Answer:
A.
[tex]y = (x - 2 {)}^{2} + 2[/tex]
Step-by-step explanation:
[tex]y = {x}^{2} - 4x + 6[/tex]
[tex] = y + 4 = {x}^{2} - 4x + 4 + 6[/tex]
[tex] = y + 4 = (x - 2 {)}^{2} + 6[/tex]
[tex] = y = (x - 2 {)}^{2} + 6 - 4[/tex]
[tex] = y = (x - 2 {)}^{2} + 2[/tex]
mary has 17 m of rope. She wishes to cut it in three pieces so that she has 3 m more than amanda, and amanda has 2 m less than Sarah.
Answer:
Length of Sarah rope = 6 m
Length of Amanda's rope = 4 m
Length of Mary's rope = 7 m
Step-by-step explanation:
Let the length of Sarah rope = x
Length of Amanda's rope= x - 2
Length of Mary's rope = (x - 2 ) + 3 = x - 2 + 3 = x + 1
Length of rope = 17 m
x + x - 2 + x + 1 = 17
Combine like terms
x + x + x - 2 + 1 = 17
3x - 1 = 17
Add 1 to both sides
3x = 17 + 1
3x = 18
Divide both sides by 3
x = 18/3
x = 6
Length of Sarah rope = x = 6 m
Length of Amanda's rope= x - 2 = 6 - 2 = 4 m
Length of Mary's rope = x + 1 = 6 + 1 = 7 m
Find the sum or difference of the polynomials. Write your answer in descending order (2x2 + 5x – 12) – (-4x2 + 2x+6)
Answer:
The correct answer is 6x^2 + 3x - 18
what's the equation of a line with slope 5 and y-intercept -2
Answer
Slope-intercept form: y=5x-2
Standard form: 5x-y=2
Explanation
Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. You can just plug in the numbers to go y=5x-2.
Standard form is Ax+By=C. This form is usually used to find the x-intercept and y=intercept. You can rearrange the numbers to get standard form; 5x-y=2.
PLEASE HELP
Explain how to find the average rate of change between n=3 and n=9.
What is the term for this question?
An _____________________________ is an answer that falls outside of the domain of the function.
Answer:
irrelevant is the answer for it doesn't belong
Solve the following system of equations. -5x - 4y= -11 7x + 3y = 18
Step-by-step explanation:
-5x - 4y= -117x + 3y = 18
-5x +117x = 3y + 4y = 18
112x = 7y = 18
What product is positive (2/5)(-8/9)(-1/3)(-2/7). (-2/5)(8/9)(-1/3)(-2/7). (2/5)(8/9)(1/3)(-2/7). (-2/5)(-8/9)(1/3)(2/7)
Answer:
d
Step-by-step explanation:
a. (2/5)(-8/9)(-1/3)(-2/7)= - 32/945
b. (-2/5)(8/9)(-1/3)(-2/7) = -32/945
c. 2/5 * 8/9 * 1/3 * - 2/7 = - 32/945
d. -2/5 * - 8/9 * 1/3 * 2/7 = 32/945
Answer:
D
Step-by-step explanation:
32/945 is the final answer
Evaluate Sigma 5 n=1 3(-2)^n-1
Answer choices
-93
-33
33
93
Answer:
93
Step-by-step explanation:
the answer is 93 no -93 i think so
Lucy ran 3 1/2 miles on Monday 5 3/5 on Tuesday 2 1/3 force on Thursday and 6 2/3 on Friday find the total distance and she ran this week
18.1
Answer:
18.1 miles
Step-by-step explanation:
TOTAL distance= sum of individual distance
[tex]3 \times \frac{1}{2} + 5 \times \frac{3}{5} + 2 \times \frac{1}{3} + 6 \times \frac{2}{3} [/tex]
[tex] = 18.1miles[/tex]
Answer:
18 1/10
Step-by-step explanation:
Add the total distances
Get a common denominator of 30
3 15/30 + 5 18/30 + 2 10/30 + 6 20/30
16 63/30
16 + 60/30 +3/30
18+3/30
18 1/10
Two cars that are 600km apart are moving towards each other. Their speeds differ by 6km per hour and the cars are 123km apart after 4.5 hours. Find the speed of each car
Answer: [tex]56\ kmph,\quad 50\ kmph[/tex]
Step-by-step explanation:
Given
Two cars are 600 km apart moving towards each other
Difference in their speed is 6 kmph
After 4.5 hr, they are 123 km apart that is, they covered a distance of [tex]600-123=477\ km[/tex] in 4.5 hours
Suppose their speeds is [tex]v_1\ \text{and}\ v_2[/tex]
[tex]\therefore v_1-v_2=6\quad \ldots(i)[/tex]
Also, distance traveled is given by
[tex]\Rightarrow 477=[v_1+v_2]4.5\\\Rightarrow v_1+v_2=106\quad \ldots(ii)[/tex]
Solve, (i) and (ii) , we get [tex]v_1=56\ kmph\ \text{and}\ v_2=50\ kmph[/tex]
The second sail has one side of length 22 feet and another of length 2 feet. Determine the range of possible lengths of the third side of the sail.
