Which system of equations could be used to solve for the point of intersection of the lines on the graph?
A)
y-2x+1 and - x+9
B)y=2x-1 and = x +9
C)y=xx-1 and 7x+9
D)y=-x-1 and - *+9
9

Which System Of Equations Could Be Used To Solve For The Point Of Intersection Of The Lines On The Graph?A)y-2x+1

Answers

Answer 1

Answer:

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

Step-by-step explanation:

step 1

Find the equation of the blue line

take the points

(0,-1) and (8,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5+1}{8-0}[/tex]

[tex]m=\frac{6}{8}[/tex]

simplify

[tex]m=\frac{3}{4}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=\frac{3}{4}[/tex]

[tex]b=-1[/tex] ---> see the graph

substitute the given values

[tex]y=\frac{3}{4}-1[/tex]

step 2

Find the equation of the black line

take the points

(0,9) and (3,5) from the graph

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute

[tex]m=\frac{5-9}{3-0}[/tex]

[tex]m=-\frac{4}{3}[/tex]

Find the equation of the line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-\frac{4}{3}[/tex]

[tex]b=9[/tex] ---> see the graph

substitute the given values

[tex]y=-\frac{4}{3}+9[/tex]

therefore

The system of equations is

[tex]y=\frac{3}{4}-1[/tex]  and   [tex]y=-\frac{4}{3}+9[/tex]

Answer 2

The equations of the blue and black lines are y = 3/4x - 1 and y = -4/3x + 9, respectively, based on their respective slopes and given points.

To find the equations of the blue and black lines, we start by determining their slopes using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on each line.

For the blue line:

Points: (0, -1) and (8, 5)

m = (5 - (-1)) / (8 - 0) = 6/8 = 3/4

Now, using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the slope m = 3/4 and the given point (0, -1):

y = 3/4x - 1

For the black line:

Points: (0, 9) and (3, 5)

m = (5 - 9) / (3 - 0) = -4/3

Substituting the slope m = -4/3 and the given point (0, 9) into the slope-intercept form, we get:

y = -4/3x + 9

Therefore, the system of equations representing the blue and black lines is:

y = 3/4x - 1

y = -4/3x + 9

The question probable may be:

Write  system of equations could be used to solve for the point of intersection of the lines on the graph?

Which System Of Equations Could Be Used To Solve For The Point Of Intersection Of The Lines On The Graph?A)y-2x+1

Related Questions

Is 10 an irrational number

Answers

Answer:

yes, it is

hope its helpful ! :)

A circle has a diameter of 12cm. What is the area of the circle in square centimeters?
A) 75.36 cm2
B)113.04 cm2
C)452.16 cm2
D)37.68 cm2

Answers

Answer:

B. 113.04 cm^2

Step-by-step explanation:

The area of a circle is:

a=[tex]\pi[/tex]r^2

Because we have the diameter, we need to find the radius.

d=2r

12=2r

Divide by 2 on both sides

r=6

Plug 6 in for "r" in the area formula.

a=[tex]\pi[/tex]r^2

a=[tex]\pi[/tex]6^2

a=36[tex]\pi[/tex]

a=36*3.14

a=113.04 cm^2

So the answer is choice B

Hope this helps!

Which is the graph of f(x) = √x

Answers

Answer:

i just need points

Step-by-step explanation:

Please help me! Pic included! will mark brainliest!

Answers

Answer:

B) Point G

Step-by-step explanation:

Because point G is equidistant to all of the angles, and cuts all of the sides in half

A mailbox on the street is 600 feet from the top of a building. From the mailbox looking up to the tops of that building and a second, taller building, the angle between the buildings is 67degrees. The tops of the buildings are 800 feet from each other. If the angle of elevation from the mailbox to the first building is 53 degrees and the taller building is 60 degrees, how tall is each building... Step by step explanation..Please..Thanks

Answers

Answer:

first building: 479.2 ftsecond building: 704.2 ft

Step-by-step explanation:

Label the mailbox viewpoint, the top of the first building, and the top of the second building points M, A, and B, respectively.

Consider the triangle MAB. You are told length MA is 600 ft, and length AB is 800 ft. Side AB is opposite the 67° angle at M, so we can use the Law of Sines to find other measures of that triangle. Specifically, we want to know the distance MB.

  sin(B)/MA = sin(M)/AB

  sin(B) = (MA/AB)sin(M) = 600/800·sin(67°) ≈ 0.690379

  B ≈ 43.66°

Then the angle at A is ...

