PLEASE BE QUICK AND ACCURATE

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.

The equation for this parabola is y = -x2 + 36.

1. In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.

2. Analyze the two functions. Answer the following reflection questions in complete sentences. What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not? What are the x- and y-intercepts of the rainbow? Explain what each intercept represents. Is the linear function you created with your table positive or negative? Explain. What are the solutions or solution to the system of equations created? Explain what it or they represent.

3. Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).

Answers

Answer 1
1. Create a Table.

We know that after a dreary day of rain, the sun peeks through the clouds and a rainbow forms. So you notice the rainbow is the shape of a parabola as shown in the first figure. This parabola has the following equation:

[tex]y=-x^2+36[/tex]

On the other hand, in the distance you notice that an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. So let's choose two points on the graph of the parabola to build up the equation of the line:

[tex]\bullet \ If \ x=-5, then: \\ \\ y=-(-5)^2+36=11 \\ \\ So: \\ \\ P_{1}(-5,11) \\ \\ \\ \bullet \ If \ x=4, then: \\ \\ y=-(4)^2+36=20 \\ \\ So: \\ \\ P_{2}(4,20)[/tex]

Therefore, the equation of the line using these two points is:

[tex]y-20=\frac{20-11}{4-(-5)}(x-4) \\ \\ y-20=\frac{9}{9}(x-4) \\ \\ y-20=x-4 \\ \\ y=x+20-4 \\ \\ y=x+16[/tex]

FOR THE PARABOLA, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=-(0)^2+36=36 \\ \\ So: \\ \\ P_{3}(0,36) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=-(1)^2+36=35 \\ \\ So: \\ \\ P_{4}(1,35)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 36\\1 & 35\end{array}\right][/tex]

FOR THE LINE, THE TABLE IS:

[tex]Other \ two \ points: \\ \\ \bullet \ If \ x=0, then: \\ \\ y=x+16=0+16=16 \\ \\ So: \\ \\ P_{3}(0,16) \\ \\ \\ \bullet \ If \ x=1, then: \\ \\ y=x+16=1+17=17 \\ \\ So: \\ \\ P_{4}(1,17)[/tex]

So the table is:

[tex]\left[\begin{array}{cc}x & y\\-5 & 11\\4 & 20\\0 & 16\\1 & 17\end{array}\right][/tex]

2. Analyzing the functions:2.1 Domain and Range:The Domain of both the quadratic function and the linear function is the set of all real numbers.  

The range of the quadratic function is [tex](-\infty,36)[/tex] while the range of the linear function is the set of all real numbers.

The domain represents the horizontal distance while the range represents the height. In this situation, all values don't make sense. First, the rainbow starts in a point on the earth's crust. Also, the airplane starts at a point on the runway, so this doesn't include all the real numbers. A similar thing happens to the height since the airplane turns into an horizontal way at a moment of its trip and this doesn't include all the real numbers.

2.2 x and y intercepts of the rainbow.

x-intercepts:

The x intercepts are the points at which the graph passes through the x-axis, that is, when [tex]y=0[/tex]. So:

[tex]-x^2 + 36=0 \\ \\ x^2=36 \\ \\ x=\pm\sqrt{36} \\ \\ x=\pm 6[/tex]

So the x intercepts are [tex]x_{1}=6 \ and \ x_{2}=-6[/tex]

y-intercepts:

The y-intercept is the point at which the graph passes through the y-axis, that is, when [tex]x=0[/tex]. So:

[tex]y=-x^2+36 \\ \\ y=-(0)^2+36 \\ \\ y=36[/tex]

So the y-intercept is [tex]b=36[/tex]

In conclusion, if we take the x-axis as the ground, the x-intercepts represent the beginning and the end of the rainbow while the y-intercept represent its maximum height.

2.3 Is the linear function positive or negative

The equation of this line is:

[tex]y=x+16[/tex]

As you can see, the slope [tex]m=1[/tex] is positive, therefore the line I've created is positive. This means as x increases y increases, but how do x and y increase? Well, they increase as the airplane is taking off, so this means the horizontal distance and the height increase.

2.4 What are the solutions or solution to the system of equations created?

The system of equations we created is:

[tex]\left\{ \begin{array}{c}y=x+16\\y=-x^{2}+36\end{array}\right.[/tex]

Remember that in Part 1, chose two points on the graph of the parabola to build up the equation of the line, so the solutions to this system is indeed those two points:

[tex]P_{1}(-5,11) \ and \ P_{2}(4,20)[/tex]

They represents that the airplane cuts through the rainbow at those two points.

3. Create a piecewise function.

A piecesewise function is a function defined by two or more equations over a domain. Our piecewise function is shown in the second figure below and is defined by:

[tex]f(x)=\left\{ \begin{array}{c}x+16\quad if\quad-16\le x\le-5\\-x^{2}+36\quad if\quad-5\le x\le4\\x+16\ \quad if\quad4\le x\le24\\40\quad if\quad x\ge24\end{array}\right.[/tex]

To graph this function, let's follows these steps:

STEP 1: Graph [tex]y=x+16[/tex] from -16 to -5. This represents the graph of the trajectory of the airplane before touching the rainbow.

STEP 2: Graph [tex]y=-x^2+36[/tex] from -5 to 4. This is represents the graph of the rainbow as the airplane passes under its path.

STEP 3: Graph [tex]y=x+16[/tex] from 4 to 24. This is represents the graph of the trajectory of the airplane after touching the second point of the rainbow.

STEP 4: Graph [tex]y=x+16[/tex] from 24 and forward. This is represents the graph of the trajectory of the airplane when turning into an horizontal way.

PLEASE BE QUICK AND ACCURATEAfter A Dreary Day Of Rain, The Sun Peeks Through The Clouds And A Rainbow
PLEASE BE QUICK AND ACCURATEAfter A Dreary Day Of Rain, The Sun Peeks Through The Clouds And A Rainbow

Related Questions

WILL MARK AS BRAINLIEST IF CORRECT AND EXPLAINED
What is the diameter of the circle whose center is at (6, 0) and that passes through the point (2, -3)?
A. (x+16)2+(y+30)2=1156
B. (x+16)2+(y+30)2=34
C. (x−16)2+(y−30)2=34
D. (x−16)2+(y−30)2=1156

Answers

Answer:

The diameter is 10 units.

The equation of the circle is [tex](x-6)^2+y^2=25[/tex].

Step-by-step explanation:

You ask for the diameter but the choices give you the equation of the circle?

I will do both.

So they actually tell us the radius is from (6,0) to (2,-3).

So the radius is whatever that length is.  We can find the length by using the distance formula.

[tex]d=\sqrt{(6-2)^2+(0-(-3))^2}[/tex]

[tex]d=\sqrt{(4)^2+(3)^2}[/tex]

[tex]d=\sqrt{16+9}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]d=5[/tex]

So the radius is 5.

The diameter is twice the radius so the diameter is 2(5)=10.

Now the equation of our circle which doesn't match any of the choices is

[tex](x-6)^2+(y-0)^2=5^2[/tex].

You are probably wondering how I got that.  I used the center-radius form for a circle which is [tex](x-h)^2+(y-k)^2=r^2[/tex].

The center is (h,k) and the radius is r.

We had the center for our circle was (6,0) and the radius was 5.

I'm going to simplifying our equation just a bit:

[tex](x-6)^2+y^2=25[/tex].

All I did was y-0 which is y and 5^2 which is 5(5) which equals 25.

Identify the mapping diagram that represents the relation and determine whether the relation is a function. {(–3, –6), (–1, –6), (5, –6), (8, –6)} Which of the following is true?

Answers

Answer:

This relation is a function.

Step-by-step explanation:

A function is a process or a relation that associates each element x of a set X, to a single element y of another set Y.

We have

{(-3, -6), (-1, -6), (5, -6), (8, -6)}

x = -3 → y = -6

x = -1 → y = -6

x = 5 → y = -6

x = 8 → y = -6

YES. This relation is a function.

/each x has one value of y/

Answer: Yes, it is a function

Step-by-step explanation:

Which statements are always true regarding the diagram?
Select three option. (Picture included)
m<5+m<3=m<4
m<3+m<4+m<5=180
m<5+m<6=180
m<2+m<3=m<6
m<2+m<3+m<5=180

Answers

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

Answer:

CDE

Step-by-step explanation:

given sin theta = -3/5 and csc theta -5/3 in quadrant 3, find the value of other trigonometric functions using a Pythagorean Identity. Show your work.

Answers

Answer:

cos theta = -4/5.

sec theta = -5/4.

tan theta = 3/4.

cot theta = 4/3.

Step-by-step explanation:

sin^2 theta + cos^2 theta = 1

(-3/5)^2 + cos^2 theta = 1

cos^2 theta = 1 - 9/25

cos^2 theta = 16/25

cos theta = -4/5 (negative because  it is in Quadrant 3).

sec theta = 1 / cos theta = -5/4.

tan theta = sin theta / cos theta = -3/5 / - 4/5

= -3/5 * -5/4

=  3/4.

cot theta  =  1 / tan theta = 4/3.

Final answer:

The other trigonometric functions can be found using the Pythagorean Identity and the definitions of the trigonometric functions. The values are cos theta = -4/5, tan theta = 3/4, csc theta = -5/3, sec theta = -5/4, and cot theta = 4/3.

Explanation:

The given values are sin theta = -3/5 and cos theta = -5/3, which are located in quadrant 3. In this quadrant, sine and cosine are both negative. To find the values of the other trigonometric functions, we will use the Pythagorean Identity and the definitions of the trigonometric functions.

We can find cosine through the Pythagorean Identity, sin² theta + cos² theta = 1. Solving for cos theta, we get cos theta = sqrt(1 - sin² theta) = sqrt(1 - (-3/5)²) = -4/5. Note the negative sign since we are in quadrant 3.

Next, we can find tan theta = sin theta/cos theta = (-3/5) / (-4/5) = 3/4.

For the reciprocal functions, we have csc theta = 1/sin theta = -5/3, sec theta = 1/cos theta = -5/4, and cot theta = 1/tan theta = 4/3.

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i don't understand the problem

Answers

Check the picture below.

Give the equation of the line passing through the point (20,2)that is perpendicular to y=−4x.

Answers

Answer:

y-2 = 1/4(x-20)  point slope form

y = 1/4x -3  slope intercept form

Step-by-step explanation:

y = -4x

The slope is -4

The slope that is perpendicular is the negative reciprocal

- (1/-4) = 1/4

The slope of our new line is 1/4

We have a point and the slope, so we can use point slope form

y-y1 = m(x-x1)

y-2 = 1/4(x-20)

If we want the line in slope intercept form, distribute

y-2 = 1/4x -5

Add 2 to each side

y-2+2 = 1/4x -5+2

y = 1/4x -3

the volume of a cone is 36 pie in. cubed. what is the volume of a cylinder with the same base and height as the cone

Answers

The volume of a cone is one third of the volume of a cylinder that has the same base and height.
The answer is 36/3=12pi in^3.

Answer:

12 pi in³

Step-by-step explanation:

convert y=-1.4x+9.6 to standard form

Answers

Answer:

14x-10y=-96

Step-by-step explanation:

we know that

The equation of the line in standard form is equal to

Ax+By=C

where

A is a positive integer

B and C are integers

so

we have

y=1.4x+9.6

Multiply by 10 both sides

10y=14x+96

isolate the variable x and y (Remember that A must be positive)

14x-10y=-96 -----> standard form

need help with 1-5 , please!!!!!!

