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3 years ago

a taxi service charges an initial fee of $5 plus $1.80 per mile. How many miles can you travel for $12

1 answer:

4 0

First you need to write an equation or an inequality.

5+1.80x<=12
the x here is how many miles you are paying for, now you just solve for x.

5+1.80x<=12
-5 -5

1.80x<=7
/1.80 /1.80
x<=3.8

you can travel only three whole miles, you do not have enough money to go four full miles.

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Find the length of LM if L is the midpoint of NM. NL = 3x + 1, LM = 8x - 24.

SashulF [63]

Answer:

LM = 16

Step-by-step explanation:

From the question given:

L is the midpoint of NM

NL = 3x + 1

LM = 8x - 24

LM =?

Next, we shall determine the value of x.

This can be obtained as follow:

Since L is the midpoint of NM, it means that NL and LM are equal i.e

NL = LM

Thus, we can obtain the value of x as follow:

NL = 3x + 1

LM = 8x - 24

NL = LM

3x + 1 = 8x - 24

Collect like terms

3x - 8x = - 24 - 1

-5x = - 25

Divide both side by - 5

x = -25/-5

x = 5

Finally, we shall determine the length of LM as follow:

LM = 8x - 24

x = 5

LM = 8(5) - 24

LM = 40 - 24

LM = 16

Therefore, the length of LM is 16

8 0

3 years ago

Kala drove 250 miles using 9 gallons of gas. at this rate how many gallons of gas would she need to drive 275 miles

Rus_ich [418]

Answer:

9.9 gallons

Step-by-step explanation:

To solve this problem, we need to cross multiply. Lets input the values (250, 275, 9) as shown below:

$\frac{9}{250} = \frac{x}{275}$

Next we cross multiply. We multiply 250 and x, and we multiply 9 and 275.

$250(x) = 250x\\$

$275(9) = 2,475$

Now, lets put the values above back into the equation:

$250x = 2,475$

Lets solve this equation. First we divide 2,475 by 250, making x by itself.

$\frac{2,475}{250} =x$

$9.9 = x$

This means that to drive 275 miles, Kala would need to use 9.9 gallons of gas.

8 0

3 years ago

Which is equivalent to V180x11 after it has been simplified completely?

inna [77]

Question:

Which is equivalent to $\sqrt{180x^{11}}$ after it has been simplified completely?

Answer:

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

Step-by-step explanation:

Given

$\sqrt{180x^{11}}$

Required

Simplify

We start by splitting the square root

$\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}$

Replace 180 with 36 * 5

$\sqrt{180x^{11}} = \sqrt{36 * 5} * \sqrt{x^{11}}$

Further split the square roots

$\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} * \sqrt{x^{11}}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{11}}$

Replace power of x; 11 with 10 + 1

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10 + 1}}$

From laws of indices; $a^{m+n} = a^m * a^n$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x^1}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10} * x}$

Further split the square roots

$\sqrt{180x^{11}} = 6*\sqrt{5} * \sqrt{x^{10}} * \sqrt{x}$

From laws of indices; $\sqrt{a} = a^{\frac{1}{2}}$

So, we have

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{10*\frac{1}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{\frac{10}{2}} * \sqrt{x}$

$\sqrt{180x^{11}} = 6*\sqrt{5} * x^{5} * \sqrt{x}$

Rearrange Expression

$\sqrt{180x^{11}} = 6 * x^{5} * \sqrt{5} * \sqrt{x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}$

From laws of indices; $\sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}$

So, we have

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}$

$\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}$

$\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}$

<em>The expression can no longer be simplified</em>

Hence, $\sqrt{180x^{11}}$ is equivalent to $6x^{5}\sqrt{5x}$

7 0

3 years ago

Read 2 more answers

Solve! Image attached! Geometry, dumb/incorrect answers will get account, and answer reported, please answer all the way through

neonofarm [45]

Answer:

+) m∠1 = m∠2 (vertical angles theorem)

+) m∠2 and ∠3 are supplementary (because a//b)

+)m∠3 = m∠4 (alternate interior angles theorem, c//d)

=> ∠1 and ∠4 are supplementary (substitution property of equality)

Step-by-step explanation:

5 0

3 years ago

Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply. (x + 1) (2x + 1) (x + 2) (5x

andreyandreev [35.5K]

Answer:

(5x-2) and (x+2)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers