Write the equation of the circle:center at (5, - 2) , passes through (4, 0)
Answers
the equation of the circle is
(x-h)^2 + (y-k)^2 = r^2
if we replace the terms
(4-5)^2 + (0-(-2))^2 = r^2
Now, we can fin the radius if we solve the previous equation
( - 1 )^2 + ( 2 )^2 =r^2
1 + 4 = r^2
5 = r^2
r = SQRT(5)
Now, since we already know r, we can replace it in the circle equation to obtain the result
so, (x-h)^2 + (y-k)^2 = r^2
iquals to, (x-5)^2 + (y+2)^2 = 5
Related Questions
3andLet's compare38ロ<ロ>=First, write the fractions with the same denominator.х?138-138Then, use <, = , or > to compare the fractions.m 100
Answers
To rewrite the fractions as fractions with the same denominator we have to determine the minimum number greater than 8 and 3 that can be exactly divided by 8 and 3 (LCM). Notice that the LCM of 8 and 3 is
[tex]24=8\cdot3.[/tex]Because:
[tex]\begin{gathered} 8=2\cdot2\cdot2, \\ 3=3. \end{gathered}[/tex]Therefore, we rewrite the given fractions as:
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]From the above fractions, we get that:
[tex]\frac{3}{8}>\frac{1}{3}\text{.}[/tex]Answer:
a)
[tex]\begin{gathered} \frac{1}{3}=\frac{8}{24}, \\ \frac{3}{8}=\frac{9}{24}\text{.} \end{gathered}[/tex]b)
[tex]\frac{1}{3}<\frac{3}{8}\text{.}[/tex]Find an equation for the line that’s passes through the following points shown in the picture. ( Please fins answer in timely answer very brief explaination :) )
Answers
The general equation of line passing through the points (x_1,y_1) and (x_2,y_2) is,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Determine the equation of line passing thgrough the point (-6,-1) and (2,5).
[tex]\begin{gathered} y-(-1)=\frac{5-(-1)}{2-(-6)}(x-(-6)) \\ y+1=\frac{6}{8}(x+6) \\ y+1=\frac{3}{4}x+\frac{9}{2} \\ y=\frac{3}{4}x+\frac{9}{2}-1 \\ =\frac{3}{4}x+\frac{7}{2} \end{gathered}[/tex]So equation of line is y = 3/4x + 7/2.
Select the point that satisfies y≤ x²-3x+2.
Answers
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
To check for the equation, substitute each point into the inequality and check validity of solution
A (4, 4)
4 ≤ 16 - 12 + 2 ⇒ 4 ≤ 6 → True hence valid solution
B (3, 3 )
3 ≤ 9 - 9 + 2 ⇒ 3 ≤ 2 → False hence not valid
C (1, 1 )
1 ≤ 1 - 3 + 2 ⇒ 1 ≤ 0 → False hence not valid
D (2, 2 )
2 ≤ 4 - 6 + 2 ⇒ 2 ≤ 0 → False hence not valid
Therefore, the point A (4, 4) satisfies the equation y≤ x²-3x+2.
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Disclaimer: The question given by you is incomplete, the complete question is
Select the point that satisfies y ≤ x² - 3x + 2.
A. (4, 4)
B. (3, 3)
C. (1, 1)
D. (2, 2)
Answer:
The point A (4, 4) satisfies the equation y≤ x²-3x+2.
Step-by-step explanation:
Which fraction and decimal forms match the long division problem? 15) 4.000 301 1 00 90 100 90 A. and 0.26 15 В. 15 and 0.26 C. and 0.26 15 15 and 0.266
Answers
Which fraction and decimal forms match the long division problem? 15) 4.000 301 1 00 90 100 90 A. and 0.26 15 В. 15 and 0.26 C. and 0.26 15 15 and 0.266
we have
4/15=0.26666
so
the answer is
4/15 and 0.26option AFind the circumference of the circle. Give the exact circumference and then an approximation. Use i 3.14. diamater of 17cm
Answers
To find the circumference of the circle, we will follow the steps below
Formula for the circumference of a circle is
C = 2 π r
where C = circumference of the circle
π is a constant
r is the radius of the circle
From the question, diameter is 17 cm
radius is half the diameter
That is:
radius = 17/2 = 8.5 cm
π = 3.14
Substituting the parameter in the formula given will yield
C = 2 x 3.14 x 8.5 cm
C =53.38 cm
The exact circumference is 53.38 cm
The circumference is approximately 53 cm to the nearest whole number
Find the future value$4013 invested for 9 years at 4.1% compounded quarterly.
