Answer:
[tex] = ( \frac{ - b}{a} )( \frac{c}{a} )[/tex]
[tex] = ( \frac{ 1}{3} )( \frac{ - 5}{3} )[/tex]
[tex] = \frac{ - 5}{9} [/tex]
Answer:
- [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Given
P(x) = 3x² - x - 4
with a = 3, b = - 1 and c = - 4
If α and β are the roots of the quadratic then
α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex] , thus
α + β = - [tex]\frac{-1}{3}[/tex] = [tex]\frac{1}{3}[/tex] and αβ = - [tex]\frac{4}{3}[/tex]
Thus
α + β by αβ
= [tex]\frac{\frac{1}{3} }{-\frac{4}{3} }[/tex] = [tex]\frac{1}{3}[/tex] × - [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
Find A ∩ B if A = {4, 7, 10, 13, 17} and B = {3, 5, 7, 9}. a.{3, 4, 5, 7, 9, 10, 13, 17} b.Ø c.{7}
Answer:
The answer is option CStep-by-step explanation:
A = {4, 7, 10, 13, 17}
B = {3, 5, 7, 9}
To find A ∩ B means to find the intersection of the two sets A and B
To find the intersection find the elements that occur in both sets.
That's for set A and B the elements that occur in both sets is only 7
So we have
A ∩ B = { 7 }Hope this helps you
A cyclist travels at $20$ kilometers per hour when cycling uphill, $24$ kilometers per hour when cycling on flat ground, and $30$ kilometers per hour when cycling downhill. On a sunny day, they cycle the hilly road from Aopslandia to Beast Island before turning around and cycling back to Aopslandia. What was their average speed during the entire round trip?
Answer:
Average speed during the trip = 24 km/h
Step-by-step explanation:
Given:
Speed of cyclist uphill, [tex]v_1[/tex] = 20 km/hr
Speed of cyclist on flat ground = 24 km/h
Speed of cyclist downhill, [tex]v_2[/tex] = 30 km/h
Cyclist has traveled on the hilly road to Beast Island from Aopslandia and then back to Aopslandia.
That means, one side the cyclist went uphill will the speed of 20 km/h and then came downhill with the speed of 30 km/h
To find:
Average speed during the entire trip = ?
Solution:
Let the distance between Beast Island and Aopslandia = D km
Let the time taken to reach Beast Island from Aopslandia = [tex]T_1\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_1 = 20 = \dfrac{D}{T_1}[/tex]
[tex]\Rightarrow T_1 = \dfrac{D}{20} ..... (1)[/tex]
Let the time taken to reach Aopslandia back from Beast Island = [tex]T_2\ hours[/tex]
Formula for speed is given as:
[tex]Speed = \dfrac{Distance}{Time}[/tex]
[tex]v_2 = 30 = \dfrac{D}{T_2}[/tex]
[tex]\Rightarrow T_2 = \dfrac{D}{30} ..... (2)[/tex]
Formula for average speed is given as:
[tex]\text{Average Speed} = \dfrac{\text{Total Distance}}{\text{Total Time Taken}}[/tex]
Here total distance = D + D = 2D km
Total Time is [tex]T_1+T_2[/tex] hours.
Putting the values in the formula and using equations (1) and (2):
[tex]\text{Average Speed} = \dfrac{2D}{T_1+T_2}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{D}{20}+\dfrac{D}{30}}}\\\Rightarrow \text{Average Speed} = \dfrac{2D}{\dfrac{30D+20D}{20\times 30}}\\\Rightarrow \text{Average Speed} = \dfrac{2D\times 20 \times 30}{{30D+20D}}\\\Rightarrow \text{Average Speed} = \dfrac{1200}{{50}}\\\Rightarrow \bold{\text{Average Speed} = 24\ km/hr}[/tex]
So, Average speed during the trip = 24 km/h
are you allowed to simplify a fractional exponent when you are rewriting radicals to have a radical exponent? for example, [tex]\sqrt[8]{y^{2} }[/tex] is written as y^2/8 , but are you allowed to simplify the 2/8 to 1/4?
Answer:
This is true
Step-by-step explanation:
Yes when you make a radical into a power you can simplify the power, like you are saying.
What is the image of (-1,-4) after a reflection over the line y=-x
Answer:
[tex]\huge\boxed{(4,1)}[/tex]
Step-by-step explanation:
The point is (-1,-4)
It is reflected over y = - x, So, the coordinate will be like: ( -y , -x )
So, when it is reflected over y = -x , it becomes (4,1)
When a point is reflected, it must be reflected over a line.
