Answer:
[tex]x^{\frac{1}{8}}y^8[/tex].
Step-by-step explanation:
The given expression is
[tex](x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}[/tex]
We need to find the expression, which is equivalent to the given expression.
The given expression can be rewritten as
[tex](x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex](x^{\frac{1}{4}\times \frac{1}{2}})(y^{16\times \frac{1}{2}})[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]x^{\frac{1}{8}}y^8[/tex]
Therefore, the required expression is [tex]x^{\frac{1}{8}}y^8[/tex].
The simplified form of the indices is [tex]x^{1/4}y^8[/tex]
Given the expression:
[tex](x^{1/4}y^{16})^{1/2}[/tex]
Using the law of indices below:
[tex](a^m)^n = a^{mn}[/tex]
Multiplying the power will give:
[tex]= (x^{1/4})^{1/2} \cdot (y^{16})^{1/2}\\=x^{1/4}y^8[/tex]
Hence the simplified form of the indices is [tex]x^{1/4}y^8[/tex]
Learn more on indices here: brainly.com/question/8952483
4. If 30 locusts eat 420 grams of grass in a week. How many days will it
take 21 locusts to consume 420 grams of grass if they eat at the same
rate
Answer:
The amount one locust eats in a week is 420/30 = 14 grams so it eats 14/7 = 2 grams per day, therefore 21 locusts can eat 21 * 14 = 42 grams per day. 420 / 42 = 10 so the answer is 10 days or 1 week and 3 days.
Esrudiantes ganaron un concurso ,lo cual el premio fue visita a fabrica de reciclaje , A mitad de la charla se retiraron 10 mujeres y se observo que el numero de varones era el doble que el de mujeres ,casi al final de la charla se retiraron 45 varones y takbiek se obeservo que el numero de mujeres era el doble que los varones ¿que cantidad de mujeres y varones estuvieron en la charla?¿cual fue el total de asistentes?
Answer:
The total number of students who attended the talk is 100.
Step-by-step explanation:
We are given that halfway through the talk, 10 women withdrew and it was observed that the number of men was twice that of women.
Then, almost at the end of the talk, 45 men withdrew and it was observed that the number of women was twice that of men.
Let the number of women who attended the talk be 'w' and the number of men who attended the talk be 'm'.
Now, according to the question;
The first condition states that the 10 women withdrew and it was observed that the number of men was twice that of women, i.e;[tex]m = 2 \times (w-10)[/tex]
[tex]m = 2w-20[/tex] ----------------- [Equation 1]
The second condition states that at the end of the talk, 45 men withdrew and it was observed that the number of women was twice that of men, i.e;[tex](w-10) = 2(m-45)[/tex]
[tex]w-10= 2m-90[/tex]
[tex]w= 2m-80[/tex]
[tex]w= 2(2w-20)-80[/tex] {using equation 1}
[tex]w= 4w-40-80[/tex]
[tex]4w-w= 120[/tex]
[tex]3w= 120[/tex]
[tex]w=\frac{120}{3}[/tex] = 40
Now, putting the value of w in equation 1 we get;
[tex]m = 2w-20[/tex]
[tex]m = 2(40) -20[/tex]
= 80 - 20 = 60
So, the number of men who attended the talk is 60 and the number of women is 40.
Hence, the total number of students who attended the talk is (60 + 40) = 100.
Question 11 PLEASE HELP find the slope of the line that passes through the points (6,2) and (8,8)
Answer:
Slope would equal 3.
slope= (y2-y1)/(x2-x1)
Plug in you get (8-2)/8-6)
Simplify (6)/(2)=3
Step-by-step explanation:
Here’s a graph of a linear function. Write the equation that describes that function.
Express it in slope-intercept form.
Answer:
y=3/4 x+2
Step-by-step explanation:
y=mx+b
take two points from graph
(0,2) and (4,5)
find b when x=0 then y=b=2
find m : y2-y1/x2-x1=5-2/4-0
m=3/4
y=3/4 x +2
what is the explicit formula for this sequence? 2,10,50,250,1250
Answer:
[tex]a_n = 2(5)^{n-1}[/tex]
Step-by-step explanation:
Explicit Geometric Formula: [tex]a_n = a_1r^{n-1}[/tex]
a₁ is 1st term
r is common ratio
n is term number
Step 1: Find common ratio r
r = 10/2 = 5
Step 2: Plug variables into formula
[tex]a_n = 2(5)^{n-1}[/tex]
Answer:
This is a geometric sequence with a₁ = 2 and r = 5 where a₁ is the first term and r is the common ratio.
Explicit formula: aₙ = a₁ * r ⁿ⁻¹
The answer is aₙ = 2 * (5ⁿ⁻¹)
How can we write 0.7 in words?
Step-by-step explanation:
You could simply say the numbers in 0.7 one at a time like this:
=> zero point seven
OR
You can also see 0.7 as a fraction (7/10) and should therefore be said and written as follows:
=> seven tenths
Hope this helps.. Good Luck
0.7 means the same thing as 7 tenths.
Below, I have made a place value chart.
You will see that 0.7 means 0 units and 7 tenths.
Solve for x 7 x − 4 = 6 Give your answer as an improper fraction in its simplest form.
Answer:
10\7
Step-by-step explanation:
7x-4=6
7x=6+4
7x=10
7x\7=10\7
x=10\7
Answer:-13/3
Step-by-step explanation:
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 50 cm/s. Find the rate at which the area within the circle is increasing after each of the following.
(a) after 1 s
(b) after 3 s
(c) after 7 s
Answer:
1.) 15,708cm^2/s
2) 47,124cm^2/s
3.) 109,956cm^2/s
Step-by-step explanation:
Given the following:
50cm/s is the radius of the ripple per second , that is, radius(r) of ripple after t seconds = speed * time(t)
Speed = 50cm/s
r = 50t
.area of a circle(A) = πr^2
Rate of change of area with radius :
dA/dt = π2r . dr/dt
Speed of ripple created = 50cm/s; this is the rate at which the radius changes with time (dr/dt)
dr/dt = 50cm/s
Rate at which area is increasing with time:
dA/dt = π2r . dr/dt
dA/dt = π2(50t).50
dA/dt = 5000πt
After 1 second:
dA/dt = 5000π(1)
= 15,707.963cm^2/s
After 3 second:
dA/dt = 5000π(3)
= 47,123.889cm^2/s
After 7 second:
dA/dt = 5000π(7)
= 109,955.74cm^2/s
Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))
Answer:
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
Step-by-step explanation:
tan(sin⁻¹x + cos⁻¹y)
Use angle sum formula:
[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]
To evaluate these expressions, I suggest drawing right triangles.
For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1. Therefore:
sin θ = x/1
θ = sin⁻¹x
Using Pythagorean theorem, the adjacent side is √(1−x²). Therefore:
tan θ = x / √(1−x²)
tan(sin⁻¹x) = x / √(1−x²)
Draw a new triangle. This time we'll make y the adjacent side to angle θ.
cos θ = y/1
θ = cos⁻¹y
Using Pythagorean theorem, the opposite side is √(1−y²). Therefore:
tan θ = √(1−y²) / y
tan(cos⁻¹y) = √(1−y²) / y
Substituting:
[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]
Multiply top and bottom by √(1−x²).
[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]
Multiply top and bottom by y.
[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]
for the function F(x)=1/x,which of these could be a value of F(x) when x is close to zero
Answer:
C. -10,000
Step-by-step explanation:
As x approaches zero, f(x) approaches infinity or negative infinity.
Answer: C. -10,000
Answer:
-10,000
Step-by-step explanation:
Solve for x 8x−6=15 Give your answer as an improper fraction in its simplest form
Answer:
[tex]\boxed{x = \frac{21}{8} }[/tex]
Step-by-step explanation:
=> 8x-6 = 15
Adding 6 to both sides
=> 8x = 15+6
=> 8x = 21
Dividing both sides by 8
=> x = 21/8 (In its simplest form)
Rewrite 4 − 5 using the additive inverse and display the new expression on a number line. (5 points) 4 + 5 An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 4 − (−5) An image of a horizontal number line is shown with labels from 0 to 10. An arrow begins at 0 and ends at 4. Another arrow begins at 4 and ends at 9. 5 − 4 An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 and ends at 5. Another arrow begins at 5 and ends at 1. 4 + (−5) An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Answer: 4 + (−5)
An image of a horizontal number line is shown with labels from negative 2 to positive 6. An arrow begins at 0 to 4. Another arrow begins at 4 to negative 1.
