5 Describe the transformations performed on the graph of f(x) = x² to obtain the graph of g(x)when g(x) = (x − 3)² — 4.
Answers
Solution:
Given:
\(\begin{gathered} f(x)=x^2 \\ g(x)=(x-3)^2-4 \end{gathered}\)The transformations that occurred are;
\(\begin{gathered} x^2\text{ to }(x-3)^2\text{ shows a horizontal shift of 3 units to the right.} \\ (x-3)^2\text{ to }(x-3)^2-4\text{ shows a vertical shift 4 units down} \end{gathered}\)The graph of the two functions showing the transformations is shown;
Therefore, the transformations performed on the graph of f(x) to obtain g(x) are;
Vertical Shift 4 units down.
Horizontal Shift 3 units right.
Related Questions
Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
$1.85 each and pencils cost $1.39 each. She bought a total of 21 notebooks and pencils. How many of
each did she buy?
Answers
Answer:
Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.
Step-by-step explanation:
Notebooks (N) = $1.85 Pencils (P) = $1.39
9N+12P= $33.33
9*1.85=16.65
12*1.39=16.68
16.65+16.68=33.33
Explain how a telescope with a few mirrors inside allows us to see things kilometers away
Answers
Answer:
Telescopes have several curved lenses inside that reflect on mirrors that gather light.
Step-by-step explanation:
You can find more information on NASA as well. They have very interesting explanations and photos there. :)
write the expression in algebraic form. [hint: sketch a right triangle, as demonstrated in example 3.] tan(arcsec(x/3))
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The expression tan(arcsec(x/3)) can be written \(1/3 \sqrt{x^2-9}\) in algebraic form.
The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.
The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to \(1/3 \sqrt{x^2-9}\).
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Billy has a set of wooden boards. Each board is 0.6 meters long. If Billy lays 4 boards end-to-end, how many meters long will the line of boards be?
Answers
Answer:
2. 4 meters long
Step-by-step explanation:
0. 6 times 4 equals 2. 4
Find the sum (9 + 6) (mod 10)
Answers
Answer:
15d10mo
Step-by-step explanation:
Simplify:
(9+6)(mod10)
=15d10mo
Can someone please help meeeee
Answers
Answer:
it will also measure 131 degree
hope it helps
131 degree
Question 2 of 15 Greece is different from most other countries in southern Europe because: A. its land has never been conquered by foreign empires. B. its most popular religion is not Catholicism. C. its culture has not spread to other regions. D. its population is mostly located in rural areas.
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Greece is different from most other countries in southern Europe because its most popular religion is not Catholicism. Option B
What is Catholicism?Catholicism refers to the traditions, beliefs, and behaviors of the Catholic Church
Greece is predominantly an Orthodox Christian country, whereas most other countries in southern Europe, such as Italy, Spain, and Portugal, are predominantly Catholic.
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Which line segments have a positive slope PLS FAST!! THANKS!!
Answers
a-b
it’s the ones where it’s pointing up to the right!
Please show work thank you math experts
Answers
Answer:
1. 35 - 176 = -141
2. 0.55 × 1.79 = 0.9845
3. 11.38 × 5.46 = 62.1348
Hope it helps and have a great day! =D
~sunshine~
OWX is a sector of a circle with a radius of 35 cm.
OYZ is a sector of a circle with a radius of 24 cm.
The central angle of both sectors is 75°.
Work out the area of the shaded shape WXZY.
Give your answer in cm² to 1 d.p.
2
Answers
The area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.
What is area of sector?The sector's area in a circle is the whole area that is included inside the sector's boundary. The middle of the circle is where a sector always begins. The sector of a circle is the region of a circle that is contained between its two radii and the arc next to them. A semicircle is the area of a circle that most frequently represents half of a circle.
Finding the area of the shaded shape WXZY:The area of the sector OWX can be calculated as:
\(A = (75/360) \times \pi \times 35^{2} = 63.62 cm^2\)
And the area of the sector OYZ can be calculated as:
\(A = (75/360) \times \pi \times 24^{2} = 34.57 cm^2\)
The shaded area WXZY is the difference between the area of the two sectors, which is:
A = 63.62 - 34.57 = 29.05 cm²
Therefore, the area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.
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Complete question -
The length of a rectangle is 3 inches longer than it is wide. If the area is 180 square inches, what are the
dimensions of the rectangle?
Answers
Answer:
Width=12 inches
Length=15 inches
Step-by-step explanation:
Let's say the width is x.
Then, the length is x+3.
The area of a rectangle is the length times width, so
x(x+3)=180
x^2+3x=180
x^2+3x-180=0
After using the quadratic formula, x comes out to be 12 or -15.
x cannot be -15 because you can't have negative distance, so we are left with x=12.
