MATHEMATICS HIGH SCHOOL

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The perimeter of the rectangle is 2(5x – 2) + 2(3x + 1). If x = 4 centimeters, what is the total distance Zohar needs to cut with the scissors? 31 centimeters 36 centimeters 62 centimeters 70 centimeters

Answers

Answer 1
Answer: This is the concept of algebra, given that the length of the rectangle is 5x-2 and the width is 3x+1, the perimeter is 2(5x-2)+2(3x+1). To get the total distance Zohar needs to  cut with the scissors, we substitute the value of x=4 in the expression for perimeter. Hence we shall have:
2(5x-2)+2(3x+1)
=2(5*4-2)+2(3*4+1)
=2(20-2)+2(12+1)
=2(18)+2(13)
=36+26
=62 cm 

The answer is 62 cm

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The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:Car A
y = 55x + 32

Car B
y = 42x + 58

After how many hours will the two cars be at the same distance from their starting point and what will that distance be?


2 hours, 142 miles
2 hours, 145 miles
3 hours, 142 miles
3 hours, 145 miles

Answers

Answer:

Option A is correct

2 hours, 142 miles

Step-by-step explanation:

As per the statement:

The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:

Car A

y = 55x + 32             ....[1]

Car B

y = 42x + 58             ....[2]

We have to find after how many hours will the two cars be at the same distance from their starting point.

Since, two cars be at the same distance

equate [1] and [2] ;

⇒55x+32 = 42x+58

Subtract 42x from both sides we have;

⇒13x+32 =58

Subtract 32 from both sides we have;

13x=26

Divide both sides by 13 we have;

x = 2 hours

Substitute in [1] we have;

y = 55(2)+32 = 110+32 = 142 miles

Therefore, after 2 hours  will the two cars be at the same distance from their starting point and 142 miles will that distance be
2hrs, 142miles
42x+58=55x+32
13x=26
x=2hrs <---- answer
42*2+58=142
55*2+32=142mi <----answer

Write an equation for each condition 1) The line with a slope of 7 and a y-intercept of -1( in slope-intercept form)

2) The line that passes through (1,-5) and has a slope of 3 (in point-slope form)

Answers

1.
m=7\n b=-1\n\n y=7x-1

2.
y-y_1=m(x-x_1)\n y_1=-5\n x_1=1\n m=3\n\n y-(-5)=3(x-1)\n y+5=3(x-1)

A family wants to have 4 children. Design and do a simulation to determine the probability that, if they do have 4 children, they will have two boys and two girls. (Hint: Use coins.)

Answers

Let B represent boy and G represent girl, Then sample space

BBBB, BBBG, BBGB, BGBB, GBBB, BBGG, BGBG, GBBG, BGGB, GBGB, GGBB, BGGG, GBGG, GGBG, GGGB, GGGG

Two boys and two girls appeared in 6 situations.

Therefore, P(6 boys and 6 girls) = 6/16 = 3/8

Answer:

Using B as the boy and G as the girl, sample space

GGBB, BGGG, GBGG, GGBG, GGGB, GGGG, BBBB, BBBG, BBGB, BGBB, GBBB, BBGG, BGBG, GBBG, BGGB, GBGB, GGGG

Six different scenarios featured two boys and two girls.

P(6 boys and 6 girls) = 6/16 = 3/8 as a result.

Step-by-step explanation:

rahehehe

A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 4sin(t) - cos(2t), measured in feet. What is the acceleration of the particle at time t = 0 seconds?

Answers

Answer:

The acceleration of the particle at time t = 0 seconds is:

                       4  feet per square  second.

                         i.e.   4 ft/s²

Step-by-step explanation:

We are given a position function in terms of the time t as:

s(t)=4\sin (t)-\cos (2t)

Now, we are asked to find the acceeleration of the particle at time t = 0 seconds.

We know that the acceleration of a particle is given by:

a=(d)/(dt)v

where v is the velocity of the particle which is calculated by:

v=(d)/(dt)s

Hence, we get:

a=(d)/(dt)((d)/(dt)s)\n\ni.e.\n\na=(d^2)/(dt^2)s\n\ni.e.\n\na=s''(t)

i.e. the acceleration of the particle is the double derivative of the position.

s'(t)=4\cos (t)+2\sin (2t)

and

s''(t)=-4\sin (t)+4\cos (2t)

i.e.

a(t)=-4\sin (t)+4\cos (2t)\n\ni.e.\ at\ t=0\ we\ have:\n\na(0)=-4\sin 0+4\cos 0\n\ni.e.\n\na(0)=4

Which represents the polynomial written in standard form?

4m – 2m4 – 6m2 + 9

Answers

If you would like to write the polynomial in standard form, you can do this like this:

4m - 2m^4 - 6m^2 + 9

Writing the polynomial in standard form means that you have to write the terms by descending degree:
- 2m^4 - 6m^2 + 4m + 9

The correct result would be - 2m^4 - 6m^2 + 4m + 9.

An equation which represents the polynomial written in standard form is 2m⁴ - 6m² + 4m + 9.

What is a polynomial?

A polynomial can be defined as a mathematicalexpression which is comprises intermediates (variables), constants and exponents with different numerical value, that are typically combined by using mathematical operations such as:

  • Addition
  • Subtraction
  • Multiplication

In this scenario, the polynomial would be written in standard form by rearranging it in descending degree of exponents:

2m⁴ - 6m² + 4m + 9.

Read more on polynomials here: brainly.com/question/1600696

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Parker is planning for a school picnic. He would like to have 2 hot dogs per person and 15 extra on hand. How many hot dogs does he need if there are 116 students and 8 teachers?

Answers

Answer: There are 263 hot dogs he needs.

Step-by-step explanation:

Since we have given that

Number of students = 116

Number of teachers = 8

Total number of persons = 116+8=124

Number of hot dogs per person = 2

Number of hot dogs extra on hand = 15

So, Total number of hot dogs will be

124* 2+15\n\n=248+15\n\n=263

Hence, there are 263 hot dogs he needs.

Number of person = 116+8 = 124

Now, hot dogs would be = 124*2 +15 = 248 +15 = 263

So, 263 is your answer!!!
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