Step-by-step explanation: The arrow from 0 running to 4 is the graph of how the point on the line is a positive 4: Four added to 0
The "additive inverse" means start there and go in the opposite direction. The arrow is 5 units long, so they ended up at -1 . Adding -5 is the same as subtracting 5
4 + (-5) = -1 is the additive inverse of 4-5= -1
The descriptions of the number lines are well done, but difficult to sort out.
Answer:
4 + (−5)
Step-by-step explanation:
it is got it correct
△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX. Triangle A Y X is shown. Line segment B C is drawn from side A Y to A X to form triangle A B C. The proof that △ABC ~ △AYX is shown. Statements Reasons 1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given 2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle 3. AB = AC and AY = AX 3. definition of congruency 4. AY • AC = AX • AC 4. multiplication property of equality 5. AY • AC = AX • AB 5. substitution property of equality 6. 6. division property of equality 7. 7. division property of equality 8. ? 8. ? 9. △ABC ~ △AYX 9. SAS similarity theorem Which statement and reason are missing in the proof?
Explanation:
Here is our take on the proof shown in the problem statement. The missing statements and reasons are shown in bold.
Statements Reasons
1. △ABC is isosceles with legs AB and AC; △AYX is also isosceles with legs AY and AX. 1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX 3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC/AX = AB 6. division property of equality
7. AC/AX = AB/AY 7. division property of equality
8. Corresponding sides are proportional 8. Definition of proportional
9. △ABC ~ △AYX 9. SAS similarity theorem
_____
The reason given in statements 6 and 7 suggest you need to divide something. For SAS similarity, you need to show corresponding sides are proportional. The missing steps are to get to the point where you can say that.
Answer:
I think its A. ∠A ≅ ∠A; reflexive property
Step-by-step explanation:
Use the first four terms of the binomial theorem to approximate 2.2^7
Answer:
248.96 which is approximately 249
Step-by-step explanation:
2.2^7
The coefficients are;
1,7,21,35,35,21,7,1
So the terms we want to use are 1,7,21 and 35
We can write 2.2 as 2+ 0.2
So the approximations are;
1(2)^7(0.2)^0 + 7(2)^6(0.2) + 21(2)^5(0.2)^2 + 35(2)^4(0.2)^3
= 128 + 89.6 + 26.88 + 4.48 = 248.96
True or false
The diagonal of a square are congruent
Answer:
True
Step-by-step explanation:
As we know that all four sides and angles of a square are equal to each other plus the diagonal is right angled to each other as they intersect at 90 degree i.e perpendicular
It contains the identical length i.e congruent
Hence the given statement is true i.e diagonal of a square are congruent to each other
the function g(x)=-5x-6
Answer:
D. the slope of f(x) is greater than the slope of g(x)
Step-by-step explanation:
slope of f(x) =rise/run
=y2 -y1 / x2 -x1
slope of f(x)= -1-2/1-0= -3
g(x)= -5x-6
slope of g(x)= -5
-3>-5
D. the slope og f(x) is greater than the slope of g(x)
If g(x) = 3x2 - 4x + 1, what is the value of g(-2)?
Answer:
21
Step-by-step explanation:
substitution
Answer:
21
Step-by-step explanation:
Plug in x as -2.
3(-2)² - 4(-2) + 1
3(4) - - 8 + 1
12 + 8 + 1
= 21
The circumference of a circular field is 285.74 yards. What is the diameter of the field? Use 3.14 for it and do not round your answer.
yards
x
?
Answer:
The diameter is 91.
