The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answers
Answer:
D
Step-by-step explanation:
We have the quadratic function:
[tex]f(x)=-x^2-4x+5[/tex]
First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.
So, we can eliminate choices A and B.
Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).
Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.
So, the range of the function is all real numbers less than or equal to 9.
Our answer is D.
It is not C because the maximum value is dependent on y and not x.
Related Questions
Consider functions f, g, and h.
F(x) = 3x^3 + 9x^2 al- 12x g(x) = x - 1 h(x) = 3x2 + 12x
Which expression defines function h?
Answers
The relation between the functions f(x), g(x), and h(x) will be f(x)/g(x) is equal to h(x). Then the correct option is B.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The functions are given below.
f(x) = 3x³ + 9x² - 12x
g(x) = x - 1
h(x) = 3x² + 12x
The function f(x) can be written as
f(x) = 3x(x² + 3x - 4)
f(x) = 3x(x² + 4x - x - 4)
f(x) = 3x(x + 4)(x - 1)
f(x) = (x - 1)(3x² + 12)
Then divide the function f(x) by the function g(x), then we have
f(x) / g(x) = (x - 1)(3x² + 12) / (x - 1)
f(x) / g(x) = (3x² + 12)
f(x) / g(x) = h(x)
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
Answer:
B
Step-by-step explanation:
edmentum
Evaluate 7!
Answers shown are:
A-120
B-40,320
C-5,040
Answers
Answer:
C) 5040
Step-by-step explanation:
[tex]7!=7*6*5*4*3*2*1=5040[/tex]
Answer:
5040
Step-by-step explanation:
! means take multiply that number and all the number down to 1
7! = 7*6*5*4*3*2*1
=5040
Jared has 20 flowers. He wants to plant all of the flowers in equal rows in his garden. What are the different ways Jared can arrange the flowers in equal rows? Solve this problem any way you choose.
Answers
Answer:
5 rows of 4 each
4 rows of 5 each
2 rows of 10 each
10 rows of 2 each
1 row of 20
20 rows of 1
Step-by-step explanation:
rational numbers.
Example 6: Write any 3 rational numbers between –2 and 0.
-20
0
ondas
-
Answers
Answer:
my firnd coli
Step-by-step explanation:
In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.
international system of 89643092 in words
Answers
Answer:
Eighty nine million six hundred forty three thousand ninety two
Step-by-step explanation:
89,643,092
=> Eighty nine million six hundred forty three thousand ninety two
Given that yx is a diameter of V, find mZVX if mYVZ=(15r -1)", mWVX =(8x- 2).mUVW =(7x +15).
and mYVU = 3x + 5).
A 32
B 45°
C 70
D. 134
Answers
Answer: the answer is (C)
Tích các nghiệm của phương trình Log(x-1)²=2 là
Answers
Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
Someone please help T.T I need help ASAP
Answers
Step-by-step explanation:
Given that,
The quadratic equation that models the ball's height above the ground h, t seconds after it was thrown is given by :
[tex]h=-16t^2+108t+28[/tex] ...(1)
(a) For maximum height, put dh/dt = 0
So,
[tex]\dfrac{d(h)}{dt}=\dfrac{d}{dt}(-16t^2+108t+28)=0\\\\-32t+108=0\\\\t=\dfrac{108}{32}=3.37\ s[/tex]
Put the value of t in equation (1).
So,
[tex]h=-16(3.37)^2+108(3.37)+28\\\\h=210.24\ ft[/tex]
(b) When the ball reaches the ground,
h = 0
So,
[tex]-16t^2+108t+28=0\\\\t=7\ s[/tex]
So, the ball hits the ground in 7 seconds.
Find the solution of the differential equation that satisfies the given initial condition.
dy/dx = x/y, y(0) = −3
Answers
Answer:
y=-sqrt(x^2+9)
Step-by-step explanation:
This problem can be solved with the help of separating the variables.
dy/dx=x/y
Multiply both sides by y
y dy/dx=x
Multiply both sides by dx
y dy=x dx
Integrate
y^2/2=x^2/2+c
Let's find c using the condition y(0)=-3.
(-3)^2/2=(0)^2/2+c
9/2=0+c
9/2=c.
The equation is y^2/2=x^2/2+9/2.
Let's make this a bit prettier multiplying both sides by 2:
y^2=x^2+9
Taking square root of both sides gives:
y=+/- sqrt(x^2+9)
Since we want y(0)=-3, then we will choose
y=-sqrt(x^2+9).
