Identify the correct justification for each step, given that m∠1+m∠2=90° and m∠2+m∠3=90°.

The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.

The formula for the height of the projectile can be used to calculate the hang time as follows;

h = ut - 0.5at²

here;

h is the height of the projectile

u is the velocity = 7.3 m/s

a is the acceleration due to gravity

The standard value of acceleration due to gravity is equal to 9.81 m/s²

The height will be zero both the times when t=0 and when the journey has been completed

Now adding these values to the formula;

h = ut - 0.5at²

0 = 7.3t - 0.5(9.81)t²

Solving for t;

4.905t² = 7.3t

4.905t² / t = 7.3

4.905t = 7.3

t = 7.3 / 4.905

t = 1.49 ≈ 1.5

Therefore; the hang time is calculated to be 1.5 seconds.

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Answer: I think 43

Step-by-step explanation:

Draw on a graph out the points and then add up the middle of your shape.

Your welcome!

The total number of different combinations is 120.

What is combination and permutation?

We are to find the number of different combinations of classes does Sylvia have to choose from.

We will be using  the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:

  nCr  = n!/r!( n - r )!

Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be

    ⁴C₁ * ²C₁  *  ³C₁  *  ⁵C₁  

= 4!/1!( 4 - 1 )!  × 2!/1! ( 2 - 1 )!  ×  3!/1! ( 3 -1)!  × 5!/1! ( 5 - 1 )!

= 4 × 2 × 3 × 5

= 120

Thus, the total number of different combinations is 120.

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Answer:

C

Step-by-step explanation:

Since the y-coordinates of both points are -3, the equation is [tex]y=-3[/tex].

The only option with a y-coordinate of -3 is option C.

The inequality which correctly represents the fact that the spending limit cannot be exceeded as described in the task content is; 100x ≤ 200.

It follows from the task content that the inequality which correctly represents the spending limit as described be determined.

Since the given spending limit is; $200.

Let, x = the number of figures made.

Therefore, the cost of making x number of figures can be written algebraically as; 100x.

Hence, since it costs $100 to make each figure, it follows that the required inequality is;

100x ≤ 200.

This follows from the fact that each figure costs $100 to make.

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Answer:

J(18)-9

Step-by-step explanation:

j times 18 minus 9

The circumference of the circle will be given by 62.84 cm.

A circle is a closed figure having a fixed point known as center of the circle and the distance from the center to any point on the boundary of circle is known as the radius of the circle. Circumference is the total length of the boundary of the circle. The circumference of the circle is given by the formula

C = 2πr where r is the radius of the circle and the value of π is given as 3.142.

Now, according to question r = 10cm

C = 2×3.142×10

C = 20×3.142

=> C = 62.84 cm

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The two values or x of roots of the polynomial are

[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]

This is further explained below.

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Generally, the equation for polynomial the is mathematically given as

x^2 - 11x + 13

Therefore

We know that,

[tex]x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]

Here,

a=1

b=-11

c=13

Putting the values,

[tex]x=\frac{-(-11) \pm \sqrt{(-11)^2-4 \times 1 \times 13}}{2 \times 1} \\[/tex]

[tex]&=\frac{11 \pm \sqrt{121-52}}{2} \\\\&=\frac{11 \pm \sqrt{69}}{2} \\[/tex]

Therefore

[tex]x=\frac{11+\sqrt{69}}{2}, \frac{11-\sqrt{69}}{2}[/tex]

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When 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2

Consider the number as x

Square of the number = [tex]x^{2}[/tex]

12 subtracted from the square of a number = [tex]x^{2} -12[/tex]

4 times the number = 4x

Then the equation will be [tex]x^{2} -12=4x[/tex]

Rearrange the terms and it will become a quadratic equation

[tex]x^{2} -4x-12=0[/tex]

Split the middle term and solve the equation

[tex]x^{2} +2x-6x-12=0[/tex]

Take common terms

x(x+2)-6(x+2) = 0

Take common term outside

(x-6)(x+2) = 0

Therefore

x = 6, -2

The negative solution is -2

Hence, when 12 is subtracted from the square of a number and the result is 4 times the number, then the negative solution is -2

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We have that the area of the infield is 81 in2.

This area is a square, which means it has equal sides, and its area is:

If the area of the square is 81 in2, we have that:

So the side of the infield is 9 inches.

Answer:

D. [tex]\sqrt{27}[/tex]

Step-by-step explanation:

A, B, and C are all perfect squares being square rooted. This means that they will all result in whole numbers.

For example: A.   [tex]\sqrt{9}=3[/tex]

However, D.         [tex]\sqrt{27}=3\sqrt{3}[/tex], which is not rational because it contains an unsimplifiable square root (sqrt 3)

Answer:

√27

Step-by-step explanation:

√9 = 3

√81 = 9

√36 = 6

√27 = not whole number

Answer: I think the answer is $1.21

Step-by-step explanation: Instead of 3 pairs it says 3 dozen. A dozen is 12.

3 x 12 = 36

Then you should do 43.56 / 36

For one pair of gloves it should be $1.21

The contractor got $14.52 because he did a dozen (12) divided by 43.56.

I hope that helps! ^^

Following the descriptions of the relationship existing  between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d

Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.

Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.

Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.

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The distance that the person bike over the past 5 weeks is 7284 feet.

Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered. Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

From the information, the forest trail is 607 feet long and a person biked from one end to the other and back again 6 times in the past 5 weeks.

Therefore, the distance that the person covered will be:

= 2 × 6 × 607

= 7284 feet.

The distance is 7284 feet.

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Answer:

See below

Step-by-step explanation:

99.87-71 = 28.81     this is   28.81/12 = z-score = +2.4

   corresponding to .9918  ( from z-score table)  =  a score of 99.18%

Answer:

answer is B

Step-by-step explanation:

Sorry if this is incorrect

The solution set of the given inequality is:

9.52  ≤  x  ≤ 22.22

Or [9.52, 22.22] if we write this as an interval.

Here we have the inequality:

200 ≤ 15.75x + 50 ≤ 400

Which represents Kali's earning potential.

To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:

200 - 50 ≤ 15.75x + 50  - 50 ≤ 400 - 50

150 ≤ 15.75x ≤ 350

Now we need to divide both all by 15.75, so we get:

150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75

9.52  ≤  x  ≤ 22.22

This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]

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Considering the definition of prime numbers, the sum of the first 11 prime numbers is 129.

Prime numbers are those that are only divisible (when divided by another gives an integer) between themselves and 1. That is, prime numbers are those numbers, greater than 1, that only admit themselves and the number as divisors. number 1.

The first 11 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31.

So their sum is:

sum= 2 +3 +5 +7 +11 +13 +17 +19 +23 +29

sum= 129

Finally, their sum is 129.

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Answer:

oh ok hope you got the answer

Step-by-step explanation:

Answer: 12.8x2

Step-by-step explanation:

Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².

The correct answer option is option a.

This is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.

For instance, from the task which is given above;

3.2x and 4x

= 3.2x × 4x

= 12.8x²

In this answer above,

12.8 is the coefficient and

x² is the variable.

In conclusion, 3.2x × 4x will give the result 12.8x².

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Answer: No, 6 boxes will give you 288 penicils.

Step-by-step explanation: 1 box is 48 penicils, so if use this to the other boxes (4x48) we get 192. Now with six boxes (6x48) we get 288.

Answer:

A. -11x + 7y

Step-by-step explanation:

4y - 9x + 3y - 2x

4y + 3y = 7y

-9x - 2x = -11x

-11x + 7y

I hope this helps!

Answer:

There are many numbers, but here are three

4.11, 4.12, 4.13

Step-by-step explanation:

If A=[-9,0,3,-1] b=[0,4,-6,2] , so the order of matrix A+B is 4x1(4 rows and 1 column).

Matrix, a set of number arranged in rows and column so as to form a rectangular array. The number are called the elements, or entries, of the matrix .

Both data and mathematical equations can be represented by the numbers in a matrix. Multiplying matrices can provide quick but accurate approximations of considerably more complex calculations in many time-sensitive engineering applications.

The elements of the matrix are nothing but the entries of the matrix.

So according, To the question we are adding matrix A which is 4 rows and 1 column to matrix B which is also of 4 rows and one column obtaining a third matrix that has also 4 rows and 1 column :

 [-9,0,3,-1]+[0,4,-6,2]=[-9,4,-3,1]

The resultant A+B is also of 4 rows and 1 column

Hence the order of matrix A+B is 4x1 (4 rows and 1 column)

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The rate of change of the level of the swimming pool is -0.019 inches per hour.

The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.

We know that the change happens between 10 pm and 7:45pm, so the number of hours is:

2 hours + 7 hours + 45 min

Where:

1 hour  = 60 min

45 min = 45/60 hours = 0.75 hour

Then the total time is:

2h + 7h + 0.75h = 9.75h

Then the rate of change is:

R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.

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