Step-by-step explanation:
The formula for circumference is 2*pi*radius(you can use circumference = diameter*pi too). Plug 285.74 into it. Divide both sides by 3.14, and you get 2*radius(aka the diameter) = 91
Answer:
91 yards
Step-by-step explanation:
The circumference of a circle can be found using the following formula:
c=π * d
We know that the circumference is 285.74 yards and we are using 3.14 for pi. Substitute 285.74 in for c and 3.14 for pi.
285.74= 3.14 *d
We want to find the diameter. Therefore, we need to get the variable d by itself. d is being multiplied by 3.14 The inverse of multiplication is division. Divide both sides of the equation by 3.14
285.74/3.14= 3.14*d/3.14
285.74/3.14=d
Divide
91=d
d= 91 yards
The diameter of the field is 91 yards.
please help me! Bethany incorrectly simplified the following expression: (4 x 10^11) (3 x 10^-14) + 0.000005 Which of Bethany’s steps show an error based solely on her previous step? Choose all that apply: A. Step one: (4 x 10^11) (3 x 10^-14) + (5 x 10^-5) B. Step two: (12 x 10^-3) + (5 x 10^-5) C. Step three: (120 x 10^-4) + (5 x 10^-5) D. Step four: (120 x 10^-4) + (50 x 10^-4) E. Step five: 170 x 10^-8 F. Step six: 1.7 x 10^-6
Answer:
Below.
Step-by-step explanation:
Step 1: it is 5 x 10^-6 not 5 x 10^-5.
Step 5 : the result of the addition is 170 x 10^-4 not 170 x 10^-8.
Answer: yes that is correct explanation:
Let T be the set of things found in a toy store, and V be the set of things that cost more than $50. The set T∪V is the set of things that found in a toy store or cost more than $50 . The set T∩V is the set of things that found in a toy store and cost more than $50 . The set T′ is the set of things that_____ A cost under $50 B not found in a toy store C not found in a toy store and cost more than $50
Answer:
B. not found in a toy store
Step-by-step explanation:
Given:
T = the set of things found in a toy store.
V = the set of things that cost more than $50.
T∪V = the set of things that found in a toy store or cost more than $50.
T∩V = the set of things that found in a toy store and cost more than $50.
The set T′ is the complement of the set T and it consists of the set of things that are not found in a toy store.
The correct option is B
PLZ HELP IM TIMED Which table represents a linear function?
Answer:
3
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
A linear function is when the y value increases or decreases at a constant rate of change whenever the x value increases or decreases. All y values increases by 1/2 every time the x values increases by 1.
Hopefully this helps & gets brainliest.
A delivery company estimates that it will take 4 minutes for their drone to fly 7 km how long will it take the drone to fly 21 km
Answer: 12 minutes
Step-by-step explanation:
7 km ........ 4 minutes
21 km ...... ?
21/7 x 4= 12 minutes
Answer: 12 minutes.
Step-by-step explanation:
It is easy to put the numbers into a ratio form to work it out. So-
4 minutes for 7 km = 4 : 7
Then ? minutes for 21 km = ? : 21
You first divide the given value by the original value of that it is proportioned to (the number on the same side of the original ratio as 21). In this case divide 21 by 7 = 3. You now have to times the answer you got by the other original value which will be 4 x 3 = 12.
Therefore your answer is 12 minutes.
What is the slope of the line that passes through the points (-3,2) and (6, -9)?
Answer:
-11/9 is the slope
Step-by-step explanation:
Use the formula and u will find this is the answer, hope this helped!
Y2 - Y1 / X2 - X1
(-9 - 2) / (6 - (-3))
<!> Brainliest is appreciated!
Answer:
-11/9
Step-by-step explanation:
In order to find the slope from 2 points, use the following formula: [tex]m=\frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]
Plug in each of the numbers into their corresponding areas. Basically, we are subtracting the y values together and dividing it with the difference of the x values:
[tex]\frac{-9-2}{6-(-3)}[/tex]
The negatives cancel out and become postive, so the denominator will then read to be 6+3:
[tex]\frac{-9-2}{6+3}[/tex]
[tex]-\frac{11}{9}[/tex]
Proofs are used to show that a mathematical statement is true. The most common form of mathematical statements are if-then statements. Give an example of a true mathematical statement and a false mathematical statement in if-then form. For the false statement, include a counterexample showing that the statement isn't true.
