can someone show me how to do this

The force of a 5.0 kg bowling ball with an acceleration of 3m/s 2 is 15 N.


True or False

Answers

Answer 1

Answer:

True

Step-by-step explanation:

We got the formula for that:

F=ma

now if you replace the given data, it's gonna be

F=5 kg×3m/s²====> F=15kg.m/s²


Related Questions

Answer the following regarding Momentum Change and Force
1. Find the force necessary to gain a velocity of 60 m s-1 within 5 minutes, when acted on a mass of 200 kg which is initially at rest.

2. A force of 150 N acts on an object of mass 600 kg for 2 minutes, which was initially at rest. Find the velocity gained by the object at the end of the second minute.

Answers

1. The force necessary to gain a velocity of 60 m/s within 5 mins is 40 N

2. The velocity gained by the object at the end of the second minute is 30 m/s

1. How to determine the forceInitial velocity (u) = 0 m/sFinal velocity (v) = 60 m/sMass (m) = 200 KgTime (t) = 5 ms = 5 mins = 5 × 60 = 300 sForce (F) =?

F = m(v –u) / t

F = 200(60 – 0) / 300

F = 40 N

2. How to determine the velocity Force (F) = 150 NMass (m) = 600 KgInitial velocity (u) = 0 m/sTime (t) = 5 ms = 2 mins = 2 × 60 = 120 sFinal velocity (v) = ?

F = m(v –u) / t

Cross multiply

m(v –u) = Ft

Divide both sides by m

v - u = Ft / m

v - 0 = (150 × 120) / 600

v = 30 m/s

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If 3 cups of flour are needed to make 60 biscuits, how much flour is needed to make 95 of the same kind of biscuits

Answers

Answer:

3 cups for 60 biscuits

60/3=20

1 cup for 20 biscuits

95/20=4.75

4.75 cups of flour

Hope This Helps!!!

Answer:4.75

Step-by-step explanation: If 3 cups equals 60 biscuits then how much with you need for 95 biscuits

60/3 equals 20 95/20 equals 4.75 just to make sure lets multiply

475x20 equals 9500 now put the decimal back in place   95.00

Which series is convergent? check all that apply. sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction sigma-summation underscript n = 1 overscript infinity endscripts startfraction n squared minus 1 over n minus 2 endfraction sigma-summation underscript n = 1 overscript infinity endscripts (one-fifth) superscript n sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction) superscript n sigma-summation underscript n = 1 overscript infinity endscripts startfraction 1 over 10 endfraction (3) superscript n

Answers

These series show convergence of series which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

According to the statement

we have given the some series and we have to find that the out of these series which series is convergent.

So, For this purpose we have to check the convergence of series.

So,

we know that the for the convergent of series there is a one condition and if those condition will satisfy on the series then the series is convergent and if not then series is divergent.

So, the condition for convergent is a series converges if the absolute value of the sum of any finite number of sequential terms can become arbitrary small by starting the addition from a term which is far enough. So, if this condition is not satisfied the series diverges.

When we apply this condition on all given series then only 2 series satisfy this condition which is

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfractionsigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

So, These series show convergence of series  which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

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Answer:

B. The series converges because it has a sum of 2/3

Here are the answers for the rest of the assignment:

C.

B.

C and D

A and C

B and D

C.

B. 0.31 and A. 0.0025

B. 1.0317 and C. 1.9683

(please read below)

Step-by-step explanation:

Had the assignment and these are the correct answers, enjoy :)

p.s Take a break here for a second, this was your last assignment before the unit test and finals, pre-calc is a very hard subject to master and calc is going to be even harder so I just want to say that I am proud of you, you have done a great job this year.

I have also taken the course(and many others) and answered countless questions for brainly (you have probably seen some of them if you took pre-calc) and this is my final answer for edge(might do one or 2 more for the finals) and it has been my greatest pleasure to bring you guys edge answers for 3 years strait but sadly this is where my road ends, I have tried my hardest to make your lives easier with my answers as others have for me. I hope some of y'all continue on my legacy and continue bringing good to the world 1 answer at a time.

So long fellows, thank you for taking the time to listen I hope y'all do well in life :)

Manju and Arif are playing a game in which one of them thinks of a number from the grid shown
below and the other has to guess it using some clues that are given. Manju thinks of a number
and gives the following clues:
It is a multiple of 3.
It is even.
It is in the third row.
What is Manju's number?

