Answer:
a) A-B = { 1 , 3, 5 }
b) The remainder is 50
c) f + g)(x) = x⁴+ 5x³
d) [tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]
Step-by-step explanation:
Step(I):-
1) a)
Let A = { 1, 3, 5, 7 } and B = { 7 , 14 , 21 }
A - B = {1,3,5,7} - { 7,14,21}
A - B = { 1 , 3, 5}
b)
Given f (x)=3x³−11x−48
x-1 ) 3 x³ - 11x -48 (- 3x²-3x -2
-3x³ +3x²
3x²-11x-48
-3x²+9x
2x -48
-2x +2
50
The remainder is 50
c) Given f(x) = x³ and g(x) = x + 5
(f. g)(x) = f(x) .g(x) = x³ . (x+5) = x³(x) + 5 x³ = x⁴+ 5x³
d)
Given function y = 3 + x²+x³y³ ...(I)
By using derivative formulas
y = xⁿ
[tex]\frac{dy}{dx} = n x^{n-1}[/tex]
Apply d/dx ( UV) = U V¹ + V U¹
Differentiating equation (I) with respective to 'x' , we get
[tex]\frac{dy}{dx} = 0 + 2x + ( x^3 3y^2(\frac{dy}{dx} )+ y^3(3x^2))[/tex]
[tex]\frac{dy}{dx} - ( x^3 3y^2(\frac{dy}{dx} )= 2x- y^3(3x^2))[/tex]
[tex]\frac{dy}{dx} = \frac{2x- y^3(3x^2)) }{ 1- x^3 3y^2}[/tex]
For the right triangle shown, use the trig functions to find the value of x. Round your answer to the nearest tenth.
1. 9.1
2. 8.2
3. 9.4
4. 7
Answer:
[tex]\boxed{\boxed {\sf 3. \ 9.4}}[/tex]
Step-by-step explanation:
First, recall the three basic right triangle trigonometry ratios.
sin(θ)=opposite/hypotenuse cos(θ)= adjacent/hypotenuse tan(θ)= opposite/adjacentTheta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.
We are also given 2 sides: 10 and x.
10 is the hypotenuse, because it is opposite the right angle. x is opposite the 70 degree angle.Since we have the opposite and hypotenuse, we must use sine.
[tex]sin (\Theta)= \frac{opposite}{hypotenuse}}[/tex]
The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.
[tex]sin(70)=\frac{x}{10}[/tex]
We are solving for x. We must isolate x on one side of the equation.
Currently, x is being divided by 10. To "undo" the division, we must perform the inverse operation, which is multiplication. Multiply both sides of the equation by 10.
[tex]10*sin(70)=\frac{x}{10}*10[/tex]
[tex]10*sin(70)=x[/tex]
[tex]10*0.939692621=x[/tex]
[tex]9.39692621=x[/tex]
Round to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.
[tex]9.4 \approx x[/tex]
x is about 9.4
Answer:
First, recall the three basic right triangle trigonometry ratios.sin(θ)=opposite/hypotenusecos(θ)= adjacent/hypotenusetan(θ)= opposite/adjacentTheta (θ) represents the angle. The angle (other than the right angle) is 70 degrees.We are also given 2 sides: 10 and x.10 is the hypotenuse, because it is opposite the right angle.x is opposite the 70 degree angle.Since we have the opposite and hypotenuse, we must use sine.sin (\Theta)= \frac{opposite}{hypotenuse}}The angle is 70 degrees, the opposite is x, and the hypotenuse is 10.sin(70)=\frac{x}{10}sin(70)= 10x
We are solving for x. We must isolate x on one side of the equation.Currently, x is being divided by 10. To "undo" the division, we must perform the inverse operation, which is multiplication. Multiply both sides of the equation by 10.10*sin(70)=\frac{x}{10}*1010∗sin(70)= 10x
∗1010*sin(70)=x10∗sin(70)=x10*0.939692621=x10∗0.939692621=x9.39692621=x9.39692621=xRound to the nearest tenth. The 9 in the hundredth place tells us to round the 3 up to a 4.9.4 \approx x9.4≈xx is about 9.4
In a right-angled triangle
, one acute angle is 30°. Find the other acute angle
VII CLASS MATHEMATICS
Answer:
60°
Step-by-step explanation:
sum of all angles is 180
and it's a right-angled triangle so there is angle = 90
so the other acute angle = 180-30-90=60°
Answer:
60
Step-by-step explanation:
90+30= 120
180-120= 60
Which statement about the value of x is true?
O x>38
Ox<39
Ox=77
OX > 103
Answer:
x = 77 and x > 38
Step-by-step explanation:
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180, therefore x = 180 - 103 = 77.
Which is also greater than 38, so x > 38 is also correct.
The solution is : x = 77 and x > 38
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
Sum of all angles in a triangle is 180.
