Determine whether each set {p1,p2} is a linearly independent set in P3.
1. The polynomials p1 (t) = 1 + t2 and p2(t) = 1 - t2.
2. The polynomials p1 (t) = 2t + t2 and p2(t) = 1 + t.
3. The polynomials p1(t) = 2t - 4t2 and p2(t) = 6t2 - 3t.

Answers

Answer 1

Answer:

1) The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient, 2) The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent, 3) The polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.

Step-by-step explanation:

A set is linearly independent if and only if the sum of elements satisfy the following conditions:

[tex]\Sigma_{i=0}^{n} \alpha_{i} \cdot u_{i} = 0[/tex]

[tex]\alpha_{0} = \alpha_{1} =...=\alpha_{i} = 0[/tex]

1) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (1+t^{2})+\alpha_{2}\cdot (1-t^{2}) = 0[/tex]

[tex](\alpha_{1}+\alpha_{2})\cdot (1) +(\alpha_{1}-\alpha_{2})\cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]\alpha_{1} + \alpha_{2} = 0[/tex] Eq. 1

[tex]\alpha_{1}-\alpha_{2} = 0[/tex] Eq. 2

From Eq. 2:

[tex]\alpha_{1} = \alpha_{2}[/tex]

In Eq. 1:

[tex]2\cdot \alpha_{1} =0[/tex]

[tex]\alpha_{1} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

The polynomials [tex]p_{1}(t) = 1 +t^{2}[/tex] and [tex]p_{2}(t) = 1-t^{2}[/tex] are linearly independient.

2) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (2\cdot t+t^{2})+\alpha_{2}\cdot (1+t) = 0[/tex]

[tex]\alpha_{2}\cdot (1) +(2\cdot \alpha_{1}+\alpha_{2})\cdot t +\alpha_1 \cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]\alpha_{2} = 0[/tex]

[tex]2\cdot \alpha_{1}+\alpha_{2} = 0[/tex]

[tex]\alpha_{1} = 0[/tex]

The polynomials [tex]p_{1}(t) = 2\cdot t +t^{2}[/tex] and [tex]p_{2}(t) = 1+t[/tex] are linearly independent.

3) The set of elements form the following sum:

[tex]\alpha_{1}\cdot p_{1}(t)+\alpha_{2}\cdot p_{2}(t) = 0[/tex]

[tex]\alpha_{1}\cdot (2\cdot t-4\cdot t^{2})+\alpha_{2}\cdot (6\cdot t^{2}-3\cdot t) = 0[/tex]

[tex](2\cdot \alpha_{1}-3\cdot \alpha_{2})\cdot t + (-4\cdot \alpha_{1}+6\cdot \alpha_{2})\cdot t^{2} = 0[/tex]

From definition this system of equations must be satisfied:

[tex]2\cdot \alpha_{1}-3\cdot \alpha_{2} = 0[/tex] (Eq. 1)

[tex]-4\cdot \alpha_{1}+6\cdot \alpha_{2} =0[/tex] (Eq. 2)

It is easy to find that each coefficient is multiple of the other one, that is:

[tex]\alpha_{1} =\frac{3}{2}\cdot \alpha_{2}[/tex] (From Eq. 1)

[tex]\alpha_{1} = \frac{6}{4}\cdot \alpha_{2}[/tex] (From Eq. 2)

[tex]\alpha_{1} = \frac{3}{2}\cdot \alpha_{2}[/tex]

Which means that polynomials [tex]p_{1}(t) = 2\cdot t - 4\cdot t^{2}[/tex] and [tex]p_{2}(t) = 6\cdot t^{2}-3\cdot t[/tex] are linearly dependent.


Related Questions

Find out the coordinates

Answers

answer:

c) (0,-8)

reason:

it may be easiest to visualize by putting (-3,-5) and (-6,-2) on a graph
you can see that to get from C to B you have to add 3 to the x value and subtract 3 from the y value
do the same to point B, which will give you (0,-8)

Question 1 (1 point)
When simplified [9(7 – 3) + 13] - [11 - (6 + 9)] equals:
53
39
43
None of these

Answers

Answer:45

Step-by-step explanation:

[9(7-3)+13]-[11-(6+9)]

[9(4)+13]-[11-(15)]

[36+13]-[4]

49-4

45

Answer: The answer is 53

an airplane is traveling at 400 miles per hour. which equation can be used to find the total distance the plane will travel in h hours.

