The relationship between the radius and diameter of a circle is that the diameter is twice the length of the radius.
In other words, the diameter of a circle is equal to 2 times the radius. Mathematically, this relationship can be expressed as:
Diameter (D) = 2 * Radius (r)
This relationship is consistent for all circles. No matter the size of the circle, the diameter will always be exactly twice the length of the radius. The radius is the distance from the center of the circle to any point on the circle's circumference, while the diameter is the distance from one point on the circumference to another, passing through the center. Understanding this relationship is essential in various geometrical calculations and formulas involving circles.
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How can you find the sum of the first 5 consecutive positive integers? You can easily add the numbers mentally—the sum is 15. But what if you want to find the sum of the first n consecutive whole numbers? Keep this question in mind and make some conjectures about a formula.
Given:
First five consecutive positive integers.
To find:
The sum of the first 5 consecutive positive integers.
Sum of the first n consecutive whole numbers.
Solution:
First five consecutive positive integers are 1, 2, 3, 4 and 5.
Sum of these numbers is
[tex]1+2+3+4+5=15[/tex]
Therefore, the sum of the first 5 consecutive positive integers is 15.
First n consecutive whole numbers are 0, 1, 2, 3,..., (n-1). These numbers are in AP.
Here, first term is 0 and common difference is 1.
Sum of n terms of an AP is
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
where, a is first term and d is common difference.
Substitute a=0 and d=1 in the above formula.
[tex]S_n=\dfrac{n}{2}[2(0)+(n-1)(1)][/tex]
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
Sum of first 5 consecutive positive integers is equal to the sum of first 6 consecutive whole number because in whole numbers 0 is extra number.
For n=6,
[tex]S_6=\dfrac{6}{2}[6-1][/tex]
[tex]S_6=3(5)[/tex]
[tex]S_6=15[/tex]
The sum of the first 5 consecutive positive integers is 15.
So, the sum of (n-1) consecutive positive integers is
[tex]S_n=\dfrac{n}{2}[n-1][/tex]
The rhombus QRST is made of two congruent isosceles triangles. Given angle QRS = 34, what is the measure of angle S?
Answer:
146
Step-by-step explanation:
Since we know that this is a rhombus, we know that opposite angles must be equal to each other. This means that angle QTS is equal to angle QRS. Therefore angle QTS also equals 34.
Now, we also know that all the interior angles in a quadrilateral add up to 360. We can subtract 360-34-34=292.
Now we know that the remaining two angles S and Q need to add up to 292. We also know that they are equal because they are opposite angles. Therefore, we can solve the equation 292÷2=146. Each of these angles is 146. So the measure of angle S is 146.
The measure angle of S is 146 .
A rhombus is a special case of the parallelogram and is a quadrilateral with four equal sides. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Also, all the sides of the rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also known as a diamond.
By symmetry ;
This means that m∠QTS is equal to m∠QRS. Therefore ∠QTS is also equals 34.
We also know that The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.
Now we know that the remaining two angles S and Q need to add up to 292.
= 360 -34 -34= 292
We also know that they are equal because they are opposite angles.
Therefore, we can solve the equation,
[tex]\frac{sum of two opposite angle}{2}[/tex] = [tex]\frac{292}{2}[/tex] = 146
Each of these angles is 146.
So the measure of angle S is 146.
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f/5n3+h=g (Solve the following equation for F)
Answer:
f = 5g/n^3 - 5h/n63
Step-by-step explanation:
Step-by-step explanation:.
The Huggins family went out to dinner. The price of the meal was $62.95. The sales tax is 8% of the
price of the meal. The tip is 15% of the meal and the sales tax. How much money did the family
pay for the meal, including tax and tip?
Answer:
$62.95 (meal) + $5.03 (sales tax) +$.75 (sales tax tip) + $9.44 (meal tip)
Total: $78.17
Answer:
$78.19
Step-by-step explanation:
To find the total after the sales tax is charged you have to do
$62.95 x 1.08 (1 = to the total and .08 to add sales tax value) =$67.986 round*
Now you take $67.99 (has been rounded) and multiply but .15 to find out what is 15% of $67.99 , it comes out to be 10.1979 (Round)
Now to finish you add $67.99 +$10.20 = $78.19
Which equation represents a line that passes through the 2 points in the table
Answer:
A
Step-by-step explanation:
I took the test
The bottles of soda are sold to the student council in a box weighing 24 pounds. If there are 60 bottles in the box, how much does each bottle of soda weigh? Each bottle of soda cost $2.50.
Answer:
.4 lbs
Step-by-step explanation:
Please HELP!!!!!!!!!!!!!!!!
Answer:
sum = (180)(20) = 3600
Step-by-step explanation:
First...
(n-2)180˚ = Sum Of Interior Angles or SOIA
So...
(22-2)180 = SOIA
Then...
20*180 = SOIA
Finally...
3600 = SOIA
which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"
Answer:
Let x be that number.
[tex] - 8 \div (x + 3)[/tex]
The quotient is the result of dividing a number by another. In this case, the numbers are - 8 and x + 3.
1) If the mean is 15.5 and the standard deviation is 2.5, Label b, c, d, e, and f
Answer:
I accidentally clicked I can’t click out
Step-by-step explanation:
Sorry
if 22,x,y,31 are in ap. find the values of x and y
Answer:
x = 25, y = 28
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 22 and
a₄ = a₁ + 3d = 31 , that is
22 + 3d = 31 ( subtract 22 from both sides )
3d = 9 ( divide both sides by 3 )
d = 3
Thus
x = 22 + 3 = 25
y = 25 + 3 = 28
Y is greater than or equal to 3 and less than 7
Answer:
y = 3to6
Step-by-step explanation:
Answer:
3 ≤ y < 7
Step-by-step explanation:
≥ means greater than or equal to
≤ means less than or equal to
< means less than
> means greater than
Given y is greater than or equal to 3
y ≥ 3
y less than 7
y < 7
Joining both of them together
3 ≤ y < 7
José and Maris work for different car dealerships. José earns a monthly salary of $3,500 plus a 8% commission on sales. Maris earns a monthly salary of $3,900 plus a 6% commission on sales. Above what value of sales are José's monthly earnings more than those of Maris?
Answer: When sales are greater than 2000 then José's monthly earnings sre more than those of Maris.
Step-by-step explanation:
Let x= Total sales
For José, monthly salary = $3,500
Commission percentage = 8% =0.08
Monthly earnings= Monthly salary + (Commission percentage) x (Total sales)
Monthly earnings= 3500 +0.08 x
For Maris, monthly salary = $3,900
Commission percentage = 6%
Monthly earnings= 3900 +0.06 x
When José's monthly earnings > Maris's monthly earnings
then, 3500 +0.08 x > 3900 +0.06 x
Subtract 3500 from both sides, we get
0.08 x > 400+0.06x
Subtract 0.06x from both sides, we get
0.02x>400
Divide both sides b 0.02
x> 20000
When sales are greater than 2000 then José's monthly earnings sre more than those of Maris.
Write these expressions as the square of a monomial.
81x4 (81x4 means 81x to the power of 4)
121a6 (the 6 means to the power of 6)
0.09y12 (The 12 means to the power of 12)
4/9b6 (The 6 means to the power of 6)
PLEASE HELP ASAP! WILL GIVE BRAINLIEST IF YOU SHOW STEPS!
Answer:
81x4 = (9x^2)^2, 121a6 = (11a^3)^2, 0.09y12 = (0.3y^6)^2, 4/9b6 = (2/3b^3)^2
Step-by-step explanation:
sqrt of 81 = 9, (we do sqrt because its the inverse to exponents) x^4, x^2 * x^2 = (9x^2)^2
sqrt of 121 = 11, a^6, a^x * a^2 = a^6, x = 3, (11a^3)^2
sqrt of 0.09 = 0.3, y^12 = y^x * y^2, x=6,(0.3y^6)^2
sqrt of 4/9 = 2/3, b^x * b^2 = b^6, x = 3, (2/3b^3)^2
^ = power, * = multiplication
Simplify 1/4 + 1.20 explain
Answer:
1/4 +1 1/10_.25 + 1.20
Step-by-step explanation:
1/4 also known as a quarter, should easily be known as .25, and .20 should be equal to 1/10 since .20x10 equals 1. that one in the equation doesn't really make a difference. (it's kinda just there¯\_(ツ)_/¯) so technically you have your answer.
Two expressions are shown below. Which of the following is the DIFFERENCE obtained when subtracting expression II from expression I?
I. y2−4xz+z2
II. x2+xz+2y2
A. 3y2−3xz+z2−x2
B. 3y2−3xz+z2+x2
C. −y2−5xz+z2−x2
D. y2+5xz−z2+x2
Answer:C.
−y2−5xz+z2−x2
Step-by-step explanation:
Took the test got it right
The solution is Option C = ( -y² - 5xz + z² - x² )
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
Given data ,
Expression 1 = y² - 4xz + z²
Expression 2 = x² + xz + 2y²
Let Expression 1 - Expression 2 = A
To find Expression 1 - Expression 2 = A
A = y² - 4xz + z² - ( x² + xz + 2y² )
By grouping the like terms , we get
A = ( y² - 2y² ) - ( 4xz + xz ) + z² - x²
Therefore,
A= - y² - 5xz + z² - x²
Hence , the solution is ( -y² - 5xz + z² - x² )
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Ben and Ella are filling goodie bags for a party. Each goodie bag needs an eraser, a bubble wand, and a few candy bar bites. Ben filled 25 goodie bags in 20 minutes. Ella filled 27 goodie bags in 24 minutes. Who filled goodie bags at a faster pace?
Answer:
Ben
Step-by-step explanation:
25 goodies = 20 minutes
27 goodies = 24 minutes
Let's use ratio, divide both of them by their minute
25/20 = 20/20
27/24 = 24/24
1.25 goodies = 1 minute
1.12 goodies = 1 minute
1.25 is bigger than 1.12.
Answer:Ben
Step-by-step explanation:
Tony drove 792 miles in 11 hours at the same rate how many miles would he drive in 13 hours
Answer:
936 miles in 13 hours.
Step-by-step explanation:
if you divide 792 by 11 you get 72, which is the unit rate. You multiply that by thirteen and it is the answer 936.
Answer:
936 miles
Step-by-step explanation:
Select True or False. The expression 3x − 4(2x − 5) is equivalent to the expression 20 − 5x. True False
Answer:
true
Step-by-step explanation:
3x − 4(2x − 5)
Distribute
3x - 8x +20
-5x +20
20 -5x
This is equal to 20 -5x
Answer:
The answer would be true.
Step-by-step explanation:
Hope this help and I took the test and got this correct! :)
Find the product
(-4)(-9)(-2)
Answer:
-72
Step-by-step explanation:
(-4)(-9)(-2)=
36(-2)=
-72
Priya has completed 12 exam questions. This is 60% of the questions on the exam. How many questions were in the exam
Answer:
there are 20 questions on the exam
Step-by-step explanation:
HELP ASSSAPP Mr. Barnes has a bag that contains 8 yellow marbles, 9 green marbles, and 3 red marbles. Each student is to draw a marble from the bag, record the result, and not replace the marble. Then draw a second marble, record the result.
What is the theoretical probability of getting Green then Yellow?
Write as a decimal.
Answer:
6C2 = 15
# of ways to select two from the bag: 20C2 = 190
---
P(2 red) = 15/190 = 3/38
Step-by-step explanation:
Length of a segment with endpoint of (-2,5) and (4,5)
Answer:
6...the length is 6
This is a horizontal line!
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Tehara has read 115 pages of a 305 page book she reads 10 pages each day how many days will it take to finish
(+16) + (-32) =
A -12
B 14
C -16
Answer:
-16
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
16+(-32)= -16
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
neither
Step-by-step explanation:
Answer:
(c)
Step-by-step explanation:
If these are
Parallel, slope of both the lines is same.
Perpendicular, if they are -ve reciprocal of each other.
In y = mx + c, slope is m.
Compare,
Slope of y=4x+1, is 4.
of 8y-16=2x is 2/8 = 1/4, which is reciprocal of 4,but not -ve.
So it is neither ll nor perpendicular.
Select all the true statements. Group of answer choices The ratio of triangles to squares is 2 to 4. The ratio of squares to smiley faces is 6:4. The ratio of smiley faces to triangles is 6 to 4. There are two squares for every triangle. There are two triangles for every smiley face. There are three smiley faces for every triangle.
Answer:
The ratio of triangles to squares is 2 to 4
There are two squares for every triangle.
There are three smiley faces for every triangle.
Step-by-step explanation:
The number of triangles, smiley and squares are shown in the diagram attached.
From the diagram, there are 6 smiley faces, 2 triangles and 4 squares.
A ratio compare two or more values, thereby showing how many times one number contains the other.
A) Correct. The ratio of triangles to squares = number of triangle / number of square = 2 / 4 = 2 to 4
B) Incorrect. The ratio of squares to smiley faces = number of square / number of smiley face = 4 / 6 = 4 to 6
C) Incorrect. The ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 6 to 2
D) Correct. Since the ratio of squares to triangles = number of squares / number of triangle = 4 / 2 = 2 / 1 = 2 to 1, hence there are two squares for every triangle
E) Incorrect. Since the ratio of triangles to smiley faces = number of triangle / number of smiley faces = 2 / 6 = 1 / 3 = 1 to 3, hence there is one triangle for every 3 smiley faces
F) Correct. Since the ratio of smiley faces to triangles = number of smiley faces / number of triangles = 6 / 2 = 3 / 1 = 3 to 1, hence there is 3 smiley faces for every one triangle
can someone help me
Answer:
cant read it :(
Step-by-step explanation:
Answer:
m = [tex]\frac{y-b}{x}[/tex]
Step-by-step explanation:
Given
y = mx + b ( subtract b from both sides )
y - b = mx ( isolate m by dividing both sides by x )
[tex]\frac{y-b}{x}[/tex] = m
Which one?
A. B. C. Or D?
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
[tex]6a^{2} - 24 = 0\\6a^{2} - 24 + 24 = 0 + 24 \\6a^{2} = 24\\\frac{6a^{2}}{6} = \frac{24}{6} \\a^2 = 4\\a = \sqrt{4} \\a = +2, -2[/tex]
Please help.
Express the following fraction in simplest form, only using positive exponents
Answer:
j^6 / 18s^23
Step-by-step explanation:
You first by flipping the fraction to get rid of the negative exponents:
(j^6)/(6s^3(3s^5)^4) =
When there are exponents that are being exponentiated together, multiply them:
(j^6) / (6s^3)(3s^20) =
When there are exponents that are being multiplied, add them:
(j^6) / (18s^23)
please help i'm stuck :,)
Jacob and Sophia are in a running club and record how long it takes them to run a 5-kilometer race. Jacob's time was 4 minutes under the average time of the running club. The difference between Jacob's time and Sophia's time is 10 minutes. The possible times of Sophia's run are ____ minutes below the average or ____ minutes above the average.
Answer:
14 minutes below or 6 minutes above
Step-by-step explanation:
Let's say Sophia's time was 10 minutes WORSE
4 minutes below average- 10 minutes= 14 minutes below average
Let's say Sophia's time was ten minutes BETTER
4 minutes below average + 10 minutes= 6 minutes above average.
Hope this helps!
14 minutes below the average
6 minutes above the average
=====================================================
Let A = average running time
Jacob's time was 4 minutes under the average, so his time is A-4 minutes. Whatever A is, subtract off 4, and you'll get Jacob's time.
Sophia and Jacob have a difference of 10 minutes. If J = Jacob's time and S = sophia's time, then S-J = 10 or J-S = 10 depending on who has the larger time.
We can use absolute value to ensure that whatever we pick (S-J or J-S) will be positive. So |S-J| = 10. Recall that absolute value represents distance on a number line. Negative distance isn't possible.
-------------
Let's plug in J = A-4 and solve for S
|S-J| = 10
|S - ( J )| = 10
|S - (A-4)|
|S-A+4| = 10
S-A+4 = 10 or S-A+4 = -10
S-A = 10-4 or S-A = -10-4
S-A = 6 or S-A = -14
S = A+6 or S = A-14
The equation S = A+6 shows Sophia is 6 minutes above the average
The equation S = A-14 shows Sophia is 14 minutes below the average
-------------
Let's pick some number for A that is over 14 minutes. Let's say the average running time is A = 20 minutes.
If A = 20, then Jacob's time is J = A-4 = 20-4 = 16
If the average running time is 20 minutes, then Jacob ran for 16 minutes.
If we subtract 10 from this, then J-10 = 16-10 = 6 is one possible time for Sophia. Notice how this is 14 minutes below the average (20-14 = 6)
If we add 10 to Jacob's time, then J+10 = 16+10 = 26, which is 6 minutes overage the average (20+6 = 26)
This is one numeric example, but you could use any value of A that you want as long as it's larger than 14. The reason A has to be larger than 14 is to ensure that Sophia's lower time value (A-14) is not negative. Having a time of zero is not feasible either.