Answer:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
Step-by-step explanation:
Function f(x)
Given the function f(x)
x f(x)
-3 -0.5
-2 0
-1 0.5
0 1
Finding the slope between any two points
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-0.5\right),\:\left(x_2,\:y_2\right)=\left(-2,\:0\right)[/tex]
[tex]m=\frac{0-\left(-0.5\right)}{-2-\left(-3\right)}[/tex]
[tex]m=0.5[/tex]
Thus,
The slope of f(x) = 0.5
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 1), we can easily observe that at x = 0, the value of y = 1.
Thus, the y-intercept of f(x) = 1
Function g(x)
Taking two points from the given graph of g(x)
(1, 0)(0, 2)Finding the slope between (1, 0) and (0, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(1,\:0\right),\:\left(x_2,\:y_2\right)=\left(0,\:2\right)[/tex]
[tex]m=\frac{2-0}{0-1}[/tex]
Refine
[tex]m=-2[/tex]
Thus,
The slope of g(x) = -2
We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.
From the given point (0, 2), we can easily observe that at x = 0, the value of y = 2.
Thus, the y-intercept of g(x) = 2
Conclusion:
FOR function f(x)
The slope of f(x) = 0.5
The y-intercept of f(x) = 1
FOR function gx)
The slope of g(x) = -2
The y-intercept of g(x) = 2
Thus:
a. Slope of f(x) is greater than g(x)
b. y-intercept of f(x) is less than the y-intercept of g
find all values of theta if theta is in the interval [0degrees,360degrees) and has the given function value
sec theta= -2
Answer:
[tex]\theta = 120, 240[/tex], in degrees
Step-by-step explanation:
The secant of an angle is given by:
[tex]\sec{\theta} = \frac{1}{\cos{\theta}}[/tex]
In this question:
[tex]\sec{\theta} = -2[/tex]
So
[tex]\frac{1}{\cos{\theta}} = -2[/tex]
[tex]-2\cos{\theta} = 1[/tex]
[tex]\cos{\theta} = -\frac{1}{2}[/tex]
In the first quadrant, the angle that has cosine of 1/2 is 60º.
The cosine is negative in the second and in the third quadrant.
The equivalent angle to 60º in the second quadrant is of 180º - 60º = 120º.
The equivalent angle to 60º in the third quadrant is of 180º + 60º = 240º
So the values of [tex]\theta[/tex] in the interval are:
[tex]\theta = 120, 240[/tex], in degrees
can someone help me please im struggling and can’t figure these 2 problems out :(
Find the remainder when f(x) = (3x + 10x² + x - 2) divided by (x + 3)
Solve the inequality: |x +5|>-1 please help i will give brainliest thank you
Step-by-step explanation:
|x + 5| > -1
Since |y| >= 0 for all real values of y and 0 is greater than -1, there are infinitely many solutions for x.
Answer:
x> -6
Step-by-step explanation:
|x+5|> -1
x+5 > -1
-5 -5
x> -6
Which of the following is equivalent to the phrase "the product of thirty and a number is six"?
n - 6 = 30
30 + n = 6
30n = 6
30 + n = 6
Answer:
"The product of thirty and a number is six".
30n=630n=6 is the right answer.
One-third x + one-sixth y = 2. When x is 3, 1 x + StartFraction 3 Over 6 EndFraction y = 6. One-half x + three-fourths y = negative 3. When x is negative 2, negative 1 x minus StartFraction 6 Over 4 EndFraction = 6. Negative 1 y = 12.
Continue solving the system of equations.
What is the solution to the system?
(
,
)
Answer:
(12, -12)
Step-by-Step:
I got it right on Edge 2021
Answer:
its 12,-
12
Step-by-step explanation:
2x+2+2x-17=180 what's x?
Answer:
x= 48.75
Step-by-step explanation:
Add like terms
2x+2x and
2-17
4x-15=180
Now subtract -15 to both sides get x by itself
4x-15+15=180+15
4x=195
Now divide by four to each side to get x by itself again
4x/4 = 195/4
x=48.75
Answer:
x=48.75
Step-by-step explanation:
2x+2+2x-17=180(Group like terms)
2x+2x+2-17=180
4x-15=180(Add 15 on both sides)
4x-15+15=180+15
4x=195(Divide both sides by 4 to find the value of x)
x=48.75
I need help with this word problem please
Answer:
Step-by-step explanation:
Given function is,
f(x) = [tex]x\sqrt{x}[/tex]
We can rewrite this function as,
f(x) = [tex]x^{\frac{3}{2}}[/tex]
a). Domain of the function is [0, ∞)
Derivative of the function in this domain,
f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]
= [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]
Since, f'(x) > 0 in the interval [0, ∞)
Function is increasing in the interval [0, ∞)
b). For local maxima and local minima,
Second derivative of the function,
f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]
= [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex] > 0
So the function should have a local minima.
But the function is continuous in the interval x ≥ 0,
There is no local minima (only absolute minima).
c). Since, second derivative is undefined at x = 0,
There are no inflection points.
d). Since, f"(x) > 0 in the interval [0, ∞)
Concavity of the curve is UPWARDS.
Kendrick walked of a mile in of an hour. How fast did he walk? _____miles per hour
Answer:
He walked at 1 mile per hour
Step-by-step explanation:
Answer:
He walked at 1 mph
Step-by-step explanation:
Y is inversely proportional to x, when Y = 7, x = 4.
True or False: the constant of proportionality, k, is 20.
Answer:
The given statement Y = 7, x = 4 is False.
Step-by-step explanation:
We are given:
Y is inversely proportional to x, when Y = 7, x = 4.
We need to tell if the statement is True or False: the constant of proportionality, k, is 20.
Y is inversely proportional to x
We can write it as: [tex]y\:\alpha \:\frac{1}{x}\\y=\frac{k}{x}[/tex]
Now, we need to check when Y=7, x = 4 is true or false
We are given k = 20
Now, I can find value of y, by putting values of k and x in the equation:
[tex]y=\frac{k}{x}\\y=\frac{20}{4}\\y=5[/tex]
When we put x = 4, and k =20, we get Y=5 and not Y=7
So, The given statement Y = 7, x = 4 is False.
Which expression is a factor of 64x^2−25?
8x−5
32x−25
32x−5
8x−25
Answer:
A
Step-by-step explanation:
Answer:
[tex](8x-5)^{2}[/tex]
Step-by-step explanation:
Rewrite 64[tex]x^{2}[/tex] as [tex](8x)^{2}[/tex]
[tex](8x)^{2}[/tex]−80x+25
Rewrite 25 as 5^2.
(8x)^2−80x+5^2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
80x=2⋅(8x)⋅5
Rewrite the polynomial. [tex](8x)^2[/tex]−2⋅(8x)⋅5+[tex]5^{2}[/tex]
Factor using the perfect square trinomial rule [tex]a^{2}[/tex] −2ab + [tex]b^{2}[/tex]= [tex](a-b)^{2}[/tex], where a=8x and b=5.
[tex](8x-5)^{2}[/tex]
6
x
−
5
y
=
14
Find
x
when
y
=
2
Answer:
4
Step-by-step explanation:
Simplify the following expression 5^-3
Answer 1/25 or decimal 0.008
Step-by-step explanation:
Answer:
0.008
Step-by-step explanation:
helo
PLEASE HELP 8 ml of a 80% acid solution was mixed with 12 ml of a 20% acid solution. What is the percentage of acid in the new solution?
Answer:
44%
Step-by-step explanation:
So you have 2 bottles. One bottle is 8ml and is 80% acid. the other is 12 ml and is 20% acid.
This means there's 6.4 ml of acid in bottle 1(8*0.8) and 2.4 ml of acid in the other one(12*0.2).
The total amount of liquid is 8+12 = 20
The total amount of acid is 6.4+2.4 = 8.8
Percentage of acid in the new solution is 8.8/20 = 0.44 = 44%
circle the staement below 1530 and 12530
Answer:
1530 < 12530
Step-by-step explanation:
i12530 is a bigger number than 1530
Answer:
what statement?
How do you write 3% as a fraction
Answer: 3/100
Step-by-step explanation:
Answer:
3/100
Step-by-step explanation:
Which of the following graphs best represents y=(x+1)(x-4)
Keiko's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee cost Keiko $4.15 per pound, and type B coffee costs $5.25 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $980.85. How many pounds of type A coffee were used?
Answer:
39 pounds of type A coffee were used.
Step-by-step explanation:
Given: Cost of type A coffee is $4.15 per pound and cost of type B coffee is $5.25 per pound. Also, blend used four times as many pounds of type B coffee as type A.
To find: How many pounds of type A coffee were used.
Let [tex]x[/tex] be the number of pounds of type A coffee and [tex]y[/tex] be the number of pounds of type B coffee.
