answers for these? pls

Answers For These? Pls

Answers

Answer 1

Answer:

6a. 13.5m

6b. 12.4m

Step-by-step explanation:

We can use trig identities to solve these problems because each triangle is a right triangle.

6a. Find the measure of the hypotenuse.

Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.

The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.

So we can set up the equation:

cos(x)=adj/hyp

If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.

cos(66)=5.5/c

Then we can multiply by c:

c*cos(66)=5.5

Then divide by cos(66):

c=5.5/cos(66)

Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

6b. Find the measure of side a.

Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.

Method 1: Use trig identity tan(x)tan(x)=opp/adj

Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:

tan(66)=a/5.5

Multiply both sides by 5.5:

a=tan(66)*5.5

Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):

Use Pythagorean Theorem:

a^2+b^2=c^2

c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:

a^2+5.5^2=13.5^2

a^2+30.25=182.25

a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.


Related Questions

will give brainly .Which statements are true regarding undefinable terms in geometry? Check all that apply.


A point has no length or width.

A point indicates a location in a coordinate plane.

A plane has one dimension, length.

A line has a definite beginning and end.

A plane consists of an infinite set of lines.

A line consists of an infinite set of points.

Answers

The true statements about terms in geometry that are undefinable are;

A point has no length or widthA point indicates a location on the coordinate planeA line consists of an infinite set of points.A plane consists of an infinite set of points.

How can the true statements be found?

Three undefinable terms in geometry are;

1) Point

2) Line

3) Plane

The above terms do not have a formal definition but they can be described based on their properties.

The other geometric terms are defined based on the above undefinable terms.

A point can be described as a location in space that is dimensionless and can be specified on the coordinate plane as an ordered pairs (x, y).

True statements about a point are therefore;

A point has no length or widthA point indicates a location on the coordinate plane

A line is infinitely long, that has no beginning or end. It has one dimension, with no thickness or height.

Given that a point is dimensionless, a line can be considered a set of points.

A true statement is therefore;

A line consists of an infinite set of points.

A plane is a two dimensional geometric figure that have infinite length and width.

An infinite set of lines that forms a two dimensional figure can be used to describe a plane.

The true statement with regards to a plane is therefore;

A plane consists of an infinite set of points.

Learn more about undefinable terms in geometry here:

https://brainly.com/question/1706041

#SPJ1

Suppose f(x) and g(x) are differentiable functions satisfying f(1) = f′(1) = 2. Let
h(x) = g(f(x)) − g(2x). Determine whether h′(1) > 1

Answers

Answer:

1777777777888876332222233

Simplify the following
Answer is 6​

Answers

Firstly changing mixed fraction.

[tex] \frac{3}{2} - \frac{5}{4} + \frac{23}{4} [/tex]

By taking the LCM

[tex] \frac{6 - 5 + 23}{4} [/tex]

-5 + 23 (-) (+) = (-)

[tex] \frac{6 + 18}{4} [/tex]

[tex] \frac{24}{4} [/tex]

[tex]6[/tex]

Hope it helps you, any confusions you may ask!

Answer:

6 (work below)

Step-by-step explanation:

1 1/2 = 3/2

1 1/4 = 5/4

5 3/4 = 23/4

The least common multiple of the denominators is 4, so 3/2 will become 6/4.

6/4 - 5/4 = 1/4 + 23/4 = 24/4 = 6

Brainliest, please :)

could anyone help me with this?

Answers

Answer:

Step-by-step explanation:

A=6x²

[tex]\frac{dA}{dt} =6\times 2x \times \frac{dx}{dt} \\\frac{dA}{dt}=12x \frac{dx}{dt}[/tex]

Suppose f(x)=2^x. What is the graph of g(x)=1/3f(x)?

Answers

Please see the blue curve of the image attached below to know the graph of the function g(x) = (1/3) · 2ˣ.

How to graph a transformed function

Herein we have an original function f(x). The transformed function g(x) is the result of compressing f(x) by 1/3. Then, we find that g(x) = (1/3) · 2ˣ. Lastly, we graph both function on a Cartesian plane with the help of a graphing tool.

