Which equation represents a line that passes through (2, –left-parenthesis 2, negative StartFraction one-half EndFraction right-parenthesis.) and has a slope of 3?

Answer:

f(x)= (6/x+5)+4

Step-by-step explanation:

y/x translated 5 units

y/x+5 then 4 units up y/(x+5) +4

Answer:

{2, 4}.

Step-by-step explanation:

A = {1, 2, 3, 4, 5} and B = {2, 4}.

A ∩ B?

This means intersection or what is in common

A ∩ B =  {2, 4}.

Answer:

a(75) = 793

Step-by-step explanation:

Arithmetic Explicit Formula: an = a1 + (n-1)d

Step 1: Find equation

d = (1-(-10)) = 11

a1 = -21

an = -21 + 11(n-1)

Step 2: Plug in 75 as n

a(75) = -21 + 11(75-1)

a(75) = 793

And we have our final answer!

Answer:

Option C

Step-by-step explanation:

Consider the function f ( x ) = 3x^2 + 4;

[tex]f ( x ) = 3x^2 + 4,\\\\4 = vertex ( y - intercept ),\\\\\\[/tex]

Now if this graph were to be translated 7 units down, considering the function was f ( x ) = 3x^2, the new graph would be f ( x ) = 3x^2 - 7. The same concept is applied to the graph f ( x ) = 3x^2 + 4;

[tex]4 - 7 = - 3,\\f ( x ) = 3x^2 - 3\\\\Solution - Option C[/tex]

* Note that a translation doesn't effect the rate with which the graph changes, it only effect's it's position on the coordinate plane

Hope that helps!

Answer:

V = 11/21

Step-by-step explanation:

Formula: V = 4/3πr³

Simply plug in r to find volume

V = 4/3π(1/2)³

V = 0.52381

And we have our answer!

Answer:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Step-by-step explanation:

There are an even number of negative factors, so the product is positive:

  Positive, because the products (–5)(–3) and (–8)(–6) are positive, and the product of two positive numbers is positive

Answer:

x= 42

Step-by-step explanation:

(2x +1)°= 85° (vert. opp. ∠s)

2x +1= 85

2x= 85 -1 (bring constant to 1 side)

2x= 84 (simplify)

x= 84 ÷2

x= 42

Answer:

1

Step-by-step explanation:

The slope is given by

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

   = (1 - -1)/(0- -2)

   = (1+1)/(0+2)

   2/2

   =1

Answer:

1

Step-by-step explanation:

by using rise over run

Answer:

Rectangle.

Step-by-step explanation:

The 2 dimensional section would be a rectangle.

Answer:

rectangle

Step-by-step explanation:

Step-by-step explanation:

Overtime rate= r+50%= 1.5r

Regular hours= 800/r

Overtime hours= 240/1.5r

Total hours worked

Answer:

the coordinates of y are (1,-4)

Step-by-step explanation:

by using midpoint formula

z(x,y)=([tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])

putting the values of coordinates

(3,-1)=[tex]\frac{5+a}{2}[/tex],[tex]\frac{2+b}{2}[/tex]

separating the coordinates

3=[tex]\frac{5+a}{2}[/tex]                and           -1=[tex]\frac{2+b}{2}[/tex]

3×2=5+a                and      -1×2=2+b

6=5+a                  and        -2=2+b

6-5=a                    and          -2-2=b

1=a                            and            -4=b

so the actual coordinates of y are (1,-4)

i hope it will help you

Answer:

⅑

Step-by-step explanation:

Let m represents number of males, and f represents number of females taking the maths course.

Given that number of males (m) taking the maths course is 8 times as much as number of females (f), total number of students taking the maths course (T).

Thus we can represent the information above with the following:

m = no. of males

f = no. of females

T = Total

m = 8f

T = m + f

Thus,

Total = 8f + f = 9f

==>The fraction of the course that are females = No. of females (f) ÷ Total no. of students (T)

= f/9f

Fraction of females in simplified form would be ⅑

Answer:

  y = -1/3x +3

Step-by-step explanation:

When given a point and slope, it is convenient to start with a point-slope form of the equation of a line.

  y = m(x -h) +k . . . . . line with slope m through point (h, k)

  y = (-1/3)(x -3) +2 . . . line with slope -1/3 through point (3, 2)

  y = -1/3x +3 . . . . . . . simplified to slope-intercept form

Answer:

11 is the answer

Step-by-step explanation: i hope so cuz my calculations gives this answer

Answer:

y=84

first : 84+13=97

second : 84+15=99

third : 84+23=107

fourth: 84+29=113

fifth : 84+40 =124

97+99+107+113+124 = 540

Step-by-step explanation:

sum of interior angles of a pentagon=540 degreas

y+13+y+15+y+23+y+29+y+40=540

5y=540-(13+15+23+29+40)

y=84

first : 84+13=97

second : 84+15=99

third : 84+23=107

fourth: 84+29=113

fifth : 84+40 =124

97+99+107+113+124 = 540

Answer:

C

Step-by-step explanation:

Got 100% on edge.

Answer:

125 cm³

Step-by-step explanation:

The volume (V) of a cube = s³ ( s is the length of the sides )

Since the shape is a cube then all sides are congruent, thus

V = 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³

Answer:

v=l×w×h 5×5×5=125cubedcm

Step-by-step explanation:

you see a cube has an equal length, width and height

Answer:

u^2 +7u -8=0  where u = 3x+2

Step-by-step explanation:

(3x+2)^2 + 7(3x+2) - 8=0

Let 3x+2 = u

u^2 +7u -8=0

Answer:

  a) h(t) = -16t^2 +41t +37

  b) see attached (3.270 seconds)

  c) (41+√4049)/32 seconds

  d) 1.28125 seconds; 63.265625 feet

  e) [1.5, 2]: -15; [2, 2.5]: -31; [2.5, 3]: -47

Step-by-step explanation:

a) The formula and initial values are given. Putting those values into the formula, we get ...

  h(t) = -16t^2 +41t +37

__

b) The graph is attached. It shows the t-intercept to be about 3.270 seconds.

__

c) Using the quadratic formula, we can find the landing time as ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-41\pm\sqrt{41^2-4(-16)(37)}}{2(-16)}\\\\=\dfrac{41\pm\sqrt{4049}}{32}\qquad\text{only $t>0$ is useful}[/tex]

The exact landing time is (41+√4049)/32 seconds.

__

d) The highest point is at t=-b/(2a) = -41/(2(-16)) = 41/32 seconds.

The value of the function at that point is ...

  h(41/32) = (-16(41/32) +41)(41/32) +37 = 41^2/64 +37 = 4049/64

The maximum height is 4049/64 = 63.265625 feet.

__

e) For a quadratic function, that average rate of change on an interval is the derivative at the midpoint of the interval. Here, the derivative is ...

  h'(t) = -32t +41 . . . in feet per second

Then the average rates of change are ...

  arc[1.5, 2] = h'(1.75) = -32·1.75 +41 = -15 ft/s

  arc[2, 2.5] = h'(2.25) = -32(2.25) +41 = -31 ft/s

  arc[2.5, 3] = h'(2.75) = -32(2.75) +41 = -47 ft/s

These are the average velocity of the water balloon over the given interval(s) in ft/s. Negative indicates downward.

Answer:

(a) h(t) = -16t² + 41t + 37

(b) About 3.3 s

[tex]\large \boxed{\text{(c) }\dfrac{41+ \sqrt{4049}}{32}\text{ s}}[/tex]

(d) -15 ft/s; -31 ft/s; -47 ft/s

Step-by-step explanation:

(a) The function

h(t) = -16t² + v₀t + s₀

 v₀ = 41 ft·s⁻¹

 s₀ = 37 ft

The function is

h(t) = -16t² + 41t + 37

(b) The graph

See Fig. 1.

It looks like the water balloon lands after about 3.3 s.

(c) Time of landing

h = -16t² + 41t + 37

a = -16; b = 41; c = 37

We can use the quadratic formula to solve the equation:

[tex]h = \dfrac{-b\pm\sqrt{b^2 - 4ac}}{2a} = \dfrac{-b\pm\sqrt{D}}{2a}[/tex]

(i) Evaluate the discriminant D

D = b² - 4ac = 41² - 4(-16) × 37 = 1681 + 2368  = 4049

(ii) Solve for t

[tex]\begin{array}{rcl}h& = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-41\pm\sqrt{4049}}{2(-16)}\\\\ & = & \dfrac{41\pm\sqrt{4049}}{32}\\\\t = \dfrac{41- \sqrt{4049}}{32}&\qquad& t = \dfrac{41+ \sqrt{4049}}{32}\\\\\end{array}\\[/tex]

[tex]\text{The water balloon will land after $\large \boxed{\mathbf{\dfrac{41+ \sqrt{4049}}{32}}\textbf{ s}} $}[/tex]

(d) Time and maximum height

(i) Time

The axis of symmetry (time of maximum height) is at t = -b/(2a)

[tex]t = \dfrac{-41}{2(-16)} = \dfrac{41}{32} = \textbf{1.281 s}[/tex]

(ii) Maximum height

The vertex is at y = h(1.281) = h(t) = -16(1.281)² + 41(1.281) + 37  = 63.27 ft

(e) Average rate of change

(i) Arc{1.5,2}

h(1.5) = 62.5

  h(2) = 55

m = (h₂ - h₁)/(t₂ - t₁) = (55 - 62.5)/(2 - 1.5) = -7.5/0.5 = -15 ft/s

The water balloon has started to fall after it has reached peak height, so it is not going very fast

(ii) Arc{2,2.5}

h(2.5) =39.5

m = (39.5 - 55)/(2 - 1.5) = -15.5/0.5 = -31 ft/s

The balloon is in mid-fall, so gravity has caused it to speed up.

(iii) Arc{2.5,3}

h(3) = 16

m = (16 - 39.5)/(2 - 1.5) = -23.5/0.5 = -47 ft/s

The balloon is about to hit the ground, so it is falling at almost its maximum velocity.