The image of (-1,-4) after a reflection over the line y=-x is (4,1).
The point is given as:
[tex]\mathbf{(x,y) = (-1,-4)}[/tex]
The rule of reflection over line y = -x is:
[tex]\mathbf{(x,y) \to (-y,-x)}[/tex]
So, we have:
[tex]\mathbf{(x,y) \to (-(-4),-(-1))}[/tex]
[tex]\mathbf{(x,y) \to (4,1)}[/tex]
Hence, the image of (-1,-4) is (4,1).
Read more about reflections at:
https://brainly.com/question/938117
420 miles in 6.5 hours unit rate
Step-by-step explanation:
Given,
distance =420 miles
time 6.5 hrs
now,
420miles took 6.5 hrs.
1mile took 6.5/420hrs
=0.015476hrs
Therefore, 0.015476hrs to cover 1 mile distance.
Hope it helps...
Answer:
64.6153846 miles/hour
0.0154761905 hours/mile
Step-by-step explanation:
If we want to find the miles driven in one hour, we must divide the total miles by the total hours.
miles / hours
We know that 420 miles were driven in 6.5 hours
420 miles/ 6.5 hours
Divide 420 by 6.5
420/6.5=64.6153846
64.6153846 miles/hour
In one hour, 64.6153846 miles are driven.
If we want to find the time to drive one mile, divide the time (hours) by the miles.
hours / miles
We know that 420 miles were driven in 6.5 hours.
6.5 hours/420 miles
Divide 6.5 by 420
6.5/420=0.0154761905
0.0154761905 hours/ mile
It will take 0.0154761905 of an hour to drive one mile.
in a right angle triangle ACB in which AC=X AB=12 and angle ACB=30° Find the value of x
Answer:
According to the Pythagoras Theorem-
[tex]hypotenuse^{2}[/tex] = [tex]alltitude^{2} + base^{2}[/tex]
Varadha bought two bags of rice of weights 45 kg and 63 kg. Find the maximum weight required, to measure the weight of rice exact number of times. options : 1.6 kg 2.35 kg 3.3 kg 4.9 kg
Answer:
3 kg
Step-by-step explanation:
given data
weights bag1 = 45 kg
weights bag2 = 63 kg
solution
we will take here first HCF of 75 and 69
factor of 75 = 3 × 5 × 5
factor of 69 = 3 × 23
so here HCF of 75 and 69 = 3
so that here maximum weight required, to measure the weight of rice exact 3 times
so correct option is 3. 3 kg
Answer:
4. 9 kg
Step-by-step explanation:
The greatest common factor of 45 kg and 63 kg is 9 kg.
45 = 9×5
63 = 9×7
A 9 kg weight could be used to weigh these amounts exactly.
_____
Comment on the problem statement
Appropriate formatting is helpful. It is difficult to tell that your answer choices are not 1.6, 2.35, 3.3, and 4.9. None of those makes any sense. With minimal formatting effort, you could list them as ...
1. 6 kg
2. 35 kg
3. 3 kg
4. 9 kg
Even better, the choices could be identified using letters and/or a separator other than a decimal point: A) 6 kg, B) 35 kg, and so on. The idea is to make it very clear what the numbers of the choices are. Less confusion is better.
find the area of a rhombus with a 120 degree angle and sides 10 cm
Answer:
A = 50√3 cm²Step-by-step explanation:
[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]
Two numbers are in ratio 3 by 2 and their difference is 5 find numbers
Answer:
The first number is 15, the second number is 10Step-by-step explanation:
a:b = 3:2 ⇒ a = 3x and b = 2x
a - b = 5
3x - 2x = 5
x = 5
a = 3•5 = 15
b = 2•5 = 10
Consider the circle of radius 10 centered at the origin. Find an equation of the line tangent to the circle at the point (6, 8)
Answer:
y = -3/4 x + 25/2
Step-by-step explanation:
x² + y² = 100
Take derivative with respect to x.
2x + 2y dy/dx = 0
2y dy/dx = -2x
dy/dx = -x/y
Evaluate at (6, 8).
dy/dx = -6/8
dy/dx = -3/4
Use point-slope form to write equation:
y − 8 = -3/4 (x − 6)
Simplify.
y − 8 = -3/4 x + 9/2
y = -3/4 x + 25/2
Please please please please help
Answer:
[tex]x^2 +4x +3 [/tex]
Step-by-step explanation:
f(x)=x²-1
g(x)= x+2
f(g(x)) =f(x+2)
=(x+2)²-1
=x²+4x+4-1
=x²+4x+3
The day before an exam, Jacob spent 2 1/5
hours studying in the morning and 3 3/4 hours
studying in the afternoon. How many hours
did Jacob spend studying that day?