The result is attached below. Please notice that the original function f(x) is represented by the red curve, while the transformed function g(x) is represented by the blue curve.

To learn more on functions: https://brainly.com/question/12431044

#SPJ1

What is the solution to the following system of equations?
x-3y=6
2x + 2y = 4
(-1,3)
(3,-1)
(1, -3)
(-3,1)

Answers

Answer:

  (b)  (3,-1)

Step-by-step explanation:

One can determine the correct answer by checking to see if it satisfies the equations.

Checking

The first equation can be rewritten to ...

  x = 6 +3y . . . . . . . add 3y to both sides

This makes it easier to check answer choices:

  a) -1 = 6 +3(3) . . . . no

  b) 3 = 6 +3(-1) . . . . yes . . . . . (3, -1) is the solution

  c) 1 = 6 +3(-3) . . . . no

  d) -3 = 6 +3(1) . . . . no

__

Additional comment

We can further convince ourselves this is the correct choice by seeing if it satisfies the second equation:

  2x +2y = 4 . . . for (x, y) = (3, -1)

  2(3) +2(-1) = 4 . . . . yes

A candy shop sells a box of chocolates for $30. It has $29 worth of chocolates plus $1 for the box. The box includes two kinds of candy: caramels and truffles. Lita knows how much the different types of candies cost per pound and how many pounds are in a box. She said,
If x is the number of pounds of caramels included in the box and y is the number of pounds of truffles in the box, then I can write the following equations based on what I know about one of these boxes:

x + y = 3
8x + 12y + 1 = 30

Assuming Lita used the information given and her other knowledge of the candies, use her equations to answer the following:

How many pounds of candy are in the box?

What is the price per pound of the caramels

What does the term 12y in the second equation represent?

What does 8x + 12y + 1 in the second equation represent?

Answers

Answer:

There are 3 lbs of candy in the box.

The caramels are $8 per pound.

12y represents the total cost of truffles in the box.

8x + 12y + 1 represents the cost of caramels in the box + the cost of truffles in the box + the cost of the box.

Step-by-step explanation:

x = the number of pounds of caramels

y = the number of pounds of truffles

x + y = total lbs. and we know x + y = 3

We know x is the number of pounds of caramels.

8x = (cost per pound of caramels) × (number of pounds of caramels)

So 8 = cost of caramels

We know y = number of pounds of truffles. So 12 is the cost of truffles by pound, and 12y is the total cost of truffles in the box.

Based on all the above,

The cost of caramels in the box + the cost of truffles in the box + the cost of the box is = total cost of the box. 8x + 12y + 1 = 30


Given the functions a(x) = 3x - 12 and b(x) = x-9, solve a[b(x)].

Oa[b(x)] = 3x²-21

O a[b(x)] = 3x² - 39

Oa[b(x)] = 3x - 21

Oa[b(x)] = 3x - 39

Answers

Answer:

Step-by-step explanation:

hello :

a(x) = 3x - 12 and b(x) = x-9, so

a[b(x)]=a(x-9) =3(x-9)-12

a[b(x)]=3x-9-12

a[b(x)]=3x+21

Evaluate the sum (for math nerds)
[tex]i {}^{0!} + i {}^{1!} + i {}^{2!} + i {}^{3!} + ... + i {}^{100!} [/tex]
Note that :
[tex]i = \sqrt[]{ - 1} [/tex]

Answers

Answer: i+96

Step-by-step explanation:

Note that [tex]i^{4k}[/tex], where k is an integer, is equal to 1.

This means that [tex]i^{4!}=i^{5!}=i^{6}=\cdots=i^{99!}+i^{100!}=1[/tex]

So, we can rewrite the sum as [tex]i^{1}+i^{1}+i^{2}+i^3+97(1)=i+i-1-i+97=i+96[/tex]

[tex]n![/tex] is divisible by 4 for all [tex]n\ge4[/tex]. This means, for instance,

[tex]i^{4!} = \left(i^4\right)^{3!} = 1^{3!} = 1[/tex]

[tex]i^{5!} = \left(i^4\right)^{5\times3!} = 1^{5\times3!} = 1[/tex]

etc, so that [tex]i^{n!} = 1[/tex] for all [tex]n\ge4[/tex].