Answers

The number from the grid that fulfills all the given clues is; 12

How to find the multiple of a number?

The grid is shown in the attached image.

Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;

It is a multiple of 3.

It is even.

It is in the third row.

Now, looking at the third row, we see the numbers as;

11, 12, 13, 14, 15

Now, the only number that fulfills all the given clues is 12.

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Round your answer to the nearest percent.

Answers

Answer:

Step-by-step explanation:

Givens

Number not using given app = 71

Total number of students  = 219

% = ?

Solution

P(~given app) = 71 / 219

P(~given app)  = 0.324

% = 0.324 * 100  = 32.4%

Answer

32.4% do not use Given App

If a car travels 368.5 miles on 50 liters of gas, how many liters of gas will it take to go 691 miles if the car travels at the same rate? (Round to the nearest tenth)

Answers

Answer is 93.8 liters gas
Step by step
We know 368.5 miles per 50 liters gas
We want to find the rate
Divide 368.5 by 50 = 7.37 miles per 1 liter
Now we want to find how many liters per 691 miles.
We take 691 divided by the rate of 7.37 miles per 1 liter = 93.8 liters gas
Problem solved

If $2000 is invested at 4% per annum compounded semiannually, how much is in the account after 8 years?

Answers

hope this helps
final balance $2,745.57

The width of a rectangle is 4 less than twice its length. if the area of the rectangle is 75 cm 2 , what is the length of the diagonal?

Answers

Answer:

Step-by-step explanation:

Consider the function f(x) = one-third(6)x. what is the value of the growth factor of the function?

Answers

6 is the growth factor in the function f(x) = (1/3)(6ˣ).

The rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.

In the question, we are given a function f(x) = (1/3)(6ˣ) and are asked to identify the growth factor of the function.

We know that the rate at which a quantity multiplies itself over the independent factor, to increase the value of the function exponentially is known as its growth factor.

In the given function, f(x) = (1/3)(6ˣ), (1/3) remains unaffected with the change in the independent factor x, but 6 is exponentially increasing with x.

Thus, 6 is the growth factor in the function f(x) = (1/3)(6ˣ).

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Quick algebra 1 question for 50 points!

Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!

Answers

The predicted value of y when x =7 is -8.5

How to predict the y value?

Start by drawing the line of best fit through the points

See attachment for the graph.

From the attached graph, we have the following value

y = -8.5 when x = 7

Hence, the predicted value of y when x =7 is -8.5

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Please help! I'm giving 25 points!!

The volume of the oceans on Earth is approximately 1,386 million km^3. As the Earth's temperature rises, the ice in the polar icecaps melts into the oceans, increasing the volume of the oceans. If 1 cm^3 of ice melts, it turns into approximately 0.92 cm^3 water.

1) There are approximately 3,800 cm^3 in a gallon. If 1.9 m^3 of ice melts, how many gallons of water does this produce? (Round your answer to the nearest gallon.)

2) Scientists estimated that the addition of 1,000 km^3 of water would increase sea levels by 364 cm. Greenland's ice sheet is especially vulnerable to melting. Recent reports indicate a melting average of 195 km^3 of ice per year from Greenland, resulting in additional yearly 179.4 km^3 of water. If melting continues at this rate, how many centimeters would the sea increase after 6 years? (Round your answer to the nearest centimeter.)

Answers

1. The number of gallons of water produced is 460 gallons

2. The amount in cm the sea would increase after 6 years is 392 cm

1. How to determine the number of gallons produced

We'll begin by by converting 1.9 m³ to cm³. This is illustrated below:

1 m³ = 1×10⁶ cm³

Therefore,

1.9 m³ = 1.9×10⁶ cm³

Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:

From the question given,

1 cm³ of ice = 0.92 cm³ of water

Therefore,

1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92

1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water

Finally, we shall determine the number of gallons produced. This is illustrated below:

From the question given,

3800 cm³ of water = 1 gallon

Therefore,

1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800

1.748×10⁶ cm³ of water = 460 gallon

Thus, 460 gallons were produced

2. How to determine the amount in cm the sea would increase to after 6 years

From the question given above,

1000 Km³ = 364 cm

Therefore,

179.4 Km³ = (179.4 × 364) / 1000

179.4 Km³ = 65.3016 cm per year

To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:

65.3016 × 6 = 392 cm

Thus, the sea will increase 392 cm after 6 years

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Common significance levels are 0.01 and 0.05. why would it be unwise to use a significance level with a number like 0.0483?

