A diver descended at a rate of 18 feet per second. What was her depth after one minute?

Answer:

2 real roots

2 imaginary roots

Step-by-step explanation:

So we have the function:

[tex]f(x)=x^4-15x^2-16[/tex]

And we want to find its zeros.

First, let u equal x². So:

[tex]0=u^2-15u-16[/tex]

Factor:

[tex]0=(u-16)(u+1)[/tex]

Zero Product Property:

[tex]u-16=0\text{ or }u+1=0[/tex]

Add 16; Subtract 1. Replace u:

[tex]x^2=16\text{ or }x^2=-1[/tex]

Take the square root:

[tex]x=\pm 4\text{ or }x=\pm i[/tex]

So, our solutions are 2 real roots and 2 imaginary roots.

Answer:

18x+9=9y

Step-by-step explanation:

16x+9=9y-2x

+2x         +2x

18x+9=9y

Answer:

please see explanation below

Step-by-step explanation:

Let's solve for x.

16x+9=9y−2x

Step 1: Add 2x to both sides.

16x+9+2x=−2x+9y+2x

18x+9=9y

Step 2: Add -9 to both sides.

18x+9+−9=9y+−9

18x=9y−9

Step 3: Divide both sides by 18.

18x /18 = 9y−9 /18

x= 1 /2y+ (−1 /2)

Answer:

1/2y+(-1/2)

OR

Let's solve for y.

16x+9=9y−2x

Step 1: Flip the equation.

−2x+9y=16x+9

Step 2: Add 2x to both sides.

−2x+9y+2x=16x+9+2x

9y=18x+9

Step 3: Divide both sides by 9.

9y /9 = 18x+9 /9

y=2x+1

Answer:

y=2x+1

HOPE THIS HELPS!!!!!! :)

<3333333333

Answer:

$50.4

Step-by-step explanation:

Cost = $28

Mark up = 80%

Sale price is:

Answer:

[tex]x^2+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C[/tex]

Step-by-step explanation:

Given the integrand [tex]\int\limits{\dfrac{2x^3 - 2x + 1}{x^2-2x} } \, dx[/tex], before evaluating the integral function, we will need to simplify the function first by applying long division as shown in the attachment.

Hence the partial form of the function [tex]\dfrac{2x^3 - 2x + 1}{x^2-2x} } = 2x+4 + \frac{6x+1}{x^2-2x}[/tex]

Integrating its partial sum

[tex]\int\limits \dfrac{2x^3 - 2x + 1}{x^2-2x} }dx = \int\limits (2x+4 + \frac{6x+1}{x^2-2x})\ dx\\\\= \int\limits {2x} \, dx + \int\limits {4} \, dx + \int\limits {\frac{6x+1}{x^2-2x} \, dx\\ = \frac{2x^2}{2}+4x -\frac{1}{2} \int\limits{\frac{1}{x} } \, dx + \frac{2}{13} \int\limits{\frac{1}{x-2} } \, dx[/tex]

[tex]= \frac{2x^2}{2}+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C[/tex]

[tex]= x^2+4x -\frac{1}{2} lnx + \frac{2}{13} ln(x-2) + C[/tex]

NB: Find the partial sum calculation also in the attachment.

Answer:

-12r^2 + 89r - 145

Step-by-step explanation:

(2r(2)−16r+29)(r−5)

=(2r(2)+−16r+29)(r+−5)

=(2r(2))(r)+(2r(2))(−5)+(−16r)(r)+(−16r)(−5)+(29)(r)+(29)(−5)

=4r2−20r−16r2+80r+29r−145

=−12r2+89r−145

Answer:

C

Step-by-step explanation:

Recall the exponent property that:

[tex]x^{\frac{1}{n}}=\sqrt[n]{x}[/tex]

And vice versa:

[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]

Thus:

[tex]\sqrt[3]{500} =(500)^{\frac{1}{3}}[/tex]

The answer is C

Answer:

[tex]\Huge \boxed{500^{\frac{1}{3} }}[/tex]

Step-by-step explanation:

Applying rule : [tex]\displaystyle \sqrt[n]{x} =x^{\frac{1}{n} }[/tex]

[tex]\displaystyle \sqrt[3]{500} =500^{\frac{1}{3} }[/tex]

Answer:

-6-4=4x-2x

10=2x

x=2÷10

x=5

There are 2 solutions with absolute value equations.

