Ask question

Ask question

All categories

2 years ago

10

Ants have 6 legs. Katie and Lukas write equations showing the proportional relationship between the number of ants, a, and the n

umber of ant legs, l.
Katie writes a = 6 • 1 and Lukas writes a = 1/6 • l.

Whose equation do you agree with?

A. Katie
B. Lukas
C. Both
D. Neither

Explain your reasoning.

1 answer:

krek1111 [17]2 years ago

6 0

Answer:

A

Step-by-step explanation:

I agree with Katie because number is legs is directly proportional to the number of ants.

1 ant has 6 legs.

So, 2 ants have 6 *2 = 12

3 ants have 6*3 = 18

You might be interested in

find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

3 years ago

I have to explained it in words pls help

lys-0071 [83]

9514 1404 393

Answer:

slope: cost per mile
y-intercept: fixed base cost

Step-by-step explanation:

The y-intercept is the value of y when x=0. The problem statement tells you that x is the number of miles driven, and y is the rental cost.

When the number of miles driven is zero, the rental cost is ...

y = 2.25×0 +70

y = 70

The cost of renting the truck is $70 when it isn't driven anywhere. The y-intercept ($70) is the basic, fixed cost of truck rental.

__

If x=1 (1 mile driven), then 2.25 is added to the cost of the truck rental. The slope (2.25) is the cost per mile driven. (That mileage cost is added to the basic rental cost.)

6 0

2 years ago

Write ✓-98 in simplest radical form.

trapecia [35]

Answer:

Step-by-step explanation:

This first step is to take the square root of the minus which is understood to be - 1

sqrt(-1) = i

So far what you have is

sqrt(-98) = i*sqrt(98)

sqrt(98) is just found the ordinary way

sqrt(98) = sqrt(7*7*2)

sqrt(7*7*2) = 7*sqrt(2)

Answer: 7 * i * sqrt(2) = i7*sqrt(2)

Pick the choice that looks like what you have done for homework.

8 0

3 years ago

At a little-known vacation spot, taxi fares are a bargain. A 14-mile taxi ride takes 16 minutes and costs $11.20. You want to

sergeinik [125]

Answer:

$29.60

Step-by-step explanation:

$11.20/14 miles = $0.80 per mile

$0.80 x 37 = $29.60

6 0

2 years ago

Read 2 more answers

If f(x)=3^2-1 and g(x)=x+2 find (f+g)(x)

Dovator [93]

9 - 1 + x + 2 ( x )
9x - x + x2 + 2x
x2 + 10x

6 0

3 years ago