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4 years ago

A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.

Mathematics

1 answer:

77julia77 [94]4 years ago

6 0

I think its 13.1 gallons for a 714 mile trip

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A(x, 1), B(5,3) and C(4,-3) are the vertices of triangle ABC. If AB=AC, find the value of x

Molodets [167]

$\\ \rm\longmapsto AB=AC$

$\\ \rm\longmapsto \sqrt{(x-5)^2+(1-5)^2}=\sqrt{(x-4)^2+(1+3)^2}$

$\\ \rm\longmapsto (x-5)^2+(-2)^2=(x-4)^2+4^2$

$\\ \rm\longmapsto (x-5)^2+4=(x-4)^2+16$

$\\ \rm\longmapsto (x-5)^2-(x-4)^2=16-4=12$

$\\ \rm\longmapsto x^2-10x+25-x^2+8x-16=12$

$\\ \rm\longmapsto -2x+9=12$

$\\ \rm\longmapsto -2x=12-9=3$

$\\ \rm\longmapsto x=\dfrac{3}{-2}=-1.5$

5 0

3 years ago

Read 2 more answers

Vanessa wants to determine the perimeter around her garden. She makes an small model of her garden and combines all the sides: 3

son4ous [18]

Answer:

Step-by-step explanation:

since it's all addition, we can remove the parentheses

$3x + x + 10 + 5x + 2x + 2 = 56$

Now we combine like terms

$3x+x+5x+2x+10+2=56$

$11x+12=56$

We subtract both sides by 12 to get,

$11x=44$

now we divide both sides by 11

$x=\frac{44}{11}$

$x=4$

8 0

3 years ago

I need help pleasee thank

Ganezh [65]

Answer:

A=51

a=22.2

c=28.6

Step-by-step explanation:

∠A=180-90-39

=51

a/sin51=18/sin39

a=22.2

c/sin90=18/sin39

c=28.6

4 0

3 years ago

Read 2 more answers

A rectangular piece of cardboard is 15 inches longer than it is wide. A 5-inch square is cut from each corner, and the remaining

HACTEHA [7]

Let x be the width of the cardboard, then the length is x+15. If 5 unches square is cut from each corner, then the new length is x+15-5·2=x+5 and the new width is x-5·2=x-10. The height of the formed box is 5 in. Now you can find the box volume:

$V=\text{ width }\cdot \text{ length }\cdot \text{ height },\\ V=(x-10)\cdot (x+5)\cdot 5,\\ V=5(x^2-5x-50)$ .

If the volume of the box is 1,250 cubic inches, then

$5(x^2-5x-50)=1250,\\ x^2-5x-50=250,\\ x^2-5x-300=0,\\ D=(-5)^2-4\cdot (-300)=25+1200=1225,\\ \sqrt{D} =35,\\ x_{1,2}=\dfrac{5\pm 35}{2} =20,-15$ .

The length of the box is x+5=20+5=25 in. (the negative x is extra, because the length couldn't be negative).

Answer: the length of the box is 25 inches.

7 0

3 years ago

Dy/dx = (sin x)/y , y(0) = 2

skad [1K]

Start with

$\dfrac{dy}{dx}=\dfrac{\sin(x)}{y}$

Separate the variables:

$y\;dy = \sin(x)\;dx$

Integrate both parts:

$\displaystyle \int y\;dy = \int\sin(x)\;dx$

Which implies

$\dfrac{y^2}{2} = -\cos(x)+c$

Solving for y:

$y = \sqrt{-2\cos(x)+c}$

Fix the additive constant imposing the condition:

$y(0) = \sqrt{-2+c}=2 \iff -2+c=4 \iff c=6$

So, the solution is

$y(x) = \sqrt{-2\cos(x)+6}$

5 0

3 years ago

A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714​-mi trip.

A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.