A choetah can run at a maximum spe 105k(m)/(h) and a gazelle can run at a mar mum spocd of 76k(m)/(h) If both rnimaly are rumning at full spee with the gazelle 79.2m ahead, how long befo the chectah catches ists prey?

The volume of the traffic cone is 1.262 cubic inches.

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.

To find the volume of the traffic cone, we need to find the volumes of the cone and the prism and then add them together.

The cone has a radius of b (since the diameter is 1 inch) and a height of h = 1 inch. The formula for the volume of a cone is:

Vcone = (1/3)πr²h

Substituting the values, we get:

Vcone = (1/3)π(1/2)²(1)

Vcone = (1/3)π(1/4)

Vcone = (1/12)π

The prism has a base of length and width equal to the diameter of the cone, or 1 inch. The height of the prism is also 1 inch. The formula for the volume of a rectangular prism is:

Vprism = lwh

Substituting the values, we get:

Vprism = (1)(1)(1)

Vprism = 1

Adding the volumes of the cone and the prism, we get the total volume of the traffic cone:

Vtotal = Vcone + Vprism

Vtotal = (1/12)π + 1

Vtotal ≈ 1.262 cubic inches (rounded to three decimal places)

Therefore, The volume of the traffic cone is 1.262 cubic inches.

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The trigonometric identity, (sec(x) ÷ cos(x)) - (tan(x) ÷ cot(x)) is equivalent to the Pythagorean identity sec²(x) - tan²(x) = 1, therefore;

(sec(x) ÷ cos(x)) - (tan(x) ÷ cot(x)) = sec²(x) - tan²(x) = 1

A trigonometric identity is an equation involving trigonometric ratio which is correct for possible values of the input variables.

The specified trigonometric identities can be presented as follows;

sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = 1

cos(x) = 1/sec(x)

tan(x) = 1/cot(x)

cot(x) = 1/tan(x)

Therefore; sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec(x) ÷ (1/sec(x)) - tan(x) ÷ (1/tan(x)) = 1

Therefore;

sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec²(x) - tan²(x)

The Pythagorean identities, indicates that we get;

sec²(x) - tan²(x) = 1

Therefore; sec(x) ÷ cos(x) - tan(x) ÷ cot(x) = sec²(x) - tan²(x) = 1

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The period of the function in this problem is given as follows:

14 units.

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

Looking at the peaks of the function, they are given as follows:

Hence the period is given as follows:

29 - 15 = 15 - 1 = 14 units.

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Answer:

need coordinates of each or side lengths of each to solve

Step-by-step explanation:

option d is correct

as,

corresponding angles are = 1 & 5 , 2 & 6 , 3 & 7 and 4 & 8

alternate interior angle are 3 & 6 and 4 & 5

alternate Exterior angles are 2 & 7 and 1 & 8

hope this answer helps you dear...may u have a great day ahead..take care!

Answer:

17

Step-by-step explanation:

Input x=4 into the equation

y= 3(4)+5

y= 12+5

y=17

Answer:

y=17

Step-by-step explanation:

if x=4,

y=3(4)+5

y=12+5

y=17

Answer:

\(x=-7\)

Step-by-step explanation:

So we have the equation:

\(x+5=-2\)

To solve, subtract 5 from both sides. This is the subtraction property of equality:

\((x+5)-5=(-2)-5\)

The left side cancels:

\(x=(-2)-5\)

Subtract on the right.

\(x=-7\)

So, our answer is -7.

Answer: The square

Step-by-step explanation:

The square has a 90 degree angle which is a right angle. Also all sides have the same length

Answer:

\((a-b)^3 = a^3 - b^3 - 3a^2b + 3ab^2\\\\a = 3x, \ b = 1\\\\(3x-1)^3 = (3x)^3 - (1)^3 - 3(3x)^2(1) + 3(3x)(1)^2\\\\\)

             \(= 27x^3 - 1-3(9x^2)+ 9x\\\\=27x^3 -27x^2 +9x -1\)

The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.

We have,

To expand the function f(x) = (3x - 1)³, we can use the binomial expansion formula, which states:

(a + b)³ = a³ + 3a²b + 3ab² + b³

In this case,

a = 3x and b = -1.