The angle PNO will hence be:
180 - 38 - 39 = 103 degrees.
The angle PNO + angle x = 180 degrees (straight line)
So 103 + x = 180,
therefore x = 180 - 103 = 77.
Which is also greater than 38,
so x > 38 is also correct.
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Given the set of vertices, determine whether parallelogram ABCD is a rhombus, rectangle or square. List all that apply. A(7,-4), B(-1,-4), C(-1,-12), D(7, -12)
a. rhombus c. square, rectangle, rhombus
b. square d. rectangle
Given:
Vertices of a parallelogram ABCD are A(7,-4), B(-1,-4), C(-1,-12), D(7, -12).
To find:
Whether the parallelogram ABCD is a rhombus, rectangle or square.
Solution:
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]AB=\sqrt{(-4-(-4))^2+(-1-7)^2}[/tex]
[tex]AB=\sqrt{(-4+4)^2+(-8)^2}[/tex]
[tex]AB=\sqrt{0+64}[/tex]
[tex]AB=8[/tex]
Similarly,
[tex]BC=\sqrt{(-1-(-1))^2+(12-(-4))^2}=8[/tex]
[tex]CD=\sqrt{(7-(-1))^2+(-12-(-12))^2}=8[/tex]
[tex]AD=\sqrt{(7-7)^2+(-12-(-4))^2}=8[/tex]
All sides of parallelogram are equal.
[tex]AC=\sqrt{(-1-7)^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
[tex]BD=\sqrt{(7-(-1))^2+(-12-(-4))^2}=8\sqrt{2}[/tex]
Both diagonals are equal.
Since, all sides are equal and both diagonals are equal, therefore, the parallelogram ABCD is a square.
We know that, a square is special case of rectangles and rhombus.
So, parallelogram ABCD is a rhombus, rectangle or square. Therefore, the correct option is c.
Solve for x. Round to the nearest hundredth. ?!?!? Please HELPP ASAP
I really don't know this I'm so sorry
Answer:
14
Step-by-step explanation:
Well, a right triangle has a total of 90 degrees, if the hypotenuse is 22, and leg b is 54, then the remaining leg a would have to be 14.
In the rectangle below, AChas a length of 32 units. What is the length of DE?
O A. 32 units
OB. 64 units
OC. 24 units
O D. 16 units
Read Question On PNG Picture
Answer:
10 1/2
Step-by-step explanation:
one and two-thirds divided by 3
Answer:
5/9
Step-by-step explanation:
Why do we say that the sun is the driving force for (it causes) the weather?
The sun evenly heats up the Earth causing winds.
The sun affects land and water the same way.
The sun supplies the energy (radiation) that drives the water cycle.
The sun evenly heats up the Earth causing water currents.
Answer: The sun supplies the energy (radiation) that drives the water cycle.
Step-by-step explanation:
Option A is wrong because the Sun does not evenly heat up the Earth. The Earth is spherical so the sun heats up some areas more than others.
Option B is wrong as well because the sun does not affect the land and the water the same way.
Option C is correct because radiation from the sun is what causes evaporation in the water cycle.
Option D is wrong because as shown in the first option, the sun does not evenly heat up the Earth.
Hello there ^^ I'd love it if you would help me :D
Answer:
Great question
Step-by-step explanation:
Where is it :p
Help I’ll mark you brainly! And give extra points!
Answer: I think #2 is either A or C
Step-by-step explanation: Hope it helped! :)
F(6) if f(x) = 4x
a 10
b. 24
c. 20
d: 30
Answer:
b. 24
Step-by-step explanation:
Hope this is right!
which number line correctly graphs the numbers in the list?
Answer:
the first option
Step-by-step explanation:
There are six doors in a hostel .In how many ways a student enters the hostel and leave by different door
Answer:
5 times
Step-by-step explanation:
Because he enters through the front door.
HELP!!!! 2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answer:
5th grade mean - 4.67
7th grade mean - 3.46
5th-grade median - 5
7th-grade median - 3.5
What is the value of the expression 24/x when x = 8?
Answer:
Itd be 3 becaus 24/8 is 3
anyone know this two questions I can't figure this out
Answer:
22) x - 46 = 74
23) 20 portions
Step-by-step explanation:
21)
Let x = the number of cars Sara sold.
Jerry sold 46 cars fewer than Sara, so Jerry sold x - 46 cars.
Jerry sold 74 cars, so the equation is
x - 46 = 74
Answer: x - 46 = 74
22)
Let the number of 1/3 lb portions = x
The weight of x number of 1/3-lb portions is 1/3 * x, or simply x/3.
The full bag weighs 6 2/3 lb.