Answers

Answer:

y=400h

Where y is distance and h is time.

Solve the equation -4 = 5 -x.

Answers

X=5+4
X=9




So the answer is, x=9

Answer:

when x goes opposite side of equals to sign of x changes and same goes with 4 then x=5+4 then the answer will be 9

The average spending at Neco's salad bar is $8.73 with a standard deviation of $3.41. The distribution follows t-distribution. The management is interested in the middle 90% of the customers (spending wise) as it believes that they represent their true customer base. What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers

Answers

Answer:

Difference between upper and lower limits is : 1,816

Step-by-step explanation:

A CI (confidence interval ) for  t student distribution is:

( μ₀  - t(α/2)* s/√n  ;    μ₀  + t(α/2)* s/√n )

Where:

μ₀  is the mean and s the standard deviation of the dstribution

n size of the sample

CI = 90 %     means   α = 10 %    α = 0,1      α/2  = 0,05

and degree of freedom   df = n - 1   df = 40

From t student table we get:

tα/2  =  1,6839

Then:

t(α/2)* s/√n  =  1,6839* 3,41/√40

t(α/2)* s/√n  =  0,908

8,73 - 0,908   =  7,822

8,73 + 0,908  = 9,638

CI (90%)  =  ( 7,822  ;  9,638 )

Difference between upper and lower cut-offs points is:

Δ = 1,816

-1/2(-6x -5/2) +1= 9x

Answers

X = 7/12 or another way x= 0.583

Answer:

x=3/8

Step-by-step explanation:

Multiplique dentro del paréntesis por -1/2.Después de haber multiplicado le ecuación le quedará así 3x + 5/4 +1 = 9x.Ahora vamos a calcular la suma de la ecuación y quedará a 3x + 9/4 =9x.Después vamos a multiplicar ambos lados de la ecuación por 4 y quedará a 12x + 9= 36x.Luego vamos a mover la constante ( que es 9) al lado derecho y cambié su signo y quedará a 12x = 36x - 9.Después vamos agrupar los términos semejantes ( en este caso x) y quedará a -24x = -9.Finalmente vamos a dividir ambos lados de la ecuación entre -24 y la respuesta nos quedará a x = 3/8.

Which of the following are dimensionally consistent? (Choose all that apply.)(a) a=v / t+xv2 / 2(b) x=3vt(c) xa2=x2v / t4(d) x=vt+vt2 / 2(e) v=x2 / at3(f) a3=x2v / t5(g) x=t(h) v=5at

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

A

is dimensionally consistent

B

is not dimensionally consistent

C

is dimensionally consistent

D

is not dimensionally consistent

E

is not dimensionally consistent

F

is dimensionally consistent

G

is dimensionally consistent

H

is not dimensionally consistent

Step-by-step explanation:

From the question we are told that

   The equation are

                        [tex]A) \   \  a^3  =  \frac{x^2 v}{t^5}[/tex]

                       

                       [tex]B) \   \  x  =  t [/tex]

 

                       [tex]C \ \ \ v  =  \frac{x^2}{at^3}[/tex]

 

                      [tex]D \ \ \ xa^2 = \frac{x^2v}{t^4}[/tex]

                      [tex]E \ \ \ x  = vt+ \frac{vt^2}{2}[/tex]

                     [tex]F \ \ \  x = 3vt[/tex]

 

                    [tex]G \ \ \  v =  5at[/tex]

 

                    [tex]H \ \ \  a  =  \frac{v}{t} + \frac{xv^2}{2}[/tex]

Generally in dimension

     x - length is represented as  L

     t -  time is represented as T

     m = mass is represented as M

Considering A

           [tex]a^3  =  (\frac{L}{T^2} )^3 =  L^3\cdot T^{-6}[/tex]

and    [tex]\frac{x^2v}{t^5 } =  \frac{L^2 L T^{-1}}{T^5}  =  L^3 \cdot T^{-6}[/tex]

Hence

           [tex]a^3  =  \frac{x^2 v}{t^5}[/tex] is dimensionally consistent

Considering B

            [tex]x =  L[/tex]

and      

            [tex]t = T[/tex]

Hence

      [tex]x  =  t[/tex]  is not dimensionally consistent

Considering C

     [tex]v  =  LT^{-1}[/tex]

and  

    [tex]\frac{x^2 }{at^3} =  \frac{L^2}{LT^{-2} T^{3}}  =  LT^{-1}[/tex]

Hence

   [tex]v  =  \frac{x^2}{at^3}[/tex]  is dimensionally consistent

Considering D

    [tex]xa^2  = L(LT^{-2})^2 =  L^3T^{-4}[/tex]

and

     [tex]\frac{x^2v}{t^4}  = \frac{L^2(LT^{-1})}{ T^5} =  L^3 T^{-5}[/tex]

Hence

    [tex] xa^2 = \frac{x^2v}{t^4}[/tex]  is not dimensionally consistent

Considering E

   [tex]x =  L[/tex]

;

   [tex]vt  =  LT^{-1} T =  L[/tex]

and  

    [tex]\frac{vt^2}{2}  =  LT^{-1}T^{2} =  LT[/tex]

Hence

   [tex]E \ \ \ x  = vt+ \frac{vt^2}{2}[/tex]   is not dimensionally consistent

Considering F

     [tex]x =  L[/tex]

and

    [tex]3vt = LT^{-1}T =  L[/tex]      Note in dimensional analysis numbers are

                                                       not considered

  Hence

       [tex]F \ \ \  x = 3vt[/tex]  is dimensionally consistent

Considering G

    [tex]v  =  LT^{-1}[/tex]

and

    [tex]at =  LT^{-2}T =  LT^{-1}[/tex]

Hence

      [tex]G \ \ \  v =  5at[/tex]   is dimensionally consistent

Considering H

     [tex]a =  LT^{-2}[/tex]

,

       [tex]\frac{v}{t}  =  \frac{LT^{-1}}{T}  =  LT^{-2}[/tex]

and

    [tex]\frac{xv^2}{2} =  L(LT^{-1})^2 =  L^3T^{-2}[/tex]

Hence

    [tex]H \ \ \  a  =  \frac{v}{t} + \frac{xv^2}{2}[/tex]  is not dimensionally consistent

We want to see which ones of the given expressions are dimensionally consistent. We will see that the correct options are:

a) x = 3*v*th) v = 5*a*t

What means to be dimensionally consistent?

This means that we have the same units in the left and in the right side of the equation.

The units are:

a = [m/s^2]x = [m]v = [m/s]t = [s]

Now we can analyze the expressions to see the units in each one, I will show you how to do it:

a) a = v/t + x*v^2

Replacing the units we have:

[m/s^2] = [m/s]/[s] + [m]*[m^2/s^2]

[m/s^2] = [m/s^2] + [m^3/s^2]

You can see that we have an m^3 in the right side, so these are not equivalent.

b) x = 3*v*t

Replacing the units we have:

[m] = 3*[m/s]*[s] = 3*[m]

So yes, the units are the same in both sides, so this is dimensionally consistent.

With the same procedure we can see that:

c) [m^3/s^2] = [m^3/s]                not consistentd) [m] = [m] + [m*s]                     not consistente) [m/s] = [m^2]                           not consistentf) [m^3/s^6] = [m^3/s]                 not consistentg) [m] = [s]                                   not consistenth) [m/s] = 5*[m/s]                        consistent

So the correct options are b and h.

If you want to learn more about dimensions, you can read:

https://brainly.com/question/20384972

You have a bin full of the letters HGUSTWQ. If four letters are drawn at random, what is the probabilty the letters drawn will spell the word GUST ( in the order they are drawn )?

Answers

Answer:

see I need help for chemistry pls anyone here helps me I must submit before 10:30

what is the domain and range of f(x)=2x+3

Answers

Answer:

D:{x∈R}

R:{y∈R}

Step-by-step explanation:

This is just a linear function. I know this because the degree of the x-variable is 1.

Domain and range are sets of possible values the function can have - though not necessarily at the same time.

Thus, there are no restrictions to the domain and range unless context is given.

Therefore, the domain and range is:

D:{x∈R}

R:{y∈R}

Perform the following operations and write the answers in radical form. Part A:√7+√3+√98−√18 Part B:3√5−3√11+2√121−3√90

Answers

Answer:

[tex]\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex] [tex]3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]

Step-by-step explanation:

Part A ;

[tex]\sqrt{7} +\sqrt{3} +\sqrt{98} -\sqrt{18} \\\\\sqrt{98}=7\sqrt{2}\\\sqrt{18}=3\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+7\sqrt{2}-3\sqrt{2}\\\\\mathrm{Add\:similar\:elements:}\:7\sqrt{2}-3\sqrt{2}=4\sqrt{2}\\\\=\sqrt{7}+\sqrt{3}+4\sqrt{2}[/tex]

Part B ;

[tex]3\sqrt{5} - 3\sqrt{11} + 2\sqrt{121} -3\sqrt{90} \\\\2\sqrt{121}=22\\3\sqrt{90}=9\sqrt{10}\\\\=3\sqrt{5}-3\sqrt{11}+22-9\sqrt{10}[/tex]

G(x) = 2x^2 and h(x) = √x^2+1 .What is (goh)^-1 and is it a function?

Answers

Answer:

Step-by-step explanation:

Hello,

[tex](goh)(x)=g(h(x))=2\left( \sqrt{x^2+1}\right)^2=2(x^2+1)\\\\x=(goh)((goh)^{-1}(x))=2((goh)^{-1}(x)^2+1)\\ \\\left((goh)^{-1}(x)\right)^2=\dfrac{x}{2}-1=\dfrac{x-2}{2}\\ \\(goh)^{-1}(x)=\sqrt{\dfrac{x-2}{2}}[/tex]

And this is a function defined for x-2 [tex]\geq[/tex] 0, meaning x [tex]\geq[/tex] 2

Thanks

Help me please this is math

Answers

Answer:

c) none of the above

Step-by-step explanation:

this is because we should put the equation like:

1/3 - (-4/3) because the distance is 5 units and

1/3 + 4/3 = 5/3

this is because (-) × (-) = (+)

help me asap i don't know this

Answers

Answer:

y = 3

Step-by-step explanation:

Step 1: Write equation

-2(7 - y) + 4 = -4

Step 2: Subtract 4 on both sides

-2(7 - y) = -8

Step 3: Distribute

-14 + 2y = -8

Step 4: Add 14 to both sides

2y = 6

Step 5: Divide both sides by 2

y = 3

What is the sum of Negative 1 + (negative 3)?

Answers

Answer:

[tex]\huge\boxed{-4}[/tex]

Step-by-step explanation:

=> [tex]\sf -1 + (-3)[/tex]

According to the rule [tex]\sf + * - = -[/tex]

=> [tex]\sf -1-3[/tex]

=> -4

Answer:

-4

Step-by-step explanation:

-1 + (-3)

To add two negative numbers, add their absolute values, and make the answer negative.

The absolute values of -1 and -3 are 1 and 3. We add 1 + 3 and get 4.

Then we make the answer negative.

-1 + (-3) = -4


4x – 3y = 20
2x + y = 30
Using the two equations above, solve for y.

Answers

Answer:

4x-3y+20

Step-by-step explanation:

x=6.875

y=2.5

2x+y=30

x=12.5

y=-5

y=1/4x + 6
that passes through the point (-4, 3) in slope-intercept form.

Answers

Answer:

The answer is

[tex]y = \frac{1}{4} x + 4[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line.

The equation is

y = 1/4x + 6

Comparing with the general equation above

Slope = 1/4

Since the lines are parallel their slope are also the same

That's

Slope of parallel line = 1/4

So the equation of the parallel line using point (-4 , 3) and slope 1/4 is

[tex]y - 3 = \frac{1}{4} (x + 4) \\ y - 3 = \frac{1}{4} x + 1 \\ y = \frac{1}{4} x + 1 + 3[/tex]

We have the final answer as

[tex]y = \frac{1}{4} x + 4[/tex]

Hope this helps you

Chris wonders whether the planes that fly over his house follow any sort of pattern. For two months, he
records whether each plane he sees follows a north-south route or an east-west route. He also records the
day of the week that he sees each plane.
Unfortunately, Chris dropped his data in the mud and can't read all of his numbers. The absolute and
relative frequency tables below show the numbers that Chris is able to read. Can you help him figure out
the rest?
Fill in the missing values from each table.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

From the relative frequency below:

For NORTH - SOUTH:

Monday - Thursday = 115 ; has a relative frequency of 75.16%,

Hence, we can obtain the row total since it amounts to 100% thus;

75.16% of row total = 115

0.7516× row total = 115

Row total = 115 / 0.7516 = 153.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

153 - 115 = 38

FOR EAST - WEST:

Monday - Thursday = 21 ; has a relative frequency of 25.30%,

Hence, we can obtain the row total since it amounts to 100% thus;

25.30% of row total = 21

0. 253 × row total = 21

Row total = 21 / 0.253 = 83.00

Hence, Friday - sunday:

Row total - (Monday-Thursday)

83 - 21 = 62

x = (38 / 100) × 100%

x = 0.38 × 100%

x = 38.00 %

Answer:

The basic explanation:

North - South/Friday - Sunday- 38 // Row total- 153

East - West/Friday - Sunday- 62 // Row total- 83

x- 38

Evaluate (5-3)^3+ -3^2(6-3)

Answers

Steps to solve:

(5 - 3)^3 + (-3)^2(6 - 3)

~Simplify

2^3 + (-3)^2(3)

2^3 + (-3)^6

~Solve exponents

8 + (-729)

~Subtract

-721

Best of Luck!

