The circumference of a circle can be found using formula 2πr where r is the radius of circle.
What is the circumference of a circle?
A circle's or an ellipse's circumference is its perimeter. The circumference would be the length of the circle's arc, if the circle were opened up and straightened out to a line segment, in other words.
Suppose the radius of a circle is 5cm
So, we can find the circumference by using formula 2πr
Circumference = 2 × π × 5 = 10π cm.
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Look at the transformation of a 2-dimensional shape on the coordinate plane.
(x, y)→(−y,−x)
Which statement is true?
In the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x), the statement which is true is that: d. Transformation preserves distance and angle measure both.
What is a transformation?In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.
Based on the transformation rule (x, y) → (-y, -x), we can reasonably infer and logically deduce that it represents or models a rotation of the geometric shape, followed by a reflection, which both preserves distance and angle measure based on these transformation rules:
Rotation: (x, y) → (-y, x).Reflection: (x, y) → (x, -y).Read more on transformation here: https://brainly.com/question/29489050
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Complete Question:
Look at the transformation of a 2-dimensional shape on the coordinate plane. (x, y) → (-y, -x). Which statement is true?
a. Transformation preserves only distance.
b. Transformation preserves only angle measures.
c. Transformation preserves neither distance nor angle.
d. Transformation preserves distance and angle measure both.
Determine where the real zeros of f(x)=x^4-2x^3+x-2 are located.a. at -1 & 2 c. at 0 & 1 b. at 1 & 2 d. at -1 & 1
The real zeroes of the given polynomial are located at (1, 2).
What are zeroes of the polynomial?The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.
Given that, x⁴-2x³+x-2
Checking the real zeroes,
Considering point (1, 2)
y = 2 and x = 1
Putting the values,
x⁴-2x³+x-2 = 1-2+1-2 = 2
And, y = 2
Therefore, LHS = RHS
Hence, The real zeroes of the given polynomial are located at (1, 2).
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which number line represents the solution set for the inequality 4x 3 2 2x
The solution to the inequality expression is x ≥ - 5
what is inequality expressions ?
Both equations and inequalities are mathematical phrases created by connecting two expressions. The two expressions are regarded as being equivalent in an equation.
solution:
The given expression - 4(x + 3) ≤ –2 – 2x
- 4x - 12 ≤ -2 - 2x
-4x + 2x ≤ -2 + 12
-2x ≤ 10
-x ≤ 5
Multiply both sides by - 1
Then x ≥ - 5
Hence the solution to the inequality expression is x ≥ - 5
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Please I need help on both part A and B
Answer:
Step-by-step explanation:
I hope anyone answers
Help
Please
What is the measure of a base angle of an isosceles triangle if the measure of the vertex angle is 80 less than the sum of the measures of the base angles?
Answer: 65 °
Step-by-step explanation:
Let x = measure of a base angle
Base angles of an isosceles triangle are equal
Sum of interior angles of a triangle is always 180:
x + x + (2x - 80) = 180
4x - 80 = 180
4x = 260
x = 65
Can the two triangles be proven congruent by SAS explain?
Yes, two triangles can be proven congruent by SAS(Side angle side) congruence.
What is SAS Congruence?If any pair of comparable sides and their included angles are the same in both triangles, then the triangles are said to be congruent.
There are five ways to determine whether two triangles are congruent. It's one of them (SAS). Congruent Triangles provides a list. If any two comparable sides and their included angle in both triangles are same, then the triangles are congruent.
Why does this matter?
Due to the congruence of the triangles:
Third sides also have identical angles.
the other two complementary angles are equal
Two triangles, congruent since all three sides are the same length, but one flipped and rotatedCongruent triangles can be turned and/or mirror images of each other (reflected).
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This exercise uses, the population growth model
A culture starts with 8300 bacteria, After 1 hour the count is 10,000 .
(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.)
n(t)=8300(1)
(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.)
17485.75 x bacteria
(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.)
50times
P is equal to 8700% for population x time in hours.
