The line L is a tangent to the circle x2 + y2 = 45 at the point (-3, 6).
The line L crosses the x-axis at the point P.
Work out the coordinates of P.
Answer:
The point P is (-15,0).
Step-by-step explanation:
We need to find the slope of the line L to get the coordinates of P.
We know that L is tangent to the circle at point (-3, 6), which means L is perpendicular to the radius of the circle (a line between the origin (0,0) and the tangent point (-3,6))
So let's find the slope or the radius.
[tex]m_{R}=\frac{6-0}{-3-0}[/tex]
[tex]m_{R}=-2[/tex]
Now, we know that if two lines are perpendiculars their slopes follow the rule:
[tex]m_{L}=-\frac{1}{m_{R}}[/tex]
[tex]m_{L}=\frac{1}{2}[/tex]
Knowing the slope of L we can find the equation of this line. The slope-intercept equation of a line is:
[tex]y=mx+b[/tex]
[tex]y=\frac{1}{2}x+b[/tex]
Using the point (-3,6) we can find b.
[tex]6=\frac{1}{2}(-3)+b[/tex]
[tex]b=\frac{15}{2}[/tex]
The line equation will be:
[tex]y=\frac{1}{2}x+\frac{15}{2}[/tex]
The point P has only an x-coordinate value (x,0)
So we have:
[tex]0=\frac{1}{2}x+\frac{15}{2}[/tex]
[tex]x=-15[/tex]
Therefore, the point P is (-15,0).
I hope it helps you!
what is the square root of 1/64
The square root of 1/64 is 1/8.
To find the square root of 1/64, we can simplify the fraction first by taking the square root of both the numerator and the denominator separately.
The square root of 1 is 1,
and the square root of 64 is 8:
So, √(1/64)
= √1 / √64
= 1/8
Therefore, the square root of 1/64 is 1/8.
Learn more about Square Root here:
https://brainly.com/question/29286039
#SPJ6
Please help! I will mark brainliest if you are correct
If MI = 15 m, SM = 20 m, and TM = 9 m, what is the value of RM?
Answer:
RM=12m
Step-by-step explanation:
You can set up a proportion of 9/15 on one side and RM/20 on the other. you would then cross multiply and solve for RM
PLEASE I BEG OF YOU TO HELP ME PLEASE
Answer:
its B
Step-by-step explanation:
i did it earlier today
Answer:
A
Step-by-step explanation:
-1x-12≤-4
-x≤8
x≥-8
In a final exam, need this rn (25 points)
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget:
2,020 − 22m
What does the coefficient of the expression represent?
a.The number of months Megan will wait to sell the gadget
b.The monthly depreciation value of the gadget
c. The amount of money Megan will get when she sells the gadget
d.The original value of the gadget
Answer: B
Step-by-step explanation:
Answer:
the answer to this question would be B
which products result in difference of squares
(x-y)(y-x)
(6-y)(6-y)
(3+xz)(-3+xz)
(y^2-xy)(y^2+xy)
Answer:
[tex](3+xz)(-3+xz)[/tex]
[tex](y^2-xy)(y^2+xy)[/tex]
Step-by-step explanation:
The Difference of Squares
Any difference of two squared monomial results in a factored form like shown below:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Similarly:
[tex](a-b)(a+b)=a^2-b^2[/tex]
For a product of binomials to be a difference of squares, they must be in the described form.
------------------------
(x-y)(y-x) can be rewritten as:
-(x-y)(x-y)
Since both binomials are identicals, the product will not result in a difference of squares.
-----------------------
(6-y)(6-Y)
Since both binomials are identicals, the product will not result in a difference of squares.
-----------------------
(3+xz)(-3+xz) can be rewritten as:
(xz+3)(xz-3). This product is a sum multiplied by a difference of the very same terms, thus the result is a difference of squares:
[tex](3+xz)(-3+xz)=(xz)^2-9[/tex]
-----------------------
[tex](y^2-xy)(y^2+xy)[/tex]. This product is a sum multiplied by a difference of the very same terms, thus the result is a difference of squares:
[tex](y^2-xy)(y^2+xy)=y^4-(xy)^2[/tex]
-----------------------
Summarizing:
(3+xz)(-3+xz)
[tex](y^2-xy)(y^2+xy)[/tex]
The point Q has coordinates (2,3)
The point R has coordinates (a, b)
A line perpendicular to QR is given by the equation 5x + 2y = 9
Find an expression for b in terms of a. W
Answer:
b= (2a+11)/5
Step-by-step explanation:
5x + 2y = 9
2y=9-5x
y= 9/2 - 5x/2
slope, m1= -5/2
for perpendicularity, m1 × m2 = -1
slope for QR= m2=
[tex] = - 1 \div \frac{ - 5}{2} = - 1 \times \frac{2}{ - 5} = \frac{ - 2}{ - 5} = \frac{2}{5} [/tex]
m2 is 2/5
[tex]qr = \frac{b - 3}{a - 2} [/tex]
[tex] \frac{2}{5} = \frac{b - 3}{a - 2} [/tex]
5(b-3)=2(a-2)
5b-15=2a-4
5b=2a-4+15
5b= 2a+11
[tex]b = \frac{2a + 11}{5} [/tex]
An expression for b in terms of a is b = (2a + 11)/5.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given an equation of a line 5x + 2y = 9 ⇒ 2y = - 5x + 9 ⇒ y = (-5/2)x + 9/2.
So, the slope of the line parallel to QR is the slope negative reciprocal of (-5/2) which is (2/5).
We know slope m = (b - 3)/(a - 2).
∴ (2/5) = (b - 3).(a - 2).
2(a - 2) = 5(b - 3).
2a - 4 = 5b - 15.
2a + 11 = 5b.
b = (2a + 11)/5.
learn more about lines and slopes here :
https://brainly.com/question/3605446
#SPJ6
Can someone help me PLEASE!!!!!!!!!!
Answer:
1, 4, and 5
Step-by-step explanation:
18-2x5
18-10
8
6+4x4
6+16
22
6x9-9
54-9
45
7x9+1
63+1
64
4x6-6
24-6
18
answer to the question dfidsjfdiujfdhfds
Answer:
Um, ya I don't know
Step-by-step explanation:
Help.me if u can need it
Answer:
78 is the correct answer hope it helps
A man is filling an empty 5-gallon bucket with water at a constant rate. there are 2.4 gallons of water in the bucket after filling the bucket for 12 minutes. At what rate, in gallons per minute, is the man filling the bucket ?
Answer: The answer is 0.2
Step-by-step explanation: 2.4g / 12 minutes
0.2g/minutes
hi, pls help.
Why do Jews consider the Western Wall in Jerusalem a sacred place? *
1. It was built by King Solomon.
2. It was all that was left of the Second Temple after the Romans destroyed it.
3. It was the place where Abraham settled.
4. It was constructed with the stones that held the Ten Commandments.
Answer:
Hope that helps
Step-by-step explanation:
It was constructed with the stones that held the Ten Commandments.
Answer:
all that was left of the second temple after the roans destroyed it
Step-by-step explanation:
y = 3x
-3.x - y = -24
solve by substitution
The sum of the success rate and the failure rate should equal the total amount of trials.
True or False
Answer: True
Step-by-step explanation:
For example, randomly guessing at a true-false statistics question has only two outcomes. If a success is guessing correctly, then a failure is guessing incorrectly.
Which equation represents this statement?
"Five more than twice a number, x
, is equal to one less than three times that same number, x
."
A: 2 x+ 5 = 3 x- 1
B: 5 x= 3 x- 1
C:2 x+ 5 = 3( x- 1)
D: 5 + 2 x= 1 - 3 x
Answer:
A
Step-by-step explanation:
5 + 2x = 3x - 1
An amount of $5,000 is invested. The interest rate is 2%.
Answer:
A = 5000(1 + 0.06/2)(2)(4) = 5000(1.03)(8) = $6333.85.
Step-by-step explanation:
Answer:
$2191.12
Step-by-step explanation:
Which of the following sets of numbers have the same mean, median, and mode?
0 3,5,8, 4.5
O 5, 1, 2, 2.5
10.6.4, 2.8
2.68.6.3
Step-by-step explanation:
calculate the each one then compare
hint :
mean : add all the numbers and divide by how many numbers there are .
median : the middle number . for example : 12345 . 3 is the middle number .
mode : the number that appears more often than the other numbers.
can someone please help me? make it right..
Answer:
6.83and 7.03 this is the answer
Answer:
6.83, 6.93, 7.03, 7.13, 7.23, 7.33 always add .10 each time.
Step-by-step explanation:
Ashton just launched a new business page on social media. After one month, she has 35 followers.
She decides to take a course that promises to triple her number of followers each month for 6
months. After 7 months, how many followers will Ashton have if this is true?
