Express 2x² + 12x + 8 in the form a(a + b)² + c, where a, b and c are
numbers.

What are the values of a, b and c ?

Answer:B

Step-by-step explanation:

After 9,075 minutes, both divers will be the same distance from the surface, that is, 181.5 feet.

To find the distance at which both divers are the same distance from the surface we must try the following mathematical operation:

Diver 1 descends at a rate of 20 feet per minute.

Diver 2 ascends at a rate of 60 feet per minute.

Diver 1 starts from sea level 0.

Diver 2 starts from 726 meters deep.

Accordingly, we must use time as a variable. For example, if diver 1 dives 20 feet every minute, after 9 minutes how deep will he be? We solve this like this:

According to the above, the diver will be at a depth of 180ft. On the other hand, to find the depth of diver 2 we do the following operation.

In this case, we must modify the time to obtain different depths, until we find the one that places the divers at the same depth. The correct time is 9.075

According to the above, after 9,075 minutes, both divers are at a depth of 181.5ft.

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Answer:

Step-by-step explanation:

Let the missing part be x.

According to triangle proportionality theorem we have:

Answer:

3x² + 2x

Step-by-step explanation:

x(3x + 2) ← multiply each term in the parenthesis by x

= 3x² + 2x

Answer: 3x^3 + 2x

Step-by-step explanation:

when multiplying 3x and another x, it combines and adds up to making 3x^2. You add coefficients. Thus 2 being the coefficient. And same matter for x times 2, they go together as 2x.

3x + x = 3x^2

x + 2 = 2x

Answer:

5q + 9

Step-by-step explanation:

The Concept in that Question is adding Like-Terms

6q + 4 - q + 5 = ( 6q - q ) + ( 4 + 5 ) = 5q + 9

51.21%  is the coefficient of determination.

What does coefficient of determination mean?

SST = SSE + SSR

Here, SSE = 100 and SSR = 105

SST = 100+105 = 205

Coefficient of determination , R^2 = 105/205  = 51.21%

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The Equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

Number of soda produced in 8 hours = 12000

We know

The number of soda produced varies directly with the hours works

Consider the number of bottle produced = b

Number of hours = h

Then the relationship will be b directly proportional to h

b ∝ h

b = k × h

Where k is the constant

Then substitute the values in the equation and find the value of k

12000 = k × 8

k = 12000/8

k = 1500

The equation will be

b = 1500h

Hence, equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

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The complete days have passed when the club has 3 remaining treats will be 7.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation 3 = -3x + 24 represents that there are 3 remaining treats after a number of days since Monday.

If the club has 3 remaining treats, we have to find complete days that have passed, which is x in the given equation,

3 = -3x + 24

-3x= 3 -24

-3x= -21

x=21/3

x=7

Thus, the complete days that have passed when the club has 3 remaining treats will be 7.

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Answer:

more than 150 cookies

Step-by-step explanation:

Let the number of cookies = x.

Since they sell each cookie at 10 cents. each cookie sells for $0.10.

x number of cookies sell for 0.1x.

To turn a profit, the amount of sales must be greater than the cost.

0.1x > 15

x > 15/0.1

x > 150

Answer: They must sell more than 150 cookies

Answer: 151 cookies

150 cookies = $15 so selling 151 cookies gives a 10 cent profit ($15.10)

The equation represent a line passing through the point (8,9) with a slope of 3 is y= 3x-15.

