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. Graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. 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. 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. 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).

Answer:

100 and 80 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.  Here we are to find two such angles that are in the ratio 5:4.  To do this, we set up and solve the following equation:

5x + 4x = 180, or

9x = 180, or

x = 20.

Then one angle is 5(20) and the other is 4(20), or 100 and 80.

Note that these two angles add up to 180 degrees, as they must.

The two supplementary angles are 100 and 80 degrees.

Answer:

I apologize for the confusion caused. Let's go through the problem again to determine the correct answer.

We have a police helicopter flying at 120 mph at an altitude of 1.5 miles above a highway. The radar detects an oncoming car at a distance of exactly 3 miles from the helicopter, and this distance is decreasing at a rate of 190 mph.

To find the speed of the car, we need to consider the relative motion between the car and the helicopter. From the perspective of the helicopter, the car's speed is the sum of its own speed and the rate at which the distance is decreasing.

Let's denote the speed of the car as "v_car" and the speed of the helicopter as "v_helicopter." The relative speed between the car and the helicopter is the difference between the two speeds, given by:

Relative speed = v_car - v_helicopter

Since the distance between the car and the helicopter is decreasing at a rate of 190 mph, the relative speed is -190 mph (negative because the car is approaching the helicopter).

However, since we want to find the speed of the car, we need to consider the magnitude of the relative speed. Taking the absolute value, we have:

|Relative speed| = |v_car - v_helicopter| = |-190|

Now, let's solve for the speed of the car:

|v_car - 120| = 190

We can solve this equation by considering two cases:

Case 1: v_car - 120 = 190

v_car = 190 + 120

v_car = 310 mph

Case 2: -(v_car - 120) = 190

-v_car + 120 = 190

v_car = 120 - 190

v_car = -70 mph

Since speed cannot be negative, we discard Case 2.

Therefore, the correct answer is that the speed of the car, as detected by the radar, is 310 mph.

Let's assume that the measure of angle 1 is represented by "x" and the measure of angle 2 is represented by "y". We are given that the ratio of the measures of angle 1 to angle 2 is 5:4. This can be expressed as:

x:y = 5:4

Since the angles are supplementary, the sum of their measures is 180 degrees:

x + y = 180

To solve this system of equations, we can use the ratio given to express one variable in terms of the other. Let's express "x" in terms of "y":

x = (5/4) * y

Substituting this expression for "x" into the second equation:

(5/4) * y + y = 180

Multiplying through by 4 to eliminate the fraction:

5y + 4y = 720

9y = 720

Dividing both sides by 9:

y = 80

Substituting the value of "y" back into the expression for "x":

x = (5/4) * 80

x = 100

Therefore, the measures of the supplementary angles that satisfy the given ratio are angle 1 with a measure of 100 degrees and angle 2 with a measure of 80 degrees.

I am very sorry maybe I did mistake in the previous questions answer so this is the revised ONE and sO please DO SEE once okay !!!

if g(x) = 0, then

x = 0 -- > g(0) = 0^2 + 2(0) = 0 + 0

AND x = -2 --> g(-2) = -2^2 + 2(-2) = 4 + (-4) = 0.

I don't know why f(x) was given at all, but when x = 0, f(0) = -5, and when x = -2, f(-2) = -8.

Answer:

[tex]y = -\frac{2}{5} x - 11[/tex]

Step-by-step explanation:

So we are given the two coordinate points (-10 , -7) and (-5 , -9).

With the question to "Complete the equation of the line."

So what we do is to compute the slope of both coordinates, which will give us

[tex]-\frac{2}{5}[/tex]

So to complete part of the equation:

[tex]y = -\frac{2}{5} x[/tex]

Now we need to compute the y intercept, since all numbers are negative, there is likely chance [tex]b[/tex] will be a subtraction method.

Compute the y intercept:

[tex]-11[/tex]

Complete the equation :

[tex]y = -\frac{2}{5} x - 11[/tex]

Here is a graph to go with the equation :

Answer:

1/2n-7

(0×3)+4

(p×5)-2

7+r

s+7

10-t

u-10

2×v

w×2

x÷5

5÷y

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

14) 1/2n - 7

15) 3o + 4

16) 5p - 2

17) 7 + r

18) s + 7

19) t - 10

20) 10 - u

21) 2v

22) 2w

23) x ÷ 5

24) 5 ÷ y

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

7:10:34

Step-by-step explanation:

1. Ratio outline:

       Length 1:Length 2:Perimeter

2. Length 1 = 35 feet

3. Length 2 = 50 feet

4. Perimeter = Length of all sides

     - Since, a ractangle has 4 sides and the opposite sides are equal, we do Perimeter = 35+50+35+50 = 170

5. Substitute the values into the ratio outline:

        35:50:170

6. Convert into simplest form: Divide by greatest common factor (5)

         7:10:34

Answer:

the slope is 0

m= 0

Step-by-step explanation:

whenever a line is horizontal and straight across the plane the slope is 0

Answer:

m = 0

Step-by-step explanation:

slope can be found using the following equation:

m  (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (-3 , -2)

(x₂ , y₂) = (1 , -2)

Plug in the corresponding numbers to the corresponding variables:

m =  (y₂ - y₁)/(x₂ - x₁) = (-2 - (-2))/(1 - (-3))

Simplify:

m = (-2 - (-2))/(1 - (-3)) = (-2 (+2))/(1 +3) = (-2 + 2)/(1 + 3)

m = (-2 + 2)/(1 + 3) = (0)/(4)

m = 0/4 = 0

The slope of the line is 0.

~

Answer:

The functions given are:

f(x) = x²

g(x) = f(-4x-3) + 1

First, find f(-4x-3):

f(x) = x²

f(-4x-3) = (-4x-3)²

Find g(x):

g(x) = f(-4x-3) + 1

g(x) = (-4x-3)² + 1

g(x) = (-1)² (4x+3)² + 1

g(x) = (4x+3)² + 1

First take

y = (x)²

Compress the graph along x axis by multiplying x with 4

y = (4x)²

Shift the graph left by 0.75 units, by adding 3 to x term.

y = (4x+3)²

Shift the graph up by 1 unit by adding 1 to the total terms.

y = (4x+3)² +1

Answer:

5.53:4.

Step-by-step explanation:

The scale factor is ∛13 : ∛8.

The surface area ratio is the square of these.

= (∛13)^2 : (∛8)^2.

= 5.53 : 4

Answer:

A) 5.12mm³

Step-by-step explanation:

Step 1

Find the volume of the bigger pyramid

This is a triangular based pyramid.

The formula to use is given as Volume of Pyramid =

1/3 × Area of the triangle × Height

Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²

Volume of the large pyramid = 1/3 × 6mm² × 5mm

= 10mm³

We are given the length of the small pyramid as 4mm

We would be using was is known as scale factor to find the volume of the small pyramid

The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³

k = 4³/5³

k = Volume of small pyramid/ Volume of large pyramid

Volume of small pyramid = X

Volume of large pyramid = 10mm³

Hence,

4³/5³ = X/10

Cross Multiply

= 4³ × 10 = 5³ × X

X = (4³ × 10)/ 5³

X = 5.12mm³

Answer:

There is a 40% chance that the next page that Luna turns to will have an ad.

Step-by-step explanation:

384 divided by 960 is equal to 4/10.  That is the same as 40%.

Hope this helps :)

Answer:

40%

Step-by-step explanation:

The probability is 384 out of 960

Which equals to:

Answer is 40%

Answer:

Step-by-step explanation:

first we will break the parts of the question down:

d= distance

t= time

function: d=t(60)

the independent variable is t, time, because the (distance) that the car travels depends   on how long the car has been traveling for (time) meaning that the dependent value is distance.

A table we can create with 5 coordinate pairs is:

(time)        (distance)

1 hr            60miles

2 hr           120 miles

3 hr          180 miles

4 hr            240 miles

5 hr           300 miles

(to graph the coordinate pairs, you can graph the points listed in the table. the time value represents the x value since it is the independent variable, and the y value will be the distance values since it is dependent.)

Answer:

There are 360° in a full circle. 36% of 360 = 0.36 * 360 = 129.6° which rounds to 130°.

Answer:

x= 130°

Step-by-step explanation:

We want to khow what is the size of the angle that coresponds 36  percent

we can state :

Answer:

change in y

over

change in x

---------------------------------------

please make me brainliest

Answer:

y = Five-sixths x – 12

Step-by-step explanation:

In the picture attached, the given line is shown. Its slope is:

m = [6 - (-4)]/[12 - 0] = 5/6

The line that is parallel to the given line has the same slope.

A line with slope m that pass through (x1, y1) satisfies:

y - y1 = m(x - x1)

Replacing with m = 5/6 and point (12, -2):

y - (-2) = 5/6(x - 12)

y + 2 = 5/6x - 10

y = 5/6x - 10 - 2

y = 5/6x - 12

Answer:

D

Step-by-step explanation:

The probability that Mark's little brother selects an outfit with a white shirt and gray slacks or an outfit with a black shirt will be [tex]\frac{1}{2}[/tex].

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]

Where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

The probability of the white shirt and the gray slack is;

[tex]\rm P(A) = \frac{1}{6}[/tex]

The probability of the outfit with the black shirt is;

[tex]\rm P(B) = \frac{F(S)}{T(S)} \\\\ \rm P(B) = \frac{5,6}{1,2,3,4,5,6)} \\\\ \rm P(B) ==\frac{2}{6} \\\\ P(B) = \frac{1}{3}[/tex]

The probability that the no favorable outfit with the white shirt and black is;

P(A∩B)=0

The probability that Mark's little brother selects an outfit with a white shirt and gray slacks or an outfit with a black shirt is found by the formula;

P(A or B)= p(A∪B)=P(A)+P(B)-P(A∩B)

P(A∪B)=P(A)+P(B)-P(A∩B)

[tex]\rm P(A \ U \ B)= \frac{1}{6}+\frac{2}{6} -0 \\\\\ P(A \ U \ B)=\frac{1}{2}[/tex]

Hence, the probability that Mark's little brother selects an outfit with a white shirt and gray slacks or an outfit with a black shirt will be [tex]\frac{1}{2}[/tex].

To learn more about the probability, refer to the link;

brainly.com/question/1210781

#SPJ2

The probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt is 1/3.

We have to given that,

Mark is going to an awards dinner and wants to dress appropriately.

And, Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie.

Since, There are six possible outfits, and we want to find the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt.

We can use the addition rule of probability:

P(A or B) = P(A) + P(B) - P(A and B)

where P(A) is the probability of selecting an outfit with a white shirt and grey slacks,

P(B) is the probability of selecting an outfit with a black shirt, and

P(A and B) is the probability of selecting an outfit with both a white shirt and grey slacks, and a black shirt.

From the six possible outfits, there is one outfit with a white shirt and grey slacks, and one outfit with a black shirt, so:

P(A) = 1/6

P(B) = 1/6

There is no outfit that satisfies both events A and B, so:

P(A and B) = 0

Therefore:

P(A or B) = P(A) + P(B) - P(A and B)

              = 1/6 + 1/6 - 0

              = 1/3

So, the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt is 1/3.

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ6

Complete question is,

Mark is going to an awards dinner and wants to dress appropriately. He is running behind schedule and asks his little brother to randomly select an outfit for him.

Mark has one blue dress shirt, one white dress shirt, one black dress shirt, one pair of black slacks, one pair of grey slacks, and one red tie. All six of his possible outfits are listed below.

Let A be the event that Mark's little brother selects an outfit with a white shirt and grey slacks and B be the event that he selects an outfit with a black shirt.

What is P (A or B) , P, left parenthesis, A, start text, space, o, r, space, end text, B, right parenthesis, the probability that Mark's little brother selects an outfit with a white shirt and grey slacks or an outfit with a black shirt?

Answer:

x = ± 3, x = ± 2i

Step-by-step explanation:

Given

f(x) = (x² + 4)(x² - 9)

To find the zeros let f(x) = 0, that is

(x² + 4)(x² - 9) = 0

Equate each factor to zero and solve for x

x² - 9 = 0 ( add 9 to both sides )

x² = 9 ( take the square root of both sides )

x = ± [tex]\sqrt{9}[/tex] = ± 3

x² + 4 = 0 ( subtract 4 from both sides )

x² = - 4 ( take the square root of both sides )

x = ± [tex]\sqrt{-4}[/tex] = ± [tex]\sqrt{4(-1)}[/tex] = ± [tex]\sqrt{4}[/tex] ×[tex]\sqrt{-1}[/tex] = ± 2i

Thus zeros are

x = - 3, x = 3 ← real

x = - 2i, x = 2i ← complex

Answer:

Square root ( 2 )

Step-by-step explanation:

We have to determine which value is equivalent to | f ( i ) | if the function is: f ( x ) = 1 - x. We know that for the complex number: z = a + b i , the absolute value is: | z | = sqrt( a^2 + b^2 ). In this case: | f ( i )| = | 1 - i |. So: a = 1, b = - 1. | f ( i ) | = sqrt ( 1^2 + ( - 1 )^2) = sqrt ( 1 + 1 ) = sqrt ( 2 ).  

Answer:

I think similar is the correct answer

Answer:

the 2nd one

Step-by-step explanation:

b/c

-5/2x-3≤2

-5/2x≤3+2

-5/2x≤5

-5x≤10

x≥10/-5

x≥-2

Answer:

x = -3.75

Step-by-step explanation:

First, combine like terms:

x - 5x = -4x

-4x = 15

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Divide -4 from both sides:

(-4x)/-4 = (15)/-4

x = 15/-4

x =  -3.75

-3.75 is your answer for x.

 ~

Answer:

x = -15/4

Step-by-step explanation:

x - 5x = 15

Combine like terms

-4x = 15

Divide each side by -4

-4x/-4 = 15/-4

x = -15/4

Answer:

B

Step-by-step explanation:

Take total displacement and divide by the time it took.

Answer:

a. 412

b. 478

Step-by-step explanation:

We have to find the corresponding probabilities using the standard normal table, that is, we must calculate the value of z, the formula of z is as follows:

z = (x - m) / sd

where x is the value to evaluate, m is the mean and sd is the standard deviation.

We are told that the mean is 8.2 cm and the standard deviation is equal to 2.8 cm.

a. smaller than 5.9cm?

In this case x would be 5.9, we replace and we are left with:

z = (x - m) / sd

z = (5.9 - 8.2) /2.8

z = -0.82

If we look for this value in the normal table (attached) it corresponds to 0.2061, to know the number of apples we must multiply this value by the total value of apples, that is 2000. Therefore:

2000 * 0.2061 = 412.2 = 412

b) larger than 10.2cm?

In this case x would be 10.2, we replace and we are left with:

z = (x - m) / sd

z = (10.2 - 8.2) /2.8

z = 0.71

In this case z corresponds to 0.7611, but since this is the value is smaller than 10.2, and we need is larger than 10.2cm, it would be the complement, that is:

1 - 0.7611 = 0.2389

Now to calculate the total number of apples we have:

2000 * 0.2389 = 477.8 = 478

Answer:

2x² - 9x - 5

Step-by-step explanation:

Step 1: FOIL

2x² - 10x + x - 5

Step 2: Combine like terms

2x² - 9x - 5

Answer:

2x^2−9x−5

Step-by-step explanation:

(2x+1)(x−5)

=(2x+1)(x+−5)

=(2x)(x)+(2x)(−5)+(1)(x)+(1)(−5)

=2x^2−10x+x−5

=2x^2−9x−5

Answer:

I think it's a,c,and e that aren't polynomials

Answer:

A, C, and E

Step-by-step explanation:

A is not a polynomial because its exponents is negative.

C is not a polynomial because the power of x is ½ and exponents can only be integers

E is not a polynomial because one cannot divide by a variable and the exponent of x is negative

Answer:

98

Step-by-step explanation:

First to do this you must turn 12 and 1/4 into an improper fraction. 12 and 1/4 as an improper fraction is 49/4, as their are 49 1/4s in 12 and 1/4.

Now to divide 49/4 by 1/8, you keep 49/4, turn the division sign into a multiplication sign, and turn 1/8 into 8/1 (flip numerator and denominator)

This turns 49/4÷1/8 into 49/4×8/1. Now to multiply you get 49 × 8 as the numerator and 4 × 1 as the denominator. This ends up being 392/4. You then can simplify by dividing both numbers by 4, and get 98/1 or 98.

Answer: 98

Step-by-step explanation: To divide 12 and 1/4 by 1/8, first write 12 and 1/4 as the improper fraction 49/4.

So we have 49/4 ÷ 1/8.

Now, since dividing by a fraction means the same thing as multiplying by the reciprocal of the fraction, we can rewrite 49/4 ÷ 1/8 as 49/4 × 8/1.

Before multiplying however, always try to cross-cancel.

In this problem, the 4 and 8 cross-cancel to 1 and 2.

So we have 49/1 × 2/1 which is 98/1 or 98.