Answer:
See explanation
Step-by-step explanation:
True Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{xy}=ab[/tex]
False Mathematical Statement
[tex]\text{If }\sqrt{x}=a$ and \sqrt{y}=b,$ then \sqrt{x+y}=a+b[/tex]
To show using a counterexample that the statement isn't true.
[tex]\text{Let x}=16\\\text{Let y}=9\\\sqrt{16}=4\\\sqrt{9}=3\\\sqrt{16+9}=\sqrt{25}=5\\a+b=3+4=7\\5\neq 7[/tex]
Therefore, the mathematical statement is false.
What is the solution of log3x − 5 16 = 2?
Which pair of quantities is LEAST likely to be directly proportional?
1. Hours worked and money earned
2. Distance and time when speed is constant
3. Area and side length of a square
4. Total cost and the number of hats purchased
Answer:
A
Step-by-step explanation:
Hours worked, probably because of commission or bonuses (the other ones seem to be proportional)
If a football player passes a football from 4 feet off the ground with an initial velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h = −16t2 + 6t + 4. Round your answer to the nearest hundredth.
Answer:
0.723 seconds
Step-by-step explanation:
Let h = 0
0 = -16t² + 6t + 4
Let’s solve by completing the square.
Subtract 4 from both sides.
-4 = -16t² + 6t
Since the coefficient of -16t² is -16, divide both sides by -16.
1/4 = t² - 3/8t
The coefficient of (-3)/8t is (-3)/8. Let b=(-3)/8.
Then we need to add (b/2)² = 9/256 to both sides to complete the square.
Add 9/256 to both sides.
73/256 = t² - 3/8t + 9/256
Factor right side.
73/255 = (t-3/16)²
Take the square root on both sides.
±√(73/255) = t-3/16
Add 3/16 to both sides.
3/16 ± √(73/255) = t
The answer has to be positive, not negative.
0.72254626884 = t
0.723 ≈ t
Answer:
Rounding to the nearest hundredth, it is 0.72
Select the correct answer.
Use the power of a product property to answer the question.
Which expression equals (
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
(7y) ^ 1/3
We know that (ab) ^c = a^c * b^c
7^1/3 * y^1/3
Answer:
7^1/3 * y^1/3
Step-by-step explanation:
7^1/3 * y^1/3
HELP NOW PLZ 20 POINTS FOR BRAINLIEST Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Step-by-step explanation:
Equation 1: [tex]3x^{2} +7x-6[/tex]
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
Equation 2: -[tex]x^{2}[/tex] + 3x - 6
Equation 2 should represent a parabola that opens down and has a negative y-intercept.
Parabola that opens down = a<0
Ax^2 + Bx + C
-[tex]x^{2}[/tex] + 3x - 6
Negative y-intercept: -(0)^2 +3(0) -6 = y= -6
Strategy to solve: Quadratic formula
Why? - This equation doesn't factor cleanly.
Show your work:
a= -1 b= 3 c= -6
Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Show step, solve.
x= 1.5 + 1.9365i
Equation 3:
Sorry, I can't do this.
Equation 4 :[tex]x^{2} -1[/tex]
You decide.
Alright, easy parabola.
1. Does parabola open up or down. UP
2. Is there a vertical stretch or compression? NO
3. What is the y-intercept- (0,-1)
[tex]x^{2} -1[/tex]
Strategy: Simple factoring patterns (Difference of squares) -
(x+1)(x-1)
x = + 1
Show work: x^2 is square of x,
Equation 5: [tex]x^{2} -3x+15[/tex]
x^2−3x+15
a=1 b= -3 c=15
([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.
D. Is no solution please help
Answer:
B
Step-by-step explanation:
I can't really see the problem, however I believe B is the only one that shows an infinite number of solutions.
Answer:
B
Step-by-step explanation:
It is too blurry BTW but B is correct