Answer:
5 19/20 or 5.95
Step-by-step explanation:
You can add these numbers as decimal numbers or as mixed numbers.
Decimal
2.2 +3.75 = 5.95 . . . hours spent studying
Mixed Numbers
(2 1/5) +(3 3/4) = (2 4/20) +(3 15/20) = (2 +3) +(4/20 +15/20)
= 5 19/20 . . . hours spent studying
Consider the functions below. Which of the following statements describes the graph of function g? f(x)=x g(x)=1/5x A.The graph of g is one-fifth of a unit to the left of the graph of f. B. The graph of g is one-fifth of a unit to the right of the graph of f. C. The graph of g is five times steeper than the graph of f. D. The graph of g is one-fifth as steep as the graph of f.
Answer:
one fifth
Step-by-step explanation:
42
Answer:
The graph of g is one-fifth as steep as the graph of f.
Step-by-step explanation:
A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 marks
Answer:
7/40 is the fraction filled with water
Step-by-step explanation:
Here we start by calculating the volume of the cylindrical tank.
Mathematically, that would be;
V = π * r^2 * h
From the question
r = 80 cm = 80/100 = 0.8 meters
h = 1.4 meters
π = 22/7
Plugging these values into the volume equation, we have;
V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3
But mathematically;
1 m^3 = 1000 liters
So 2.816 m^3 = 2.816 * 1000 = 2816 liters
So the fraction filled with water will be;
492.8/2816 = 0.175 = 175/1000 = 7/40
The minimal passing score for a test is 80%. There are 12 exercises on the test. What is the minimum number of correct exercises needed to earn a passing score?
Getting each exercise correct gets you 8.3(recurring)%. Therefore if you answer 10 exercises correctly you get 83.3%, and if you answer 9 exercises correctly you get 75%, this means that the minimal exercises you need to get correct is 10.
plz help me with this problem
p^2 - 36
Answer:
[tex]\large \boxed{ (p+6)(p-6) }[/tex]
Step-by-step explanation:
[tex]p^2 - 36[/tex]
Rewrite 36 as 6 squared.
[tex]p^2 - 6^2[/tex]
Apply difference of two squares formula:
[tex]a^2-b^2 =(a+b)(a-b)[/tex]
[tex]a=p\\b=6[/tex]
[tex]p^2 - 6^2=(p+6)(p-6)[/tex]
Answer:
since is its a possibility of 7 or 11 we add the individual probabilities
so the answer is 1/6+ 1/18=3/18+1/18=4/18=2/9
2/9.
I hope now you'll understand
Another way to write g(h(x)) is
Answer:
((x)h)g
Step-by-step explanation:
Hope this helps and if this is wrong then please comment the right answer and I will edit it thanks :)
Simplified. 2c+2d+5d
Answer:
2c +7d
Step-by-step explanation:
2c+2d+5d
Combine like terms
2c + d(2+5)
2c +7d
Answer:
The simplified answer of this expression is 2c + 7d
Step-by-step explanation:
For this problem, you will have to combine like terms.
2c + 2d + 5d
Combine 2d and 5d.
2c + 7d
1 person = 40 min = 1 bag, 4 person = ? min = 1575 bags
Answer:
15 750 minStep-by-step explanation:
4 person = 1575 bags
1 person = 1575:4 = 393.75 bags
40 min = 1 bag
393,75 bags = 40 min•393,75 = 15 750 min
if x^2+y^2=14 annd xy=5 find the value of (1/2x+1/2y)^2
Answer:
7Step-by-step explanation:
[tex]\left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7[/tex]
Angle A is circumscribed about circle O. What is the measure of angle O? 46
Answer:
m<O = 134°
Step-by-step explanation:
OC = OB = radius of the circle
AC = AB = tangents of circle O
m<C = m<B = 90°. (Tangent and a radius always form 90°)
m<A = 46°
Therefore,
m<O = 360° - (m<C + m<B + m<A) => sum of angles in a quadrilateral.
m<O = 360° - (90° + 90° + 46°)
m<O = 360° - 226°
m<O = 134°.
Measure of angle A = 134°
how do you solve this problem ? 4(-3x+1)-3x=71
Answer:
x = -67/15 = -4-46667
Step-by-step explanation:
4(-3x+1) - 3x = 71
4*-3x + 4*1 - 3x = 71
-12x + 4 - 3x = 71
-15x = 71-4
-15x = 67
x = 67/-15
x = -4.46667
check:
4(-3*-4.46667 + 1) - 3*-4.4666= 71
4(13.4+1) + 13.4 = 71
4*14.4 + 13.4 = 71
57.6 + 13.4 = 71
What is the solution to -33 + m = 10?
A. m = -43
B. m = -23
C. m = 23
D. m = 43
Answer:
D. m = 43
Step-by-step explanation:
Answer: D. m=43
Step-by-step explanation:
-33 +m = 10move 33 and make it postive m = 10 + 33m = 43I NEED HELP ON THE PROBLEM!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!!
Answer:
A.) As x increases, the rate of change of g exceeds the rate of change of f
Step-by-step explanation:
Let's take the options given and look at them to actually know which is true.
Option A
We notice that as x increase in value the rate of change of g starts exceeding the rate of change of f.
Then it's exceeds it from the value x = 5
Option B
At x= 4.39
F= 2616.689
G= 2606.657
They are different values
Option C
That's opposite of option A
But option A is true which signify option C to be false
Option D
Not true also.
We can see from x= 0 to 4 the rate of change of F exceeds that of G
luis almuerza 1/3 de una pizza y juan 2/5 de la misma si deciden distribuirse el resto de la pizza en partes iguales determina que fraccion le tocaria a cada uno
Answer:
A cada uno le toca:
2/15
del total de la pizza.
Step-by-step explanation:
1/3 + 2/5 = 5 / 15 + 6 / 15 = 11/15
los dos, inicialmente, han almorzado
11/15
de la pizza.
Si el resto lo dividen en dos partes:
15/15 - 11/15 = 4/15
el resto es de 4/15
al dividir este resto entre los dos:
(4/15) / 2 = 4/(15*2) = 4/30 = 2/15
A cada uno le tocarían:
2/15
del total de la pizza
Need help will give good rating.
Answer:
the third one is correct
Answer:
Step-by-step explanation:
dlklf,vkvkdcñclcdliffoIf the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?
Answer:
8.94~9.0
Step-by-step explanation:
If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!
The required length of the hypotenuse of the triangle is 16√5.
Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.
In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.
Here,
Applying the Pythagorean theorem,
Hypotenuse² = perpendicula² + base²
Hypotenuse² = 8² + 4²
Hypotenuse² = 64 + 16
Hypotenuse² = 80
Hypotenuse = √80
Hypotenuse = 16√5
Thus, the required length of the hypotenuse of the triangle is 16√5.
Learn more about Pythagorean triplets here:
https://brainly.com/question/10174253
#SPJ2
Prove the identity sin^2theta x csc^2 theta = sin^2 theta + cos^2 theta 20 points!!
Answer:
Step-by-step explanation:
sin² Θ csc² Θ =sin² Θ + cos² Θ
sin² Θ 1/sin² Θ = sin² Θ + cos² Θ
1 = sin² Θ + cos ² Θ (this is a trig identity)
The three-dimensional figure shown consists of a cylinder and a right circular cone. The radius of the base is 10 centimeters. The height of the cylinder is 16 centimeters, and the total height of the figure is 28 centimeters. The slant height of the cone is 13 centimeters. Which choice is the best approximation of the surface area of the figure? Use 3.14 to approximate pi.
Answer:
2,041 square centimeters
Step-by-step explanation:
surface area = (2 × π × r × h) + ((π × r) × (r+ (√(c² + r²))))+(π × r²)
where,
cylinder base radius (r) = 10 cm
height of cylinder (h) = 16 cm
total height = 28 cm
cone height (c) = total height - height of cylinder = 28 - 16 = 12cm
π = 3.14
surface area = (2 × 3.14 × 10 × 16) + ((3.14 × 10) × (10+ (√(12² + 10²))))+(3.14 × 10²)
surface area = 1004.8 + (31.4 * 25.6) + 314
surface area = 2122.64 cm²
therefore the approximate surface area given is 2,041 square centimeters
Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4
Answer:
[tex]\frac{1}{9^4}[/tex].
Step-by-step explanation:
[tex]9^{-4}[/tex]
= [tex]\frac{1}{9^4}[/tex]
= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]
= [tex]\frac{1}{81 * 81}[/tex]
= [tex]\frac{1}{6561}[/tex]
= 0.0001524157903.
Hope this helps!
