Solve the triangle. Round the side length to the nearest tenth and the angle measures to the nearest degree.

Answers

Answer 1

Answer: 41, 54, 6.1

Step-by-step explanation:

By the law of Cosines,

[tex]b^2=4^2 +5^2 -2(4)(5)\cos 85^{\circ}\\\\b=\sqrt{4^2 +5^2 -2(4)(5)\cos 85^{\circ}} \\\\ =\sqrt{41-40 \cos 85^{\circ}}\\\\\approx 6.1[/tex]

By the law of sines,

[tex]\frac{\sin A}{a}=\frac{\sin C}{c}=\frac{\sin B}{b}\\\\\frac{\sin A}{4}=\frac{\sin C}{5}=\frac{\sin 85^{\circ}}{\sqrt{41-40 \cos (85^{\circ})}}\\\\\implies \sin A=\frac{4\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle A \approx 41^{\circ}\\\\\implies \sin C=\frac{5\sin 85^{\circ}}{\sqrt{41-40 \cos 85^{\circ}}} \implies \angle C \approx 54^{\circ}[/tex]

Related Questions

If Andy continues descending at this rate, where will he be in relation to sea level after 6 minutes write your answer as a integer

Answers

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.

How to illustrate the information?

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

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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

I need helppppppppp I d don't know what to do

Answers

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

Eli loads identical crates onto a truck with a load limit of 2000 pounds. Each crate weighs 125 pounds.

A function modeling this situation, where y represents the total weight of the crates in pounds, has a range described by which inequality?
0 < y < 16
0 ≤ y ≤ 125
0 ≤ y ≤ 2,000
0 < y < 2,000

Answers

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).

What is inequality?

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.

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There are 14 red marbles and 20 blue marbles in a bag of marbles.
A. What is the ratio of red to blue marbles in simplest form?
B. What is the ratio of blue marbles to total marbles in simplest form?

Answers

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.

Please answer this question to 1 decimal place

Answers

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

Anyone know how to prove these are equal to one another? I also need all the steps.

Answers

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.

find a value for c so that the polynomial y^2 + 10y + c factors to (y+5)^2

Answers

Notice that

[tex]\begin{gathered} (y+5)^2=y^2+10y+25 \\ \text{and} \\ y^2+10y+c=(y+5)^2 \\ \Rightarrow y^2+10y+c=y^2+10y+25 \\ \Rightarrow c=25 \end{gathered}[/tex]

Then, the answer is c=25.

i earn an annual salary of $30,572 and my commission is 5% on all sales. How much must my sales be if i want my annual salary to be $31,836?

Answers

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

How much must my sales be to get the desired salary?

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

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The questions are at the bottom of the page. This is easy im just bad pls help

Answers

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

How to identify the translation applied?

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)

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Factorise completely.
Pq - 2rq + pr-2r²

Answers

Answer:
q x (p - 2r) + r x (p - 2r)
(q + r) (p - 2r)

on a drive, a football team gained 3 yards, lost 11 yards, and gained 15 yards. What was their total yardage for that drive?

Help me :(

Answers

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.

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which of the following expressions is equivalent to (2x-2)(x+5)

Answers

your final answer would be '2x² × 8x − 10'

a study of how noise impacts student performance on exams is being proposed. eighty student volunteers will be randomly assigned to two groups of forty and each student will take a test on how much trivia they know. one group will take the test while construction sounds are being played and the other group will take the test without any background sounds. what will be the biggest problem with the results of this study?

Answers

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

What is realism about?

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.

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The options are:

a. Lack of attention to experimental detail

b. Lack of realism

c. Placebo effect

mother ate pies in the morning, she ate one pie, while she gave half of all those left to Little Red Riding Hood who gave it to her grandmother. On the way, Little Red Riding Hood ate 2 pies and gave a third of the rest to the wolf. Little Red Riding Hood brought 8 pies to her grandmother. How many pies did mother bake?

Answers

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

How many pies did the mother bake?

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

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Solve for j.
-20j + 6j + 18j – 9j + 17 = −3
j= [

Answers

Answer:

-20j+ 6j=-14j

-14j + 18j=4j

4j-9j=-5j

-5j=-3-17

-5j =-20

j =-20÷-5

j =4

i need help on this, thanks

Answers

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:

m∠3 = m∠1 = 143°m∠4 = m∠2 = 37°

2|x+3|+1>3 I need help!!

Answers

Answer:

x < -4 or x > -2

Step-by-step explanation:

[tex]2 |x + 3| + 1 > 3[/tex]

[tex]2 |x + 3| > 2[/tex]

[tex] |x + 3| > 1[/tex]

x + 3 > 1 or x + 3 < -1

x > -2 or x < -4

Answer:

Step-by-step explanation:

Of which type of equation are there the greatest number:
A )Equations with no solutions
B) Equations with infinitely many solutions
C) Equations with exacly one solution
EXPLAIN YOUR REASONING

Answers

The greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.

As given in the question,

Let us discuss

option A) Equations with no solutions

examples are:

x+ y = 0

x+ y = 1

Many such pairs of simultaneous linear equations can be formulated and number of such equations possible is infinite.

Let us discuss

option B) Equations with infinitely many solutions

example:

x+ y = 0

Number of such equations possible is infinite.

Let us discuss

option C) Equations with exactly one solution

example:

x=4

Number of such equations possible is infinite.

Therefore, the greatest number of equations are available in all the types specified in option A), option B) and option C). So 'all of the above' is the correct choice.

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A reservoir has an area of about 1.8 × 104 square miles. Its volume is about 28,000 cubic miles. Find the area of the reservoir in standard form and its volume in scientific notation.

Answers

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

Writing an expression in standard form

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

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Grace has a job power washing houses.
She needs to power wash 11 houses to
earn enough money to pay for a new robot
kit. If each house takes the same amount
of time, and she can wash 2 houses in 8
hours, how long will it take her to wash 11
houses?

Answers

2 houses = 8 hours
1 house = 4 hours

4*11= 44 hours

will take her 44 hours (1 day and 20 hours)

Mayerlin is deciding between two different movie streaming sites to subscribe to. Plan A costs $34 per month plus $2 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Mayerlin watches xx per month, and let BB represent the monthly cost of Plan B if Mayerlin watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine the number of monthly movies watched, x,x, that would make the two plans have an equal monthly cost.

Answers

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.

Definition of equation

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:

When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.

Number of monthly movies watched

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

Plan A costs $34 per month plus $2 per movie watched. → A= 34 + 2xPlan B costs $8 per month plus $3 per movie watched. → B= 8 + 3x

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.

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At the sewing store, Brooke bought a bag of mixed buttons. The bag included 76 buttons, of which 75% were large. How many large buttons did Brooke get?

Answers

Answer:

Step-by-step explanation:

75/100 *76

5700/100 =57

On january 1, 2021, frontier world issues $39.3 million of 7% bonds, due in 10 years, with interest payable semiannually on june 30 and december 31 each year. the proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride.

Answers

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

What is the present value?

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%

Semi-Annual Interest Payments:

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

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Question Completion:

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)

A binomial experiment has independent trials and the outcome of a trial can be classified as either a success or a failure. Which two of the following statements also describe features of a binomial experiment?.

Answers

The features of a binomial experiment are

Identical number of trialsEqual probability of success

How to determine the features of a binomial experiment?

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

True False

These outcomes can also be represented as

SuccessFailure

The representation of the outcomes are:

Success = pFailure = q

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

The binomial experiment has a number of n identical or unique trialsThe probability of success on one trial is the same for all other trials

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Find the L.C.M of: 3x² + 7x + 2 and 2x² + 3x-2
Best of luck

Answers

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

What is lcm ?

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)

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Write 9.75 as a mixed number.

Answers

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.

The temperature of a place was 6°F in the morning. At noon, the
temperature rose by 13°F and dropped by 4°F at night. What was the
temperature recorded at the end of the day?

Answers

The answer should be 15°f

Which graph matched matches the equation
Y+6=3/(x+4)

Answers

Answer: The graph that matches the equation:

Work out √45 - √5
Give your answer as an integer or as a
surd in its simplest form.

Answers

Answer for this question is 2 root 5

A silo containing 800 gallons of grain is emptied at a constant rate of 400 gallons every 1
hour.
Enter an equation in the form y = mx + b that represents the amount of grain y, in gallons,
remaining in the silo after x hours.

Answers

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

What are linear equations?

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

How to determine the equation that represents the amount of grain?

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