The function g(x) is a linear function, and the rate of change over the interval -2 ≤ x ≤ 4 is 6
How to determine the rate of change?The function f is given as:
f(x) =6x - 4
When translated down by 6 units, the rule of translation is:
g(x) = f(x) - 4
So, we have:
g(x) = 6x - 4 - 4
Evaluate
g(x) = 6x - 8
The rate of change over -2 ≤ x ≤ 4 is then calculated using:
g'(x) = [g(b) - g(a)]/[b - a]
So, we have:
g'(x) = [g(4) - g(-2)]/[4 + 2]
Evaluate
g'(x) = [g(4) - g(-2)]/[6]
Calculate g(4) and g(-2)
g(4) = 6 * 4 - 8 = 16
g(-2) = 6 * -2 - 8 = -20
So, we have:
g'(x) = (16 + 20)/6
Evaluate
g'(x) = 6
Hence, the rate of change over the interval -2 ≤ x ≤ 4 is 6
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Write the expression in repeated multiplication form. Then write the expression as a power.
(6^4)^2
The expression in repeated multiplication form is
The expression as a power is
Answer:
Step-by-step explanation:
a. (6)^(4*2) or (6^4)(6^4)(6^4)(6^4)
b. 6^8
pls help odd numbers only
Answer:
The question asks, "find the slope".
9) -4/15
10) -1/14
11) -3/4
12) -1/4
13) 11/17
14) -18/13
15) 0
16) -30
17) -5
19) -1/5
21) 1/4
23) -1
25) -2/3
Its a math problem Please help me !!! For the data sets below, which of the following statements is FALSE?
Answer:
fist bubble i am pretty sure
Step-by-step explanation:
A cube has a volume of 1000 cubic feet. what is the length of an edge of the cube? show how you found the answer. please help
volume = (side length)³
Alternatively we could say that;
Side length = ∛volume
(we have just found the cube root of both sides here, remember we can do what we like to an equation, as long as we do the same to both sides!)
Because we cubed side length to get volume, side length must be the cubic root of the volume, the ∛.
We know that the volume is 1000 cubic feet, so;
Side length = ∛1000
∛1000 = 10
So the length of an edge of the cube is 10 feet.
Can someone please help me
Answer:
1. a=3
2. a=3
3. a=9
Step-by-step explanation:
1. 9/a+9-4=12-56/8+3
We move all terms to the left:
9/a+9-4-(12-56/8+3)=0
Domain of the equation: a=0
a∈R
We add all the numbers together, and all the variables
9/a+9-4-8=0
We add all the numbers together, and all the variables
9/a-3=0
We multiply all the terms by the denominator
-3*a+9=0
We add all the numbers together, and all the variables
-3a+9=0
We move all terms containing a to the left, all other terms to the right
-3a=-9
a=-9/-3
a=+3
Using the equation, y=5x²−17x −12, determine whether the parabola opens upward or downward.
Answer:
opens upwards
Step-by-step explanation:
given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 )
• if a > 0 then parabola opens upwards
• if a < 0 then parabola opens downwards
given
y = 5x² - 17x - 12
with a = 5 > 0
then parabola opens upward
Select all the correct answers.
If the measure of angle is 0 is 7pi/4, which statements are true?
The measure of the reference angle is 45°.
The measure of the reference angle is 30°.
tan(0) = -1
The measure of the reference angle is 60°.
cos(0) = -√2/2
sin(0) = -√2/2
The statement(s) that are true is that the measure of the reference angle is 45°.
What is the conversion of radians to degrees?The conversion of an angle in radian to a degree can be determined by the multiplication of the given angle in radian by 180/π.
From the given information:
[tex]\mathbf{\theta = \dfrac{7 \pi}{4}}[/tex]
To degrees, we have:
[tex]\mathbf{\theta = \dfrac{7 \pi}{4} \times \dfrac{180}{\pi}}[/tex]
[tex]\mathbf{\theta =315^0}[/tex]
A reference angle is an angle that measures the remaining distance (called the terminal distance) to the x-axis.
315° is in the 4th quadrant, i.e.
= 360° - 315°
= 45°
Therefore, the statement(s) that is true is:
The measure of the reference angle is 45°.Learn more about the conversion of radians to degrees here:
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Answer:
sin(0)=-√2/2
tan(0) = -1
The measure of the reference angle is 45°
Step-by-step explanation:
I took the test
a right cylinder has a height of 22 1/4ft and a diameter 2 2/5 times it’s height. what is the volume of the cylinder
Answer:
Step-by-step explanation:
Answer:
Check Below
Step-by-step explanation:
given things : 1. height of cone = 22* 1/4 feet or 89/4 feet
2. diameter of cylinder = 2* 2/5 times of height
= 12/5 times of height or 12/5 * 89/4
= 89*3/5 feet
now formula of volume of cone = Pi R² * H
= (3.14) ( D/2)² * H
= (3.14)* (89*3/10)² * 89/4
= (3.14) * (26.7)² * 22.25
= (3.14) * 712.89 * 22.25
= (49806.06)
Hope u find this answer Helpful !
