Passed through (6, -6), slope = 5

Answer:

3/8

Step-by-step explanation:

Answer:

C: 3/8

Step-by-step explanation:

edg2021

There are a total of 16 outcomes, and 6 of them have equal heads and tails. Simplify and its 3/8

We have the following coordinates given:

And we want to find US so we can use the following formula:

And using this formula we got:

And after solve we got:

and rounded to the nearest cent would be Us= 27.46

Answer: It is undefined

Step-by-step explanation:

Hope this helps-just had a test on this!

The rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.

The given formula for the amount of bacteria present in a medium after t hours is:

\(a(t) = 16e^ (0.32t)\)

Now, we need to find out at what rate the amount of bacteria is changing after 12 hours.

This means we need to find out the derivative of a(t) with respect to t and then substitute t = 12 in the derivative formula to get the rate of change of bacteria after 12 hours.

Differentiating the given formula for a(t) with respect to t, we get:

a'(t) = \(16(0.32)e^(0.32t)\)

On substituting, t = 12, we get

a'(12) = \(16(0.32)e^ (0.32X12)\)

On solving this, we get a'(12) = 21.698.

Therefore, the rate at which the amount of bacteria is changing after 12 hours is 21.698 units/hour.

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From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.

From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

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The true statements about the arcs and angles in circle C are:

In Geometry, the sum of the measures of the interior angles in a quadrilateral is equal to 360°. Thus, we have:

m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

60 + 90 + m∠DCE + 90 = 360

240 + m∠DCE = 360

m∠DCE = 360 - 240

m∠DCE = 120°.

Since ∠DFE is an inscribed angle that is subtended by arc DE, we have:

m∠DFE =  m∠DCE

m∠DFE =  120

m∠DFE = 1/2 × 120

m∠DFE = 60°.

Therefore, ∠EFD ≅ ∠EGD.

From circle C, we can deduce that side ED is subtended by arc ED and side FD is subtended by arc FD (side ED ≅ side FD). Thus, arc ED ≅ arc FD and m arc FD is equal to 120°.

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Answer:

A C E

took quiz

Answer:

it cannot be determined not enough info

Answer:

The four consecutive odd numbers are \(7,9,11,13\)

Step-by-step explanation:

Let the four consecutive odd integers be \(x,x+2,x+4,x+6\)

The sum of the first two and the greatest of 4 consecutive odd integers is 29.

\(x+x+2+x+6=29\\3x+8=29\\3x=29-8\\3x=21\\x=7\)

Therefore,

\(x=7\\x+2=7+2=9\\x+4=7+4=11\\x+6=7+6=13\)

The four consecutive odd numbers are \(7,9,11,13\)

Base e used in exponential functions because base e is the base rate of growth shared by all continually growing processes which lets us take a simple growth rate.

In an exponential function, the base b is a constant. The exponent x is the independent variable in which the domain is the set of real numbers. There are two types of exponential functions, those are exponential growth and exponential decay. In the function f (x) = b^x when b > 1, the function represents exponential growth.

Base e allows us to take a simple growth rate, where all change occurs at the end of the year, and find the influence of compound, continuous growth, where every nanosecond or faster, we are growing slightly.

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The equation is true when putting parentheses. The equation becomes:

(5 - 3)(-1 + 6)² = 50.

What is an equation?

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

The given equation is 5 - 3 - 1 + 6² = 50.

Here we need two parentheses.

Since 50 can be written as 50 = 25 × 2 = 5² × 2

Now 2 can be written as (5-3) and 5 can be written as (-1+6).

Now put the parentheses:

(5 - 3)(- 1 + 6)²

= 50

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Answer:

its b

Step-by-step explanation:

Answer:

V = 12,348·π

Step-by-step explanation:

The given parameters of the glass Vase are;

The shape of the glass vase = A sphere

The radius of the vase, r = 21 inches

The given formula for finding the volume of a sphere is \(V = \dfrac{4}{3} \cdot \pi \cdot r^3\)

Therefore, when r = 21 inches, we get;

\(V = \dfrac{4}{3} \cdot \pi \cdot 21^3 = {12,348 \cdot \pi}\)

Therefore, the expression for finding the equation of the spherical glass vase, V = 12,348·π

Answer:

93/5

Step-by-step explanation:

(0, 3) and (5, 96)

m= (y2-y1)/(x2-x1)

m= (96-3)/(5-0)

m= 93/5

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

x2 + x - 20.

Step-by-step explanation:

(x-4)(x+5) = x^2-4x+5x-20 = x^2+x-20 = x^2 + x - 20.

Hope This Helped

\(\mathbb{PROBLEM :}\)

\( \tt \: 6. Multiply: ( \times - 4)(x + 5)\)

==========================================

\(\mathbb{ANSWER:}\)

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \underline \color{green}{x2 + x - 20}\)

==========================================

\(\mathbb{SOLUTION:}\)

\( \: \: \: \: \: \: \: \: \tt( \times - 4)( \times + 5)\)

\( \: \: \: \: \: \: \: \: \tt = \: x(x + 5) -4(x + 5)\)

\( \: \: \: \: \: \: \: \: \tt{ = \times 2 + 5 \times 4 \times - 20}\)

\( \: \: \: \: \: \: \: \: \tt{= x2 + x - 20}\)

\( \tt \: So \: possible \: Answer \: is : \underline \green{ \times 2 + \times - 20}\)

==========================================

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︎ CarryOnLearning ૮₍˶ᵔ ᵕ ᵔ˶₎ა

︎︎└─────── °∘❁∘° ───────┘

Answer:

(33+7)-(15/3) = 35

Step-by-step explanation:

35

Step-by-step explanation:

fancy way of saying (33+7) - (15/3)

33 + 7 = 40

15 / 3 = 5

40 - 5 = 35

The length of B’C’ for the triangle A’B’C' is 7.5 cm if a dilation maps triangle ABC onto A’B’C'.