The width is 12 inches and the length is 12+3=15 inches.
Check: 12*15=180
Answer:
The width is 12 and the length is 15.
Step-by-step explanation:
You set the equation as x is equal to the width and since the lenght is 3 units longer than the width, it can be seen as "x + 3"
\(Area=(Length)(Width)\)
180= x × (x + 3)
Then from there you just solve for x.
BCDF is a square with FD=55. Find BD. Round to the nearest tenth, if necessary.
Answers
The diagonal BD of the square BCDF will be 55√2 units.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
BCDF is a square with FD = 55.
The diagonal of the square is given by the Pythagoras theorem. Then we have
D² = 55² + 55²
D² = 55²(2)
D = 55 √2 units
The diagonal BD of the square BCDF will be 55√2 units.
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The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Answers
Since the volume of the pyramid is 18 cubic inches, then the volume of the prism is 3 times that amount which is 54 cubic inches 2.
Therefore, the answer is D. 54 cubic inches.
A car is 180 inches long.A truck is 75% longer than the car
How long is the truck?
Answers
Use the range rule of thumb to identify the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high.
A test is used to assess readiness for college. In a recent year, the mean test score was 21.2 and the standard deviation was 4.9 . Identify the test scores that are significantly low or significantly high.
Answers
The Significantly low test score is 12.1 and significantly high score value is 31.7.
What is z-score?
The standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.
Here, we are dealing with z scores, then the distribution is a normal distribution. The formula for determining the z score is expressed as
z = (x - µ)/σ
Where, x = sample mean, µ = population mean σ = standard deviation
From the information given,
µ = 21.9
σ = 4.9
For significantly low values, z = - 2
Therefore,
- 2 = (x - 21.9)/4.9
- 2 × 4.9 = x - 21.9
- 9.8 = x - 21.9
x = - 9.8 + 21.9
x = 12.1
Significantly low test score = 12.1
For significantly high values, z = 2
Therefore,
2 = (x - 21.9)/4.9
2 × 4.9 = x - 21.9
9.8 = x - 21.9
x = 9.8 + 21.9
x = 31.7
Thus, the Significantly low test score is 12.1 and significantly high score value is 31.7.
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Consider the line 2x-3y=-3.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answers
Parallel slope=2/3
If EFG=35 and GFH=63 what is EFH
Answers
Answer:
98
Step-by-step explanation:
if EFG=35 and GFH=63 then you would just add them to get 98
For the given figure, the value of ∠EFH is 98°.
What is an angle?When two lines meet at a point then two angles are formed. In the same way, when two planes are intersected, angles are also formed.
Here, the value of the ∠EFG = 35° and the value of the ∠GFH = 63°.
From the given figure, it is clear that, the sum of the angles ∠EFG and ∠GFH is equal to the ∠EFH.
Therefore, ∠EFH = ∠EFG + ∠GFH = 35° + 63° = 98°
Hence, the value of ∠EFH is 98°.
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Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (2,-4). A) y = 1/2x-4 - 15 B) y = -2x-4 + 15 C) y = -2x-5 D) y = 1/2x - 5
Answers
Answer:
D
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = \(\frac{1}{2}\) x + 3 ← is in slope- intercept form
with slope m = \(\frac{1}{2}\)
• Parallel lines have equal slopes , then
y = \(\frac{1}{2}\) x + c ← is the partial equation
to find c substitute (2, - 4 ) into the partial equation
- 4 = \(\frac{1}{2}\) (2) + c = 1 + c ( subtract 1 from both sides )
- 5 = c
y = \(\frac{1}{2}\) x - 5 ← equation of parallel line
A homeowner puts a passcode-enabled lock on her front door. To choose a passcode, she must choose a number, a letter from a list of 5 letters, and then another number.
Number Letter Number
0 A 0
1 E 1
2 I 2
3 O 3
4 U 4
5 5
6 6
7 7
8 8
9 9
How many possible passcodes can she make?
Answers
Answer:
500
Step-by-step explanation:
I assume each number is from 0 to 9. Also there are 5 letters.
10 * 5 * 10 = 500
The sum of the reciprocals of two consecutive even integers is 9/40
This can be represented by the equation shown.
1/x +1/x+2 =9/40
Use the rational equation to determine the integers. Show all work.
