A submarine drops at a rate of 16 feet per minute. What is the submarines depth after 4 minutes?

Answer:

Factor 10 into its prime factors

          10 = 2 • 5  

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified

At the end of this step the partly simplified SQRT looks like this:

        sqrt (10p3)  

STEP

2

:

Simplify the Variable part of the SQRT

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

     (3.1) sqrt(x8)=x4

    (3.2) sqrt(x-6)=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     (4.1) sqrt(x5)=x2•sqrt(x)

    (4.2) sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

     SQRT(p3) = p • SQRT(p)  

Combine both simplifications

        sqrt (10p3) =

       p • sqrt(10p)  

Simplified Root :

p • sqrt(10p)

[tex]\text {Hey! Let's Solve this Equation!}[/tex]

[tex]\text {\underline {The First Step is to do Keep Change Change (KCC)}}[/tex]

[tex]\text {Keep: 4.25}\\\text {Change: - into +}\\\text {Change: 2.5x into -2.5x}[/tex]

[tex]\text {\underline {The Next Step is to Flip the Equation}}[/tex]

[tex]\text {Before: 4.25+-2.5x=14.75}\\\text {After: -2.5x+4.25=14.75}[/tex]

[tex]\text {\underline {The Next Step is to Subtract 4.25}}[/tex]

[tex]\text {-2.5x+4.25-4.25=14.75-4.25=10.5}\\\text {-2.5x=10.5}[/tex]

[tex]\text {\underline {The Final Step is to Divide -2.5}}[/tex]

[tex]\text {-2.5x/-2.5=10.5/-2.5}[/tex]

[tex]\text {Remember that Dividing a Positive to a Negative will Equal a Negative.}[/tex]

[tex]\text {Your Answer Would Be:}[/tex]

[tex]\fbox {x=-4.2}[/tex]

[tex]\text {Best of Luck!}[/tex]

Hey there!☺

[tex]Answer:\boxed{x=-4.2}[/tex]

[tex]Explanation:[/tex]

[tex]4.25-2.5x=14.75[/tex]

Let's start by simplifying both sides in the equation.

[tex]4.25+-2.5x=14.75\\-2.5x+4.25=14.75[/tex]

Now we subtract 4.25 from both sides in the equation.

[tex]-2.5x+4.25-4.25=14.75-4.25\\-2.5x=10.5[/tex]

Now in our third/final step, we will divide both sides by -2.5.

[tex]\frac{-2.5x}{-2.5}= \frac{10.5}{-2.5}[/tex]

Now we simplify 10.5/-2.5.

[tex]\frac{10.5}{-2.5}=-4.2[/tex]

[tex]x=-4.2[/tex]

Hope this helps!

Answer:

x^2 -14x+49

Step-by-step explanation:

(x-7) ^2

(x-7)(x-7)

FOIL

first ( x*x) = x^2

outer -7x

inner -7x

last -7*-7 = 49

Add these together

x^2 -7x-7x+49

Combine like terms

x^2 -14x+49

Answer: Function g reflected function f across the x-axis.

For function g, as x approaches negative infinity, g(x) approaches negative infinity.

Function f is symmetrical about the point (4,6).

The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.

Here given that the function g(x)= -(x-4)²+6

vertex of the graph of the function g is

dg/dx=0

⇒2(x-4)=0

⇒x-4=0

⇒x=4

putting x=4 in g(x) , g(4)= -(0-0)²+6=6

Hence the vertex of the graph of g is (4,6).

The parent function is f(x)= x²

here the vertex of the function is (0,0).

Option A: This option is true as the graph of function g is the inverse image of f. So,  Function g is reflected of function f across the x-axis.

Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).

Option C:  This option is true because

 [tex]\lim_{x \to- \infty} g(x)[/tex]

= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]

= -(∞-4)²+6

=-∞²+6

=-∞

Hence as x approaches to the -∞, g approaches to the -∞

Option D. This option is incorrect because

if the function is always decreasing its derivative is negative for all x∈R

dg/dx<0

⇒2(x-4)<0

⇒x-4<0

⇒x<4

so the function is decreasing for x<4 not for all x.

Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6

g(x)>0

⇒-(x-4)²+6 >0

⇒-(x-4)²>-6

⇒(x-4)²<6  

⇒|x-4|<√6

⇒4-√6<x<4+√6

so, g(x) is positive for 4-√6 < x < 4+√6

Option E:
This option is incorrect as g(x) is symmetrical about line x=4.

Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.

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Answer:

Its Graph B

Step-by-step explanation:

I got the quiz correct

The Definition Of a Midpoint says that is B is the

midpoint of segment AC, then segment AB ≅ AC.

Since segment AB ≅ segment BC, we can setup

the equation 2(3x - 1) = 8x - 20 and we can solve from here.

Start by distributing the 3 through the parenthses on the left side.

So we get 6x - 2 = 8x - 20.

Now subtract 8x from both sides to get -2x - 2 = -20.

Now add 2 to both sides and we have -2x = -18.

Finally, dividing both sides by -2, we find that x = 9.

If x = 9, segment BC must be 3(9) - 1 or 27 - 1 which is 26.

Answer:

(4,-9/2)

Step-by-step explanation:

(1+7/2,-6-3/2)

(4,-9/2)

Answer:

=2456

Step-by-step explanation:23456

Answer:

15 i think good luck

Step-by-step explanation:

Answer:

15°

Step-by-step explanation:

m<B: Supplementary: 180°-110°=70°

Triangles have an inner angle of 180°. Using this, you can then do:

180°-70°-(30°+20°)=60°

3x+x=60°

4x=60°

x=15°

Answer:

-25

Step-by-step explanation:

-9r - 7

-9(2) - 7

-18 - 7

-25

Answer:

7/5

Step-by-step explanation:

What is 1.4 in fraction form? 7/5 is the fraction form of 1.4. 1.4 as a Fraction in simplest form to convert 1.4 to a fraction and simplify to the lowest form.

------------

14/10 = 1.4

7 is half of 14

5 is half of 10

The simplest form of given number is  [tex]\frac{7}{5} [/tex].

Given number is, 1.4

Converted into fraction,  [tex]=\frac{14}{10} [/tex]

It is observed that, 2 is common in both numerator and denominator.

               [tex]\frac{14}{10} =\frac{2*7}{2*5}=\frac{7}{5} [/tex]

Hence, The simplest form of given number is  [tex]\frac{7}{5} [/tex].

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Answer:

The slope is -4/3

I hope this helps :)

Answer:

2-30,42

3-15,21

5-5,7

7-1,7

-1,1

LCM of 30 and 42 is 210

Answer:

210

Step-by-step explanation:

30*42 by HCF of 30,42

1260 by 6 =210

Answer:

(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)

Ok, we have a rectangle of length x by r.

At the extremes of length r, we add two semicircles.

So the perimeter will be equal to:

Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).

The radius of the semicircles is r, and the perimeter of a circle is:

C = 2*pi*r

where pi = 3.14

Then the perimeter of the track is:

P = 2*x + 2*pi*r.

b) now we want to solve this for x, this means isolating x in one side of the equation.

P - 2*pi*r = 2*x

P/2 - pi*r = x.

c) now we have:

P = 660ft

r = 50ft

then we can replace the values and find x.

x = 660ft/2 - 3.14*50ft = 173ft

Answer:

f + 6

Step-by-step explanation:

Answer:

Hey there!

-36+7x=76-x

-36+8x=76

112=8x

x=14

Let me know if this helps :)

Answer:

467

Step-by-step explanation:

7 is greater than 5 so the six is rounded to a 7

Hope this helped please mark me brainiest

Answer:

497

Step-by-step explanation:

If x ≥ 5, we round up.

If x < 5, we round down.

Since 7 ≥ 5, we round 496.739386253 to 497.

Answer:

  $108.90

Step-by-step explanation:

James pays 75% of the amount, so he pays ...

  0.75 × $145.20 = $108.90

James' total after the discount is $108.90.