1. |2x-6| = 4x+4

Remove absolute value:

2x-6 =4x + 4

Subtract 4x from both sides:

-2x -6 = 4

Add 6 to both sides:

-2x = 10

Divide both sides by -2:

X = -5

2nd solution

Remove absolute value and add a negative sign to the right side:

2x-6 = -4x -4

Add 4x to both sides::

6x-6 =-4

Add 6 to both sides:

6x = 2

Divide both sides by 6:

X = 2/6

X = 1/3

The two answers are x = -5 and x = 1/3

Answer:

26 is a composite number. 26 = 1 x 26 or 2 x 13. Factors of 26: 1, 2, 13, 26. Prime factorization: 26 = 2 x 13.

Answer:

The Prime factorization: 26 = 2 x 13.

Explain:

26 is a composite number. 26 = 1 x 26 or 2 x 13. Factors of 26: 1, 2, 13, 26. So the Prime factorization: 26 = 2 x 13.

Hoped I helped

Answer:

A P value of 0.05 is considered as the gold standard of the significance level, but it depends on the type of study

Step-by-step explanation:

The scientists make experiments to collect relevant data and their conclusions are often based on statistical analyses of their results. In scientific method, the correct interpretation of the statistical results may be critical for obtaining conclusions. The statistical significance level or 'P value' is an index aimed at summarizing the results of a research. Karl Pearson created the term P value in 1900 and used this index in association with his chi-square test. The P-value can be defined as the probability of observing statistical results that are equal to or more extreme than the one observed when null hypothesis is correct. A P value of 0.05 is generally considered to be correct in many studies; however, this index may change according to the level of significance required for a particular case. It is also important to note the factors that may lead to errors in P value calculation (P>0.05): small sample sizes, errors in study design, errors in measurement methods, etc.

Answer:

please this search in Google

Answer:

B

Step-by-step explanation:

Answer:

177 cm²

Step-by-step explanation:

Area of circle = [tex]\pi[/tex]r²

Radius = diameter/2 = 15/2 = 7.5

Therefore,

Area = 22/7 × 7.5 × 7.5

        = 176.7 = 177 cm²

Answer:

The answer is

Step-by-step explanation:

Area of a circle is given by πr²

where

r is the radius

From the question we were given the diameter

To find the radius using the diameter we use the relation

[tex]radius = \frac{diameter}{2} [/tex]

diameter = 15 cm

[tex]radius = \frac{15}{2} [/tex]

radius = 7.5 cm

Substitute the value into the above formula and solve for the area

Area = (7.5)²π

= 56.25π

= 176.714586

We have the final answer as

176.71 cm² to 2 decimal places

Hope this helps you

Multiplying both sides by [tex]y^2[/tex] gives

[tex]xy^2\dfrac{\mathrm dy}{\mathrm dx}+y^3=1[/tex]

so that substituting [tex]v=y^3[/tex] and hence [tex]\frac{\mathrm dv}{\mathrm dv}=3y^2\frac{\mathrm dy}{\mathrm dx}[/tex] gives the linear ODE,

[tex]\dfrac x3\dfrac{\mathrm dv}{\mathrm dx}+v=1[/tex]

Now multiply both sides by [tex]3x^2[/tex] to get

[tex]x^3\dfrac{\mathrm dv}{\mathrm dx}+3x^2v=3x^2[/tex]

so that the left side condenses into the derivative of a product.