Meanwhile,

[tex]i^{0!} = i^1 = i[/tex]

[tex]i^{1!} = i^1 = i[/tex]

[tex]i^{2!} = i^2 = -1[/tex]

[tex]i^{3!} = i^6 = (-1)^3 = -1[/tex]

Then the sum we want is

[tex]i^{0!} + i^{1!} + i^{2!} + i^{3!} + 97\times1 = i + i - 1 - 1 + 97 = \boxed{95+2i}[/tex]

To the nearest percent how much greater is 8 than 6

Answers

The percent greater of 8 than 6 to the nearest percent is 25%

Percentage

Percent greater = difference / higher chance value × 100

= 2/8 × 100

= 0.25 × 100

Percent greater = 25%

Therefore, the percent greater of 8 than 6 to the nearest percent is 25%

Learn more about percentage:

https://brainly.com/question/843074

#SPJ1

i don’t understand!!!

Answers

Answer:  12/13

In other words, 12 goes in the top box and 13 goes in the bottom. The fraction slash sign is not part of either box.

===========================================================

Explanation:

Cosine is the ratio of adjacent over hypotenuse.

cos(angle) = adjacent/hypotenuse

For the reference angle X, the adjacent leg is 36 units long. It's the leg closest or touching angle X.

The hypotenuse is always the longest side. It is always opposite the 90 degree angle. The hypotenuse in this case is 39 units.

Therefore,

cos(X) = 36/39 = (12*3)/(13*3) = 12/13

Alan is building a garden shaped like a rectangle with a semicircle attached to one short side. If he has 70 feet of fencing to go around​ it, what dimensions will give him the maximum area in the​ garden? Round the answers to the nearest tenth.

Answers

The dimension that would give the maximum area is 20.8569

How to solve for the maximum area

Let the shorter side be = x

Perimeter of the semi-circle is πx

Twice the Length of the longer side

[tex][70-(\pi )x -x][/tex]

Length = [tex][70-(1+\pi )x]/2[/tex]

Total area =

area of rectangle + area of the semi-circle.

Total area =

[tex]x[[70-(1+\pi )x]/2] + [(\pi )(x/2)^2]/2[/tex]

When we square it we would have

[tex]70x +[(\pi /4)-(1+\pi)]x^2[/tex]

This gives

[tex]70x - [3.3562]x^2[/tex]

From here we divide by 2

[tex]35x - 1.6781x^2[/tex]

The maximum side would be at

[tex]x = 35/2*1.6781[/tex]

This gives us 20.8569

Read more on areas and dimensions here:

https://brainly.com/question/19819849

#SPJ1

Write these decimals in order from smallest to largest: 0.507, 0.75, 0.5, 0.078

Answers

0.078, 0.5, 0.507, 0.75.

Hope it helps ; )
0.078, 0.5, 0.507, 0.75

Suppose you have $1500 in your savings account at the end of a certain period of time. You invested $1000 at a 2.71% simple annual interest rate. How long, in years, was your money invested? State your result to the nearest hundredth of a year.

Answers

The time taken in years for money invested to accumulate to $1500 is 18.45 years

Simple interestPrincipal = $1000Interest rate = 2.71% = 0.0271t = ?

Simple interest = Total savings - principal

= 1500 - 1000

= $500

Simple interest = principal × rate × time

500 = 1000 × 0.0271 × t

500 = 27.1 × t

500 = 27.1t

t = 18.4501845018450

Approximately,

t = 18.45 years

Learn more about simple interest:

https://brainly.com/question/20690803

#SPJ1

What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?

What point is 2/3 of the distance from point A(3, 1) to point B(3, 19)?

(3, 13)

(9/3, 13)

(2, 12)

(3, 19)

Answers

Answer: (3, 13)

Step-by-step explanation:

If we let the point be P, then AP:BP=2:1.

