The tallest man in the world is about 101 inches tall. The shortest man in the world is about 29 inches tall. How much taller is the tallest man than the shortest man?

Answer:

Part A)

2nd and 5th choice.

Part B)

[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]

Step-by-step explanation:

For the given parabola, our focus is (-3, 2), and our directrix is given by y = 4.

Part A)

We are given a point (x, y) on the parabola.

Since our directrix is an equation of y, the distance from (x, y) to the directrix will simply be the absolute value of the difference in y-values. So:

[tex]d_1=|y-4|=|4-y|[/tex]

Recall the distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]

Our distance from (x, y) to the focus (-3, 2) can be determined using the distance formula. Let (x, y) be (x₂, y₂) and let our focus (-3, 2) be (x₁, y₁). Therefore:

[tex]d_2=\sqrt{(x-(-3))^2+(y-2)^2}=\sqrt{(x+3)^2+(y-2)^2[/tex]

Hence, for Part A, our answers are the 2nd and 5th choices.

Part B)

Recall that by the definition of a parabola, any point (x, y) on it is equidistant to the directrix and focus. Hence:

[tex]\sqrt{(x+3)^2+(y-2)^2}=|y-4|[/tex]

Solve for y. Square both sides. We may remove the absolute value since anything squared is positive:

[tex](x+3)^2+(y-2)^2=(y-4)^2[/tex]

Square:

[tex]x^2+6x+9+y^2-4y+4=y^2-8y+16[/tex]

Rearrange:

[tex](x^2+6x+13)+(-16)=(y^2-y^2)+(-8y+4y)[/tex]

Combine like terms:

[tex]x^2+6x-3=-4y[/tex]

Divide both sides by -4. Hence, our equation is:

[tex]\displaystyle y=-\frac{1}{4}x^2-\frac{3}{2}x+\frac{3}{4}[/tex]

Heyo! :D

Distance to the directrix is |y - 4|.

Distance to the focus is [tex]\sqrt{(x+3)^2+(y-2)^2}[/tex].

Hope this helps! If so, please lmk! Tysm and good luck!

Answer:

14

Step-by-step explanation:

Just add both the numbers as positive to get total length since one is negative

5.3+8.7=14

Answer:

The length of the segment is 14.

Step-by-step explanation:

8.7 - (-5.3) = 14.

An easier way to do this is just by counting backwards kinda on the number line.

Answer:

21 is the answer your welcome

Answer:

The answer is 7.4 × 10³ ( or 0.74 × 10⁴).

Step-by-step explanation:

The steps are :

(1.5 × 10⁴) - (7.6 × 10³)

= (15 × 10³) - (7.6 × 10³)

= (15 - 7.6) × 10³

= 7.4 × 10³

Answer:

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

i think its C because don't you have to add the numbers together

The answer is 40 degrees :]

Answer:

Under couch

Step-by-step explanation:

Answer:

[tex]-21 < 109[/tex]

Step-by-step explanation:

Given

[tex]Savings = \$109[/tex]

[tex]Checking = -\$21[/tex]

Required

Represent as an inequality

On a number line -21 comes before 109 (from left to right)

This means that -21 is smaller/lesser than 109.

So, the inequality that compares the two account values is:

[tex]-21 < 109[/tex]

Answer:

Car B is travelling at the faster speed.

Step-by-step explanation:

Given that,

The distance covered by car A = 100 m

Time of car A, t = 5 s

The distance covered by car B = 100 m

Time of car B, t = 2 s

We need to find which one is travelling at the faster speed.

Speed = distance/time

For car A,

[tex]v_A=\dfrac{100\ m}{5\ s}\\\\v_A=20\ m/s[/tex]

For car B,

[tex]v_B=\dfrac{100\ m}{2\ s}\\\\v_B=50\ m/s[/tex]

So, car B is travelling at the faster speed.

Answer:

30

Step-by-step explanation:

6*4+2*9/3

24+2*9/3

24+6

30

Denote x2 by y.

(x2-3)7=(y-3)7

This is a binomial expansion in y, and you want the coefficient of y4 because y4=x8

You have 7 terms of (y-3) in (y-3)7.  To get the fourth power of y, you need to choose y from four of the terms.  The number of ways you can do this is the combinations of 7 things taken 4 at a time.  This is:

7!/(4!3!)=35

So, the coefficient of x8 in the given expansion will be 210.

