Answer:
Here we have:
f(x) = 2^x
g(x) = 0.5*2^(x - 3) - 1
We want to compare g(x) and f(x).
The first thing we should do here, is to define the transformations used.
Vertical translation:
For a function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N
if N > 0, the translation is upwards
if N < 0, the translation is downwards.
Horizontal translation:
For a function f(x), a horizontal translation fo N units is written as:
g(x) = f(x + N)
if N > 0, the translation is to the left
if N < 0, the translation is to the right.
Vertical dilation:
For a general function f(x), a vertical dilation of scale factor k is written as:
g(x) = k*f(x).
Ok, now let's start with f(x), and try to use transformations to construct g(x).
We start with f(x).
If we start with a vertical dilation of scale factor k = 0.5, then:
g(x) = 0.5*f(x)
if now we apply a horizontal translation of 3 units to the right, we get:
g(x) = 0.5*f(x - 3)
if now we apply a vertical translation of 1 unit down, we get:
g(x) = 0.5*f(x - 3) - 1
Replacing by the actual function we get
g(x) = 0.5*2^(x - 3) - 1
So we got g(x).
Then, the graph of g(x) is the graph of f(x) dilated vertically by a scale factor of 0.5, then moved to the right 3 units, and then moved down one unit.
6. Find the function with x-intercepts (-3,0) and (5,0), which also goes through the point (1,8)
Answer:
f(x) = (-1/2)(x^2 + 8x - 15)
Step-by-step explanation:
This function has two roots: -3 and 5. Most likely it is a quadratic (all of which have two roots).
Then f(x) = a(x + 3)(x - 5)
The graph goes through (1. 8): Therefore, y = 8 when x = 1:
f(1) = a(1 + 3)(1 - 5) = 8, or
a(4)(-4) = 8, or
-16a = 8, which leads to a = -1/2.
Thus the quadratic in question is f(x) = (-1/2)(x + 3)(x - 5), or
f(x) = (-1/2)(x^2 + 8x - 15)
The function is a quadratic function given by f(x) = (-1/2)(x + 3)(x - 5) and f(x) = (-1/2)(x² + 8x - 15).
What is a Function?A function is a law that relates a dependent and an independent variable.
The function has x-intercepts at (-3,0) and (5,0),
The function has two roots: -3 and 5
So, the equation is a quadratic equation represented by
f(x) = a(x + 3)(x - 5)
The function goes through the point (1. 8)
y = 8 when x = 1
f(1) = a(1 + 3)(1 - 5) = 8
-16a = 8,
a = (-1/2)
f(x) = (-1/2)(x + 3)(x - 5)
f(x) = (-1/2)(x² + 8x - 15)
To know more about Function
https://brainly.com/question/12431044
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Can someone explain if this is correct. I’m unsure!
Answer:
Step-by-step explanation:
Which of the following represents
the graph of this equation?
Help Resources
y = |x - 2|
Answer:
There isnt a graph.
Step-by-step explanation:
Solve the equation n3 = 8/125 for n n=______
Answer:
2/5
Step-by-step explanation:
which inequality best represents the graph?
Answer:
A y ≥ (1/2)x + 5
Step-by-step explanation:
The shaded area is above the solid line
the correct symbol is ≥
-3 + 4x = 25
help mee
Answer:
are u solving for x if so then
x=7
Step-by-step explanation:
hope this helps ...brainliest please!
find the area of the irregular figure. 4 in. 7in. 5in. 3in. 4in. 9in.
Answer:
79 sq in
Step-by-step explanation:
cut it into separate shapes then add the areas of each individual
(4 x 3) + (13 x 4) + (3 x 5)
5m - 3n = 19; m - 6n = -7 /pls. help me solve this linear equation with two variables.
Answer:
m = 5, n = 2
Step-by-step explanation:
[tex]5m - 3 n = 19\\m - 6n = - 7 \ => m = -7 + 6n\\\\Substitute \ m \ in \ 5m - 3n = 19\\\\5(-7 + 6n) - 3n = 19\\-35 + 30n -3n = 19\\27n = 19 + 35 \\27n = 54 \\n = 2\\\\Substitute \ n = 2 \ in \ m = -7 + 6n\\\\m = -7 + (6 \times 2) = -7 + 12 = 5[/tex]
What are the possible values of x in x2 + 3x + 3 = 0?
Answer:
Step-by-step explanation:
Answer:
=3
Step-by-step explanation:
given the general form ax2 +bx+c=0
there exist two solutions where: a=1,b=3andc=3
What is the slope of the line that contains these points?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\boxed{m=8}[/tex]
»»————- ★ ————-««
Here’s why:
[tex]\boxed{\text{The Slope Formula:}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\------------\\m - \text{slope}\\\\(x_1,y_1) \text{ and }(x_2,y_2) - \text{points in the given function}[/tex]
⸻⸻⸻⸻
[tex]\text{\underline{Choosing two points from the table and applying the formula...}}\\\\m = \frac{34-26}{2-1}\\\\\boxed{m = \frac{8}{1}}[/tex]
⸻⸻⸻⸻
[tex]\text{The slope is 8.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Figure 2 was constructed using figure 1. For the transformation to be defined as a rotation, which statements must be true? Selext three options.
Answer:
The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).
The transformation is rigid.
Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.
If figure 1 is located 360° about point C, it will be mapped onto itself.
Step-by-step explanation:
Please help the question is in the picture.
Answer:
[tex]\text{A. }\frac{5}{6}\pi x^2[/tex]
Step-by-step explanation:
The area of a sector with measure [tex]\theta[/tex] is equal to [tex]r^2\pi\cdot \frac{\theta}{360}[/tex]
Since there are 360 degrees in an angle, the measure of sector K must be 360-60=300 degrees.
What we know:
[tex]\theta[/tex] of [tex]300^{\circ}[/tex] [tex]r[/tex] of [tex]x[/tex]Thus, the area of the sector is [tex]x^2\pi\cdot \frac{300}{360}=\boxed{\text{A. }\frac{5}{6}\pi x^2}[/tex]
3. Find the measure of each indicated arc or the measure of an inscribed angle.
b. Find the measure of Arc BAD
Answer:
Step-by-step explanation:
Arc BAD is intercepted by inscribed angle BCD which measures 110. The rule is that an intercepted arc is twice the measure of the angle that intercepts it. Therefore, arc BAD is 110(2) which is 220.
f^3+11g-4hf 3 +11g−4hf, cubed, plus, 11, g, minus, 4, h when f=3f=3f, equals, 3, g=2g=2g, equals, 2 and h=7h=7h, equals, 7.
Given:
The expression is:
[tex]f^3+11g-4h[/tex]
The given values are [tex]f=3,\ g=2,\ h=7[/tex].
To find:
The value of the given expression for the given values.
Solution:
We have,
[tex]f^3+11g-4h[/tex]
After substituting [tex]f=3,\ g=2,\ h=7[/tex], we get
[tex]f^3+11g-4h=(3)^3+11(2)-4(7)[/tex]
[tex]f^3+11g-4h=27+22-28[/tex]
[tex]f^3+11g-4h=49-28[/tex]
[tex]f^3+11g-4h=21[/tex]
Therefore, the value of the given expression is 21.
Which statement best describes why the value of the car is a function of the number of years since it was purchased?
Answer:
What are the statements?
Step-by-step explanation:
You have to list the statements.
Simplify...................
Answer:
(a+b)/2(a-b)
Step-by-step explanation:
Explained in the paper
Goodluck
simplify the following: 4(y + 2)
Answer:
answer
4( y+ 2 )
4y + 8
y = 8/4
y = 2
Answer:4
(
+
2
)
4(y+2)
4(y+2)
Simplify
1
Distribute
4
(
+
2
)
{\color{#c92786}{4(y+2)}}
4(y+2)
4
+
8
{\color{#c92786}{4y+8}}
4y+8
Solution
4
+
8
Step-by-step explanation:
Please please help me
Answer:
49
Step-by-step explanation:
Find the equation of a vertical line passing through the point B(2,-1)
Answer:
x = 2
Step-by-step explanation:
In a vertical line, all x-coordinates are the same.
x = 2
Answer:
x =2
Step-by-step explanation:
A vertical line means the x value remains constant
The x value is 2
x =2
can someone help with this one im confused.
Answer:
C
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4.
Answer:
[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]
Step-by-step explanation:
We want to write the equation of a line that passes through the point (3, -1) and is perpendicular to the line:
[tex]y=6x-4[/tex]
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
The slope of the given equation is 6.
So, the slope of our perpendicular line is the negative reciprocal of 6, which is -1/6.
Next, we are given that it passes through the point (3, -1). Since we are given a point and know the slope, we can use the point-slope form. Point-slope form is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
We will substitute -1/6 for m and (3, -1) for (x₁, y₁). Hence:
[tex]\displaystyle y-(-1)=-\frac{1}{6}(x-(3))[/tex]
Simplify:
[tex]\displaystyle y+1=-\frac{1}{6}(x-3)[/tex]
Our answer is valid as it as, but we can simplify this into slope-intercept form. Distribute:
[tex]\displaystyle y+1=-\frac{1}{6}x+\frac{1}{2}[/tex]
And subtract one from both sides. Therefore, our equation is:
[tex]\displaystyle y=-\frac{1}{6}x-\frac{1}{2}[/tex]
Pls help will mark brainliest
Answer:
1/ 4^2
Step-by-step explanation:
4^4 * 4^-6
We know that a^b * a^c = a^(b+c)
4^(4-6)
4^-2
We also know that a^-b = 1/a^b
1/4^2
Comes with a picture
multiple-choice answer please help I need immediate help
Thank youuuu
Answer:
The answer is A. 31,250.
Step-by-step explanation:
To solve for the 7th term in the geometric sequence, start by plugging 7 into the explicit formula, and the formula will look like [tex]a_{7}=2*5^{(7-1)}[/tex].
Next, subtract 1 from 7, and the formula will look like [tex]a_{7}=2*5^{6}[/tex].
Then, raise 5 to the power of 6, which will look like [tex]2*15625[/tex].
Finally, multiply 2 by 15,625, and the answer will be 31,250.
Please help and show clear instructions will give brainliest !
Answer:
Answer is 3 because
Step-by-step explanation:
a=2
20*2= 40
40-1 = 39
b = 13
so 39/13 = 3
If d = -3 what is the value of 15 - 3d ?
Answer:
24
Step-by-step explanation:
15 - 3d
Let d = -3
15 - 3(-3)
Multiply
15 +9
Add
24
Answer:
24
Step-by-step explanation:
15 - 3d
* plug in -3 *
15 - 3(-3)
simplify -3(-3)
-3(-3) = + 9
add
15 + 9 = 24
Which of the following is/are equal to 3.4?i)314ii)5115iii)3410
How much would $500 invested at 6% interest compounded monthly be
worth after 5 years? Round your answer to the nearest cent.
int
A09) P(124
A. $512.63
B. $669.11
C. $674.43
D. $886.41
Answer:
$669
Step-by-step explanation:
Given data
Principal= $500
Rate= 6%
Time= 5 years
The compound interest formula is given as
A= P(1+r)^t
A=500(1+0.06)^5
A=500(1.06)^5
A=500*1.338
A=$669
PLEASEEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
rhombus
Step-by-step explanation:
Need this in now like ASAP.
Fill the blanks in with yes or no
Answer-
a. no
b. yes
c. no
A question abouts angles
Answer:
x = 16
Step-by-step explanation:
These are corresponding angles meaning they are equal to each other.
4x + 30 = 94
4x = 64
x = 16