Fig. 2 shows the height of the balloon at the above times.

Answer:Land area: 302.6 mi²

Population: 8.399 million

Step-by-step explanation:

New York City can be described as very big and it has actually been ranked as the 24th biggest city in the United States in terms of land area it ...

Answer:

Land area: 783.8 km²

Population: 8.399 million

Step-by-step explanation:

Step-by-step explanation:

29-12 is a 17 difference

52-29 is a 23 difference (adding 6 to the number 17)

81-52 is a 29 difference (adding 6 to the number 23)

116-81 is a 35 difference (adding 6 to the number 29)

Answer:

29-12 is a 17 difference

52-29 is a 23 difference (adding 6 to the number 17)

81-52 is a 29 difference (adding 6 to the number 23)

116-81 is a 35 difference (adding 6 to the number 29)

Step-by-step explanation:

Answer:

Z=+6

Step-by-step explanation:

Z^5=-7776i

Let's note that i I mathematics means negative one i.e

i = -1

So the equation is equal to

Z^5=-*-(7776)

Z^5 = 7776

Z= 5√7776

Since it's a divisible by 6

It's giving us a clue that 6 it's the answer.

Ok let's check the 5th root of 7776 in our calculator.

Z=+6

+6 is the solution to the equation

Z^5=-7776i

[tex]AB=8.391[/tex]

[tex]AC=13.05407[/tex]

Answer:

AB =8.4

AC = 13.1

Step-by-step explanation:

Use SOH CAH TOA, which means Sin= Opposite/Hypotenuse, Cosine= Adjacent/Hypotenuse, and Tangent= Opposite/Hypotenuse.

AB is the opposite compared to the angle, BC is the adjacent compared to the angle, and AC is the hypotenuse.

Write down what you know in the formulas:

theta = 40 degrees

BC = adjacent = 10

Plug them in to solve what you need:

AB is opposite, so use the tangent equation:

tangent (40 degrees) = AB / 10

AB =8.4

AC is the hypotenuse, so use the cosine equation:

cosine (40 degrees) = 10 / AC

AC = 13.1

Answer:

x = 14

Step-by-step explanation:

Tan 25 = [tex]\frac{opposite}{adjacent}[/tex]

Where opposite = x, Adjacent = 30 m

=> 0.466 x 30 = x

=> x = 14

Answer:

[tex]\Huge \boxed{\mathrm{14 \ meters}}[/tex]

Step-by-step explanation:

We can use trigonometric functions to solve for the problem.

[tex]\displaystyle \sf tan( \theta )=\frac{opposite \ side}{adjacent \ side}[/tex]

Plug in the values and evaluate.

[tex]\displaystyle \sf tan( 25\° )=\frac{x}{30}[/tex]

Multiply both sides by 30.

[tex]\displaystyle \sf 30 \cdot tan( 25\° )=x[/tex]

[tex]\sf x=13.98922974...[/tex]

The height of the traffic light is 14 meters (rounded to nearest whole number).

Answer:

7

Step-by-step explanation:

We want to evaluate the fraction below for x = 3. We will put the value of x to be 3:

[tex]\dfrac{7^2}{x^2-2}\\\\= \dfrac{7^2}{3^2-2}\\\\= \dfrac{49}{9-2}\\\\= \dfrac{49}{7} = 7[/tex]

The answer is 7.

Answer:

Step-by-step explanation:

goodluck khan academy users

Answer:

a = -3

Step-by-step explanation:

5^a = 1/125

The fraction 1/125 can be written as a power with base 5.

5^a = 5^(-3)

Cancel the same bases on both sides.

a = -3

Answer:

a = -3.

Step-by-step explanation:

5^a = 1/125

1/125 = 1 / 5^3

= 5^-3

5^a = 5^-3

so a = -3.

Answer:

B)

1.) 7/64 (2.) 27/32 (3.)15/64 (4.)5/8 (5.)21/32

Step-by-step explanation:

Given the following :

Two 8 - sided fair die (1, 2, 3, 4, 5, 6, 7, 8)

Total sample space = 8^2 = 64

B1)

Probability = (number of required outcome / number of total possible outcomes)

probability of getting a prime number:

number of prime numbers in possibility diagram = 7

1) P(getting a prime number) = 7/64

11) P(not a perfect square)

Not a perfect square values in the diagram = 54

= 54 / 64 = 27 / 32

111) a multiple of 5:

Multiple of 5 in the diagram = 15

= 15 / 64

IV) Less than or equal to 21:

= 40/64 = 5/8

V) divisible by 4 or 6:

Numbers divisible by four or 6 = 42

= 42 / 64 = 21 / 32

Answer:

a rational number

Step-by-step explanation:

a rational number + a rational number will always be a rational number.

Answer:

2 hours

Step-by-step explanation:

Time= 5 hrs

Ashley's speed= 40 mph

Beth's speed= 60 mph

Beth's time in travel= x

Since they drove the same distance, we have this equation: