Find the midpoint of the line segment joining the points C= (4,7) and D= (-2,-3)

Write properties of function:

x intercept/zero: t₁ = -1, multiplicity 1; t₂ = 10 , multiplicity 1

vertex form: g (t) = (t - 9/2)² - 121/4

vertex: (9/2, -121/4)

The requried,
1. Zeros fo the function G(t) = (t – 10)(t + 1) are -1 and 10.
2. Vertex of the parabola is (9/2, -121/4).

A parabola is a cross-section cut out of the cone and represented by an equation G(t) = (t – 10)(t + 1.

Given function: G(t) = (t – 10)(t + 1)

1. To find the zeros of the function, we set G(t) to 0 and solve for t:

(t – 10)(t + 1) = 0

This gives us t = 10 and t = -1. Therefore, the smaller t is -1 and the larger t is 10.

So, the zeros of the function are:

smaller t = -1

larger t = 10

2.To find the vertex of the parabola, we can rewrite the given function in vertex form:

G(t) = (t – 9/2)² - 121/4

The vertex of the parabola is given by (h, k), where h is the x-coordinate and k is the y-coordinate. Therefore, the vertex of the parabola is:

Vertex: (9/2, -121/4)

Learn more about parabola here:

brainly.com/question/4074088

#SPJ2

Answer:

12 sin 75°

Step-by-step explanation:

See the attached images!

Answer:

640; 581 R 90; 90

Step-by-step explanation:

you can round 110 to 100

64000/100 is simply 640

then you do the real math

the quotient is 581 r 90

this means the remainder is 90

Answer: 6

Step-by-step explanation:

If the lines are parallel, then this means that by the corresponding angles theorem, the two angles marked in the image are congruent.

If we consider the right triangle, then by the exterior angle theorem, [tex]4x+90=11x-8 \longrightarrow x=14[/tex].

So, if [tex]x=14[/tex], then the indicated angle measures [tex]56^{\circ}[/tex], and since vertical angles are congruent, [tex]9y+2=56 \longrightarrow \boxed{y=6}[/tex]

Answer:

[tex]37 - c = x[/tex]

Step-by-step explanation:

We'll use c to represent the amount taken away (subtracted) and x to represent the amount left (the answer).

We begin with 37 balloon, and take away c amount to make x.

37 - c = x

Answer:

See below ~

Step-by-step explanation:

a)

b)

c)

Answer:

a) 4.60 (2 dp)

b)  1.31 (2 dp)

c)  8.8

Step-by-step explanation:

The "Frequency" part of a frequency table is the measure of how often the data value occurs.

To calculate the mean of data presented in a frequency table, we need to multiply each data value by its given frequency, sum these, then divide by the sum of the frequency.

The formula for mean is:

[tex]\textsf{mean}=\overline{x}=\dfrac{\displaystyle \sum fx}{\displaystyle\sum f}[/tex]

Add a row showing the values of [tex]fx[/tex]

Add a column showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} & & & & & & & \sf Total \\\cline{1-8} x & 2 & 3 & 4 & 5 & 6 & 7 & \\\cline{1-8} \textsf{Frequency}\:f & 11 & 17 & 24 & 23 & 18 & 15 & 108\\\cline{1-8} fx & 22 & 51 & 96 & 115& 108 & 105 &497 \\\cline{1-8}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{497}{108}=4.60\:\textsf{(2 dp)}[/tex]

Add a column showing the values of [tex]fx[/tex]

Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Frequency}\: f & fx \\\cline{1-3} 0 & 35 & 0 \\\cline{1-3} 1 & 76 & 76\\\cline{1-3} 2 & 48 & 96\\\cline{1-3} 3 & 22 & 66 \\\cline{1-3} \sf Total & 181 & 238 \\\cline{1-3}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{238}{181}=1.31\:\textsf{(2 dp)}[/tex]

Add a column showing the values of [tex]fx[/tex]

Add a row showing the totals of [tex]f[/tex] and [tex]fx[/tex]

[tex]\large\begin{array}{| c | c | c |}\cline{1-3} x & \textsf{Tally}\: f & fx \\\cline{1-3} 8 & 7 & 56\\\cline{1-3} 9 & 10 & 90\\\cline{1-3} 10 & 3 & 30\\\cline{1-3} \sf Total & 20 & 176\\\cline{1-3}\end{array}[/tex]

Now use the formula to calculate the mean:

[tex]\implies \textsf{mean}=\overline{x}=\dfrac{176}{20}=8.8[/tex]

Answer:

Step-by-step explanation:

The available area is found by subtracting twice the border width from each of the overall lot dimensions. The accommodation that provides is found by dividing the area by the area required per dog.

__

The 10 foot setback from each lot line means the usable space has dimensions that are 20 feet shorter than the lot dimensions.

  usable rectangle = (120 ft -20 ft)×(80 ft -20 ft) = (100 ft)(60 ft)

  usable rectangle = 6000 ft²

There will be 6000 square feet in the smaller lot.

__

The space required for each dog is ...

  (12,500 ft²)/(50 dogs) = 250 ft²/dog

Then the number of dogs that can be accommodated in 6000 ft² is ...

  (6000 ft²)/(250 ft²/dog) = 24 dogs

The number of dogs allowed is 24.

Answer:

A and D

Step-by-step explanation:

Answer:

A and D is correct

Step-by-step explanation:

just did test on edg

The percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

The density curve is a type or way of representation of numbered distribution data over a graph. Here, the outcomes are continues. The density curve can not be below the x-axis or horizontal line of the graph.

In a density curve,

Records show that Oliver is typically 10-30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

Oliver will get a written warning if he is more than 16 minutes late for work. The time remain after the 16 minutes is,

t=30-16

t=14 min

Thus, the percentage of the time will Oliver get a written warning is,

p=(14/30)*100

p=46.7 %

Thus, the percentage of the time will Oliver get a written warning when  he is more than 16 minutes late for his shift at work is 46.7%.

Learn more about the density curve here;

https://brainly.com/question/25334760

#SPJ1

Answer:

46.7%

Step-by-step explanation:

Answer:

y = -3x - 3

Step-by-step explanation:

The line intercepts the y-axis at -3, and moves down 3 on the y for moving to the right 1 along the x-axis

Answer:

The number in the middle

Answer:

the answer is the one fully in line like perfect like pyramid

Step-by-step explanation:

I took the test

The measure of the unknown angle in the full circle is calculated as: 310 degrees.

The angle measure of a full circle equals 360 degrees.

The full circle given is divided into two angles, of which 50 degrees is a measure of one of the angles.

The unknown angle = 360 - 50 = 310 degrees.

Learn more about a full circle on:

https://brainly.com/question/16724928

#SPJ1

Answer:

6 visits

Step-by-step explanation:

Here the involved variables should be :

⇒ y = total number of rewards points

⇒ x = number of visits to the movie theater

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

Given :

⇒ points earned on signing up = 60

⇒ points per visit = 9.5

⇒ total points required = 117

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

Making the equation :

⇒ y = mx + b

⇒ m = points earned per visit

⇒ b = points earned on signing up

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

Solving by substitution :

⇒ 117 = 9.5x + 60

⇒ 9.5x = 117 - 60

⇒ 9.5x = 57

⇒ x = 6 visits

If Latanya receives 60 rewards points just for signing up. She earns 9.5 points for each visit to the movie theater. She needs 117 points for a free movie ticket. Then 6 visits Latanya make to earn a free ticket.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that,

Latanya has 60 rewards points just for signing up.

For each visit to theatre she earns 9.5 points.

To get free ticket she has to have 117 points.

We need to find how many visits she has to do to get free ticket.

We use Linear equation to solve this

Let y = total number of rewards points

x = number of visits to the movie theater

m=Points for each visit

y=mx+b

117=9.5x+60

Subtract 60 on both sides

117-60=9.5x

57=9.5x

x=6

Hence she has to make 6 visits to earn a free ticket.

To learn more on slope intercept form click:

https://brainly.com/question/9682526

#SPJ2

Answer:

56

Step-by-step explanation:

To find the area of a rectangle we have the foruma A=WxL.

But we already have the area and length so we can plug that in

5488=Wx98

Now its an algebreic expression.

SInce its multiplying we do the opposite, so we divide 98 on both sides.

98/98 crosses itself out so now its 5488/98. Which equals 56. So now our expression is W=56. To fact check we put the numbers 56 and 98 into the formula to see if we get 5488.

A=56x98

A=5488

Answer:

Hello, please send me which of these 3 numbers is the base or height. You can also just send me an image of this. I need this because the area can change based on which value is which. However, I will still tell you how to solve the problem.

The equation for finding the area of a trapezoid is A=((a+b)/2)*h. Now, you just have to plug in your values that were given to you.

Answer:

Step-by-step explanation:

Speed is the ratio of distance to time. Speeds can be compared by comparing the times for the same distance, or by comparing the distances for the same time. A faster speed means more distance is covered in less time.

__

Here, we observe that 68 feet is a multiple of 34 feet, so it is easiest to compare the speeds of the insects by comparing their times for the same distance.

  butterfly: 68 ft in 5 seconds

  dragonfly: 2×34 ft in 2×3 seconds, or 68 ft in 6 seconds

The butterfly covers the same distance in less time, so it can fly faster.

__

Since our comparison of speeds is made using travel times, we can say the answer to "how much faster" is "1 second less over a distance of 68 feet."

_____

Additional comment

You may be expected to figure the speeds in units of feet per second. You do that by dividing feet by seconds.

  butterfly: 68 ft/(5 s) = 13.6 ft/s

  dragonfly: 34 ft/(3 s) = 11 1/3 ft/s

The difference in speeds is ...

  (13 3/5) -(11 1/3) = 2 4/15 . . . ft/s

The butterfly's speed is 2 4/15 ft/s faster than the dragonfly's speed.

__

You see time comparisons in human foot races, often with differences measured in milliseconds. Almost never are speeds compared in terms of feet (or meters) per second.

-7+(n-1)6

-7 is the starting term

n is the term that you are looking for

6 is the common difference

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

It is a sequence where the difference between each consecutive term is the same.

We have,

We are given the first four terms of an arithmetic sequence:

a₁ = -7, a₂ = -1, a₃ = 5, a₄ = 11

To find the formula for the nth term, we need to find the common difference (d) first.

We can do this by subtracting any two consecutive terms:

d = a₂ - a₁ = (-1) - (-7) = 6

Now we can use the formula for the nth term of an arithmetic sequence:

a(n) = a₁ + (n - 1)d

Substituting the values we found:

a(n) = (-7) + (n - 1)(6)

Simplifying:

a(n) = -7 + 6n - 6

a(n) = 6n - 13

Therefore,

The formula for the nth term in the arithmetic sequence is:

a(n) = 6n - 13

Learn more about arithmetic sequence here:

https://brainly.com/question/10396151

#SPJ7

Answer:

t^v=w

Step-by-step explanation:

if y=b^x then x=logbY

b= base

for example:

log2(8)=3

2^3=8

Answer:

12n + 16

Step-by-step explanation:

2 (6n + 8)

= (2*6n) + (2*8) [distributive property]

= 12n + 16

Hope it helps ⚜

Answer:

12n + 16

Step-by-step explanation:

Distributive Property

Distributing the terms

Answer:

$5,505

Step-by-step explanation:

Compound interest formula :

Solving after substituting the given values :

Answer:

y = 2x - 1

Step-by-step explanation:

Given equation:

y = 2(x + 1)

y = 2x + 2

slope = 2

y = mx + b

y = 2x + b

Point: (2/3, 1/3)

1/3 = 2(2/3) + b

1/3 = 4/3 + b

b = -3/3

b = -1

y = 2x - 1

Step-by-step explanation:

estimation of 6$+_+_?_!(_

Answer:

b = 13√3

c = 26

Step-by-step explanation:

tan 30  = a /b

b = a/ tan 30 = 13 / (1/√3) = 13√3

sin 30 = a /c

c = a/ sin 30 = 13 / (1/2) = 13 * 2 = 26

Answer:

if a = 13 than..

c = 26

b = 13√3

Step-by-step explanation:

Answer:

A. 9.9%

Step-by-step explanation:

[tex] {e}^{14r} = 4[/tex]

[tex] ln(4) = 14r[/tex]

[tex]r = \frac{ ln(4) }{14} = .099 = 9.9\%[/tex]

Answer:

60 miles per hour.

Step-by-step explanation:

speed = distance / time

= 750 / 12.5

= 60 miles per hour.

Answer:

So our unknown width is X and the unknown length is X + 3.  We know the perimeter is 2 times the length plus 2 times the width so let's set up that equation:

2 X + 2 (X+3) = 24

Now solve for X

2 X + 2 X + 6 = 24

4 X + 6 = 24

4 X = 18

X = 4.5 - this is the width

X + 3 = 4.5 + 3 = 7.5 - this is the length

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

the codomain are the values of f(x) from the y- coordinate of the vertex upwards.

given a quadratic in standard form

y = ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{V}[/tex] = - [tex]\frac{b}{2a}[/tex]

f(x) = 2x² + 4x - 1 ← is in standard form

with a = 2 and b = 4 , then

[tex]x_{V}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1

substitute x = - 1 into f(x) for y- coordinate of vertex

f(- 1) = 2(- 1)² + 4(- 1) - 1 = 2 - 4 - 1 = - 3

vertex = (- 1, - 3 )

since the coefficient of the x² term > 0 then the graph opens up U

then codomain is [ - 3, ∞ )