In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -5. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answers
To get the x-intercepts, we will need to equate the equation to zero and solve for x.
For the parent function, we have:
x² = 0
x = 0
Therefore, the function intersects the x-axis at one point which is the origin.
For the image function we have:
-x² - 5 = 0
x² = -5
x = √-5 which does not exist in real numbers
This means that the image function does not intersect the x-axis at all.
Based on the above, the parent function has one x-intercept while the image one doesn't have any x-intercepts.
Part (2):
I have attached the image containing the two functions , the parent one as well as the image.
As we can note, two changes occurred to the parent function in order to form the image:
1- The parabola was flipped to be pointing downwards instead of pointing upwards
2- The vertex was translated 5 units downwards to be at (0,-5) instead of (0,0)
x^2 only touches the x axis when x=0 and it increases without bound on either side of 0.
-x^2-5 never touches the x axis reaching a maximum at (0,-5) and decreasing without bound on either side of 0
g(x) is f(x) inverted and moved down five units...
Related Questions
Two samples are randomly selected from each population. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Answers
hey can you please help me posted picture of question
Answers
The solution is shown below:
[tex] x^{2} +16 \\ \\ = x^{2} +(4)^{2} \\ \\ = x^{2} -(-1)(4)^{2} \\ \\ = x^{2} -i^{2} (4)^{2} \\ \\ = x^{2} -(4i)^{2} \\ \\ =(x+4i)(x-4i) [/tex]
Form a sequence that has two arithmetic means between -13 and 89. a. -13, 33, 43, 89 c. -13, 21, 55, 89 b. -18, -36, -72, -144 d. -18, -81, -144
Answers
Solution:
Since it has to be between -13 and 89, letter d and b are not anymore considered to be the answer.
for a:
33-(-13)=46=d
43-33=10=d the value for this d is different from the two sequence,
89-43=46=d
they have different value for d, thus this is not the answer!
for c:
21-(-13)=34=d
55-21=34=d
89-55=34=d
they have the same value for d, thus the correct answer is c. -13, 21, 55, 89
The equation of a parabola is given.
y=−14x2+4x−19
What are the coordinates of the vertex of the parabola?
Enter your answer in the boxes.
Answers
Answer:
vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
Step-by-step explanation:
Given : The equation of a parabola is given.
y=−14x²+4x−19
To find : What are the coordinates of the vertex of the parabola.
Solution : We have given that
y = −14x²+4x−19
we will be "completing the square" .
Factor out -14 to make leading coefficient 1
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}[/tex])
Add and subtract [tex](\frac{-1}{7}) ^{2}[/tex]
y = -14 ([tex]x^{2} -\frac{2x}{7} +\frac{19}{14}+\frac{-1}{7}) ^{2} - (\frac{-1}{7})^{2})[/tex] .
Complete the square
y = -14 ( [tex](x -\frac{1}{7}) ^{2} +\frac{19}{14}- (\frac{-1}{7})^{2})[/tex].
y = -14 ( [tex](x-\frac{1}{7}) ^{2} -\frac{131}{7}[/tex]
Standard form of parabola vertex form y = a(x - h)²+ k,
Where, ( h, k) are vertex
On comparing a = -14 , h= [tex]\frac{1}{7}[/tex], k = [tex]\frac{131}{7}[/tex]
Therefore, vertex ( [tex]\frac{1}{7}[/tex], [tex]\frac{131}{7}[/tex]).
Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side sides are 5.
Answers
We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5
Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:
AH = (AB - DC) ÷ 2
= (7 - 5) ÷ 2
= 2 ÷ 2
= 1
Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²)
= √(5² - 1²)
= √(25 - 1)
= √24
= 2√6
Last, we have all the information needed in order to calculate the area by the formula:
[tex]A = \frac{(AB + CD)DH}{2} [/tex]
A = (7 + 5) × 2√6 ÷ 2
= 12√6
The area of the regular trapezoid is 12√6 square units.
Explain how you can tell when a formula represents a length an area or a volume
Answers
Ex:
d = 2r (this would only involve multiplying by one dimension, therefore it is a length)
A = bh (this involves multiplying 2 dimensions, giving a measurement of area)
V = lwh (this involves multiplying 3 dimensions, giving a measurement of volume)
To determine if a formula represents a length, area, or volume, consider the units used in the formula.
