true
any given point in a circle is equal distance from the center
Answer: TRUE.
Step-by-step explanation:
It knows that the distance "d" between any two points is equal to [tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex].
In a circle the distance between a point that belongs to the circumference and the center ([tex]x_0,y_0[/tex]) is always the same. Then:
[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex] is always equal to a constant called "r".
This is:
[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}=r[/tex]
Square both sides of the equality:
[tex](\sqrt{(x-x_0)^2-(y-y_0)^2})^2=r^2[/tex]
[tex](x-x_0)^2-(y-y_0)^2=r^2[/tex]
Note that we obtain the General equation of a circle.
This prove that if the distance between a given point in the plane and a collection of points is equal, then the equation of a circle is obtained.
Therefore, the statement "A circle is the collection of points in a plane that are the same distance from a given point in the plane." is true.
solve kx+7=4 for x[tex]kx+7=4[/tex]
Answer:
x = [tex]\frac{-3}{k}[/tex]
Step-by-step explanation:
Given
kx + 7 = 4 ( isolate the term in x by subtracting 7 from both sides )
kx = - 3 ( divide both sides by k )
x = [tex]\frac{-3}{k}[/tex] = - [tex]\frac{3}{k}[/tex]
Answer:
The value of the equation for x is [tex]x=\frac{-3}{k}[/tex]
Step-by-step explanation:
Consider the provided equation.
[tex]kx+7=4[/tex]
We need to solve the equation for x.
Subtract 7 from both the sides.
[tex]kx+7-7=4-7[/tex]
[tex]kx=-3[/tex]
Divide both sides of the equation with k.
[tex]\frac{kx}{k}=\frac{-3}{k}[/tex]
[tex]x=\frac{-3}{k}[/tex]
Hence, the value of the equation for x is [tex]x=\frac{-3}{k}[/tex]
estimate each to the nearest integer. square root of 44
The square root of 44 is 6.633249581
If you were going to round to the nearest whole number, it would be seven.
Hope that helps!
The value square root of 44 is 6.63 thus nearest integer of the square root of 44 will be 7.
How do round any digit?To round up or down tens place then we need to look at the unit place if it is less than 5 then we need to keep it as it and if it is greater than 5 then we need to round up the tens digit.
In order to round to a hundred, we need to look at the tens digit if it is less than 5 then we keep it as it is.
As per the given,
The square root of 44 = √44
√44 = 6.633249581
Since 6 > 5 so it will round up to the nearest integer.
6.633249581 → 7
Hence "The value square root of 44 is 6.63 thus nearest integer of the square root of 44 will be 7".
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Solve this rational equation 1/x-4 + x/x-2 = 2/x^2-6x+8
Answer:
one solution : x = -1
Step-by-step explanation:
look this solution :
The solutions of the given rational equation are negative one and three.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
The rational equation is given below.
[tex]\rm \dfrac{1}{x-4} + \dfrac{x}{x-2} = \dfrac{2}{x^2-6x+8}[/tex]
By solving the equation, then we have
[tex]\begin{aligned} \dfrac{1}{x-4} + \dfrac{x}{x-2} &= \dfrac{2}{x^2-6x+8}\\\\ \dfrac{x- 2 + x(x - 4)}{(x-4)(x - 2)} &= \dfrac{2}{x^2-6x+8}\\\\\dfrac{x^2 -4x + x - 2}{x^2 - 6x + 8} &= \dfrac{2}{x^2-6x+8}\\\\x^2 - 3x - 2 &= 2\\\\x^2 - 3x - 4 &= 0\end[/tex]
Then the solution of the equation will be
x² - 3x - 4 = 0
x² - 4x + x - 4 = 0
x(x - 4) + 1 (x - 4) = 0
(x - 4)(x + 1) = 0
x = -1, 4
More about the rational number link is given below.
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which of the following rational functions is graphed below
Answer:
D
Step-by-step explanation:
This graph shows two vertical asymptotes, one at x = +3, the other at x = 4. Thus, we omit the first two answer choices. Next, we substitute 0 for x and determine the y value in Answer Choice C: F(0) = 0. Does the graph go through (0, 0)? Yes, it does. Next, evaluate F at x = 3.5 (halfway between x = 3 and x = 4); that is, evaluate function D at x = 3.5. Does the y value come out to be -4 as shown in the graph? Yes, it does. So D is the correct function to match this graph.
