What substitution should be used to rewrite 16(x³ + 1)² − 22(x³ + 1) − 3 = 0 as a quadratic equation?
O u = (x³)
Ou= (x³ + 1)
Ou = (x³ + 1)^2
Ou= (x³ + 1)^3

The value of the length DF is 17

The statement Triangle ABC = Triangle ADF means that the triangles ABC and ADF are congruent triangles.

So, we have:

AB = AD

AC = A F

BC = DF

Given that BC = 17;

The equation BC = DF becomes

17 = DF

Rewrite as:

DF = 17

Hence, the value of the length DF is 17

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The study benefit from adding a control group as it would help in the correlation

A control group is s used to establish a cause-and-effect relationship by isolating the effect of an independent variable.

The best way to randomly place the bulls into the Therapy A, Therapy B, and control groups is random testing. The best blocking method will be breeding.

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Answer:

55/16 cups or 3.4375 cups

Step-by-step explanation:

there are 5 dozens (12) in 60, so there are 2.5 2 dozens in 60, so you would multiply 1 3/8 by 2.5 to find how many cups are needed in 60 cupcakes because 1 3/8 cups is for 2 dozen cupcakes

Answer:

a

x

2

+

b

x

+

c

=

0

the two roots of the equation take the form

x

1

,

2

=

−

b

±

√

b

2

−

4

a

c

2

a

So, start by adding

−

5

to both sides of the equation to get

2

x

2

+

x

−

5

=

5

−

5

2

x

2

+

x

−

5

=

0

Notice that you have

a

=

2

,

b

=

1

, and

c

=

−

5

. This means that the two solutions will be

x

1

,

2

=

−

1

±

√

1

2

−

4

⋅

2

⋅

(

−

5

)

2

⋅

2

x

1

,

2

=

−

1

±

√

41

4

You can simplify this if you want to get

x

1

=

−

1

+

√

41

4

≅

1.35078

and

x

2

=

−

1

−

√

41

4

≅

−

1.85078

Answer:

(2x-2)=

     +2 =+2

(2x)=2

----------

    2

x= 1

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

(x+5)=

   -5=-5

x= -5

Step-by-step explanation:

You just need to separate the variable from the numbers

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

The equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The equation made by the given situation is:-

For kyle, there are g students attending 8 classes sp total number of students will be 8g similarly for h students there are 6 classes so the total number of h students will be 6h. The total number of students for both g and h students attending kyle's class is 62. So the equation will be given as:-

8g   +  6h  =  62

Now for Lauren, there are g students attending 5 classes so the total number of students will be 5g similarly for h students there are 10 classes so the total number of h students will be 10h. The total number of students for both g and h students attending Lauren's class is 70. So the equation will be given as:-

5g  +  10h  =  70

Therefore the equation which shows the situation are 8g + 6h = 62 and 5g + 10h = 70.

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The probability that the student was NOT a female that got a "C" is 15 / 32.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the student was NOT a female that got a "C" = number of males that got a C / total number of people that got a C =  15 / 32.

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Answer:

the width is 59

Step-by-step explanation:

302/2-92=59

Multiply the top equation by -3 and then adding both the equations one variable will be eliminated. So the correct answer is option D.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

We are having two equations:-

2x - 4y = 5

6x - 3y=10

When we multiply the first equation by -3 the equation will become as follows:-

-6x  +  12y = - 15

6x   -  3y  =   10

By adding both the equations one variable will be eliminated:-

9y = - 5

Therefore Multiply the top equation by -3 and then add both the equations one variable will be eliminated. So the correct answer is option D.

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Answer:

1347 hours

Step-by-step explanation:

Assuming the income is net income (total after taxes etc.):

To calculate the number of hours to be worked to save enough to buy the car, divide the cost of the car by hourly net income:

[tex]\begin{aligned}\implies \textsf{Number of hours to work} & = \dfrac{\textsf{Cost of car}}{\textsf{hourly net income}}\\\\& = \sf \dfrac{17500}{13}\\\\& = \sf 1346.1538...\end{aligned}[/tex]

We have to round the number up to 1347 hours, as only $17,498 will be saved if 1346 hours are worked.

The average working week is approximately 40 hours, therefore to calculate how many weeks it would take to earn enough money to purchase the car, divide the number of hours by 40:

⇒ 1347 ÷ 40 = 33.675

So it would take 34 weeks, working an average of 40 hours a week and not spending any of the money earned, to save enough to purchase the car.

Total hours

Round to the next whole instead of nearest whole to avoid depicit

In most of the countries the average working hours per week is

Total weeks

Answer:

16x^6(3x^5)

48x^11

Answer:

1st mechanic:20hours

2ndmechanic:15hours

Step-by-step explanation:

1stmechanic:20hours=20x95

                                   =$1900

2nd mechanic:15hours=15x110

                                     =$1650

total=$1900+$1650

       =$3550

Answer:

Hi! I think you are referring to the Pythagorean Theorem.

Essentially, given a right triangle, the sum of the squares of the shorter sides equals the square of the longer (slant) side or hypotenuse.

The formula is a squared + b squared = c squared

If the triangle has side lengths 3 and 4 (for the shorter sides), the longer side can be solved like this:

3 squared + 4 squared = x squared

(Let x =  the longer side)

3 squared = 9

4 squared = 16

9+16 = x squared

25 = x squared

x =  5

So there you go, that's the Pythagorean theorem.

Let me know if this helped!

Answer:

a theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

Step-by-step explanation:

Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

Answer:

C)

Step-by-step explanation:

f(x)=[tex]8x^{2} -16x-15[/tex]
[tex]8x^{2} -16x-15=0[/tex]
[tex]x=\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]  ,  a=8, b= - 16, c= - 15

[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4*8*(-15)} }{2*8} = \frac{16+-\sqrt{736} }{16} =\frac{16+-4\sqrt{46} }{16} = 1 +- \frac{\sqrt{46} }{4} = 1+- \frac{\sqrt{23} \sqrt{2}}{2\sqrt{2} \sqrt{2} } =1+-\frac{\sqrt{23} }{2\sqrt{2} } = 1+-\frac{\sqrt{23} }{\sqrt{8} }[/tex]

A function assigns the values. The graph of the function f(x) and g(x) can be plotted as shown in the below image.

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function f(x) and g(x) can be plotted as shown in the below image.

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Answer:

4 pints

Step-by-step explanation:

Therefore each can would contain 8/2 =  4 pints

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Please feel free to comment, ask questions, give feedback, or correct me if I am wrong!

Have a great day!

:)

A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.101. The half-life is 2.98 days.

Exponential decay obeys the equation

[tex]m(t) = m_0 e^{-kt}[/tex]

where t = time, days

Given:

Initial mass, m₀ = 8 g

Decay constant, k = 0.101

For half-life, the mass is m = m₀/2.

Therefore,

[tex]m(t) = m_0 e^{-kt}[/tex]

e^{-0.101t} = 1/2

-0.101t = ln 0.5

t = ln 0.5/-0.101

t = 2.98

Therefore, The half-life is 2.98 days.

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Answer:

See below

Step-by-step explanation:

Interest   3%   in decimal form is  .03

  interest in ONE year    7000 * .03

         interest in SEVEN years   7000 * .07 * 7

           this is added to the original deposit of 7000

              to become   7000 + 7000 * .03 * 7

                                        or  7000 ( 1 + .03*7 )

                                              or   7000 ( 1.21 ) = $ 8470

IF the interest is compounded

   the money in the account will be    7000 ( 1+.03)^7  

Answer:

See below ~

Step-by-step explanation:

⇒ t represents the years after 1992

⇒ So, in 1992, t = 0

⇒ Apply in the formula

⇒ n(0) = 89e^(0.02 × 0)

⇒ n(0) = 89e⁰

⇒ n(0) = 89,000,000

The rat population in 1992 was 89,000,000.

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

⇒ Number of years after 1992 : 2003 - 1992 = 11

⇒ Substitute for t in the formula

⇒ n(11) = 89e^(0.02 × 11)

⇒ n(11) = 89e^(0.22)

⇒ n(11) = 89 × 1.24607673

⇒ n(11) = 110,900,829 rats

The model predicts that in the year 2003 there will be a rat population of 110,900,829 rats.

Answer:

(a) 89,000,000 rats

(b) 110,900,829 rats

Explanation:

Given equation:

To find the initial population (1992):

insert t = 0

To find the rat population in 2003 (after 11 years):

insert t = 11

Answer:

3-x is the inverse of f(x)=x-3

I think it's 12 because here it comes out

Answer:

wait I will edit and answer it in a few minutes

Answer:

A

Step-by-step explanation:

tan60=opp/adj

tan60=15/x

15tan60=x

25.98=x (when you calculate 15 root 3 it is the same number)

A parallelogram is a quadrilateral with four sides and the opposite sides of the parallelogram are equal and parallel.

In the given figure, AB||DC. AD is the transversal, such that:

∠A + ∠D = 180-degrees.

The parallelogram is a quadrilateral with equal such that the interior angles present on the same side of the transversal are supplementary. The sum of supplementary angles is equal to 180-degrees.

From the theorem of same-side interior angles, the supplementary angles present on the parallel lines must be intersected by a transversal.

From the property of transversal, the interior angles on the same side of the transversal are supplementary. Therefore, ∠A and ∠D are supplementary and their sum is equivalent to 180-degrees.

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[tex] \textsf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} } ) \sdot(2 {}^{ \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{2}{x} + \frac{4}{x} } ) = 2 {}^{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:(2 {}^{ \frac{6}{x} } ) = 2 {}^{12} [/tex]

Now, since the base on both sides are equal, therefore their exponents are equal as well ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{6}{x} = 12[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{6}{12} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{1}{2} [/tex]

or

[tex]\qquad \sf  \dashrightarrow \:x = 0.5[/tex]

Hope you got the required Answer ~

Answer:

A

Step-by-step explanation:

Inflation decreases the amount of goods and services that can be purchased with a dollar.

Any proper CDF [tex]F(x)[/tex] has the properties

• [tex]\displaystyle \lim_{x\to-\infty} F(x) = 0[/tex]

• [tex]\displaystyle \lim_{x\to+\infty} F(x) = 1[/tex]

so we have to have a = 0 and b = 1.

This follows from the definitions of PDFs and CDFs. The PDF must satisfy

[tex]\displaystyle \int_{-\infty}^\infty f(x) \, dx = 1[/tex]

and so

[tex]\displaystyle \lim_{x\to-\infty} F(x) = \int_{-\infty}^{-\infty} f(t) \, dt = 0 \implies a = 0[/tex]

[tex]\displaystyle \lim_{x\to+\infty} F(x) = \int_{-\infty}^\infty f(t) \, dt = 1 \implies b = 1[/tex]

To solve the theorem, we will  take the square of the longest side of a right triangle and equate to the sum of the squares of the other two sides

Pythagoras theorem states that the square of the longest side of a right triangle is equal to the sum of the squares of the other two sides

For instance, let;

According to the theorem above, mathematically;

c² = a² + b²

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