Dexter is curious as to whether there is a relationship between a person’s height and thumb length. Fourteen of his classmates volunteered to be measured. He listed his data in a table.

Examine the data set and determine the relationship, if any, between height, h, and thumb length, t. Use your model to predict the thumb length of a person who is 174 cm tall.

Answer:

The solutions to the system of the equations by the elimination method will be:

[tex]x=2,\:z=-1,\:y=2[/tex]

Step-by-step explanation:

Given the system of the equations

[tex]2x\:+\:2y\:+z\:=\:7[/tex]

[tex]-x-\:y\:+z\:=\:-5[/tex]

[tex]x+3y-4z=12[/tex]

solving the system of the equations by the elimination method

[tex]\begin{bmatrix}2x+2y+z=7\\ -x-y+z=-5\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-x-y+z=-5\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y+2z=-10[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ -2x-2y+2z=-10\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]-2x-2y+2z=-10[/tex]

[tex]+[/tex]

[tex]\underline{2x+2y+z=7}[/tex]

[tex]3z=-3[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ x+3y-4z=12\end{bmatrix}[/tex]

[tex]2x+6y-8z=24[/tex]

[tex]-[/tex]

[tex]\underline{2x+2y+z=7}[/tex]

[tex]4y-9z=17[/tex]

[tex]\begin{bmatrix}2x+2y+z=7\\ 3z=-3\\ 4y-9z=17\end{bmatrix}[/tex]

Rearranging the equations

[tex]\begin{bmatrix}2x+2y+z=7\\ 4y-9z=17\\ 3z=-3\end{bmatrix}[/tex]

solve [tex]3z=-3[/tex] for z:

[tex]z=-1[/tex]

[tex]\mathrm{For\:}4y-9z=17\mathrm{\:plug\:in\:}z=-1[/tex]

solve  [tex]4y-9\left(-1\right)=17[/tex] for y:

[tex]4y-9\left(-1\right)=17[/tex]

[tex]4y+9=17[/tex]

[tex]4y=8[/tex]

[tex]y=2[/tex]

[tex]\mathrm{For\:}2x+2y+z=7\mathrm{\:plug\:in\:}z=-1,\:y=2[/tex]

solve [tex]2x+2\cdot \:2-1=7[/tex] for x:

[tex]2x+2\cdot \:2-1=7[/tex]

[tex]2x+3=7[/tex]

[tex]2x=4[/tex]

[tex]x=2[/tex]

Therefore, the solutions to the system of the equations by the elimination method will be:

[tex]x=2,\:z=-1,\:y=2[/tex]

Answer:

The correct answer is -6x⁶

Step-by-step explanation:

Given that:

[tex]3x^2 ( - 2x^4 ) \\ \\ =3(-2)x^{2.4} \\ \\ = 6x^8[/tex]

From the second step above, using the law of indices the correct format should be

[tex]= (3\times -2)x^{2+4}[/tex]

So, the problem lies where we have 2.4, it is not supposed to be (2*4). It supposed to be 2+4 because the law of indices states that we multiply the index together and add their power.

Then the result of that yields

= -6x⁶

In the third step, they also omit the negative sign, when multiplying (3 * -2).

Thus, the correct answer is -6x⁶

Answer:

-2

Step-by-step explanation:

Answer:

the answer would be t56 im guess ing along with x

Step-by-step explanation:

The line of symmetry for the parabola represented by the equation is

x = 1.

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

Given an equation of a parabola, y = -x²+2x+6

Factorizing the equation, we get,

x = 1+√7 or x = 1-√7

We know that the line of symmetry of a parabola is equal to the x-coordinate of the vertex of the parabola.

We also know that the x-coordinate of the vertex of a parabola is equal to the average of zeros. So the x-coordinate of the vertex of the parabola would be:

(1+√7 + 1-√7)/2 = 1

Hence, the equation represents the line of symmetry of the given parabola is x=1.

For more references on parabola, click;

https://brainly.com/question/21685473

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Answer:

1 solution

Step-by-step explanation:

You can solve these equations by using substitution. y = 3x+4, so 3y-6x=2 can also be written as 3(3x+4)-6x = 2 if you plug in the y value in the second equation. Then, simplify and you will get your x answer. If you plug that into the first equation, you will get your y answer.

Answer:

uuuuuuuuuuuuuu

Step-by-step explanation:

Answer:

0.00462962962

Step-by-step explanation:

Answer:

1 3/8 pounds

Step-by-step explanation:

divide 8 1/4 by 6

Answer:

The answer is 1

Step-by-step explanation:

14 = 2 × 7

51 = 3 × 17

21 = 3 × 7

Answer:

1 hour ago-0*C3

hours ago-(-3*C)

4.5 hours ago- (-9*C

Answer: 35 minutes

Step-by-step explanation:

For us to solve the question, we have to calculate the amount of gallons of water that is drained every minute. This will be:

= (1320 - 1040) / (9 - 2)

= 280/7

= 40 gallons per minute

Since we are told that 1,320 gallons of water remain in the pool after 2 minutes. This means that the total water in the pool at the beginning was:

= 1320 gallons + (40 × 2)

= 1320 gallons + 80 gallons

= 1400 gallons

The time taken for the pool to be completely drained will be:

= Total water in pool / Gallons drained per minute

= 1400 / 40

= 35 minutes

Answer:

x = 11/2

Step-by-step explanation:

We would first put it in an equation

5x - 1 = 10 + 3x

We would first add 1 on both sides

5x = 11 + 3x

Then we subtract 3x on both sides

2x = 11

Divide both sides by 2

x = 11/2

The value of x from the given algebraic statement expression is;

x = 11/2

This is about simple Algebra.

       5x - 1 = 3x + 10

Let's add 1 to both sides to get;

5x - 1 + 1 = 3x + 10 + 1

⇒ 5x = 3x + 11

Let's subtract 3x from both sides to get;

2x = 11

Divide both sides by 2 to get;

x = 11/2

Read more at; https://brainly.com/question/18358801

Answer:

x= 40

Step-by-step explanation:

The reason this is so is because a straight line's degree is always 180. And 4(40)-20=140 and 180-40=140. This is how you would work out the right side. This gives you your answer.

Answer:

40

Step-by-step explanation:

[tex]x + 4x - 20 = 180 \\ 5x = 180 + 20 \\ x = 200 \div 5 \\ x = 40[/tex]

please mark as brainliest

Answer:

88°

Step-by-step explanation:

m∠AOB = m∠DOE = 88°

Answer:

The answer is C, because those are the points that cross the x-axis.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

When you look at the graph, you can see that all the points are listed where they should be

Answer:

No.

Step-by-step explanation:

80/100 equals 0.8

Answer:

17.79

Step-by-step explanation:

16.78*1.06=17.886

Answer:

3a+9

Step-by-step explanation:

Answer:

3a+9

Step-by-step explanation:

5-2=3 then 3a=9 it pretty simple

Answer:

Step-by-step explanation:

Step one:

given

speed, v= 4mph

time taken t=1 hour

The velocity is defined and the rate of change of displacement

Required:

Distance traveled

we know that the expression relating distance, velocity and time is

velocity= distance/time

distance= velocity* time

substitute we have

Distance=4*1

Distance= 4miles

The distance traveled and the displacement of the honeybee in miles  4miles

Answer:

She got 10% of the questions wrong !

Step-by-step explanation:

To solve this problem I used cross multiplication

[tex]\frac{x}{100}= \frac{18}{20}[/tex]

18 x 100 =1800

1800 / 20 = 90

Since they are asking what she got wrong, not what she got right, you just need to subtract.

100% - 90% = 10%

hope this helped !

Answer:

10%

Step-by-step explanation:

18/20 Questions = 0.9 or 90% she got right

2/20 Questions = 0.1 or 10% she got wrong

Answer:

hi do You have tiktok?mm

Answer:

ok, so the answer would be 27 hot dogs and 53 tacos salads

Step-by-step explanation:

Answer:

It is d

Step-by-step explanation:

Answer: I think its answer choice b

Step-by-step explanation:

You're dividing so you would be subtracting the exponents

Answer:

9, 16, 21, 9

Step-by-step explanation:

I hope this help and it was going in order

Answer:

165

Step-by-step explanation:

We solve the first 5

1*(10-1)=9

2*(10-2)=16

3*(10-3)=21

4*(10-4)=24

5*(10-5)= 25

and notice

when you go from 6 on its getting the same number because say 3*(10-3) = 3*7 and 7*(10-7) = 7*3 and 7*3 = 3*7 so

You add the first 5 integer you solved up

9 16 21 24 25 = 95

and then you double it no extra 25

and then you get 165 = answer

Answer:

Matching the population trend to a contributing factor:

Contributing Factors                                                 Population Trends

government-sponsored family control programs    Low birth rate

agricultural economies                                              increase in food supply

medical advancements                                             low death rate

Industrial Revolution                                                 high birth rate

Step-by-step explanation:

a) Contributing factors are some negative or positive factors that influence or cause a single event or chain of events that result to the incident.

b) Defining population trends:

1) High birth rate: the industrial revolution triggered high birth rate, following increased food supply and medical advancements.

2) Low death rate: medical advancements brought about low death rate as better healthcare is provided to the sick.

3) Increase in food supply: large-scale agricultural economies ensured increasing food production and supply.

4) Low birth rate: when governments started sponsoring family control programs, the resulting effect was low birth rate.

Answer:

The first one is children and adolescents

the second one is adults

the third one is pregnancy

the last one is indivisuals with brittle bones

Step-by-step explanation:

hope this helps :D

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

[tex]ax^2+bx+c[/tex]

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

[tex]a(x-h)^2+k[/tex]

There are also two details that can be conveyed by a quadratic in vertex form:  (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

[tex]a(x-p)(x-q)[/tex]

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.