Amanda drove 355 miles using 17 gallons of gas. At this rate how many gallons of gas would she need to drive 284 miles?

Final answer:

To solve the literal equation for y in the given equation a=9y-3yx, we can rearrange the terms and isolate y on one side. The solution for y is (a - 9y) / (-3x).

Explanation:

To solve the literal equation for y, we need to isolate y on one side of the equation.

Given the equation a = 9y - 3yx, we can start by rearranging the terms.

Subtract 9y from both sides:

a - 9y = -3yx

Divide both sides by -3x:

(a - 9y) / (-3x) = y

So, the solution for y is (a - 9y) / (-3x).

Final answer:

To solve the given literal equation for y, factor out y and then divide by (9 - 3x) to obtain the equation y = a / (9 - 3x), which allows y to be expressed in terms of a and x.

Explanation:

To solve the literal equation for y given as a = 9y - 3yx, we want to isolate y on one side of the equation. To do this, we first factor out y from the terms on the right side of the equation:

a = y(9 - 3x)

Next, we divide both sides of the equation by (9 - 3x) to get y by itself:

y = a / (9 - 3x)

This equation represents the value of y in terms of a and x. In the context of a linear equation, such as y = 9 + 3x, the number 9 is the y-intercept (denoted as the b term), and the number 3 is the slope (denoted as the m term).

s =1/2(u+v)t

u = 16, v=16, t=90

s = 1/2(16+16)90

s = 1/2(36)90

s = 16*90

s = 1440

Answer:

It would be 3

Step-by-step explanation:

The type of rice which is most expensive is [tex]\boxed{\text{\bf type B}}[/tex].

Further details:

It is given that the rice seller mixes three types of rice and the total number of mixture is three.

The first mixture consists [tex]1\text{ kg}[/tex] rice of type [tex]\text{A}[/tex], [tex]2\text{ kg}[/tex] rice of type [tex]\text{B}[/tex] and [tex]4\text{ kg}[/tex] rice of type [tex]\text{C}[/tex].

The selling price of the first mixture is [tex]19500[/tex].

In equation form it can be written as follows:

[tex]\boxed{\text{A}+2\text{B}+4\text{C}=19500}[/tex]      .......(1)

The second mixture consists [tex]2\text{ kg}[/tex] rice of type [tex]\text{A}[/tex] and [tex]3\text{ kg}[/tex] rice of type [tex]\text{B}[/tex].

The selling price of the second mixture is [tex]19000[/tex].

In equation form it can be written as follows:

[tex]\boxed{2\text{A}+3\text{B}=19000}[/tex]   ......(2)

The third mixture consists [tex]1\text{ kg}[/tex] rice of type [tex]\text{B}[/tex] and [tex]1\text{ kg}[/tex] rice of type [tex]\text{C}[/tex].

The selling price of the third mixture is [tex]6250[/tex].

In equation form it can be written as follows:

[tex]\boxed{\text{B}+\text{C}=6250}[/tex] ........(3)

Rearrange the equation (3) to obtain the value of [tex]\text{B}[/tex] as follows:

[tex]\text{B}=6250-\text{C}[/tex]            ...........(4)

Substitute this value of [tex]\text{B}[/tex] in equation (2).

[tex]\begin{aligned}2\text{A}+3(6250-\text{C})&=19000\\2A+(3\cdot 6250)-3\text{C}&=19000\\2\text{A}-3\text{C}+18750&=19000\\2\text{A}-3\text{C}&=19000-18750\\2\text{A}-3\text{C}&=250\end{aligned}[/tex]  

Further solve the above equation,

[tex]\text{A}-1.5\text{C}=125[/tex]   ......(5)

Now substitute the value of [tex]\text{B}[/tex] from equation (4) in equation (1) to obtain an equation in the form of [tex]\text{A}[/tex] and [tex]\text{C}[/tex] as follows,

[tex]\begin{aligned}\text{A}+2(6250-\text{C})+4\text{C}&=19500\\ \text{A}+(2\cdot 6250)-2\text{C}+4\text{C}&=19500\\ \text{A}+12500+2\text{C}&=19500\\ \tex{A}+2\text{C}&=19500-12500\end{aligned}[/tex]

Further the above equation can be simplifies as follows,

[tex]\text{A}+2\text{C}=7000[/tex]            .......(6)

Subtract the equation (4) from (5) to obtain the value of [tex]\text{A}[/tex] and [tex]\text{C}[/tex].  

[tex]\begin{aligned}\text{A}+2\text{C}-\text{A}+1.5\text{C}&=7000-125\\3.5\text{C}&=6875\\ \text{C}&=1964.3\end{aligned}[/tex]

Substitute this value of [tex]\text{C}[/tex] in equation (5) to obtain the value of [tex]\text{A}[/tex] as follows,

[tex]\begin{aligned}\text{A}+(2\cdot 1964.3)&=7000\\ \text{A}&=7000-3928.6\\ \text{A}&=3071.4\end{aligned}[/tex]

Again substitute [tex]\text{C}=1964.3[/tex] in equation (4) to obtain the value of [tex]\text{B}[/tex].

[tex]\begin{aligned}\text{B}&=6250-1964.3\\&=4285.7\end{aligned}[/tex]  

Therefore, the most expensive type of rice is [tex]\boxed{\text{\bf type B}}[/tex].

Learn more:

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2. Problem on unit conversion factor: https://brainly.com/question/5009365

3. Problem on to find the value in pounds: https://brainly.com/question/4837736

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Mixtures

Keywords:  Rice seller, mixture, sold, expensive, type A, type B, type C, simplification, consist, 19500, 1 kg,addition, substitution, multiplication.

Answer:

B. [tex]8\sqrt2+2\sqrt{10}[/tex] units

Step-by-step explanation:

We are given that a parallelogram PQRS in which point P(-2,5), Q(2,1),R(1,-2) and S(-3,2).

We have to find the perimeter of parallelogram PQRS.

Distance formula : [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Using the formula

[tex]SR=\sqrt{(1+3)^2+(-2-2)^2}=4\sqrt2[/tex]units

[tex]QR=\sqrt{(1-2)^2+(-2-1)^2}=\sqrt{10} units[/tex]

Now, the perimeter of parallelogram =2(SR+QR)

The perimeter of parallelogram =[tex]2(4\sqrt2+\sqrt{10})=8\sqrt2+2\sqrt{10} units[/tex]

Answer:B. [tex]8\sqrt2+2\sqrt{10}[/tex] units

1/10 of 400 = 40

1/4 of 40 = 10

1/2 of 10 = 5

the number is 5

Answer:  The required simplified expression is -2c.

Step-by-step explanation:  We are given to simplify the following expression :

[tex]E=\dfrac{1}{8}(-8c+16)-\dfrac{1}{3}(6+3c)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We will be using the following distributive property :

[tex]a(b+c)=ab+ac.[/tex]

From expression (i), we get

[tex]E\\\\\\=\dfrac{1}{8}(-8c+16)-\dfrac{1}{3}(6+3c)\\\\\\=\dfrac{1}{8}\times(-8c)+\dfrac{1}{8}\times16-\dfrac{1}{3}\times6-\dfrac{1}{3}\times3c\\\\=-c+2-2-c\\\\=-2c.[/tex]

Thus, the required simplified expression is -2c.

There is a solution. Starting from C−1(A+X)B−1=In C−1(A+X)B−1=In, multiply both of the sides of the equation, by C and multiply both sides of the equation by B.

In other terms, this is the solution:

Given: C^(-1)(A + X)B^(-1) = In

= CC^(-1)(A + X)B^(-1)B = CInB

= In(A + X)In = CB

= AInIn + XInIn = CB


= A + X = CB


X = CB – A

The final answer Is X = CB – A

Answer:

$166.50

Step-by-step explanation:

Answer: –5x – x2

Step-by-step explanation:

edge.