Answer:
122.5
Step-by-step explanation:
If it triples her followers per 6 months then it gives her half of her followers in one month. So 35 times 3.5 which is 122.5
After [tex]7[/tex] months, Ashton will have [tex]25,515[/tex] followers.
What is modelling ?Modelling is the process of creating a mathematical representation of a real-world scenario to make a prediction or provide insight.
We have,
Number of followers [tex]=35[/tex]
So, Every month increase is triple i.e. [tex]3[/tex] times for next [tex]6[/tex] months.
So,
According to the question,
Every month increase [tex]=\ 3\ *\ Current\ Follower[/tex]
So,
Followers after [tex]7[/tex] months [tex]= 35*(3)^6[/tex]
Because followers are increasing at the rate of three times per month,
So,
Followers after [tex]7[/tex] months [tex]= 35*(3)^6=25,515[/tex]
Hence, we can say that After [tex]7[/tex] months, Ashton will have [tex]25,515[/tex] followers.
To know more about Modelling click here
https://brainly.com/question/14425880
#SPJ3
One angle of a triangle measures 75. The other two angles are in a ratio of 5:16. What are the measures of those two angles?
Answer:
25 and 80
Step-by-step explanation:
180 - 75 = 105
105 / (5+16) = 5
multiply each side of the ratio 5:16 by 5
5x5 : 16x5 = 25:80
Mikayla worked the same number of hours each day for 4 days during one week. She worked less than 20 hours total for that week. Which graph represents the number of hours per day she could have worked? (Assume the number of hours is greater than 0.)
I made this just to tell everyone that the answer is : A number line from 0-10 theres an open circle on 5 and everything to the left is shaded . On my screen it was A
Answer:
A
Step-by-step explanation:
Correct On EDG
Pls mark me brainllest
Answer:
A.
Step-by-step explanation:
when solving a quadratic equation by completing a square which of the following is NOT a step you would take?
A. Take half of b, then square it
B. Subtract x squared from both sides
C. Take the square root of both sides
S. Use the following symbol when taking root. +
-
I dont know if you understand the symbol i tried
Answer: D
Step-by-step explanation:
A textbook store sold a combined total of 435 psychology and sociology textbooks in a week. The number of sociology textbooks sold was 61 less than the number of psychology textbooks sold. How many textbooks of each type were sold?
Answer:
248 psych books, 187 soc books.
Step-by-step explanation:
x psych books were sold
x-61 soc books were sold
Total books was 435.
So -
x+x-61 = 435
2x-61 = 435
2x = 496
x = 248.
so x-61 = 187 and
248+187 = 435.
248 psych books, 187 soc books.
Leo makes a cake by mixing flour, eggs and sugar in the ratio 5 : 3 : 2. If he uses 120 g of sugar, what weight of eggs will he need?
Answer:
180g of eggs
Step-by-step explanation:
divide 120 by 2 = 60
then times 60 by 3 = 180g
Order Numbers least to greatest -4.3, 5/4 ,8.2, -6/2, 4, -2.5, 5.33
which similarity statement is true for the triangles shown?
- ABC = DEF
- ABC = FED
Answer:
I’m pretty sure it’s Triangle ABC is congruent to Triangle DEF.
Step-by-step explanation:
If you rotate Triangle DEF to where the 90 degree angle is on the bottom right, you can the compare the two triangles. You can divide 300/25, 240/20, and 180/15. They all result in 12 meaning they are congruent and similar in that way. (I’m only 90% this is right btw)
Solve for Y
13= 4y+5
y=?
Please help this is my last question and it’s due by 10 PM
sorry there’s only 11 points •.•
I would appreciate if you could help and explain on how you do it. :)
<ABC and <DEF are complementary angles.
What is the measure of x?
Answer:
x=35
Step-by-step explanation:
chris worked 3 1/2 hours at his uncles farm. He was paid 8$ for every 1/4 hour he worked. How much money did chris make
Answer:
$112
Step-by-step explanation:
So first figure out how much he makes an hour
8*4 is 32.
32*3 1/2 is $112
The amount that Chris will make will then be $112.
The first thing to do is to divide 3 1/2 by 1/4. This will be:
= 3 1/2 / 1/4
= 7/2 × 4/1
= 14
Now we'll then multiply 14 by $8. This will be:
= $8 × 14
= $112
The amount made will be $112.
Read related link on:
https://brainly.com/question/19965204