  180° -67° -43.66° = 69.34°

and the side MB can be found from ...

  MB/sin(A) = AB/sin(M)

  MB = (sin(A)/sin(M))AB = sin(69.34°)/sin(67°)·800 ≈ 813.2 . . . feet

__

Now, label points on the ground below A and B as A' and B'. This problem is asking for the heights AA' and BB'. Each of these is opposite the angle of elevation to points A and B, respectively, so can be found using the sine relation:

  sin(elevation to A) = AA'/MA

  AA' = MA·sin(elevation to A) = 600·sin(53°) ≈ 479.2 . . . ft

Similarly, ...

  BB' = MB·sin(elevation to B) = 813.2·sin(60°) ≈ 704.2 . . . feet

The first building is 479.2 ft tall; the second is 704.2 ft tall.

2(11x-6)-18 is equal to 22x-30

Answers

Answer: Yes they are equal

Step-by-step explanation: First you have to solve 2(11x-6)-18:

2(11x-6)-18

22x - 12 - 18

22x - 30

They equal!

Answer:

0

THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.

Step-by-step explanation:

2(11x-6)-18 is equal to 22x-30

the above question can as well be expressed as

2(11x-6) - 18 = 22x -30

the next thing is to apply the BODMAS(BRACKET, OF, DIVISION, MULTIPLICATION, ADDITION , SUBTRACTION.) rule by first opening the bracket

22x - 12 -18 = 22x -30

We will proceed to collect the like terms

22x -22x = -30+12+18

0 = -30 +30

0=0

the answer is = 0

THEREFORE THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.

each of five friends has X action figures in his or her collection. Each friend buys 11 more action figures. Now the five friends have a total of 120 action figures.write an equation that models this problem then solve

Answers

Answer:

Each friend has 13 actions

Step-by-step explanation:

Let x represent the actions of each friends

5friends will have 5x actions

And each friend has 11 more actions which means 5(11)=55

It means 5x+55

The total of their actions is 120

It can be written as 5x+55= 120

To solve

5x+55=120

Substrate 55 from both sides

5x=120-55

5x=65

X=65/5

x=13

Which each friend has 13 actions

Final answer:

To model the problem, the equation 5X + 5(11) = 120 is used. Solving this equation leads to finding that the original number of action figures each friend had is X = 13.

Explanation:

Initially, each of the five friends has X action figures in their collection. After purchasing 11 more action figures each, they collectively have a total of 120 action figures. To represent this problem, we can set up an equation where 5 times the original number of action figures per friend, plus 5 times 11 (because each friend buys 11 more), equals 120. Thus, the equation is:

5X + 5(11) = 120

To find the value of X, we need to solve the equation:

Multiply 5 times 11 to simplify the equation: 5X + 55 = 120

Subtract 55 from both sides of the equation: 5X = 120 - 55

Calculate the result on the right side: 5X = 65

Divide both sides by 5 to find X: X = 65 / 5

Thus, the original number of action figures each friend had is X = 13.

Mar 12: 3
Mar 13: 8
Mar 14: 11
Mar 15: 16
Mar 16: 25
Mar 17: 50

Whats the pattern? Is the pattern linear, quadratic, or exponential? Can you predict the number of cases for march 18, 19 and 20? What about March 25th?

Answers

Answer:

Mar 18: 125Mar 19: 318Mar 20: 743Mar 25: 15,070

Step-by-step explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

  (6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

  3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070

Answer: Mar 18: 125

Mar 19: 318

Mar 20: 743

Mar 25: 15,070

Step-by-step explanation:

The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.

The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...

(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60

where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.

____

The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.

The values for Mar 12 through Mar 25 are ...

3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070

Step-by-step explanation:

.

Meat costs $8.00 per pound at the store. What is the slope and y-intercept?

Answers

y-intercept is 0 and the slope is 8

Using your math skill add 3/4+1/3

Answers

Answer: 9/12 + 4/12 which equals 13/12 or 1 1/12

Explanation: The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Keep the denominators the same with the answer then add!

ANSWER FAST!! BRAINLIEST AND 20 POINTS!! calculate the return on investment in dollars and as a percentage for an investment that you purchase for $500 and sell for $600

Answers

MARK BRAILIEST !!!

Answer:

10 percent

600 - 500 = 100

100 divided by .10 = 10 %

Step-by-step explanation:

⭐ Answered by Kash ʕ •㉨• ʔ⭐

⭐ Brainliest would be appreciated!⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

A circle with a radius of 5 has a sector with a central angle of 9/10pi radians what is the area of the sector

Answers

Answer:

11.25pi units² or 35.3 units² (3 sf)

Step-by-step explanation:

½×r²×theta

½ × 5² × 0.9pi

11.25pi units²

Or, 35.3 units² (3 sf)

Find the area of the rectangle whose vertices have
coordinates (-2,-2), (3,-2), (3, 4) and (-2, 4).​

Answers

Answer:

Area = 30 square units

Step-by-step explanation:

First, let's try to visualize the problem:

(-2, 4) • | • (3, 4)

|

|

___________|___________

|

(-2, -2) • | • (3, -2)

|

|

Let's find the side lengths;

(-2) - 3 = |-5|, the Base of the rectangle is 5 units.

4 - (-2) = 6, the Height of the rectangle is 6 units.

The formula for area of a rectangle is B × H.

5 × 6 = 30, so the area of the rectangle is 30 units.

In the figure BC || DE . Angles__________
CAF and EFA
GAC and DFE
CAF and EFH
GAB and EFA
are congruent______________________________________
By linear pair theorem
because they are corresponding angles of parallel lines cut by a transversal
by vertical angles theorem
by the transistive property of congruence


∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal. ∠AFE ≅ ∠HFD by the Vertical Angles Theorem. ∠GAC ≅ ∠HFD by the_______________ Property of Congruence.
addition
subtraction
substitution
transistive

Answers

CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal. ∠GAC ≅ ∠HFD by the transitive Property of Congruence.

What are congruent angles?

Angles that are of the same measurement are called congruent.

Suppose that two angles ∠A and ∠B are of the same measure,

then

[tex]m\angle A = m\angle B[/tex]

is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.

We write the congruency between them as;

[tex]\angle A \cong \angle B[/tex]

In the figure BC || DE .

Angles

CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal.

GAC and DFE are not congruent

CAF and EFH are not congruent

GAB and EFA are not congruent

∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal.

∠AFE ≅ ∠HFD by the Vertical Angles Theorem.

Therefore, ∠GAC ≅ ∠HFD by the transitive Property of Congruence.

∠AFD = ∠AFE

Two angles that are equal to the same angle must themselves be equal.

( By Transitive property of equality)

Learn more about congruent angles;

https://brainly.com/question/12038510

#SPJ2

A bag contains 77 orange marbles and 21 green marbles. If a representative sample contains 33 orange ​marbles, then how many green marbles would you expect it to​ contain? Explain. 100 points :)

Because the ratio of orange marbles to green marbles is ___ in the​ population, the expected number of green marbles is ___ times the number of orange marbles in the representative sample. There should be ___ green marbles.

Answers

9 green marbles are expected in the representative sample.

The expected number of green marbles is 0.27 times the number of orange marbles in the representative sample.

Step-by-step explanation:

Given that,

A bag contains 77 orange marbles and 21 green marbles.A representative sample contains 33 orange ​marbles  and the green marbles not known.So, the expected number of green marbles can be assumed as 'x'.

The ratio of orange marbles to green marbles is in proportion to the ratio of orange marbles to green marbles in the representative sample.

To find the value of x :

The proportions are 77/21 = 33/x

Cross multiplying the denominators and keeping x alone on one side,

x = (33 × 21) ÷ 77

x = 693 ÷ 77

x = 9 green marbles.

Therefore, the number of green marbles expected in the representative sample is 9.

To find the how many times the green marbles is to the number of orange marbles in representative sample = 9/33 = 0.27 times.

The green marbles is 0.27 times to orange marbles in the representative sample.

01:5

The US Environmental Protection Agency issues a daily report for pollution levels called the

A. Pollution Advisory Warning

B. Air Rating Level

C. Particulates and Pollution Index

D. Air Quality Index

Please select the best answer from the choices provided.

O

A

OB

Answers

Answer:D

Step-by-step explanation:

The United States Environmental protection agency (EPA) issues the Air Quality Index (AQI) daily report to communicate to the public the quality of the surrounding air( clean or bad). It also forecast how the quality of air in the environment will be in the nearest future.