Correct answer plz. 15 points. Reported for wrong answer. Thx
Answers
Third option is the right answer:
−2x + 4y ≥ 0
Which is the simplified form of m-8pº?
Answers
Answer:
m-8
Step-by-step explanation:
p⁰ = 1
If l=10 b=5 and h=2, find the values of 2(lb+bh+lh)
Answers
Answer:
160
Step-by-step explanation:
[tex]2((10)(5)+(5)(2)+(10)(2))\\2(50+10+20)\\2(80)\\160[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{2(lb + bh + lh)}\\\\\large\textsf{= 2(10(5) + 5(2) + 10(2))}\\\\\large\textsf{10(5) = \boxed{\bf 50}}\\\\\large\textsf{= 2(50 + 5(2) + 10(2))}\\\\\large\textsf{5(2) = \boxed{\bf 10}}\\\\\large\textsf{= 2(50 + 10 + 10(2))}\\\\\large\textsf{50 + 10 = \boxed{\bf 60}}\\\\\large\textsf{= 2(60 + 10(2))}\\\\\large\textsf{10(2) = \boxed{\bf 20}}\\\\\large\textsf{= 2(60 + 20)}\\\\\large\textsf{60 + 20 = \boxed{\bf 80}}\\\\\large\textsf{= 2(80)}\\\\\large\textsf{= \boxed{\bf 160}}\large\checkmark[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \bf 160}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Convert: (a) 250 liters to kiloliters, (b) 4.5 liters to milliliters.
Answers
Answer:
a) 0.25 kl
b) 4500 ml
Step-by-step explanation:
a)
1 kiloliter = 1000 liters
x kiloliters = 250 liters
[tex]x = \frac{250}{1000} = 0.25 \ kiloliters[/tex]
b)
1 liter = 1000 milliliters
4.5 liters = x
[tex]x = 4.5 \times 1000 = 4500 \ milliliters[/tex]
-5x=25 how to solve this problem
Answers
The goal of this problem is to solve for x.
To solve x in this problem you need to find a way to get it by itself on the left side, the way to do this is divide -5x by -5.
You then also have to do the same for the right side. This gives you -5.
What’s the word for this definition? “The change in the Y values divided by the change in X values”
Answers
Answer:
slopes is the ratio of the change in the y value over the change in the x value
Which angles are complementary? I'm not sure if its B.
Answers
Answer:
You are right, it's B
Step-by-step explanation:
Complementary angles are angles that add up to 90 degrees.
Answer:
The answer is B. the measure of angle GPF and the measure of angle GPH.
Step-by-step explanation:
Two angles are called complementary when their measures add to 90 degrees.
Since the measure of angle FPD has a known angle measure of 90 degrees, the measure of angle FPH is also 90 degrees.
Thus, causing the measure of angle GPF and the measure of angle GPH to add up to 90 degrees, which makes the two angles complementary.
PLEASEEEEE HELPPPPPPPP
Answers
Answer:
f(-5) = -195
Step-by-step explanation:
Given that,
[tex]f(x)=x^3-2x^2+3x-5[/tex] ....(1)
and
[tex]g(x)=x^2+x-1[/tex]
We need to find the value of f(-5).
Put x = -5 in equation (1).
[tex]f(-5)=(-5)^3-2(-5)^2+3(-5)-5\\\\=-195[/tex]
So, the value of f(-5) is equal to (-195).
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8% What percentage of students receive between a 70% and 94% enter the value of the percentage without the percent sign
Answers
Answer:
49.87
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose the mean percentage in Algebra 2B is 70% and the standard deviation is 8%.
This means that [tex]\mu = 70, \sigma = 8[/tex]
What percentage of students receive between a 70% and 94%
The proportion is the p-value of Z when X = 94 subtracted by the p-value of Z when X = 70. So
X = 94
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{94 - 70}{8}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a p-value of 0.9987.
X = 70
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 70}{8}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
0.9987 - 0.5 = 0.4987.
0.4987*100% = 49.87%.
So the percentage is 49.87%, and the answer, without the percent sign, is 49.87.
HELP!! I don’t know part c or d and I need to know if part a and b are correct thanksss
Answers
Answer:
d=67257
c=93
Step-by-step explanation:
Polygon ABCDE is reflected to produce polygon A’ B’ C’ D’ E’. What is the equation for the line of reflection?
