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Compare the properties of the diagonals of a kite with those of a square.
Diagonals of square are congruent while diagonals of kite are not congruent to each other.
What is diagonal?
" Diagonal is a straight line segment which connects the opposite vertices of any polygon or polyhedron."
Compare the properties of diagonal of square and kite
1) Diagonals of square are congruent while diagonals of kite are not of same length.
2) Diagonals of square bisect each other while in kite longer diagonals bisects the smaller one.
3) Diagonals of square and kite are perpendicular to each other.
Hence, diagonals of square are congruent while diagonals of kite are not congruent to each other.
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What is the area of a sector with a central angle of 2pi/9 radians and a diameter of 20.6mm? Use 3.14 for Ali and round your answer to the nearest hundredth.
The area of the sector rounded to the nearest hundredth is [tex]$37.02 \, \text{mm}^2$[/tex].
To find the area of a sector, we use the formula:
[tex]\[ \text{Area of sector} = \frac{\text{Central angle}}{2\pi} \times \pi r^2 \][/tex]
Given that the central angle is [tex]\( \frac{2\pi}{9} \)[/tex] radians and the diameter (which is twice the radius) is [tex]$20.6 \, \text{mm}$[/tex], the radius is [tex]\( \frac{20.6 \, \text{mm}}{2} = 10.3 \, \text{mm} \)[/tex].
Now, substituting these values into the formula:
[tex]\[ \text{Area of sector} = \frac{\frac{2\pi}{9}}{2\pi} \times \pi (10.3)^2 \][/tex]
[tex]\[ = \frac{1}{9} \times \pi \times 10.3^2 \][/tex]
[tex]\[ = \frac{1}{9} \times 3.14 \times 106.09 \][/tex]
[tex]\[ = \frac{1}{9} \times 333.2086 \][/tex]
[tex]\[ \approx 37.02 \, \text{mm}^2 \][/tex]
Rounded to the nearest hundredth, the area of the sector is approximately [tex]$37.02 \, \text{mm}^2$[/tex].
What is the sum of the geometric series
Answer:
Hence, the sum of the geometric series is:
259
Step-by-step explanation:
We are given a geometric series as:
[tex]\sum_{i=1}^4 6^{i-1}[/tex]
i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1
Since, the series is:
[tex]6^0+6^1+6^2+6^3[/tex]
Also, the common ratio of the series is: r=6
Since, each of the term of the series is 6 times it's preceding term.
Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:
[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]
Here we have: a=1 and r=6 and n=4
Hence,
[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]
Hence, the sum of the series is:
259
Consider the functions f(x) = (4/5)^x and g(x) = (4/5)^x + 6. What are the ranges of the two functions?
f(x): {y| y > _____}
g(x): {y| y > _____}
(Fill in the blank with the correct answer)
The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.
Explanation:The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.
For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.
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A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for the surface area of a sphere.
Find the slope of the line that contains the points named.
X(2, -1), Y(0, 4)
5/2
2/5
-5/2
Fan for everyone who helps, medal for whoever helps the most! :)
1. What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)
2. Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)
3. Which expression can be used to find the difference of the polynomials?
(4m – 5) – (6m – 7 + 2n),
Answer:
1- The sum is: 2m + 2n + 7 = 2(m+n) + 7
2- The difference is: 3m - 2
3- The difference is: -2m - 2n + 2 = -2(m+n-1)
Explanation:
Before we begin, remember the following:
+ve * +ve = +ve
-ve * -ve = -ve
+ve * -ve = -ve
-ve * +ve = -ve
Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree
Now, let's check the problems:
Problem 1:
Adding two polynomials:
(m + n + 3) + (m + n + 4)
We first start by getting rid of the brackets:
m + n + 3 + m + n + 4
Now, we add like terms:
2m + 2n + 7
As an additional step, we can take 2 as a common factor from the first two terms:
2(m+n) + 7
Problem 2:
Subtracting two polynomials:
(10m - 6) - (7m - 4)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
10m - 6 - 7m + 4
Now, we add/subtract like terms:
3m - 2
Problem 3:
Subtracting two polynomials:
(4m - 5) - (6m - 7 + 2n)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
4m - 5 - 6m + 7 - 2n
Now, we add/subtract like terms:
-2m - 2n + 2
As an additional step, we can take -2 as a common factor from the above expression:
-2(m+n-1)
Hope this helps :)
On the rectangular coordinate system, what is the shortest distance between points (−4, 3) and (−2, −1)?
Answer:
In other words to what the dude above me said, the answer is "a''
Step-by-step explanation:
Please help
According to Cavalieri's principle,
A) the volume of the sphere is equal to the volume of the cones.
B) the volume of the sphere is equal to the volume of the cylinder.
C) the volume of the sphere is equal to two times the volume of the cones.
D) the volume of the sphere is equal to the volume of the solid between the cones and the cylinder.
Answer:
Step-by-step explanation:
The answer is d.
Answer:
d
Step-by-step explanation:
Two angles that are supplementary have a ratio of 7 to 5. what are their measurements?