Considering the vertical asymptotes of the function, and it's behavior, it is found that the rational function graphed below is given by:
D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]
What are the vertical asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
In this problem:
There are vertical asymptotes at x = 3 and x = 4, hence the denominator of the function is (x - 3)(x - 4).At x = 3.5, we have that f(x) is approximately 4, hence the numerator is 1.Thus, the correct option is:
D. [tex]f(x) = \frac{1}{(x - 3)(x - 4)}[/tex]
More can be learned about vertical asymptotes at https://brainly.com/question/11598999
ABC is a triangle. D is a point, vectors 2BD = 3DC
Prove vectors 2AB + 3AC = 5AD
3Ac?????????????????
A rock weighing 15.0 g is
placed in a graduated cylinder,
displacing the volume from
25.0 mL to 36.2 mL. What is
the density of the rock in
grams/cubic centimeter?
Answer: [tex]1.38\frac{g}{cm^3}[/tex]
Step-by-step explanation:
You need to remember the formula for calculate the density:
[tex]density=\frac{mass}{volume}[/tex]
In this case:
[tex]density_{(rock)}=\frac{mass_{(rock)}}{Volume_{(rock)}}[/tex]
You know that:
[tex]mass_{(rock)}=15.5g[/tex]
And when it is placed in a graduated cylinder, the volume is displaced from 25.0 mL to 36.2 mL.
Then, the volume of the rock is:
[tex]Volume_{(rock)}=36.2mL-25.0mL=11.2mL[/tex]
Since [tex]1mL=1cm^3[/tex], you can rewrite the volume as:
[tex]Volume_{(rock)}=11.2cm^3[/tex]
Substituting values into the formula, you get that the density of the rock is:
[tex]density_{(rock)}=\frac{15.5g}{11.2cm^3}=1.38\frac{g}{cm^3}[/tex]
What is the solution of log base 3x + 4 * 4096 = 4?
x = −1
x = 0
x = 4 over 3
x = 3
Answer:
[tex]x=\frac{4}{3}[/tex]
Step-by-step explanation:
The given logarithmic equation is
[tex]\log_{3x+4}(4096)=4[/tex]
We take antilogarithm to get:
[tex]4096=(3x+4)^4[/tex]
We write the left hand side as a power.
[tex]8^4=(3x+4)^4[/tex]
Since the exponents are the same the bases are also equal.
[tex]8=3x+4[/tex]
[tex]8-4=3x[/tex]
[tex]4=3x[/tex]
Divide both sides by 3;
[tex]x=\frac{4}{3}[/tex]
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Rewrite the equation of the circle (x − 2)2 + y2 = 3 in general form.
Answer:
y = √-2x+7
y = -√-2x+7
Answer:
x² + y² - 4x + 1 = 0
Step-by-step explanation:
The equation of a circle in general form is
x² + y² + 2gx + 2fy + c = 0
Given
(x - 2)² + y² = 3 ← expand the squared factor
x² - 4x + 4 + y² = 3 ( subtract 3 from both sides )
x² + y² - 4x + 1 = 0 ← in general form
Find the slope intercept form.
1. 2y + 4 = 8x
2. y = -5x + 6
3. y = -3x - 9
4.6y + 12 = 18x
2. and 3. are already in slope intercept form.
1. y=4x-2
4. y=3x-2
Use the function below to find F(1). F(t)=2•1/2^3t
Answer:
Final answer is [tex]F\left(1\right)=0.2625[/tex].
Step-by-step explanation:
Given function is [tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex].
Now we need to use that function [tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex] to find the value of F(1).
F(1) means value of functino F(t) at t=1, So plug t=1 into given function.
[tex]F\left(t\right)=\frac{2.1}{2^3t}[/tex]
[tex]F\left(1\right)=\frac{2.1}{2^3(1)}[/tex]
[tex]F\left(1\right)=\frac{2.1}{8(1)}[/tex]
[tex]F\left(1\right)=\frac{2.1}{8}[/tex]
[tex]F\left(1\right)=0.2625[/tex]
Hence final answer is [tex]F\left(1\right)=0.2625[/tex].
Answer:
The solution is [tex]F(1) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given function is [tex]2\times \frac{1}{2^{3t}}[/tex]
We need to find the value of function [tex]F(t) = 2\times \frac{1}{2^{3t}}[/tex] at t = 1
Replace t with 1 in [tex]F(t) = 2\times \frac{1}{2^{3t}}[/tex]
[tex]F(1) = 2\times \frac{1}{2^{3(1)}}[/tex]
[tex]F(1) = 2\times \frac{1}{2^{3}}[/tex]
[tex]F(1) = 2\times \frac{1}{8}[/tex]
[tex]F(1) = \frac{2}{8}[/tex]
[tex]F(1) = \frac{1}{4}[/tex]
Therefore, the solution is [tex]F(1) = \frac{1}{4}[/tex]
Through a point, not a given line, how many perpendicular lines can be drawn to the given line?
A. Two
B. Infinite
C. None
D. Only one
Answer:
D. Only one
Step-by-step explanation:
Lines are perpendicular if they intersect to form a right angle (90°).
The perpendicular postulate tells you that when you have a line and a point not on the line, then there is only one perpendicular line that can be drawn through the point to the line.
Final answer:
From a point not on a given line, only one perpendicular line to the given line can be drawn, as it is the shortest and unique path between the point and the line.
Explanation:
The question relates to the geometric concept of drawing perpendicular lines to a given line from a point outside of that line. According to geometric principles, through a point not on a given line, you can draw only one perpendicular line to the given line. This is because the perpendicular line is the shortest path between a point and a line, and only one unique shortest distance exists, as any other line from the point to the given line will be longer. Therefore, if you were given a point and a line that the point is not on, you could take a ruler or a straight edge and draw exactly one line that crosses the original line at a 90-degree angle, demonstrating a perpendicular connection.
a falcon can fly at a speed of 87 kilometers per hour. a goose can fly at a speed of 78 kilometers per hour. Suppose a falcon and a goose each fly for 6 hours. How much further will the falcon fly?
Answer:
54 kilometers
Step-by-step explanation:
87x6 or 522km - 78x6km or 468 = 54
The falcon can fly 54km further than the goose.
How to find the difference between the distance traveled by the falcon and the goose?
Speed of the falcon = 87km/hr
Speed of the goose = 78km/hr
speed = [tex]\frac{distance}{time}[/tex]
distance = speed*time
Distance traveled by falcon in 6 hours = 87*6 km = 522km
Distance traveled by goose in 6 hours = 78*6 km = 468 km
How much further the falcon fly
= Distance traveled by falcon - Distance traveled by goose
= (522 - 468 )km
=54km
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becky visited the great pyramid of Giza she learned that the pyramid was originally 481 feet tall and it’s square base has size measuring 751 feet in link Becky wants to know the volume of the pyramid what is the volume of the pyramid?
Final answer:
90,708,501 cubic feet .
Explanation:
The volume of a pyramid is calculated by using the formula V = (1/3) × (base area) × (height). Since Becky learned that the Great Pyramid of Giza has a square base with each side measuring 751 feet, we can calculate the base area as follows: base area = side × side = 751 feet × 751 feet. We then multiply this area by the height of the pyramid, which is 481 feet, and divide by 3 to find the volume. The calculation is as follows:
base area = 751 ft × 751 ft
Volume = (1/3) × base area × height
Volume = (1/3) × (751 × 751) ft² × 481 ft
Volume = 90,708,501 ft³
I need help please?!!!
Answer:
Step-by-step explanation:
This explains step by step
Hope this helps! <3 -K
Charlotte needs to collect at least 5,000 signatures for her petition. She has already collected 3,187 signatures. Write and solve an equation to determine how many more signatures Charlotte needs.
Okay!
The most important part of this problem is knowing which inequality sign to use
Greater than >
Less Than <
Equal to .. =
Greater or equal to ≥
Less than or equal to ≤
Charlotte needs AT LEAST 5,000 votes, meaning she has to have 5,000 votes or more
That means we use this sign → ≤
Now lets set up an equation to find how many more we need
5,000 ≤ 3,187 + X
solve for X
1,813 ≤ X
Hope I helped :) Sorry for the long explanation
Complete the table for the given rule.
Rule: y=x-5
x y
7
25
15
Answer:
I don't understand the question take a snip it or take a picture of the question
Step-by-step explanation:
Answers= 12, 30 and 10.
Explanation: 12-5 is 7
30-5 is 25
15-5 is 10
The slope of a line is 2/3 What is the slope of a line that is perpendicular to this line?
Answer:
3 /2
Explanation:
If two lines are perpendicular , when you multiply the gradients together you get -1
The slope of a line is 2/3 What is the slope of a line that is perpendicular to this line?
Answer:
-3/2
What is the value of x
X = 50
To solve this equation you would use 2x-5=95
Then you would solve and X = 50
The box-and-whisker plot shows the ages of employees at a video store. What fraction of the employees are 20 years or older?
About
of the employees are 20 years or older.
Sarah went on a one-day bus tour from Las Vegas to the Grand Canyon. The cost of the bus ticket was $80. She also paid 15% of the cost of the ticket as a tip to the bus driver. What was the amount of the tip that Sarah paid the bus driver?
$5
$12
$15
$19
PLEASE HELP! AND SHOW WORK!
Answer: the answer is 12 dollars
Step-by-step explanation: turn the percent 15 into a decimal, then just multiply .15*80 to get your answer
Answer: $12
Step-by-step explanation: 80$ is the cost. you're taking 15% of the cost. 15% of the cost is .15 of 80$. .15 x 80 is 12
Find the vertex form of y=-x^2-10x-21
Answer:
[tex]\large\boxed{y=-(x+5)^2+4}[/tex]
Step-by-step explanation:
[tex]\text{The vertex form of an quadratic equation}\\\\f(x)=ax^2+bx+c=a(x-h)^2+k\\\\h=\dfrac{-b}{2a}\\\\k=f(k)=\dfrac{-(b^2-4ac)}{4a}\\=================================[/tex]
[tex]\text{We have:}\\\\y=-x^2-10x-21\\\\a=-1,\ b=-10,\ c=-21\\\\h=\dfrac{-(-10)}{2(-1)}=\dfrac{10}{-2}=-5\\\\k=f(-5)=-(-5)^2-10(-5)-21=-25+50-21=4\\\\y=-(x-(-5))^2+4=-(x+5)^2+4[/tex]
Final answer:
The vertex form of the quadratic equation [tex]y = -x^2 - 10x - 21[/tex]is [tex]y = -(x + 5)^2 + 4[/tex], with the vertex being (-5, 4).
Explanation:
To find the vertex form of the quadratic equation [tex]y = -x^2 - 10x - 21[/tex], we need to complete the square. Here's a step-by-step guide:
Start with the given quadratic equation: [tex]y = -x^2 - 10x - 21.[/tex]
Factor out the coefficient of the [tex]x^2[/tex]term from the first two terms: [tex]y = -(x^2 + 10x) - 21.[/tex]
Find the number that completes the square for the expression [tex]x^2 + 10x.[/tex]This is [tex](10/2)^2 = 25.[/tex]
Add and subtract this number inside the parentheses, then group the perfect square and the constant terms: y = -[tex](x^2 + 10x + 25 - 25) - 21.[/tex]
Rewrite the equation, recognizing the perfect square trinomial: [tex]y = -[(x + 5)^2 - 25] - 21.[/tex]
Combine the constant terms: [tex]y = -(x + 5)^2 + 4.[/tex]
The vertex form of the equation is [tex]y = -(x + 5)^2 + 4[/tex], where the vertex of the parabola is (-5, 4).
A dime is 1.25 mm thick. How many meters high would a stack of dimes worth $50 be?
Answer:
625 mm
Step-by-step explanation:
$50 worth in dimes is 500 dimes. 500 dimes times 1.25mm per dime = 625mm
Pipe A can fill a tank in 40 minutes, while pipe B takes 60 minutes to fill the same tank.
If both pipes are used at the same time, how long will it take to fill the tank?
Answer:
24 minutes.
Step-by-step explanation:
This question shows up in a great many places in math or physics, so it is a pretty good question to learn how to do.
First you should note that answer will be under 40 minutes.
1/40 + 1/60 = 1/TimeTotal
The common denominator on the left is 120 minutes
3/40*3 + 2/60*2 = 1/timetotal
3/120 + 2/120 = 1/ timetotal
5/120 = 1/time total Now to use to the key stop
What you do now is you always turn the left side over. You do the same thing to total time.
120/5 = total time
24 = total time
What this means is that if you let both pipes run for 24 minutes, they will fill the tank working together.
henry had 20 convertibles and 5 trucks in his miniature car collection.After Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertibles .how many trucks did his aunt buy?
Answer:
75
Step-by-step explanation:
Henry started with 20 convertibles and 5 trucks.
His aunt bought him x miniature trucks.
Now, his convertibles represent 1/5 of his collection. How many trucks did her aunt buy?
So, if his convertible represent 1/5 of his collection now, that means his collection is 5 times larger than the number of convertibles. We know he has 20 convertibles... so the collection now counts 100 (5 * 20) items.
Out of 100 items, we remove the 20 convertibles to get a total of 80 trucks.
Then we subtract the initial 5 trucks... so, his aunt bought him 75 trucks.
His aunt bought 75 trucks
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem!
Let :
Number of Additional Miniature Trucks from Henry's Aunt = X
Initial Number of Convertibles = 20
Initial Number of Trucks = 5
Henry's aunt bought him some more miniature trucks,Henry found that one-fifth of his collection consisted of convertible.
[tex]\frac{1}{5}( 20 + 5 + x ) = 20[/tex]
[tex]\frac{1}{5}( 25 + x ) = 20[/tex]
[tex]( 25 + x ) = 20 \div \frac{1}{5}[/tex]
[tex]25 + x = 20 \times \frac{5}{1}[/tex]
[tex]25 + x = \frac{20 \times 5}{1}[/tex]
[tex]25 + x = \frac{100}{1}[/tex]
[tex]25 + x = 100[/tex]
[tex]x = 100 - 25[/tex]
[tex]x = \boxed {75 ~ \texttt{trucks}}[/tex]
Conclusion:Henry's aunt bought him 75 trucks
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
Helen determined she walks about 1,800 steps per 4/5 mile. How many steps did she take if she walked 2 miles?
Divide 1800 by 1/5 and then add the answer to 1800 (4/5) so you get a whole: then double.
Huong collects coins. Over a three-year period she collected 1,000 nickels. After organizing them by year, she found that the number of nickels from a given year was related to the number minted that year:
minted (100 mill) | 3.3 | 7.8 | 11.8 | 12.6 | 15.1 | 16.4 |
In sample | 3 | 19 | 27 | 24 | 30 | 43 |
a.) Logarithmic
b.)exponential
c.)linear
d.)quadratic
Answer:
C.) Linear
Step-by-step explanation:
The line of best fit is a straight line.
Linear also make sense because the more nickles minted in a year, the more chance for a nickle to be from that year.
Which of the following has no solution ?
ANSWER
{x|x<0} and {x|x>0}
EXPLANATION
If the two inequalities have an intersection,then it has a solution.
If the two inequalities have no intersection, then there is no solution.
The inequality {x|x<0} and {x|x>0} has no intersection, there is no solution.
The inequalities
{x|x≤0} and {x|x≥0},
{x|x≤0} or {x|x≥0}
both have intersection, therefore have solutions.
a box without a top is made from a rectangular piece of cardboard, with dimensions 6 feet by 8 ft, by cutting out square corners with side length x. which expression can be used to determine the greatest possible volume of the cardboard box?
The answer is:
The second option:
[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]
Why?From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).
So,
Working with the length of the box:
Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(8-(x+x))=(8-2x)[/tex]
Now,
Working with the width of the box:
Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(6-(x+x))=(6-2x)[/tex]
Now that we already know the length and the width of the box, we must remember that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:
[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]
Have a nice day!
Answer: The second option!
Step-by-step explanation:
Solve for x in the triangle
A 1.7
B 2.6
C 2.7
D 3.0
Answer:
A
Step-by-step explanation:
Given 2 sides and the included angle use the Cosine rule to solve for x
x² = 1.6² + 1.1² - (2 × 1.6 × 1.1 × cos78° )
= 2.56 + 1.21 - ( 3.52 × cos78° )
= 3.77 - 0.7318
= 3.0382
Take the square root of both sides
x = [tex]\sqrt{3.0382}[/tex] = 1.7 → A
The point A(-3, -2) is translated using T: (x,y) → (x + 5, y - 3). What is the distance from A to A'?
Answer:
d=5.39 units
Step-by-step explanation:
Given A (-3, -2)
T= (x+5, y-3)
T= (-3+5, -2-3)
T=(2,-5)
Applying the translation on;
A( -3,-2)
A' (-3+2, -2+ -5)
A'= (-1, -7)
Distance
d= [tex]\sqrt { X2-X1)^2 + (Y2-Y1)^2[/tex]
A = (-3,-2) and A'(-1, -7)
d=√ (-1--3)² + (-7--2)²
d=√ (2)²+(-5)²
d=√4+25
d=√29
d=5.39 units