The total area between the function f(x) = -6x and the x-axis over the interval [-4, 2] is -60 square units.
To find the total area between the function f(x) = -6x and the x-axis over the interval [-4, 2], we need to calculate the definite integral of the absolute value of the function over that interval.
Since the function f(x) = -6x is negative for the given interval, taking the absolute value will yield the positive area between the function and the x-axis.
The integral to find the total area is:
∫[-4, 2] |f(x)| dx
Substituting the function f(x) = -6x:
∫[-4, 2] |-6x| dx
Breaking the integral into two parts due to the change in sign at x = 0:
∫[-4, 0] (-(-6x)) dx + ∫[0, 2] (-6x) dx
Simplifying the integral:
∫[-4, 0] 6x dx + ∫[0, 2] (-6x) dx
Integrating each part:
[tex][3x^2] from -4 to 0 + [-3x^2] from 0 to 2[/tex]
Plugging in the limits:
[tex](3(0)^2 - 3(-4)^2) + (-3(2)^2 - (-3(0)^2))[/tex]
Simplifying further:
[tex](0 - 3(-4)^2) + (-3(2)^2 - 0)[/tex]
(0 - 3(16)) + (-3(4) - 0)
(0 - 48) + (-12 - 0)
-48 - 12
-60
Therefore, the total area between the function f(x) = -6x and the x-axis over the interval [-4, 2] is -60 square units. Note that the negative sign indicates that the area is below the x-axis.
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gradient of line 6x+2y+9=0
Answer:
gradient = - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c( m is the slope (gradient) and c the y- intercept )
Given
6x + 2y + 9 = 0 ( subtract 6x + 9 from both sides )
2y = - 6x - 9 ( divide the 3 terms by 2 )
y = - 3x - [tex]\frac{9}{2}[/tex] ← in slope- intercept form
with gradient m = - 3
Evaluate the expression. 6(3+5)/4
Answer:
12
Step-by-step explanation:
6(3+5)/4 add number inside parentheses
6(8)/4 multiply 6 and 8
48/4 divide
12
Hope this helped you!
Concept Check: Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable.
75°
174°
300°
-61°
-90°
Step-by-step explanation:
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How many square feet of outdoor carpet will we need
8 square feet will be needed. 3x2= 6 + 2x1= 2= 8 square feet
help plz i’ll give extra points
Answer:
A
Step-by-step explanation:
if a function f(x)=x^3 has the domain {-3,0,2,4} what is it's range
Step-by-step explanation:
Range is y-values
= {-27,0,8,64}
In ΔIJK, i = 74 inches, j = 23 inches and ∠K=20°. Find the area of ΔIJK, to the nearest square inch.
Answer:
291in^2
Step-by-step explanation:
Using the formula
Area of the triangle = 1/2absin theta
A = 1/2ijsin<K
Given
i = 74in
j = 23in
<K = 20 degrees
Area = 1/2 * 74*23sin20
Area = 37*23sin20
Area = 852sin20
Area = 291.059in^2
Hence the area of the triangle to nearest square inch is 291in^2
A small plane flying from Los Angeles to San Diego averaged 175 mph with a tailwind. On the return trip with headwind the average speed was only 125 mph. Write and solve a system to reflect this relationship. Find the speed of the headwind/ tailwind AND the speed of the plane on a calm day.
Answer: System of equations:
p + w = 175
p - w = 125
p is the plane's speed, w is the wind speed
The wind speed is 25 mph. The plane's speed on a calm day is 150 mph.
Step-by-step explanation:
Solve by elimination: Add the equations. w "cancels" solve for p:
p + w = 175
p - w = 125
2p = 300 divide both sides by 2
p = 150 the plane's speed
Substitute 150 for p and solve for w
150 + w = 175 Subtract 150 from both sides.
w = 25 the wind speed
plzzzzzzzzzzzzz help
Answer:
[tex]5*\frac{1}{2}[/tex]
Step-by-step explanation:
We have a picture and are being asked to identify the multiplication problem that represents it.
So we have 5 triangles, all of which are color-coded in red, but only half of them are filled. When multiplying, the number that is before the * sign is the amount there is, while the number that is after the * is the amount going to multiply the amount of items there are. So looking at the picture, we can see 5 triangles, therefore :
5 *
2 * 1/5 is scratched out as an answer. As is starts with 2.
As for the second number, we acknowledge that all triangles are half in red, therefore the number is 1/2.
5 * 1/2
Scratching all other answers.
2.
2.3*-1-3*
3*- 3x-1
Answer:
i got 27x-3.3 by simplifying
Step-by-step explanation:
PLZ HELP ME I NEED HELP ASAP
Answer:
75 I hope this helped and brainliest please!
Step-by-step explanation:
The equation for surface area for a square pyramid is A=a squared + 2a times the square root of (a squared over 4) + height squared. Since everything is 5 yd, the answer is 75.
if the measure of angle 1 = 17x - 30 and the measure of angle 2 = 7x + 18, what is the value of x?
Answer:
do you know the answer
The value of x is 4.8.
Given that,
The measure of angle 1 = 17x - 30 and the measure of angle 2 = 7x + 18.Based on the above information, the calculation is as follows:
Angle 1 = ANgle 2
17x - 30 = 7x + 18
17x - 7x = 18 + 30
10x = 48
x = 4.8
Therefore we can conclude that the value of x is 4.8.