Options:
A. y=0
B. x=0
C. x=2
D. y=1
Answers
Answer:
B. x=0
Step-by-step explanation:
The Polygon ABCDE is reflected by
y-axis => x=0 , to produce polygon A’ B’ C’ D’ E’
Answer:
B. x = 0
Step-by-step explanation:
Plato
A communications company has developed three new designs for a cell phone. To evaluate consumer response, a sample of n = 120 college students is selected and each student is given all three phones to use for one week. At the end of the week, the students must identify which of the three designs they prefer. The distribution of preference is as follows:
Design 1 Design 2 Design 3
54 38 28
Required:
Do the results indicate any significant preferences among the three designs?
Answers
Answer:
There is significant preference among the 3 designs
Step-by-step explanation:
Given :
Design 1 Design 2 Design 3
54 38 28
H0 : no significant preference among the 3 designs
H1 : The preference among the designs are different
To test, we use the Chisquare test for independence ;
χ² = (observed - Expected)² / Expected
The sample size, n = 120
Expected = 120 / number of designs = 120 / 3 = 40
(54-40)^2/ 40 + (38 - 40)² / 40 + (28 - 40)² / 40
= 4.9 + 0.1 + 3.6
= 8.6
The Chisquare critical value at 95% = 5.99
Since ;
|χ² critical| < χ² statistic ; we reject the null and conclude that there is significant preference among the 3 designs
Which of the following lists of ordered pairs is a function?

A.
(1, 2), (1, –2), (3, 2), (3, 4)

B.
(0, 2), (2, 3), (0, –2), (4, 1)

C.
(1, 6), (2, 7), (4, 9), (0, 5)

D.
(2, 4), (0, 2), (2, –4), (5, 3)
Answers
The answer is C
Step-by-step explanation:
Not sure I can't really give an explanation but its C
your teacher plotted a set of cordinetes that contained a negative x and positive y Wich point graphed below could represent the point plotted
Answers
Answer:a
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
This set of coordinates does represent a point [tex]P(x,y)[/tex].
Considering a Euclidian plane, such that [tex]P(x,y) \in\mathbb{R}^2[/tex], we have [tex]x\in(-\infty, 0)[/tex] and [tex]y\in[0, \infty)[/tex] . Therefore, the point is in Quadrant II. You possibly forgot to give the points, but point like [tex](-1, 2), (-20, 5), (-1.234, 78)[/tex] could be the answer. In fact, you can just define the point as
[tex]P(x,y) \in\mathbb{R}^2 : x\in(-\infty, 0) \text{ and } y\in[0, \infty)[/tex]
The math score for ten of Mrs. Moore's students are shown below. How many students made a score of more than 69 but less than 90?
Answers
Answer:
8
Step-by-step explanation:
first, 70-79 have 3 students
then 80-89 have 5 students
Help me complete this
Answers
Answer:
x = 9.9 in.
Step-by-step explanation:
area of triangle = base * height /2
49 = x*x /2
49*2 = x^2
98 = x^2
[tex]\sqrt{98}[/tex] = x
[tex]7\sqrt{2}[/tex] = x
9.9 = x
What are some easy ways to find the value of
(2017^4−2016^4)/(2017^2+2016^2) without calculator
Answers
Answer:
Step-by-step explanation:
[tex]\frac{2017^4 - 2016^4}{2017^2 + 2016^2}[/tex]
[tex]= \frac{(2017^2 - 2016^2)(2017^2 + 2016^2)}{2017^2 + 2016^2}[/tex]
[tex]= (2017^2 - 2016^2)[/tex]
[tex]= (2017 - 2016)(2017 + 2016)\\= 4033[/tex]
prove that
SinA÷tanA=cosA
Answers
Step-by-step explanation:
sinA/tanA
=>sinA ÷ sinA/cosA
=>sinA x cosA/sinA
=>cosA
Step-by-step explanation:
Hey there!
LHS
[tex] = \frac{ \sin(a) }{ \tan(a) } [/tex]
[tex] = \sin(a) \times \frac{ \cos(a) }{ \sin(a) } [/tex]
= cos A
Proved!!
Hope it helps!
Find the Diameter of the circle, whose radius is 17 cm.
Answers
Answer:
34 cm
Step-by-step explanation:
The radius is half of the diameter, so 17 cm is half of 34 cm.
Diameter = 34 cm
if f is the function defined by f(x) = 3x-1, find the solution set for F(x)=2
Answers
Answer:
x = 1
Step-by-step explanation:
3x - 1 = 2
Add1 to both sides
3x = 3
Divide both sides by 3
x = 1
mong moi nguoi giup do