Nina paid $37.57 for 13 gallons of gas Fred paid $55.67 for 19 gallons of gas Eleanor paid $48.62 for 17 gallons of gas. Who got the best buy?
(Find the unit price for each

Answer:

Step-by-step explanation:

Point slope form: y - y1 = m(x -x1)

[tex]y - [-16] = \dfrac{1}{2}(x - [-3] )\\\\y + 16 = \dfrac{1}{2}(x + 3)\\\\\\y + 16 = \dfrac{1}{2}x + \dfrac{3}{2}\\\\y =\dfrac{1}{2}x+\dfrac{3}{2}-16\\\\y=\dfrac{1}{2}x +\dfrac{3}{2}-\dfrac{32}{2}\\\\\\y=\dfrac{1}{2}x - \dfrac{29}{2}[/tex]

Answer:

[tex]y= -\frac12 x +\frac{29}2[/tex]

Step-by-step explanation:

Let's start with the point- slope form:

[tex]y-y_0=m(x-x_0)[/tex]

and replace the values we have

[tex]y-(-16) = -\frac12 (x-(-3))[/tex]

We're almost there, we just need to write it in a better looking form.

[tex]y+16= -\frac12 (x+3)\\y=-\frac12 x - \frac32 + \frac{32}2\\y= -\frac12 x +\frac{29}2[/tex]

Answer:

Number of Spiders: 8

Number of Dragonflies: 7

Number of Houseflies: 5

Step-by-step explanation:

s= spider

d= dragonfly

h= housefly

Heads:

20= s+d+h

Legs:

136= 8s+6d+6h

Wings:

19= 0s+2d+1h

Solve with substitution.

Divide the second equation by 2.

136= 8s+6d+6h

68= 3d+3h+4s

Set the last equation in terms of d.

19= 0s+2d+1h

d= [tex]\frac{19}{2} -\frac{1}{2}h[/tex]

Substitute what we just found (d) into the first and our new second equation. Simplify.

20= s+d+h

20= s+[tex]\frac{19}{2} -\frac{1}{2}h[/tex]+h

h+2s=21

68= 3d+3h+4s

68= 3([tex]\frac{19}{2} -\frac{1}{2}h[/tex])+3h+4s

3h+8s=79

Take both simplified equations and solve with elimination. Do this by multiplying the top equation by negative 3.

h+2s=21

3h+8s=79

-3h-6s=-63

3h+8s=79

2s=16

s=8

Plug in s=8 into the other equation.

h+2s=21

h+2(8)=21

h=5

Plug in h=5 into the last equation we rewritten.

[tex]d= \frac{19}{2} -\frac{1}{2} h[/tex]

[tex]d=\frac{19}{2} -\frac{1}{2}(5)[/tex]

d=7

(d,h,s)= (7,5,8)

Step-by-step explanation:

only the second one fulfills the rule that every value of x must have exactly 1 assigned result value (y).

the first option has two different result values (3 and 5) for x = 1.

the third has 2 different result values (3 and 4) for x = 2.

the fourth has 2 different result values (2 and 4) for x = 2, and also 2 different result values (0 and 2) for x = 0.

Answer:

1+1???????? 1+1=2. :/

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

( h ≥ -2 ).

Answer:

Refer to the attachment

Answer:

Angle K = 70degrees

Angle L = 68degrees

Step-by-step explanation:

Angle in a triangle add up to 180degrees

Figure out triangle the small triangle to the left side of the paper.

42+68+x=180

110+x=180

X=70

Angle K = 70degrees

Knowing that figure for angle L

70+42+x=180

112+x=180

X=68

Angle L = 68degrees

Answer:

24

Step-by-step explanation:

Answer: -8/15

Step-by-step explanation:

-(2/15)/(1/4)

-[(2/15)/(1/4)]*(4/4)

= (-2/15)*(4/1)

= -8/15

Answer:

$68.53. 67%

Step-by-step explanation:

$68. 58 I think I'm not sure

Answer:

x = 6

Step-by-step explanation:

Using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] , then

[tex]3^{-2}[/tex] × [tex]3^{x}[/tex] = 81 , that is

[tex]3^{x-2}[/tex] = [tex]3^{4}[/tex]

Since the bases on both sides are equal, both 3 then equate the exponents

x - 2 = 4 ( add 2 to both sides )

x = 6

Answer:

y = 1/6x -1

Step-by-step explanation:

Use point-slope form: y - y₁ = m (x - x₁)

y - (-2) = 1/6 (x - (-6))

y + 2 = 1/6x + 1

y = 1/6x - 1

Answer:

[tex]y=\frac{1}{6}x-1[/tex]

Step-by-step explanation:

According to,

y = mx + c

They have already given the slope of the line.

