Answers
Answer:
smaller r = ( 6.5 , 0)
larger r = ( 21.5 , 0)
vertex = ( 14, -56.25)
Step-by-step explanation:
f(r) = (r -14)² -56.25 square (r-14)
f(r) = r² -28r +196 -56.25 simplify
f(r) = r² -28r + 139.75
use quadratic formula
x=−b±√(b²−4ac)/ 2a
a = 1, b =-28, c = 139.75
x=−(−28)±√(−28)2−4(1)(139.75)2(1)
x=(28±√225)/2
x=43/2 or x=13/2
or 21.5 and 6.5
This parabola is given in vertex form f (r) = a(r - h)² + k, where (h, k) is the vertex of the parabola so just write the given numbers ( 14, -56.25)
Related Questions
Given f(x) = 2x5 + 12, what is the value of (f-1 o f)(2)?
Answers
Answer:
2
Step-by-step explanation:
You are trying to find (f' o f)(2). This means that you need to put f(x) into f'(x) and solve for 2.
First, find f'(x). To do this, take the original function and switch the x and y values.
y = 2x⁵ + 12
x = 2y⁵ + 12
x - 12 = 2y⁵
(x - 12)/(2) = y⁵
y = ⁵√(x - 12)/(2)
Now, you need to put f(x) into the inverse function through the x-value. Simplify completely.
y = ⁵√((2x⁵ + 12) - 12)/(2)
y = ⁵√((2x⁵)/(2)
y = ⁵√x⁵
y = x
Now plug in the value given to you.
(f⁻¹ o f)(2) = 2
The answer is 2.
Which shows the image of RST after the rotation (x, y) (y, -x)
Answers
Answer:
Option A shows the image of RST after the rotation
Step-by-step explanation:
Coordinates of S=(1,3)
Coordinates of R = (-2,1)
Coordinates of T = (-1,7)
We are given that after rotation(x,y)→(y,-x)
So, The new coordinates after rotation will be :
Coordinates of S'=(3,-1)
Coordinates of R'= (1,2)
Coordinates of T'= (7,1)
These are the coordinates of triangle of Option A
So, Option A is true .
Hence Option A shows the image of RST after the rotation
A. shows the image of RST after the rotation.
In the geometry, an equilateral triangle is the triangle in which have all 3 sides have same length. an equilateral triangle is also equiangular; that is, all 3 internal angles are also congruent to each other and are each 60 degrees It is also a regular polygon, so it is also referred to as the regular triangle.
Which plane does the triangle RST belong to?
The XY-coordinate plane or triangle RST are equilateral. Points R or In the x y -coordinate plane, triangle R S T is equilateral. Points R and T had coordinates ( 0, 2) and ( 1, 0), respectively.
Coordinates of S=(1,3)
Coordinates of R = (-2,1)
Coordinates of T = (-1,7)
We are given that after rotation(x,y)→(y, -x)
So, The new coordinates after the rotation will be :
Coordinates of S'=(3,-1)
Coordinates of R'= (1,2)
Coordinates of T'= (7,1)
These are the coordinates of the triangle of Option A
So, Option A is true.
Hence Option A shows the image of RST after the rotation.
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what is the solution to the graph below?
Answers
Answer:
1,5
Step-by-step explanation:
1,5 is located within the shaded region.
when sunayana purcased a video-game she paid Rs 162.50 as VAT at the rate of 13%. find its cost without levying VAT. Rs 1250 is answer please how to take out this answer PLEASE HELP ME
Answers
Answer: 1250
Step-by-step explanation:
Let price be x
13/100x = 162.50
x = (162.50/100) / 13 = 1250
Which equation represents a circle with a center at (2,8) and a radius of 11?
(x – 3)2 + (y + 2)2 = 11
(x-2)2 + (y + 8y2 = 121
(x + 2)2 + (y - 3)2 = 11
(x + 3)2 + (y – 2y = 121
Answers
Answer:
[tex](x-2)^2+(y-8)^2=121[/tex]
Step-by-step explanation:
This is because if you can see that the, x is being subtracted by 2, making the x-coordinate +2. and the y is being subtracted by 8, making the y coordinate +8.
(2, 8) = Coordinates
And the reason it has a radius of 11 is because the 121 on the other is the product of 11 times 11.
Find the sum of the first 18 terms of the arithmetic sequence whose nth term is an = 3n - 1.