Answer:

1.6g

Step-by-step explanation:

1 cup of tea= 0.8g

2 cups of tea= 0.8g×2= 1.6g

Answer:

-3 >-5

5>-4

Step-by-step explanation:

Negative 3 is closer to zero so that statement is true. Also it's obvious 5 is greater than negative 4

hope this helps. Please mark me brainiest          

Answer:

The indifference point is 500 calls.

Step-by-step explanation:

Giving the following information:

Plan 1 charges ​$32 per month for unlimited calls and Plan 2 charges ​$17 per month plus ​$0.03 per call.

I assume we have to determine the indifference point between the two plans.

First, we need to structure the cost formulas:

Plan 1= 32

Plan 2= 17 + 0.03*x

x= call

Now, we need to equal both formulas:

32 = 17 + 0.03x

15= 0.03x

500= x

The indifference point is 500 calls.

Plan 1= $32

Plan 2= 17 + 0.03*500= $32

Answer:

Step-by-step explanation:

Answer:

D and E are correct

Step-by-step explanation:

Here, we want to select the set of values which could be the values of the sides of triangle z.

What we want here are sets of values which is a direct scale up value of the sets of values of triangle M:

We proceed as follows;

a. 8, 11 and 14.

This cannot be correct

Looking at the values of M, 4,7 and 10; We can see that while 4 and 7 are directly scaled up by factor 2 to give 8 and 14, by correspondence, 10 should be 20 and not 11 as in this case.

B. 10, 7.5 and 25

This cannot be correct too. Looking at the way 4 and 10

are scaled up by a value of 2.5; then the value of 7 should be scaled by 2.5 too, but 2.5 * 7 is not 7.5, so this cannot be correct

C. 6 , 9 and 11

This is not correct. In fact, we cannot identify a pattern between these numbers and their values before scaling up

D 6, 10.5 and 15

This looks correct. We can see that the values of triangle M if multiplied by 1.5 each can give these

4 * 1.5 = 6

7 * 1.5 = 10.5

and 10 * 1.5 = 15

e. 8, 14 and 20

Multiplying the sides of triangle M by 2, we can get these values.

4 * 2 = 8

7 * 2 = 14

and 10 * 2 = 20

The scale up value here is simply 2

Answer:

actually it's B, E, and D. At least that's what I got and it said it was correct.

Step-by-step explanation:

Answer:

the answer should be 0.96

Answer:

the answer for this question is 18

Answer:

The distance between both points is 4√2 units

Step-by-step explanation:

Here in this question, we want to calculate the distance between two given points.

These points are (8,-3) and (4,-7)

Mathematically, the distance between two points can be given as;

D = √(x2-x1)^2 + (y2-y1)^2

where x1 = 4, x2 = 8 , y1 = -7 and y2 = -3

Substituting these values;

D = √(8 -4)^2 + (-3-(-7)^2

D = √(4)^2 + (4)^2

D = √(16+16)

D = √(32)

D = 4√2 units

Answer:

32 Number C

Step-by-step explanation:

Answer:

A=[tex]\frac{-3}{4}[/tex]

Step-by-step explanation:

a−3=a1(5)

Step 1: Simplify both sides of the equation.

a−3=a1(5)

a+−3=5a

a−3=5a

Step 2: Subtract 5a from both sides.

a−3−5a=5a−5a

−4a−3=0

Step 3: Add 3 to both sides.

−4a−3+3=0+3

−4a=3

Step 4: Divide both sides by -4.

-4a/-4 = 3/-4

The total number of classes that were taken by you was 28.

The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question.

Registration fee for the dance class = $15

Amount of money charges for each dance class = $24

Amount of money paid for c number of classes = $687

⇒ [tex]687 = 24c + 15[/tex]

Solve the above linear equation in one variable for c.

[tex]687 = 24c + 15[/tex]

⇒ [tex]687 - 15 = 24c[/tex]

⇒ [tex]672 = 24c[/tex]

⇒ [tex]c = \frac{672}{24}[/tex]

⇒ [tex]c = 28[/tex]

Hence, the number of classes is 28.

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