Answers
We are to find the future value
The future value can be calculated using
[tex]FV=PV(1+\frac{r}{100\alpha})^{n\alpha}[/tex]From the given information
PV = $4013
r = 4.1
n = 9 years
Since the investment is compounded quarterly then
α = 4
By substituting these values we get
[tex]FV=\text{ \$4013(1 }+\frac{4.1}{100(4)})^{9(4)}[/tex]Simplifying the equation we get
[tex]\begin{gathered} FV=\text{ \$}4013(1\text{ }+\frac{4.1}{400})^{36} \\ FV=\text{ \$}4013(1\text{ }+0.01025)^{36} \\ FV=\text{ \$}4013(1.01025)^{36} \\ FV=\text{ \$}4013(1.44436) \\ FV=\text{\$}5793.17 \end{gathered}[/tex]Therefore,
The Future Value is $5793.17
What is the correct classification of the system of equations below?14x + 2y = 10y + 7x = -5A. parallelB. coincidentC. intersecting
Answers
Given:
14x + 2y = 10
y + 7x = -5
Required:
To tell which option is correct
Explanation:
14x + 2y = 10
y + 7x = -5
the given two lines intersect each other
Required answer:
Option C
if you shift the function F(x) = log10 x up four units, what is the new function, G(x)?*PHOTO*
Answers
Given:
The function
[tex]F(x)=log_{10}x[/tex]Required:
If you shift the function up for four units. What is the new function G(x)?
Explanation:
We have that function is shifting up for four units that is on y axis.
So, the new function will look like
[tex]G(x)=log_{10}x+4[/tex]Answer:
option A is correct.
For this problem identify P, FV, I, r, n, and t.
Answers
a) P = 180,000cents
b) FV = 298,418cents
c) I = 118,418cents
d) r = 0.003375
e) n = 12
f) t = 15 years
Explanations:a) P is the principal in the given question. The principal can be the amount invested or borrowed.
According to the question, the amount invested is $1,800.00, hence the principal P is $1,800 which is equivalent to 180,000cents to the nearest cents
b) The future value is the amount after 15 years of investing the money. According to the question, Sandra earned a total interest of $1,184.18 after 15 years.
Future value = Principal + Interest
Future value = $1,800.00 + $1,184.18
Future value = $2,984.18
Hence FV to the nearest cent is 298,418cents
c) Given the total interest of $1,184.18
Convert to nearest cents
I = 1,184.18 * 100
I = 118,418cents
d) r is the rate in percentage. From the question the rate in percent is
3 3/8 %
Convert to decimal
[tex]\begin{gathered} r=3\frac{3}{8}\% \\ r=\frac{27}{8}\% \\ r=\frac{27}{800} \\ r=0.03375 \end{gathered}[/tex]e) n is the time of compounding. From the question, we are told that amount invested was compounded monthly. Since there are 12 months in a year, hence the value of n is 12.
f) "t" is the time taken by Sandra to invest $1,800 to earn the given interest. From the question, the time it takes is 15 years. Hence;
t = 15 years
1. Write a function V(x) that models the volume of the box where the length of the sides of the squares is x cm. (The formula for the volume of a box is: V = l ⋅ w ⋅ ℎ).2. Graph V(x). (You may use Desmos or draw in the provided grid.)
Answers
From the problem, the length and the width will be reduced by twice the side of the square.
The length of the box will be :
[tex]26-2x[/tex]The width of the box will be :
[tex]20-2x[/tex]and the height will be the measurement of the square side :
[tex]x[/tex]Note that the volume of a box is length x width x height.