[tex]\dfrac{\mathrm d}{\mathrm dx}[x^3v]=3x^2[/tex]

Integrate both sides, then solve for [tex]v[/tex], then for [tex]y[/tex]:

[tex]x^3v=\displaystyle\int3x^2\,\mathrm dx[/tex]

[tex]x^3v=x^3+C[/tex]

[tex]v=1+\dfrac C{x^3}[/tex]

[tex]y^3=1+\dfrac C{x^3}[/tex]

[tex]\boxed{y=\sqrt[3]{1+\dfrac C{x^3}}}[/tex]

Answer:

$845

Step-by-step explanation:

13 lawns x $65 each = $845

Answer:

x= -1  and also x = -2

Which agrees with the second option in your list of answers

Step-by-step explanation:

We look for two numbers whose product is "2" (constant term in your quadratic equation) and which added give "3" (coefficient in the middle term with "x"). So we find the factors 1 and 2:

1 times 2 = 2 and 1 + 2 = 3

So we use these factor to expand the middle term and then factor by grouping:

[tex]x^2+3x+2=0\\x^2+x+2x+2=0\\x(x+1)+2(x+1)=0\\(x+1)(x+2)=0[/tex]

Then for this product of binomials to give zero, each binomial must be zero. That is

x= -1  and also x = -2

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{10 {x}^{2} + 2x - 9}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{3 {x}^{2} + 2x - 5 + ( - 4 + 7 {x}^{2} )}[/tex]

When there is a ( + ) in front of an expression in parentheses, there is no need to change the sign of each term.

That means , the expression remains the same.

⇒[tex] \sf{3 {x}^{2} + 2x - 5 - 4 + 7 {x}^{2} }[/tex]

Collect like terms

⇒[tex] \sf{ {10x}^{2} + 2x - 5 - 4}[/tex]

Calculate

⇒[tex] \sf{10 {x}^{2} + 2x - 9}[/tex]

Hope I helped!

Best regards!!

Answer: -4.25 ≤ x ≤ 6.25

Step-by-step explanation:

The midpoint of a segment is located at the same distance of each of the endpoints of the segment.

The midpoint is at x = 1.

The length of the segment is 10.5, if we divide it by two we have:

10.5/2 = 5.25

Now, if we want the endpoints to be at the same distance of the midpoint, then the endpoints will be:

Xmax = midpoint + 5.25

Xmin = midpoint - 5.25

Then the extremes are:

Xmax = 1 + 5.25 = 6.25

Xmin = 1 - 5.25 = -4.25

Then this segment can be written as:

Xmin ≤ x ≤ Xmax

-4.25 ≤ x ≤ 6.25

Answer:

12.33

Step-by-step explanation:

3r-4s

3×5-4×2/3

15-8/3

12.333

Answer:

0

Step-by-step explanation:

The base is 3. You are taking the log base 3 of 1.

Since 3^0 = 1,

log_3 1 = 0

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

[tex]P=2w+2l[/tex]

Where w is the width and l is the length.

The width is 4x and the length is 5x+2.

We also know the perimeter is 184. So, substitute:

[tex]184=2(4x)+2(5x+2)[/tex]

Distribute:

[tex]184=8x+10x+4[/tex]

Combine like terms:

[tex]184=18x+4[/tex]

Subtract 4 from both sides:

[tex]180=18x[/tex]

Divide by 18:

[tex]x=10[/tex]

So, the value of x is 10

And we're done :)

Answer:aw45

Step-by-step explanation:

w

Answer:

negative

Step-by-step explanation:

positives and negatives make a negative

Answer:

Step-by-step explanation:

(.45)(288)= $129.60

(.75)(72)= $54

$129.60 + 54 = $184.60 is Audrey's pay

By assembling 288 small baskets and 72 large ones she earned  $183.6.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The owner pays her $0.45 per small basket and $0.75 per large basket and she assembled 288 small baskets and 72 large ones.

So, Her total pay can be obtained if we multiply pay per box by the no. of boxes and add them it will be her total pay which is,

= (0.45)(288) + (0.75)(72).

= $(129.6 + 54)

= $183.6

learn more about numerical expressions here :

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Answer:

1.) 93.35

2.) 7.582

Step-by-step explanation:

Answer:

1. 3.4 + .95 +89 = 93.35

2. 5.9 +.85 +.832 = 7.582

Answer:

Option (C)

Step-by-step explanation:

State                   Year entered into Union

Pennsylvania                      1787

Indiana                                1816

Florida                                1845

Texas                                  1845

West Virginia                      1863

Since North Carolina entered the Union 'x' years after Pennsylvania, expression that represents the the year North Carolina entered the Union will be = (1787 + x)

Therefore, Option (C) will be the answer.

