Is 4.887888 a rational number

Answer:

M∠2 = 37°

M∠3 = 143°

M∠4 = 37°

Step-by-step explanation:

∠3 is the complete opposite of ∠1

143° + 143° = 286°

there is 360° in a full circle or a repeating angle (aka the scissors)

360°-286°=74°

since ∠2 and ∠4 is opposite of each other

74°÷2=37°

Answer:

[tex]m \angle 2= \boxed{37}\;^{\circ}\\\\m \angle 3= \boxed{143}\;^{\circ}\\\\m \angle 4= \boxed{37}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠1 + m∠2 = 180°

⇒ 143° + m∠2 = 180°

⇒ m∠2 = 37°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

The function modeling given situation, where y represents the total weight of the crates in pounds, has a range described by the inequality 0 ≤ y ≤ 2000. The correct answer would be an option (C).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The set that includes all the output values that the function expects is the range of a function.

The following information is provided regarding the input and output for this problem

The number of containers placed inside the vehicle as input.

Total weight of the crates loaded into the truck or output.

The range of this problem is represented by the following inequality:

0 ≤ y ≤ 2000.

The weight of an amount will never assume a negative value, and the maximum weight is 2,000 pounds, as stated in the problem.

Learn more about the inequalities here:

brainly.com/question/20383699

#SPJ1

If you want to make an annual salary of $31,836, then your sales must be $25,280

Ok, so you want to earn a total of $31,836, and he has a fixed salary of $30,572, so the missing amount is:

$31,836 - $30,572 = $1,264

Now, we know that you make a commission of the 5% of what you sell, so if X is what you sell, then to make the desired salary X must be:

X*0.05 = $1,264

Solving that linear equation for X we get:

X = $1,264/0.05 = $25,280

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

The biggest problem with the results of this research study is B. Lack of realism.

It should be noted that when an experiment's procedures, participants, or setting are unrealistic. The ability of researchers to apply the findings of an experiment to the situations that hold the most interest may be constrained by a lack of realism.

The study is how how noise impacts student performance on exams is being proposed.

An experiment's subjects, medications, or environment might not accurately replicate the circumstances we truly wish to explore. In that circumstance, we are unable to extrapolate the experiment's findings broadly.

Learn more about research on:

https://brainly.com/question/25257437

#SPJ1

The options are:

a. Lack of attention to experimental detail

b. Lack of realism

c. Placebo effect

Considering the definition of an equation and the way to solve it, the number of monthly movies watched that would make the two plans have an equal monthly cost is 26.

An equation is an algebraic equality in which there are unknowns with unknown value. The unknown represents the number, if any, that makes the equality true. This unknown number is the solution of the equation.

This is, the solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the number of monthly movies watched, you know that:

If the two plans have an equal monthly cost, the equation in this case is:

A= B

34 + 2x= 8 + 3x

Solving:

34 - 8= 3x - 2x

26= x

Finally, 26 monthly movies watched would make the two plans have an equal monthly cost.

Learn more about equations:

brainly.com/question/20386726

brainly.com/question/4983716

brainly.com/question/13314678

#SPJ1

The equation in slope-intercept form is y = 2x + 6

The equation is given as

6x - 3y = -18

The above equation is a linear function, and it is in its general form

To determine the slope-intercept form of the equation, we simply make y the subject of the formula in the equation

So, we have

6x - 3y = -18

Divide through  the equation by -3

So, we have

-2x + y = 6

Add 2x to both sides

y = 2x + 6

Hence, the slope-intercept form of the equation is y = 2x + 6

Read more about linear equations at

https://brainly.com/question/14323743

#SPJ1

The number of pies that Red Riding Hood's mother made is 25.

Let x represent the number of pies mother baked in the morning.

Pies left after mother ate 1 = x - 1

The number of pies that Red Riding Hood takes to her grandmother: 1/2(x - 1)

0.5(x - 1)

0.5x - 0.5

Pies left after Red Riding Hood ate 2: [(0.5x - 0.5) - 2]

Pie after she gave the wolf 1/3 ; (1 - 1/3) × [(0.5x - 0.5) - 2]

2/3 × [(0.5x - 0.5) - 2]  = 8

In order to determine the value of x, take the following steps:

Multiply both sides of the equation by 3/2.

[(0.5x - 0.5) - 2] = 12

Add 2 to both sides of the equation: 0.5x - 0.5 = 12 + 2

0.5x - 0.5 = 12

Add 0.5 to both sides of the equation

0.5x = 12 + 0.5

0.5x = 12.5

Divide both sides by 0.5

x = 25

To learn more about mathematical equations, please check: https://brainly.com/question/26427570

#SPJ1

EXPLANATION

The perimeter Perimeter is given by the sum of the sides as follows:

P = z + 5 + z + 5 + z + z

Substituting P=26 and adding like terms,

26 = 10 + 4z

Subtracting -10 to both sides:

26 - 10 = 10 - 10 + 4z

Simplifying:

16 = 4z

Dividing both sides by 4:

16/4 = z

Switching and simplifying:

z = 4

So,

Equation: 26 = 10 + 4z

z = 4

By using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.

We are given that:

On a drive,

A football team first gains = 3 yards.

Then it lost = 11 yards.

Then it again gained = 15 yards.

We need to find its total yardage.

For this, we will subtract the yards lost from the yards gained by the team.

So, we get that:

total yardage = 3 + 15 - 11

total yardage = 18 - 11

total yardage = 7 yards.

Therefore, by using subtraction, we get that, the total yardage for the drive was that they gained 7 yards.

Learn more about subtraction here:

https://brainly.com/question/17301989

#SPJ1

Answer:

-20j+ 6j=-14j

-14j + 18j=4j

4j-9j=-5j

-5j=-3-17

-5j =-20

j =-20÷-5

j =4

The equation of the line is y = -400x + 800

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

Initial number of gallon, c = 800

Constant rate, m = -400 gallons per hour

This means that

Slope = -400

y-intercept = 800

A linear equation is represented as

y = slope * x + y-intercept

i.e.

y = mx + c

So, we have

y = -400x + 800

Hence. the equation of the amount of grain is y = -400x + 800

Read more about linear equation at

https://brainly.com/question/14323743

#SPJ1

Answer:

To one decimal place, x = 7.7 cm

Step-by-step explanation:

Let y equal BD.

Since AD is a bisector of angle BAC, angle DAB is 17°.

tan(17°) = y/21, so y = 21 tan(17°)

tan(34°) = (x + 21 tan(17°))/21

21 tan(34°) = x + 21 tan(17°)

x = 21(tan(34°) - tan(17°)) = 7.7 cm

1. The rate of the descent of Andy as a unit rate will be -4 feet per minute.

2. If Andy continues descending at this rate, the relation to sea level after 6 minutes is -24 feet.

From the information, the following can be deduced'

1. Distance = -10 feet

Time = 2 1/2 minutes = 2.5 minutes

Speed = Distance / Time

Speed = -10 / 2.5

Speed = -4 feet per minutes

2. When Andy continues descending at this rate, the relation to sea level after 6 minutes will be:

= -4 × 6

= -24

Learn more about rate on:

brainly.com/question/18403815

#SPJ1

Andy is scuba diving. He starts at sea level and then descends 10 feet in 212 minutes. Part A How would you represent Andy's descent as a unit rate? Express your answer as an integer. Enter your answer in the box. feet per minute Part B If he continues at this rate, where will Andy be in relation to sea level after 6 minutes? feet

Answer: The graph that matches the equation:

Answer:

57

Step-by-step explanation:

75/100 *76

5700/100 =57

If the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7.

The given equation is

1/3(2x - 3/7)+(1/6)x = 4/7

First we have to apply the distributive property of subtraction in the equation

1/3(2x - 3/7)+(1/6)x = 4/7

(3/2)x - 1/7 + (1/6)x = 4/7

Here we have to rearrange the terms and group the like terms

Move the 1/7 to right hand side of the equation

(3/2)x + (1/6)x = (4/7)+(1/7)

Addition of like terms

(5/3)x = 5/7

Move the 5/3 to the right hand side of the equation

x = 5/7 ÷ 5/3

x = 5/7 × 3/5

x = 3/7

Hence, if the equation is 1/3(2x - 3/7)+(1/6)x = 4/7 , then the value of x is 3/7

Learn more about equation here

brainly.com/question/14603452

#SPJ1

Answer:

Step-by-step explanation:

it can be simplified to [tex]\frac{sec \theta}{cot\theta+tan\theta} =sin\theta[/tex]  . if you multiply each side by the denominator, it becomes [tex]sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta[/tex] since [tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex] and cotan is the reciprocal of that. Because [tex]sec\theta=\frac{1}{cos\theta}[/tex] so multiplying each side gives [tex]1=sin^2\theta+cos^2\theta[/tex], and [tex]sin^2\theta+cos^2\theta[/tex] is equal to 1.

The issue price (present value) of the bonds issued by Frontier World is $42,223,423.81.

The present value refers to the discounted future cash flows of the bonds (including interests and the repayment of the bonds).

The present value represents the current price of the bonds, at which they are issued.

The present value can be computed using the online finance calculator.

N (# of periods) = 20 (10 x 2)

I/Y (Interest per year) = 6% (Market Rate)

PMT (Periodic Payment) = $1,375,500

FV (Future Value) = $39,300,000

Bond Interest Rate = 7%

June 30 = $1,375,500 ($39,300,000 x 3.5%)

Dec. 31 = $1,375,500 ($39,300,000 x 3.5%)

Results:

Present Value (PV) = $42,223,423.81

Sum of all periodic payments = $27,510,000 ($1,375,500 x 20)

Total Interest = $24,586,576.19

Learn more about the price of bonds at https://brainly.com/question/15567868

#SPJ1

Required: 1-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)

Answer:

9  57/ 100

Step-by-step explanation:o convert the decimal 9.57 to a fraction, just follow these steps:

Step 1: Write down the number as a fraction of one:

9.57 = 9.57/ 1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point:

As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. So,

9.57 / 1

= (9.57 × 100)

(1 × 100)

= 9 57/ 100

.

(This fraction is alread reduced, We can't reduce it any further).

As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 9 57/ 100

is also equal to 9 57/ 100

when expressed as a mixed numbeR

Answer:

9 3/4

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over 100. Reduce the fraction.

Least Common Multiple of  3x² + 7x + 2 and 2x² + 3x-2 is  (2x-1)(x+2)(3x+1)

Least Common Multiple is the meaning of the abbreviation LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It can also be computed using two or more numbers. Finding the LCM of a given collection of numbers can be done in a variety of ways. Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

Given that :  3x² + 7x + 2 and 2x² + 3x-2

3x² + 7x + 2

3x² +6x +x + 2

3x(x +2)+1(x+2)

(3x+1)(x+2)

2x² + 3x-2

2x² + 4x-x -2

2x(x+2)-(x+2)

(2x-1)(x+2)

L.C.M of  3x² + 7x + 2 and 2x² + 3x-2 is

(2x-1)(x+2)(3x+1)

To know more about L.C.M visit :

https://brainly.com/question/20739723

#SPJ9

The features of a binomial experiment are

From the question, we understand that the experiment is a binomial experiment

As a general rule, a binomial experiment is any experiment that has only two possible outcomes

These outcomes are represented as

These outcomes can also be represented as

The representation of the outcomes are:

There are other features of a binomial experiment.

One of these features is:

The binomial experiment has a number of n identical or unique trials

Another features of a binomial experiment is

The probability of success on one trial is the same for all other trials

Hence, the two other features of a binomial experiment are

Read more about binomial experiment at

https://brainly.com/question/15246027

#SPJ1

We have a translation of 3 units to the left and 4 units upwards.

To find the translation, we only need to look at one of the vertices of the triangle.

We can see that the coordinates of B are (4, 1), while the coordinates of the translated point B' are (1, 5)

The translation is given by the difference:

(1, 5) - (4, 1) = (1 - 4, 5 - 1) = (-3, 4)

So the translation is defined by (-3, 4)

Learn more about translations:

https://brainly.com/question/24850937

#SPJ1

Answer:

A. 7:10

B. 10:17

Explanation: The ratio of A. would be 14:20, simplified would be 7:10. The ratio of B. would be 20:34, simplified being half of both numbers. Giving you 10:17.

The area of the reservoir in standard form is 1.8 × 10⁴ square miles

The volume of the reservoir in scientific notation is 2.8 × 10⁴ cubic miles

From the question, we are to determine the area of the reservoir in standard form and the volume of the reservoir in scientific notation

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form

Thus,

To write a number in standard form, we will write the number as a product of a number between 1.0 and 10.0 and a power of 10

From the given information,

The area of the reservoir is 1.8 × 10⁴ square miles.

The area of the reservoir is already written in standard form

Now,

To write the volume of the reservoir in scientific notation

NOTE: Standard form is the same as scientific notation

From the given information,

The volume of the reservoir is 28000 cubic miles

28000 = 2.8 × 10⁴

Hence, the volume in scientific notation is 2.8 × 10⁴ cubic miles

Learn more on Writing in standard form here: https://brainly.com/question/27862246

#SPJ1