1. The volume will be :
[tex]V(x)=x(26-2x)(20-2x)[/tex]Expand and simplify the function :
[tex]\begin{gathered} V(x)=x(26-2x)(20-2x) \\ V(x)=x(520-40x-52x+4x^2) \\ V(x)=x(4x^2-92x+520) \\ V(x)=4x^3-92x^2+520x \end{gathered}[/tex]2. Graph the function using desmos.
Would to ask question about composite shape perimeter. Having trouble sending drawing
Answers
First let's split the shape in two, like this:
As you can see, now we have a triangle on the right, the length of the base of this triangle is the length of the bottom side of the original figure minus the lenght of the top side of the original figure, we can find it like this:
b = 100 ft - 70 ft = 30 ft
The height of the triangle "h" equals the height of the rectangle, which is 50 ft, then we can find the length of the missing side a (the hypotenuse of the triangle) by means of the Pythagorean theorem, like this:
[tex]\begin{gathered} a^2=h^2+b^2 \\ a=\sqrt[]{h^2+b^2} \end{gathered}[/tex]Where "a" is the length of the hypotenuse, "h" is the height and "b" is the base. By replacing 30 for b and 50 for h, we get:
[tex]a=\sqrt[]{50^2+30^2}=\sqrt[]{2500+900}=10\sqrt[]{34}=58.3[/tex]Then the length of the missing side of the composite shape is around 58.3 ft:
Now that we know the lengths of the sides of this figure we can calculate its perimeter by summing them up, like this:
Perimeter = 70 + 50 + 100 + 58.3 = 278.3
The perimeter of this plot of land equals 278.3 ft
In quadrilateral ABCD, MZA = 72, mZB = 94, and m2C = 113. What is m2D?
Answers
First, let's picture the problem
Let's label the angle D as x
Remember that the sum of angles in a quadrilateral is 360
[tex]\begin{gathered} 72^0+94^0+113^0+x=360^{\square} \\ x=81^0 \\ m\angle D=81^0 \end{gathered}[/tex]According to the graph of H(w) below, what happens when w gets very large?H)5.6.20.00)A. H(w) gets very large.B. H(w) approaches a vertical asymptote.C. H(w) equals zero.D. H(w) gets very smallSUBMIT
Answers
Considering the graph H(w),
As w gets larger, H(w) continues to approach a horizontal asymptote.
Hence, H(w) gets very small.
Therefore, the correct option is option D
100 POINTS!! I NEED THIS KNOWW!!!!The number line shows the distance in meters of two birds, A and B, from a worm located at point X:A horizontal number line extends from negative 3 to positive 3. The point labeled as A is at negative 2.5, the point 0 is labeled as X, and the point labeled B is at 2.5.Write an expression using subtraction to find the distance between the two birds.Show your work and solve for the distance using additive inverses.
Answers
The expression used to represent the distance between the two birds on the number line is 2.5 - (-2.5) and the distance is 5 units.
Let us represent the bird A is sitting at one point on the number line.
Bird B is sitting at another point.
Both of them are at a an equal distance from a worm which is at the position O which is the origin.
Now it is given that A and B are at the positions of the number line marked 2.5 and -2.5
Now the distance between A and B can be calculated by finding the distance between A and O and adding the additive inverse to it to get the distance between O and B using subtraction.
AO = 2.5 - 0 = 2.5 units
The additive inverse of this is -2.5 units.
Therefore the distance AB :
= AO - BO
= 2.5 -(-2.5)
=2.5 +2.5
=5 units.
Hence they are at a distance of 5 units from each other.
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You are given two overlaying squares with side length a. One of the squares is fixed at the
bottom right corner and rotated by an angle of α (see drawing). Find an expression for the
enclosed area A(α) between the two squares with respect to the rotation angle α.
Answers
The expression for the area enclosed between the two squares with respect to the rotation angle α is
(α/90)a².
What is a square?A Square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given as side²
We have,
Side of the square = a
Area of the square = a²
The full angle that can be rotated is 90°.
Now,
The area enclosed if the angle is 90°.
= a²
We can write as,
The area enclosed in terms of the angle.
= (angle rotated / 90) x side²
= (angle rotated / 90) x a²
Now,
The angle rotated is α.
The area enclosed is (α/90)a².
Thus,
The expression for the area enclosed between the two squares with respect to the rotation angle α is
(α/90)a².
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what's the solution to this system
Answers
Remember that
when solving a system by graphing, the solution is the intersection point both graphs
so
In this problem
the intersection point is (-2,2)
therefore
the solution is (-2,2)need help asappppppp
Answers
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable)
For the ordered pairs given, we have inputs and outputs as shown below
The values of the input should be unique
Checking all the options given,
The pair (4,2) when added to the pairs will not make the relation a function because
4 will have two
Directons: Write each equation in slope-intercept form. Identify the slope and y-intercept.
Answers
Given:
The equation is x - y = -8.
Explanation:
The slope intercept form of linear equation is,
[tex]y=mx+c[/tex]Here, m is slope and c is y-intercept.
Simplify the given equation to obtain in slope-intercept form.
[tex]\begin{gathered} x-y=-8 \\ y=x+8 \\ y=1\cdot x+8 \end{gathered}[/tex]So slope of line is m = 1 and y-intercept is 8.
Answer:
Equation in slope ntercept form: y = x + 8
Slope: 1
Y-intercept: 8 OR (0,8)
Find the value of r so that the line through (-4, r) and (-8, 3) has a slope of -5.
Answers
The value of r is -17.
Given,
Points (-4,r) and (-8,3)
slope=-5
Let
A(x1,y1)=(-4,r)
B(x2,y2)=(-8,3)
To find 'r' use formula,
[tex]slope=\frac{y2-y1}{x2-x1}\\ \\-5=\frac{3-r}{-8-(-4)}\\\\-5=\frac{3-r}{-8+4}\\\\-5=\frac{3-r}{-4}\\\\20=3-r\\\\20-3=-r\\\\17=-r\\\\-17=r[/tex]
Thus, the value of r is -17.
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-2(y+5)+21<2(6-y) Solving for y
Answers
the points (v,-3) and (8,5) fall on a line with a slope of -8. what is the value of v?
Answers
The slope m is given by:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \text{Where:} \\ (x1,y1)=(v,-3) \\ (x2,y2)=(8,5) \\ m=-8 \\ so\colon \\ -8=\frac{5-(-3)}{8-v} \\ \text{solve for v:} \\ -8(8-v)=5+3 \\ -64+8v=8 \\ 8v=72 \\ v=\frac{72}{8} \\ v=9 \end{gathered}[/tex]Solve this equation.
2/3x−1/5x=x−1
A. 1 13/15
B. 1 7/8
C. 1 7/15
D. 7/8
Answers
Answer:
your answer would be c 1 7/15 tell me if I'm wrong
Step-by-step explanation:
Answer:
B 1 7/8
Step-by-step explanation:
2/3x−1/5x=x−1
1. multiply both sides by 15
10x-3x=15x-15
2. collect like terms
7x = 15x -15
3. move the variable to the left
7x-15x=-15
4. collect like terms
-8x = -15
5. divide both sides by -8
x=15/8
or
1 7/8
The boxplot below shows salaries for Construction workers and Teachers.ConstructionTeacher2025465030 35 40Salan (thousands of S)If a person is making the median salary for a construction worker, they are making more than what percentage ofTeachers?They are making more than% of Teachers.Check Answer
Answers
Const Workers , Teachers
Median salary of const Worker =45
Median salary of teacher = 40
Then, they are making more than 100% of teachers
Answer is
100%
Consider the function g. 9(-) = 6() For the x-values given in the table below, determine the corresponding values of g(x) and plot each point on the graph.. -1 0 1 2 g(x) Drawing Tools Click on a tool to begin drawing * Delete Undo Reset Select Point 14 13 12 11 10 9 00 reserved.