I have 4 questions

1. Suppose point T is between points R and V on a line. If RT = 63 units and RV = 131 units,
then what is TV?

131

194

68

80

2.Given point P is between M and N. If MN = 26, MP = x + 4, and PN = 2x + 1, what is the value of x?

x = 3

x = 7

x = 12.5

x = 22

3.Given M is the midpoint of HJ, HM = 4x - 12, and MJ = 3x + 9. What is the value of x?

4.If D is the midpoint of CE, DE = 2x + 4, and CE = 6x + 2, then what is CD?

Answers

The first one is C. 68. The second one is B. 7. The third one is x = 21. The fourth one is CD = 10

Angles 1 and 2 form a right angle. 2 lines form a right angle. Another line extends between the 2 lines to form 2 angles. The top angle is labeled 1, and the bottom angle is labeled 2. Which word describes their measures? linear congruent complementary supplementary

Answers

Answer:

complementary

Step-by-step explanation:

yes

The word that describes their measures of ∠1 and ∠2 is: complementary.

Recall:

Angles that are complementary are angles whose sum equals 90 degrees.A right angle equals 90 degrees.

From the information given, we know that:

m∠1 and m∠2 forms a right angle.

Since a right angle = 90 degrees, therefore:

m∠1 + m∠2 = 90° (complementary)

Therefore, the word that describes their measures of ∠1 and ∠2 is: complementary.

Learn more about complementary angles on:

https://brainly.com/question/11242655

please help :)) ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

Answers

34 is a rational number hole this helped :))

I
rep
What is the solution of 4(2y + 1) = 2(y - 13)
What is the answer

Answers

Answer:

- 5

Step-by-step explanation:

Step 1:

4 ( 2y + 1 ) = 2 ( y - 13 )

Step 2:

8y + 4 = 2y - 26

Step 3:

6y + 4 = - 26

Step 4:

6y = - 30

Answer:

y = - 5

Hope This Helps :)

Which of the following is an example of a translation?
a) The preimage is twice the size as the image.
b) The preimage is moved 5 spaces up.
c) The preimage is rotated 90 degrees about the origin.
d) The image is a mirror reflection of the preimage.



Answers

Answer:

Step-by-step explanation:

a)the pre image us twice the same size as the image

What number line correctly shows one way to find 2-6 ?

Answers

0? Because it separates the negative and positives??

The velocity of an object is given by the following function defined on a specified interval. Approximate the displacement of the object on this interval by subdividing the interval into the indicated number of subintervals. Use the left endpoint of each subinterval to compute the height of the rectangles. v = 1/(2t + 4) (m/s) for for 0 ≤ t ≤ 88; n = 22

Answers

Answer:

The displacement of the object on this intervals is 1.33 m.

Step-by-step explanation:

Given that,

The function of velocity is

[tex]v=\dfrac{1}{2t+4}\ m/s[/tex]

For 0 ≤ t ≤8 , n = 2

We need to calculate the intervals

Using formula for intervals

For, n = 1

[tex]\Delta x=\dfrac{t_{f}-t_{i}}{n}[/tex]

[tex]\Delta x=\dfrac{8-0}{2}[/tex]

[tex]\Delta x=4[/tex]

So, The intervals are (0,4), (4,8)

We need to calculate the velocity

Using given function

[tex]v=\dfrac{1}{2t+4}[/tex]

For first interval (0,4),

Put the value into the formula

[tex]v_{0}=\dfrac{1}{2\times0+4}[/tex]

[tex]v_{0}=\dfrac{1}{4}[/tex]

For first interval (4,8),

Put the value into the formula

[tex]v_{4}=\dfrac{1}{2\times4+4}[/tex]

[tex]v_{4}=\dfrac{1}{12}[/tex]

We need to calculate the total displacement

Using formula of displacement

[tex]D=(v_{0}+v_{4})\times(\Delta x)[/tex]

Put the value into the formula

[tex]D=(\dfrac{1}{4}+\dfrac{1}{12})\times4[/tex]

[tex]D=1.33\ m[/tex]

Hence, The displacement of the object on this intervals is 1.33 m.

The displacement of the object whose velocity function is given is 1.33 m

The given parameters are:

[tex]\mathbf{v = \frac{1}{2t + 4},\ 0 \le t \le 8; n =2}[/tex]

The end point of intervals is calculated as:

[tex]\mathbf{\triangle t = \frac{b - a}{n}}[/tex]

So, we have:

[tex]\mathbf{\triangle t= \frac{8 - 0}{2}}[/tex]

[tex]\mathbf{\triangle t = \frac{8}{2}}[/tex]

[tex]\mathbf{\triangle t= 4}[/tex]

So, the intervals are (0,4) and (4,8)

Calculate the velocity at the beginning of each interval

[tex]\mathbf{v_0 = \frac{1}{2(0) + 4} = \frac 14}[/tex]

[tex]\mathbf{v_4 = \frac{1}{2(4) + 4} = \frac 1{12}}[/tex]

Calculate the displacement (S) using:

[tex]\mathbf{S = (v_0 + v_4) \times \triangle t}[/tex]

So, we have:

[tex]\mathbf{S = (1/4 + 1/12) \times 4}[/tex]

Expand

[tex]\mathbf{S = 1 + 1/3}[/tex]

Add

[tex]\mathbf{S = 1 \frac 13}[/tex]

Express as decimals to 2 decimal places

[tex]\mathbf{S = 1.33}[/tex]

Hence, the displacement is 1.33 m

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Martin's average score after 4 tests is 89. What score on the 5th test would bring Martin's average up to exactly 90?

Answers

Answer:

104

Step-by-step explanation:

89x4=356 90x5=450

450=356=104

Answer:

94

Step-by-step explanation:

((89x4)+94) divided by 5 = 90

Jack is packing snacks for him and his three brothers. He bought 10 1/2 ounces of pretzels. He wants to put the pretzels into bags so that he and his three brothers have the same of pretzels in their bags. How many ounces of pretzels should he put into each bag?

Answers

Answer:

3.5

Step-by-step explanation:

total pretzel=10 1/2 or10.5

no. of brother = 3

now,

10.5 pretzel for each borther= 10.5/3

=3.5 ans

The three volumes of Lord of the Rings sit in order on a shelf. Each is 1 1/4 inches thick, comprising an inch of pages and 1/8 inch for each cover. A bookworm bores from page 1, volume I, to the last page of volume III. How far does it travel?

Answers

Answer:

4 2/4 (NOT SIMPLIFIED)

Step-by-step explanation:

Comprising means made of (aka including). You just add 1 1/4+1 1/4+1 1/4.

=3 3/4

The 1/8 is for the front and back cover. The bookworm ate through 3 volumes so there is 6 covers. So times 1/8 by 6. I turned the 6 into a fraction by putting it over 1. So now you have 1/8×6/1=6/8. Now you are going to add the 3 3/4 to the 6/8. You are going to turn the whole fraction to an improper. You are going to multiply the whole number(3) to the denominator(4), add that to the numerator(3) , and put it over the original denominator (4)= 15/4. Now you are going to set up the problem were you add the 6/8 to the 15/4. To add fractions the denominator have to be the same. With this problem you have two options: you can either do an equation to change the 6/8 denominator equal to 4 or an equation to change the 15/4 denominator equal to 8. Either one would work fine. I'm going to show you how to set the 6/8 denominator to 4.

1. Set it up as an equation                       6/8=x/4

2. Find what gets the first denominator to the second in this case dividing by 2                                                          6/8=x/4

3. What you do to the bottom is what you have to do with the top. So to find x, you need to divide 6 by 2= 3

So now your new equation is now 3/4+15/4. Adding this should give you 18/4, but most likely you have to write it as a proper fraction. To do this you are going to divide the 18 by 4. Your remainder will become your new numerator and the 4 will still be you denominator. The number times 4 fully goes into 18 will be your new whole number.

18/4=4.5

If KL = x + 4, LM = 2, and KM = 5x − 3, what is KL?

Answers

Step-by-step explanation:

then put x valule into KL equation

What is the fractional equivalent of the repeating decimal 0.2 ?​

Answers

Answer:

1/5

Step-by-step explanation:

I put it in a graphing calculator and converted it into a fraction

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