Explain how to modify the graphs F(x) and g(x) to graph the solution to set the following system of inequalities. How can the solution set be identified? Y>x^2-1
Y<-x^2+4
Answers
The following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is found by the fact that the domain of quadratic functions is the entire real domain.
How to apply rigid transformations to understand the differences between two given functions
According to the Euclidean geometry, rigid transformations are those transformations applied on geometrical loci such that Euclidean distances are conserved in every point of the loci. Reflections and translations are sound examples of rigid transformations.
In this question we must derive all needed rigid transformations to turn f(x) into g(x), both quadratic functions. After a careful analysis we conclude that the following rigid transformations are applied:
Reflection around the line y = -1.Translation 5 units in the +y direction.The solution set is represent by all x-values such that the function exists. According to real algebra we remember that the domain of quadratic functions is the real domain. Thus, the solution sets of f(x) and g(x) are the real domain.
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Related Questions
how to simplify 8 + ( -6 ) + 4
Answers
Answer:
6
Step-by-step explanation:
[tex]8-6+4[/tex]
[tex]2+4\\6[/tex]
PART A
Mrs. Jackson is planning an outdoor barbeque. She will cook 2 ears of corn per person plus two extra. If 16 people plan to come, how many ears of corn will Mrs. Jackson cook?
Answers
Answer:
34
Step-by-step explanation:
2 x 16 + 2
_________
2 x 16 = 32
_________
32 + 2 = 34
Answer:
30 or 64
Step-by-step explanation:
30 Because... 2 corns for every one till they rech 15..
that's mean (2 x 15)
64 Because... 2 corns plus 2 extra if they rech 16....
that's mean (4x16)
What is the solution for the following equation 2(y+3) squared
Answers
Answer:
2y² + 12y + 18
Step-by-step explanation:
2(y + 3)²
First use formula (a + b)² = a² + 2ab + b² to expand (y + 3)²:
(a + b)²
(y + 3)²
y² + 2*y*3 + 3²
y² + 6y + 9
Dont forget the 2:
2(y² + 6y + 9) <== distribute and multiply
2y² + 12y + 18
Hope this helps!
volume(12) pls help fast
Answers
Answer:
G
Step-by-step explanation:
Volume of a triangular prism = area of the base x height
(where the "bases" are the triangles)
Area of a triangle = 1/2 x base x height
Given:
base = 3.1 cmheight = 4.8 cm⇒ area of base of prism = 1/2 x 3.1 cm x 4.8 cm = 7.44 cm²
Given:
area of base = 7.44 cm²height of prism = 2.6 cm⇒ Volume of the prism = 7.44 cm² x 2.6 cm = 19.344 cm³
Tom has read 5/8 of the 360 pages in the book how many pages are left to read?
Answers
Answer:
135
Step-by-step explanation:
5/8=0.625
1-0.625=0.375
0.375 times 360=135
Divide.
0.4) 29
Enter your answer as a decimal in the box.
Answers
Answer:
0.0138
Step-by-step explanation:
the division gives a value which is almost recurring hence we round off to get 0.0138
Answer:
72.5 (I did the math)
Dwayne is making a documentary about the formation of rocks. He started on Wednesday with
a certain amount of film footage and then added 3.75 hours. Then, on Friday he cut 0.28 hours
of footage. Over the weekend he cut another 1.3 hours of footage. On Monday he added 1.25
more hours of footage and finally on Tuesday got rid of another 2.7 hours of footage to have his
final film length. If Dwayne started on Wednesday with 6.8 hours of footage, what was the final
length of his documentary? Round your answer to the nearest tenth if necessary.
Answers
x + 3.75 - 0.28 - 1.3 + 1.25 - 2.7
x = 6.8
6.8 + 3.75 - 0.28 - 1.3 + 1.25 - 2.7 = 7.25
Dwayne has 7.25 hours of footage.
Hope that helps
HELP ASAP! WILL MARK BRAINLIEST
Identify each number as rational or irrational by circling the word that describes it:
Rational or Irrational:
Rational or Irrational: 0.46
Rational or Irrational: √100
Rational or Irrational: -16
Rational or Irrational: √21
Rational or Irrational: 10
Answers
Answer
0.46 : rational(/ ); irrational(x);
Solving Steps
Question 2
Answer
1100 : rational(/): irrational(x);
Solving Steps
Categorize the number :
Question 3
Answer
-16 : rational(V); irrational(x);
Solving Steps
Categorize the number:
-16 : rational(/); irrational(x);
Question 4
Answer
V21: rational (×); irrational(r);
Solving Steps
Categorize the number
V21 : rational(×): irrational():
b) The perimeter of a squared field is 60 m. Find its area.