Answers
we have the function
[tex]g(x)=6(\frac{3}{2})^x[/tex]Find out the value of function g(x) for each value of x
so
For x=-1
substitute the value of x in the function g(x)
[tex]\begin{gathered} g(-1)=6(\frac{3}{2})^{-1} \\ g(-1)=6(\frac{2}{3}) \\ g(-1)=4 \end{gathered}[/tex]For x=0
[tex]\begin{gathered} g(0)=6(\frac{3}{2})^0 \\ g(0)=6 \end{gathered}[/tex]For x=1
[tex]\begin{gathered} g(1)=6(\frac{3}{2})^1 \\ g(1)=9 \end{gathered}[/tex]For x=2
[tex]\begin{gathered} g(2)=6(\frac{3}{2})^2 \\ g(2)=13.5 \end{gathered}[/tex]using a graphing tool
plot the different points
so
we have
(-1,4)
(0,6)
(1,9)
(2,13.5)
see the attached figure to better understand the problem
please wait a minute
If f -1(x) = (6/5)x - 9, find f (x).
Answers
Solution
Step 1
Write the inverse function:
[tex]f^{-1}(x)\text{ = }\frac{6}{5}x\text{ - 9}[/tex]Step 2
[tex]\begin{gathered} Let\text{ f}^{-1}(x)\text{ = y} \\ \\ y\text{ = }\frac{6}{5}x\text{ - 9} \\ \\ Make\text{ x the subject of the formula} \\ \\ y\text{ + 9 = }\frac{6}{5}x \\ \\ Divide\text{ both sides by }\frac{6}{5} \\ \\ x\text{ = }\frac{5}{6}(y\text{ + 9\rparen} \\ \\ f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen} \end{gathered}[/tex]Final answer
[tex]f(x)\text{ = }\frac{5}{6}(x\text{ + 9\rparen}[/tex]Translate the following into algebraic equation and solve: Twice the sum of a number and five is equal to 40.
Answers
Let:
x = Unknown number
Twice the sum of a number and five:
[tex]2(x+5)[/tex]Is equal to 40:
[tex]2(x+5)=40[/tex]Solve for x:
Expand the left hand side using distributive property:
[tex]2x+10=40[/tex]Subtract 10 from both sides:
[tex]2x=30[/tex]Divide both sides by 2:
[tex]x=15[/tex]Need answer to pictured problem! The answer should be in reference to trig identities
Answers
Step 1. The expression that we have is:
[tex]cos^2(5x)[/tex]and we need to find the equivalent expression.
Step 2. The trigonometric identity we will use to solve this problem is:
[tex]cos^2A=1-sin^2A[/tex]In this case:
[tex]A=5x[/tex]Step 3. Applying the trigonometric identity to our expression, substituting 5x in the place of A:
[tex]cos^2(5x)=\boxed{1-sin^2(5x)}[/tex]This is shown in option d).
Answer:
[tex]\boxed{d)\text{ }1-s\imaginaryI n^2(5x)}[/tex]IIIDECIMALSRounding decimalsRound 0.434 to the nearest hundredth.0x
Answers
Answer
Explanation
In rounding off numbers, when the number after the required level of precision is less than 5, we round it down. But if that number is 5 or more, we round it up.
For the rotation -1046°, find the coterminal angle from 0° < O < 360°, the quadrant and the reference angle.
Answers
Solution
Step 1
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Step 2
The reference angle is the smallest possible angle made by the terminal side of the given angle with the x-axis. It is always an acute angle (except when it is exactly 90 degrees). A reference angle is always positive irrespective of which side of the axis it is falling.
Coterminal angle
[tex]\begin{gathered} Coterminal\text{ angle = -1046 + 3}\times360 \\ Coterminal\text{ angle = -1046 + 1080} \\ Coterminal\text{ angle = 34} \end{gathered}[/tex]Quadrant = 1st quadrant
Reference angle
0° to 90°: reference angle = angle
Reference angle = 34
Final answer
Admission to the fair costs $6.00. Each ride costs you$0.50. You have $22.00 to spend at the fair on rides and admission. Express the number of tickets you can buy as an inequality.
Answers
Let:
x = Number of rides
Total money spent = $6.00 + $0.50x
Since you have $22.00 to spend at the fair on rides and admission:
[tex]\begin{gathered} 6+0.5x\leq22 \\ \text{solving for x:} \\ 0.5x\leq22-6 \\ 0.5x\leq16 \\ x\leq\frac{16}{0.5} \\ x=32 \end{gathered}[/tex]