That means they've given value for m

So,

m = [tex]\frac{1}{6}[/tex]

And now we have to find the value of c ( the intercept on the y axis) using (-6,-2)

Here,

 ( -6 , -2 )

   ↑    ↑

  ( x ,  y )

Let us find the c now.

y = mx + c

[tex]-2 =\frac{1}{6} *-6+c\\-2=\frac{-6}{6} +c\\-2=-1+c\\-2+1=c\\-1=c[/tex]

Now let's write the equation of the line like this

y = mx+ c

[tex]y=\frac{1}{6}x-1[/tex]

Hope this helps you.

Let me know if you have any other questions :-)

Answer:

They are similar triangles so the sides are equal

3y-2=y+4

2y=6

y=3

so we can insert y=3 to calculate the side length

3y-2=3*3-2=7=PR side

calculate the perimeter:

4+6+7=17ft

Step-by-step explanation:

Add the lengths.of all sides together

4+6+(3y-2)

= 4+6+3y-2

=8+3y ft

Answer:

3x^2+15x-1=0

Step-by-step explanation:

4/(3x+15)=4x

4=12x^2+60x

12x^2+60x-4=0

3x^2+15x-1=0

Please solve after that, I cannot do everything for you

Answer:

4hours

um...

57×10-== 4 hours

Answer:

A and D

Step-by-step explanation:

Rational numbers that can be written as a fraction of two integers (without a denominator of 0).

The other three cannot be written as a fraction or two integers.

Answer:

Step-by-step explanation:

We can answer this in two ways:  Differentiation and Graphing.

Differentitate:

The first derivative of a function yields a function that provides the slope for any point on the line of the original function.  The slope of a vertex is zero, so we can set the first derivative to 0 and solve for x.

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

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

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

f(x) = 3x^2 - 6x + 7

f'(x) = 6x -6

Set this = 0 and find x:

0 = 6x -6

x = 1

The value of y when x=1 in the original equation is:

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

y = 4

The vertex is (1,4)

Graph:

You can use DESMOS to plot the function.  The result is attached.  Look for the vertex and read the coordinates.  (1,4) seems to work.

Answer:

It must be two

Step-by-step explanation:

Answer:

.006453

Step-by-step explanation:

6.453 x 10^-3

Move the decimal 3 places to the left since the exponent is negative

006.453

.006453

Answer:

approximately 43 - 44 minutes exact

Answer:

It would take you 2917 hours.

Step-by-step explanation:

Do 777,777,777 divided by 266,560.

I hope this helped at all.

Answer:

The answer is 39.3

Step-by-step explanation:

81.6 - 3 = 78.6

78.6 ÷ 2 = 39.3

Step-by-step explanation:

168/3 = 56

so 112 sodas

56 hotdogs

Answer:

[tex] \sqrt[6]{729} [/tex]

Answer:

y is 3,hmmmmmmmmmmmmmmm......aha! x= 46! hope this helps!

Step-by-step explanation:

Slope = (y₂ - y₁)  ÷  (x₂ - x₁)

          =  (-85 - (-83)) ÷  (-11 - 75)

          =  -2 ÷ -86

          = ¹/₄₃

Checking my answer:

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.

                               ⇒  y - (-83) =  ¹/₄₃ (x - 75)

                               ⇒     y + 83 =  ¹/₄₃ (x - 75)

 I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given.

Answer:

x = 4.4 cm

Step-by-step explanation:

Since this is a right triangle, the Pythagorean Theorem applies:  a^2 + b^2 = c^2, where a and b are leg lengths and c is the length of the hypotenuse.

Thus, (5.3 m)^2 + x^2 = (6.9 m)^2, or, solving for x^2:

x^2 = (6.9 m)^2 - (5.3 m)^2, or

x^2 = 47.61 - 28.09 = 19.52

Then the length, x, of the unknown side is x = +√19.52 m, or

x = 4.4 cm

Answer:

656.36

Step-by-step explanation:

you just divide then have to round the decimal point to 36

Answer:

it should be C

Step-by-step explanation:

hope this is helpful

Answer:

[tex]2.5y^{3}x[/tex]