To make a linear equation, there is several methods depending on what known:

If you know 2 points, for example point A(x1, y1) and B(x2, y2). Then the formula that can be used is:

[tex]\frac{y-y_{1} }{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]

If one point is known, for example point A(x1,y1) and slope m. Then the formula that can be used is:

[tex]y-y_{1}=m(x-x_1)[/tex]

If there are other linear equations that have certain properties (parallel or perpendicular) to the linear equation to be searched for, then we can first find out the slope of the linear equation. If the gradient of another linear equation is m1 and the gradient of the linear equation to look for is m2

If the two lines are parallel

[tex]m_{2}=m_1[/tex]

If the two lines are perpendicular

[tex]m_2=\frac{-1}{m_1}[/tex]

In the problem, it is known 1 point and slope. Then the formula that can be used is:

[tex]y-y_{1}=m(x-x_1)[/tex]

1 known point is (8,9) and the slope of m is 3. Then substitute it into the formula:

[tex]y-9=3(x-8)\\y-9=3x-24\\y=3x-24+9\\y=3x-15[/tex]

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The unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.

What is the unit rate?

A unit rate is the price for one unit of something. This is written as a ratio with a denominator of one. For instance, if you ran 70 yards in 10 seconds, you averaged 7 yards per second. Both ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but only the latter is a unit rate.

For 1/8,

Divide the numerator and denominator by '8', to make the denominator 1.

                        [tex]=\frac{\frac{1}{8}}{\frac{8}{8}} \\\\\=\frac{0.125}{1} \\=0.125[/tex]

for 1/4,

Divide the numerator and denominator by '4', to make the denominator 1.

                            [tex]=\frac{\frac{1}{4}}{\frac{4}{4}} \\\\\\\=\frac{0.25}{1} \\\\=0.25[/tex]

Hence, the unit rate of 1/8 is 0.125 and the unit rate of 1/4 is 0.25.

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The maximum height reached by the rocket is 122.5 m.

In this question, given parameters:

time (t) = 5.0 seconds

By applying second equation of motion the maximum height of the model rocket would be,

h = v₀t + 1/2 (gt²)

where, v₀ is the initial velocity

g is acceleration due to gravity

(9 = 9.8 m/s²)

Since initial velocity v₀ = 0 we get an equation,

h = 0 + 1/2 (gt²)

h = 1/2 (9.8 x 5²)

h = 122.5 m

Therefore, the maximum height is 122.5 m.

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The distance from Maria's desk to Monique's desk is √61 feet.

According to the question,

We have the following information:

Maria's desk is located at (1 −1), and Monique's desk is located at (−4, 5). And each unit represents 1 foot.

Now, we know that the following formula is used to find distance between two points:

Distance = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} }[/tex]

In this case, we have x1 = 1, y1 = -1, x2 = -4 and y2 = 5.

D = [tex]\sqrt{(5+1)^{2} +(-4-1)^{2} }[/tex]

(We have converted -1 of y1 directly to 1 because the multiplication of two negative integers give positive results.)

D = [tex]\sqrt{(6)^{2} +(5)^{2} }[/tex]

D = [tex]\sqrt{36+25}[/tex]

D = [tex]\sqrt{61}[/tex] feet

Hence, the correct option is D (the last one).

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Answer:

The solution to this question is (D) - Square root of (61) feet

Step-by-step explanation:

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) [tex]=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}[/tex]

So n [tex]=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2[/tex]

where n=sample size

We firstly find the value of ME and [tex]z_{\alpha /2}[/tex].

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of [tex]z_{\alpha /2}[/tex].

Te given interval is 99%=99/100=0.99

The value of [tex]\alpha[/tex] =1−0.99

The value of [tex]\alpha[/tex] =0.01

Then the value of [tex]\alpha /2[/tex] = 0.01/2 = 0.005

From the standard table of z

[tex]z_{0.005}[/tex] =2.58

Now putting in the value in formula of sample size.

n=[tex](2.58\times\frac{1.55}{0.25})^2[/tex]

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance([tex]\sigma[/tex])= 2×1.55

Standard deviation of resistance([tex]\sigma[/tex])= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=[tex](2.58\times\frac{3.1}{0.5})^2[/tex]

Simplifying

n=(7.998/0.5[tex])^2[/tex]

n=(15.996[tex])^2[/tex]

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

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

According to the diagram, angle BCD is exterior angle and angles BAC & ABC are remote interior angles of the triangle ABC.