[tex]P=\left(\frac{(2)(3)+(1)(3)}{2+1}, \frac{(2)(19)+(1)(1)}{2+1} \right)=(3, 13)[/tex]

What is the volume of the cylinder?

Answers

The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The volume of a cylinder with radius (r) and height (h) is:

Volume = πr²h

Given that h = 10 ft, r = 16/2 = 8 ft

The volume = π * 8² * 10 = 2010.62 ft³

The volume of a cylinder with a diameter of 16 feet and height of 10 feet is 2010.62 ft³

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

inverse function of f(x)=x-7/x+4

Answers

Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7

as part of a competition, diego must spin around in a circle 6 times and then run to a tree. the time he spends on each spin is represented by S AND THE TIME HE SPEND RUNNING is R. He gets to the tree 21 seconds after he starts spinning. If it takes diego 1.2 seconds to spin around each time, how many seconds did he spend running

Answers

The time he spent running is 13.80 seconds.

How much time did he spend running?

The equation that can be used to represent the time he gets to the tree is:

Time he gets to the tree = (time of each spin x total spins) + time he spent running

21 = (6 x 1.2) + r

21 = 7.20 + r

r = 21 - 7.20

r = 13.80 seconds

To learn more about mathematical equations, please check: https://brainly.com/question/26427570

#SPJ1

A random variable X has a gamma density function with parameters α= 8 and β = 2.
Without making any assumptions, derive the moment generating function of X and use to
determine the mean and variance of X.

Answers

I know you said "without making any assumptions," but this one is pretty important. Assuming you mean [tex]\alpha,\beta[/tex] are shape/rate parameters (as opposed to shape/scale), the PDF of [tex]X[/tex] is

[tex]f_X(x) = \dfrac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha - 1} e^{-\beta x} = \dfrac{2^8}{\Gamma(8)} x^7 e^{-2x}[/tex]

if [tex]x>0[/tex], and 0 otherwise.

The MGF of [tex]X[/tex] is given by

[tex]\displaystyle M_X(t) = \Bbb E\left[e^{tX}\right] = \int_{-\infty}^\infty e^{tx} f_X(x) \, dx = \frac{2^8}{\Gamma(8)} \int_0^\infty x^7 e^{(t-2) x} \, dx[/tex]

Note that the integral converges only when [tex]t<2[/tex].

Define

[tex]I_n = \displaystyle \int_0^\infty x^n e^{(t-2)x} \, dx[/tex]

Integrate by parts, with

[tex]u = x^n \implies du = nx^{n-1} \, dx[/tex]

[tex]dv = e^{(t-2)x} \, dx \implies v = \dfrac1{t-2} e^{(t-2)x}[/tex]

so that

[tex]\displaystyle I_n = uv\bigg|_{x=0}^{x\to\infty} - \int_0^\infty v\,du = -\frac n{t-2} \int_0^\infty x^{n-1} e^{(t-2)x} \, dx = -\frac n{t-2} I_{n-1}[/tex]

Note that

[tex]I_0 = \displaystyle \int_0^\infty e^{(t-2)}x \, dx = \frac1{t-2} e^{(t-2)x} \bigg|_{x=0}^{x\to\infty} = -\frac1{t-2}[/tex]

By substitution, we have

[tex]I_n = -\dfrac n{t-2} I_{n-1} = (-1)^2 \dfrac{n(n-1)}{(t-2)^2} I_{n-2} = (-1)^3 \dfrac{n(n-1)(n-2)}{(t-2)^3} I_{n-3}[/tex]

and so on, down to

[tex]I_n = (-1)^n \dfrac{n!}{(t-2)^n} I_0 = (-1)^{n+1} \dfrac{n!}{(t-2)^{n+1}}[/tex]

The integral of interest then evaluates to

[tex]\displaystyle I_7 = \int_0^\infty x^7 e^{(t-2) x} \, dx = (-1)^8 \frac{7!}{(t-2)^8} = \dfrac{\Gamma(8)}{(t-2)^8}[/tex]

so the MGF is

[tex]\displaystyle M_X(t) = \frac{2^8}{\Gamma(8)} I_7 = \dfrac{2^8}{(t-2)^8} = \left(\dfrac2{t-2}\right)^8 = \boxed{\dfrac1{\left(1-\frac t2\right)^8}}[/tex]

The first moment/expectation is given by the first derivative of [tex]M_X(t)[/tex] at [tex]t=0[/tex].

[tex]\Bbb E[X] = M_x'(0) = \dfrac{8\times\frac12}{\left(1-\frac t2\right)^9}\bigg|_{t=0} = \boxed{4}[/tex]

Variance is defined by

[tex]\Bbb V[X] = \Bbb E\left[(X - \Bbb E[X])^2\right] = \Bbb E[X^2] - \Bbb E[X]^2[/tex]

The second moment is given by the second derivative of the MGF at [tex]t=0[/tex].

[tex]\Bbb E[X^2] = M_x''(0) = \dfrac{8\times9\times\frac1{2^2}}{\left(1-\frac t2\right)^{10}} = 18[/tex]

Then the variance is

[tex]\Bbb V[X] = 18 - 4^2 = \boxed{2}[/tex]

Note that the power series expansion of the MGF is rather easy to find. Its Maclaurin series is

[tex]M_X(t) = \displaystyle \sum_{k=0}^\infty \dfrac{M_X^{(k)}(0)}{k!} t^k[/tex]

where [tex]M_X^{(k)}(0)[/tex] is the [tex]k[/tex]-derivative of the MGF evaluated at [tex]t=0[/tex]. This is also the [tex]k[/tex]-th moment of [tex]X[/tex].

Recall that for [tex]|t|<1[/tex],

[tex]\displaystyle \frac1{1-t} = \sum_{k=0}^\infty t^k[/tex]

By differentiating both sides 7 times, we get

[tex]\displaystyle \frac{7!}{(1-t)^8} = \sum_{k=0}^\infty (k+1)(k+2)\cdots(k+7) t^k \implies \displaystyle \frac1{\left(1-\frac t2\right)^8} = \sum_{k=0}^\infty \frac{(k+7)!}{k!\,7!\,2^k} t^k[/tex]

Then the [tex]k[/tex]-th moment of [tex]X[/tex] is

[tex]M_X^{(k)}(0) = \dfrac{(k+7)!}{7!\,2^k}[/tex]

and we obtain the same results as before,

[tex]\Bbb E[X] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=1} = 4[/tex]

[tex]\Bbb E[X^2] = \dfrac{(k+7)!}{7!\,2^k}\bigg|_{k=2} = 18[/tex]

and the same variance follows.

in triangle ABC, AC=13, BC=84, and AB=85. find the measure of angle C.

Answers

The sides all satisfy the Pythagorean Theorem so it is a right triangle. I attached an image of how the triangle should look like and as you can see, the angle is 90 degrees or pi/2 radians.

in triangle ABC, AC=13, BC=84, and AB=85.  the measure of angle is C.5.1 degrees,

How can the angle be found?

Using the The Law of Cosines in any triangle which can be expressed as;

[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]

Then if we expressed the given sides in the cosine formula we have

[tex]13^2 = 85^2 + 84^2 - 2 * 85 * 84 * cos(C)[/tex]

Then we have [tex]169 = 7225 + 7056 - 14280 * cos(C)[/tex]

[tex]14280 * cosC = (7225 + 7056 - 169)[/tex]

[tex]cosC = \frac{14212}{ 14280}[/tex]

cos 0.9947

[tex]C = cos^-1(0.9947)[/tex]

C = 5.1 degrees

Learn more about angle at;

https://brainly.com/question/25716982

#SPJ2

Complete the equations to solve 1{,}860 \div61,860÷61, comma, 860, divided by, 6.
\phantom{=}\greenD{1{,}860}\div{\blueD6}=1,860÷6empty space, start color #1fab54, 1, comma, 860, end color #1fab54, divided by, start color #11accd, 6, end color #11accd
=(\greenD{1{,}800}\div\,=(1,800÷equals, left parenthesis, start color #1fab54, 1, comma, 800, end color #1fab54, divided by
) \, + \,(\greenD{60}\div\,)+(60÷right parenthesis, plus, left parenthesis, start color #1fab54, 60, end color #1fab54, divided by
))right parenthesis
= 300 +=300+equals, 300, plus
==equals

Answers

The division of the figure based on the information is 14.09.