Answers
Answer:
Only integer solution is x=8
Step-by-step explanation:
\(\displaystyle \frac{1}{x}+\frac{1}{x+2}=\frac{9}{40}\\\\\frac{x+2}{x^2+2x}+\frac{x}{x^2+2x}=\frac{9}{40}\\\\\frac{2x+2}{x^2+2x}=\frac{9}{40}\\\\40(2x+2)=9(x^2+2x)\\\\80x+80=9x^2+18x\\\\0=9x^2-62x-80\\\\0=x^2-62x-720\\\\0=(x-72)(x+10)\\\\0=(x-8)(9x+10)\\\\x=8,\,x=-\frac{10}{9}\)
Therefore, the only integer solution is x=8
6.
If the parent function is y = 2x, which is the function of the graph?
A. y = 0.5(2)x
B. y = −0.5(2)x
C. y = 3(2)x
D. y = −3(2)x
Answers
Answer:
A. y = 0.5(2)^x
Step-by-step explanation:
Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is y = 0 .
Horizontal Asymptote:
y = 0
What number makes the equation true? Enter the answer in the box. 4= 36 - N
Answers
Answer:
as i see
the answer is 32.....
Solve 4x+3>3x+7
This one is so confusing
Answers
Answer:
x>4
Step-by-step explanation:
Answer:
x > 4
Step-by-step explanation:
1. 4x+3>3x+7
2. x>4
Find the equation of the line perpendicular to y= 3x - 6 that runs through the point (-1, -3).
Answers
Answer:
The equation of the line is;
\(y=-\frac{1}{3}x-\frac{10}{3}\)Explanation:
Given that the line is perpendicular to the equation;
\(y=3x-6\)So, the slope of the line will be the negative inverse of the slope of the equation above;
\(m=-\frac{1}{3}\)Also, the line passes through the point;
\((-1,-3)\)Applying the point-slope form of linear equation;
\(y-y_1=m(x-x_1)\)Substituting the values of the slope and coordinates;
\(\begin{gathered} y-(-3)=-\frac{1}{3}(x-(-1)) \\ y+3=-\frac{1}{3}(x+1) \\ y+3=-\frac{1}{3}x-\frac{1}{3} \\ y=-\frac{1}{3}x-\frac{1}{3}-3 \\ y=-\frac{1}{3}x-3\frac{1}{3} \\ y=-\frac{1}{3}x-\frac{10}{3} \end{gathered}\)Therefore, the equation of the line is;
\(y=-\frac{1}{3}x-\frac{10}{3}\)Garrett ran 21 1/2 miles last week. He ran
17 7/8 miles this week. How many miles did
he run in all?
Answers
Answer:
39 3/8
Step-by-step explanation:
Solve for the indicated variable in the literal equation. REAL ANSWERS ONLY!
Answers
Answer:
\( \large \boxed{l = \frac{P + 9}{ - 4} }\)
See below for two alternative solutions.
Step-by-step explanation:
Goal
Solve for the l-term.Given Equation
\(P = - 3 - 4l - 6\)Step 1
Make the l-term as the subject of equation by moving - 3 and - 6 to another side so we can leave l-term as the subject.\(P + 3 + 6 = - 4l\)
Simplify by adding 3 and 6.
\(P + 9 = - 4l\)
Remember that we cannot combine a variable and a constant. We can only combine a like term.
Step 2
Move -4 to divide P+9 so we can finally solve for l-term.\( \frac{P + 9}{ - 4} = l\)
Alternative Solutions
1) We change the position of the negative sign of 4.\( - \frac{P - 9}{4} = l\)
2) Simplify in the simplest form.\( \frac{P + 9}{ - 4} = l \\ \frac{P}{ - 4} + \frac{9}{ - 4} = l \\ - \frac{P}{4} - \frac{9}{4} = l\)
Please help me with part a and b
Answers
Answer:Hey Its Not showing anything on me end
Step-by-step explanation:
Subtract 5 - 4i from 19 - 3i.
Answers
Answer:
Step-by-step explanation:
19 - 3i - 5 + 4i
14 + i
help here's a pic on the problem
Answers
The linear function that shows the proportional relationship between the distance and time is d = 100t
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2.
A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b? Yes, this is because a linear function represents a line, i.e., its graph is a line. Here,
'm' is the slope of the line'b' is the y-intercept of the line'x' is the independent variable'y' (or f(x)) is the dependent variableFrom the table given, we can find the slope of the function by using the formula
m = y₂ - y₁ / x₂ - x₁
m = 300 - 200 / 3 - 2
m = 100
To find the y - intercept,
y = mx + c
300 = 100(3) + c
300 = 300 + c
c = 300 - 300
c = 0
The equation that shows the relationship is
d = 100t
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A school had 1,200 students last year and only 1,040 students this year. What was the percentage decrease in the number of students?
Answers
Answer:
Step-by-step explanation:
160