Cory drinks water from a bottle during a bike ride. The average amount of water, in
ounces, in his water bottle can be represented by the equation y = -8x+32, where y is the amount of water remaining after x hours. Based on the equation, what amount of water, in ounces, will remain in the bottle after Cory rides for 2 1/2 hours?

Cory Drinks Water From A Bottle During A Bike Ride. The Average Amount Of Water, Inounces, In His Water

Answers

Answer 1
Answer is (B.) 12
Reason
They give you the formula
Y= -8x +32
Y is water remaining, the number we are looking for
X = 2.5 hours, insert in place of X

Y= (-8) (2.5) + 32
Y= -20 + 32
Y = 12
Answer 2

The amount of water will remain in the bottle after Cory rides for 2 1/2 hours will be;

⇒ y = 12 ounces

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The average amount of water, in ounces, in his water bottle can be represented by the equation,

⇒ y = - 8x + 32

Where, y is the amount of water remaining after x hours.

Now,

Since, The average amount of water, in ounces, in his water bottle can be represented by the equation,

⇒ y = - 8x + 32

Hence, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,

Substitute x = 2 1/2 in above equation,

⇒ y = - 8 × 2 1/2 + 32

⇒ y = - 8 × 5/2 + 32

⇒ y = - 20 + 32

⇒ y = 12 ounces

Thus, The amount of water will remain in the bottle after Cory rides for 2 1/2 hours is,

⇒ y = 12 ounces

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Related Questions

Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.

Answers

It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.

This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]

A man wants to cut down a tree in his yard. To ensure that the tree doesn’t hit anything, he needs to know the height of the tree. He measures his distance from the tree at 13 meters and the angle of elevation to the tree at 53°. What is the height of the tree to the nearest tenth of a meter

Answers

The height of the tree to the nearest tenth of a meter is 73.7m

What is angle of elevation?

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given:

base = 13 m

angle of elevation = 53

Using trigonometry

tan 53 = P/B

5.671 = P/ 13

P= 5.671 * 13

P= 73.723

Hence, the height of the tree is 73.7 m.

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What is the product of (2x - 1) (x + 4)

Answers

Answer: 2[tex]x^{2}[/tex]+7x-4

Step-by-step explanation:

Product implies multiplication so just multiply it out.

(2x-1) (x+4)

2x^2+8x-1x-4  (Combine like terms)

2x^2+7x-4

urgent help needed algebra 2

Answers

Answer:

it's 5 degrees celsius I think you must have entered a 4-32 instead of a 41-32 is what threw you off

Step-by-step explanation:

Trigonometry is crazy

Answers

Answer:

see the attachment photo!

i hope this can help you! :)

Which equation represents an exponential function with the initial value of 500?

Answers

Answer:

A exponential equation is usually of the form f(x)=a (1±r)ˣ.

Our limitation: Initial Vale is 500.

Let's look at our options:

#1- Initial Value of 1000  --- WRONG!

#2- Initial Value of 1000  --- WRONG!

#3- Initial Value of 500 ---- Maybe

#4- Initial Value of 500 ---- Maybe

Let's look at 3 and 4:

#3- Fits Our Form of f(x)=a (1±r)ˣ ---- CORRECT!

#4- Does not fit Our Form of f(x)=a (1±r)ˣ, It's to the 2nd power, not the x power! ---- WRONG!

Hence, #3 Is correct!

Step-by-step explanation:

Well, I hope you understood, and I'd gladly explain anything that didn't make sense. A brainliest would be appreciated, thank you!

-Zylynn Jade Ardenne

Which graph represents the function f(x)=2·4^x?

Answers

Answer:

A (top left)

Step-by-step explanation:

Assuming that the dot is multiplying the numbers, we get the function:

[tex]f(x) = 8^{x}[/tex]

First, lets knock off the obviously wrong answers.

Substitute 0 into the x spot, as anything to the power of zero is one.

[tex]f(0) = 8^{0}=1[/tex]

Automatically, the two answers on the right are incorrect, as y is not equal to 1 when x is 0.

Next, lets substitute 1 into the x spot, as anything to the power of one is itself.

[tex]f(1) = 8^{1} = 8[/tex]

As a result, the top left graph is correct, as y is equal to 8 when x is 1, unlike the bottom left graph.

What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621

Answers

Answer:

[tex]a = 7[/tex]

Step-by-step explanation:

[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]

Compute the projection of u on v.