Substituting these values into the formula, we get:

\((3x - 1)^3 = (3x)^3 + 3(3x)^2(-1) + 3(3x)(-1)^2 + (-1)^3\)

Simplifying further:

(3x - 1)³ = 27x³ - 9x³ + 9x - 1

Therefore,

The expanded form of the function f(x) = (3x - 1)³ is 27x³ - 9x² + 9x - 1.

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Answer:

Answer:

The 65 tells us the constant speed the car is travelling at.

The car travels 97.5 miles in 1.5 hours

0.4 of an hour to travel 26 miles

Step-by-step explanation:

d is the distance, we get  that by multiplying speed and time, we are told t is time, so 65 must be speed

Step-by-step explanation:Substitute in 1.5 into the equation as the t, time

d=65t

d=65×1.5

d=97.5

The car takes 0.4 hours to travel 26 miles, substitute in 26 as the d, and isolate t to get the time it takes to travel 26 miles

d=65t

26=65t

26÷65=t

0.4=t

Answer:

c: y=(x-1)(x-3)

Step-by-step explanation:

Hilbert's euclidean parallel postulate implies the converse to the alternate interior angle theorem since if α = β, then l and m cannot be parallel.

Hilbert's Euclidean parallel postulate states that given a line and a point not on that line, there exists exactly one line passing through the point and parallel to given line.

Suppose we have two parallel lines l and m, and a third line n that intersects both l and m, forming alternate interior angles α and β. We want to prove that if α = β, then l and m are not parallel.

Let's assume contrary, that l and m are parallel despite α = β. Then, by Hilbert's parallel postulate, there exists exactly one line passing through any point on n that is parallel to l and m.

Therefore, if we draw a line parallel to l and m through point where n intersects l, it must be same as line passing through point where n intersects m.

But this leads to a contradiction, because if lines are same, then alternate interior angles α and β are congruent.

Thus, we have shown that if α = β, then l and m cannot be parallel. This is  converse to alternate interior angle theorem.

Therefore, we have proved that Hilbert's Euclidean parallel postulate implies converse to the alternate interior angle theorem.

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Answer:

3. x = 30

4. x=-6

5. x=-2

6. x=0.5

Answer:

a) checkpoint 5

b) checkpoint 3

c) Its above sea level

hope that helps :)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

9, 10, 11, 12, 13, 14, 15, 16

Hope that helps!

A discrete function is a function with distinct and separate values. This means that the values of the functions are not connected with each other. For example, a discrete function can equal 1 or 2 but not 1.5.

Let's analize the options:

• Option A: This is continuos, the faucet can fills with 1 gallon, 1.1 gallon, and so. Also any previous value is connected with the next.

• Option B: As in option B, the car drives for a continuos time.

• Option C: This is a discrete relation, because Jacqueline could not sells a half of a chocolate bar, she sells discrete values of chocolate bars 1, 2, 3, ....

• Option D: This is the same as option A.

we have -4.5 + 4.4 + x = 0

<=> -0.1 + x = 0

<=> x = 0.1 ( P/s: x is the answer to fill in the blank )

Now look in the answer below we have :

+) A. -6.7 + 6.8 = 0.1 (S)

+) B. -6.7 +(-6.6) = -13.3 (NS)

+) C. 7.2 + (-7.2) = 0 (NS)

+) D. 7.2 + (-7.3) = -0.1 (NS)      ( P/s: NS : not selected , S : selected )

So A is the correct answer

Ok done. Thank to me :>

Answer:it is D

Step-by-step explanation:

Replace m with 12 and simplify.

m-8 = 12-8 = 4

Answer:

63

Step-by-step explanation:

60% of $100 is just %60 and 5% of 60 is 3 so, 60 + 3 = $63

Answer:

$45

Step-by-step explanation:

So, first we would find 60% of the $100

100 x .60 = 60

(When finding the amount of a percentage we move the decimal over twice)

then subtract what we got from the original price to find what he paid before tax:

100 - 60 = 40

Now we find 5% of $100:

100 x .05 = 5

Finally, we add this to what he was paying before taxes:

40 + 5 = 45, so $45

Hope this helps!! :)

Answer:

1. 1.25 or 1 1/4

2. 4.8 or 4 4/5

3. 15 and 5

4.D

5. 1 1/4

Answer:

1. 1.25 or 1 1/4

2. 4.8 or 4 4/5

3. 15 and 5

4.D

5. 1 1/4

Step-by-step explanation:

I am pretty sure this is it!