Help?????????????????
Answer:
please make the image less blurry
Step-by-step explanation:
Which graph represents the function 3x – 2y = 6?
Answer:
graph 19 because since it is that means also like the thingy equals that number si then like when the thing is at the highest point it cab maybe actually it will equal that number
8.
A circular plate has a diameter of 11 inches. An ant walking along the edge makes 1.5 revolutions in 4
minutes. Approximately how many inches does the ant travel in one minute? Round your answer to the
nearest tenth of an inch.
Answer:
[tex]12.95 \: inches[/tex]
Step-by-step explanation:
We were told that the diameter of the circular plate is 11 inches. In order to find the distance the ants travel to make one revolution we have to first find the circumference of the circular plate. Circumference is:
[tex]2\pi \: r[/tex]
The radius would be half of the diameter (11). Therefore the radius is 5.5.
[tex]r = 5.5 \: \: \: \: \: \pi = 3.14 \\ cir = 2(3.14) \: (5.5) \\ cir = 6.28 \times 5.5 \\ cir = 34.54[/tex]
Since we found the circumference of the circular plate that means that we know how much one revolution made by the ants would be (34.54). Since the ant made 1.5 revolutions we have to multiply 34.54 by 1.5.
[tex]34.54 \times 1.5 = 51.81[/tex]
So we now know that the ant walked 51.81 inches in 4 minutes, now we have to find the distance he would walk in 1 minute.
Let x be the unknown value*
[tex] 51.81 \:inches = 4 \:minutes \\ x \:inches = 1 \: minutes\\ \\ 51.81=4x \\ \\\frac{51.81}{4} = x \\ \\ 12.95 = x[/tex]
use Demoiure's Theorem to find (-2-2√3i)³
Let z = -2 - 2√3 i.
Find the modulus of z :
|z| = √((-2)² + (-2√3)²) = √16 = 4
Find the argument of z (note that z lies in the third quadrant):
arg(z) = arctan(2√3/2) - π = arctan(√3) - π = -2π/3
Then in polar form, we have
[tex]z = -2 - 2\sqrt 3\, i = 4 \exp\left(-i\dfrac{2\pi}3\right)[/tex]
By DeMoivre's theorem, the cube of z is
[tex]z^3 = \left(4 \exp\left(-i\dfrac{2\pi}3\right)\right)^3 = 4^3 \exp(-i 2\pi) = \boxed{64}[/tex]
PLEASE HELP ILL MARK BRAINEST!!!!
Answer:
1, 6, 11, and 16 in that order
Step-by-step explanation:
every time the x value increases by 1, the f(x) value increased by 5
if u want to u can answer question 16 and 17 but if u don’t just answer 16
Answer:
the answer to 16 is C i know cause i had the same thing and the answer for 17 is A.
Step-by-step explanation:
Hope thi helps
What is the value of x in the equation 2/3(1/2x+12)=1/2(1/3x+14)-3
A.-24
B.-6
C.-2/3
D.0
The radius of circle a is 5 cm. the radius if circle b is 5 cm greater than the radius of circle a. the radius of circle c is 3 cm greater than the radius of circle b. the radius of circle d is 1 cm less than the radius of circle c. what is the area of each circle? how many times greater than the area of circle a is the area of circle d? the area of circle a is ___ cm2.
Answer:
Theres a lot going on in this question but i tried my best to answer it all, correctly. Sorry if something is wrong or i misread the question. check explanation for answer.
Step-by-step explanation:
I'm not sure to use pi or 3.14 so i just did both.
Circle A's radius = 5cm
Circle B's radius = 10cm
Circle C's radius = 13cm
Circle D's = 12cm
(circle A)
π = 3.14
A = πr²
A = 3.14(5²)
A = 3.14(25)
A = 78.5cm²
π = π
A = πr²
A = π(5²)
A = π(25)
A = 78.54cm²
(circle B)
π = 3.14
A = πr²
A = 3.14(10²)
A = 3.14(100)
A = 314cm²
π = π
A = πr²
A = π(10²)
A = π(100)
A = 314.16cm²
(circle C)
π = 3.14
A = πr²
A = 3.14(13²)
A = 3.14(169)
A = 530.7cm²
π = π
A = π(13²)
A = π(169)
A = 530.9cm²
(circle D)
π = 3.14
A = πr²
A = 3.14(12²)
A = 3.14(144)
A = 452.2cm²
π = π
A = πr²
A = π(12²)
A = π(144)
A = 452.4cm²
452.2 / 78.5 =5.8
circle d is 5( almost 6) times greater than circle A
Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)
a. 5x + 9y = -45
c. -9x + 5y = 45
b. 9x + 5y = -45
d. 5x - 9y = 45
Answer:
Step-by-step explanation:
Determine the standard form of the equation of the line that passes through (-5,0) and (0,-9)
a. 5x + 9y = -45
c. -9x + 5y = 45
b. 9x + 5y = -45
d. 5x - 9y = 45
Identify the image of ∆XYZ for a composition of a 10 degree rotation and 80 degree rotation, both about point X.
The equation of the trend line is y = -0.36x + 12.6 use the equation to of the trend line to predict the wind chill for a wind speed of 23 mi/h round your answer to the nearest degree. The wind chill at 23 mi/h
Answer:
4°C
Explanation:
Equation: y = -0.36x + 12.6
To find wind chill at 23 mi/hInsert x = 23Simplify
y = -0.36(23)+12.6
y = 4.32°C
y = 4°C (rounded to nearest degree)
If alpha and beta are zeroes of polynomial fx = 4x2-5x-1. Pls answer full questiob
Line segment EF begins at (-1,5) and ends at (-1, -3). The segment is translated to the right 4 units and down
2 units to form line segment E'F.
Enter the length, in units, of line segment E'F.
The coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
Line segment EF begins at (-1, 5) and ends at (-1, -3). The segment is translated right 4 units and down 2 units to form line segment E'F'. Then the coordinate of E' and F' will be:
E' = (-1 + 4, 5 – 2) = (3, 3)
F' = (-1 + 4, -3 - 2) = (3, -5)
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The length of the E'F' = √(0 + 64) = 8 units
Thus, the coordinates for the line segment E'F' are (3, 3) and (3, -5) and the length of the segment E'F' is 8 units.
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please only answer question b
Answer:
P = 12 + 2π cm
Step-by-step explanation:
arc length is calculated as
arc = circumference × fraction of circle
the angle subtended at the centre of the sector = 360° - 300° = 60° , then
arc = 2πr × [tex]\frac{60}{360}[/tex]
= 2π × 6 × [tex]\frac{1}{6}[/tex]
= 2π
the perimeter (P) = 6 + 6 + 2π = 12 + 2π
A piece of ribbon is 63 inches long. it is cut into pieces that are each 7 inches long. how many pieces of ribbon are there?
Aldo is a software salesperson. His base salary is $2500 and he makes $80 more for every copy of English is Fun he sells. His total pay, p (in dollars), after selling c copies is given by the following.
p=80c+2500
Answer the following questions.
(a)
If Aldo's total pay is $5140, how many copies did he sell?
? copies
(b)
What is Aldo's total pay if he sells 23 copies?
$
Answer:
A: He sold 33 copies
B: $4340
Step-by-step explanation:
A: p=80(33) + 2500
p=2640+ 2500
p=5140
B: p = 80(23) + 2500
p=1840+ 2500
p=4340
given b( 5, -7), under which reflection is B' (-5, -7)?
Answer:
reflection in the y- axis
Step-by-step explanation:
under a reflection in the y- axis
a point (x, y ) → (- x, y )
B (5, - 7 ) → B' (- 5, - 7 ) ← is a reflection in the y- axis
Which of the following has the same value as the expression?
(-3+5)+2
Answer:
Answer(s):
1x4
2+2
2x2
Step-by-step explanation:
Hope this helps!
The potential energy of an object varies jointly with the mass of the object and the height of the object off the ground. a 40-kg object is 2 meters off the ground. the potential energy of the object is 784 joules. a 10-kg object is 3 meters off the ground. what is the potential energy of the 10-kg object? 33 joules 131 joules 294 joules 1,176 joules
The potential energy of the 10-kg object is 294 joules.
What is Variation?Variation is a mathematical term that shows the relationship between two or more parameters or quantities in an equation.
Analysis:
let potential energy be = P
let mass be = m
let height be = h
P ∝ mh
P = kmh
when P = 784, m = 40kg, h = 2 meters
784 = k x 40 x 2
k = 9.8
P = 9.8mh
when m = 10kg, h = 3 meters
P = 9.8 x 10 x 3 = 294 joules.
In conclusion, the potential energy of the object at 3 meter height is 294 joules.
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There are three sets. A = {1,2,3}, B = {4,5} and C = {6,7,8}
What is the probability of A∩B∩C
The three sets are independent sets and the value of the probability of A∩B∩C is: 0
How to determine the probability?The sets are given as:
A = {1,2,3}, B = {4,5} and C = {6,7,8}
The total number of elements in the three sets is:
Total = 8
The number of elements of A∩B∩C is 0, because the sets do not have a common element.
So, the probability of A∩B∩C is:
P = 0/8
Evaluate
P = 0
Hence, the probability of A∩B∩C is: 0
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Can someone help me with this
Ans57 , 58 , 59
Step-by-step explanation:
whats 2 divide by 1/6.
Answer:
1/3
Step-by-step explanation:
2 divided by 1/6
2/1 divided by 1/6
2/6 ---> Simplify: 1/3
Answer:
12
Step-by-step explanation:
the answer is 12 because 2 dived by 1/6 is 12 i used a calculator to fund the answer btw