8 – 5x = -4............

Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 m

weqwewe [10]

Given Information:

Distance = 160 miles

Required Information:

Rate = r = ?

Answer:

Rate = r = 20 mph

Step-by-step explanation:

Recall that the rate is given by

Rate = distance/time

$r = \frac{d}{t} \\\\t = \frac{d}{r} \\\\t = \frac{160}{r} \\\\$

It is given that the same trip would have taken 2 hours longer if he had decreased his speed by 4 mph.

Mathematically,

$\frac{160}{(r-4)} = \frac{160}{r} + 2 \\\\$

Simplify the equation

$\frac{160}{(r-4)} - \frac{160}{r} = 2 \\\\\frac{160r - 160(r-4)}{r(r-4)} = 2 \\\\\frac{160r - 160r+640)}{r(r-4)} = 2 \\\\160r - 160r+640 = r(r-4) (2) \\\\640 = r(r-4) (2) \\\\640 = (r^2 - 4r) (2) \\\\640 = 2r^2 - 8r \\\\2r^2 - 8r-640 =0 \\\\2(r^2 - 4r-320) =0 \\\\r^2 - 4r-320 =0 \\\\$

Now we are left with a quadratic equation.

We may solve the quadratic equation using the factorization method

$r^2 - 4r-320 =0 \\\\r^2-20r+16r-320=0 \\\\r(r-20)+16(r-20)=0 \\\\(r-20) (r+16)=0 \\\\$

So,

$(r-20) = 0 \\\\r = 20 \\\\$

OR

$(r+16)=0 \\\\r = -16 \\\\$

Since rate cannot be negative, discard the negative value of r

Therefore, the rate is

$r = 20 \: mph$

3 0

4 years ago

Solve for the value of x

Mice21 [21]

Answer:

x = 50°

Step-by-step explanation:

130 and x are adjacent angles on a straight line and sum to 180° , so

x + 130° = 180° ( subtract 130° from both sides )

x = 50°

3 0

2 years ago

Read 2 more answers

The formula for the area of a triangle is A =12bh, in which b represents the length of the base and h represents the height. If

vaieri [72.5K]

Answer:

Step-by-step explanation:

Write it out: A = 1/2(bh)

substitute values: 232 = 1/2(16b)

Simplify: 232 = 8b

Divide each side by 8: b = 29

The base is 29 millimeters

5 0

3 years ago

Given P space equals space P subscript 0 space plus space rho g h, your objective is to determine the uncertainty of P by measur

son4ous [18]

Answer:

the g's contributing term for the overall uncertainty of P is $dP_g = [\frac{dg}{g}]$

Step-by-step explanation:

From the question we are told that

The pressure is $P = P_o + \rho gh$

The first step in determining the uncertainty of P in by obtaining the terms in the equation contributing to it uncertainty and to do that we take the Ln of both sides of the equation

$ln P = lnP_o + ln(\rho gh )$

=> $ln P = lnP_o + ln \rho + ln g + ln h$

Then the next step is to differentiate both sides of the equation

$\frac{d(ln P)}{dP} = \frac{d(ln P_o)}{dP_o} + \frac{d(ln \rho)}{d\rho} +\frac{d(ln g)}{dg} + \frac{d(ln h)}{dh}$

=> $\frac{dP}{P} = \frac{dP_o}{P_o} + \frac{d \rho}{\rho} +\frac{d g}{g} + \frac{d h}{h}$

We asked to obtain the contribution of the term g to the uncertainty of P

This can deduced from the above equation as

$dP_g = [\frac{dg}{g}] P$

8 0

4 years ago

Solve the inequality. Graph your solution. $$ - 5.3 x > 21 |

kobusy [5.1K]

The solution to the inequality - 5.3 + x > 21 is x > 26.3

In mathematics, inequality refers to a relation which makes a non-equal comparison between two numbers or other mathematical expressions. In other words, it is a relationship between two expressions or values that are not equal to each other. It is used generally used to compare two numbers on the number line by their size.

In order to solve the given inequality - 5.3 + x > 21, add 5.3 both sides.

- 5.3 + x + 5.3 > 21 + 5.3

x > 26.3

The solution means that the value of x is greater than 26.3. The solution is graphed on a number line.

Learn more about Inequality:

brainly.com/question/25275758

#SPJ4

4 0

1 year ago

8 – 5x = -4............​

8 – 5x = -4............