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
Perimeter of square is :
[tex]\qquad \sf \dashrightarrow \:4 \times side \: length[/tex]
so, we can take side length as a, and solve for a ~
[tex]\qquad \sf \dashrightarrow \:4a = 60[/tex]
[tex]\qquad \sf \dashrightarrow \:a = 60 \div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:a = 15[/tex]
Now, since we know the side length. let's find Area of square :
[tex]\qquad \sf \dashrightarrow \: {15}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:area = 225 \: m {}^{2} [/tex]
Solve for w : 5w squared - 5w = 0
Answers
Answer:
The answer is 1
Step-by-step explanation:
5w² – 5w = 0
Add 5w both side
5w² – 5w + 5w = 5w – 5w
5w² = 5w
Now, Divide both side by 5w we get,
5w²/5w = 5w/5w
w = 1
Thus, The value of w is 1
Answer:
w = 1
Step-by-step explanation:
Given :
5w² - 5w = 0Bring 5w to the other side.
5w² = 5w 5 and w are each present on both sides so they cancel out, leaving us with :w = 1Lisa deposits $625 in an account that earns 4% interest
annually. How much money is in the account
compounded
after 3 years? (8.12D)
Answers
Answer:
$703.04
Step-by-step explanation:
The equation for this is 625 x [tex]1.04^{years\\}[/tex].
So using the formula 625 x [tex]1.04^{3}[/tex] = $703.04
Answer:
$703.04
Step-by-step explanation:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $625r = 4% = 0.04n = 1t = 3Substituting given values into the formula:
[tex]\implies \sf A=625(1+\frac{0.04}{1})^{3}[/tex]
[tex]\implies \sf A=625(1.04)^{3}[/tex]
[tex]\implies \sf A=703.04[/tex]
NEED HELP!! THX! please answer part b, I already have part a.
Answers
Answer:
See below ~
Step-by-step explanation:
3.25% is the interest rate, meaning it won't be constant, but a coefficient of the function$15,000 is a constant as the interest gets added to itThe function can be written as :
aₙ₊₁ = 0.325aₙ + 15000Help, question is in image.
Answers
Answer:
-31
Step-by-step explanation:
substitute- y-8b = -7-8(3)
8(3)=24
-7- -24=
solve- -31
Answer:
-31
Step-by-step explanation:
Given
binomial: y - 8b
y = - 7
b = 3
Solution
-7 - 8(3) Substitute 3 in for b and - 7 in for y
-7 - 24 Combine -8 and 3 (which is - 24
-31 Answer. - 31
9. The growth of mold in Specimen A can be modeled by A(t) = The growth
of mold in Specimen B can be modeled by B(t)
a. Find (A - B)(t).
b. Explain what the function (A - B)(t) represents
Answers
The value of the difference of the functions is 3t^2/3
The difference in the growth of the specimen is 3t^2/3
Exponential functionsExpoenential functions are written in the form y= ab^x
Given the following expoenential functions
A(t) = 5/6t^2/3
B(t) = 1/3t^2/3
a) Determine the function (A-B(t)
(A-B)(t) = A(t) - B(t)
Substitute
(A-B)(t) = 5/6t^2/3 - 1/3t^2/3
(A-B)(t) = (5/6-1/3)t^2/3
(A-B)(t) = 9/3t^2/3
(A-B)(t) = = 3t^2/3
b) This means that the difference in the growth of the specimen is 3t^2/3
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Find x . Round your answer to the nearest tenth of a degree.
Answers
The value of a, b and <A are 17.4, 119.3 and 42 degrees respectively
Trigonometry identityFrom the given right angles triangle, we have the following parameters;
<A + 48 + 90 = 180 (sum of angles in a triangle)
<A =180 - 138
<A = 42 degrees
Using the SOH CAH TOA identity
sin48 = b/26
b = 26sin48
b = 19.3
For the value of a
sin42 = a/26
a = 26sin42
a = 19.3
a =17.4
Hence the value of a, b and <A are 17.4, 119.3 and 42 degrees respectively
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what are the magnitude and direction of u+v+w ?
Answers
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
How to determine the magnitude and the direction of a resultantVectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
Resultant[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Magnitude[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex] (2)
Direction[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex] (3)
Where [tex]\theta[/tex] is resultant angle, measured in degrees.
If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:
Resultant[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]
[tex]\vec r = (-54.824, 18.531)[/tex]
Magnitude[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]
[tex]\|\vec r\| \approx 57.871[/tex]
Direction[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]
[tex]\theta \approx 198.676^{\circ}[/tex]
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]
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Find the reciprocal of 7/2 multiplied by 3/5
Answers
6/35
hope it helps...!!!
Answer:
(2/7) x (3/5)= fraction form: 6/35 decimal form: 0.1714285
Step-by-step explanation:
What is the perimeter?
Answers
Answer:
30 m is the original, and 60 m would be expanded
Step-by-step explanation:
perimeter=l+w+l+w so 12+3+12+3=30 and you could multiply that by 2 to make it 60m i believe
The bakers at healthy bakery can make 320 bagels in 10 hours. How many bagels can they make in 15 hours? What was the rate per hour?
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use Unitary method ~
[tex]\qquad \sf \dashrightarrow \:10 \:hr = 320 \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \: 1\: hr = (320 \div 10) \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \:1 \: hr = 32 \: bagels[/tex]
So, the rate per hour is 32 bagels ~
[tex]\qquad \sf \dashrightarrow \:15 \: hr = (15 \times 32) \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \:15 \: hr = 480\: bagels[/tex]
So, they can prepare 480 bagels in 15 hours
Answer:
480 bagels
Step-by-step explanation:
320 bagels in 10 hours.
⇒ 320 bagels = 10 hours
Divide 10 both sides to find the rate per hour:
⇒ 320/10 bagels = 10/10 hours
⇒ 32 bagels = 1 hours
Multiply 15 both sides to find the number of bagels in 15 hours
⇒ 32 bagels = 1 hours
⇒ 32 x 15 bagels = 1 x 15 hours
⇒ 480 bagels = 15 hours
Miguel did the following math problem: 6 ^5 · 6^ 4 = 36^ 9.
Which of the following is a true statement?
He is incorrect because he multiplied the bases.
He is incorrect because he should have multiplied the exponents.
He is correct.
He is incorrect because he should have subtracted the exponents.
Answers
Answer:
He is incroredct because he should have multiplied the bases
Step-by-step explanation:
Answer:
A: He is incorrect because he multiplied the bases.
Step-by-step explanation:
The correct answer would have been: [tex]6^{9}[/tex]
what is the surface area of the cylinder
Answers
Answer:
The formula to calculate the total surface area of a cylinder is expressed as, total surface area of cylinder = 2πr(r + h). This total surface area includes the area of the 2 bases (2πr2) and the curved surface area (2πrh). Here 'r' is the radius and 'h' is the height of the cylinder.
Step-by-step explanation:
Which expression should you simplify to find the 90% confidence interval,
given a sample of 65 people with a sample proportion of 0.42?
O A. 0.42
1.645-0.42
165
OB. 0.42 65
0.42(1–0.42
1.645
O c. 0.42 +1.645.
0.42(1-0.42)
65
O D. 0.42 +1.645.
V0.42(1–0.42)
65
Answers
Answer:
i think is would be D
hope that helps if not i can change it
Step-by-step explanation:
In the diagram below,EF is parallel to BC. IF BC is the twice length of ED,BD=26 and EF=14, find the length of ED. Figure are not necessary drawn to scale. State your answer in simplest ratio form if necessary.
Answers
Answer: sqrt(182)
Step-by-step explanation:
ΔEDF is congurent with ΔBDC
DE/EF = DB/BC
The length of the ED is √182.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
EF is parallel to BC.
This means,
ΔEDF is congurent with ΔBDC
So,
DE/EF = DB/BC
BC = 2ED
DB = 26
EF = 14
Now,
DE/EF = DB/BC
DE/14 = 26/2ED
2ED² = 14 x 26
ED² = 7 x 26
ED = √182
Thus,
The length of the ED is √182.
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The radius of a semicircle is 17 millimeters. what is the semicircle's perimeter?
Answers
Answer:
87.407
Step-by-step explanation:
circumference = 2*pie*r
= 2*pie*17
=106.8/2
=53.4
53.4+(17*2)
=87.4
Answer:
Step-by-step explanation:
it 87.38
TRUST ME
Find the perimeter of the composite figure using pi
Answers
Answer:
(3 +1.5π) ft ≈ 7.71 ft
Step-by-step explanation:
We see a semicircle, not a "composite figure." The perimeter of the semicircle is the sum of the length of the arc and the length of the straight edge:
P = (1/2)πd +d . . . where d is the diameter and πd is the full circumference
P = d(1 +π/2)
P ≈ (3 ft)(1 +1.57) = 7.71 ft . . . . . using 3.14 for π
The perimeter of the figure is about 7.71 feet.
__
In terms of pi, the perimeter is ...
P = (3 +1.5π) ft
7
In a circle, which ratio is equivalent to t?
- One
er
O A. area of a circle to its circumference
OB. radius of a circle to its area
-67
Q
67
O C. diameter of a circle to its radius
OD, circumference of a circle to its
diameter
Answers
Answer:
D
Step-by-step explanation:
The circumference of a circle is [tex]2\pi r[/tex], while the diameter of a circle is 2r. [tex]\frac{2\pi r}{2r} = \pi[/tex]
A fence installation company sells 4 models of chain-link fencing, 2 models of wood fencing, and 3 models of iron fencing. What is the total number of models of fencing that the company sells?
A. 24
B. 11
C. 6
D. 9
Answers
Answer:
D.
Step-by-step explanation:
Here’s another geometry workbook question I need help with!
Answers
Answer: D
Step-by-step explanation:
What is the area of this rectangle?
Answers
Answer:
39
Step-by-step explanation:
You find the area by multiplying the length times the height which is what I did 13 x 3 = 39
2) Michael purchased a used car for $6,150 and had to pay 6.5% sales tax. How much tax
did he pay?
Answers
Answer:
$399.75
Step-by-step explanation:
6.5% of $6,150 =
= 0.065 × $6,150
= $399.75
Answer: $399.75
He had to pay $399.75
formula: Tax = Tax Rate * Purchase Price
$6,150 * 6.5%$399.75