As we know, the exterior angle is the sum of remote interior angles.

Answer:

x = 12

Step-by-step explanation:

Exterior Angle Theorem

The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

Given angles:

Apply the exterior angle theorem and solve for x:

[tex]\implies m \angle BCD=m \angle BAC+m \angle ABC[/tex]

[tex]\implies 6x+2=3x+15+2x-1[/tex]

[tex]\implies 6x+2=3x+2x+15-1[/tex]

[tex]\implies 6x+2=5x+14[/tex]

[tex]\implies 6x+2-5x=5x+14-5x[/tex]

[tex]\implies x+2=14[/tex]

[tex]\implies x+2-2=14-2[/tex]

[tex]\implies x=12[/tex]

The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.

Given that

The function f(x)=5000(0. 98)0. 3x represents the number of white blood cells.

We need to evaluate this, for this

f ( x ) = 5000 * ( 0.98 ) ^(0.3 x)

f ( 1 ) = 5000 * 0.98^(0.3) = 5000 * 0.99396 = 4,969.788

f ( 5 ) = 5000 * 0.98 ^(5*0.3) = 5000 * 0.98^(1.5) = 5000 * 0.97 = 4,850.753

Average rate of change:

( 4,850.753 - 4,969.788 ) / ( 5 - 1 ) = - 29.75

Hence the answer is The average rate of change in white blood cells between days 1 and 5 is -29.75 mm³/day.

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For the functions f(x) = 3x - 4 and g(x) = x - 41,

Information given in the question

functions f(x) = 3x - 4

functions g(x) = x - 41

ƒ(4) - 2g(3) = ?

the expression ƒ(4) - 2g(3) is solved by substituting x = 4 in f(x)

f(4) = 3 * 4 - 4

f(4) = 12 - 4

f(4) = 8

and x = 3 in g(x)

2g(3) = 2(3 - 4)

2g(3) = 2 *-1

2g(3) = -2

substituting ƒ(4) - 2g(3)

= 8 - 2

= 6

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The fraction of the cake that Jenny and Brett eat in all is C. 8 over 15 of the cake.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Jenny ate 1/5

Brett ate 1/3.

The fraction that they eat will be:

= Jenny + Brett

= 1/5 + 1/3

= 3/15 + 5/15

= 8/15

Therefore, the correct option is C.

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Answer: 763*42 = 32,046

32,046/82 = 390.8048

A collection of equations with the same variables is known as a system of equations. The only difference is that you're working with inequalities rather than equations in a system of inequalities.

What are inequalities?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

A system of equations has one solution for each variable, whereas a system of inequalities has a range of possible values for each variable.

Set up the equations as follows:

ax + by = c

dx +ey = f

Let the inequitable system exist:

ax + by <c

dx +ey > f

The same technique, such as graphing, substitution, and elimination, can be used to solve both systems.

But there's a difference because:

A system of equations can only have one solution for each variable, whereas a system of inequalities can have any number of solutions for each variable.

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Answer:

The lim for f(1-x^2) is 1

Step-by-step explanation:

Lim f(1 - x^2) as x -> 0

break them apart

Lim (1) - lim (x)^2

where the lim of 1 = 1

for the lim of x^2, sub the value of x = 0, so now:

Lim (1-0) = 1

The graph of the function f is shown in the figure above. The value of lim ƒ(1-x²) is 1. Therefore, the correct option is option A.

In mathematics, a function is a phrase, regulation, or statute that establishes the connection between an independent variable and a dependent variable.

In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837.

Lim f(1 - x²) as x -> 0

Lim (1) - lim (x)²

where the lim of 1 = 1

for the lim of x², substituting the value of x = 0, so now:

Lim (1-0) = 1

Therefore, the correct option is option A.