Batteries for an MP3 player usually cost $8.00, but they are on sale for 40% off. What is the discount amount? What is the sale price for these batteries?
Answer:
its b!
Step-by-step explanation:
discount is $8 = 40/100 to find that discout
is $3.20
sale price : $8.00 - $3.20 which is $4.80!
Your welcome! :D
hat is the volume of this prism?
Rectangular prism composed of unit cubes. Prism is 6 units by 9 units by 7 units.
-----units3
Jason draws an angle and then places the compass on the vertex and draws arc that intersects both rays. He then places the compass on each intersecting mark on each ray and draws arcs that intersect inside the angle. Which construction is he creating?
A. copying an angle
B. angle bisector
C. perpendicular bisector
D. perpendicular line through vertex of angle
Which coordinate Gird shows the correct locations of P (1,2.5) Point Q which is a reflection Of point P across the Y-axis And R (2.-2.5)
Write an equation to represent, "sum of eight and a number is one hundred". What is the number?
Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?
This question has been asked before but the answer is unclear to me.
Question 1. Evaluate 4 times a number q plus 25 when q=2
A. 27
B.31
C.33
D.42
Question 2. If p=8, evaluate 4 )2 / 9.3
A.2
B.3
C.6
D. 8
Question 3. If q=2, evaluate (24 + 18 .q) - (5q + 7)
A. 38
B. 79
C. 31
D. 21,
Please help(:
Two planes intersect to ____ form a line
A. Always
B. Sometimes
C. Never.
D. Inconclusive.
Which of the following is true?
A. All quadrilaterals are polygons with two pairs of parallel sides.
B. All quadrilaterals are polygons with four sides.
C. All quadrilaterals are polygons with at least one pair of parallel sides.
D. All quadrilaterals are polygons with four sides at least one pair of parallel sides.
Answer:
1. Two planes intersect to ALWAYS form a line. If two planes intersect, they intersect in a line. The two planes that do not intersect, they form parallel lines.
2. The true statement is :
All quadrilaterals are polygons with four sides. A quadrilateral is a geometrical shape that has four sides and four angles. These are also called polygons. There are many types of quadrilaterals like - the parallelogram, the rectangle, the square, rhombus etc.
Two cones have the same radii but one has a height four times larger than the other. How many small cones would be needed in order to have the same volume as the larger cone?
4
8
16
64
Experimental vs. Theoretical Probability:
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
Answer:
Guy above is correct
Step-by-step explanation:
please help me please
what is the value of x that equals 14 y=310-25(x)
What is the solution for the system of equations?
Use the substitution method to solve.
2x+y=20−5y=−6x+12
Enter your answer in the boxes.
( , )
Answer:
2x+y=20 and -5y=6x+12 are your equations.
You can turn 2x+y=20 into y=-2x+20
Substitute this value of y into the other equation.
-5(-2x+20)=-6x+12
10x-100=-6x+12
16x=112
x=7
Substitute this value of x into the other equation.
2(7)+y=20
y=6
Your answer is x=7 and y=6.
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
The probability that it'll rain tomorrow in Ohio is 30%
The probability that it'll rain tomorrow in both Ohio and Alaska is 12%
If it rains tomorrow in Ohio what is the probability that it will rain tomorrow in Alaska?
How to find out how much you pay if there was a sale tax?
Suzy likes to mix and match her 3 necklaces, 2 bracelets, and 6 hats. The colors are listed in the table. On Monday, she randomly picks a bracelet, a necklace, and a hat. What is the probability of Suzy choosing a red bracelet and silver hat? NECKLACE COLORS: RED ,GREEN ,GOLD BRACELET COLORS: RED AND BLACK HAT COLORS: SILVER, YELLOW, GREEN, GOLD, BLACK, AND WHITE A. one-half B. one-fourth C. start fraction 1 over 6 end fraction D. start fraction 1 over 12 end fraction
Answer:
The probability of Suzy choosing a red bracelet and silver hat is 1/12
Step-by-step explanation:
Each one of the red, green, and gold necklace have a probability of 1/3.
Each one of the red and black bracelet have a probability of 1/2.
Each one of the silver, yellow, green, gold, black, and white hat have a probability of 1/6.
Hence, the probability of Suzy choosing a red bracelet and silver hat becomes:
[tex]\frac{1}{2}*\frac{1}{6} =\frac{1}{12}[/tex]
So, the answer is 1/12.
Karen paid $43.70 for a book. The price of the book was $40. what was the sale tax rate
Answer:
9.25%
Step-by-step explanation:
We have the price book of $40 but karen pais $43.70 then the $3.70 extra that she paid it's the value of taxes. Then to know the tax rate we have to do the next procediment:
[tex]$40\longrightarrow 100\%[\text]
[tex]$3.70\longrightarrow x\%[/tex]
Where x is the tax rate, then:
[tex]x=\dfrac{\$3.70\cdot 100\%}{\$40}[/tex]
[tex]x=\dfrac{370\%}{40}=9.25\%[/tex]