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.
Which expressions represent 1 more then the product 5 and 2
Answer:
1+5*2 or simplified, 1+10= 11
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
estimate 782 divided by 50
Answer: about 15.72
Step-by-step explanation: i used a calculator
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.
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
learn more; https://brainly.com/question/2591482?referrer=searchResults
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:
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:
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?
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]
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
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
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
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
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).
learn more about translation here :
https://brainly.com/question/13176891
#SPJ5
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.
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.
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:
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
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
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
To learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ4
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
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
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
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
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.
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]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Student's Shirt : https://brainly.com/question/909783Answer detailsGrade: Middle School
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
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
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
Learn more about Constant of proportionality here:https://brainly.com/question/17793140
#SPJ3
3/7-2/14 (8-1/2) +2/7
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.
To learn more about the Number system visit:
https://brainly.com/question/17200227
#SPJ4