Answers
Answer:
495
Step-by-step explanation:
In order to find the sum of the first 18 terms you have to find the 18th term and the first term using the equation given.
a1=3(1)-1 a1=2
a18=3(18)-1 a18= 53
Then plug in 53 for an, 18 for n, and 2 in for a1 in the sum equation: Sn=n/2(a1+an)
Sn=18/2(2+53) Solve for sn= 495
what is the circumference of a circle with radius 20cm
Answers
Answer:125.66cm
Step-by-step explanation:
Circumference formula is C=2pi (r)
So C=2(pi or 3.14) (20)
Just plug the 20 (radius for the r) and you have the answer.
The perimeter of a rectangle is 16.6km, and its area is 13.42km2. Find its length and width. length : km width : km
Answers
Answer:
l=5.12 & w=2.62
Step by step explanation:
A=l×w
13.42=lw
w=13.42/l
[tex]p = 2(l + w) \\ 16.6 = 2(l + \frac{13.42}{l} ) \\ 16.6 = 2( \frac{ {l}^{2} + 13.42}{l}) \\ 16.6 = 2(l + 13.42) \\ 16.6 = 2l + 26.84 \\ 2l = 26.84 - 16.6 \\ 2l = 10.24 \\ l = \frac{10.24}{2} \\ l = 5.12km[/tex]
Since you have found the value of the length you can find the value.of the width.
[tex]w = \frac{13.42}{l} \\ w = \frac{13.42}{5.12} \\ w = 2.62km[/tex]
Pia used 2/3of her sugar to make 3/4of a batch of cookies. How much of her sugar would she need to make the whole batch? Write the expression you would use and then solve it.
Please answer
Answers
Answer:
Equation;
(3/4)x = 2/3
Solving;
x = 8/9
she would need 8/9 of her sugar to make a full batch.
Step-by-step explanation:
Let x represent the amount of sugar that would be needed to make the whole batch.
Given that;
Pia used 2/3 of her sugar to make 3/4 of a batch of cookies.
Since 2/3 of her sugar is needed to make 3/4 of a batch of cookies, then;
(3/4)x = 2/3
Solving the equation, dividing both sides by 3/4;
(3/4)x ÷ 3/4 = 2/3 ÷ 3/4
x = 2/3 × 4/3
x = 8/9
Therefore she would need 8/9 of her sugar to make a full batch.
please can you help for this questiong
Answers
Find the volume of a pyramid with a square base, where the perimeter of the
base is 12.8 m and the height of the pyramid is 12.5 m. Round your answer
to the nearest tenth of a cubic meter.
Answer:
m3
Submit Answer
Answers
Answer:
[tex]42.7\,\,cubic\,\, meters[/tex]
Step-by-step explanation:
Given: Perimeter of base of a pyramid = 12.8 m
Height of the pyramid = 12.5 m
To find: volume of a pyramid
Solution:
Perimeter of base of a pyramid = 12.8 m
As base of the pyramid is a square,
12.8 = [tex]4(side\,\,of\,\,a\,\,square)[/tex]
side of a square = [tex]\frac{12.8}{4}=3.2\,\,m[/tex]
Area of a square (A) = [tex](side\,\,of\,\,a\,\,square)^2=(3.2)^2=10.24\,\,m^2[/tex]
Height of the pyramid (h) = 12.5 m
Volume of the pyramid = [tex]\frac{Ah}{3}=\frac{1}{3}(10.24)(12.5)=42.7\,\,cubic \,\,meters[/tex]
Ellen has $14,000 in a savings account, has a $500 outstanding credit card
bill, owes $2400 on her car payment, and has $18,000 left on her student
loans. What is the total of her liabilities?
Answers
Answer:
It'd be $4,700
Step-by-step explanation:$500 + $2,400 + $1,800 = $4,700. Minus that amount from her savings account total and that's how much money she has left.
Brainliest question please please help me please
Answers
Answer: C outside of the circle
Step-by-step explanation:
The answer is c because
point 4, -1 falls outside of the
circle.
Hope this helps :)
Answer:
Its on the circle
Step-by-step explanation:
Q6.
2
(8 + 2 x 6)2 =
the two at the end of the brackets is squared it a small two
Answers
Answer: 1600
Step-by-step explanation:
2(8+2x6)
2(8+12)
2(20)
40
[tex]40^{2}[/tex]
1600
Mark me as the brainiest answer.
= (8+12)2^2
=(20)2^2
=20x4
=80
Someone pls help me it would be amazing thank u a lot
Answers
Answer:
36.87°
Step-by-step explanation:
With reference angle C
perpendicular (p) = 27
base(b) = 36
Now
Tan C = p/b
Tan C = 27/36
C = tan ^-1( 27/36)
= 36.87°
Hope it helps
:)
Answer:
36.87
Step-by-step explanation:
Calculate the length of the opposite side of a right triangle with a hypotenuse of 16 inches and angle of 25 formed at the intersection between the adjacent side and the hypotenuse
Answers
Answer:
6.76 in
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Sin α = opposite side / hypotenuse
Where α is the angle formed at the intersection between the adjacent side and the hypotenuse , and the opposite side is x :
Replacing with the values given:
Sin 25 = x/ 16
Solving for x
sin25 (16) =x
x= 6.76 in
Feel free to ask for more if needed or if you did not understand something.
Tamir wants to build a square wooden stage. His original pin for a stage x
feet long and x feet wide had to be made smaller to fit the space. The stage
needs to be 5 feet narrower and 3 feet shorter than his original plan. Which
multiplication problem represents this situation? What is the area of the
smaller stage?
Answers
Answer:
b .
Area=(x-5) (x-3)
Area = x^2 -8x+15
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Area of a rectangle = width x length
The original length and width was x, so if the stage needs to be 5 feet narrower and 3 feet shorter.
x-5
x-5
The formula is:
A=(x-5) (x-3)
Solving:
A = (x.x) + (x.-3) + (-5.x)+ (-5.-3)
A = x^2 -3x -5x+15
A = x^2 -8x+15
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was to . If there were 12,779 total votes, how many yes votes were there?
Answers
Answer: The question is incomplete
Step-by-step explanation: The answer to this question cannot be determined correctly since an important detail is missing.
However, let me explain how you would normally go about it by using an example of mine. If for example the ratio of yes votes to no votes was 8 to 5, and the question requires you to calculate how many yes votes were there as indicated in your question, then the first step would be to find the total number of both sides of the ratio. That is add 8 to 5 which gives you 13. This means if there was a total of 13 votes cast, every yes vote stands for 8 out of 13 votes and every no vote stands for 5 out of 13 votes.
To express it mathematically, every yes vote would be 8/13 of the total (12779) and every no vote would be 5/13 of the total (12779).
Therefore to determine how many yes votes there was, is calculated as follows;
Let yes votes be y and no votes be x'
y = (8/13) * 12779
y = 102232/13
y = 7864
Based on my example that the ratio of yes votes to no votes is 8 to 5,
Then the number of yes votes was 7,864.
PLEASE HELP 20 POINTS!
This pattern follows the rule add 2. What is another feature of this pattern?
An image of a pattern. Term one has one dot, term two has three dots, term three has five dots, term four has seven dots.
A. The terms appear even, odd, even, odd.
B. All the terms are even.
C. Two terms are even, then two terms are odd.
D. All the terms are odd.
Answers
Answer:
Option D
Step-by-step explanation:
According to the image description provided:
Term one starts with one dot. One is an odd number.
If you add two to an odd number, the sum would be another odd number. This is what's happening with the pattern.
For example:
[tex]3+2 =5[/tex]
Three is an odd number. If you add two to it, you would get five, which is another odd number.
Term two has 3 dots, term three has 5 dots, term four has 7 dots.
So, all terms should be odd.
Option D should be the correct answer.
What is the volume of this rectangular prism?
2 cm
3 cm
7
cm
4
Answers
Answer:
4 cm and 2cm
Step-by-step explanation:
Volume of the rectangular prism is 10.5 cm³.
What is Rectangular Prism?Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.
Given three dimensions of a rectangular prism as given below in the image.
Length = 3 cm
Width = 7/4 cm
Height = 2 cm
Volume of a rectangular prism = Length × Width × Height
= 3 × 7/4 × 2
= 3 × 7/2
= 10.5 cm³
Hence the volume of the rectangular prism is 10.5 cm³.
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Which polynomial is in standard form? 2xy^3 +3x^3 y^4 -4x^4 y^5 +9x^5 y^6 Which polynomial is in standard form?
Answers
Answer:
(D) [tex]5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9[/tex]
Step-by-step explanation:
A polynomial is said to be in standard form when it is arranged in descending powers of x.
When there are more than one variable, the alphabetical order is followed. For example, if there are variables x and y in the polynomial, x must be in descending order and y will be in ascending order.
From the given options, the polynomial which is in standard form is:
[tex]5x^7y^2+7x^6y^5-14x^3y^7+51x^2y^9[/tex]
The correct option is D.
Answer:
d
Step-by-step explanation:
Caitlin bought 6 cookies for a total of $10. At this rate, what is the cost of 9 cookies?
Answers
Answer:
15$
Step-by-step explanation:
cost of 1 cookie = 10/6
cost of 9 cookies = 9* 10/6 = $15
Answer:
15 dollars
Step-by-step explanation:
6 cookies for 10 dollars
3 cookies for 5 dollars.
6+3 cookies for 10+5 dollars
Ashley's car used 10 gallons of gas to drive 478 miles. At what rate does her car use gas in miles per gallon? Express your answer in simplest form.
Answers
Answer:
47.8
_____
1
Step-by-step explanation:
Answer:
she got it by breaking up the problem step by step for
Step-by-step explanation:
she has done this putting the form like so
10 - 478
I hope this
What is an equation of the line that passes through the point (− 2, 5) and is parallel to the line 3x + 4y = 12 ?
Answers
Answer: [tex]y=-\frac{3}{4} x+3.5[/tex] or [tex]y=-\frac{3}{4}x+\frac{7}{2}[/tex]
Step-by-step explanation:
A parallel line has the same slope and different y-intercepts.
Let's change our equation to slope-intercept.
[tex]3x+4y=12[/tex]
[tex]4y=12-3x[/tex]
[tex]y=\frac{12-3x}{4} =3-\frac{3}{4}x[/tex]
[tex]y=3-\frac{3}{4} x[/tex]
Now that we know our slope is -3/4, we know the equation will have -3/4 as the slope. Let's leave b blank so that we can find the y-intercept of the parallel line.
[tex]5=-\frac{3}{4}(-2)+b[/tex]
[tex]5=\frac{3}{2} +b[/tex]
[tex]3.5=b[/tex]
Our parallel equation is [tex]y=-\frac{3}{4}x+3.5[/tex] or [tex]y=-\frac{3}{4} x+\frac{7}{2}[/tex]
May i have some help please?
Answers
Answer:
1/5 = 0.2
0.3 = 1/3
1/2 = 0.5
Answer:
1/5 =0.2
3/10 = 0.3
1/2 =0.5
Multiply the binomials using the box method.
(y+3)(y−6) =
Answers
Answer:
y^2 -3y - 18
Step-by-step explanation:
y x y= y^2
3 x y = 3y
y x -6 = -6y
-6y +3y = -3y
3 x -6 = -18
y^2 -3y - 18
PLEASE HELP!!!!!!!! IMAGE ATTACHED!!!!
Answers
Answer:
Step-by-step explanation:
4) (-2,3) ; (-1,-2)
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{-2-3}{-1-[-2]}\\\\=\frac{-5}{-1+2}\\\\=\frac{-5}{1}\\\\=-5[/tex]
5) line is parallel to x-axis. So, slope= 0
6) (1,1) ; (-2, -1)
[tex]Slope=\frac{-1-1}{-2-1}\\\\=\frac{-2}{-3}\\\\=\frac{2}{3}[/tex]
If f(x) = 3x^2 +1 and g(x) = 1-x, what is the value of (f-g)(2)
Answers
Answer:
14
Step-by-step explanation:
Let's find (f-g)(x)
[tex]3x^{2} + 1 - (1-x)\\3x^{2} + 1 -1 + x\\3x^{2} + x[/tex]
Now let's plug in x=2, so to find (f-g)(2)
[tex]3(2)^{2} + 2\\12 + 2 = 14[/tex]
Please help! Correct answer only, please! I need to finish this assignment this week. Determine the value of the following if it is possible. If it is not possible, explain.
Answers
Answer:
Option D is the correct answer
Step-by-step explanation:
Since, dimensions of both the matrices are different. Hence we can't add them.
The parallelogram shown below has an area of 30 units^2
2
squared.
Find the missing height.
h = units
Answers
Answer:
6
Step-by-step explanation:
The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
The area of a parallelogram is given as (1/2) × (sum of parallel sides) × (distance between parallel sides).
Area = (1/2) × (5 + 5) × h
30 = 10h/2
5h = 30
h = 6 units.
Hence "The measure of the missing side of the given parallelogram with an area of 30 unit² will be 6 units".
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Given the question missing the figure attached below,