Mathematics :asked ondondre54

19.05.2023the following question

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19.05.2023, solved by verified expert

50% of 50 questions is 25 questions.

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Mathematics

If i have a 50 question test final and i need a 50% to maintain my grade how many questions do i have to get right?

Step-by-step answer

**P** Answered by PhD 1

50% of 50 questions is 25 questions.

Mathematics

Graph the function y = 6/x . draw a chart to show the ordered pairs that are on the graph. x y -3 -2 -1 1 2 3

Step-by-step answer

**P** Answered by PhD

see the attachment for the graph and chart

Step-by-step explanation:

A spreadsheet or graphing calculator is convenient for making a chart of ordered pairs.

There are 4 consecutive integers that add up to 154. what is the least of these integers?

Step-by-step answer

**P** Answered by PhD 1

Step One

Set up the equation.

Let x be the smallest number. A consecutive integer is one that follows after another number that is smaller. The difference between the two numbers is one.

x + x + 1 + x + 2 + x + 3 = 154

Step Two

Collect all the like terms on the left.

4x + 6 = 154

Step 3

Solve

4x + 6 = 154 Subtract 6 from both sides.

4x = 154 - 6

4x = 148 Divide by 4

x = 148 / 4

x = 37

The smallest number is 37 <<<<< answer.

Mathematics

Part 1: solve the system by graphing. draw the graphs on paper and indicate their intersection point. type the ordered pair solution here as your answer to part 1. part 2: solve the system using the substitution method. show all work here and indicate the solution for the system as an ordered pair. part 3: solve the system using the addition method. show all work here and indicate the solution for the system as an ordered pair. 2x+3y=6 x-2y=10

Step-by-step answer

**P** Answered by Specialist 1

Part (1):

The graph is shown in the attached image.

As we can note from the graph, the solution of the system of equations is indicated by the point of intersection between the two lines which is (6,-2)

Part (2):

The equations given are as follows:

2x + 3y = 6 ...........> equation I

x - 2y = 10

which can be rewritten as:

x = 2y + 10 ...........> equation II

Substitute with equation II in equation I and solve for y as follows:

2x + 3y = 6

2(2y+10) + 3y = 6

4y + 20 + 3y = 6

7y = 6 - 20

7y = -14

y = -2

Substitute with y in equation II to get x as follows:

x = 10 + 2y

x = 10 + 2(-2)

x = 10 - 4

x = 6

The solution is (6,-2)

Part (3):

The equations given are:

2x + 3y = 6 .............> equation I

x - 2y = 10 ...........> equation II

Multiply equation II by -2, this will give:

-2x + 4y = -20 ............> equation III

Add equation I and equation III as follows:

2x + 3y = 6

+ -2x + 4y = -20

.........................................

0x + 7y = -14

7y = -14

y = -2

Substitute with y in equation II to get x as follows:

x - 2y = 10

x - 2(-2) = 10

x + 4 = 10

x = 10 - 4

x = 6

The solution is (6,-2)

Hope this helps :)

Mathematics

What is the ordered pair of real numbers $(x, y)$ which satisfies the equation $|x+ y-7|+ |4x - y+ 12|= 0$?

Step-by-step answer

**P** Answered by PhD 2

We know that

if|x+ y-7|+ |4x - y+ 12|= 0

then

x+ y-7=0

and

4x - y+ 12=0

using a graph tool

see the attached figure

the solution is the point (-1,8)

the answer is

the ordered pair of real numbers is (-1,8)

Mathematics

The density of air is approximately 1.225 kg/m^3 what is the volume of a soccer ball if the mass of the air it contains is 0.08 kg

Step-by-step answer

**P** Answered by Specialist 6

Using the the density(D)-mass(m)-volume(V) formula, we can calculate the volume

Mathematics

How do i find the coodinates of the vertices?

Step-by-step answer

**P** Answered by Specialist

When you want to find the coordinates of vertices on coordinate plane, first :

1- look for the movement of the vertice parallel to x-axis (how many square houses did the vertice move to left or right?)if it moved right, the number is positive. if it moved left, then it's negative.

2- find out the movement of the vertice parallel to y-axis (how many square houses did the vertice move up or down?) if it moved up, the number is positive. if it moved down, it's negative

3- write the numbers as coordinates (x,y)

for example: the coordinates of this vertice is:

it moves 4 to right(positive) and 6 to down(negative)

good luck

Mathematics

Given that p(5,4), q=7,3), r=(8,6) and s=(4,1) find the component from of the vector pq+5rs use the information from above to find the magnitude of the vector pq+5rs

Step-by-step answer

**P** Answered by PhD 5

For this case we have the following ordered pairs:

P (5.4)

Q = 7.3)

R = (8.6)

S = (4.1)

For the PQ vector we have:

PQ = Q-P = (7, 3) - (5, 4)

PQ = (2, -1)

For the RS vector we have:

RS = S-R = (4, 1) - (8, 6)

RS = (-4, -5)

Then the vector PQ + 5RS is given by:

PQ + 5RS = (2, -1) + 5 (-4, -5)

PQ + 5RS = (2, -1) + (-20, -25)

PQ + 5RS = (-18, -26)

Finally, the magnitude of the vector is:

lPQ + 5RSl = root ((- 18) ^ 2 + (-26) ^ 2)

lPQ + 5RSl = 31.6

Vector:

PQ + 5RS = (-18, -26)

Magnitude:

lPQ + 5RSl = 31.6

Mathematics

Aresearcher has funds to buy enough computing power to number-crunch a problem in 5 years. computing power per dollar doubles every 23 months. when should he buy his computers to have finished the problem as soon as possible? give your answer as a decimal in months, accurate within 0.1 months suppose the problem would take c months on current computers. what is the largest value of c for which he should buy the computers immediately? give an answer as a decimal accurate to 0.1 months.

Step-by-step answer

**P** Answered by PhD 1

A) In t months, the number of months required to number-crunch the problem will be

60*2^(-t/23)

By waiting t months, the researcher has made the total time f(t) to the solution of his problem be

f(t) = t + 60*2^(-t/23)

The derivative of this is

f'(t) = 1 + 60*ln(2)*(-1/23)*2^(-t/23)

We want to find the value of t that makes this be zero.

0 = 1 - 60*ln(2)/23*2^(-t/23)

2^(-t/23) = 23/(60*ln(2))

(-t/23)*ln(2) = ln(23/(60*ln(2)))

t = -23/ln(2)*ln(23/(60*ln(2))) ≈ 19.655

In order to finish his problem as soon as possible, the researcher should wait 19.7 months to buy his computers.

b) For this part of the problem, we want to find the value of "60" that makes t=0 be the solution. Taking the last expression and substituting t=0, 60=c, we get

0 = -23/ln(2)*ln(23/(c*ln(2)))

1 = 23/(c*ln(2)) . . . . . taking antilogs

c = 23/ln(2) ≈ 33.2

The largest value of c for which he should buy the computers immediately is 33.2.

Mathematics

How does multiplying a vector by a scalar value of 2pi change the vector? a.) the vector will change direction and increase in magnitude. b.) the vector will change direction and decrease in magnitude. c.) the vector will not change direction but will increase in magnitude. d.) the vector will not change direction but will decrease in magnitude.

Step-by-step answer

**P** Answered by Master 27

This is a problem of geometry. So, ascalarhasmagnitude(size)only. Therefore, we can conclude that ta scalar is justa number. If we multiply a vectorby a scalar it is called scalinga vector, because we change how big or small the vector is. Given that 2π is a positive scalar then the answer is:

C) The vector will not change direction but will increase in magnitude.

This is true because:

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