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The given equation is y = x + 12 and in terms of x is x = y - 12

Define Linear equation

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.  The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

The given expression is ,

y = x + 12

Now, we have to solve for 'x'

so, for that just take constant term right side

y - 12 = x

Next, swap the sides like this

x = y - 12

Hence, the equation in terms of x is x = y - 12.

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Answer:

see explanation

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are in proportion.

(a)

[tex]\frac{PQ}{AB}[/tex] = [tex]\frac{RS}{CD}[/tex] ( substitute values )

[tex]\frac{PQ}{6}[/tex] = [tex]\frac{12}{8}[/tex] ( cross- multiply )

8 × PQ = 72 ( divide both sides by 8 )

PQ = 9 cm

(b)

[tex]\frac{AD}{PS}[/tex] = [tex]\frac{CD}{RS}[/tex] ( substitute values )

[tex]\frac{AD}{10.5}[/tex] = [tex]\frac{8}{12}[/tex] ( cross- multiply )

12 × AD = 84 ( divide both sides by 12 )

AD = 7 cm

(c)

given 2 similar figures with ratio of sides = a : b , then

ratio of areas = a² : b²

here ratio of sides CD : RS = 8 : 12 = 2 : 3

then ratio of areas = 2² : 3² = 4 : 9

let the area of PQRS be x , then using proportion

[tex]\frac{4}{48}[/tex] = [tex]\frac{9}{x}[/tex] ( cross- multiply )

4x = 432 ( divide both sides by 4 )

x = 108

then area of PQRS = 108 cm²

Answer:

The answer for questions A is 2 over 8

Step-by-step explanation:

The robot can complete 7 tasks is one 2 over 5 hour so you multipy 7 by 2 over 5 because then you get 2 over 8

Answer:

n = 4/21

Step-by-step explanation:

[tex]\frac{7}{3} =\frac{4}{9n}[/tex]

==> cross multiply (multiply top of first fraction by bottom of second fraction and top of second fraction by bottom of first fraction)

7 x 9n = 4 x 3

==> simplify

63n = 12

==> divide both sides by 63

n = 12/63

==> simplify fraction

n = 4/21

Answer:

If RU = 16, UT = 20, and SR = 16, what is the perimeter of △SUT?    S    U

If SV = 38, SU = 26, and the perimeter of △SUV is 102, what is the value of RU?

If S‾V ≅ U‾V , SR = 4x − 1 and RU = x + 8, what is the value of SU?     V

Johnson electronics sells electrical and electronic components through catalogs. Catalogs are updated and printed every year. The variable production cost is $5 per catalog. Data indicate that, on average, each printed catalog generates a profit of $35 from sales.

The optimal order quantity will be 11450.

Let’s use the news vendor model here.

The profit means that if we print less we will incur a certain opportunity loss. This is also known as cost of understocking (Cu) = 35

The production cost is $5 and if the product is not sold, we will incur a cost of (Co) = 5. The fixed cost is incurred either way in a year. As a result we need to consider the critical fractile value

C.F. = Cu/(Cu + Co) = 35/(40) = 0.875

The value of z at 0.875 is 1.15. This means that the optimal order/production will be 8000 + 1.15*3000 = 11450

Hence the answer is, the optimal order quantity will be 11450.

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The simplified expression for the given functions f and g is 11-x

What is the value of the function?

The value of the function at a point can be found by substituting the point in the function. This value also depend on the nature of the Function.

We are given a function

f(x) =6-x

Now when we say f(2x) it means the x in the function should be replaced with 2x

Hence the function becomes

f(2x) =6-2x

Similarly

g(x) = (x/3)+8

g(3x-9)= (3x-9/3)+8

g(3x-9)= x-3+8

g(3x-9) = x+5

Now we are asked to add the functions, we simply add the new functions and simplify them

f(2x) + g(3x-9)

=6-2x+x+5

=11-x

Which is the required value

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Answer:

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

Simplify f(2x) + g(3x - 9):

Firstly find the inverse of g(x):

Now solve the equation:

Answer:

0.02

Step-by-step explanation: