could someone please assist...it would really help alot...thank you:)
I just need help with 4.2 and 4.3
Answers
Problem 4.2
We're told that y = 2x is the equation of the tangent line through point Q.
Plug this into the equation of the circle (that was given at the very top of the page). Solve for x.
x^2 + y^2 - 18x - 6y + 45 = 0
x^2 + (2x)^2 - 18x - 6(2x) + 45 = 0 ... every "y" replaced with "2x"
x^2 + 4x^2 - 18x - 12x + 45 = 0
5x^2 - 30x + 45 = 0
5(x^2 - 6x + 9) = 0
5(x-3)^2 = 0
(x-3)^2 = 0
x-3 = 0
x = 3
This then means y = 2x = 2*3 = 6
The coordinates of point Q are (x,y) = (3,6)
----------
Answer: (3,6)===========================================================
Problem 4.3
We first need to find the location of point S. That will involve solving this system of equations
[tex]\begin{cases}x-2y+12=0\\y = 2x\end{cases}[/tex]
which represent the equations of lines SR and QS in that exact order.
Like before, we'll apply substitution to solve for x.
x-2y+12 = 0
x-2(2x)+12 = 0
x-4x+12 = 0
-3x+12 = 0
12 = 3x
12/3 = x
4 = x
x = 4
Which leads to y = 2x = 2*4 = 8
Point S is located at (4,8)
Point R is given to be located at (6,9)
Apply the distance formula for these two points to find the length of SR (aka the distance from S to R).
[tex]S = (x_1,y_1) = (4,8)\\\\R = (x_2,y_2) = (6,9)\\\\d = \text{Length of SR, aka distance from S to R}\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-6)^2 + (8-9)^2}\\\\d = \sqrt{(-2)^2 + (-1)^2}\\\\d = \sqrt{4 + 1}\\\\d = \sqrt{5}\\\\d \approx 2.236068\\\\[/tex]
The exact length is [tex]\sqrt{5}[/tex] and that approximates to roughly 2.236068 units.
----------
Answer:Exact length = [tex]\sqrt{5}[/tex] units
Approximate length = 2.236068 units
Related Questions
Anne deposited $500 in an account that earns 6% simple annual interest. Shelly deposited $500 in an account that earns 6% annual interest compounded annually. They leave the money in the account for 4 years. What is the difference between the two accounts?
Answers
Answer:
$11.23
Step-by-step explanation:
A) 500 + 4(.06*500)
[tex]500+4\left(0.06\cdot \:500\right)=620[/tex]
B) [tex]500\cdot \:1.06^4=631.23848[/tex]
Ken needs a surgery on his foot. The estimated cost of the surgery is $5,000. The insurance policy provided by Ken's company has $500 deductible and 20% co-pay. How much will Ken have to pay for foot surgery?
Answers
9514 1404 393
Answer:
$1400
Step-by-step explanation:
Ken will be required to pay the deductible and 20% of the remaining amount.
Ken pays $500 + 0.20(5000 -500) = $500 +900
Ken pays $1400
Solve 3x - 4 ≤ 2 or 2x + 11 ≥ -1.
Answers
Answer:
true for all x
Step-by-step explanation:
3x - 4 ≤ 2
Add 4 to each side
3x - 4+4 ≤ 2+4
3x<6
Divide by 3
3x/3 <6/3
x<2
or
2x + 11 ≥ -1
Subtract 11 from each side
2x + 11-11 ≥ -1-11
2x≥ -12
Divide by 2
2x/2 ≥ -12/2
x ≥ -6
x<2 or x ≥ -6
true for all x
A number added to -25 results in an even less
value. Which of the following could be that
number? Select all that apply and model the situation to prove your choice(s).
a) 3
b) 2
c) 1
d)0
e)-1
f)-2
g) -3
Answers
Not A because: -25+3= -22 which is more than -25
Not B because: -25+2=-23 which is more than -25
Not C because: -25+1=-24 which is more than -25
Not D because: -25+0=-25 which is not less than -25
E because: -25+-1=-26 which is less than -25
F because: -25+-2=-27 which is less than -25 G because: -25+-3=-28 which is less than -25
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 2 milliliters of compound B. If a chemist wants to make 280 milliliters of the drug, how many milliliters of compound B are needed?
Answers
Answer:
42 milliters of compound B are needed......Actually I am not sure hope this may urr answer....
Mr. Ellington has a total of 32 students in his class , The ratio of girls to boys is 3:5, how many girls are in Mr . Ellington's class ?
Answers
Add the ratio: 3 + 5 = 8
Divide total students by that:
32/8 = 4
The ratio for girls is 3, multiply the 4 by 3:
4 x 3 = 12
There are 12 girls
Answer:
12
Step-by-step explanation:
If the ratio of girls to boys is 3:5, that means that for every 8 total students, 3 would be girls and 5 would be boys. Therefore 3/8 of the students are girls and 5/8 are boys. If 3/8 are girls, then:
[tex]\frac{3}{8}[/tex] of 32
= [tex]\frac{3}{8} * 32[/tex]
[tex]=\frac{3 * 32}{8} \\= \frac{96}{8} \\= 12[/tex]
There are 12 girls.
could anyone help with this tyy!
Part IV: Sketch the graph of y = x2 - 9x + 20. Identify the vertex and x- and y-
intercepts on your sketch. (3 points)
Answers
intercepts
y = x^2 - 9x + 20
y = (x - 5)(x - 4)
x-ints at (5, 0) and (4, 0)
y = (0 - 5)(0 - 4)
y = 20
y-int at (0, 20)
vertex
y = 1x^2 - 9x + 20
-b / 2a = 9/2(1)
vertex (4.5, y)
y = (x - 5)(x - 4)
y = (4.5 - 5)(4.5 - 4)
y = -0.5(0.5)
y = -0.25
vertex (4.5, -0.25)
i recommend using desmos if in the future you need help
Look at this cube
If the side lengths are halved, then which of the following statements about its surface area will be true?
Answers
Answer:
the new surface Will be 1/4 pf the old surface
Step-by-step explanation:
because the surface with 7 in Is about 294 and with 3.5 (1/2 of 7) Is 73.5.
so 294:4 Is 73.5
excuse me for my bad English but I'm italian
Graph the function f(x) = 2√x+2 .
All help is appreciated!
Answers
Answer:
Not sure which was your intended, but here are two options.
Step-by-step explanation:
In ΔABC, m∠A=a, m∠B=β, m∠C=y. AB = c, AC = b, BC = a. Find the remaining parts of each triangle if the following parts are given.
a=5, b=7, y=31°
Answers
Answer:
9.013 square units
Step-by-step explanation:
The denominator of a fraction exceeds twice the numerator of the fraction by 10. The value of this fraction is 5/12. Find the fraction.
Answers
Answer:
25/60
Step-by-step explanation:
Numerator = n
[tex]\frac{n}{2n + 10} = \frac{5}{12}[/tex]
Cross multiply:
n * 12 = (2n + 10) * 5
12n = 10n + 50
12n - 10n = 10n + 50 - 10n
2n = 50
n = 25
Fraction = [tex]\frac{25}{60}[/tex]
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
25/60
Step-by-step explanation:
Study Island:)
Suppose there are approximately 220 calories in 3 servings of a particular brand of cereal and 362 calories in 5 servings of the same cereal. Find the rate of change.
Answers
Answer:
.93 calories per serving
Step-by-step explanation:
220 ÷ 3 = 73.3333333 calories per serving
3 ÷ 220 = 0.0136363636
362 ÷ 5 = 72.4
5 ÷ 362 = 0.0138121547
73.3333333 - 72.4 = 0.9333333 = around .93
Will Mark Brainlest Help pls
Answers
Answer:
Hello,
[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Of the following points, name all that lie on the same vertical line?
(0,8) (-5,0) (-1,0) (0,7)
A. (0,8) (-5,0) (-1,0) (0,7)
B. none
C. (-5,0) (-1,0)
D. (0,8) (0,7)
Answers
Answer:
D
Step-by-step explanation:
vertical is basically the x axis, so the y axis has to be 0. using elimination, (0,8) and (0,7) are the only ones left.
Question 5 10 pts Which function represents the inverse of f(x) = (x + 6)2 - 5? of 1(1) = V1 + 5 - 6 of '(x) = (x + 5)2 - 6 of '(x) = V1 – 6 + 5 Of '(x) = (x + 6 – 5
Answers
Answer:
f(x)^-1(x) =sqrt(x+5) -6
Step-by-step explanation:
f(x) = (x + 6)^2 - 5
y = (x + 6)^2 - 5
Exchange x and y and solve for y
x = (y + 6)^2 - 5
Add 5 to each side
x+5 = (y + 6)^2 - 5+5
x+5 = (y + 6)^2
Take the square root of each side
sqrt(x+5 )= sqrt( (y + 6)^2 )
sqrt(x+5 )=(y + 6)
Subtract 6 from each side
sqrt(x+5 ) -6=y + 6-6
sqrt(x+5) -6 = y
15x + 14 = 149
Plz solve for x
Answers
Answer:
x = 9
Step-by-step explanation:
When doing these types of problems, the main goal is to get the variable by itself. Its kind of hard to explain with words so I will just use numbers.
15x + 14 = 149
(Subtract 14 on both sides. Remember, when you do something (Like subtracting, adding, etc.) on one side you have to do it to the other.)
15x + 14 = 149
-14 = -14
---------------------------
15x = 135
(Divide 15 on both sides. Since we need to use inverse operation to cancel the 15 out, we would divide 15 on both sides.)
15x/15 = 135/15
x = 9
Hope this helps :)
Answer:
x=9Step-by-step explanation:
[tex]\sf 15x + 14 = 149[/tex]
[tex]\sf 15x+14-14=149-14[/tex]
[tex]\sf 15x=135[/tex]
[tex]\sf \cfrac{15x}{15}=\cfrac{135}{15}[/tex]
[tex]\sf x=9[/tex]
Need answer asap algebra 2 math
Answers
Answer:
B
Step-by-step explanation:
f(x) = 2x^2 - 4x + 5 Put brackets around the first 2 terms.
f(x) = (2x^2 - 4x) + 5 Take out the common factor of 2
f(x) = 2(x^2 - 2x) + 5 1/2 the second term and square.
f(x) = 2(x^2 -2x + (2/2)^2) + 5 Express brackets as a perfect square.
f(x) = 2(x - 1)^2 + 5 Multiply 2 * 1 (the term without an x. Subtract.
f(x) = 2(x - 1)^2 + 5 - 2 Combine
f(x) = 2(x - 1)^2 + 3
Aug 10,9:55:10 AM
Find the length of the third side. If necessary, round to the nearest tenth.
16
10
Submit Answer
Answer:
attempt 1 out of 2
Answers
12.5
Step-by-step explanation:
a^2 + b^2 = c^2
a^2 + 10^2 = 16^2
a^2 + 100 = 256
a^2 = 256 - 100
a^2 = 156
a = 12.48 or 12.5
How much gift wrap is
needed to cover a box
measuring 18 inches by
12 inches by 4 inches?
Answers
Answer:
All we need to do here, is to find the total surface area.
In this case, we have:
2(18x12 + 18x4 + 12x4) which is equal to 672
Let me know if this helps!
please help
Find f(1/3) if f(n) = 3n.
Answers
Answer:
1
Step-by-step explanation:
f(n) = 3n
f(1/3)= 3*(1/3)=1
f(1/3)=1
Answer:
3
Step-by-step explanation:
Plugin n = 1/3
f(n) = 3n
[tex]f(\frac{1}{3})=3*\frac{1}{3} = 3[/tex]
A boat travels 160 miles per hour. What is the speed in miles per minute?
Answers
Now
[tex]\\ \sf\longmapsto 160\times \dfrac{1}{60}[/tex]
[tex]\\ \sf\longmapsto \dfrac{160}{60}[/tex]
[tex]\\ \sf\longmapsto 2.6miles/min[/tex]
А.
10 ft
6 ft
N
B.
8 ft.
С
Find the area of the triangle ABC.
[?] fto
Enter
Answers
Answer:
24 ft^2
Step-by-step explanation:
Area of ABC=(1/2)*b*h
=(1/2)*8*6=24 ft^2
If the fourth term in a geometric sequence is –1 and the common ratio is –1, find the explicit formula of the sequence.
A)
an = (1) ⋅ (–1)n – 1 for n ≥ 1
B)
an = (– 1) ⋅ (1)n – 1 for n ≥ 1
C)
an = (–1) ⋅ (–1)n – 1 for n < 1
D)
an = (1) ⋅ (1)n – 1 for n ≥ 2
Answers
Answer:
Hello,
Answer A
Step-by-step explanation:
[tex]a_4=-1\\q=-1\ common\ ratio\\\\a_4=a_1*q^3\ -1=a_1*(-1)^3 \Longrightarrow\ a_1=1\\\\\\\boxed{a_n=1*(-1)^{n-1}}\\\\\\Since \ all \ formula\ are\ so\ bad\ written,\ I\ suppose\ that\ the\ answer \ is \ A\\[/tex]
Answer:
an = (1) ⋅ (–1)n – 1 for n ≥ 1
Step-by-step explanation:
took the test and got it right
hope this helps
this geometric sequence?
What is the explicit formula for
8, 4, 2, 1, ...
Answers
Answer:
D
Step-by-step explanation:
the first term is 8, the ratio is 1/2 ( 8*1/2 = 4, 4*1/2 = 2, 2*1/2 = 1)
the formula for an explicit geometric formula is :
[tex]a_{n} = a_{1} * r^{(n-1)}[/tex]
plug in your numbers :
[tex]a_{n} = 8 * (\frac{1}{2}) ^{(n-1)}[/tex]
3. A publishing house is selling subscriptions to its magazines for 20% off the original price. If a
subscription to Newsweek Magazine is on sale for $72, how much does it usually cost?]
a) $14.40
b) $57.60
c) $86.40
d) $90
Answers
Explanation: 20% of 90 dollars is 18 dollars. So 90-18 is $72/the sale price.
So the original price was $90
Adam is three years older than Joe. After three years, Adam’s age will be four years less than two times Joe's age. Considering Adam's present age as x years and Joe’s present age as y years, write a pair of linear equations to model the above situation.
Answers
Answer:
2y=2y-4=x
Step-by-step explanation:
Which shows two triangles that are congruent by ASA?
Answers
Answer:
A and D
Step-by-step explanation:
The two triangles that are congruent by ASA is discussed below.
What is Congruency?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. "Congruent" refers to things that are precisely the same size and shape.
Angle-Side-Angle refers to the ASA Congruence rule.
According to this rule, two triangles are said to be congruent if any two of their respective angles and the side that is included between them are equal to the corresponding angles and the included side of the other triangle.
For example, there are ABC and DEF in which ∠ B = ∠ E, ∠ C = ∠ F, and BC = EF
Then, the triangle that Δ ABC ≅ Δ DEF by ASA congruence rule.
Learn more about Congruency here:
https://brainly.com/question/7888063
#SPJ5
Help ASAP plssss! Thanks
Answers
Points are
(-2,-2)(4,4)[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(4+2)^2+(4+2)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{6^2+6^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{36+36}[/tex]
[tex]\\ \sf\longmapsto \sqrt{72}[/tex]
[tex]\\ \sf\longmapsto 8.4[/tex]
Me ajudem!
f(x) = 2x + 4
para f(5)
Answers
Answer:
f(5) = 2(5) + 4
= 10 + 4
f(5) = 14
Each cat at the animal shelter gets
5/6 pound of food. Allie has 9 1/2
pounds of cat food. How many cats
can Allie feed?
A: 7
B:9
C: 11
D:13
Answers
Answer: C : 11
Step-by-step explanation:
So divide 9 1/2 by 5/6
So the answer is 11,4 and it round off to 11
So the answer is 11 option C
