What is the sum of the measures of the exterior angles of any convex polygon
Answer:
360 degrees is sum of the measures of the exterior angles of any convex polygon.
Step-by-step explanation:
Convex Polygon:
A convex polygon is a polygon with all its interior angle less than 180 degrees.Thus, all the vertices of the polygon will be away from the interior of the polygon.If all the angles are not less than 180 degrees then it becomes concave polygon.Example: Triangle is a convex polygon with three sides.Exterior angle sum Property:
If we extend the side of the polygon, then the angle formed by the extended side and polygon side is an exterior angle.The sum of all the exterior angles if a convex polygon is 360 degrees.If this convex polygon is a regular polygon, then the sum is 360 degrees and each exterior angle is equal to [tex]\frac{360}{n}[/tex], where n is the number of sides in regular polygon.The sum of the measures of the exterior angles of any convex
polygon is 360°.
What is a Convex polygon?This is the polygon that is the boundary of a convex set and has
all the interior angles to be less than 180°.
The interior angles is 180(n-2) degrees and each exterior angle
is supplementary to its interior angle thereby resulting in the
sum of the exterior angles to be 360°.
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How do i graph the line y=2/3x+ 490 using the slope intercept method?
Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
What is slope?
"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."
Formula used
standard equation of line
y = mx + c
m = slope of the line
c = y- intercept
According to the question,
Given equation of line,
[tex]y = \frac{2}{3} x+490[/tex]
Compare it with standard equation of line y = mx + c we get,
Slope [tex]m = \frac{2}{3}[/tex]
y-intercept = 490
Calculate x-intercept by putting y=0
x-intercept = -735
Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]
Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.
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What is the value for B, after the equation A=3/7(B-25) is rearranged?
Answer:
[tex]B=\frac{7A}{3}+25[/tex]
Step-by-step explanation:
We have been given an equation [tex]A=\frac{3}{7}(B-25)[/tex]. We are asked to find the value of B for our given equation.
Upon multiplying both sides of our equation by [tex]\frac{7}{3}[/tex], we will get:
[tex]\frac{7}{3}*A=\frac{7}{3}*\frac{3}{7}(B-25)[/tex]
[tex]\frac{7}{3}*A=B-25[/tex]
[tex]\frac{7A}{3}+25=B-25+25[/tex]
[tex]\frac{7A}{3}+25=B[/tex]
[tex]B=\frac{7A}{3}+25[/tex]
Therefore, the value of B is [tex]\frac{7A}{3}+25[/tex].
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Which of the following expressions is not equal to p^2?
A.
p^-3 * p^5 * p^-2 * p^2
B.
p^-9 * p^0 * p^2 * p^5
C.
p^-3 * p^-1 * p * p^5
D.
p^-5 * p^9 * p^-2 * p^0
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
Here,
We have to find the expression is not equal to p^2.
What is Property of addition in power of number?
This property states that when multiplying two powers with the same base, we add the exponents.
Now,
Let an expression [tex]x^{a} x^{b}[/tex]
Then it can be written as, [tex]x^{a} x^{b} = x^{a+b}[/tex]
So, Option B is given as,
[tex]p^{-9} *p^{0} * p^{2} *p^{5} = p^{-9+0+2+5} = p^{-2}[/tex]
Which is not equal to [tex]p^{2}[/tex].
Similarly, we check all options.
We get only option B is not equal to [tex]p^{2}[/tex].
Hence,
Option B, [tex]p^{-9} *p^{0} * p^{2} *p^{5}[/tex] is not equal to [tex]p^{2}[/tex].
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Complete the solution of the equation. find the value of y when equals -7
-3x+6y=-21
The value of y when equals -7 would be equal to -7.
What does it mean to solve an equation?An equation represents equality of two or more mathematical expression.
When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true
Solutions to an equation are those values of the variables involved in that equation for which the equation is true.
We are given the equation as-3x+6y=-21
if x = -7 then we get;
-3x+6y=-21
Substitute;
-3(-7) +6y = -21
21 + 6y = -21
6y = -42
y = -7
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Classify the variable as discrete or continuous. weights of backpacks of first graders on a school bus
Pythagoras is planting a rose garden in the center of his rectangular yard, which is 20 feet long and 8 feet wide. He wants to dig up an area in the shape of an equilateral triangle with sides 5 feet each. After he digs up the rose-bed section, approximately how much grass will be left? Round to the nearest foot.
Answer:
The approximate remaining grass area is 144 square feet.