What is population growth model?P is equal to 8700% for population x time in hours. 2Ae%5E%28kx%29
K's model must be solved. ln%28p%29=ln%288700%29%
2Bkx%2Aln%28e%
29\skx%
2A1=ln%28p%29-ln%288700%
29\sk=%281%
2Fx%29%
28ln%28p%29-ln%288700%29%29
Replace the point (1,10000).
k=%281%
2F1%29%
28ln%2810000%
29-ln%288700%
29%
29\sk=ln%2810000%
29-ln%288700%
29 k=0.13926, which you might only desire to three or maybe even two significant figures.
You may just enter 10000% if you want p after two hours.
And it SHOULD be the same as 8700% (2810000%2F8700%).
Just give it a shot and see, 2Ae%5E%280.139%2A2%29. More particular, the model is highlighted by p=8700%. 2Ae%5E%280.139% 2Ax%29% 29.
Determine how long to double x.
Take the logs on both sides, then find x.
To put it more simply, start with this form: 2=1%2Ae%5E%280.13926%2Ax%29
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3. Represent and Connect Write 2,857 using only hundreds and ones.
By using a linear combination, we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
How to write the number using only hundreds and ones?To write the number using only hundreds and ones we need to write our number as a linear combination of ones and hundreds, so we can write:
2,857 = a*100 + b*1
There are multiple solutions for this, we can use b to cover the ones and the tens, so:
57 = b*1
57 = b
And we can use a to cover the hundreds and thousands, so:
2,800 = a*100
2,800/100 = a
28 = a
Then we can write our number using only hundreds and ones as:
2,857 = 28*100 + 57*1
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Why is it important to make ten?
It is important to make a ten in lower grades to make students understand the subtraction.
According to the question,
We have the following information:
Making a ten
Now, we know that in making a ten method we take 1 from the next left digit of the number from which we are subtracting any other number. Now, this number 1 is treated as 10 instead of 1 and then 10 is added to the digit to ease subtraction in lower grades.
Now, the subtraction can be easily performed by subtracting the smaller number from the larger number.
Hence, it is important to make tens in lower grades to make students understand the subtraction.
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A certain triangle has a 30° angle and a 60° angle. Which must be a true
statement about the triangle?
OA. The longest side is 3 times as long as the shortest side.
OB. The second-longest side is twice as long as the shortest side.
OCTwo sides of the triangle have the same length.
Sons
D. The longest side is twice as long as the shortest side.
Answer:
D. The longest side is twice as long as the shortest side.
Step-by-step explanation:
Given one angle is 30° and another is 60°, the third must be 90°, making a Special 30-60-90 triangle. In a 30-60-90 triangle, the hypotenuse (longest side) is twice (two times) as long as the shortest side.
NO LINKS!! Use tests for symmetry to determine which graphs from the list below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply.) Part 1
Answer:
[tex]\begin{aligned}\textsf{(a)} \quad y&=-6x^2\\y&=4x^2-2\end{aligned}[/tex]
[tex]\textsf{(b)} \quad x=\dfrac{1}{4}y^2[/tex]
Step-by-step explanation:
Part (a)A graph is symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph.
Linear functions are not symmetric with respect to the y-axis.
Quadratic functions are symmetric with respect to the y-axis if the y-axis is their axis of symmetry, so when the variable x is squared.
Cubic functions are not symmetric about the y-axis.
Square root functions are not symmetric about the y-axis.
There are two quadratic functions with x² in the given answer options.
Test to see if they are symmetric with respect to the y-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Given function:
[tex]y=-6x^2[/tex]
Replace x with (-x):
[tex]\implies y=-6(-x)^2[/tex]
[tex]\implies y=-6x^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Given function:
[tex]y=4x^2-2[/tex]
Replace y with (-y) and x with (-x):
[tex]\implies y=4(-x)^2-2[/tex]
[tex]\implies y=4x^2-2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the y-axis.
Part (b)A graph is symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, -b) on the graph.
Linear functions are not symmetric with respect to the x-axis.
Quadratic functions are symmetric with respect to the x-axis if the x-axis is their axis of symmetry, so when the variable y is squared.
Cubic functions are not symmetric about the x-axis.
Square root functions are not symmetric about the x-axis.
There is one quadratic functions with y² in the given answer options.
Test to see if it is symmetric with respect to the x-axis.
Test for symmetry
To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Given function:
[tex]x=\dfrac{1}{4}y^2[/tex]
Replace y with (-y):
[tex]\implies x=\dfrac{1}{4}(-y)^2[/tex]
[tex]\implies x=\dfrac{1}{4}y^2[/tex]
Therefore, as the function is equal to the original function, this function is symmetric with respect to the x-axis.
Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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Evaluate the expression.
(6 x 4) + (15÷ 5) =
?
Answer:
27
Step-by-step explanation:
first you multiply 6x4 which is 24 the you divive 15 by 5 you'll get 3 then you add 24 + 3 and your answer is 27
if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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Lydia and Claudia have the same number of charms in their collections. Lydia started with 6 charms and bought 3 more packs. Claudia started with 9 charms and bought 2 more packs. If each pack had x charms, which equation be used to find x?
A. x=(2+3)-(6+9)
B. x=6+3+9+2
C. 6x+3=9x+2
D. 3x-2x=6+9
E. 3x+6=2x+9
The equation that can be used to find x is
3x + 6 = 2x + 9
Option E is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Lydia started with 6 charms and bought 3 more packs.
Claudia started with 9 charms and bought 2 more packs.
If each pack had x charms.
This can be written as,
Lydia:
Number of charms = 6 + 3x
Claudia:
Number of charms = 9 + 2x
Now,
Lydia and Claudia have the same number of charms in their collections.
This can be written as,
6 + 3x = 9 + 2x
3x + 6 = 2x + 9
Thus,
The equation that can be used to find x is
3x + 6 = 2x + 9
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André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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What does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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what is the range of the function on the graph all real numbers
The required range is [0,∞]
All values, or inputs, constitute a function's domain, while all values, or outputs, constitute its range.
When examining a graph, the range of the function is from up to down, and the domain refers to all of the values on the graph from right to left.
Therefore , the range of the function on the graph of all real numbers extends from zero to positive infinity.
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What is the rule of proof?
The rules of proof is that every statement should be justified and never assume things when proofing in contradiction
The basic rules of proofs are as followings:
Each assertion should be legitimate.A support can allude to earlier lines of the verification, the speculation as well as recently demonstrated explanations from the book.Cases are frequently expected to finish a proof which has proclamations with an "or" in them.A logical inconsistency is reached when an assertion goes against any of the speculations, an earlier line of the confirmation, or any well established truth .A proof by logical inconsistency is possibly finished when a logical inconsistency has been arrived at for each situation.On the off chance that you can't find a defense and you are certain it is valid, you might wish to compose a separate verification as an after thought to demonstrate that support and afterward apply it to your unique circumstanceDuring a proof you might present new factors by saying "Let x be..."To know more about Proof here
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Luke and Cade have started running. Luke runs 15 more than three times the number of miles Cade runs. Together they run a total of 63 miles. Write an equation to determine the number of miles Luke and Cade ran.
*
1 point
3x + 15 = 63
x + 15 + 3x = 63
x - 15 + 3x = 63
3x - 15 = 63
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
Linear Equation:A linear Equation is a Mathematical expression that is used to calculate an unknown number of values or any unknown quantity. Here we use variables to represent the unknown numbers.
Here given that
Luke and Cade have started running
Luke runs 15 more miles than thrice of that of number of miles Cade runs
Since we don't know the number of miles run by Cade
Let us assume that Cade runs x miles
=> Number of miles run by Cade = x miles
From the given data,
The number of miles run by Luke will be = 3x + 15
=> Number of miles run by Luke and Cade = x + 3x + 15
Given that the total mile run by Luke and Cade = 63 miles
=> x + 3x + 15 = 63
Therefore,
The Linear equation that represents the above situation is given by
x + 3x + 15 = 63
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Use diagram to answer the questions below
a. Angle g is corresponding to angle c.
b. Angle f is alternate to angle d.
c. Angle d is corresponding to angle h.
d. Angle c is vertically opposite to angle a.
e. Angle c is alternate to angle e.
f. Angle f is vertically opposite to angle h.
g. Angle e is corresponding to angle a.
h. Angle e is vertically opposite to angle g.
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2. The two polygons below are congruent.
Which statement is a valid congruence statement?
