The relationship between time and the number of laps is not proportional across all swimmers. which two swimmers swam at the same rate (had time and laps in the same proportion)?

The absolute value function graphed in this problem is given as follows:

A. y = |x - 5| - 4.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

The leading coefficient a does not influence the vertex of the absolute value function.

The vertex of the graph is the turning point, hence it is given as follows:

(5, -4).

Hence, considering a leading coefficient 1, h = 5 and k = -4, the equation is given as follows:

y = |x - 5| - 4.

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A) The ball in the ground is represented by h(t)=0, that is, the height is equal to 0, the reference level.

Then, we can find for which values of t we have h(t).

We equal h(t) to 0 and calculate t as:

The ball is in the ground at time t=0 (an instant before it is kicked) and then again at time t=4, that is the value we are looking for: the ball landed again in the ground 4 seconds after kicked.

B) The maximum height can be find in two ways:

- By finding the t-value of the vertex, that in this case will be correspond to the maximum height as this is a concave down parabola with only one extreme point.

- Deriving the function and equaling to 0 and finding t.

If we apply the first method, we have:

As the vertex is at time t=2 seconds, the maximum height happens at t=2.

Answer: A) t = 4 seconds B) t = 2 seconds

NOTE for Part B:

If we derive the expression, we get:

The volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

What is the volume of the rectangular prism?
Four rectangular faces and two parallel rectangular bases make up a rectangular prism. We are aware that a rectangular prism's cross section is a rectangle. The term "Cuboid" is another name for the rectangular prism.
Therefore, the following formula is provided to determine a rectangular prism's volume: Volume = l*b*h cubic units.

Given, the length of the rectangular prism = l = x
Also, the width of the rectangular prism = w = x²
Again, the height of the rectangular prism = h = 5x² + 4x + 1
Volume of the rectangular prism = l*w*h = x*(x²)*(5x² + 4x + 1)
= x³(5x² + 4x + 1) = 5x⁵ + 4x⁴ + x³
Thus, the volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

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Answer:

ojsjsnajnbaknrkmlamsl

Answer:

144x - 24

Step-by-step explanation:

Answer:

Classification by Angles: Obtuse

Classification by Sides: Scalene

Step-by-step explanation:

    ➜ This triangle has an obtuse angle, or an angle greater than 90°, so it is an obtuse triangle. This is the classification by angles.

    ➜ This triangle's sides are all different lengths, as shown by the three different angle measurements. This means this triangle is scalene, and scalene is the classification by sides.

The line DE is parallel to line PQ and line DE is parallel to XY.

If any one line is parallel to any other line and any of one line (from two parallel line) is parallel to third line then all three line are parallel to each other.

So line PQ, line XY and line DE all three parallel to each other.

Option B is correct.

The polynomial with zeros of −3, −1, and 2, and passes through the point (3,11) is:

P(x) = (11/24)*(x + 3)*(x + 1)*(x - 2)

We know that the zeros are −3, −1, and 2, so if we define the leading coefficient as A, the polynomial can be written as:

p(x) = A*(x + 3)*(x  + 1)*(x - 2)

Now we want this to pass through the point (3, 11), then we get:

p(3) = 11 = A*(3 + 3)*(3 + 1)*(3 - 2)

         11 = A*6*4*1

         11 = A*24

         11/24 = A

Then the polynomial is:

P(x) = (11/24)*(3 + 3)*(3 + 1)*(3 - 2)

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Answer:

y = [tex]\frac{28+3x}{4}[/tex]

Step-by-step explanation:

- 3x + 4y = 28 ( add 3x to both sides )

4y = 28 + 3x ( isolate y by dividing both sides by 4 )

y = [tex]\frac{28+3x}{4}[/tex]

Given data:

The given expression is -4/9 x=3/8

The given expression can be written as,

The product is less than both the factors.

Thus, option C) is correct.

Answer:

245

Step-by-step explanation:

6 - 42

35 - x

cross multiply

6x = 35 × 42

6x = 1470

x = 1470 ÷ 6

x = 245

Answer: 31

Step-by-step explanation:

The numbers are increasing by 1, then 2, then 3, ...

In other words, the second difference is 1.

So, the next number is likely [tex]24+7=31[/tex].

Step-by-step explanation:

The total number of cars=24

Number of black cars=12

Divide 12 by 24,multiplied by 100%

12÷24 ×100=50%

Therefore, 50% of the cars are black

a) the maximum error in surface area  and  the relative error  is 25.4 cm² and 1.25%

b) the maximum error in the volume and  the the relative error  is 162.1 cm³ and 1.875%

As we know  the  formula for surface area is

                                    Surface Area , S= 4*π*r^2.

So  differentiating both sides we get

                                     dS/dr = 8*π*r .....1

and  the  formula for  the circumference is :2*π*r

, so the error on the circumference will be respect to radius

=> Δc = 2*π*Δr  

=> Δr = ΔC / (2*π)

substituing the value ofΔr in  the equation 1, we get

The maximum error in surface area which is :

ΔS = 8*π*r*Δr = 4*r*Δc

      = (2/π)*c*Δc.

    = 25.4

where for the relative error

                 ΔS/S = 4*r*Δc/(4*π*r^2)

                          = Δc/(π*r)

                          = 2*Δc/c

                        = 1.25%

Now Since  the formula for  the volume of a sphere  is :

                                       V = 4/3*π*r^3

dofferentiating both sides we get ,

                           => dV/dr = 4*π*r^2.

So,  the   the maximum error in the calculated volume  will be :

ΔV = 4*π*r^2*Δr

       = 2*r^2*Δc

       = 1/(2*π^2)*c^2*Δc

      =162.1

Where as the relative error for the volume will be

ΔV/V = 3*Δr / r = 3*ΔC/C = 1.875%

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Answer:

Step-by-step explanation:

The perimeter of the triangle is 46.4 and the length of a triangle's boundary taken as a whole is referred to as its perimeter.

Calculate the perimeter of a triangle:

Perimeter of a triangle = a +b + c

Therefore, the triangle's perimeter is 46.4, and the whole length of a triangle's boundary is referred to as the triangle's perimeter.

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Answer:

2x - 5y

Step-by-step explanation:

Hello!

We can distribute the value outside the parenthesis to the terms inside to simplify the expression.

The simplified expression is 2x - 5y.

Answer:

Step-by-step explanation:

The time interval of interest is 6 hours

There is an average of 18 trains per 24 hours or 18/(24/6)=49/12 trains per 6 hours.

The probability can be found using the Poisson distribution with parameter

λ=49/12

The percentage of red pins in total pins ordered by Eric is 30%.

According to the question,

We have the following information:

Eric received 70 pins in all.

21 of the pins are red.

Now, we will find the percentage of red pins:

Percentage of red pins = (Number of red pins*100/total number of pins)

Percentage of red pins = (21*100)/70

Percentage of red pins = 2100/70

Percentage of red pins = 30%

(In the same way, we can also find the number and percentage of yellow pins from the total pins.)

Hence, the percentage of red pins in total pins ordered by Eric is 30%.

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if we replace y for -3 in the given equation and then we despejate x, we wiil going to have a values for the ordered pair that satisfy the equation:

then

the ordered pair woul be (4,-3)

The equation of the line is g(x) = -1/4x + 9.

Given,

g(0) = 9

g(8) = 7

Here,

We can consider this as points:

(x₁, y₁) = (0, 9)

(x₂, y₂) = (8, 7)

Now lets find the slope of the line.

Slope, m = (y₂ - y₁) / (x₂ - x₁)

Slope, m = (7 - 9) / (8 - 0)

Slope, m = -2/8

Slope, m = -1/4

Now, the slope-intercept form:

y = mx + b

here,

9 = -1/4 × 0 + b

9 = b

Now,

equation of line,

y = -1/4x + 9

That is,

g(x) = -1/4x + 9

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Answer:

Step-by-step explanation:

Given a transversal crossing parallel lines and supplementary angles (x+8°) and (2x-5°), you want to find the measures of angles L and O, supplementary to each of these.

Where a transversal crosses parallel lines, consecutive interior angles are supplementary. Using the given expressions, this means ...

  (x +8°) +(2x -5°) = 180°

  3x +3° = 180° . . . . . . . . . simplify

  x +1° = 60° . . . . . . . divide by 3

  x = 59°  . . . . . . subtract 1°

Then the acute angle is ...

  x+8° = 59° +8° = 67°

and the obtuse angle is ...

  2x -5° = 2(59°) -5° = 113°

Angle L corresponds to angle (2x-5°), so is congruent:

  ∠L = 113°

Angle O is an alternate interior angle with respect to angle (x+8°), so is congruent:

  ∠O = 67°

Answer: (-1, 4)

Step-by-step explanation: y=-2x+2, y=-4x Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer this question using SUBSTITUTION:

Substitution is a method to solving a system of equations through substituting one of the variables for another equation.

y + 2x = 2

y + 4x =0 (rewrite this equation so y is isolated: y =4x)

Since y=4x you can substitute the y in y +2x =2 and solve for x:

4x + 2x =2

6x = 2

x = [tex]\frac{1}{3}[/tex]

Now, plug in x into y =4x:

y = 4 ([tex]\frac{1}{3}[/tex]) = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]

x= [tex]\frac{1}{3}[/tex]

y = [tex]\frac{4}{3}[/tex] or [tex]1\frac{1}{3}[/tex]

Answer:

0.321    repeating 1

Step-by-step explanation:

Given the expression:

using the distributive property we get the following:

therefore, the simplified expression is 0

This can be solved using the properties of a parallelogram.

What is a parallelogram?

A parallelogram is a basic (non-self-intersecting) quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. The congruence of opposing sides and angles is a direct result of the Euclidean parallel postulate, and neither condition can be established without resorting to the Euclidean parallel postulate or one of its equivalent formulations. A quadrilateral having just one set of parallel sides is known as a trapezoid in American English or a trapezium in British English. A parallelepiped is a parallelogram's three-dimensional counterpart.

1. If ABCD is a parallelogram, then

(A) Opposite sides of the parallelogram are congruent

2. In a parallelogram opposite sides are equal, so

 6x = 4x + 19

or, 6x - 4x = 19

or, 2x = 19

or, x = 19/2 = 9.5

Hence, x =

(C) 9.5

3. CD = 6x9.5 = 57 units

(D) 57

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Answer:

1655.64 miles

Step-by-step explanation:

because 108 people times 15.33 miles for all the total people would be 1655.64 miles

Answer:

y=8X

Explanation:

The ratio 13 to X = 13:X

The ratio 104 to y = 104:y

If they are equivalent, we have that:

We write the ratios in fraction form.

We then make y the subject of the equation.

We can simplify further to get:

This is the equation that represents y in terms of X.

Answer:

a. 57 m

Step-by-step explanation:

The figure is not shown here---please draw and label it. Additionally, make sure your calculator is in degree mode.

[tex] \tan(67) = \frac{134}{x} [/tex]

[tex]x \tan(67) = 134[/tex]

[tex]x = \frac{134}{ \tan(67) } = 57[/tex]