Answer:

The answer is C

Answer:

9

Step-by-step explanation:

-15 - -14y = -9

two negatives (close together) makes a positive

-15y + 14y = -9

add like terms

-1y = -9

get y alone (divide whats in front of it) and do the same on the other side

-1y/-1 = -9/-1

if you divide two negatives it makes it positive so youll get 9

Answer:82 Step-by-step explanation: by putting the numbers in order, 82 lands in the middle.

Answer:

  f^-1(-47) = -5

Step-by-step explanation:

You want to find the value of x that gives f(x) = -47.

  -47 = 8 + 11x

  -55 = 11x

  -5 = x

Then f^-1(-47) = -5.

Answer:

c $99,400

Step-by-step explanation:

$195,00-$120,000=$75,000

$75,000+$5,000+$1,400=81,400

$81,400+$38,000-$20,000=$99,400

Ben’s net worth is $99400 which is the correct answer would be an option (C).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

Given that Ben owns a townhome valued at $195,000,

To determine Ben’s net worth

But still owes $120,000 on the loan.

So, 19500 - 120000

⇒ 75000

He has $5,000 in savings and a balance of $1,400 on his credit cards.

So, 75000 + 5000+ 1400

⇒ 81400

There is a balance of $20,000 owed on Ben’s car which is valued at $38,000.

So, 81400 + 38000 - 20000

⇒ 99400

Thus, Ben’s net worth is $99400.

Learn more about Arithmetic operations here:

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Answer:      " x = - 2.5 " .

___________________________________________

Step-by-step explanation:

Given:  

         9(3x + 7) - 3.5  = - 8 ;   Solve for "x" ;

First: Let us add "3.5" ;  to both sides of the equation:

    9(3x + 7) - 3.5   = - 8    ;

                  + 3.5  = + 3.5 ;

___________________________________________

to get:    

    9(3x + 7)           =  - 4.5 ; [Note that " -3.5 + 3.5 = 0" ; [Cancels out to "0".].  

Second: Let us expand the expression on the "left-hand side" of the equation.

 "  9(3x + 7) " ;

Note the "distributive property" of multiplication:

     " a(b + c) = ab + ac " ;

As such:

       9(3x + 7)  =  9(3x) + 9(7)  = 27x + 63 ;

Third:

Now, replace this term for the original expression, on the "left-hand side" of the equation;  & Rewrite the equation:

   27x + 63 = - 4.5 ;

Fourth:  Now, we can divide each side of the equation by "9" ;

(27x + 63) / 9 = (-4.5)/9 ;

to get:

(27x/9) + (63/9) = (-4.5/9) ;

  to get:

   3x + 7 = -0.5 ;            

Fifth:

Subtract "7" ; from Each side of the equation:

   3x + 7   =  -0.5 ;

        - 7   =   - 7  ;

___________________________________________

to get:

  3x          =   -7.5 ; [Note that " +7 - 7 = 0" ; [Cancels out to "0".]  ;

___________________________________________

Sixth:  Divide each side of the equation by "3";  

            to isolate "x" on one side of the equation; & to solve for "x" ;

___________________________________________

  3x / 3  =  -7.5 / 3 ;

 to get:

    x = - 2.5 .

___________________________________________

Hope this helps!  

 Best wishes!

___________________________________________

Step-by-step explanation:

Hey there!

Given;

[tex]9(3x + 7) - 3.5 = - 8[/tex]

Perform the operations in left side.

[tex]27x + 63 - 3.5 = - 8[/tex]

Simplify the like terms and find value of x.

[tex]27x + 59.5 = - 8[/tex]

[tex]27x = - 8 - 59.5[/tex]

[tex]27x = - 67.5[/tex]

[tex]x = \frac{ - 67.5}{27} [/tex]

Therefore the value of x is "-2.5".

Check;

9(3×-2.5+7) - 3.5 = -8

-4.5 - 3.5 = -8

-8 = -8 (True).

Hope it helps...