A. polygon PQRST Ξ polygon XWVZY
B. polygon PQRST Ξ polygon WXYVZ
C. polygon PQRST Ξ polygon XYZVW
D. polygon PQRST Ξ polygon WVZYX
EVALUATE ₈C₇ and ₁₁P₅
₈C₇=
₁₁P₅=
The permutation and combination expressions have their values to be ⁸C₇ = 8 and ¹¹P₅ = 55440
How to determine the permutation and combination expressions?From the question, we have
⁸C₇ and ¹¹P₅
The combination expression: ⁸C₇
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 8 and r = 7
Substitute the known values in the above equation
Total = ⁸C₇
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
⁸C₇ = 8!/7!1!
Evaluate
⁸C₇ = 8
(b) The permutation expression: ¹¹P₅
The number of ways of selection could be drawn is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 11 and r = 5
Substitute the known values in the above equation
Total = ¹¹P₅
Apply the permutation formula
ⁿPᵣ = n!/(n - r)
So, we have
¹¹P₅ = 11!/6!
Evaluate
¹¹P₅ = 55440
Hence, the values are 8 and 55440
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Write an expression to represent: 8 less than the product of 2 and x.
How do you know if AB and CD are congruent?
If the length of two segments is equal then the two segments are congruent.
If l(AB) = l(CD) then seg AB ≅ seg CD.
Two line segments to be congruent if and only if they have the same length.
Two shapes are congruent if they are exactly the same shape and exactly the same size. In congruent shapes, all corresponding sides will be the same length and all corresponding angle will be the same measure.
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Find the number of distinguishable permutations of the letters in each word below.
(a) bigger
(b) Hollywood
(c) possess
The number of distinguishable permutations in the given letters are:
a.) Bigger= 720
b.) Hollywood = 362,880
C.) possess = 5040
What is permutation?Permutation is defined as the arrangement of data set in a definite form which involves multiplication from the given number to 1.
The word 'bigger' contains 6 letters. Therefore the permutation of 6 = 6×5×4×3×2×1 = 720
For the word 'hollywood' contains 9 letters. Therefore the permutation of 9 =9×8×7× 6×5×4×3×2×1= 362,880
For the word 'possess' contains 7 letters. Therefore the permutation of 7 = 7× 6×5×4×3×2×1 = 5040.
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5 2/3 divided by 2 1/8 Perform the indicated operation.
Answer: 2 and 2/3
Step-by-step explanation: To divide these mixed numbers, I would first rewrite them as improper fractions.
You should be familiar with how do this and if you aren't, send me a comment below and I can give you a quick review.
So 5 and 2/3 becomes 17/3 and 2 and 1/8 becomes 17/8.
This gives us 17/3 ÷ 17/8.
When we divide fractions, we just change the division sign
to multiplication and take the reciprocal (flip) the second fraction.
So we have 17/3 · 8/17.
before multiplying, we can cross-cancel the 17's by dividing by their greatest common factor of 17 to get 1.
So we have 1/3 · 8/1 which is 8/3.
Now since 3 goes into 8 twice, our we have 2 as our whole fraction.
Since there is 2/3 left over, we have a fraction of 2/3.
So our final answer is 2 and 2/3.
Match each equation with a graph above:
log (x) a. red R
10× b. black K
e× c. green G
ln (x) d. blue B
The equations are matched as below and the graph is plotted and attached
log (x) b. black K 10× d. blue Be× c. green Gln (x) a. red RWhat is logarithm graph?A log-log graph, also known as a log-log plot, is a two-dimensional graph of numerical data used in science and engineering that use logarithmic scales on both the horizontal and vertical axes.
The exponential graph is the opposite of logarithmic graph
In the given functions
log (x) is logarithmic function
10× is exponential function
Similarly, the natural exponent graph is the opposite of natural logarithm graph
in the given functions
e× is the natural exponential
ln (x) is the natural logarithm
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convert 1/2 into a decimal
Answer:0.5
Step-by-step explanation:
here you go
Can someone explain the formula I'd use to solve this
The formula for slope-intercept form is: y = mx + b
m = the slope of the line
b = the y-coordinate of the y-intercept, (0,b)
In this case, the slope is 3, since you go up 3 and to the right 1 to get from the point at (1,1) to the point at (2,4). 3/1 = 3
The line crosses the y-axis at (0,-2), so your b-value is -2.
The equation is y = 3x - 2.
In general, lines that increase (go uphill) from left-to-right have a positive slope. Lines that decrease (go downhill) from left-to-right have a negative slope.
