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Angelina_Jolie [31]
3 years ago
11

What is the slope of a line that is parallel to the line represented by the equation y=7/6x+4

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
4 0
7/6
The slope of the equation in the form y=Mx+c is m
Parallel lines have Same gradient
Which makes gradient 7/6


Please mark as brainliest
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A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses
mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for x days.

So, for x days the total expense = $360

<em>Thus the daily expense in dollars can be given by</em> = \frac{360}{x}

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

<em>Tour duration now</em> = (x+4) days

On extension, his daily expense is cut by $3

<em>New daily expense in dollars </em>= (\frac{360}{x}-3)

Total expense in dollars can now be given as:  (x+4)(\frac{360}{x}-3)

Simplifying by using distribution (FOIL).

(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))

360-3x+\frac{1440}{x}-12

348-3x+\frac{1440}{x}

We know total expense remains the same which is = $360.

So, we have the equation as:

348-3x+\frac{1440}{x}=360

Multiplying each term with x to remove fractions.

348x-3x^2+1440=360x

Subtracting 348x both sides

348x-348x-3x^2+1440=360x-348x

-3x^2+1440=12x

Dividing each term with -3.

\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}

x^2-480=-4x

Adding 4x both sides.

x^2+4x-480=-4x+4x

x^2+4x-480=0

Solving using quadratic formula.

For a quadratic equation: ax^2+bx+c=0

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Plugging in values from the equation we got.

x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}

x=\frac{-4\pm\sqrt{16+1920}}{2}

x=\frac{-4\pm\sqrt{1936}}{2}

x=\frac{-4\pm44}{2}

So, we have

x=\frac{-4+44}{2}   and x=\frac{-4-44}{2}

x=\frac{40}{2}   and x=\frac{-48}{2}

∴ x=20           and x=-24

Since number of days cannot be negative, so we take x=20 as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0
3 years ago
Help math question derivative!
atroni [7]
Let f(x)=\sec^{-1}x. Then \sec f(x)=x, and differentiating both sides with respect to x gives

(\sec f(x))'=\sec f(x)\tan f(x)\,f'(x)=1
f'(x)=\dfrac1{\sec f(x)\tan f(x)}

Now, when x=\sqrt2, you get

(\sec^{-1})'(\sqrt2)=f'(\sqrt2)=\dfrac1{\sec\left(\sec^{-1}\sqrt2\right)\tan\left(\sec^{-1}\sqrt2\right)}

You have \sec^{-1}\sqrt2=\dfrac\pi4, so \sec\left(\sec^{-1}\sqrt2\right)=\sqrt2 and \tan\left(\sec^{-1}\sqrt2\right)=1. So (\sec^{-1})'(\sqrt2)=\dfrac1{\sqrt2\times1}=\dfrac1{\sqrt2}
5 0
3 years ago
What is the value of the expression below?<br> (3 x 4) - 6] + 4 x 2
Olegator [25]
14 is your answer :)
8 0
2 years ago
5. You are making your Halloween costume this year. You have 6 yards of fabric and the pattern says that you need to cut it in t
REY [17]

Answer:

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

Step-by-step explanation:

Total yards of fabrics = 6 yards

you need to cut it in two pieces where one is two feet longer than the other.

First piece= x feet

Second piece= x+2 feet

Convert 6 yards to feet

6 yards = 18 feet

First piece + second piece = total piece of fabrics

x + (x+2) = 18

x + x + 2 = 18

2x + 2 = 18

2x = 18 - 2

2x = 16

Divide both sides by 2

x = 16 / 2

x = 8 feet

8 feet = 2.66667 yards

x + 2

= 8 + 2

= 10 feet

10 feet = 3.33333 yards

The shorter side piece of fabric = x = 8 feet

The longer side piece of fabrics = (x + 2) = 10 feet

7 0
3 years ago
Find the measure of 4
schepotkina [342]

Answer:

147º

Step-by-step explanation:

180-33=147

5 0
3 years ago
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