1) Since the equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And we've been told the Center (1,-5) and one point located at the circumference, (2,1). So let's find the radius, i.e. the distance from the center to any point to the circumference.
2) Let's use the Formula for the distance between (1,-5) and (2,1), derived from the Pythagorean Theorem:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(2-1)^2+(1_{}+5)^2} \\ d=\sqrt[]{37} \end{gathered}[/tex]3) So d = radius, and now we can plug those pieces of information into the formula of the circle:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-1)^2+(y+5)^2=(\sqrt[]{37})^2 \\ (x-1)^2+(y+5)^2=37 \end{gathered}[/tex]So we now have the formula for that circle.
Answer:
Radius (R) is equal to the distance between the points (-2,1) and (3,1)
R² = (1 - 5)² + (1 - 1)² = (-24)² + 0 = 579
R = 23.16
I'll give brainliest!!
Solve for m.m- 15 = 20
Answer:
m=35
Explanation:
Given the equation:
[tex]m-15=20[/tex]We solve for the value of m by adding 15 to both sides.
[tex]\begin{gathered} m-15+15=20+15 \\ m+0=35 \\ m=35 \end{gathered}[/tex]The value of m is 35.
Which of the following equations describes the line shown below? Check allthat apply.(-5,6)(-1,-1)
Options E and F are the correct options
Here, we need to get the equation of the line that passes through the two points given
Mathematically, the equation of a line can be generally expressed as ;
y = mx + c
where m is the slope of the line and c is the y-intercept of the lien ( where it crosses the y-axis)
To get the slope m , we are goint to use the formula below;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_{2\text{ - }}x_1} \\ \\ x_{1\text{ }}=-5,x_2=-1,y_1\text{ = }6,y_2\text{ = -1} \end{gathered}[/tex]Substituting these values into the slope equation , we have
m = (-1-(6))/(-1-(-5)) = -7/4
The equation is now in the form;
y = -7x/4 + c
what is left is to get the y-intercept
We can get the value of the y-intercept by substituting for x and y using any of the points
Let us use the second point
Here, x = -1 and y = -1
Thus;
-1 = -7(-1)/4 + c
-1 = 7/4 + c
c = -1-7/4 = -11/4
So the complete equation of the line is;
y = -7x/4 - 11/4
To properly answer the questions, we need the forms in the options that looks like or can be manipulated arithmetically to look like what we have as our answer
We proceed with each of the options one after the other to see if they can be written in the form of our answer
Option A
y - 5 = -7/4 ( x + 6)
Opening the bracket and evaluating;
y - 5 = -7x/4 - 42/4
y = -7x/4 -42/4 + 5
y = -7x/4 -22/4
we can see this is not a correct option
Option B
y - 6 = -4/7 (x + 5)
Multiply through by 7
7y - 42 = -4x - 20
7y = -4x - 20 + 42
7y = -4x + 22
divide through by 7
y = -4x/7 + 22/7
We can see this is incorrect also
Option C
y - 1 = -4/7(x-1)
Multiply through by 7
7y - 7 = -4x + 4
7y = -4x + 4 + 7
7y = -4x + 11
divide through by 7
y = -4x/7 + 11/7
This is incorrect too
Option D
y + 1 = -4/7 ( x + 1)
Multiply through by 7
7y + 7 = -4x - 4
7y = -4x -4 -7
7y = -4x - 11
y = -4x/7 - 11/7
This is incorrect also
Option E
y - 6 = -7/4 (x + 5)
Multiply through by 4
4y - 24 = -7x - 35
4y = -7x - 35 + 24
4y = -7x -11
y = -7x/4 - 11/4
This is a correct option
Option F
y + 1 = -7/4 ( x + 1)
Multiply through by 4
4y + 4 = -7x - 7
4y = -7x - 7-4
4y = -7x - 11
y = -7x/4 - 11/4
This is a correct option too
A backpack weighs 10 N. What is the mass of the backpack?
The mass of the backpack is 1.02 kilograms.
What is the mass of the backpack?On earth, the weight of an object of mass M is given by:
W = M*g
Where g is the gravitational acceleration:
g = 9.8m/s^2
In this case, the weight is 10N, then we can write:
10N = M*9.8m/s^2
Solving this for M we get:
10N/(9.8m/s^2) = M = 1.02 kg
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If f(x)=x²-3x+5 and g(x)=-2x, find the following composition.
(f ° g)(2)
(f ° g)(2) = ____ (Simplify your answer.)
The value of the composite function (fog)(2) is equivalent to 0
Composite functionsA mathematical procedure called "function composition" combines two functions, f and g, to produce a third function, h, where g is the sum of f and
Given the functions below;
f(x) = x^2-3x+5
g(x) = -2x
Determine the composite function (gof)(2)
(fog) = f(g(x))
f(g(x)) = g(x^2-3x+5)
f(g(x)) = -2(x^2-3x+5)
f(g(2)) = -2(2^2-3(2)+2)
f(g(2)) = -2(0) = 0
This gives the equivalent composite value
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Please help with this problem
Answer:
The answer is I think 16
Step-by-step explanation:
You can look at the figure beside andfind this answer
How many pairs of parallel edges are there this rectangular prism
Answer:
6 i think
Step-by-step explanation:
if you count the top and bottom one, thats 2, the two sides, and the front and back. add 2+2+2 which is 6.
Which of the following is the equation that represents the graph?
Graph of a line the passes through the points negative 3 comma 0 and 0 comma negative 2.
y equals negative two thirds times x minus 3
y equals negative three halves times x minus 2
y equals negative three halves times x minus 3
y equals negative two thirds times x minus 2
y equals negative two thirds times x minus 2 is the equation of graph.
What is slope of line?The slope of the line is the ratio of the rise to the run, or rise divided by the run.
The given two points are 3 comma 0 and 0 comma negative 2.
i.e (3,0)(0,-2)1)
The formula for slope is (y₂-y₁)/(x₂-x₁)
slope = (-2 - 0) / (0 - 3)
= -2 / -3
The negative negative are multiplied we get positive
= 2/3
The standard form of a line is y = mx + b, where m is slope of line and b is y intercept.
slope(m) = 2/3
We can use either of points (0,-2)...x = 0 and y = -2
now sub and find b, then y intercept
-2 = 2/3(0) + b
-2 = b
so equation is : y = 2/3x - 2
Hence y equals negative two thirds times x minus 2 is the equation of graph.
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Evaluate f(3) for f(x)=2x+6
Nakeisha needs to order some new supplies for the restaurant where she works. The restaurant needs at least 566 forks. There are currently 188 forks. If each set on sale contains 8 forks, which inequality can be used to determine xx, the minimum number of sets of forks Nakeisha should buy?
The inequality that can be used to determine the minimum number of set of forks Nakeisha should buy is xx ≥ (566 - 188) / 8.
What is the minimum set of forks she should buy?The first step is to determine the appropriate inequality signs that can be used.
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is ≥.
The form of the inequality is: xx ≥ (least number of forks needed - forks they current have) / number of forks in one set
xx ≥ (566 - 188) / 8
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Answer:
566 < 188 + 8x
Step-by-step explanation:
find 5 consecutive odd integers who's sum is -45(solve algebraically)
let the consecutive odd integers be
x, x+ 1, x+ 2, x + 3, x + 4
Average = sum / total number
Average = -45
Total number = 5
-45 = x + x + 1 + x + 2 + x + 3 + x + 4 / 5
Introduce cross multiplication
-45 x 5 = x + x + 1 + x + 2 + x + 3 + x + 4
-225 = x + x + x + x + x + 1 + 3 + 4 + 5
-225 = 5x + 16
A particle moves along the x-axis so that at time t\ge 0t≥0 its velocity is given by v(t)=3t^2-18t+15.v(t)=3t2−18t+15. Determine all values of tt when the particle is at rest.
When a particle is at rest, the velocity = 0. Therefore, we equate the v(t) term to zero (0)
[tex]undefined[/tex]#8.Verify algebraically if the function is even, odd, or neither
g(x)= x^4 √(1+x)
g(-x) = (-x)^4 √1-x
g (-x) = x^4 √1-x
Since the obtained function is not the same or the opposite it is neither.
What is a(b(x)) if a(x) = 3x 2 and g(x) = -3x + 1?
The equivalent composite function is expressed as -9x + 5
Composite functionsComposite functions are also known as function of a function.
Given the following functions:
a(x) = 3x+2 and
b(x) = -3x + 1
Determine the value of a(b(x))
a(b(x)) = a(-3x+1)
a(b(x)) = 3(-3x+1) + 2
a(b(x)) = -9x + 3 + 2
a(b(x)) = -9x + 5
This gives the equivalent composite function.
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First person to help gets brainliest!!
The value of x from the equation represented by the given bar diagram is 20.
The equation is represented using the bar diagram and from the bar diagram be can observe that the equation will be the following equation mentioned below:
3.5 x + 12.5 x = 320 equation 1
The bar diagram represents 3.5 x + 12.5 x = 320 equation. Now we will simplify this equation and will find the value of x from this equation. The steps that need to be followed to simplify this equation are shown below;
3.5 x + 12.5 x = 320
16 x = 320
Divide both sides of equation by 16 , we will get
x = 320/16
x = 20
The value of x from the equation 3.5 x + 12.5 x = 320 is 20.
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Simplify using exponent: B³ x B⁵
HELPPPPPP
Answer:
B⁸
Step-by-step explanation:
When you have the same base, which in this case is B, you add the exponents and you get 8.
Hope this helps!
P.S, could I get Brainliest? Thanks!
If a1 = 7 and an3an-1 + 4 then find the value of a4.
A1 = 7
An = 3A(n-1) + 4. According to this, A2 would be= 3*7 + 4 =25
A1 = 7, A2 = 25, then the difference is d = 18
The general formula for an aritmethic progression is An = A1 + (n -1)d
For A4 = 7 + (4-1)*18 = 61
The graphs below have the same shape. f(x) = x2What is the equation of the graph of g(x)?10g(x)f(x)X10510-10O A. g(x) = (x+3)2B. g(x) = (x - 3)2C. g(x) = x2 - 3D. g(x) = x2 + 3
The equation of f(x) is
[tex]f(x)=x^2[/tex]The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.
For horizontal translation, we follow the following rule >>>
Let parent function be f(x), then
• f(x+a) is the parent translated "a" units left
,• f(x-a) is the parent translated "a" units right
Thus, following the rule, we can clearly say that g(x) = f(x+3)
We can write >>
Central Bank pays 8.5% interest, compounded daily, from the date of deposit to the date of withdrawal. The daily interest rate (to the nearest millionths place) forJuly 28 (92 days in the quarter) on this account is:0.000198.0.0002070.000231.0.000216None of these choices are correct.
ofGiven the yearly interest rate as 8.5%
To find the daily interest, we will divide the yearly interest rate by 365 as shown below:
[tex]\text{daily interest rate=}\frac{yearly\text{ interest rate}}{365}[/tex][tex]\text{daily interest rate=}\frac{\frac{8.5}{100}}{365}=\frac{0.085}{365}=0.0002328767[/tex]Hence, the daily interest rate (to the nearest millionths place)= 0.000232, The third option
Can you help me find the slope, y-intercept, and the equation based off this chart?
y-interceptis As given by the question
There are given that the value of x and y.
Now,
For finding the value of the slope, choose two-point from the given table
So,
Suppose the two points are:
[tex](1,\text{ 5) and (}3,\text{ 3)}[/tex]Now,
From the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3[/tex]Put all the above value into the given formula
So,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3_{}-5_{}}{3_{}-1_{}} \\ m=-\frac{2}{2} \\ m=-1 \end{gathered}[/tex]Hence, the value of the slope is -1.
Now,
For the equation of the line that is based on the given chart, use two supposes point and the given slope.
So,
The two poin and slope is:
[tex](1,\text{ 5) and (3, 3) and m=-1}[/tex]Then,
From the formula of two point form;
[tex](y-y_1)=m(x-x_1)[/tex]Where,
[tex]x_1=1,y_1=5,x_2=3,y_2=3,\text{ m=-1}[/tex]Then,
Put all the given value into the above formula
So,
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ (y-5_{})=-1(x-1_{}) \\ (y-5)=-x+1 \\ y-5+x-1=0 \\ y+x-6=0 \end{gathered}[/tex]Hence, the equation of the line is:
[tex]y=-x+6[/tex]Now,
To find the y-intercept, put x=0 and solve for x
So,
The y intercept of the given equation is:
[tex]\begin{gathered} y=-x+6 \\ y=-(0)+6 \\ y=6 \end{gathered}[/tex]Hence, the y-intercept is (0, 6)
tommie works at a local store on the weekends. He earns $11.50 per hourr. tommie will get a 10% raise after working 4 weeks. How much will he make per hour after his raise?
Tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
What is Percentage?In mathematics, a percentage is a number or ratio expressed as a fraction of 100.
Given is tommie who earns $11.50 per hour and he will get a 10% raise after working 4 weeks.
The amount tommy will earn after 10% raise can be calculated as follows-
10% of 11.50
10/100 x 11.5
1.15
Earnings per hour after raise = 11.5 + 1.15 = $12.65
Therefore, tommie will earn $12.65 per hour after his 10% raise after 4 weeks.
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I was explained this by another tutor but it didn't make too much sense
Given a right angle triangle
The hypotenuse of the triangle = x
The adjacent side to the angle 50 = 6
We will find x using the cosine function as follows:
[tex]\begin{gathered} \cos 50=\frac{adjacent}{hypotenuse} \\ \\ \cos 50=\frac{6}{x} \\ \\ x=\frac{6}{\cos 50}=9.334 \end{gathered}[/tex]Rounding to the nearest tenth
So, the answer will be x = 9.3
Please help I will mark branlist
Answer: True
Step-by-step explanation:
I believe it's true since a quadratic equation can either have one real solution, two real solutions, or no real solutions. Hope this helps.
confused on this please help!!
Answer:
12.75
Step-by-step explanation:
it is the same as the other side just like the similar triangle is.
PLS HELP ASAP WILL GIVE BRAINLIST
The angles in the parallelogram is as follows:
a = 27°b = 55°c = 55°How to find angles in a parallelogram?A parallelogram is a quadrilateral with opposite sides equal to each other and opposite side parallel to each other.
The diagonal of a parallelogram bisect each other.
Therefore, the angles a, b and c in the parallelogram can be found as follows:
180 - 118 - 35 = a (sum of angles in a triangle)
180 - 153 = a
a = 27 degrees.
Therefore, let's find angle b.
62 + 63 + b = 180 (sum of angles in a triangle)
125 + b = 180
180 - 125 = b
b = 55 degrees
Let's find the angle c
Hence,
b = c (alternate angles)
Therefore,
c = 55 degrees.
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The diameter of Mars is about 9^4 kilometers. Write 9^4 as a product. Then find the value of the product.
Suppose that Kevin's checking account shows a balance of $910.25 at the beginning of the month. During this month, he makes deposits of $175.35, $472.25, $235.40, and $450.15, and he writes checks for $307.50, $289.25, $150.30, and $327.00. Find the end-of-the-month balance in his account.
Answer:
The answer is $1,169.35
Step-by-step explanation:
Deposits is when you put money into your account, so, you'll add what he deposits. which will be $2,242.4, Next when he writes a check it means he took money out of his account so you'll subtract. You'll add up the amount of checks he wrote and subtract your answer with the deposits so, $2,243.4, - $1,074.05 = 1,169.35 and thats how you get your answer.
Question 1 (10 points)
Listen ▶
Twelve major Earthquakes had Richter magnitudes shown here.
6.8 6.0 7.5 6.8 6.2 6.0 7.0 5.2 6.2 6.3 7.0 5.2
Find Mean
5.35
6.35
7.35
6.95
I want answer. I need t’s solution.And I want explanation too.
we have the equation
[tex]log(\frac{1,000}{253.95})=12tlog(1+\frac{0.08}{12})[/tex]Solve for t
That means
Isolate the variable t
[tex]t=\frac{log(\frac{1,000}{253.95})}{12log(1+\frac{0.08}{12})}[/tex][tex]t=17.2[/tex]how many 4 letter code words can be made using the letters in the word pencil
Combination is a way of selecting items from a collection where the order of selection does not matter.
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
We have,
Total number of letters in the word pencil = 6
i,e P E N C I L
Combination formula:
[tex]^nC_r[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
Here,
n = 6
r = 4
The number of 4-letter code words that can be made using the letters in the word pencil:
[tex]^6C_4[/tex] = 6! / 4! 2! = (6 x 5) / 2= 15
Thus,
The number of 4-letter code words that can be made using the letters in the word pencil is 15.
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