How to illustrate the information?

It should be noted that the question is simply to divide 860 by 61.

The division based on the information will be illustrated thus:

= 860 ÷ 61

= 14.09

In conclusion, the correct option is 14.09.

Learn more about division on:

brainly.com/question/1622425

#SPJ1

3 5/6 + 2 4/9 in its simplest form

Answers

Answer:

>>   [tex]6\frac{5}{18}[/tex]

Step-by-step explanation:

1) Add the whole numbers first.

[tex]5+\frac{5}{6} +\frac{4}{9}[/tex]

2) Find the Least Common Denominator (LCD) of [tex]\frac{5}{6} ,\frac{4}{9}[/tex] . In other words, find the Least Common Multiple (LCM) of [tex]6,9[/tex].

Method 1: By Listing Multiples

1. List the multiples of each number.

Multiples of 6 : 6, 12, 18, ...

Multiples of 9 : 9, 18, ...

2. Find the smallest number that is shared by all rows above. This is the LCM.

LCM = 18

3. Make the denominators the same as the LCD.

[tex]5+\frac{5\times 3}{6\times 3}+\frac{4\times 2}{9\times 2}[/tex]

4. Simplify. Denominators are now the same.

[tex]5+\frac{15}{18}+\frac{8}{18}[/tex]

5.  Join the denominators.

[tex]5+\frac{15+8}{18}[/tex]

6. Simplify.

[tex]5+\frac{23}{18}[/tex]

7. Convert [tex]\frac{23}{18}[/tex] to mixed fraction.

[tex]5+1\frac{5}{18}[/tex]

8. Simplify.

[tex]6\frac{5}{18}[/tex]

Decimal Form: 6.277778

Cheers.

The addition of 3 5/6 + 2 4/9  is 113/18

What is fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

3 5/6 + 2 4/9

Now, writing it into normal fraction

3 5/6 + 2 4/9

= 23/ 6 + 22/9

= 23/6 x 3/3 + 22/9 x 2/2

= 69/ 18 + 44/18

= 113/18

Hence, the addition is 113/18

Learn more about fraction here:

https://brainly.com/question/10354322

#SPJ5

Which expression is equivalent to
xay
8
700
8√√√x
y
8√√y
Mark this and return
128x56
√ 2x75
? Assume x > 0 and y> 0.
Save and Exit

Answers

The equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex]

Divide 128 by 2

[tex]\sqrt{\frac{64x^5y^6}{x^7y^5}}[/tex]

Apply the law of indices to the variables

[tex]\sqrt{\frac{64y^{6-5}}{x^{7-5}}}[/tex]

Evaluate the differences

[tex]\sqrt{\frac{64y}{x^2}}[/tex]

Take the square root of 64

[tex]8\sqrt{\frac{y}{x^2}}[/tex]

Take the square root of x^2

[tex]\frac{8\sqrt y}{x}[/tex]

Hence, the equivalent expression of [tex]\sqrt{\frac{128x^5y^6}{2x^7y^5}}[/tex] is [tex]\frac{8\sqrt y}{x}[/tex]

Read more about equivalent expression at:

https://brainly.com/question/2972832

#SPJ1

Please look at the attachment and answer my question :(

Answers

Answer:

AB / BC = 2 / 3

A equals 9 and C = 13

AC = 13 - 9 = 4

AB + BC = 13

A) AB + BC = 4

B) AB / BC = 2/3   Therefore BC = AB / (2/3)  

B) BC = 1.5 AB  

A) BC = 4 - A/B

Multiplying equation A) by -1

A) -BC = -4 + AB then we add equation B)

B) BC = 1.5 AB then adding both equations

0 = 2.5 AB -4

2.5 AB = 4

AB = 1.6

Since A = 9 then the number at B is 9 + 1.6

equals 10.6

Step-by-step explanation:

Answer:

The number at B is 10.6

Step-by-step explanation:

Let the number at B be x.

We know that distance between two points on the number line is the absolute value of the difference of numbers at those points.

Then distances representing the lengths of segments AB and BC are:

AB = x - 9BC = 13 - x

We are given the ratio of segments:

AB/BC = 2/3

Substitute and solve for x:

(x - 9)/(13 - x) = 2/33(x - 9) = 2(13 - x)3x - 27 = 26 - 2x3x + 2x = 26 + 275x = 53x = 53/5x = 10.6

Solve [tex]2 cosx=4cosx sin^2x[/tex]

Answers

There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

How to solve a trigonometric equation

In this problem we must simplify the trigonometric equation by both algebraic and trigonometric means and clear the variable x:

2 · cos x = 4 · cos x · sin² x

2 · sin² x = 1

sin² x = 1/2

sin x = ± √2 /2

There are several solutions:

x₁ = π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₂ = 3π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₃ = 5π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex]

There are four solutions for the trigonometric equation 2 · cos x = 4 · cos x · sin² x are x₁ = π/4 ± 2π · i, x₂ = 3π/4 ± 2π · i, x₃ = 5π/4 ± 2π · i and x₄ = 7π/4 ± 2π · i, [tex]i \in \mathbb{N}_{O}[/tex].

To learn more on trigonometric equations: https://brainly.com/question/27821667

#SPJ1

A particle travels so that its distance D (in metres) from its origin O is modelled by the equation D = 24 + 15t - [tex]\frac{t^{2} }{2}[/tex], where t is the time in minutes after the particle has started to move.

a. calculate the particle's distance from O when it first started to move.

b. determine the time when the particle first reaches O. Give your answer to 2 decimal places.

c. determine the particle's speed when it has been moving for 3 minutes. Give your answer in m [tex]S^{-1}[/tex]

Answers

(a) The particle's distance from O when it first started to move is 24 m.

(b) The time when the particle first reaches O is 15 mins.

(c) The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

Particle's distance from O when it first started to move

D = 24 + 15 - t²/2

when the time, t  = 0

D = 24 m

When the object first reaches O

When the object reaches O, its final velocity, v = 0

v = dD/dt

v = 15 - t

0 = 15 - t

t = 15 mins

Speed of the particle after 3 minutes

v = 15 - t

v = 15 - 3

v = 12 m/min

v = 12 m/min x 1min/60s = 0.2 m/s

Thus, the particle's distance from O when it first started to move is 24 m.

The time when the particle first reaches O is 15 mins.

The particle's speed when it has been moving for 3 minutes is 0.2 m/s.

Learn more about speed here: https://brainly.com/question/6504879

#SPJ1

a 300-acre farm produced 20,000 bushels of corn last year. what is the minimum rate of production, in bushels per acre, that is needed this year, so the farm's two-year production total will be at least 49,100 bushels of corn?

Answers

The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.

How to calculate the minimum production rate?

To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.

49,100 - 20,000 = 29,100

Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.

29,100 ÷ 300 = 97

According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.

Learn more about production rate in: https://brainly.com/question/15043824

#SPJ1

look at the pictures​

Answers

The key feature that the function of f(x) and g(x) has in common is the domain.

What is the domain and range of a function?

The domain of a function is the set of input or argument values for which the function is valid and well defined. The range is the set of the dependent variable for which a function is defined.

From the given information, we are to find the domain, range, x-intercept, and, y-intercept of the given equation:

[tex]\mathbf{f(x) = -4^x+5}[/tex]

[tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

For [tex]\mathbf{f(x) = -4^x+5}[/tex];

The domain of a function [tex]\mathbf{-4^x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

The range f(x) < 5. The x-intercepts, when y is zero = [tex]\mathbf{(\dfrac{In(5)}{2In(2)},0)}[/tex]The y-intercepts; when x is zero = (0,4)

For [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex]

The domain of a function [tex]\mathbf{g(x) = x^3 +x^2 -4x+5}[/tex] has no undefined points or constraints. Thus, the domain is -∞ < x < ∞.