The equation is
x/3 = 6 2/3
Now we solve for x.
x/3 = 20/3
Multiply both sides by 3.
x = 20
Answer: 20 portions
Answer:
let 's' = Sara's amount
let 's-46' = Jerry's amount
equation: s - 46 = 74
s = 120
Step-by-step explanation:
2nd question: [tex]\frac{20}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex] = [tex]\frac{20}{3}[/tex]· [tex]\frac{3}{1}[/tex] = 20
Find the unit rate. Round the nearest hundredth if necessary.
$420 for 15 tickets.
A. $28 per ticket
B. $0.04 per ticket
C. $405 per ticket
D. $840 per 30 tickets
Answer:
28 dollars per ticket
Step-by-step explanation:
just divide 420 by 15 to get 28
A principal purchased a total of 32 gas cards and movie passes for prizes. Each gas card cost $25.75, and each movie pass cost $7.25. If the principal spent a total of $454.00, how many gas cards did the principal purchase?
Answer: 12
Step-by-step explanation: 25.75a+7.25b=454
a+b=32
Please help me answer this !
Answer:
[tex] y = -\frac{1}{2}x + 4 [/tex]
Step-by-step explanation:
The equation of the line can be written in slope-intercept form, as y = mx + b.
We need to find the slope (m) and the y-intercept (b) of the line, then plug their values into the slope-intercept equation, to find the equation of the line shown.
y-intercept (b) = the point where the line intercepts the y-axis = 4
Using two points on the line, say, (0, 4) and (2, 3):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 4}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} [/tex]
m = -½.
Substitute m = -½, and b = 4 into y = mx + b.
The equation of the line would be:
[tex] y = -\frac{1}{2}x + 4 [/tex]
- 5 + 7k = -19
Help pwease
Answer:
k = -2
Step-by-step explanation:
-5 + 7k = -19
7k = -14
k = -2
1. Display the data in a matrix A with rows indicating years. What is element a 14?
Answer:
LOL i don't even know
Step-by-step explanation:
Answer:
63
Step-by-step explanation you just killed my brainmeats
L.B Johnson middle miguel took part
Answer:
Johnson Middle School held a track and field event during the school year. Miguel took part in a four-person shot put team. Shot put is a track and field event where athletes throw (or "put") a heavy sphere, called a "shot," as far as possible.
Step-by-step explanation:
PLZZ MARK BRAINLIEST!!!!!
Round 48.47 to the ones place
Answer:
48.7 I think
Step-by-step explanation:
hears the sender buddy
Answer:
48.5 the 7 is close to 10 so it rounds the 4 to 5
Find the value of the expression. 12 - (-13) + (-1)
Answer:
24
Step-by-step explanation:
Answer:
The value is equvilant to 24
12−(−13)−1
=24
The problem was already simplified-
Oh and try using this website called math papa its an algebra calculator it really helps and it even shows you the step by step process!
A study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons. On a given day, 99.7% of the cows will produce an amount of milk within which of the following ranges?
Answer: 4.1 gallons to 8.3 gallons
Step-by-step explanation:
just took the quiz
99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.
What is a normal distribution?It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.
The missing options are:
A. 5.5 gallons to 6.9 gallonsB. 4.8 gallons to 7.6 gallonsC. 4.1 gallons to 8.3 gallonsD. 3.4 gallons to 9.0 gallonsWe have:
A study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons.
The mean = 6.2 gallons
Standard deviation = 0.7 gallons
The range can be calculated:
Lower range = 6.2 - 0.7 = 5.5 gallons
Upper range = 6.2 + 0.7 = 6.9 gallons
Thus, 99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.
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What is 3/5 converted into a percent.
Answer:
60%
Step-by-step explanation:
multiply 3/5 by 20
Answer:
60%
since 100/100 is 100%, we just have to find a number that will make the denominator 5 equal to 100. That is 20 so we multiply 20 for both 3 and 5. This equals to 60/100, which is 60%
A circular tablecloth has a diameter of 6 feet,as show on the picture.
What is the area,in square feet,of the tablecloth.
Which of the following is the equation in slope-intercept form for the line that passes through the points (-2, 4) and (2.0) ?
O y = x + 2
O y = x-2
O y = -x + 2
Answer:
y = -x + 2
Step-by-step explanation:
Find the slope with rise over run:
(y2 - y1) / (x2 - x1)
(0 - 4) / (2 + 2)
-4 / 4
= -1
Find the y intercept by plugging in the slope and a point:
y = mx + b
4 = -1(-2) + b
4 = 2 + b
2 = b
Plug in the slope and y intercept:
y = -x + 2
So, the correct answer is y = -x + 2
While President, Obama received an average of 60, 000 letters per week at the White House.
Approximately how many letters does he receive in a day?
Answer:
8571 letters per day
Step-by-step explanation:
60,000/1 week is the same as 60,000/7 days so
60,000/7 = 8571.428571
is aproximately 8571 letters per day