Answer:

16 cubic units

Step-by-step explanation:

\(\displaystyle V=\int^b_aA(x)\,dx\\\\V=\int^6_2(\sqrt{x})^2\,dx\\\\V=\int^6_2x\,dx\\\\V=\frac{1}{2}x^2\biggr|^6_2\\\\V=\frac{1}{2}(6)^2-\frac{1}{2}(2)^2\\\\V=\frac{1}{2}(36)-\frac{1}{2}(4)\\\\V=18-2\\\\V=16\)

A(x) represents the area of the cross-section, so in this case, we square \(\sqrt{x}-0\) which is just \(\sqrt{x}\)

Answer:

Step-by-step explanation:

Area of the rectangle = (3x + 7)(2x- 2)

                                     = 3x(2x - 2) + 7*(2x - 2)

                                     = 3x*2x - 3x*2   +7*2x  - 7*2

                                     = 6x² - 6x + 14x - 14

                                      = 6x² + 8x - 14

Answer:

110 cm²

Step-by-step explanation:

17 · 8

136 cm²

4 · 1.5

6 cm²

5 · 4

20 cm²

20 cm² + 6 cm²

26 cm²

136 cm² - 26 cm²

110 cm²

F'(8) = 450 and G²(8) = 202,500.

To find F'(8) and G²(8), we need to apply the chain rule and use the given information about f(x). Let's start with F(x) = f(f(z)). Since F(x) is composed of nested functions, we can use the chain rule to find its derivative. Applying the chain rule, we have:

F'(x) = f'(f(z)) * f'(z)

Now, we need to find F'(8). From the information given, f'(8) = 15. To find f'(z), we can use f'(5) = 5, since f(5) = 3. Using the chain rule, we can calculate f'(z) as follows:

f'(z) = f'(5) * f'(z)

      = 5 * f'(z)

Since f'(8) = 15, we can substitute these values into the equation for F'(x) to find F'(8):

F'(8) = f'(f(z)) * f'(z)

     = f'(f(8)) * f'(8)

     = f'(3) * 15

     = 5 * 15

     = 75

Thus, F'(8) = 75.

Next, we need to find G²(8). Given that G(x) = F²(x), we can express G²(8) as (F²(8)). Using the chain rule, we can calculate (F²(x))' as follows:

(F²(x))' = 2 * F(x) * F'(x)

Substituting F(x) = f(f(z)) and F'(x) = F'(8) = 75, we can find (F²(8))':

(F²(8))' = 2 * F(8) * F'(8)

        = 2 * f(f(8)) * F'(8)

To find f(f(8)), we can substitute f(8) = -5 into f(x):

f(f(8)) = f(-5)

       = 5(-5)²(1-4(-5))³

       = 5 * 25 * 9

       = 1125

Plugging in the values, we can calculate (F²(8))':

(F²(8))' = 2 * 1125 * 75

        = 2250 * 75

        = 168,750

Finally, to find G²(8), we square (F²(8))':

G²(8) = (F²(8))'²

      = 168,750²

      = 202,500

Therefore, G²(8) = 202,500.

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I'm confused what's being asked here...but if you're looking for someone to check it then:

The line of best fit is drawn correctly; there are about the same amount of dots on the top and bottom of the line.

And the correlation is positive

Given:

The bases of a trapezoid lie on the lines

\(y=2x+7\)

\(y=2x-5\)

To find:

The equation that contains the midsegment of the trapezoid.

Solution:

The slope intercept form of a line is

\(y=mx+b\)

Where, m is slope and b is y-intercept.

On comparing \(y=2x+7\) with slope intercept form, we get

\(m_1=2,b_1=7\)

On comparing \(y=2x-5\) with slope intercept form, we get

\(m_2=2,b_2=-5\)

The slope of parallel lines are equal and midsegment of a trapezoid is parallel to the bases. So, the slope of the bases line and the midsegment line are equal.

\(m=m_1=m_2=2\)

The y-intercept of one base is 7 and y-intercept of second base is -5. The y-intercept of the midsegment is equal to the average of y-intersects of the bases.

\(b=\dfrac{b_1+b_2}{2}\)

\(b=\dfrac{7-5}{2}\)

\(b=\dfrac{2}{2}\)

\(b=1\)

So, the y-intercept of the required line is 1.

Putting m=2 and b=1 in slope intercept form, we get

\(y=2x+1\)

Therefore, the equation of line that contains the midsegment of the trapezoid is \(y=2x+1\).

Answer:

I don't see what the question is