You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get out and ride it around. It doesn't run on straight gasoline, you have to mix the oil and gas together in a specific ratio of 2.4 fl. oz. of oil for every gallon of gasoline.
You have 3.75 gallon of gas. How much oil should you add?

Answer:

2nd option is the correct answer

Answer:

x = 36 , y = 64 , z = 80

Step-by-step explanation:

Exterior angle equals the sum of opposite interior angle.

3x +  8 = x +  z

3x - x - z = -8

2x  -  z = -8   ------------ (I)

z + 3x - 8 = 180 {linear pair}

3x + z = 180 + 8

3x + z = 188 --------------(II)

Add (I) and (II) and z will be eliminated and we can find the value of 'x'

(I)            2x - z = -8

(II)           3x + z = 188   {Now add}

               5x      = 180

x = 180/5

x = 36

Plugin x = 36 in equation (II)

     3*36 +z = 188

        108 + z = 188

                z = 188- 108

z = 80

x + y + z = 180 ----------------(III)  {angle sum property of triangle}

36 + 80 +y = 180

       116 + y = 180

               y = 180 - 116

y = 64

Answer:

A,B,E,F

Step-by-step explanation:

Answer:

3x +9 + 3x + 3x +8 = 3x + 3x + 4x + 6

9x + 17 = 10x + 6

x = 11

AB 42

BC 41

AC 33

PQ 33

QR 33

PR 50

Answer:

x = 11

Step-by-step explanation:

if the perimeters are equal then:

the perimeter of the first triangle : 3x + 9 + 3x + 3x + 8 = 9x + 17

the perimeter of the second triangle : 3x + 3x + 4x + 6 = 10x + 6 and

9x + 17 = 10x + 6 export like terms to the same side of the equation

17 - 6 = 10x - 9x

11 = x

we can find the lengths by replacing x with 11 in given expressions.

Answer:

None of the option is correct.

The right answer is 18/7 or 2.57

Step-by-step explanation:

Answer:

[tex]D)\:(3x^{2} +2)(x+4)[/tex]

Step-by-step explanation:

[tex]3x^{3} + 12x^{2} + 2x + 8[/tex]

Group, [tex]3x^3+12x^2+2x+8[/tex]  [tex]=(3x^{3} +12x^{2} )+(2x+8)[/tex]factor out [tex]3x^{2}[/tex]in the first and 2 in the second group.

[tex]3x^{2} (x+4)+2(x+4)[/tex]

Factor out common term [tex]x+4[/tex] by using distributive property.

polynomial [tex]3x^{2} +2[/tex] is not factored since it does not have any rational roots.

[tex](3x^{2} +2)(x+4)[/tex]

_____________________________

Answer:d

Step-by-step explanation:

Answer:

2/3multiply by20 u get 13.3 pounds

Answer:

the shop keeper will return $301.00

As we know :

now let's plug the value of given terms :

Answer:

babawi lang sana

Step-by-step explanation:

naul pi

Answer:

Depends, rise over run could be considered a fraction, or if it's a number that has a whole number like one and 3/4 then you just plot the point to the best of your ability. In other words guess.

Answer:

we can do it again and I am a great time with you and your family and friends and family is not good

Answer:

N+5

Step-by-step explanation:

4,9,14,19

4+5=9+5=14+5=19….

The sequence of the number of girl attendees at each Barangay is nonzero, given by multiplying the number of attendees in the previous Barangay by 2

The required values are;

a. The completed table is presented as follows;

[tex]\underline{\begin{array}{|l|c|c|c|c|c|c|c|}\mathbf{Barangay}&1&2&3&4&5&6&7\\\mathbf{Number \ of \ attandees}&4&8&16&32&64&128&256\end{array}}[/tex]

b. The sequence of the number of girls attendees aₙ = 4×2⁽ⁿ⁻¹⁾

c. The sum of beneficiaries of the lecture from the twelve Barangay is 16,384 girls

Reason:

Known parameters are;

Number of girls that attended the lecture at Barangay 1 = 4 girls

Number of girls that attended from Barangay 2 = 8 girls

Number that attended from Barangay 3 = 16 girls

a. The required table with the assumption that the number of girls that attended at each Barangay from Barangay 1 to Barangay 7 doubles, is presented as follows;

b. The sequence of the number of girls who attended the lecture from Barangay 1 to Barangay 7 is presented as follows;

The sequence is a geometric progression having the form, aₙ = a·r⁽ⁿ⁻¹⁾

The first term of the sequence, a = 4

The common ratio, r = 2 (each term is twice the previous term)

n = The number of terms

The sequence is therefore;

c. The total number of girls in the geometric progression, (G. P.) is given by the sum of a G. P. as follows

[tex]S_n = \dfrac{a \cdot (r^n - 1 )}{r - 1}[/tex]

Where;

n = The number of terms = 7 + 5 = 12

Which gives;

The total number of girls who will benefit from the lectures, S₁₂ = 16,384 girls

Learn more about geometric progression here:

https://brainly.com/question/14256037

Answer:

[tex]- 5 {x}^{3} - {x}^{2} - 11x + 7 \\ [/tex]

Step-by-step explanation:

Before solving that we have to know that,

[tex]( + ) \times ( + ) = ( + ) \\ ( - ) \times (- ) = ( + ) \\ ( + ) \times ( - ) = (- )[/tex]

Let's solve now.

[tex]7 {x}^{3} - 11x - 1 - (12 {x}^{3} + {x}^{2} - 8) \\ 7 {x}^{3} - 11x - 1 - 12 {x}^{3} - {x}^{2} + 8 \\ 7 {x}^{3} - 12 {x}^{3} - {x}^{2} - 11x - 1 + 8 \\ = - 5 {x}^{3} - {x}^{2} - 11x + 7[/tex]

Hope this helps you.

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

Answer:

∆K = 98°

∆M = 82°

∆G = 118°

∆H = 62°

Step-by-step explanation:

∆K & ∆G is by corresponding angle

and

∆M & ∆H is by linear pairs

Answer:

Step-by-step explanation:

300/100 = 3 = 1%

if 3 = 1% then 3/2 or 1.5 = 0.5%

5 x 3 = 15 = 5%

15 + 1.5 = 16.5 = 5.5%

(1)

(a) Use the fact that [tex]\sqrt{x^2} = |x|[/tex] for all [tex]x[/tex]. Since [tex]x\to+\infty[/tex], we have [tex]x>0[/tex] and [tex]|x| = x[/tex].

[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ x \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= \frac{\sqrt9}1 = \boxed{3}[/tex]

(b) This time [tex]x\to-\infty[/tex], so [tex]x < 0[/tex] and [tex]|x| = -x[/tex].

[tex]\displaystyle \lim_{x\to\infty} \frac{\sqrt{9x^2 - 2}}{x + 4} = \lim_{x\to\infty} \frac{\sqrt{x^2} \sqrt{9 - \frac2{x^2}}}{x + 4} \\\\= \lim_{x\to\infty} \frac{ \boxed{-x} \sqrt{9 - \frac2{x^2}}}{x+4} \\\\= (-1) \times \lim_{x\to\infty} \frac{\sqrt{9 - \frac2{x^2}}}{1 + \frac4x} \\\\= -\frac{\sqrt9}1 = \boxed{-3}[/tex]

(c) We immediately have

[tex]\displaystyle \lim_{x\to\infty} (x - \sqrt x) = \boxed{\infty}[/tex]

since [tex]x > \sqrt x[/tex] for all [tex]x > 1[/tex].

(d) Introduce a difference of squares by factoring in the limand's conjugate. The rest mirrors what we did in (a)/(b).

[tex]\displaystyle \lim_{x\to\infty} \left(\sqrt{x^2 + 12x} - x\right) = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x} - x\right) \left(\sqrt{x^2+12x} + x\right)}{\sqrt{x^2 + 12x} + x} \\\\ = \lim_{x\to\infty} \frac{\left(\sqrt{x^2+12x}\right)^2 - x^2}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12x}{\sqrt{x^2+12x}+x} \\\\ = \lim_{x\to\infty} \frac{12}{\sqrt{1 + \frac{12}x} + 1} = \frac{12}{\sqrt1 + 1} = \boxed{6}[/tex]

(e) Divide through by the highest-degree exponential term.

[tex]\displaystyle \lim_{x\to\infty} \frac{12e^{2x} - 3e^{3x}}{2e^{2x} + 4e^{3x}} = \lim_{x\to\infty} \frac{12e^{-x} - 3}{2e^{-x} + 4} = \frac{0 - 3}{0 + 4} = \boxed{-\frac34}[/tex]

(2) By definition of the derivative, we have

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h) - f(x)}h[/tex]

For [tex]f(x) = \sqrt{x^2+1}[/tex], the limit becomes

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\sqrt{(x+h)^2+1} - \sqrt{x^2+1}}h[/tex]

Factor in the conjugate.

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1} - \sqrt{x^2+1}\right) \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\left(\sqrt{(x+h)^2+1}\right)^2 - \left(\sqrt{x^2+1}\right)^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{\bigg((x+h)^2+1\bigg) - (x^2+1)}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2xh + h^2}{h \left(\sqrt{(x+h)^2+1} + \sqrt{x^2+1}\right)}[/tex]

[tex]f'(x) = \displaystyle \lim_{h\to0} \frac{2x + h}{\sqrt{(x+h)^2+1} + \sqrt{x^2+1}}[/tex]

[tex]\implies \boxed{f'(x) = \displaystyle \lim_{h\to0} \frac{x}{\sqrt{x^2+1}}}[/tex]

(3) The tangent line to

[tex]y = \frac1{x^2+1}[/tex]

at the point (2, 1/5) has slope equal to the derivative [tex]\frac{dy}{dx}[/tex] when [tex]x = 2[/tex]. Compute the derivative; since [tex]y = \frac1{f(x)^2}[/tex] where [tex]f(x)[/tex] is the function from the previous problem, using the chain rule gives

[tex]y = \dfrac1{f(x)^2} \implies \dfrac{dy}{dx} = -\dfrac{2f'(x)}{f(x)^3} = -\dfrac{2 \times \frac{x}{\sqrt{x^2+1}}}{\left(\sqrt{x^2+1}\right)^3} \\\\ \implies \dfrac{dy}{dx} = -\dfrac{2x}{(x^2+1)^2}[/tex]

The tangent line at (2, 1/5) then has slope

[tex]\dfrac{dy}{dx}\bigg|_{x=2} = -\dfrac{2\times2}{(2^2+1)^2} = -\dfrac4{25}[/tex]

Using the point-slope formula, the equation of the tangent line is

[tex]y - \dfrac15 = -\dfrac4{25} (x - 2) \implies \boxed{y = -\dfrac{4x - 13}{25}}[/tex]

Answer: 5h+9

Step-by-step explanation:

10h + (-5h)

5h+(6(+3))

Answer:

a

Step-by-step explanation:

Answer: 0.8333

Step-by-step explanation:

Answer:

82 - 2i

Step-by-step explanation:

(5 - 2i) + (-4 + 81)

5 - 2i + 77

= 82 - 2i

1 + 6i

we open the brackets to give us

5 - 2i - 4 + 8i

collecting like terms, we have,

-2i + 8i + 5 - 4

6i + 1

or

1 + 6i

Answer:

75 times

Step-by-step explanation:

Answer:

18 units

Step-by-step explanation:

You don't need to use slope since both are using 13 for y.

22 - 4 (both x values) = 18

B. 18 units

Answer:

The other angle's measure is 2/3 (54) = 108/3 = 36 degrees.

Answer:

keep the car at a friends house untill you find a place to get it fixed at... or keep it at a trustworthy family members house.

If these don't help then im sorry.

Answer:

answer is below

Step-by-step explanation:

so 32.14 is breakable. first break it up by the tens place you have 3 tens.

next the ones place you have 2 ones

then the tenths place you have 1 tenth

then the hundredth place you have 4 hundreths

so the 3 tens is equal to 30

the 2 ones is equal to 2

the 1 tenth is equal to 0.1

the 4 hundredth is equal to 0.04  

this is easier to understand and is a good way to think about more complext numbers

Answer:

A. Personal vacation expenses

Step-by-step explanation:

Because everything else either helps the community or is a required expense