Susan's cat loses 1 1/4 pounds. then then it loses another 1/8 pound. what what is the total change in the cat's weight?​

Answers

Answer:

decrease of 1 3/8 lbs (= 11/8 lbs)

Step-by-step explanation:

given that the cat loses 1 1/4 lbs and 1/8 lbs

1 1/4  can be expressed as an improper fraction 5/4

hence the total weight loss

= 1 1/4 + 1/8

= 5/4 + 1/8

= 10/8 + 1/8

= 11/8

= 1 3/8

Answer:

1 3/8

Step-by-step explanation:

change 1/4 into /8 which is 2/8 then add together which is 3/8 the add the one so 1 3/8

what is unusual about the arrangement of the fossils in the diagram ​

Answers

Answer:

The oldest fossil is closer to the surface.

Step-by-step explanation:

Usually, the closer to the core of the Earth, the older the fossils. However, in this image, the oldest fossil is closer to the surface.

Answer:

The younger fossil is in the bottom layer, while the older fossil is in the top layer. These locations are opposite to the principle of superposition.

Step-by-step explanation:

Plato

For questions 3 - 5, answer the questions about the equations.
3. How many solutions are there to this equation?
3(x - 4) + 5 - x= 2x-7

Answers

Answer:

  infinite solutions

Step-by-step explanation:

Eliminate parentheses and collect terms:

  3x -12 +5 -x = 2x -7

  2x -7 = 2x -7

This is true for any value of x. There are an infinite number of solutions.


The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles.

Answers

Answer:

the fractions of all the shapes are circles can be obtained would be computed as:  

                      [tex]\frac{450}{1600}=\frac{9}{32}[/tex]        

Step-by-step explanation:

The fraction of the number of white shapes to the number of black shapes is 5/11.

Let us consider that there are:

500 white shapes1100 black shapes

As the fraction of the number of white circles to the number of white squares is 3:7

It means out of 10 total parts, 3/10 are white circles and 7/10 are white squares.

Calculating Number of white circles:

                                                           [tex]\frac{3}{{10}} \times 500=150[/tex]

                                                           

Calculating Number of white squares:

                                                            [tex]\frac{7}{{10}} \times 500=350[/tex]

As the fraction of the number of black circles to the number of black squares is 3:8.

Calculating Number of black circles:

                                                            [tex]\frac{3}{{11}} \times 1100=300[/tex]

Calculating Number of black squares:

                                                            [tex]\frac{8}{{11}} \times 1100=800[/tex]

As

the total number of circles is 150 + 300 = 450, and the total number of shapes is 500 + 1100 = 1600

Therefore, the fractions of all the shapes are circles can be obtained would be computed as:

                            [tex]\frac{450}{1600}=\frac{9}{32}[/tex]                            

I need the value of O and N in the picture (the diagonal lengths)

Answers

Answer:

N=15 O=17

Step-by-step explanation:

since we know this is a rectangle and the lines are diagonals we can assume they create right triangles. For line N we set up the Pythagorean Theorem which is a^2 + b^2 = c^2 and to find N we plug in 9 for a and 12 for b. 9^2 + 12^2 = c^2 c^2 = 225 so now we find the square root of c^2 so c or in this case N = 15, now we repeat this same exact sequence for O but N is now our base and 8 is our height of the triangle so we will plug in 8 for a and 15 for b: 8^2 + 15^2 = c^2 c^2 = 289 and the square root of 289 is 17.

Check the picture below.

Great a word problem for x+2=3x-8

Answers

The answer will be x=5 because first you subtract the x from x and from 3x you will be left with 2=2x-8 then you add 8 under the -8 and +2 so then you left with 10=2x then divide both sides by 2 so you get x=5.

What is the Pythagorean Thereom

Answers

Answer:

Step-by-step explanation:

The Pythagorean theorem states that for a right triangle, the sum of the square for each of the sides is equal to the square of the hypotenuse.

See attached for graphic and formula

Could you guys please help

Answers

Answer:

t = 2.76

PLEASE VOTE BRAINLIEST

Step-by-step explanation:

What is 2.3375 rounded to the nearest dollar

Answers

Answer:

2.34

Step-by-step explanation:

Nope, it is 2.34 because you round it off and the 2 stays the same the three does to but the other 3 turns into a 4 because the number next to it which is a 7 is 5 and higher so that makes it 2.34 this would make sense from a mathematician even if my profile doesn't say it.

Answer:

The answer is $2

step-by-step explanation:

What is the point of intersection of these two lines? -4x + y = 8 2x - y = 4 (2, 0)


(-6, -16)


(−2/3, −16/3)



(-2, -8)

Answers

Answer:

(- 6, - 16 )

Step-by-step explanation:

Given the 2 equations

- 4x + y = 8 → (1)

2x - y = 4 → (2)

Adding the 2 equations term by term will eliminate the term in y

- 2x = 12 ( divide both sides by - 2 )

x = - 6

Substitute x = - 6 into either of the 2 equations and soilve for y

Substituting x = - 6 into (2)

2(- 6) - y = 4

- 12 - y = 4 ( add 12 to both sides )

- y = 16 ( multiply both sides by - 1 )

y = - 16

Solution is (- 6, - 16 )

Express 0.15 as a fraction in simplest form.

Answers

Final answer:

To express 0.15 as a fraction, write it as 15/100 and simplify by dividing both the numerator and denominator by 5 to get 3/20 in simplest form.

Explanation:

To express the decimal 0.15 as a fraction in its simplest form, we start by writing it as a fraction with a denominator that reflects its place value. Since 0.15 has two digits after the decimal point, its denominator should be 100. Hence, we have:

0.15 = 15/100

Now, we need to reduce this fraction to its simplest form by canceling equivalent terms in the numerator and the denominator. We notice that both 15 and 100 are divisible by 5. Dividing the numerator and the denominator by 5, we get:

15 ÷ 5 = 3

100 ÷ 5 = 20

Therefore, the fraction 15/100 simplifies to 3/20, which is in its simplest form.

Final answer:

To simplify 0.15 as a fraction, convert it to 15/100 and then divide both numerator and denominator by 5 to get the simplest form, which is 3/20.

Explanation:

To express 0.15 as a fraction in simplest form, we start by recognizing that 0.15 is the same as 15 hundredths, which can be written as 15/100. To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. Both 15 and 100 can be divided by 5, which would give us 3 in the numerator and 20 in the denominator after dividing both by 5. Therefore, the simplest form of the fraction is 3/20.


What is the distance between (0, 0) and
(8, 15) on the coordinate plane?
A. 7 units
B. 8 units
C. 17 units
D. 23 units
Please help me!!!

Answers

Answer:

C. 17

Step-by-step explanation:

Distance formula:

[tex] \sqrt{(x_2 - x_1)^{2} + {(y_2 - y_1)}^{2} } \\ \\ = \sqrt{ {(8 - 0)}^{2} + ( {15 - 0})^{2} } \\ \\ = \sqrt{ {(8)}^{2} + {(15)}^{2} } \\ \\ = \sqrt{64 + 225} \\ \\ = \sqrt{289} \\ \\ = 17[/tex]

The correct answer is C. 17 units.

To find the distance between two points on the coordinate plane, one can use the distance formula derived from the Pythagorean theorem. The distance formula is given by:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

where [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \)[/tex] are the coordinates of the two points.

Given the points [tex]\( (0, 0) \) and \( (8, 15) \)[/tex], we can substitute these values into the formula:

[tex]\[ d = \sqrt{(8 - 0)^2 + (15 - 0)^2} \] \[ d = \sqrt{8^2 + 15^2} \] \[ d = \sqrt{64 + 225} \] \[ d = \sqrt{289} \] \[ d = 17 \][/tex]

Therefore, the distance between the points[tex]\( (0, 0) \) and \( (8, 15) \) is 17[/tex]units.

3 887 860 round it to the nearest million

Answers

4,000,000

because the hundred thousand place value is the digit 5 or higher, the millions rounds up!! in this case, the 3 in the millions rounds up to 4 and the rest of the digits on the right turn to 0, also remember commas!!!!!

3 887 860 rounded to the nearest million is 4 000 000.

From the given number 3 887 860, stating the place value of each digit

We have 0 ones (or unit), 6 tens, 8 hundreds, 7 thousands, 8 ten thousands, 8 hundred thousands and 3 million.

Hence, the number we are rounding is 3 (since we are asked to round to the nearest million)

To round a number, we either round up or round down.  

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down; and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Since, the number that follows the digit we are rounding is 8, then we round up. We round up by adding 1 to the digit we are rounding and turn the remaining numbers to zeros.

(3+1 = 4)

Hence, 3 887 860 rounded to the nearest million is 4 000 000.

Learn more here: https://brainly.com/question/22958284

A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, which takes the ball back to the starting point. What angles are formed by these tosses. Step by Step explanation.. Please

Answers

angles formed by these tosses are  [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Step-by-step explanation:

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]

⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]

⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]

⇒ [tex](cosx) =0.18310[/tex]

⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]

⇒ [tex]x = 79.45[/tex]

The Law of Sines (or Sine Rule) is very useful for solving triangles:

[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]

We can now find another angle using the sine rule:

⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]

⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]

⇒[tex]Y = 59.02 degrees[/tex]

So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]

Therefore, angles formed by these tosses are  [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Other Questions
Which of the following organisms do not carry out photosynthesis If gasoline costs $47.86 for 12.5 gallons of gasoline, how much does it cost for 8 gallons?Round your answer to the nearest cent. Variable Cost Ratio, Contribution Margin RatioHead-First Company plans to sell 5,000 bicycle helmets at $75 each in the coming year. Unit variable cost is $45 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Fixed factory overhead is $20,000 and fixed selling and administrative expense is $29,500.Required:1. Calculate the variable cost ratio.%2. Calculate the contribution margin ratio.% Which BEST describes the organization of paragraph 27?( the Oval Office: a place in history)A.cause and effectB.sequence of events C.compare And contrastD.main idea and deatails The manufacturer of cell phones spends $320 to make each cell phone and sells them for 440 . The manufacturer also has fixed costs each month of $11400 . Consider the following matrix transpose routine: typedef int array[4] [4]; void transpose2(array dst, array src) { int i, j; for (i = 0; i < 4; i++); for (j = 0; j < 4; j++); dst [j] [i] = src[i][j];}}} Assume this code runs on a machine with the following properties: (a) sizeof (int) = 4(b) The src array starts at address 0 and the dst array starts at address 64 (decimal).(c) There is a single LI data cache that is direct-mapped, write-through, write-allocate, with a block size of 16 bytes.(d) The cache has a total size of 32 data bytes (i.e. not considering tags, etc.), and the cache is initially empty.(e) Accesses to the src and dst arrays are the only sources of read and write misses, respectively. For each row and col, indicate whether the access to src [row] [col] and dst [row] [col] is a hit (h) or a miss (m). For example, reading src [0] [0] is a miss and writing dst [0] [0] is also a miss. Jake swims a distance from one end of a 50 meter pool to the other end in 25 seconds. What is his average speed? What is the molar mass for N5O9 As a cell becomes larger, its Select one: a. volume increases faster than its surface area. b. surface area increases faster than its volume. c. volume increases, but its surface area stays the same. d. surface area stays the same, but its volume increases. Which of the following is punctuated correctly? The meeting started at noon; it lasted until late in the evening. The meeting started at noon, it lasted until late in the evening. The meeting started at noon: it lasted until late in the evening. Why is it unethical to provide an incentive that is too large to refuse (for example, offering undergraduate students free tuition for a semester for participating in a study)? need help with 3x48 and 48x3 x + 4y 12 = 0 x = 3y 7 Which of the following is the resulting equation? -7y 19 = 0 y 5 = 0 7y + 19 = 0 7y 19 = 0 a store had three baskets with an equal number of flower bouquets in each. customers purchased 8 bouquets from each basket, and there are now a total of 18 bouquets left. Write and solve an equation to find how many bouquets of flowers were initially in each basket. Why is the standing quadriceps stretch a better stretching exercise than the sitting quadriceps stretch? A. It stretches the quadriceps muscle further. B. It can also be performed while lying down. C. It exerts less force on the knees. D. It causes sideways torque on the knees. Please select the best answer from the choices provided. A B C D iron is a solid phase of iron still unknown to science. The only difference between it and ordinary iron is that Iron forms a crystal with an fcc unit cell and a lattice constant a=0.352 nm. Calculate the density of Iron Round your answer to 3 significant digits. cm The natural rate of unemployment is the rate of unemployment (a) that occurs when the money market is in equilibrium (b) that occurs when the markup of prices over costs is zero (c) where the markup of prices over costs is equal to its historical value (d) that occurs when both the goods and financial markets are in equilibrium Sandra just finished planting avacados,carrots, radishes, tomatoes, and spinach in her new garden. Thegarden is a circle whose diameter is 50 yards. If she planted equalregions of each vegetable, what is the area of Sandra's garden thathas carrots? . What is the frequency of highly energetic ultraviolet radiation that has a wavelength of 129 nm? The speed of light is 3 108 m/s. Answer in units of Hz. What is the justification for step 1 in the solution process?8x + 15= 11x + 2Step 1: 8x= 11x 13A. the division property of equalityB. the addition property of equalityC. the subtraction property of equalityD. the multiplication property of equality