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Considering the vertex of the quadratic function, it is found that:

A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the function is given by:

y = 0.75x² - 13.5x + 57.75.

Which means that the coefficients are a = 0.75 > 0, b = -13.5, c = 57.75.

Thus, the minimum value is given by:

[tex]y_v = -\frac{(-13.5)^2 - 4(0.5)(57.75)}{4(0.75)} = -22.25[/tex]

Thus:

A robot traveling along the surface of the curved pit reaches a minimum depth of -22.25 feet.

More can be learned about the vertex of a quadratic function at https://brainly.com/question/24737967

Answer:

Step-by-step explanation:

Isolate the term of x and y from one side of the equation.

⇒ x+2y=11

⇒ x=11-2y

Substitute.

4(11-2y)-y=8

Solve.

Distributive property:

⇒ A(B+C)=AB+AC

4(11-2y)

4*11=44

4*2=8

Rewrite the problem down.

44-9y=8

Subtract by 44 from both sides.

44-9y-44=8-44

Solve.

-9y=-36

Divide by -9 from both sides.

-9y/-9=-36/-9

Solve.

-36/-9=4

y=4

Substitute of y=4.

⇒ x=11-2*4

Use order of operations.

PEMDAS stands for:

11-2*4

Multiply.

2*4=8

Rewrite the problem down.

11-8

Subtract.

11-8=3

x=3

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

21120 Feet

6.437376 Kilometer

Step-by-step explanation:

Looked it up

Answer:

7040 yd and 21120 ft

Step-by-step explanation:

1 mile = 1760 yards

1 yard = 3 feet

4*1760=7040 yards per day

7040*3=21120 feet per day

Answer:

Step-by-step explanation:

Rotate triangle DEF 90° and translate it up 1 point, and left 2 points.

Answer:

amount of paint:

If divide into 6 jars:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

let's solve ~

Total jars = 6

Total cups of blue paint :

[tex]\qquad \tt \dashrightarrow \: \frac{1}{2} + (1 \times 3) + 1 \frac{1}{2} + 2[/tex]

[tex]\qquad \tt \dashrightarrow \: \frac{1}{2} + 3 + \frac{3}{2} + 2[/tex]

[tex]\qquad \tt \dashrightarrow \: \frac{1 + 6 + 3 + 4}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \: \frac{14}{2} [/tex]

[tex]\qquad \tt \dashrightarrow \:7 \: cups[/tex]

So, teacher distributes all blue paint equally in each jar, then amount of paint in each jar is :

[tex]\qquad \tt \dashrightarrow \: \dfrac{7}{6} [/tex]

[tex]\qquad \tt \dashrightarrow \:1 \frac{1}{6} \: \: cups[/tex]

So, option B is correct

Answer:

76

Step-by-step explanation:

The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number. This is the median. If there are 2 numbers in the middle, the median is the average of those 2 numbers.

Answer:

d

Step-by-step explanation:

Answer:

It is the first one

Step-by-step explanation:

Hi, it is the first one because there is 4 - 1/2 3 - 3/4 and 2 - 1/4

Answer:

Both are 1/2

Step-by-step explanation:

Count just the tails, that's the numerator

Count all the heads and tails, that's the denominator.

And for the 2nd fraction:

Count just the evens, that's the numerator

Count all the even and odd numbers, that's the denominator.

Answer: The answer to this question is 3/4

Step-by-step explanation:

In this problem, there are 12 outcomes. Of those, 3 result in an even number and a tail, 3 more in an even number but not tail and 3 in a tail but an odd number, hence there are 9 desired outcomes.

Hence, the probability is given by: p=9/12=3/4

13/25

hope it helps..!!!

Answer:

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

a and b are legs, c is the hypotenuse

[tex]9^{2}[/tex] + [tex]11^{2}[/tex] = [tex]c^{2}[/tex]

81   + 121 = [tex]c^{2}[/tex]

202 = [tex]c^{2}[/tex]     ( square root each side  [tex]\sqrt{202}[/tex]

14.2126704036   = c

c = 14.2

Answer:

x=2.87083

Step-by-step explanation:

y = –2x^2 + 4x +5

ax^2 + bx + c = 0

a= -2

b= 4

c= 5

Quadratic formula: x= -b±√b^2-4ac over 2a

1. plug in the numbers

2. x= -4 ± √4^2 -4(-2)(5) over 2(-2)

3. x= -4 ± √16+40 over -4

4. x= -4 ± √56 over -4

next simplify ratidal

x= -4 ± √2·2·2·7 over -4

x= -4 ± 2√2·7 over -4

x= -4 ± 2√14 over -4

divide both sives over four

x= -4 over -4 ± 2√14 over -4

x= -1 over -1 ± √14 over -2  

answer:

x=2.87083

Sam first one

Craig second one

Randy third one

Charlie fourth one

From the data second is Craig, third is Randy and fourth is Charlie.

Given that, 4 persons ran a race.

Craig took 25.9 minutes

32.28 minutes took by Charlie

32.2 minutes by Randy

25.85 by Sam

To find who own second, third and fourth

Arranged the decimals in ascending order and found the answers.

By arranging in ascending order:

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

First is Sam = 25.85

Second is Craig = 25.9

Third is Randy = 32.2

Fourth is Charlie = 32.28

Hence, from the data second is Craig, third is Randy and fourth is Charlie.

To learn more about the comparison of decimals visit:

https://brainly.com/question/18270620.

#SPJ3

Answer:

340°

Step-by-step explanation:

To convert radians to degrees, multiply by [tex]\frac{180}{\pi }[/tex] since a full circle is 360° or

2[tex]\pi[/tex] radians.

[tex](\frac{17}{\pi } )[/tex] x [tex]\frac{180}{\pi }[/tex]

Factor [tex]\pi[/tex] out 0f 17[tex]\pi[/tex]

[tex]\frac{\pi (17)}{9}[/tex] x [tex]\frac{180}{\pi }[/tex]

Cancel the common factor "[tex]\pi[/tex]"

Rewrite the expression as:

[tex]\frac{17}{9}[/tex] x 180

Factor 9 out of 180.

[tex]\frac{17}{9}[/tex] x(9(20))

Cancel out the common factor "9"

Rewrite the expression as:

17 x 20

=340°

The volume of the cylinder that has same height and radius with the given cone is: D. 5,346 cubic centimeters

Volume of a cylinder = 3(volume of a cone), given that the cylinder and the cone has the same radius and the same height.

We are told that a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder, therefore:

Volume of the cylinder = 3(1,782)

Volume of the cylinder = 5,346 cubic centimeters

Learn more about volume of cylinder on:

https://brainly.com/question/9554871

Answer:

Step-by-step explanation:

The volume of the cylinder that has same height and radius with the given cone is: D. 5,346 cubic centimeters

What is the Volume of a Cylinder?

Volume of a cylinder = 3(volume of a cone), given that the cylinder and the cone has the same radius and the same height.

We are told that a cone that has a volume of 1,782 cubic cm, has the same radius and height with a cylinder, therefore:

Volume of the cylinder = 3(1,782)

Volume of the cylinder = 5,346 cubic centimeters

Learn more about volume of cylinder on:

brainly.com/question/9554871

Answer:

97 oz

Step-by-step explanation:

12 oz per pound

8 pounds + 1 oz

(12 · 8)+ 1

97 oz

Hope this helps!

Answer:

The C option is correct

TRUST ME

Step-by-step explanation:

Question

Answer

[tex]→ \frac{3 \times - 12}{5 \times - 20} \\ [/tex]

[tex] \sf \: solution→ \sf \: factor \: the \: expression \: \frac{7(a + b)}{ {a}^{2} - b } \\ [/tex]

[tex] \sf \red{ answer \: is→ \frac{9}{a - b}} \\ [/tex]

x=12

.................

Considering the function for it's height, it is found that the ball traveled for 3 seconds before returning to the ground.

The height of the ball after t seconds is given by:

h(t) = -16t² + 48t.

It is at the ground at the instants of t for which:

h(t) = 0.