Answers

Answer:

1)

[tex] \frac{26 + 16 + 11 + 13 + 24}{5} = \frac{90}{5} = 18[/tex]

2)

[tex] \frac{51 + 20 + 32 + 18 + 45 + 8}{6} = \frac{174}{6} = 29[/tex]

3)

[tex] \frac{17 + 39 + 15 + 42 + 37 + 61 + 19 + 40}{8} = \frac{270}{8} = 33.75[/tex]

4)

[tex] \frac{62 + 21 + 18}{3} = \frac{101}{3} = 33.67[/tex]

5)

[tex] \frac{9.2+8.6+9.4+9.2}{4} = \frac{36.4}{4} = 9.1[/tex]

TIME REMAINING
01:54:53
O
At a grocery store, blueberries come packaged in 8-ounce containers for $2.80 At a farmer's market, blueberries cost $4.20
for 14 ounces. There are 16 ounces in one pound. Which statement accurately compares the cost of blueberries?

Answers

$0.30 (farmer's market) < $0.35 (grocery store), the farmer's market offers blueberries at a lower price per ounce.

To compare the cost of blueberries from a grocery store and a farmer's market below:-

Cost of blueberries at the grocery store:

Price for an 8-ounce container: $2.80  Price per ounce = [tex]\frac{2.80}{8} = 0.35[/tex]
Therefore, the cost is $0.35 per ounce.

Cost of blueberries at the farmer's market:

Price for a 14-ounce container: $4.20  Price per ounce = [tex]\frac{4.20}{14} = 0.30[/tex]
Therefore, the cost is $0.30 per ounce.

Thus,

The cost of blueberries at the grocery store is $0.35 per ounce.The cost of blueberries at the farmer's market is $0.30 per ounce.

Please help I’m stuck!

Answers

Answer:

1. the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. 2x+2.1=7.5

Step-by-step explanation:

Given:

1.

A scalene triangle with sides y, 4y and x

and perimeter,p= 60cm

As per perimeter formula:

p= sum of all sides

Putting values we get

60=x+4y+y

60=x+5y

so correct options are

the value of x can equal 25

the shortest length can equal 7

the longest length can equal 30

2. An isosceles triangle with sides y=2.1, x and x

and perimeter,p = 7.5

As per perimeter formula:

p= sum of all sides

Putting values we get

7.5=2.1 + x +x

7.1=2.1+2x !

Find my number, if a third of it is equal to a fifth of 10.

Answers

Answer:

The answer is 6.

Step-by-step explanation:

A fifth of 10, or 10 divided by 5, is 2. Two is a third of 6. Therefore, the answer must be 6.

The number whose one - third is equal to one - fifth of 10 is 6.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a number such that one - third of it is equal to a one - fifth of 10.

Assume that the number is [x].

Then, one - third of the number = 1/3 of x = x/3

Now, one - third of the number = one - fifth of 10, so we can write -

x/3 = 1/5 of 10

x/3 = 1/5 x 10

x/3 = 10/5

x = 10/5 x 3

x = 6

The number is 6.

Therefore, the number whose one - third is equal to one - fifth of 10 is 6

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Samuel has 5 bags of almonds. A full bag weighs 3 pounds. How many pounds of almonds does Samuel have? (Multiply)

A.15 Pounds
B.12 pounds
C.8 pounds

Answers

Answer:

15 pounds

Step-by-step explanation:

5 bags @ 3 pounds

5 x 3 = 15 lbs.

Samuel has 5 bags of almonds, each weighing 3 pounds. By multiplying the number of bags by the weight of each bag (5 * 3), we find that Samuel has a total of 15 pounds of almonds.

The total weight of Samuel's 5 bags of almonds is:

Multiply the weight of a full bag (3 pounds) by the number of bags (5): 3 pounds/bag x 5 bags = 15 pounds

Therefore, Samuel has 15 pounds of almonds.

solve the equation -9x+1=-x+17​

Answers

Answer:

x=-2

Step-by-step explanation:

-9x+1=-x+17

Add 9x on both sides:

     1=8x+17

Subtract 17 on both sides:

   -16=8x

Divide both sides by 8:

     -2=x

Check x=-2!

-9x+1=-x+17     with x=-2

-9(-2)+1=-(-2)+17

18+1=2+17

19=19

19=19 is a true equation so x=-2 is correct.

Answer: b

Step-by-step explanation:

Solve: ^3 sqrt x^2-8=2

Answers

Answer:

∛x²-8 = 2

-2∛x² = 2

∛x² = 2+2

x² = 4³

x = √64

x = 8

Answer:

C. x = –4 or x = 4

Step-by-step explanation:

B. s = 7 (for the second one)

In a triangle, the measure of the second angle is twice the measure of the first angle. the third angel is equal to the sum of the other angels

Answers

Answer:

So the angles have measurements 30,60, and 90 degrees.

Step-by-step explanation:

We have a triangle which means the interior angles of that triangle has sum 180 degrees.

Let's call the angle measurements: A, B, and C.

A+B+C=180

B=2A            (The second angle is twice the first.)

C=A+B          (The third angle is the sum of the other 2.)

If C=A+B, then C=A+2A  (since B=2A).

So we have this system:

A+B+C=180

B=2A

C=3A     (since C=A+2A=3a).

Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:

A+B+C=180 with B=2A and C=3A.

A+2A+3A=180

6A=180  

Divide both sides by 6:

A=180/6

A=30

If B=2A and A=30, then B=2(30)=60.

If C=3A and A=30, then C=3(30)=90.

So the angles have measurements 30,60, and 90 degrees.

how do you calculate this

Answers

Answer:

Step-by-step explanation:

Josh has to drive at least 6 hours.                 d≥ 6 Answer 2

Amelia walking 35 min or less                       b ≤ 35 Answer 3

Nancy < 35 hours = part time                         y < 35 Answer 1

Sarah at least 6 hours math                           f > 6 Answer 4

Which algebraic expression has a term with a coefficient of 3?
A. 3y+1
B. -2y + 5+ 3
C. 5y-7
D. 3(y-6)

Answers

A. Is the answer because a coefficient is the number that is attached to a variable or in front of it. There cannot be a parenthesis in between them like in letter D. So your answer is letter A because the 3 in 3y+1 is a coefficient. Hope this helps!

The algebraic expression 3y+1 has a term with a coefficient of 3.

What is a coefficient?

A coefficient is a constant value accompanying a variable that is multiplied by it. For example, 2 is the coefficient of x in 2x.

We can find the algebraic expression as shown below:

We can evaluate the given options.

In Option A, we have 3y+1. Here the expression has a term with a coefficient of 3.

In Option B, we have -2y + 5+ 3. Here the expression does not have a term with a coefficient of 3.

In Option C, we have 5y-7. Here the expression does not have a term with a coefficient of 3.

In Option D, we have 3(y-6). Here the expression does not have a term with a coefficient of 3.

Therefore, we have found that the algebraic expression 3y+1 has a term with a coefficient of 3.

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if tan θ= -3/8 which expression is equivalent to cot θ?

Answers

Answer:

                 -8

If cot Ф = ------

                  3

Step-by-step explanation:

Justine, when you're given answer choices, please share them.  Thank you.

                 -3

If tan Ф = ------

                  8

then:

                 -8

If cot Ф = ------

                  3

How do you graph this and know if it is continuous or not?

Answers

Answer:

Continuous because there are no breaks.

The graph is included as an attachment.

Step-by-step explanation:

Alright we want to graph:

y=x-4 for x<2

y=-2x+2 for x=2 or x>2

So let's graph the first piece y=x-4 for x<2.

I'm going to plug in 2 for x:   y=2-4=-2.   So this one line is going to contain an open circle at (2,-2). I say open circle because we did not have that we could actually include x=2 here because it says for x less than 2.

Now we are going to enter in one more number less than 2....your choice.

Let's go with x=0. When you plug in 0 for x into y=x-4 you get y=0-4=-4. So our line is going to include (0,-4).

So we are going to graph the points (0,-4) and (2,-2) again where (2,-2) is an open circle.  Connect these points. You may extend your line left because we have x<2, but do not extend it right of x=2.

Let's look at the other piece now: y=-2x+2 for x=2 or x>2.

I'm going to plug in 2 for x:  y=-2(2)+2=-4+2=-2 so we are going to include the point (2,-2) on our line.  This was actually a point we used from above that we didn't want to include.  We do now want to include because of the x=2 in our inequality so the dot can now be filled in. We need one more point to graph this line.  Let's plug in a number greater than 2 since our inequality say x=2 or x>2.  You choose.  How about x=3?

y=-2(3)+2=-6+2=-3.   So we are going to include the point (3,-3). So starting at (2,-2) and going right to connect it to (3,-3), you could extend passed the (3,-3) to the right.

I will show you my graph.

There are no breaks in the "curve", so it is continuous for all real numbers.

Kerry donated 1/10 of her $500 savings to a charity. How much money did she donate?

Answers

Answer:

Kerry donated $50 to a charity.

Step-by-step explanation:

500/10=50

Answer:

$50

Step-by-step explanation:

1/10 of $500 =

= 1/10 * $500

= $500/10

= $50

Which of the sets of ordered pairs represents a function?
A = {(1, -2). (3.-5), (5,2), (7,5)}
B = {(4,2), (4, -2), (9,3), (9, -3)}

Answers

Answer:

The correct answer is A. Each x-value corresponds to exactly one y-value.

Y=8x-3/-4x-10 has a vertical asymptote with equation(enter equation of the vertical asymptote

Answers

Answer:

x=-2.5 if the function is [tex]f(x)=\frac{8x-3}{-4x-10}[/tex]

Step-by-step explanation:

[tex]y=\frac{8x-3}{-4x-10}[/tex] has discontinuities when the denominator is 0.

You will either have a hole or a vertical asymptote depending on what happens to the numerator after you find when the bottom is 0.

That is whatever you found that makes the bottom 0, if it makes the top also 0 then you will have a hole at x=the number that made the bottom 0.

If it makes the top anything other than 0, then it is a vertical asymptote at x=the number you found that made the bottom 0.

Let's do this now.

When is -4x-10 equal to 0?

We have to solve the equation:

-4x-10=0

Add 10 on both sides:

-4x=10

Divide both sides by -4:

x=10/-4

Reduce by dividing top and bottom by 2:

x=5/-2

x=-5/2

or

x=-2.5  (if you want decimal form)

Now does it make the top 0? This is the deciding factor on whether you have a hole at x=-2.5 or a vertical asymptote at x=-2.5.

Let's see.

8(-2.5)-3=-23

Since the top is not 0 at x=-2.5 then you have a vertical asymptote at x=-2.5.

If the top were 0, then you would have had a hole at x=-2.5.

The tax on a property with an assessed value of $67,000 is $975. Using a proportion, find the tax on a property with an assessed value of $96,000​

Answers

Answer:

1,440

Step-by-step explanation:

1.5 percent of 96k

Given the triangle below, what is the length of the third side, rounded to the nearest whole number?

Answers

Answer:

Hi there!

The answer to this question is: C. 14

Step-by-step explanation:

Using the formula for sine I solved the missing side.

sin(62)= 12/x

then you need to solve for x

x= 12/ sin(62)

and you get 13.59 so round up to get 14

The length of the third side of a triangle is 16.

How to find the length of the third side of a triangle?

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Use the Law of Cosine to find the third side of the triangle.

Law of Cosine is given by

[tex]$$a^{2}=b^{2}+c^{2}-2 b c$$[/tex]

Substituting the known values, we get

[tex]$$a^{2}=12^{2}+19^{2}-2 \cdot 12 \cdot 19 \cos 56$$[/tex]

By simplifying, we get

[tex]&a^{2}=505-456 \cos 56 \\[/tex]

[tex]&a^{2}=250.008 \\[/tex]

[tex]&a=15.81[/tex]

When rounded to the nearest whole number, the length of the third side is 16.

The length of the third side of a triangle is 16.

To learn more about the Law of Cosine refer to:

https://brainly.com/question/4372174

#SPJ2

What is the factored form of 3x2 + 5x - 12?

Answers

Answer:

[x + 3][3x - 4]

Step-by-step explanation:

First off, we need to find two numbers that when differed to 5, they also multiply to -36 [3 × -12]. Those numbers are -4 and 9. Next, we find the Greatest Common Factor [GCF], which means the LEAST DEGREE TERM possible:

[3x² - 4x] + [9x - 12]

x[3x - 4] 3[3x - 4]

As you can see, whenever we have a leading coefficient greater than 1, we need to break up our B into our two numbers we found [in BOLD], and have to attach an x to them because it replaced Bx, according to the Quadratic Equation of y = Ax² + Bx + C. So, after we completed our factoring, you see two identical factors, which we use ONCE. The other factor comes from the terms outside the duplicates. So, you get the above answer after you completed the steps: [x + 3][3x - 4].

I am joyous to assist you anytime.

Shane biked 1 mile than three times the number of miles lissette bike a total of 7 miles. Write an equation to determine how many miles lissette bike

Answers

To find the number of miles Lissette biked, the provided information leads to an algebraic equation where Lissette's distance is represented as 'x' and Shane's as '3x + 1', combining to equal 7 miles.

The subject of this question is mathematics, specifically algebra, where you need to write an equation based on a word problem.

The problem states that Shane biked 1 mile more than three times the number of miles Lissette biked, and their combined total is 7 miles. If we let x represent the number of miles Lissette biked, then Shane biked 3x + 1 miles. The equation to determine the number of miles Lissette biked is:

x + (3x + 1) = 7

What is the slope of the line in the graph?

Answers

To find the slope of a line you must do [tex]\frac{rise}{run}[/tex]

Look at the image to find the rise (in pink) and run (in green) on the graph:

In this case the rise is 3 and the run is -4 (the reason the four is negative is because it "runs" to the left, which is the negative direction of the coordinate plane) so the slope of this line is:

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

Hope this helped!

~Just a girl in love with Shawn Mendes

Find the quadratic function that fits curve below. Select the correct answer.

Answers

Hello!

The answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

Why?

We can solve the problem and find the correct function that fits the curve below by finding which function intercepts the y-axis at -5 (we can see it from the picture), also, we need to look for a function that represents a parabola opening upwards. We need to remember that when a parabola is opening upwards, its quadratic term coefficient is negative.

So, we can see that from the given functions, the only function that represents a parabola opening upwards and its y-intercept is located at y equal to -5 is the second option:

[tex]y=-3x^{2}+13x-5[/tex]

We have that :

[tex]a=-3(negative)\\b=13\\c=-5(y-intercept)[/tex]

We can see that the quadratic term (a) is negative, and the quadratic function intercepts the y-axis at y equal to -5.

Hence, the answer is:

The quadratic function that fits the given picture is:

[tex]y=-3x^{2}+13x-5[/tex]

Have a nice day!

Note: I have attached a picture for better understanding.

The Garcia family and the Lee family each used their sprinklers last summer. The Garcia family's sprinkler was used for 40  hours. The Lee family's sprinkler was used for 20  hours. There was a combined total output of 2000L  of water. What was the water output rate for each sprinkler if the sum of the two rates was 60L  per hour?

Answers

Answer:

Lee= 20 L per hour.

Garcia = 40L per hour

Step-by-step explanation:

This formula is:

40x + 20y = 2000L

with if being known that x + y = 60.

In this x is the rate for Garcia and y is the rate for Lee.

You can also say that x = 60 - y, which you can fill in.

40 * (60-y) + 20y = 2000

2400 - 40y + 20y = 2000

-20y = -400

y = 20 L per hour.

So x = 60 - 20 = 40L per hour

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