Explanation:When determining if a formula represents a length, area, or volume, you need to consider the units used in the formula. Length is typically measured in units such as meters or feet. Area is measured in square units, such as square meters or square feet. Volume is measured in cubic units, such as cubic meters or cubic feet.
For example, suppose you have a formula that involves only one variable and it includes units such as meters. This formula would most likely represent a length. If the formula involves two variables and includes units like square meters, then it represents an area. And if the formula involves three variables and includes units like cubic meters, then it represents a volume.
It's important to pay attention to the units to determine whether a formula represents a length, area, or volume.
How do you divide a decimal
Answers
if i had 7 apples and someone took away 5 how many would i have left
Answers
how do I solve 9y+3=6y+15 then y =
Answers
Using the photo I have provided, you can see the steps. I performed these steps as you need to isolate the variable, Y. Once you do that, you must preform a one or two step equation to then get what said variable equals.
Hope this helps!
9y-9y+3=6y-9y+15
3=-3y+15
3-15=-3y+15-15
-12=-3y
-12/-3=-3y/-3
y=4
A ____________ is a graph that uses adjacent rectangles to display frequencies, or relative frequencies, of quantitative data values. box-and-whisker plot histogram convenience sample mean absolute deviation
Answers
Explanation:
In simple terms histogram is a graph that consists of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval. It represents the distribution of the numerical data. Hence the correct answer is histogram as it conforms to the explanation about graph given in the question.
hey can you please help me posted picture of question
Answers
f (c) = (9/5) c + 32
Substituting the value of c = 20 we have:
f (20) = (9/5) (20) + 32
Rewriting we have:
f (20) = (9) (4) + 32
f (20) = 36 + 32
f (20) = 68
Answer:
The conversion for this case is given by:
f (20) = 68
option A
Solve for y in terms of x.
2/3y - 4 = x
Please help . Time is critical for me in school rn
Answers
Answer:
[tex]y=\frac{3}{2}(x+4)[/tex]
Step-by-step explanation:
We are given
[tex]\frac{2}{3}y-4=x[/tex]
Since, we have to solve for y
so, we will isolate y on anyone side
Firstly, we add both sides by 4
[tex]\frac{2}{3}y-4+4=x+4[/tex]
[tex]\frac{2}{3}y=x+4[/tex]
Multiply both sides by 3
[tex]3\times \frac{2}{3}y=3\times(x+4)[/tex]
[tex]2y=3\times(x+4)[/tex]
now, we can divide both sides by 2
and we get
[tex]y=\frac{3}{2}(x+4)[/tex]
Find the pair of numbers whose sum is 46 and whose product is a maximum.
Answers
1. Let's call:
x the first number and and the other number 46-x
2. Then, the product of both numbers is:
y=x(46-x)
3. When you apply the distributive property, you obtain:
y=46x-x^2
4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.
5. Then, you have:
h=-b/2a
h=-46/2(-1)
h=23 (x coordinate)
6.Then:
y=46x-x^2
y=46(23)-(23)^2
y=529
Therefore the answer is: 23 and 529.
What is the quotient? x-1/7x2-3x-9
Answers
The quotient of the expression (x - 1)/(7x² - 3x - 9) cannot be determined
How to determine the quotient of the expression
From the question, we have the following parameters that can be used in our computation:
(x - 1)/(7x² - 3x - 9)
From the above, we have
degree of the numerator = 1
degree of the denominator = 2
The degree of the numerator is less than the degree of the denominator
This implies that the quotient of the expression cannot be determined
The diameter of a small gear is 16cm. This is 2.5 cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger g!ear
Answers
16 cm = 2.5 cm + (1/4)*(large gear diameter)
We can subtract 2.5 cm and multiply by 4 to find the large gear diameter.
13.5 cm = (1/4)*(large gear diameter)
54 cm = (large gear diameter)
The diameter of the larger gear is 54 cm.
hey can you please help me posted picture of question
Answers
There are 5 ways to select the pant, 7 ways to select a shirt and 3 ways to select the shoes.
Total number of combinations will be the product of all these ways the dress items can be selected.
So, number of combination of outfits = 5 x 7 x 3 = 105
Therefore, option B gives the correct answer
Apply the commutative property to 13 × 7 × 21 to rearrange the terms and still get the same solution
Answers
13 × 21 × 7
7 × 13 × 21
7 × 21 × 13
21 × 7 × 13
21 × 13 × 7
Any of these arrangements will give the same answer, 1,911.
The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.
Explanation:The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.
Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.
https://brainly.com/question/5637942
#SPJ11
can someone help me!!!
Answers
s=√A
s=√2940
s1= 54.22
s 2= √62
s2= 7.9
e is correct
2) Use spherical coordinates to find the integral of f(x,y,z) = z over x^2 + y^2 + z^2 < 4 and x,y,z < 0
Answers
[tex]\begin{cases}x=r\cos u\\y=r\sin u\\z=v\end{cases}[/tex]
and [tex]\mathcal D[/tex] is obtained by varying the parameters over [tex]0\le r\le3[/tex], [tex]0\le u\le2\pi[/tex], and [tex]0\le v\le6[/tex]. The volume element is
[tex]\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm du\,\mathrm dv[/tex]
so the integral becomes
[tex]\displaystyle\iiint_{\mathcal D}xz\,\mathrm dV=\int_{v=0}^{v=6}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=3}r^2v\cos u\,\mathrm dr\,\mathrm du\,\mathrm dv=0[/tex]
2. Now let [tex]\mathcal D[/tex] denote the region bounded by the sphere [tex]x^2+y^2+z^2=4[/tex] and the coordinate planes in the octant in which each coordinate of the point [tex](x,y,z)[/tex] is negative.
Converting to spherical coordinates, we set
[tex]\begin{cases}x=\rho\cos u\sin v\\y=\rho\sin u\sin v\\z=\rho\cos v\end{cases}[/tex]
where we obtain [tex]\mathcal D[/tex] by varying over [tex]0\le\rho\le2[/tex], [tex]\pi\le u\le\dfrac{3\pi}2[/tex], and [tex]\dfrac\pi2\le v\le\pi[/tex]. The volume element is now
[tex]\mathrm dV=\rho^2\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv[/tex]
so the integral becomes
[tex]\displaystyle\iiint_{\mathcal D}z\,\mathrm dV=\int_{v=\pi/2}^{v=\pi}\int_{u=\pi}^{u=3\pi/2}\int_{\rho=0}^{\rho=2}\rho^3\cos v\sin v\,\mathrm d\rho\,\mathrm du\,\mathrm dv=-\pi[/tex]
A ball is thrown upward and outward from a height of 77 feet. the height of the ball, f(x), in feet, can be modeled by f left parenthesis x right parenthesis equals negative 0.2 x squared plus 1.4 x plus 7f(x)=−0.2x2+1.4x+7 where x is the ball's horizontal distance, in feet, from where it was thrown. use this model to solve parts (a) through (c).
Answers
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
A woman is looking for a bigger square office. She finds an office twice the area of her current office. if the perimeter of her current office is 88feet, how many square feet is the new office?
Answers
The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.
The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.
Calculate the side length of the current office from the given perimeter. The formula for the perimeter of a square is 4 × side length. Given that the perimeter is 88 feet, we divide by 4 to find that the side length of the current office is 22 feet. (88 ÷ 4 = 22)To find the area of the current office we square the side length (side length × side length). Thus, the area is 22 feet × 22 feet = 484 square feet.The new office has twice the area of the current one, so its area is 2 × 484 square feet = 968 ft².The area of the new, larger office is 968 ft².
what does life expectancy measure
Answers
Hope this helps! :)
given the function, f(x)=(x^3)-(3x^2)+(64x)-192 find the zeros
Answers
NOTE: GCF = Greatest Common Factor
The function: [tex]f(x) = x^3 - 3x^2 + 64x - 192[/tex]
Lets group [tex]x^3 - 3x^2[/tex] and [tex]64x - 192[/tex]
Factor [tex]x^3 - 3x^2[/tex]
Find GCF
GCF = [tex]x^2[/tex]
Divide out the GCF [tex]x^2[/tex]
[tex]\frac{x^3 - 3x^2}{x^2} = (x - 3)[/tex]
Factor From:
[tex]x^2(x - 3)[/tex]
Now factor 64x -192
GCF of 64 and 192 = 64
Factor out 64 from 64x - 192
[tex]\frac{64x - 192}{64} = (x - 3)[/tex]
Factor Form:
[tex]64(x - 3)[/tex]
Now that we have factored the groups, bring them together.
[tex] x^2(x-3)[/tex]
[tex] 64(x-3)[/tex]
[tex]x^2(x-3) + 64(x-3)[/tex]
Since (x-3) is the GCF of [tex]x^2(x-3) + 64(x-3)[/tex], factor (x-3) out.
[tex]\frac{x^2(x-3) + 64(x-3)}{(x-3)} = x^2 + 64[/tex]
Factor Form:
[tex](x-3)(x^2 + 64)[/tex]
Now set [tex](x^2 + 64)(x-3)[/tex] to zero and solve for x.
[tex](x^2 + 64) = 0[/tex]
[tex]x^2 = - 64[/tex]
Take the square root of both sides of the equal sign:
[tex]\sqrt{x^2} = \sqrt{-64}[/tex]
[tex]x = \sqrt{-64}[/tex]
[tex]x = \pm 8i[/tex]
Now for (x-3)
x - 3 = 0
x - 3 + 3 = 3
x = 3
The zeros and answers:
[tex]x = -8i[/tex]
[tex]x = 8i[/tex]
x = 3
HELP ME PLEASE WILL PICK BRAINLYEST
Answers
AB ≅ AC . . . . . . . . . . given
∠BAY ≅ ∠CAY . . . . given
AY ≅ AY . . . . . . . . . . reflexive property
ΔBAY ≅ ΔCAY . . . .. SAS congruence
XY ≅ XY . . . . . . . . . . reflexive property
∠AYB ≅ ∠AYC . . . . CPCTC
BY ≅ CY . . . . . . . . . . CPCTC
ΔXYB ≅ ΔXYC . . . .. SAS congruence
Therefore ...
∠XCY ≅ ∠XBY . . . . CPCTC
Use the drop-down menus to identify the method used to collect data for each scenario. Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years. Mia asked 20 random students at her school how many hours they spend on the computer each day. Beatriz recorded the number of customers entering a store for each hour interval.
Answers
Answer:
Step-by-step explanation:
Given:
1) Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years.
Published data - Already recorded data used
2) Mia asked 20 random students at her school how many hours they spend on the computer each day.
Survey by Random sampling -- since a small size of whole population selected at random
3) Beatriz recorded the number of customers entering a store for each hour interval.
This is observational data because data was collected after really observing and recording the number of customers entering a store for each hour interval.
what is the point slope form of a line with a slope 4/5 that contains the point (-2,1)
Answers
[tex]We\ have:\\\\m=\dfrac{4}{5}\\\\(-2;\ 1)\to x_1=-2\ and\ y_1=1[/tex]
[tex]Substitute:\\\\y-1=\dfrac{4}{5}(x-(-2))\\\\\boxed{B.\ y-1=\dfrac{4}{5}(x+2)}[/tex]
On the 4th of July, the probability of a person having a car accident is 0.08. What is the probability of a person driving while intoxicated or having a car accident if the probability of a person driving while intoxicated is 0.25 and the probability of a person having a car accident while intoxicated is 0.13?
Answers
0.25 + 0.08 - 0.13 = 0.20
Factor completely 121x2 − 16.
Answers
(11x+4)(11x-4)
Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let P(t), left parenthesis, t, right parenthesis denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula
Answers
The function's formula that represents the number of pages Naoya has left to read at time t would be P(t) = 570 - 55t.
Explanation:From the information given we know that Naoya reads at a rate of 55 pages per hour. After 4 hours of reading, he still has 350 pages left to read. This means that before he started reading, he had (55 pages/hour * 4 hours + 350 pages) = 570 pages in total. Since he reads at constant rate, the function that describes the remaining pages to read would be P(t) = 570 - 55t, where t represents the time in hours and P(t) is the number of pages left to read.
Learn more about Writing functions for practical situations here:https://brainly.com/question/33554757
#SPJ2
The trash can is in the shape of a cylinder that has a radius of 2 ft and a height of 5 feet what is the volume of the trash can round to the nearest tenth
Answers
(2)^2 * 5 * 3.14 = V
4 * 5 * 3.14 = V
20 * 3.14 = V
V = 62.8
Volume is a three-dimensional scalar quantity. The volume of the trash can is 62.8318 ft³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the trash can = π×r²h = π×(2ft)²×(5ft) = 62.8318 ft³
Hence, the volume of the trash can is 62.8318 ft³.
Learn more about Volume:
https://brainly.com/question/13338592
#SPJ2