Explanation:
To find the area of the rectangular yard, we use the formula:
Area of rectangle [tex]= \text{length} \times \text{width} \)[/tex]
Given that the length is 20 feet and the width is 8 feet, we have:
Area of Rectangle [tex]= 20 \times 8 = 160 \text{ square feet} \)[/tex]
Next, we find the area of the equilateral triangle. Since we know the length of each side (5 feet) and an equilateral triangle can be divided into two congruent 30-60-90 triangles, we can use the formula for the area of an equilateral triangle:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (\text{side length})^2 \)[/tex]
Plugging in the value of the side length (5 feet), we get:
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times (5)^2 \)[/tex]
Area of equilateral triangle [tex]= \frac{\sqrt{3}}{4} \times 25 \)[/tex]
Area of equilateral triangle [tex]= \frac{25\sqrt{3}}{4} \text{ square feet} \)[/tex]
Now, to find the remaining grass area after Pythagoras digs up the rose-bed section, we subtract the area of the equilateral triangle from the total area of the rectangle:
Remaining grass area [tex]= \text{Area of rectangle} - \text{Area of equilateral triangle} \)[/tex]
Remaining grass area [tex]= \ 160 - \frac{25\sqrt{3}}{4} \)[/tex]
Using a calculator, we find:
Remaining grass area [tex]\approx 144.3 \text{ square feet} \)[/tex]
Rounded to the nearest foot, the approximate remaining grass area is 144 square feet.
what is the correct name for the angle shown
Answer: The correct name is (B) ∠S.
Step-by-step explanation: We are given to find the correct name for the angle shown in the figure.
We can see in the figure that the rays RS and ST are intersecting at the point S. Therefore, RS and ST are making an angle at the point 'S'.
So, the name of the angle will be ∠S or ∠RST or ∠TSR.
First option is ∠R. This is not correct.
Second option is ∠S. This is the correct option.
Third option is ∠RTS. This is also not correct.
Fourth option is ∠SRT. This is not correct.
Thus, the correct option is (B) ∠S.
Jessica plots the data points relating the amount of money she needs to repay a loan and the number of months she has been making payments.
She calculates two regression models. Which is true?
A.) The linear model better represents the situation because the amount she owes is decreasing by about the same amount every 6 months.
B.) The linear model better represents the situation because according to the exponential model, the repayment amount will never be 0.
C.) The exponential model better represents the situation because the amount she owes decreases by about the same amount every 6 months.
D.) The exponential model better represents the situation because according to the linear model, the repayment amount will eventually be negative.
The regression models used by Jessica is such that A.) The linear model better represents the situation ... owes is decreasing by about the same amount every 6 months.
What regression model is best?The linear regression model is best for a situation where there is a constant rate of change while the exponential model is for situations where change isn't constant.
Jessica's data shows that there is a constant rate of reduction in the amount to repay because the amounts are quite similar to each other as shown by the graph.
In conclusion, option A is correct.
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solve the equation 14.50-p=53 please help
Find the directrix of the parabola y = (1/8)(x – 5)2 - 3.
Answer:
y= -5
Step-by-step explanation:
rewrite as standard form [tex]4.2(y-(3-))=(x-2)^{2}[/tex]
(h.k) = (2, -3), P=2
y= -3 -P
y= -3 -2
y= -5
A student reader is making $5.90 per hour and gets a $0.52 raise. what is the percent increase? (round to the nearest tenth of a percent.)
Given the function g(x) = 4(3)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
A) Find the average rate of change of each section. (4 points)
At what angle do the angle bisectors of two same side interior angles intersect in construction with two parallel lines and a transversal?
Angle x is an acute angle in a triangle. If cos x=4/5, then the sin x=
Answer:
[tex]\bf \sin x =\frac{3}{5}[/tex]
Step-by-step explanation:
Angle x is an acute angle in a triangle.
The measure of cosine angle is given to be :
[tex]\cos x = \frac{4}{5}[/tex]
Now, we need to find the measure of the sine angle for the same triangle.
[tex]\cos x = \frac{Base}{Hypotenuse}[/tex]
⇒ Base = 4 units and Hypotenuse = 5 units
So, Length of perpendicular = 3 units ( By using Pythagoras theorem)
[tex]\sin x=\frac{Perpendicular}{Hypotenuse}\\\\\implies\bf \sin x =\frac{3}{5}[/tex]
If ABCDE is translated 3 units to the right and 4 units down, what will happen to the polygon?
When polygon ABCDE is translated 3 units to the right and 4 units down, its shape and size remain unchanged, but its position on the coordinate plane changes, maintaining the same orientation and angles.
Explanation:If a polygon ABCDE is translated 3 units to the right and 4 units down, the shape and size of the polygon will remain the same, but its position will change. Each vertex (point) of the polygon will move 3 units to the right on the x-axis and 4 units down on the y-axis. This type of transformation is known as a translation, which is a slide of the entire figure in a specific direction. As a result, the translated polygon will maintain the same orientation and angles; it will simply be in a different location on the coordinate plane.
Katie earned $54.30 in interest from two accounts. One account Paid 4.1% apr and the other paid 3.2% apr. if she had a total of $1500 in the two accounts, How much was in each account?
