Please show work and thank you

Answer:

Paul and Krystal spent 13 hours at the pool

Step-by-step explanation:

I Thank

Answer:

a) -3

b) 9

c) -3

Step-by-step explanation:

a)

[tex]2^5 * 2^{-8} = 2^a[/tex]

In cases where we have a multiplication with exponents we keep the integer as it is and we add the exponents. 5 + -8 = -3. Therefore a is 3.

b)

[tex]\frac{4^7}{4^-{2}} = 4^b[/tex]

In cases when we have a division with exponents we keep the integers as it is and we subtract the exponents. 7 - (-2) = 7 + 2 = 9. Therefore, b is 9

c)

[tex]\frac{7^9}{7^c} = 7^{12}[/tex]

We are dividing again however we are finding the denominator.

9 - (c) = 12

Subtract from both sides: -c = 3, To make c positive we just make the value negative, c = -3. Therefore c is -3

Answer:

[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]

Step-by-step explanation:

I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:

[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]

Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.

Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.

The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

A differential equation is an equation that contains one or more functions with its derivatives.

The given function is four times of cos2x plus logx plus x.

f(x)= 4cos2x + logx + x

We need to find the derivative of it f'(x)

d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

We know that

d/dx(cosx)=-sinx

d/dx(logx)=1/x

d/dx(x)=1

Apply in above equation

f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)

f'(x)=4.2(-sin2x)+1/x+1

f'(x)=-8sin2x+1/x+1

Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.

To learn more on Differentiation click:

https://brainly.com/question/24898810

#SPJ2

The correct answer is option B which is the volume of the prism is 216 km³.

A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.

The volume of the prism will be calculated by using the formula below:-

V  =  Area of the base   x   Height

Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.

V  =  Area of the triangle  x  Height

V  =  ( 1/2 ) x 8 x 6 x ( 9 )

V  =  216 km²

Therefore the correct answer is option B which is the volume of the prism is 216 km³.

To know more about volume follow

https://brainly.com/question/1972490

#SPJ1

The number of each tortilla type that Mathew would need to feed everyone is = 6 packages of Soft tortillas and 5 packages of Crispy taco shells.

The number of people Matthew is expecting including himself = 60

The Soft tortillas coke appear = 10/pack

The Crispy taco shells appear = 12/pack

Since each person is to get 1 soft and 1 crispy taco, the number of tortilla type that Mathew would need to feed everyone is

= 60/10 = 6 packages of Soft tortillas

= 60/12 = 5 packages of Crispy taco shells

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

Answer:

16cm and 48 degrees

Step-by-step explanation:

Answer:

z=4

Step-by-step explanation:

subtract 47-35

3z=12

divide both sides by 3

z=4

Answer:

Yes

Step-by-step explanation:

There is only one output value for each input value, which is the definition of a function.

Answer:

= .75 gallons or 3 quarts

Step-by-step explanation:

Known

Problem:

4 gallons 2 quarts - 3 gallons 3 quarts

⇒ 2 quarts: 0.5 gallons

⇒ 3 quarts: 0.75 gallons

Add on both sides

4 + 0.5 = 4.5 gallons

3 + 0.75 = 3.75 gallons

This leaves the equation at:

This equals 3 quarts or 0.75 gallons.

Answer:

5,125

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

we know the line goes through the origin, so we have point (0,0). next, find another point the line goes through. for example, point (2,4)

the slope formula for points (x1, y1) and (x2, y2) is (y2 - y1) / (x2 - x1). plug in the 2 points to get (4-0)/(2-0) = 4/2 = 2

Answer:

C

Step-by-step explanation:

the explicit formula for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

from the recursive formula in the form

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d

given

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 7

with d = - 7 and a₁ = 4 , then explicit formula is

[tex]a_{n}[/tex] = 4 + (n - 1)(- 7)

Answer:

68 inches

Step-by-step explanation:

y = x + 2

x = 66

y = 66 + 2

y = 68

Answer:

19 is suitable no in which 1 is square of itself and 9 is of 3

Answer:

The answer is C: (2x +3, 2y)

Step-by-step explanation:

When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.

Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.

(x, y) -----> (2x, 2y)

Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.

Translation 2 units right:

(2x, 2y) -----> (2x +3, 2y)

Answer:

[tex]\displaystyle x=-\frac{9}{2},\:x=-4[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36[/tex]

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4[/tex]

The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.

The slope and y-intercept of an equation can be easily found using slope intercept equation.

y = mx + b

where

Therefore,

3x + 2y = 14

2y = -3x + 14

y = -3 / 2 x + 7

Therefore,

slope = - 3 / 2

y-intercept = 7

learn more on slope here: https://brainly.com/question/3605446

#SPJ1

Answer:

2.6 and 2.7

Step-by-step explanation:

The actual square root of 7 is 2.64 and that is between 2.6 and 2.7.

Answer:

a) they are corresponding angles

b) B=55° (proven)

C=55 (Angles opposite equal sides)

B+C+X=180° ( sum of angles of a triangle)

55°+55°X=180

110°+X=180°

X=180°-110°

X=70°

Answer:

B) h=63

Step-by-step explanation:

Multiply both sides by 9.

h/*9=9*7

Simplify

h=63

[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]

Multiply both sides by 9.

Multiply 7 and 9 to get 63.

Therefore, the correct option is "B".

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

c. (x+7)^2+(y-6)^2=50

Step-by-step explanation:

The equation of a circle is; (x+7)²+(y-6)² = 50

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The points on the circle are L(-2, 11) and centre is N(-7, 6)

Find the radius,

D = √(-7+2)²+(6-11))²

D = √25+25

D = √50

We know that, the equation of a circle is given by,

( x − a )² + ( y − b )² = r² , where ( a , b ) represents the centre of the circle,

Here, centre is N(-7, 6)

Therefore, the equation of a circle is;

(x+7)²+(y-6)² = 50

Hence, the required equation is (x+7)²+(y-6)² = 50

For more references on circle, click;

https://brainly.com/question/29142813

#SPJ2

Answer:

9 inches

Step-by-step explanation:

I assume you mean the volume of the box is 450.

In that case, to figure out for the volume we multiply 10 by 5. This gives us 50.

450/50=9

The height of the box is 9 inches

Give brainliest please!

hope this helps :)

Answer:

-2

-1

-2

-3

Step-by-step explanation:

For an odd function, f(-x) = -f(x).

f(2) = 2; f(-2) = -2

f(3) = 1; f(-3) = -1

f(4) = 2; f(-4) = -2

f(6) = 3; f(-6) = -3

Answer:

  (d)  32

Step-by-step explanation:

An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.

__

An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.

We are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.

Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.

The desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.

Ryder's estimate was 32.

_____

Additional comment

The actual product is ...

  (25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).

As a first approximation of the error in the product 32.5, we can sum the middle two terms:

  -0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.

Then the first refinement of the estimate will give us ...

  32.500 -0.276 = 32.224

The actual value is obtained by adding the final error term:

  32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.

Answer:

yo

Step-by-step explanation:

its C, or 20

edge

ur welcome

Applying the Pythagorean theorem, the missing side of the right triangle is: √788.

To find the hypotenuse (c) of a right triangle, having two other legs a and b, the Pythagorean theorem states that, c = √(a² + b²).

Given the following:

Plug in the values

x = √(2² + 28²)

x = √788

Missing side is: √788.

Learn more about the Pythagorean theorem on:

https://brainly.com/question/343682

#SPJ1