HOPE IT HELPS

THANK YOU

Answer:

Step-by-step explanation:

C is 135'

A is 90'

B is 90'

D is 45'

E is 45'

F is 135'

Answer:

I'ma just take the free points, Give the other person a brainlest

Step-by-step explanation:

Answer:

Given:

Andrew walked during a walkathon to raise money= 24 laps

Each lap= [tex]\frac{1}{4}[/tex] of a mile

Andrew's dad donated= $5.25 for every mile

Step-by-step explanation:

Total money donated by Andrew's dad=Andrew walked x each lap distance                                                           x donated money

                                                               =24 x [tex]\frac{1}{4}[/tex] x 1 x 5.25

                                                               =6 x  5.25

                                                               = $31.50

Answer:

26

Show Your Work:

Answer:

26 sq.ft.

Step-by-step explanation:

i did the diagnostic

Answer:

Some Facts about lines (1) For non vertical line L, if L passes a point (x0,y0) with slope m, then an equation of line L is y − y0 = m(x − x0). (2) If a non vertical line L passes through distinct points (x1,y1) and x2(y2), then the slope of L is m = y2 − y1 x2 − x1 . x a + y b = 1.

Step-by-step explanation:

Answer:

The distance from the boat to the foot of the lighthouse is 359.36 ft

Height is the measurement of an item in the vertical direction, whereas distance is the measurement of an object in the horizontal direction from a certain location.

Given that, From the top of a lighthouse 160 feet high, the angle of depression of a boat out at sea is 24.

The whole situation is representing a right triangle (refer to figure)

Let  the distance from the boat to the foot of the lighthouse be x

We know that, angle of depression = angle of elevation

Then, using formula of height and distance,

tan 24° = 160 / x

x = 160 / tan 24°

x = 359.36

Hence,  the distance from the boat to the foot of the lighthouse is 359.36 ft

For more references on height and distance, click;

https://brainly.com/question/15939509

#SPJ2

Answer:

1. x-intercept = 3/-5 = -0.60000

 y-intercept = 3/1 = 3

2. x-intercept = 3/3 = 1

 y-intercept = 3/1 = 3

Step-by-step explanation:

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  y-5x-3  = 0 and calculate its properties

When y = 0 the value of x is 3/-5 Our line therefore "cuts" the x-axis at x=-0.60000

Answer:

434.9 cm³

Step-by-step explanation:

Volume of a sphere: 4/3πr³

Substitute the information to find the volume.

4/3π(4.7)³ = 434.9

Answer (this one's written in slope-intercept form):

[tex]y= \frac{3}{5}x -3[/tex]

Step-by-step explanation:

1) Lines that are parallel to each other have the same slope. The line [tex]y=\frac{3}{5} x-8[/tex] is in slope intercept form, or [tex]y = mx + b[/tex] form, and the number in place of [tex]m[/tex] represents the slope. Knowing this, it looks like [tex]\frac{3}{5}[/tex] is in the place of the [tex]m[/tex] in that equation, so  [tex]\frac{3}{5}[/tex] is the slope - and the slope we need to use for the answer, too.

2) Once you know a point that the line must pass through and a slope, you can write an equation with point-slope form, or [tex]y-y_1 = m (x - x_1)[/tex]. [tex]m[/tex] is the slope and [tex]x_1[/tex] and [tex]y_1[/tex] are the x and y values of the point it must pass through. So, substitute [tex]\frac{3}{5}[/tex] for [tex]m[/tex], 0 for [tex]x_1[/tex], and -3 for [tex]y_1[/tex]. Simplify and isolate y to put it in slope-intercept form:

[tex]y-(-3) = \frac{3}{5} (x - 0) \\y + 3 = \frac{3}{5} x - 0 \\y = \frac{3}{5} x - 3[/tex]

3) Thus, [tex]y = \frac{3}{5} x - 3\\[/tex] is the answer. It's written in slope-intercept form.

Answer:

let number be n

by question

(5n+3)=(n-9)

5n-n=-9-3

4n=-12

n=-12/4=-3

required no. is -3.

Answer:

5

Step-by-step explanation:

33p is separated into 3p and 2p

4 more 2p than 3p

5 3 points

9 2 points

Answer:

37

Step-by-step explanation:

Answer:

35 Students

Step-by-step explanation:

So if 40% of the students like Baseball and that there are 14 students in the class room.

Another way to interpret this is that you can divide 14 by 40% to find the total amount.

This gets you: 14 divided by 0.40 = 35 Students

Answer:

This is a controlled experiment.

Step-by-step explanation:

A controlled experiment is one in which all variables are kept constant except one, which is the independent variable. The samples are divided into the experimental and the control groups. The control group is the normal state of the condition being tested and would be compared to the experimental groups to check for changes.  

In the experiment above, the experimental group is given the new drug while the group that was administered the placebo is the control group. The two groups are compared after six months to check for changes.