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Danielle makes $5,000 per week as a surgeon. Soon she will receive a 15% raise. How much money will she make per week after this raise? $750 54.250 55.150 55.750 $7,500
Answer:
50000
Step-by-step explanation:
Answer:
$50,000 would be the answer
Step-by-step explanation:
Find the slope and initial value of the graph below. Then write the equation of the line. Write the equation of the line.
Answer:
y= x + 2
Hope this helps.
SOMEONE ANSWER THESE ASAP
MARKING BRAINLIEST
PLEASE HELPPPPP
Sorry this took a while; calculated a lot of things.
Step-by-step explanation:
A.
Combined:
2.67 times 23.76 = 63.4392
2.67 times - 21 and 5/6 = -58.295
63.4392 - 31.85 -58.295 = -26.7058
If you mean do both separate:
63.4392 - 31.85 = 31.5892
-58.295 - 31.85 = -90.145
B.
Combined:
11 and 3/4 times 23.76 = 279.18
11 and 3/4 times 21 and 5/6 = 256.541666667
279.18 + 256.541666667 + 56 and 3/8 = 592.096666667
If you mean do both separate:
279.18 + 56 and 3/8 = 335.555
256.541666667 + 56 and 3/8 = 312.916666667
ILL GIVE BRAINLIEST AND 10 POINTS
A rectangular prism has a length of 9 in., a width of 4 in., and a height of 112 in.
The prism is filled with cubes that have edge lengths of 12 in.
How many cubes are needed to fill the rectangular prism?
Answer:
432
Step-by-step explanation:
Rectangles Volume / Cubes Volume
9.4.3/2/1/2.1/2.1/2
54/1/8
54.8
432
Bethany uses the equation d = 4.25h to find the distance, d, she travels while walking for h number of hours. What is the constant of proportionality between d and h?
Answer:
4.25
Step-by-step explanation:
The distance Bethany travels is directly proportional to the number of hours she spends working
The formula for direct proportion is :
y = kx
Where k is a constant
in this question, the constant is given by 4.25
I need to write a word problem for this equation and I don't know how to get started. Help!!!! N + (n + 8) + 2n = 364
Answer:
n = 89
Step-by-step explanation:
Ok so,
n + (n+8) + 2n =364
n+n+8+2n = 364
4n + 8 = 364
4n = 356
n = 89
I checked it...its right
if you have any questions please ask me
hope this helps. have a good day :)!!
help help help help help help ill give brainiest
Answer:
wowee,,, i hope these are right :,)
Step-by-step explanation:
5/3-x+1/3 : -3/2+2+1/2x
3/5-13/5 = 6.9+4.9
3x+0 = 3x
2x-3 = x-3+x
2x-6 = -6+2x
Write an expression for the perimeter of the triangle shown below:
Answer:
7.8x - 17
Step-by-step explanation:
1.8x - 7 + 1.8x - 7 + 3.4x - 3 now add like terms
(variables + variables and Coefficient + Coefficient) so the answer is
7.8x - 17
y= 2/3 x +7
X= -4
please help me asap!
-6 x (-8) =
What is this answer I am stuck on it?
Answer:
It is 48
Step-by-step explanation:
Since the negative signs cancel out it is positive and 6 times 8 is 48.
HOPE THIS HELPS!
y = 3x + 6
y = (x + 4)2 – 10
What’s the solution set for this
The answer is,
y = -18, x = -8
Jared made 12 3 fourhs cups of snack mix for a party his guests ate two thirds of the mix how much snack mix did his guests eat
Answer: Jared guests ate = 8 1/2 cups of the snack mix.
Step-by-step explanation:
Total snack mix made by Jared = 12 3/4 CUPS
Amount eaten by guests = 2/3 of Total snack mix
which means they ate = 2/ 3 x12 3/4
= 2/3 x 51/ 4
=17/2 = 8 1/2 cups of snack mix.
Jared guests ate 8 1/2 cups of the snack mix.
What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar? Hi and have a good day :D
Answer:
33.33%
Step-by-step explanation:
the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%
Answer:
33.33%
Step-by-step explanation:
the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%
A nesting box for a falcon is put on top of a 96 ft pole. There are 3 ft in 1 yd.
Answer:
32 yards
Step-by-step explanation:
−4p+9=−5
Plzzzzzzz help
Answer:
p = 3.5 or p = 7/2
Step-by-step explanation:
-4p+9= -5
or, -4p = - 14
or, p = -14/-4
or, p = 7/2 = 3.5
Answer:
p = 3.5
Step-by-step explanation:
What you would do to get p is subtract 5 from both sides of the equation to leave the number and p, THEN divide both sides by the numerator of -4.
-4p + 9 = -5
- 9 -9
__________
-4p = -14
__ __
-4 -4
Thus, p = 3.5
Petrol is poured into a barrel.
The graph shows the number of litres of petrol in the barrel.
Calculate how much petrol is being poured into the barrel each minute.
ans of this question
4 (3c+4d)
Answer: 12c+16d
Step-by-step explanation: 4(3c+4d)
(4)(3c+4d)
(4)(3c)+(4)(4d)
12c+16d
Answer:
Întâi faci paranteza și după de ie faci cu 4
please help.......................
Answer:
FD = 8
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{FD}{BA}[/tex] = [tex]\frac{FE}{BC}[/tex] , substitute values
[tex]\frac{x+3}{2x+2}[/tex] = [tex]\frac{16}{24}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
2(2x + 2) = 3(x + 3) ← distribute parenthesis on both sides
4x + 4 = 3x + 9 ( subtract 3x from both sides )
x + 4 = 9 ( subtract 4 from both sides )
x = 5
Thus
FD = x + 3 = 5 + 3 = 8