If $10,000 is invested in an account at the rate of 6.25% compounded monthly, then the amount after 15 years is approximately
The amount after 15 years is approximately $26,971.67.
Explanation:To calculate the amount after 15 years, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the final amountP = the principal amount (initial investment)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = number of yearsIn this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:
A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).
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If f(x)=5x-7 and g(x)√x-2 which statement is true?
-5 is in the domain or
-5 is not in the domain
-5 is in the domain of the function f(x)=5x-7, but not in the domain of the function g(x)√x-2. The domain of a function is the set of all acceptable input values.
Explanation:The question is asking whether -5 is in the domain of the given functions, f(x)=5x−7 and g(x)√x−2. The domain of a function is the set of all permissible inputs or arguments, i.e. x-values that can be inserted into the function.
In the case of f(x)=5x-7, the domain is all real numbers, as we can substitute any real number into 'x' and obtain a valid result. Hence, -5, indeed, is in the domain of the function f(x). However, for the function g(x)√x-2, the domain is all non-negative real numbers since we can't take the square root of a negative number in the real number system, hence -5 is not in the domain of g(x).
Thus, the statement '-5 is not in the domain' would be true if we are referring to g(x). However, if we are referring to f(x), the statement would be false because -5 is in the domain.
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A bag contains 5 apples and 3 oranges. if you select 4 pieces of fruit without looking, how many ways can you get 4 apples?
Answer:
5 ways
Step-by-step explanation:
I got it correct on founders edtell
Evaluate [(30 + 6) − 3^2] ÷ 9 ⋅ 2
Evaluate the expression:
the difference of 26 and 22
Select one:
a. 48
b. 91
c. 4
d. 13/11
find the slope of the line through points (1,8) and (2,7). write the answer in simplest form.
What is the area the shaded triangle?
Answer:
96
Step-by-step explanation:
The area of the shaded triangle will be 96 mm² so option (B) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given two inscribed triangles.
The bigger one is the right-angle triangle.
The area of the right-angle triangle will be as,
A = 1/2 x 8 x (6 + 24)
A = 4 x 30= 120 mm².
The area of the smaller right-angle triangle,
a = 1/2 x 8 x 6 = 24 mm²
The area of the shaded triangle = 120 - 24 = 96 mm².
Hence "The area of the shaded triangle will be 96 mm²".
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Rewrite in simplest radical form 1/x^3/6.
Can anyone solve this.
Evaluate the following expression using the values given: Find 3x − y − 3z if x = −2, y = 1, and z = −2. −13 −1 1 13
The correct answer is -1
How many ways are there to arrange the first five letters of the alphabet?
Answer:
120 ways
Explanation:
Since there are no repeating letters, and there are 5 total letters, there are 5!= 120 ways to arrange them. In other words, there are 5 slots to place the first letter in, then 4 slots for the second letter, 3 for the third, 2 for the fourth, and then the last letter goes in the 1 slot that is left.
I hope this is correct and if it is I hope it helps. I hope you have a great day and remember it doesn't matter what other people say or think about you, you are still and always will be strong, smart, and an amazing person. Have a wonderful day.
I am happy to help with anything.
The balance in Beth's checking account is $75. She must deposit enough money in her account to be able to pay the electric bill, which is $110. How much should she deposit?
Answer:
She should deposit $35.00 in her account.
Step-by-step explanation:
The balance in Beth's checking account = $75.00
She must deposit enough money in her account to be able to pay the electric bill, which is = $110.00
So we have to subtract 75 from 110 to get how much more money she needs to deposit the electric bill.
$110.00 - $75.00= $35.00
She should deposit $35.00 in her account.
Doug read 231 pages in seven hours. he read the same number of pages each hour. how many pages do you read in one hour ?
Doug can read 33 pages in one hour.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total pages in a book= 231 pages
Time to read books= 7 hours
so, in 1 hour he can read = 231/7
= 33 pages.
Hence, he can read 33 pages in one hour.
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A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white? 9% 15% 21% 57%
Answer: 15 % ( approx)
Step-by-step explanation:
Let S represents the event that the car is SUV.
And W is the event that the car is white.
Then According to the question,
23% of the cars manufactured last year were SUVs,
Thus, the probability of SUV Car,
[tex]P(S)= \frac{23}{100} =0.23[/tex]
Similarly Probability that the car is white,
[tex]P(W)= \frac{13}{100} =0.13[/tex]
And, the probability that cars manufactured were white SUVs,
[tex]P(S\cap W)= \frac{2}{100} =0.02[/tex]
Thus, the probability that a car is an SUV, given that it is white,
[tex]P(\frac{S}{W} )= \frac{P(S\cap W)}{P(W)} = \frac{0.02}{0.13}[/tex] = 0.15384615384= 15.384615384 % ≈ 15 %
Therefore, Option B is correct.