Answer:
20 < L < 24
Step-by-step explanation:
We know that in any given triangle, the length of two sides is always greater than the length of the third side.
Since the sail is a triangle having length of one side as 22 feet and the length of another side as 2 feet, and let L be the length of the third side.
It follows from our triangle rule of sides above that
22 + 2 > L (1)
22 + L > 2 (2)and
L + 2 > 22 (3)
It follows that from (1)
22 + 2 > L
⇒ 24 > L (4)
It follows that from (2)
22 + L > 2
⇒ L > 2 - 22
⇒ L > - 44 (5) and
It follows that from (3)
L + 2 > 22
⇒ L > 22 - 2
⇒ L > 20 (6)
Since from (5) and (6),
L > -44 and L > 20
and 20 > -44 ⇒ L > 20
⇒ 20 < L (7)
From (4) 24 > L ⇒ L < 24 (8)
Combining (7) and (8), we have
20 < L < 24
So, the possible range of values of the third side are 20 < L < 24
The president of the math club is conducting a survey to see where the 12th grade class wants to go to their field trip. Instead of asking the whole class, she surveys only the 12th grade members of the math club. She records the choices and plans to present the results to the school principal. what kind of sampling did she use?
Convenience sampling.
d²y/dx²=12x-12. express y in terms of x
Answer:
y(x)=2x^3-6x^2+ax+b, a and b are constants
Step-by-step explanation:
d2y/dx2=12x-12, integrating both sides we get
dy/dx=6x^2-12x+a, where a is the integration constant.
Again integrating both sides, we get
y(x)=2x^3-6x^2+ax+b, where b is the integration constant
if c/d - a/b =x, a =2c, and b=5d, what is the value of c/d in terms of x?
a) 2/3 x
b) 3/4 x
c) 4/3 x
d) 5/3 x
Answer:
d)
Step-by-step explanation:
c/d - 2c/5d = 5c/5d - 2c/5d = 3c/5d = x
3c/d = 5x
c/d = 5x/3 = 5/3 × x
f ( x ) = 1 x − 6 , g ( x ) = 6 x + 1 x Use composition to prove whether or not the functions are inverses of each other. Express the domain of the compositions using interval notation.
Answer:
Two functions f(x) and g(x) are inverses if and only if:
f( g(x) ) = x
and
g( f(x) ) = x
In this case, we have:
f(x) = 1*x - 6
g(x) = 6*x + 1
Let's check if the functions are inverses.
f( g(x) ) = 1*g(x) - 6 = 1*(6x + 1) - 6 = 6x + 1 - 6 = 6x - 5
and
g( f(x) ) = 6*f(x) + 1 = 6*(1x - 6) + 1 = 6x - 36 + 1 = 6x - 35
So we can see that:
f( g(x) ) ≠ x
g( f(x) ) ≠ x
Thus, f(x) and g(x) are not inverses.
Particularly, the two compositions are:
f( g(x) ) = 6x - 5
g( f(x) ) = 6x - 35
Both of these are linear functions, thus the domain in both cases is the set of all real numbers, that can be written as:
domain = (-∞, ∞)
Does anybody know the answer? I need help
I saw that this is from 2 weeks ago so it's probaly too late to answer... if you ever have trouble multiplying exponents use symbolab it's an online calculator that's really good (i use it on all my math exams :)
Lmk if you understand thanks
Answer:
y = 100,000 (1 + 0.04) ²⁰
Step-by-step explanation:
Here:
100,000 = original amount.
0.04 = rate (a percent)
and
20 = number of times you need to run the simulation.
Rewrite the expression in the picture in the form k times x^n.
Answer:
8 x^-2
Step-by-step explanation:
2 sqrt(x) * 4x ^ -5/2
Rewriting
2 x^1/2 * 4x ^ -5/2
2*4 = 8
x^1/2 * x^ -5/2
We know a^b * a^c = a^(b+c)
x^ 1/2 * x^ -5/2 = x^ (1/2 -5/2 ) = x^ (-4/2) = x^-2
8 x^-2
When the focus and directrix are used to derive the equation of a parabola, two distances were set equal to each other. = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot = StartRoot (x minus 0) squared + (y minus p) squared EndRoot The distance between the directrix and is set equal to the distance between the and the same point on the parabola.
Answer:
The answer is "A point on the parabola and Focus".
Step-by-step explanation:
[tex]= \sqrt{(x - x)^2 + (y- (-p))^2} = \sqrt{(x-0)^2+ (y-p)^2} \\\\= \sqrt{(0)^2 + (y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= \sqrt{(y+p))^2} = \sqrt{(x)^2+ (y-p)^2} \\\\= (y+p) = (x)+ (y-p) \\\\= y+p = x+ y-p \\\\=2p=x\\\\=x=2p[/tex]
Whenever the focus and also the guideline are utilized in determining the parabolic formula, two distances have indeed been equal.
The distance from the direction, as well as a parabolic point, was equal to the distance from the center to a parabolic point.
Answer:
The distance between the directrix and a point on the parabola is set equal to the distance between the focus and the same point on the parabola.
Step-by-step explanation:
Hope this helps! :)
I need help plz I don’t understand
Answer:
Step-by-step explanation:
If AD is an altitude, then by definition it drops from the vertex angle (the top angle) and meets the base at a right angle, which measures 90 degrees. That means that 17x + 73 is a right angle:
17x + 73 = 90 and
17x = 17 so
x = 1
Simplify
please answer this question and attach a photo of your solution
Answer:
7q
Step-by-step explanation:
that is the procedure above
Jeanette wants to raise $3,200 in a marathon fundraiser. Her sponsers will donate
$35 for each (whole) kilometer she runs this summer.
The minimum amount Jeanette will have to run to reach her goal of $3, 200 is
kilometers.
Answer:
92
Step-by-step explanation:
= 3200 ÷ 35
= 91.43
round up to nearest whole number
= 92 km
I need halp on this question plzz and ty
Answer:
Positive
Step-by-step explanation:
It gose upwards
Determine what type of transformation is represented.
A. none of these
B. dilation
C. reflection
D. rotation
The given figure represents translation transformation. Therefore, option A is the correct answer.
What is transformation?"It is the method of transforming the shape or size of a geometric object using different rules and methods."
What is translation?"It is a geometric transformation in which the object is moved from one place to another without change in its shape, size and orientation."
What is dilation?"It is a transformation where changing the size of an object without changing its shape."
What is rotation?"It is a geometric transformation in which the object is rotated about the axis of rotation without changing the size and shape of an object."
In the given figure, ΔABC is transformed to ΔA'B'C' we can observe that the transformation is translation.
The given figure represents translation transformation. Therefore, option A is the correct answer.
Learn more about the transformation here:
brainly.com/question/22532832
#SPJ2
1, Tính:
a,√27 + 7√5 : √2
[tex]\rightarrow\sf \sqrt{27} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{9(3)} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{ {3}^{2} } \times 3 + 7 \sqrt{5} : \sqrt{2} \\ \rightarrow \large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}[/tex]
Answer:[tex]\large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}[/tex]
[tex]\color{red}{==========================}[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
ꕥᴀʀᴀꕥ
What is the slope of the line?
Answer:
1/2
slope = Δy/Δx
start at (-1,3) to get to the line from there you can go down 1 ( Δy = -1)
and left 2 (Δx = -2)
-1/-2 = 1/2
Step-by-step explanation:
Pleasee help me with this!!
Answer:
#1 is f.
#2 is d.
#3 is a.
#4 is b.
#5 is c.
#6 is g.
#7 is e.
Step-by-step explanation:
The digit "9" is in the ten's place because it is two numbers/spaces left from the decimal. If you make all the other digits "0", you'll be left with a value of 90.
The digit "1" is in the one's place because it is one number/space left from the decimal. Applying the same concept of making all the other digits "0", you'll be left with a value of 1.
The type of digits to the right of the decimal, starting from left to right, are the tenths place, hundredths place, thousandths place, ten-thousandths place, and millionths. Remember and know those digit types based on their position away from the decimal. The value will be there for you to see afterward.
Can someone help me out please
Answer:
the answer is 216 m²
Step-by-step explanation:
3 time 6 equals 18
18 times 2 is 36
3 times 10 is 30
30 times 2 is 60
6 times 10 is 60
60 times 2 is 120
120+60+36=216
On a horizontal number line, positive numbers are . On a vertical number line, negative numbers are . The number 0 is .
Answer:
on horizontal (x axis) positive numbers are to the right, negative to the left...
on the vertical axis (y-axis) the positive numbers go up (north) and the negative numbers go down (south) the zeros on each axis meet at the "origin"
Step-by-step explanation:
