circumference of a circle can be calculated using
C = 2πr
Substitute the known values in the above equation, so, we have the following representation
C = 2 * 3.14 * 4
Evaluate
C = 25.12
Hence, the circumference is 25.12 inches
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The length and width of a rectangle are consecutive integers. The area of the rectangle is 156 square feet. Find the length and width of the rectangle.
Answers
Answer:
L = 12ft
W = 13ft
Step-by-step explanation:
Let's use the two pieces of information to make 2 equations (we need 2 eqns to solve for 2 variables: Length and Width).
The length and width are consecutive integers
L+1=W
The area of the rectangle is 156 square feet.
L*W=156
We know that W=L+1 from our first equation, so substituting that information into our second equation we get
L*(L+1)=156
Let's distribute that L
L^2 + L = 156
and subtract 156 from both sides
L^2 + L - 156 = 0
Now we can use the quadratic formula to find L. L cannot be negative, so
L = 12
using our very first equation we know L, so we can solve for W.
L+1=W
12+1=W
W = 13
You buy the following at Target:
1 bottle of lotion for $5, 1 t-shirt for $12, 1 birthday card for $3
What is the subtotal: $
You use your Target RedCard and save 5%, what is your savings:
New Subtotal: $
Sales tax is 6%: $
Total: $
4
Answers
The subtotal is $20, Savings is $ 1, New Subtotal is $19, Sales tax is $1.14 and the Total is $20.14
How to determine the subtotal?
A sales discount is a reduced price offered by a business on a product or service
Given:
1 bottle of lotion = $5
1 t-shirt = $12
1 birthday card = $3
Subtotal = $5 + $12 + $3 = $20
If you use your Target RedCard and save 5%, savings will be:
Savings = 5% of Subtotal
Savings = 5/100 × $20 = $1
New Subtotal: $20 - $1 = $19
Sales tax is 6%: 6/100 × $19 = $1.14
Total: New Subtotal + Sales tax = $19 + $1.14 =$20.14
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5. The first five terms of a sequence are -7.7, -7.4, -7.1, -6.8, -6.5.
a. Find an expression for the nth term.
Answers
The expression of the nth term of the given sequence is
-7.7 + (n - 1)0.3
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
Example:
2, 4, 6, 8, 10 is an arithmetic sequence.
We have,
-7.7, -7.4, -7.1, -6.8, -6.5
This is an arithmetic sequence.
Now,
a = -7.7
d = -7.4 + 7.7 = 0.3
The nth term of an arithmetic sequence.
= a + (n - a)d
Now,
a + (n - a)d
= -7.7 + (n - 1)0.3
Thus,
The nth term is -7.7 + (n - 1)0.3.
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John spread 45 minutes after school reviewing his notes before taking a 15 minute break for a snack. After that snack, he continues reading his notes for the other 30 minutes. What would you add to find the total time that John studied?
Answers
Answer:
its A
Step-by-step explanation:
Ben
Anil completes the 72km journey between Bristol and Cardiff in 48 minutes. He then drives 69km from Cardiff to Swansea at an average speed of 60km/h
Work out Anil's average speed (in km/h) for his total journey from Bristol to Swansea.
(with working out pls)
Answers
Answer:
75 km/h
Step-by-step explanation:
48 minutes = 48/60
(48 : 12)/(60:12)
4/5
0.8 hours
average speed between Bristol and Cardiff = 72/0.8 = 90 km/h
average speed of the journey = (60 + 90)/2 = 150/2 = 75 km/h