Answers

Answer:

[tex]\frac{3}{7}.v[/tex]    option (C) is correct

Step-by-step explanation:

projection of vectors: The vector projection of one vector over another vector is the length of the shadow of the given vector over another vector.

projection of vector u on v is given by :

[tex](\frac{u.v}{v.v}).v[/tex]

Given,

vector u = <5, 7, 1>

vector v = <2, -1, 3>

substituting these values in the above formula

[tex][\frac{(2,-1,3)(5,7,1)}{(2,-1,3).(2,-1,3)} ].v[/tex]  =  [tex]\frac{6}{14}.v= \frac{3}{7}.v[/tex]

thus the correct answer is option (C)

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Pleas hurry!!!!! Which line is perpendicular to a line that has a slope of -5/6
line JK
line LM
line NO
line PQ

Answers

Answer:

LM

Step-by-step explanation:

Perpendicular slope would be   - 1 / m   =   - 1/(-5/6)   = 6/5

slope m = rise / run       line   LM   rises 6    for a run of 5      

How can I find the three iterations of 3^(x)= 2^(-x)+4

Answers

After factorizing the given equation, we can find the three iterations by putting the consecutive values of x.

The given equation is 3∧x = 2∧(-x) + 4. We can modify it as shown below:

Take logarithm on both the sides

log(3∧x) = log[2∧(-x) + 4]

xlog3 = log[2∧(-x) + 4]

x = log[2∧(-x) + 4] / log3

For the first iteration, put x = 1

x = log[2∧(-1) + 4] / log3

x = log4.5 / log3

x = 0.477

For the second iteration, put x = 2

x = log[2∧(-2) + 4] / log3

x = log4.25 / log3

x = 0.477

For the third iteration, put x = 3

x = log[2∧(-3) + 4] / log3

x = log4.125 / log3

x = 0.477

So, this is how we can find three iterations.

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How many kilometers are in 462 meters? How many kilometers are in 462 meters ?​

Answers

Answer:

0.462

Step-by-step explanation:

1km=1000m

so to get from metres to kilometres you divide by 1000

so 462÷1000=0.462

Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark

quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1

Answers

The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

What is an ellipse?

An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.

We have:

The vertices of the ellipse = (1, 0) and (11, 0)

Eccentricity of ellipse = 3/5

We have equations:

[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]

[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]

[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]

From the fourth equation:

The vertices of the ellipse:

(1, 0) and (11, 0)

The eccentricity:

c²  = a² - b²

c² = 25-16

c = 3

e = c/a = 3/5

Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.

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the ufugfldldd

5+9x+3gg3g3\
1 b

Answers

the correct answer is B

Find the length of the side labeled . Round intermediate values
to the nearest tenth. Use the rounded values to calculate the next
value. Round your final answer to the nearest tenth.

Answers

Step-by-step explanation:

ATTACHED IS THE SOLUTION!!PLEASE DON'T HESITATE TO ASK WHERE YOU DON'T UNDERSTAND.

Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of a function in your answer

Answers

Explanation:

A function is a relationship where any one x-value/input only has one corresponding y-value/output. (note: a y-value can have multiple x-values).

> This can be called "assigning one y-value to every x element".

The vertical line test places a line that would connect all y-values of an x-value (that is, if it were to have multiple y-values). If multiple points can be found along the vertical line, it is, therefore, by the definition of a function, not a function. (Because an x-value will have more than one y-value).

So, a graph that fails the vertical-line test does not represent a function because an x-value will correspond with more than one y-value.

hope this helps!!

which expression is equivalent to...​

Answers

Answer:

B

Step-by-step explanation:

Which of the following is the solution to 7√22 + 3√7

Answers

The value of this irrational Expression is 40.77 .

What is an Expression ?

An expression is a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

7√22 +3√7

√22 = 4.69

√7 = 2.65

32.83 + 7.94

40.77

The value of this irrational Expression is 40.77 .

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190 divided by 2 over 3

Answers

Answer is 285
Reason
When you divide by a fraction, you flip the fraction and multiply
So 190 divided by 2/3 becomes 190 x 3/2
Factor 190 x 3/2, multiply across
190 x 3 = 570 then
570 divided by 2 = 285

Lydia writes the equation below with a missing value.

y = 5 x minus box

She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation?
If she puts 0 in the box she would have a direct variation.
If she puts 5 in the box she would have a direct variation.
The equation is not of the form y = k x, so it cannot represent a direct variation.
The equation has a minus sign, so it cannot represent a direct variation.

Answers

If she puts 0 in the box she would have a direct variation.

Lydia writes the equation y = 5x - __ with a missing value.

She puts a value in the box and says that the equation represents a direct variation.

We have to choose the correct option from the given options that explain that the equation could represent a direct variation.

When two variables are such that one is a constant multiple of the other, we said they are in Direct variation.

What is the direct variation?

In form of y = ax, where y and x are in direct variation.

Consider the given equation y = 5x  - __

For the equation to be in direct variation the value of the missing term has to be 0.

then the equation becomes,

y = 5x

Thus, If she puts 0 in the box she would have a direct variation.

Option (a) is correct.

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Answer:

a

Step-by-step explanation:

statement that is assumed to be true without proof is . A statement that has been shown to be true by vigorous application of logic is . is a statement that is believed to be true but hasn't been proven.

Answers

An axiom is a statement that is assumed to be true without proof.

What are the types of statements?

In logic, a statement could be shown to be valid or true by the use of premises that lead to a sound conclusion.

The following terms can be used to describe the statements;

Axiom -  a statement that is assumed to be true without proofTheorem - a statement that has been shown to be true by vigorous application of logicHypothesis -  a statement that is believed to be true but hasn't been proven.

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Answer:

The answer is axiom, theorem, and then conjecture

Step-by-step explanation:

curved surface area of a cone = Trl, where r is the
radius and I is the slant height.
surface area of a sphere = 42, where r is the
radius.
The shape below is made from a hemisphere and a
cone, each with a radius of 6 cm.
Work out the surface area of this shape in terms of .
16 cm
6 cm
Not drawn accurately

Answers

Answer:

  168π cm²

Step-by-step explanation:

The total surface area is the sum of the areas of the parts: a hemisphere and a cone.

__

area formula

The area of a hemisphere is half the area of a sphere, so the total area is ...

  total area = hemisphere area + cone area

  = 2πr² +πrl

  total area = πr(2r +l)

__

application

For the given dimensions, r = 6 cm, l = 16 cm, the total surface area is ...

  total area = π(6 cm)(2(6 cm) +16 cm) = π(6)(28) cm²

  total area = 168π cm²

18 / 48 hrs left

Divide and answer the question.

Answers

Answer: I don’t understand

Step-by-step explanation:

You need more context for us to answer

Evaluate using the trigonometric ratios Tan 60° + Cos 30° sin 60° + Cot 30° /CSC 30° Sec 30°

Answers

Answer:

(24 + 3√3) / 16.

Step-by-step explanation:

Tan 60° + Cos 30° sin 60° + Cot 30 /  csc 30 sec 30

= √3 + √3/2 * √3/2 + √3 /   2 * 2/√3

= 2√3 + 3/4 / 4/√3

= (8√3 + 3)/ 4 / √3

= 24 + 3√3 / 16

Multiply and remove all perfect squares from inside the square roots. Assume a is positive.

3[tex]3\sqrt{5a}*8\sqrt{35a^{2} }[/tex]









Answers

The multiplication is 120*[tex]a^{3/2}[/tex].

What is exponents and powers?

Power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.

Given:

3√(5a) * 8 √(35a²)

= 3√(5a)* 8* a *√7* √5

= 3*8*5*a *√(7a)

= 120 [tex]a^{1/2+1}[/tex]

=120*[tex]a^{3/2}[/tex]

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Answer:

[tex]120a\sqrt{7a}[/tex]

Step-by-step explanation:

It's right on khan academy

solve the following inequality:
ALGEBRA 1

Answers

Answer:

[tex]m \leqslant 10 \: or \: m > 4[/tex]

Step-by-step explanation:

[tex] \frac{m - 2}{3} \leqslant - 4 \\ \frac{m - 2}{3} \times 3 \leqslant - 4 \times 3 \\ m - 2 \leqslant - 12 \\ m - 2 + 2 \leqslant - 12 + 2 \\ m \leqslant 10[/tex]

OR

[tex]3m - 8 > 4 \\ 3m - 8 + 8 > 4 + 8 \\ 3m > 12 \\ \frac{3m}{3} > \frac{12}{3} \\ m > 4 [/tex]

!!WILL GIVE BRAINLIES PLS HELP!!!
Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (-6,
12) and includes the point (-9, 15) on the boundary?

Answers

Answer:

is B

Step-by-step explanation:

this is the best possible answer

Which of the following are true statements?

Answers

Pretty sure the answer is b

Find the next number in the sequence: 2, 2, 5, 12, 62, 749, 46450,

Answers

Answer:

34791112

Step-by-step explanation:

Please check the attached for the explanation.

The next number for given sequence is 34791112.

The given sequence is 2,2,5,12,62,749,46450,......

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same.

Each number in the sequence is of the form Number3 × Number2 + Number1 = Number4

5×2+2=12

12×5+2=62

62×12+5=749

749×62+12=46450

So, the required number is

46450×749+62=34791112

Therefore, the next number for given sequence is 34791112.

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Question 1 of 10
What is the midpoint of the segment shown below?
O A. (6,3)
O B. (6,5)
O C. (3,5)
OD. (3, 3)

Answers

Answer:

[tex]\textsf{C.} \quad \left(3,\dfrac{5}{2}\right)[/tex]

Step-by-step explanation:

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints of the line segment:

[tex]\textsf{Let }(x_1,y_1)=(-1,2)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(7,3)[/tex]

Substitute the defined endpoints into the midpoint formula and solve:

[tex]\implies \textsf{Midpoint}=\left(\dfrac{7+(-1)}{2},\dfrac{3+2}{2}\right)[/tex]

[tex]\implies \textsf{Midpoint}=\left(3,\dfrac{5}{2}\right)[/tex]

(-1,2) and (7,3)

Midpoint

(-1+7/2,2+3/2(6/2,5/2)3,5/2)
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