Hence:

-16t² + 48t = 0

-16t(t - 3) = 0.

We want t different of 0, hence:

t - 3 = 0 -> t = 3.

The ball traveled for 3 seconds before returning to the ground.

More can be learned about functions at https://brainly.com/question/25537936

Answer:

3 seconds is the answer

Step-by-step explanation:

The value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.

The interseting chord theorem states that, when two chords in a circle intersect each other, then the product of their segment is equal.

For circle h in the given problem,

[tex]JN = 5, \\NK= 4, \\LN =2[/tex],

The value of segment NM is x.  The figure of the circle h is attached below. In this figure, using the interseting chord theorem the chords can be given as,

LN×NM=JN×NK

2×x=5×4

x=20/2

x=10

Thus, the value of x for the circle h with chords jk and lm intersecting at n inside the circle is 10.

Learn more about the interseting chord theorem here;

https://brainly.com/question/5432495

Step-by-step explanation:

I use desmos . com so it's easier.

A) 1.29

B) 0.91

C) 0.97

D) 1.05

Good Luck!

Answer:

30th percentile = 105 90th percentile = 176

Step-by-step explanation:

Arrange the data set in order from smallest to largest:

100, 100, 105, 113, 129, 132, 146, 152, 176, 200

30th percentile

r = number of data values = 10

q = percentile = 30

q/100 = 30/100 = 0.3

q/100 × r = 0.3 × 10 = 3

Therefore, count the 3rd number in the ordered set.

⇒ 30th percentile = 105

90th percentile

r = number of data values = 10

q = percentile = 90

q/100 = 90/100 = 0.9

q/100 × r = 0.9 × 10 = 9

Therefore, count the 9th number in the ordered set.

⇒ 90th percentile = 176

30th percentile = 105, 90th percentile = 176

Explanation:

data {129, 113, 200, 100, 105, 132, 100, 176, 146, 152}

arrange in ascending order:

{100, 100, 105, 113, 129, 132, 146, 152, 176, 200}

The recursive definition of the geometric sequence is given by:

A. [tex]a_n = (0.8)a_{n-1}[/tex]

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The basic recursive relation is given as follows:

[tex]a_n = qa_{n-1}[/tex]

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem, considering the given sequence, the common ratio is given by:

[tex]q = \frac{6144}{7680} = \frac{7680}{9600} = \frac{9600}{12000} = 0.8[/tex]

Hence option A is correct.

More can be learned about geometric sequences at https://brainly.com/question/11847927

The values of the motorcycle follows a geometric sequence

The recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

The values are given as:

$12,000 $9,600, $7,680, $6,144

Calculate the common ratio using:

r = a2/a1

So, we have:

r = 9600/12000

Divide

r = 0.8

Recall that:

r = a2/a1

So, we have:

a2/a1 = 0.8

Multiply both sides by a1

a2 = 0.8a1

Rewrite as:

[tex]a_{2} = 0.8a_{2-1[/tex]

Substitute n for 2

[tex]a_{n} = 0.8a_{n-1[/tex]

Hence, the recursive definition of the sequence is (a) [tex]a_{n} = 0.8a_{n-1[/tex]

Read more about sequence at:

https://brainly.com/question/7882626

Answer:

t = 3 seconds

Step-by-step explanation:

You can think of this as a quadratic and find the zeros. i will use x and y to make it easier.

y = -16x^2 + 48x

y = (x)(-16x+48)

y = (-16)(x)(x-3)

This means your zeros are at x = 0 and x-3 = 0, so 0 and 3.

0 is when the ball leaves the ground, so 3 is when it returns.

Answer:

Amplitude 0.03m, wavelength 2.86m, frequency 0.57Hz, period 1.8s

Step-by-step explanation:

The traveling wave is described with the following equation:

[tex]y=Asin(kx-wt)[/tex]

y=0.03sin(2.2x−3.5t)

A=0.03m

λ=2π/k=2π/2.2≈2.86m

T=1/f≈1.8s

Answer:

the first one is 0.5 inches 1.27 centimeters

the second is 0.25 inches or 0.635 centimeters

Step-by-step explanation: