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Alenkasestr [34]
3 years ago
8

Justin fills his car with 40 litres of petrol. After travelling 35 miles it's down to 35 litres. Let be the number of litres in

a tank after driving miles (a) How much petrol does the car use each mile? (b) Write down the equation linking and , and check i
Mathematics
1 answer:
mixas84 [53]3 years ago
4 0

Answer:

a) 1/7 liters of petrol is used for each mile

Step-by-step explanation:

Justin fills his car with 40 litres of petrol. After travelling 35 miles it's down to 35 litres.

From the above statement:.

The difference is :

40 litres - 35 liters = 5 liters

Hence:

After travelling 35 miles he used 5 liters

(a) How much petrol does the car use each mile?

This is calculated as:

35 miles = 5 Liters

1 mile = x liters

Cross Multiply

35x = 5 Liters

x = 5/35

x = 1/7 liters

Hence, for each mile, 1/7 liters of petrol is used

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Choose the best answer that represents the property used to rewrite the expression.
Andre45 [30]

Answer:

The Quotient Property.

Step-by-step explanation:

Since all three logarithms have the same base (base-5), and you are subtracting 6 and 3, to solve this all you need to do is 6 / 3 because of the Quotient Property.

You aren't multiplying anything, so you wouldn't use the Product Property.

You are not messing around with powers, so you wouldn't use the Power Property.

And you aren't using addition or multiplication, so you wouldn't use the Commutative Property.

Hope this helps!

5 0
3 years ago
One fourth the sum of x and ten is identical to x minus 4."
Lynna [10]

Answer and Step-by-step explanation:

We are given the word format of an equation.

Let's right it out in numerical form.

\frac{1}{4} (x + 10) = x - 4

The first part says One fourth the sum of x and 10

The sum of x and 10 would be shown as x + 10, and one fourth of that means that \frac{1}{4} is multiplying (x + 10).

In this case, identical would mean equal to.

So, \frac{1}{4}(x + 10) would be = to something.

It says that it is identical to x minus 4 (x - 4).

\frac{1}{4} (x + 10) = x - 4<u> is the equation.</u>

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

5 0
2 years ago
Perform the indicated operation. Be sure the answer is reduced.
avanturin [10]
<h3>Given Equation:-</h3>

\boxed{ \rm  \frac{4x^{2}y^{3}z}{9} \times  \frac{45y}{8 {x}^{5} {z}^{5} }}

<h3>Step by step expansion:</h3>

\dashrightarrow \sf\dfrac{4x^{2}y^{3}z}{9} \times  \dfrac{45y}{8 {x}^{5} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{ \cancel4x^{2}y^{3}z}{9} \times  \dfrac{45y}{ \cancel8 {x}^{5} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{9} \times  \dfrac{45y}{2{x}^{5} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{ \cancel9} \times  \dfrac{ \cancel{45}y}{2{x}^{5} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{1} \times  \dfrac{5y}{2{x}^{5} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{x^{0}y^{3}z}{1} \times  \dfrac{5y}{2{x}^{5 - 2} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{y^{3}z}{1} \times  \dfrac{5y}{2{x}^{3} {z}^{3} }

\\  \\

\dashrightarrow \sf\dfrac{y^{3}z {}^{0} }{1} \times  \dfrac{5y}{2{x}^{3} {z}^{3 - 1} }

\\  \\

\dashrightarrow \sf\dfrac{y^{3}}{1} \times  \dfrac{5y}{2{x}^{3} {z}^{2} }

\\  \\

\dashrightarrow \sf  \dfrac{5y \times  {y}^{3} }{2{x}^{3} {z}^{2} }

\\  \\

\dashrightarrow \sf  \dfrac{5y {}^{0}  \times  {y}^{3 + 1} }{2{x}^{3} {z}^{2} }

\\  \\

\dashrightarrow \sf  \dfrac{5 \times  {y}^{4} }{2{x}^{3} {z}^{2} }

\\  \\

\dashrightarrow \bf  \dfrac{5 {y}^{4} }{2{x}^{3} {z}^{2} }

\\  \\

\therefore \underline{ \textbf{ \textsf{option \red c \: is \: correct}}}

8 0
2 years ago
Solve for the 3 sides
mel-nik [20]

Answer:

1. x = 2√3 or 3.46

2. y = 4√3 or 6.93

3. z = 4√6 or 9.80

Step-by-step explanation:

1. Determination of the value of x.

Angle (θ) = 60°

Opposite = 6

Adjacent = x

Tan θ = Opposite /Adjacent

Tan 60 = 6 / x

√3 = 6/x

Cross multiply

x√3 = 6

Divide both side by √3

x = 6 / √3

Rationalise

x = (6 / √3) × (√3/√3)

x = 6√3 / 3

x = 2√3 or 3.46

2. Determination of the value of y.

Angle (θ) = 60°

Opposite = 6

Hypothenus = y

Sine θ = Opposite /Hypothenus

Sine 60 = 6/y

√3/2 = 6/y

Cross multiply

y√3 = 2 × 6

y√3 = 12

Divide both side by √3

y = 12/√3

Rationalise

y = (12 / √3) × (√3/√3)

y = 12√3 / 3

y = 4√3 or 6.93

3. Determination of the value of z.

Angle (θ) = 45°

Opposite = y = 4√3

Hypothenus = z

Sine θ = Opposite /Hypothenus

Sine 45 = 4√3 / z

1/√2 = 4√3 / z

Cross multiply

z = √2 × 4√3

z = 4√6 or 9.80

8 0
3 years ago
Picture of math assignment
n200080 [17]

Answer:

{5}^{ - 7}

Step-by-step explanation:

You have to use the property of quotient of powers, you subtract the power of the fraction denominator from the numerator

6 0
3 years ago
Read 2 more answers
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