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3 years ago

Question 5 of 13, Step 1 of 1

Mathematics

1 answer:

Georgia [21]3 years ago

6 0

Answer:

It will take Mrs Chandler 18 hours 45 minutes or 18.75 hours to catch up Mr Chandler

Step-by-step explanation:

What we want to know here is that at how many hours will they have traveled same distance.

Let the total time taken by Mrs Chandler to catch up be x hours

Since Mr Chandler left 2.5 hours earlier , then the total time taken by him would be x + 2.5 hours

Now, we know that distance = speed * time

Since it’s same distance covered;

For Mr Chandler, his distance is calculated as 75(x + 2.5)

For Mrs Chandler, her distance is calculated as 85x

We equate both since they are equal;

75(x + 2.5) = 85x

75x + 187.5 = 85x

85x -75x = 187.5

10x = 187.5

x = 18.75 hours or 18 hours 45 minutes

You might be interested in

What is the value of the expression 6 3/4 (−11.5)

notka56 [123]

Answer:

-75.9

Step-by-step explanation:

5 0

3 years ago

The Washington Monument in Washington, D.C., is about 556 ft. tall. A three-dimensional puzzle of the Washington Monument is 24

Umnica [9.8K]

Set up a ratio. But first convert the height of the puzzle to feet so we are comparing the same unit of measure.

STEP 1
convert 24 inches to feet

12 inches= 1 foot

24 inches= 2 feet

STEP 2
set up ratio.

= 2 feet/556 feet or 2:556
simplify both by 2

= 1 ft/278 ft or 1:278

ANSWER: 1/278 or 1:278 (can be written either way)

Hope this helps! :)

8 0

3 years ago

A bookstore had 90 copies of a magazine. Yesterday, it sold 1/6 of them. Today, it sold 1/5 of what remained. How many copies do

MA_775_DIABLO [31]

Answer:

60 copies

Step-by-step explanation:

first you take 1/6th of the original 90 copies which is 15 and subtract that from the 90, you are left with 75 copies which is how many they had left at the end of yesterday. then you take 1/5th of the 75 copies that are left which is also 15 and you subtract that from 75 and you get 60. that's why at the end of today there are 60 copies left.

6 0

3 years ago

List all possible rational roots. Then use synthetic division to confirm which rational roots exist:

Kisachek [45]

Answer:

$\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}$

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

$\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}$

In your function, the constant term is -10 and the leading coefficient is 2, so

$\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}$

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

$\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}$

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

$\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}$

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

6 0

3 years ago

Jack earns $40 in interest each year on an investment. What is his interest rate if his principal was $200

Fudgin [204]

Answer:

The interest rate is 20%.

Step-by-step explanation:

In order to calculate the interest rate, we need to compute how many percents the value he recieves is related to the total he invested. In this case he recieves 40 every year and he invested 200, to calculate that we will apply a rule of three. We have:

$200 -> 100%

$40 -> x%

200/40 = 100/x

200*x = 40*100

200*x = 4000

x = 4000/200 = 20

The interest rate is 20%.

8 0

2 years ago