The range  -∞ < f(x) < ∞. The x-intercepts, when y is zero = (-2.939, 0)The y-intercepts; when x is zero = (0,5)

Learn more about the domain and range of a function here;

https://brainly.com/question/26098895

#SPJ1

Hi I would like to know how I can solve this problem.

Answers

The [tex]n[/tex]-th term is

[tex]U_n = \dfrac14 n^2 (n+1)^2[/tex]

so the 39th term is

[tex]U_{39} = \dfrac14 39^2 40^2 = \boxed{608,400}[/tex]

Observe that

[tex]2^3 + 4^3 + 6^3 = 2^3 + 2^3\times2^3 + 2^3\times3^3 = 8\left(1^3+2^3+3^3)[/tex]

which suggests that

[tex]V_n = 8U_n = \boxed{2n^2(n+1)^2}[/tex]


The lengths of the sides of the right triangle above are a, 3, and c. What is a in terms of c?

Answers

The expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

Pythagorean theorem

From the question, we are to determine the expression for a in terms of c

In the given right triangle, we can write that

[tex]c^{2} = a^{2} +3^{2}[/tex] (Pythagorean theorem)

Thus,

[tex]c^{2} = a^{2} +9[/tex]

[tex]a^{2}= c^{2} -9[/tex]

[tex]a^{2}= \sqrt{c^{2} -9}[/tex]

Hence, the expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

Learn more on Pythagorean theorem here: https://brainly.com/question/23994492

#SPJ1

Other Questions
Which of the following is commutative for rational numbers Class 8?subtraction and divisionmultiplication and divisionaddition and subtractionaddition and multiplication rights of merchandising The answers please I need them fast Which statement is an ineffective claim? Civics education is beneficial to America's youth. Screen time has detrimental effects on children's brain development. The voting age should be lowered for three clear reasons. The United States should increase spending for cancer research. 1. A complete income statement potentially has the following sections: (1 point)a. Items from continuing operations and earnings per share for a corporation.b. Income or loss from operating a discontinued segment for the current period.c. The loss from disposing of the discontinued segment's net assets.d. Extraordinary items.e. Continuing operations, discontinued segments, extraordinary items, changes in accounting principles, and earnings per share for a corporation. Due to covid-19 pandemic, the number of available seats in a hall was reduced from 125 to 93. Calculate the percentage decrease in the number of available seats. x+y=3x^2+y^2=17Solve the simultaneous equations please help please due soon ty sm easy! Use the Taylor rule to predict the Fed funds rate in each of the following situations.a. Inflation is 2 percent, the inflation target is 5 percent, and output is 2 percent below potential.Instructions: Round your answer to 1 decimal place.percent.b. Inflation is 5 percent, the inflation target is 2 percent, and output is 2 percent above potential.Instructions: Round your answer to 1 decimal place.percent.c. Inflation is 5 percent, the inflation target is 2 percent, and output is 2 percent below potential.Instructions: Round your answer to 1 decimal place.percent. What is the third section in An Occurrence at Owl Creek Bridge? It takes approximately 3.7*10^4 hours for the light in Proxima Centauri, the next closest star to our son, to reach us from there. The speed of light is 6.71 *10^8 miles per hour. What is the distance from there to earth? Given distance = rate x time. Express your answer in scientific notation. Help please for this geo Mixed crop and livestock farming. Describe the irony between the amount of land devoted to crops vs animals and the income generated by each in this region? which one do i chooose? When marginal revenue is maximum marginal revenue is also maximum? Can someone help me please? thank you. If f(x) is divided by x-2 what is the remainder? Expand 3(t - 2). (Simplify your answer.) Two sides of a triangle each measure 8 inches. Maria says the triangle must be isosceles. Is maria correct? explain. Which of the following web sites is most likely to be a credible source for a research paper about the migratory patterns of bald eagles?