Answers

Common significance levels are 0.01 and 0.05. Because the observations in the sample do not come from a random pool, it is impossible to conduct a test based on a population percentage by utilizing the normal approximation approach. This is further explained below.

What is probability?

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, Both 0.01 and 0.05 are considered to be significant values. It is not feasible to perform a test based on a population percentage using the normal approximation technique because the observations in the sample do not originate from a random pool. This makes it impossible to utilize the normal approximation approach.

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Select the interval where g is negative.
Choose 1 answer:
A)0B)2C)3

Answers

Answer:

A). 0

Step-by-step explanation:

If you look at the graph, you can see that the only time it passes through the X- Axis is at (0, -20). Therefore, the solution to y=g(x) where g is negative, would be 0.

Solve the linear equation
x/2 + 2y/3 = -1 and x - y/3 = 3​

Answers

x/2+2y/3=-1

Multiply by 6

3x+4y=-6-»eq(1)

And

x-y/3=3

Multiply by 3

3x-y=9-»eq(2)

eq(1)-eq(2)

5y=-15y=-3

Then

3x+4(-3)=-63x-12=-63x=6x=2

From Equation 1

[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]

[tex] \dfrac{3x + 4y}{6} = - 1[/tex]

[tex]3x + 4y = - 6 [/tex]

From Equation 2

[tex]x - \dfrac{y}{3} = 3 [/tex]

[tex] \dfrac{3x - y}{3} = 3[/tex]

[tex]3x - y = 9[/tex]

By eliminating ;;

For that multiply equation 2 by 4

12x - 4y = 36 _(3)

By taking equation (1) and (3)

3x + 4y = -6

12x - 4y = 36

__________

15x = 30

x = 30/15

x = 2

Putting the value of x in 2

[tex]3(2) - y = 9[/tex]

[tex]6 - y = 9[/tex]

[tex]6 - 9 = y[/tex]

[tex]-3 = y[/tex]

So The value of x = 2 and y = -3

Which equation can be used to find y, the year in which both bodies of water have the same amount of mercury? 0.05 – 0.1y = 0.12 – 0.06y 0.05y 0.1 = 0.12y 0.06 0.05 0.1y = 0.12 0.06y 0.05y – 0.1 = 0.12y – 0.06

Answers

The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.

First, we will find the equations showing the level of mercury in each body of water.

For the first water body:

Initial measure of mercury = 0.05 ppb.

Rate of rising = 0.1 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.05 + 0.1y.

For the second water body:

Initial measure of mercury = 0.12 ppb.

Rate of rising = 0.06 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.12 + 0.06y.

We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.

As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:

0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.

Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

please help with this

Answers

Answer:

a) x = 1, x = -7

b) (-3, -48)

c) x = -3

d) upwards

Step-by-step explanation:

Given quadratic equation:

[tex]y=3(x-1)(x+7)[/tex]

Part (a)

Intercept form of a quadratic equation:  

 [tex]y=a(x-p)(x-q)[/tex]

where:

p and q are the x-interceptsa is some constant

Comparing the formula with the given equation:

⇒ p = 1

⇒ q = -7

Therefore, the x-intercepts of the given equation are x = 1 and x = -7.

Part (b)

The midpoint between the two x-intercepts is the x-coordinate of the vertex.

[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]

Therefore, the x coordinate of the vertex is -3.

To find the y-coordinate of the vertex, substitute this into the given equation:

[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]

Therefore, the coordinates of the vertex are (-3, -48).

Part (c)

The x-coordinate of the vertex is the axis of symmetry.

Therefore, the axis of symmetry is x = -3.

Part (d)

If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.

If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.

From inspection of the given equation, the leading coefficient is 3.

Therefore, the parabola opens upwards.

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There are 450 eighth graders at Wilson Middle School. In the class president election, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris. What percent of eighth graders voted for Luke

Answers

Using Percentage, the eighth graders voted for Luke is of 72 percentage or 72%.

According to the question,

They are 450 eighth graders at Wilson Middle School. In the class president, 324 students voted for Luke, 81 students voted for Alice, and 45 students voted for Chris.

In order to find the percentage of eighth graders voted for Luke only if 252 divided by 350.

[tex]\frac{252}{350} = 0.72[/tex]

To convert decimal into Percentage multiply 0.72 into 100.

0.72*100 = 72%.

Hence, the percentage of the eighth graders voted for Luke is of 72 percentage or 72%.

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PLEASE HELP IM SERIOUSLY STUCK E

Answers

Answer:  2.12 × [tex]10^{-3}[/tex]

               The coefficient (in green) will be 2.12

Step-by-step explanation:

     Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.

     Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.

    To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.

    To get back to the original value, we multiply this by [tex]10^{-3}[/tex]. This gives us our answer.

What value, written as a decimal, should lena use as the common ratio? 1.0 1.5 2.5 2.0

Answers

The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0

According to the question,

1.0  1.5  2.5  2.0

a = 1.0

r = 1.5/1 = 1.5

r = 2.5/1.5 = 1.6667

r = 2/2.5 = 0.8

common ratio is different, so given sequence is not geometric sequence.

Hence,  the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.

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La suma de un número con su mitad es igual a 75. ¿Cuál es ese número?

Doy corona porfis

Answers

Considerando la definición de una ecuación, el número desconocido es 50.

Definición de ecuación

Una ecuación es la igualdad existente entre dos expresiones algebraicas conectadas a través del signo de igualdad en la que figuran uno o varios valores desconocidos, llamadas incógnitas, además de ciertos datos conocidos.

Los miembros de una ecuación son cada una de las expresiones que aparecen a ambos lados del signo igual.

Número desconocido

En este caso, "La suma de un número con su mitad es igual a 75" puede ser expresado mediante una ecuación, donde consideras que "x" es la incógnita, que representa el número desconocido.

Teniendo en cuenta que la mitad de un número se calcula dividiendo el número por 2, entonces la ecuación queda expresada como:

x + x÷2= 75

O lo que es lo mismo

x + [tex]\frac{1}{2}[/tex]x= 75

Resolviendo:

[tex]\frac{3}{2}[/tex]x= 75

x= 75 ÷[tex]\frac{3}{2}[/tex]

x= 75×[tex]\frac{2}{3}[/tex]

x=50

Finalmente, el número desconocido es 50.

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determine the fall (drop) on 20' of drainage piping with a 1/4" per ft. grade

Answers

The Fall (drop)  of drainage piping is: A. 5".

Fall (drop) of drainage piping

In order to determine the fall (drop) of drainage piping we would need to multiply the drainage piping by the inch per feet.

Hence:

Using this formula

Fall (drop) of drainage piping = Drainage piping× inch per feet

Where:

Drainage piping=20

Inch per feet=1/4"

Let plug in the formula

Fall (drop) of drainage piping =20×1/4"

Fall (drop) of drainage piping =5"

Therefore the correct option is A. 5".

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Given that SQ⎯⎯⎯⎯⎯ bisects ∠PSR and PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯, which of the following triangle congruence statements can be used to prove that ∠P≅∠R?

The figure shows two triangles P S Q and R S Q with a common side S Q.

Answers

The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.

How to prove Triangle Congruence?

From the figure as seen online, we can see that;

The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.

Thus, the 2 column proof to show that ∠P≅∠R is;

Statement 1; ∠SPQ≅∠SRQ

Reason 1; Given

Statement 2; SQ bisects ∠PSR

Reason 2; Given

Statement 3; ∠PSQ≅∠QSR

Reason 3; Definition of angle bisector

Statement 4; SQ ≅ SQ

Reason 4; Reflexive Property of Congruence

Statement 5; △PQS≅△RQS

Reason 5; Angle - Angle Side (AAS) Congruency Postulate

Statement 6; PS ≅ SR

Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)

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Whats the solution √x-6-x-12

Answers

I believe you want the simplified version of this expression, thus the simplified version is √x-18-x.

help me I need the good answers!!!?
1) Q.1 Find the equation of a line that passes through (1, 2) and (5, 4).

Answers

equation of a line is y=mx+ c

where m is that gradient and c is y intercept

so first we find the gradient (m)

M= change in y intercept ÷change in x

M=4-2÷5-1

M=2÷4=1/2(as a fraction)(you can also use o.5)

there 1/2is the gradient

then to find the equation of the line

y= 1/2x +c (from coordinates 1,2 we substitute)

2=1/2(1)+c

2-1/2=c

c=1.5

or

from the coordinates 5,4

4=1/2(5) +c

4=5/2+ c

c=4-5/2

c=1.5

equation of the line=y=0.5x + 1.5

or y=1/2x +1.5

hope it helps you^_^

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 10t 68, where t is the number of years since the end of 2008. what does the constant term of the expression represent in terms of the context?

Answers

The company earned 68 billion dollars from 2008 to 2018.

According to the statement

we have given that the company's particular sales in expression are represented by (t² + 10t + 68)

And we have to find the constant terms in this expression which represent the sale of the company.

So, The given expression is (t² + 10t + 68)

From above expression it is clear that the it is in the form of Quadratic Equations.

So, The Quadratic equation, is an equation containing a single variable of degree 2. Its general form is ax^2 + bx + c = 0, where x is the variable and a, b,c are the known numbers and C is the Constant.

The general representation of Quadratic equation is

ax^2 + bx + c = 0  -(1)

and the given expression are

(t² + 10t + 68)  -(2)

After comparing both equations

Here C =68 = Constant.

So, 68 is the Constant term of the expression represent in terms of the context.

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Disclaimer: The question was incomplete. Please find the full content below.

Question:

A particular company's net sales, in billions, from 2008 to 2018 can be modeled by the expression t2 + 10t + 68, where t is the number of years since the end of 2008. What does the constant term of the expression represent in terms of the context?

The company earned 68 billion dollars from 2008 to 2018.

The company earned 68 billion dollars in 2008.

The company earned 10 billion dollars from 2008 to 2018.

The company earned 10 billion dollars in 2008.

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Which of the following exponential functions is represented by the graph?
OA)
A) f(x) = -2x
B) f(x) = 2x
C) f(x) = (¹/2)-x
OD) f(x) = (¹/2)*

Answers

Answer:

D) f(x) = (1/2)^x

Step-by-step explanation:

at least that is what I think answer D is supposed to be.

I guess the other answer options are actually

A) f(x) = -2^x

B) f(x) = 2^x

C) f(x) = (1/2)^-x

let's look at the most interesting point here : (1, 1/2).

when x=1, then y = 1/2

A fails. because for x = 1 we get y = -2.

B fails. because for x = 1 we get y = 2.

C fails. because for x = 1 we get (1/2)^-1

and that is 1 / 1/2 = 2

so, the only function giving us (1, 1/2) is D, as

(1/2)¹ = 1/2

Which of these is a zero of the polynomials p(y) = 3y^3 - 16 y - 8? * - 8 0 2 - 2

Answers

The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

According to the question,

The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.

p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]

= 3(8) + 32 -8

= 0

Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

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7. A kids furniture warehouse ships small tables and chairs in certain combinations to consumers in the United States. The weight of 3 tables and 5 chairs is 62.5lbs and the weight of 3 tables and 2 chairs is 52lbs. Create and solve a system of equations to find out how much each table and chair weighs.

Answers

The weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

Simultaneous equation

Let

Weight of tables = xWeight of chairs = yCost of 3 tables and 5 chairs is 62.5lbsCost of 3 tables and 2 chairs is 52lbs

3x + 5y = 62.5

3x + 2y = 52

Subtract the equation to eliminate x

5y - 2y = 62.5 - 52

3y = 10.5

y = 10.5/3

y = 3.5 lbs

Substitute y = 3.5 into

3x + 2y = 52

3x + 2(3.5) = 52

3x + 7 = 52

3x = 52 - 7

3x = 45

x = 45/3

x = 15 lbs

Therefore, the weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

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Question 15 of 46
Which of the following statements about the polynomial function
F(x) = 2x³ - 2x² +1 is true?

Answers

The given polynomial function has 1 relative minimum and 1 relative maximum.

What are the relative minimum and relative maximum?The relative minimum is the point on the graph where the y-coordinate has the minimum value.The relative maximum is the point on the graph where the y-coordinate has the maximum value.To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)

Calculation:

The given function is

f(x) = 2x³ - 2x² + 1

derivating the above function,

f'(x) = 6x² - 4x

At slope = 0, f'(x) = 0 (for maximum and minimum values)

⇒ 6x² - 4x = 0

⇒ 2x(3x - 2) = 0

2x = 0 or 3x - 2 = 0

∴ x = 0 or x = 2/3

Then the y-coordinates are calculated by substituting these x values in the given function,

when x = 0;

f(0) = 2(0)³ - 2(0)² + 1 = 1

So, the point is (0, 1)

when x = 2/3;

f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27

So, the point is (2/3, 19/27)

Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.

So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.

Thus, option A is correct.

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1. Determine the most precise name for the quadrilateral.

Answers

rhumbos

it is the most precise name because it gives more information about the quadrilateral

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