If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute:
[tex]OP=\sqrt{(2-7)^2+(0-12)^2}=\sqrt{(-5)^2+(-12)^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OP=13}\\\\OQ=\sqrt{(2-(-3))^2+(0-(-12))^2}=\sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}\\\\\boxed{OQ=13}\\\\OR=\sqrt{(2-14)^2+(0-5)^2}=\sqrt{(-12)^2+(-5)^2}=\sqrt{144+25}=\sqrt{169}\\\\\boxed{OR=13}[/tex]
OP = OQ = OR, therefore the points P, Q and R lie on one circle.
What is the equation of a line with a slope of −4 and a point (−2, 5) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
Enter your answer in the box.
Expressing the equation in the form y = mx + b where m is slope and b is y-
intercept is represented as y = -4x - 3
The slope intercept form is represented as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
m = -4
using the coordinate (-2, 5) lets find b
y = -4x + b
5 = -4(-2) + b
5 = 8 + b
b = 5 - 8
b = -3
Therefore,
y = -4x - 3
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What number comes between 2 and 4
Answer:
3
Step-by-step explanation:
Count 1 to 5 (1,2,3,4,5). You can see 3 is between 2 and 4.
A number that comes between 2 and 4 would be 3.
Used the concept of a number system that states,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
Two numbers are 2 and 4.
Let us assume that the number that comes between 2 and 4 is, x
Then,
[tex]x = \dfrac{(2 + 4)}{2}[/tex]
[tex]x = \dfrac{(6)}{2}[/tex]
[tex]x = 3[/tex]
Therefore, the number would be 3 which comes between 2 and 4.
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Find the constant of proportionality (r)in the equation y=rx.
r =
Answer:
Constant of proportionality, [tex]r = \frac{1}{10}[/tex]
Step-by-step explanation:
Constant of proportionality states that the constant value of the ratio of two proportional quantities x and y,
it is written in the form of y = kx, where k is the constant of proportionality.
Given the equation: [tex]y =rx[/tex] .....[1]
where r is the constant of proportionality.
From the table we consider
x = 14 and y = 1.4
Substitute these given values in [1] to solve for r;
[tex]1.4 = r(14)[/tex]
Divide both sides by 14 we get;
[tex]r = \frac{1.4}{14} = \frac{14}{140} = \frac{1}{10}[/tex]
therefore, the Constant of proportionality, [tex]r = \frac{1}{10}[/tex]
The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x.
Explanation:The constant of proportionality, denoted as 'r', represents the ratio between the dependent variable (y) and the independent variable (x) in a linear equation. It determines the rate of change of y with respect to x. For example, in the equation y = rx, 'r' represents how much y changes for every unit change in x.
For instance, if the equation is y = 2x, then the constant of proportionality is 2. This means that for every unit increase in x, y increases by 2 units.
Keywords: constant of proportionality, linear equation, rate of change
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Write the quadratic equation whose roots are 6 and -5, and whose leading coefficient is 3
To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.
Explanation:The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5).
Expanding this, we have:
3(x² + 5x - 6x - 30)3(x² - x - 30)3x² - 3x - 90The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.
HELP PLEASE WILL GIVE 30 POINTS !!!!!! Determine the amount you need to invest to have $22,000 dollars in 4 years if you invest at 5% annual interest, compounded quarterly. ADD WORK PLEASE
Answer:
$18 034.42
Step-by-step explanation:
The formula for the future value of an account paying 5 % annual interest compounded quarterly for four years is
[tex]A = P(1 +\frac{r }{n })^{nt}[/tex]
A = $22 000
r = 0.05
n = 4 times per year
t = 4 years
[tex]22 000 = P(1 +\frac{0.05 }{4 })^{4\times4}[/tex]
[tex]22 000 = P(1 + 0.0125)^{16}[/tex]
[tex]22 000 = P(1.0125)^{16}[/tex]
22 000 = P x 1.220
P = 2 000/1.220
P = $18 034.42
You must invest $18 034.42.
Find the Nonpermissible replacement for y in this expression y-9/y+3
Answer:
y = - 3
Step-by-step explanation:
Providing you mean (y - 9)/(y + 3) then it is always the variable in the denominator that is going to cause trouble. If it equals zero at any point, it's game over.