A triangle is a three-sided polygon that has three angles, three vertices, and three sides. It is a basic geometric shape that is often studied in mathematics and geometry. Triangles come in different shapes and sizes, but the sum of their interior angles always adds up to 180 degrees. Triangles can be classified based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, or obtuse.

Here,

We can use the property that the ratio of corresponding sides of similar triangles is equal to the scale factor of dilation. In this case, we have:

AC/A'C' = BC/B'C'

Substituting the given values:

24/6 = 30/B'C'

Simplifying:

4 = 30/B'C'

Multiplying both sides by B'C':

4B'C' = 30

Dividing both sides by 4:

B'C' = 7.5

Therefore, B'C' is 7.5 cm.

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Complete question:

A dilation maps triangle ABC onto triangle A’B’C if AC = 24 cm A’C =6 cm and BC= 30 cm then B’C’ equals?

Answer:

7.5

Step-by-step explanation:

19-11.5=7.5

19-7.5=11.5

it works the same way around

We want to write and solve an algebraic equation to find how many milliliters of medicine a person uses each month.

The solution is 2 ml per month.

We know that in each pen injector we have 0.75mg of active component in 0.5 mL of liquid (written as 0.75mg/0.5 mL).

So, if the person takes 4 of these in a month, then the amount of mass that you get is given by:

x = 4*0.75mg = 3mg of active component per month.

And the volume that the person takes each month is:

y = 4*0.5 mL = 2 mL

Then, answering the question, the person gets 2 mL each month.

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The ray of light will be reflected off the parabolic mirror, according to the equation (y−2)2=4(x+1).

The equation of a parabola in standard form is given by y = a(x-h)² + k, where (h, k) represents the vertex of the parabola, and "a" determines the orientation and size of the parabola.

In the given equation, (y-2)² = 4(x+1), we can see that the vertex of the parabola is at the point (-1, 2), which is obtained by shifting the standard parabolic equation horizontally by 1 unit to the left and vertically by 2 units upward.

The coefficient "4" in the given equation determines the orientation and size of the parabola. Since "4" is positive, the parabola opens to the right.

The value of "4" also determines the focal length of the parabola, which is the distance between the vertex and the focus of the parabola. In this case, the focal length is 1/4 of the coefficient, which is 1 unit.

Now, let's consider how this equation relates to the reflection of a ray of light. A parabolic mirror is designed to reflect light rays in a specific way, such that all incoming parallel rays are reflected and converge to a single point called the focus of the parabola.

This property of a parabola is used in various applications, such as telescopes, satellite dishes, and headlights of vehicles.

In the given equation, (y-2)² = 4(x+1), the equation represents the shape of the parabolic mirror. When a ray of light intersects with this parabolic mirror, it will be reflected off the mirror surface according to the law of reflection, which states that the angle of incidence is equal to the angle of reflection with respect to the normal at the point of incidence.

The parabolic shape of the mirror ensures that the reflected rays converge to the focus of the parabola, which is at the point (-1, 2) in this case.

In summary, the given equation represents a parabolic mirror with a specific shape and focal length, and it describes how a ray of light will be reflected off the mirror surface according to the law of reflection.

Understanding the properties of the parabola represented by the equation can help in analyzing the behavior of light rays and predicting the reflection pattern in practical applications involving parabolic mirrors.

Since the light is moving parallel to the x-axis, it will reflect at a right angle, meaning that the reflected ray must pass through the point (2,0).

This is the answer to the question, so the correct answer is B. (2,0).

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Soo :

1.73, 2.23, 3.46

The solution set of the given equation is x = 8.39 or x = -12.39

\( \frac{1}{4} {{(x + 2} )}^{2} = 27\)

cross product

\( {1} {{(x + 2}^{} )}^{2} = 27 \times 4\)

(x + 2²) = 108

find the square root of both sides

\( \sqrt{ ({x + 2)}^{2} } = ± \sqrt{108}\)

x + 2 = ± 10.39

So,

x = 10.39 - 2 or x = -10.39 - 2

x = 8.39 or x = -12.39

Therefore, the equation has a solution set of x = 8.39 or x = -12.39

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Answer:

5,400,300...........

5004300

........

......

....

...

..

.

The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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1) what is the slope of a line that is parallel to the x-axis?

Is a horizontal line, the slope is zero

so

m=0

2) what is the slop of a line that is perpendicular to the x-axis?

Is a vertical line

so the slope is undefined

3) what is the slope of a line that is parallel to the y-axis?

Is a vertical line

so

The slope is undefined

4) what is the slop of a line that is perpendicular to the y-axis?

Its a horizontal line

so

the slope is zero

m=​0

Part 2

To find out the slope we need two points

take the points (1,0) and (0,-3)

therefore

m=(-3-0)/(0-1)

m=-3/-1

m=3

the slope is 3

Part 3

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then theior slopes are inverse reciprocal (the product of their slopes is equal to -1)

Answer:

Okay, where's the question?

Answer:

THANK YOU?

Step-by-step explanation:

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