Then, according to question,
[tex]4.15x+5.25y=980.85[/tex] and [tex]y=4x[/tex]
Substituting [tex]y=4x[/tex] in [tex]4.15x+5.25y=980.85[/tex], we get
[tex]4.15x+5.25(4x)=980.85[/tex]
⇒[tex]4.15x+21x=980.85[/tex]
⇒[tex]25.15x=980.85[/tex]
⇒[tex]x=\frac{980.85}{25.15}[/tex]
⇒[tex]x=39[/tex]
Therefore, 39 pounds of type A coffee were used.
PRE CALC HELP!!! 100 PTS AND BRAINLIEST
(the one I chose isn't correct I just accidentally pressed it)
Hello!
[tex]\large\boxed{\frac{\pi }{4} < x < \frac{5\pi }{4}}[/tex]
To begin, we can solve the inequality:
sin(x) > cos(x)
Divide both sides by cos(x):
sin(x) / cos(x) > 1
tan(x) > 1
x > π/4
However, we can also solve it the other way to produce the end to the interval:
sin(x) > cos(x)
1 > cot(x)
x < 5π/4
Therefore, sin(x) > cos(x) on the interval π/4 < x < 5π/4.
Answer:
π/4 < x < 5π/4.
six less than six times a number is 12
Answer:
x = 3
equation: 6x - 6 = 12
Step-by-step explanation:
6x - 6 = 12
aka:
6x + -6 = 12
+6. +6
6x = 18
/6. /6
x = 3
check: 6(3) - 6 = 12
18 - 6 = 12
12 = 12
Which functions are linear
Answer:
its c
Step-by-step explanation:
Hi I’m doing a test and I need help please tell me the answer |
V
Answer: It’s 8
Step-by-step explanation: I just went to desmos
help please pleasdes
Answer: Triangle A'B'C is an enlargement of triangle ABC
Step-by-step explanation: When figuring out whether a dilation of a triangle is an enlargement or reduction, you see if the scale factor is larger or smaller than 1. If the scale factor is less than 1, it's a reduction. If the scale factor is larger than 1, it's an enlargement. 4/3 > 1 so this means the triangle gets bigger and is an enlargement. This means triangle A'B'C is an enlargement of triangle ABC.
6 Cassius is purchasing flower baskets to
be placed on each table at a volunteer
appreciation lunch. Store A charges $19.25
per flower basket plus a $15.00 delivery fee.
Store B charges $17.50 per flower basket
plus a $30.00 delivery fee. Which inequality
can determine x, the maximum number of
flower baskets that can be ordered for the
total cost at Store A to be less than the total
cost from Store B?
A 19.25 + 15x > 17.5 + 30x
B 19.25 + 15x< 17.5 + 30x
C 19.25x + 15 > 17.5x + 30
D 19.25x + 15 < 17.5x + 30
Lynn me
Answer:
b
Step-by-step explanation:
i took the test
x-2y what is the coefficient of x
Answer:
the coefficient of x is an implied 1
any variable that's by itself without a coefficient has an implied 1
Step-by-step explanation:
I hope this helps :)
You bought a car that had factory installed tires marked as "P185 75/R14". You bought and installed tires on your car that are marked "P205 75/R14". What is the circumference of the P185 tire?
A) 24.93 inches
B) 27.93 inches
C) 78.31 inches
D) 81.99 inches
Ted's taxi service has cabs that can seat 4 people and vans that can seat 15 people. The taxi service can transport a maximum of 134 people in its 17 units. How many vans does Ted's Taci Service have in it's fleet?
A. 19
B. 11
C. 9
D. 6
Answer:
D. 6
Step-by-step explanation:
What is the slope-intercept equation for the following line? I need help answering
Answer:
y = -4x - 3
Step-by-step explanation:
The b in the slope-intercept equation represents the y-intercept.
The line crosses the y-axis at (0,-3). Therefore, b = -3.
Since the line is decreasing from left to right, the slope will be negative.
From (0,-3) to the next point on the line is down 4 units and to the right 1 unit.
The slope will be -4/1 or -4.
Therefore, the equation of the line will be y = -4x - 3.
Hope that helps.
What is the surface area of a unit cube?
Answer:
6 units
Step-by-step explanation:
The total area that the surface of a 3-dimensional object would cover if its sides were laid flat is called it's surface area. Surface area is measured in square units. The surface area of a unit cube is 6 square units.
Use the four-step method in problem-solving to solve the problem.
Ashley owns 14 acres of land which she rents to a Timber grower for $3131 per acre per year. Her property taxes are $882 per acre per year. How much profit does she make on the land each year?
A. $56,182
B. $42,952
C. $31,486
D. $44,716
Answer:
A. $56,182
Step-by-step explanation:
$3131 x 14= $43834
$882 x 14= $12348
$43834 + $12348= $56,182
$56,182 x 1= $56,182