It's a little better if you get a result like 0/0. That problem has a "depends" as an answer, but by and large, you don't want to monkey around with 0 in the bottom of a fraction.
y + 3 = 0 Subtract 3 from both sides.
y + 3 - 3 = 0 - 3 Combine
y = - 3
Ellentown college has appoximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students. how many times as much is the number of students at pengrove university as the number of students at Ellwntown college
Answer:
Given: Ellentown college has approximately 3 times 10 to the 3 power students and pengrove university approximate 30,000 students.
⇒ number of students approximately in Ellentown college = [tex]3 \times 10^3[/tex]
also,
the number of students approximately in Pengrove university = 30,000 or [tex]3 \times 10^4[/tex]
We have to find how many times as much is the number of students at pengrove university as the number of students at Ellentown college.
[tex]\frac{number of students in Pengrove University}{number of students in Ellentown college}[/tex] = [tex]\frac{3 \times 10^4}{3 \times 10^3} = 1 \times 10^1 = 10[/tex]
therefore, 10 times as much is the number of students at pengrove university as the number of students at Ellentown college.
javier opens a savings account with a starting balance of $200 and plans to deposit $75 each week after opening the account and savings over time is represented by the graph below how would the graph change if javier open his account with a starting balance of $300 instead
If Javier starts with a higher initial balance of $300, the initial point on his savings graph would be higher by $100, and all subsequent points would reflect this initial increase, though the slope of the graph would remain unchanged.
If Javier opens a savings account with a starting balance of $300 instead of $200 and then deposits $75 each week, the graph representing his savings over time would change in the following way:
The initial point on the graph, representing the starting balance, would be higher.
This is because the starting balance would be $300 instead of $200.
After this initial change, the slope of the graph, representing the weekly deposits of $75, would remain the same.
However, every point on the graph after the initial deposit would be $100 higher than it was before because each point on the savings graph accumulates the effects of the higher starting balance.
Colin and Rosie had the same number of cashews at first. Each day, Colin ate 5 cashews and Rosie ate 8 cashews. When Rosie had 4 cashews left, Colin had 10 times as many cashews left as Rosie. How many cashews did each child have at first?
PLEASE HELP! I will award brainliest to the most helpful answer. I need an in depth explanation, not just the answer. How do you know which side to shade/ where to shade? Thank you so much!
Answer:
y ≤ -4x+25
Step-by-step explanation:
First we need to figure out the equation for the line
The y intercept is 25
Next figure out the slope
slope = (y2-y1)/((x2-x1)
= (49-25)/(-6-0)
= 24/-6
= -4
The equation for a line in slope intercept form is y = mx+b
y = -4x+25
This is a solid line so our inequality will have an equals in it.
It is shaded below, so y is less than.
If it was shaded above, y would be greater than
y ≤ -4x+25
estimate 782 divided by 50
Answer: about 15.72
Step-by-step explanation: i used a calculator
Multiply.
Express the product in simplest form.
3/9·18=b
2
6
154
5
Answer:
The answer is 6
Step-by-step explanation:
What you do is this.
3/9 times 18/1 because you need to make 18 a fraction and then multiply. And you will get 6
if you have 10 cookies and you want to give 1/2 of them to a friend. How many do you give to your friend
Answer: You would give your friend 5 cookies
Step-by-step explanation:
One half of the cookies, is basically saying divided by two. 10 divided by 2 is 5. To check that answer, multiply 5 by 2, and you will get 10
3/7-2/14 (8-1/2) +2/7
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000i in decimal form
Answer:
3030.033
Step-by-step explanation:
Multiply each piece out and add them together
3 X 1,000 + 3 X 10 + 3 X 1/100 + 3 in X 1/1000
3000 + 30+.03 + .003
3030.033
please help???????????
Answer:
x - [tex]\sqrt{7}[/tex]
Step-by-step explanation:
A polynomial has the form
first term is the term of highest degree followed by term of second etc.
note that x = [tex]x^{1}[/tex] ← degree 1
x - [tex]\sqrt{7}[/tex]
fits this description and is a polynomial of degree 1
I don't get this problem from maths.
Answer:
100/3 or 33.33
Step-by-step explanation: If the perimeter of the whole figure is 220, we can use that number to solve the equations on the trapezoid.
2(2x-3) + 2(4) + 2(4x+1)
4x - 6 + 8 + 8x + 2
12x + 2
Now we have to set the equation equal to the perimeter to find the value of x
12x + 2 = 220
12x = 218
x = 109/6
Since we are only finding the length of PS, we will plug x into its equation (2x - 3).
2(109/6) - 3
109/3 - 3
109/3 - 9/3
100/3
check the picture below.
[tex]\bf \stackrel{\textit{perimeter of the trapezoid}}{(4x+1)+(4x+1)+(4)+(4)+(2x-3)+(2x-3)} \implies 12x+4[/tex]
Write the expression (4x-6) x 6(2x+7)
Answer:
48x² + 96x - 252
Step-by-step explanation:
(4x - 6) × 6(2x + 7) Reorder the factors
= 6(4x – 6)(2x+ 7) Multiply the binomials
= 6(8x² + 16x - 42) Remove parentheses
= 48x² + 96x - 252
Reagan surveyed a number of her classmates about what time they usually go to bed. Of the fifteen classmates she asked, three said 9 p.m. What percent of the students is this?
Answer:
20%
Step-by-step explanation:
We can say that 3/15 students usually go to bed at 9 P.M. We can set up a proportion to solve this problem.
3/15=x/100
We cross multiply to find x
15x=300
Divide both sides by 15
x=20
So 20% of the classmates usually sleep at 9 P.M.
Answer:
20% of the students
Step-by-step explanation:
How much of a spice that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt?
Please Helpppp!!
Answer:
Let y represents the ounces of first spice.
From the given statements, we draw a table as shown below:
ounces of spice Percentage ounces of salt
First spice y 3% 0.03x
Second spice 175 6% 175(0.06)
Final mixture y + 175 5% (x+15)(0.05)
Now, to solve for y
we have;
Final spice = First spice + second spice
[tex]0.03y + 175(0.06) = (y+175)(0.05)[/tex]
[tex]0.03y+ 10.5= 0.05y+ 8.75[/tex]
Subtract 10.5 on both sides we have;
[tex]0.03y+ 10.5 -10.5= 0.05y+ 8.75 -10.5[/tex]
Simplify:
[tex]0.03y = 0.05y -1.75[/tex]
Subtract 0.05y on both sides
[tex]0.03y -0.05y= 0.05y -1.75-0.05y[/tex]
Simplify:
[tex]-0.02y = -1.75[/tex]
Divide both sides by -0.02, we get;
[tex]y = \frac{-1.75}{-0.02} = 87.5[/tex]
Therefore, 87.5 ounces of spices that is 3% salt should be added to 175 ounces of a spice that is 6% salt in order to make a spice that is 5% salt
It needs 87.5 ounces of spice that is 3% salt.
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 !
[tex]\texttt{ }[/tex]
Given:
175 ounces of a spice that is 6% salt
[tex]\texttt{mass of salt from this spice} = s_1 = 6\% \times 175 = 10,5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
x ounces of a spice that is 3% salt
[tex]\texttt{mass of salt from this spice} = s_2 = 3\% \times x = 0.03x \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
(175 + x) ounces of a spice that is 5% salt
[tex]\texttt{total mass of salt} = s_1 + s_2[/tex]
[tex]5\% \times ( 175 + x ) = 10.5 + 0.03x[/tex]
[tex]8.75 + 0.05x = 10.5 + 0.03x[/tex]
[tex]0.05x - 0.03x = 10.5 - 8.75[/tex]
[tex]0.02x = 1.75[/tex]
[tex]x = 1.75 \div 0.02[/tex]
[tex]x = 175 \div 2[/tex]
[tex]x = 87.5 \texttt{ ounces}[/tex]
[tex]\texttt{ }[/tex]
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Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3
Which expressions represent 1 more then the product 5 and 2
Answer:
1+5*2 or simplified, 1+10= 11
Jake wants to estimate 15.92+0.85 . How can he use rounding to estimate the sum? What is the estimate?
Answer:
17
Step-by-step explanation:
15.92 is close to 16
0.85 is close to 1
15.92 + 0.85 is close to 16 + 1
16 + 1 = 17
15.92 + 0.85 is approximately 17
what is the slope of the line shown
(4, 2) (-4, -2)
m=?
(4, 2) (-4, -2)
Slope is the change in Y over the change in X
From the two points given:
Slope =( -2 - 2 ) / ( -4 -4)
Slope = -4 / -8
Slope = 1/2
m = 1/2
PLEASE HELP I HAVE 49 POINTS!
show work
Answer:
1. y = 2x-4
2 y = -1/2x+3
Step-by-step explanation:
Slope intercept form of the equation is y= mx+b
where m is the slope and b is the y intercept
1. y- 2x = -4
We need to solve for y
Add 2x to each side
y -2x+2x = 2x-4
y = 2x-4
2 y-3 = -1/2 x
We need to add 3 to each side
y-3+3 = -1/2x +3
y = -1/2x+3
Answer:
1. y = 2x - 4
y = -1/2x + 3
Step-by-step explanation: You have to isolate or get y by itself.
1:
y - 2x = -4
+ 2x + 2x
y = 2x - 4
2:
y - 3 = -1/2x
+ 3 + 3
y = -1/2x + 3
Help me with question 15 plz?
Answer:
B
Step-by-step explanation:
well plug in x and y
so if it says y=2x-3 put it as 7=(2x2)-3 and see if it gives u 7 and if it does di the next set of x and y numbers
Answer:
B y=2x+3
Step-by-step explanation:
We need to find the slope of the relationship in the table
m = (y2-y2)/(x2-x1)
= (13-7)/(5-2)
= 6/3
=2
The slope is 2
We can use point slope form to make an equation
y-y1=m(x-x1)
y-7 = 2(x-2)
Distribute the 2
y-7 =2x-4
Add 7 to each side
y-7+7 =2x-4+7
y = 2x+3
a maximum speed, and airplane travels 2460 miles against the wind in 6 hours. flying with the wind, the plane can travel the same distance in 5 hours
Answer:
for pluto answer is 451
Step-by-step explanation:
Please help What is the equation of a line with a slope of −4 and a point (−2, 5) on the line?
Express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have m = -4 and the point (-2, 5). Substitute:
[tex]y-5=-4(x-(-2))[/tex]
[tex]y-5=-4(x+2)[/tex] use distributive property
[tex]y-5=(-4)(x)+(-4)(2)[/tex]
[tex]y-5=-4x-8[/tex] add 5 to both sides
[tex]\boxed{y=-4x-3}[/tex]
Answer:
all is work is shown and pictured
Find the equation that represents a line that passes through the point (7,-5) and has slope -4/7
Answer:
The equation would be y = -4/7x - 1
Step-by-step explanation:
Given that we have the slope and the point, we can solve for the equation using point-slope form.
y - y1 = m(x - x1)
y + 5 = -4/7(x - 7)
y + 5 = -4/7x + 4
y = -4/7x - 1
The equation that represents a line that passes through the point (7,-5) and has a slope of -4/7 is,
⇒ 7y = - 4x - 7
The equation of a line in point-slope form passing through the point
(x₁ , y₁) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Given that,
The equation of line passes through the point (7,-5) and has a slope of -4/7.
Here we have,
[tex](x_1 , y_1) = (7, - 5)[/tex]
And, [tex]m = \frac{- 4}{7}[/tex]
Substitute the given values in the above equation,
[tex]y - y_1 = m (x - x_1)[/tex]
[tex]y - (- 5) = \frac{-4}{7} (x - 7)[/tex]
[tex]y + 5 = \frac{-4}{7} (x - 7)[/tex]
Multiply by 7 on both sides,
[tex]7 (y + 5) = - 4 (x - 7)\\7y + 35 = - 4x + 28\\ 7y =- 4x 28 - 35\\ 7y = - 4x- 7\\[/tex]
So, the equation of a line is,
7y = - 4x - 7
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Using the given scale factor and center dilate the following figures and state the new coordinates
Answer:
B' = (-8,-1) , C' = (4, 5)
Step-by-step explanation:
The coordinates of A are (-5,-7)
The coordinates of C are 3 units to the right and 4 up from A.
So for a dilation factor 3 C' will be 9 to the right and 12 up from A.
C' = (-5 + 9) , (-7 + 12)
= (4, 5).
The point B is 1 unit to left and 2 up from A.
So B' is (-5 -3) , (-7+ 6)
= (-8, -1).
After a dilation scale factor of 3 centered at A, B'(- 18, - 15), and C'(- 6, - 9).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
Given, A triangle ABC.
The coordinate of B is (- 6, - 5), and the coordinate of C is (- 2, - 3).
After a dilation scale factor of 3 centered at A coordinates of B' would be
(- 6×3, - 5×3) = (- 18, - 15) and C'(- 2×3, - 3×3) = (- 6, - 9).
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An animal shelter had 9/10 of its crates filled with animals. 1/2 of the filled crates are holding dogs.What fraction of the total number of crates are holding dog?
Answer:
9/20
Step-by-step explanation:
9/10 times 1/2 equals 9/20
Answer:
9/20
Step-by-step explanation: