Mathematics College

paula earned a 56% on her test. If she got 14 problems correct. how many did she get incorrect

Answers

Answer 1

21 problems total taken so 7 were correct

Related Questions

a student uses a solution that contains 16 grams of water to conduct an evaporation experiment

Answers

What’s the full questions yeah he uses 16 grams then what

the correct option is:

Step 1:0.035 xx16=0.56

Step 2: 16-0.56=15.44

Step 3: 0.0425 xx15.44=0.6562

Step 4: 15.44-0.6562=14.7838

Let's break down the calculations:

Step 1: Calculate the amount of water lost at the end of the first hour.

[tex]\[ \text{Amount lost} = 0.035 \times 16 = 0.56 \][/tex]

Step 2: Subtract the amount lost from the initial amount to find the remaining water at the end of the first hour.

[tex]\[ \text{Remaining water} = 16 - 0.56 = 15.44 \][/tex]

Step 3: Calculate the amount of water lost at the end of the second hour.

[tex]\[ \text{Amount lost} = 0.0425 \times 15.44 = 0.6562 \][/tex]

Step 4: Subtract the amount lost from the remaining water at the end of the first hour to find the remaining water at the end of the second hour.

[tex]\[ \text{Remaining water} = 15.44 - 0.6562 = 14.7838 \][/tex]

So, the correct option is:

Step 1:0.035 xx16=0.56

Step 2: 16-0.56=15.44

Step 3: 0.0425 xx15.44=0.6562

Step 4: 15.44-0.6562=14.7838

The complete Question is given below:

A student uses a solution that contains 16 grams of water to conduct an evaporation experiment.

At the end of one hour, the amount of water in the solution has decreased by 3.5% .

At the end of two hours, the amount of water in the solution has decreased by another 4.25% .

Which calculations can be used to determine the amount of water, in grams, remaining in the solution at the end of the second hour?

Step 1:0.035 xx16=0.56

Step 2: 16-0.56=15.44

Step 3: 0.0425 xx15.44=0.6562

Step 4:16-0.6562=15.3438

Step 1:0.035 xx16=0.56

Step 2: 16-0.56=15.44

Step 3: 0.0425 xx15.44=0.6562

Step 4: 15.44-0.6562=14.7838

Step 1:0.35 xx16=5.6

Step 2: 16-5.6=10.4

Step 3: 0.425 xx10.4=4.42

Step 4:16-4.42=11.58

Step 1: 0.35 xx16=5.6

Step 2: 16-5.6=10.4

Step 3: 0.425 xx10.4=4.42

Step 4:10.4-4.42=5.98

In a right rectangles pyramid with base edges a= 18 cm and b= 10 cm the slant height toward a is k= 13 cm while the slant height towards b is l= 15 cm. What is the surface area of the pyramid

Answers

To find the surface area of the pyramid, you will need to find the areas of all 5 faces.

rectangular base:
A = lw
18 x 10
A = 180 square cm

side a triangular lateral faces:
A = 1/2bh
1/2 x 18 x 13
A = 117 square cm x 2= 234 square cm

side b triangular lateral faces:
A = 1/2bh
1/2 x 10 x 15
A = 75 square cm x 2= 150 square cm

Add all the bold areas together:
150 + 234 +180 = 564

The surface area is 564 square cm.

A 16 ounce package of cereal cost $4.00? what is the unit cost

Answers

Here, we need to find unit cost. Unit cost can be defined as a cost per unit of a product.

We are given that 16 ounce will cost $ 4.00.

That means -

Cost of 16 ounce of cereal package = $ 4.00

Cost of 1 ounce of cereal package -

(We will divide both sides by 16)

Cost of 16 ounce of cereal package ÷ 16 = $ 4.00 ÷ 16

Cost of 1 ounce of cereal package = $ 0.25.

Thus, the cost of 1 ounce of cereal package = $ 0.25.

Answer: 1 oz. Over 0.25 is your answer.

Step-by-step explanation:

Factor the monomial t^2-16t+48

Answers

Your trinomial can be factored as
(t -4)(t -12)

_____
A monomial (single term) doesn't need factoring, unless you intend to factor to prime factors.

A quadratic trinomial (ax^2 +bx +c) can often be factored by looking for divisors of the product ac that sum to the coefficient b. Here, those are -4 and -12.

Explain why a counter with an upper limit of five(101) resets at six (110)

Answers

Because the preconfiguration set 5 (101) as the upper limit.

Before going to a higher number than 5 which next is 6(110) or beyond the upper limit, It resets.

You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Which expression describes the percent of increase in the tree's height?

Answers

36 - 100%43 - x %
we multiply by cross -> 36 * x = 100 / 43
we should remove '100%' from new value, because we find only increase.. no new value in percent.
x + 100 = (43 * 100)/36
x = 4300/36 - 100x = 119+ 16/36 -100x = 19 +4/9

the answer is

19.44% increase

HOW TO FIND THE GROWTH PERCENTAGE:

Percent Problem:
You need to calculate percent increase from 36 to 43.

First Step: Find the difference between two numbers, in this case, it's 10 - 2 = 8.

Second Step: Take the difference, 7, and divide by the original number: 7/36 = 0.194444.

Last, convert the decimal to a percent.

FINAL ANSWER: 19.44%

A number, half of that number, and one fifth of that number are added. The result is 51. What is the original number?

Answers

Let the original number be ‘x’
Then half of that number= 1/2x or simply x/2
Similarly one fifth of that number = x/5
According to the question
x+x/2+x/5=51
Taking LCM
10x/10+2x/10+5x/10=51
Multiplying 10 throughout
10x+2x+5x=510
17x=510
x=510/17
Therefore x=30

Final answer:

The original number is determined by setting up an algebraic equation based on the relationship given in the problem, solving for the variable, and using algebraic operations. The original number is found to be 30.

Explanation:

To find the original number when its half and fifth are added to it to get 51, we can set up an algebraic equation. Let's denote the original number as x. Half of that number would be x/2 and one fifth of that number would be x/5. The equation representing the given condition is:

x + x/2 + x/5 = 51

To solve this, we need a common denominator to combine the fractions:

Find the least common multiple (LCM) of 2 and 5, which is 10.Multiply the entire equation by 10 to clear the fractions: 10x + 5x + 2x = 510.Combine like terms: 17x = 510.Divide both sides by 17 to solve for x: x = 510 / 17, which simplifies to x = 30.

Therefore, the original number is 30.

Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain.

Answers

Hello!

First you have to find the probability of rolling a 6 one time

There is one 6 and 6 total number

That is a probability of 1/6

Multiply this by the amount of times you roll the cube

1/6 * 120 = 20

The answer is 20

Hope this helps!

You would expect to roll a 6 approximately 20 times in 120 rolls. This is because, on average, in the long run, you would expect a specific outcome (in this case, rolling a 6) to occur with a frequency proportional to its probability (1/6) over a large number of trials (120 rolls).

When rolling a fair 6-sided number cube, each of the six faces has an equal probability of landing face up. The probability of rolling a 6 on a fair 6-sided number cube is 1/6.

To find out how many times you would expect to roll a 6 in 120 rolls, you can use the probability formula:

Expected number of successful outcomes = Probability of success * Total number of trials

Expected number of times to roll a 6 = (1/6) * 120

Expected number of times to roll a 6 = 20

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Q2 Q13.) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.

Answers

let
A (-5,-4) and B (5,10)

Part 1) write an equation for the line in point-slope form

we know that
the equation of a line in point-slope form is
y-y1=m*(x-x1)

step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5

strep 2
with m=7/5 and the point B (5,10)
find the equation of a line
y-y1=m*(x-x1)-----> y-10=(7/5)*(x-5)

the answer Part 1) is
y-10=(7/5)*(x-5)

Part 2) write an equation for the line in slope-intercept form

we know that
the equation of a line in slope-intercept form is
y=mx+b

step 1
find the slope m
m=(y2-y1)/(x2-x1)------> m=(10+4)/(5+5)----> m=14/10---> 7/5

step 2
with m=7/5 and the point B (5,10)
find b
y=mx+b
10=(7/5)*5+b-----> 10=7+b-------> b=3

the equation of the line is
y=(7/5)x+3

the answer Part 2) is
y=(7/5)x+3

Density is mass divided by volume. Find the mass of a gold bar if the density is 19.32 g/cm3 and the volume is 50 cm3.

Answers

density = mass / volume
mass = density * volume
mass = 19.32 * 50
mass = 966 grams

Answer:

Step-by-step explanation:

denisity * volume = mass

HELP ASAP PLEASE
Name the quadrant in which the point (x, y) lies.

x > 0 and y < 0

III

II

IV

I

Answers

x > 0 refers to the right half of the coordinate plane.
y < 0 refers to the bottom half of the coordinate plane.

Both these conditions are met in the lower right quadrant of the coordinate plane. Quadrants are numbered counterclockwise from upper right, so the lower right quadrant is number IV.

The name of the quadrant in which (x >0, y < 0) lies is
IV

Answer: quadrant 4

Step-by-step explanation:

How do you solve 6<_2g?

Answers

Divide both sides by 2 to isolate variable g.

You're left with 6 / 2 < g which equals 3 < g.

if you laid one of each size bolt end to end, how long would the row of bolts be?
3/8 inch, 1/2 inch, 5/8 inch, 7/8 inch, 1 1/4 inches.

Answers

Ok, you would convert all fractions to have the same denominator, and... well, you should get, 5.125 inches, or 41/8 inches long.

The length of row of bolt will be calculated by adding the size of all the bolts.

A school typically sells 500 yearbooks each year for 50 dollars each. The economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. Let x represent the number of $5 decrease in price. If the expression that represents the revenue is written in the form R(x)=(500+ax)(50-bx). Find the value of a and b

Answers

Final answer:

For the expression R(x)=(500+ax)(50-bx), a represents the increase in yearbooks sold for each $5 decrease in price and b represents the corresponding decrease in price per yearbook. The correct values for a and b are 100 and 5 respectively, resulting in the revenue expression R(x) = (500 + 100x)(50 - 5x).

Explanation:

The student's question revolves around the concept of revenue generation based on the number of items sold and the selling price per item.

When examining revenue, we understand it as the product of price per unit times the number of units sold. In the given example, a school is selling yearbooks with a base scenario of 500 yearbooks at $50 each. We are given that for every $5 decrease in price, the school can sell an additional 100 yearbooks. This can be formulated as:

R(x) = (500 + ax)(50 - bx)

Here x represents the number of $5 decreases from the original price. With each decrease, the number of books sold increases by 100, and the price decreases by $5.

Therefore, variable a must represent the increase in quantity sold for each $5 price decrease (a = 100), and variable b must represent the decrease in price per yearbook for each price decrease (b = 5).

Therefore, the values of a and b are 100 and 5, respectively.

The expression for the revenue becomes:

R(x) = (500 + 100x)(50 - 5x)

what value represents the horizontal translation from the graph of the parent function f(x)=x^2 to the graph of the function g(x)=(x+5)^2+3

Answers

The graph [tex]y=x^2[/tex] is the parent function with a vertex at the origin (0, 0). In our parabola, we have (x+5)^2 which indicates side to side movement of the vertex. The standard form for the parabola is [tex](x-h)^2+k=y[/tex], where h and k are the coordinates of the vertex. If your parabola has (x+5)^2, it originally was written as (x-(-5)). So our vertex has moved 5 units to the left. It also moves up 3 but you are only asking about the horizontal movement. 5 units to the left.

Use any method to solve the equation. If necessary, round to the nearest hundredth.

x^2 + x − 30 = 0

A. –5, 6

B. 10, –12

C. 5, –6

D. 5. 5, –5.5

Answers

Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.

In the method, we will split 30, in such factors, which when added or subtracted gives us 1, and when multiplied gives us -30.

So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.

Now, the equation will be written as -

x² - 5x + 6x - 30 = 0

Taking common, we get

x(x - 5) +6(x-5) = 0

(x-5)(x+6) = 0

So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6

Thus, the correct option is C). x = 5 and -6

Use spherical coordinates. let h be a solid hemisphere of radius 1 whose density at any point is proportional to its distance from the center of the base. (let k be the constant of proportionality.) (a) find the mass of h.

Answers

whereas the density of the hemisphere at any point is proportional to it's density, then

The full answer in attachment, we use the partial integral using the spherical coordinates,

and we find that the mass of h = πK/2

Final answer:

To find the mass of the solid hemisphere using spherical coordinates with density proportional to distance from center, integrate the density times the volume element over the hemisphere.

Explanation:

To find the mass of the solid hemisphere using spherical coordinates, we first need to understand that the density at any point is proportional to its distance from the center of the base. Let's denote the constant of proportionality as k. The mass can be found by integrating the product of density and volume over the entire hemisphere. The volume element in spherical coordinates is given by ρ² sinϕ dρ dϕ dθ, where ρ is the radial distance, ϕ is the polar angle, and θ is the azimuthal angle.

We can denote the density as ρ = kρ, where ρ is the radial distance from the center. The mass element dm is then given by dm = ρ² sinϕ dρ dϕ dθ = kρ³ sinϕ dρ dϕ dθ. To obtain the mass of the hemisphere, we need to integrate the mass element over the appropriate limits, which are ρ = 0 to 1, ϕ = 0 to π/2, and θ = 0 to 2π.

Performing the integration, we get the mass as M = ∫∫∫ kρ³ sinϕ dρ dϕ dθ = πk/6.

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Write the standard form of the number shown. three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven

Answers

ok really answer is this 389,936,206,767 ur welcome plz give me brainiest u can even put in the answer and it will right ur welcome.

The standard form of the given number is 3.89936206767 × 10¹¹

From the question, the given number is

three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven.

First, we will write the number in figures before writing it in standard form.

The number, three hundred eighty-nine billion, nine hundred thirty-six million, two hundred six thousand, seven hundred sixty-seven, written in figure is

389,936,206,767.

Now, to write in standard form,

A number is said to be in standard form, if it is written in form A × 10ⁿ. Where A is a number bigger than or equal to 1 and less than 10 ( That is, A ≥ 1 and A < 10)

and n is any positive or negative whole number

∴ The number, 389,936,206,767, written in standard form is 3.89936206767 × 10¹¹

Hence, the standard form of the given number is 3.89936206767 × 10¹¹

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Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.
Please show all your work! (30 points)

Answers

2x² = 7x + 6

Subtract both terms so that we can get 0 on one side.

2x² - 7x - 6 = 0

Find what factors of - 12 (2 * - 6) add up to be - 7. It's - 4 and - 3.

2x² - 4x - 3x - 6 = 0
2x(x - 2) - 3(x - 2) = 0
(x - 2)(2x - 3) = 0

Now set each equal to 0.

x - 2 = 0
x = 2

2x - 3 = 0
2x = 3
x = 3/2

x = 3/2, 2

the quadratic formula can be aplied as follows:
for [tex]ax^2+bx+c=0[/tex], [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

given [tex]2x^2=7x+6[/tex]
we need to get it into [tex]ax^2+bx+c=0[/tex] form

minus (7x+6) from both sides
[tex]2x^2-7x-6=0[/tex]
now, a=2, b=-7 c=-6
subsitute
[tex]x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-6)}}{2(2)}[/tex]
[tex]x=\frac{7 \pm \sqrt{49+48}}{4}[/tex]
[tex]x=\frac{7 \pm \sqrt{97}}{4}[/tex]

so [tex]x=\frac{7 + \sqrt{97}}{4}[/tex] or [tex]x=\frac{7 - \sqrt{97}}{4}[/tex]

Which set of ordered pairs represents a function?

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

Answers

{(3, -1), (7,1), (-6,-1), (9,1), (2,-1)} is the right answer because each input has only one output. (none of the x's repeat).

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

A set of ordered pairs in the format [tex](x,y)[/tex] represents a function if for each value of x, there is only one value for y.

The first set of ordered pairs is:

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}

There are two values of y for [tex]x = 1[/tex]. This means that this set of ordered pairs does not represent a function.

The second set of ordered pairs is:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

For each value of x here, there is only one value of y. This means that this set of ordered pairs represents a function. This is the answer.

The third set of ordered pairs is:

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}

There are two values of y for [tex]x = -2[/tex]. This means that this set of ordered pairs does not represent a function.

The fourth set of ordered pairs is:

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

There are two values of y for [tex]x = -3[/tex]. This means that this set of ordered pairs does not represent a function.

Please help me with this

Answers

The correct answers are the second option (Option B) and the last option (Option E).

The explanation is shown below:
1. By definition, a geometric sequence is a sequence of numbers each number, after the first one, is the result of multiply the previous number by a common ratio.
2. The Option B has the following common ratio:
(2/3) / (4/9)=1.5
1/(2/3)=1.5
r=1.5
3. The Option E has the following common ratio:
-15/3=-5
75/-15=-5
r=-5

24. Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.

Answers

the complete question is
Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
1) What is the volume of the cylinder rounded to the nearest cubic centimeter?
2) What is the total volume of the four balls rounded to the nearest cubic centimeter?
3) What percent of the volume of the container is occupied by the four balls?

Part 1) volume of the cylinder=pi*r²*h
r=4/2----> 2 cm
h=4*4----> 16 cm
volume of the cylinder=pi*2²*16----> 200.96 cm³----> 201 cm³

the answer Part 1) is 201 cm³

Part 2) volume of a sphere=(4/3)*pi*r³ ( is equal to volume of one golf ball)
r=2 cm
volume of a sphere=(4/3)*pi*2³ ----> 33.49 cm³
so
volume of four golf ball-----> 4*33.49----> 133.97 cm³----> 134 cm³

the answer part 2) is 134 cm³

part 3)
volume of cylinder=201 cm³
volume of the four golf ball=134 cm³
so
if 201 cm³-----------> 100%
134 cm³--------> x
x=134*100/201----> x=66.67%

the answer part 3) is 66.67%

Write 2018 to the power of 2019 + 2018 as the sum of two perfect squares

Answers

[tex] 2018^{2019} + 2018=2018( 2018^{2018} +1)=( 13^{2}+ 43^{2})(( 2018^{1009})^{2} + 1^{2}) [/tex]
According to Brahmagupta-Fibonnaci identity
[tex]( a^{2} + b^{2}) (c^{2}+ d^{2}) = (ac+bd)^{2} + (ad-bc )^{2} [/tex]
Then, we can write that
[tex](13^{2}+ 43^{2})(( 2018^{1009})^{2} + 1^{2})[/tex]
[tex][(13*2008^{1009}+43)^{2} +(13-2008^{1009}*43)^{2}] [/tex]
Q.E.D

Answer: I, III, and IV only

Step-by-step explanation:

how many number between 200 and 800 have the number 6?

Answers

220 or 195.

Those options are the most likely.

So we are dealing with hundreds. It has three places for digits. I'm taking more or less brute force way.

_ _ _

Let's start with one place. We can force it to be six, then count how many possible digits for other places. We forbid other place to be six for now so counting would be easier.

_ _ 6

Hundred place can be 2, 3, 4, 5, or 7, so that would be 5 possible digits for hundred place

Ten place can be 0,1, 2, 3, 4, 5, 7, 8, 9 so that would be 9 possible digits

So there are 9 × 5 = 45 numbers between 200 and 800 with 6 in only one place.

Now do ten place:

_ 6 _

Again hundred place has 5 possible digits

One place would have 9 possible digits

So again there are 45 numbers between 200 to 800 with 6 only in ten places.

Now put 6 in hundred place

6 _ _

Ten and one place can be 0, 1, 2, 3, 4, 5, 7, 8, 9, so that's 9 × 9 = 81

So then we add up all amount of numbers we gathered. 45 + 45 + 81 = 171. However we under-counted because we did not allow other places to be 6.

Let's count how many numbers have exactly two 6's We can do the same thing. Let one and ten place be 6.

_ 6 6

So possible digits for hundred place would be 2,3,4,5,7, so that's 5 numbers

Now do 6 _ 6. Ten place can be 0, 1, 2, 3, 4, 5, 7, 8, 9, so that's 9 numbers.

Finally, 6 6 _. Again same as ten place, there's another 9 numbers.

So 171 + 5 + 9 + 9 = 194

Finally there's 666, so we add one then we get 195.

Overall there are 195 numbers those have 6.

Hope this helps.

hey can you please help me posted picture of question

Answers

The correct answer is option D.

F(G(x)) denotes the composition of the two functions F(x) and G(x). The composition of two functions result in x, if the two functions are inverses of each other. So in this case F(x) and G(x) will be the inverse of each other. So option D is the correct answer.

Q9 Q13.) Find the products AB and BA to determine whether B is the multiplicative inverse of A.

Answers

Hello there!

See pictures below for the answer!

P.S. I think I answered this question already. I still have it on Microsoft Word :)

As always, it is my pleasure to help students like you!

Brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. Determine the angles at which the fences of the three sides will meet.

Rounding each angle to the nearest degree: m<A=___degrees

Answers

If you're going to get help, you may as well get help from an appropriate calculator. Many graphing calculators will solve triangles, as will stand-alone apps for phone or tablet.

The angle measures are ...
∠A = 115°
∠B = 27°
∠C = 38°

_____
You can use the Law of Cosines to solve for angle A, then the Law of Sines for the others.
A = arccos((1.5²+1.1²-2.2²)/(2*1.1*1.5)) = arccos(-1.38/3.3) ≈ 115°
C = arcsin(1.5/2.2*sin(115°)) ≈ 38°
B = 180° -115° -38° = 27°

The angles for Brian's triangular plot of farmland are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C.

To determine the angles of a triangular plot of land with sides measuring 1.1 miles, 1.5 miles, and 2.2 miles, we can use the Law of Cosines. The Law of Cosines states:

⇒ c² = a² + b² - 2ab × cos(C)

Let's label the sides as follows:

⇒ a = 1.1 miles

⇒ b = 1.5 miles

⇒ c = 2.2 miles

First, we calculate ∠C (opposite side c):

⇒ cos(C) = (a² + b² - c²) ÷ (2ab)

⇒ cos(C) = (1.1² + 1.5² - 2.2²) ÷ (2 × 1.1 × 1.5)

= (1.21 + 2.25 - 4.84) ÷ (3.3)

= (-1.38) ÷ (3.3)

= -0.4182

Then, we find ∠C by taking the inverse cosine (cos-1):

⇒ ∠C ≈ 115°

Next, we calculate ∠A (opposite side a) using the same method:

⇒ cos(A) = (b² + c² - a²) ÷ (2bc)

⇒ cos(A) = (1.52 + 2.22 - 1.12) ÷ (2 × 1.5 × 2.2)

= (2.25 + 4.84 - 1.21) ÷ (6.6)

= (5.88) ÷ (6.6)

= 0.8909

Then, we find angle A:

⇒ ∠A ≈ 27°

Finally, we calculate angle B (opposite side b) using:

⇒ ∠B = 180° - ∠A - ∠C

= 180° - 27° - 115°

= 38°

The angles at which the fences of the three sides will meet are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C, when rounded to the nearest degree.

Complete question:

Brian wants to fence in his triangular plot of farm land that measures 1.1 × 1.5 × 2.2 miles.

Determine the angles at which the fences of the three sides will meet.

Rounding each angle to the nearest degree:

Find the equation for the plane through the points upper p 0 left parenthesis negative 2 comma negative 5 comma negative 4 right parenthesis, upper q 0 left parenthesis 5 comma 1 comma negative 4 right parenthesis, and upper r 0 left parenthesis negative 1 comma 2 comma 5 right parenthesis.

Answers

We can suppose the equation of the plane is in the form ...
ax +by +cz = 1
By using the given point coordinates for x, y, and z, we end up with three equations in 3 unknowns. These can be described by the augmented matrix ...
[tex] \left[\begin{array}{ccc|c}-2&-5&-4&1\\5&1&-4&1\\-1&2&5&1 \end{array}\right] [/tex]
Putting this in reduced row-echelon form, we find
a = 54/35
b = -63/35
c = 43/35

The equation of the plane through [tex]P_{0}(-2,-5,-4), Q_{0}(5,1,4), R_{0}(-1,2,5)[/tex] is ...
54x -63y +43z = 35

What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of .

3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0

Answers

The only line that passes through the given point is ...
x -3y -7 = 0

_____
It has a slope of 1/3.

Find the area of the following ellipse. a = 4.5 m; b = 5.5 m

Answers

Answer:

Area of ellipse is ≈ 77.78 [tex]m^{2}[/tex]

Step-by-step explanation:

Given the dimension of ellipse

a = 4.5 m

b = 5.5 m

Now, Area of ellipse = [tex]\pi ab[/tex]

= [tex]\frac{22}{7}\times 4.5\times 5.5[/tex]

= [tex]\frac{5445}{70}[/tex]

= 77.78 [tex]m^{2}[/tex]

Hence Area of ellipse will be 77.78 [tex]m^{2}[/tex]

The area of the ellipse is calculated using the formula A = ab, with the given semi-major axis of 4.5 m and semi-minor axis of 5.5 m, estimated to two significant figures as 78 m².

The area A of an ellipse with semi-major axis a and semi-minor axis b is given by the formula A = \ab. Given that a = 4.5 m and b = 5.5 m, we can calculate the area of the ellipse using a calculator. Keeping in mind that we should report our final answer to the same number of significant figures as the least precise measurement provided (which in this case is two significant figures), we have:

A = \(4.5 m)(5.5 m)

A = 3.1415927... × 24.75 m²

A = 77.66546225 m²

However, due to the significant figures rule our reported answer should be:

A = 78 m²

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