Circle equal groups to solve. count the number of items in 1 group.

Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t

WINSTONCH [101]

Answer:

Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

Step-by-step explanation:

Let $v_1$ be the speed and $t_1$ be the time Barbara drives in clear weather, and let $v_2$ be the speed and $t_2$ be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). $v_2 = v_1 -22$

Also,

(2). $v_1t_1 = 45miles$

(3). $v_2 t_2 = 57$ ,

and

(4). $t_1+t_2 = 2.25hr$

From equations (2) and (3) we get:

$t_1 = \dfrac{45}{v_1}$

$t_2 =\dfrac{57}{v_2}$

putting these in equation (4) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25$

and substituting for $v_2$ from equation (1) we get:

$\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25$

This equation can be rewritten as

$2.25v_1^2-151.5v_1+990=0$

which has solutions

$v_1 = 60$

$v_1 = 7.33$

We take the first solution $v_1 =60$ because it gives a positive value for $v_2:$

$v_2 = v_1 -22$

$v_2 = 60 -22\\$

$v_2 = 38$ .

Thus, Barbara's speed in clear weather is $60mph$ and in the thunderstorm is $38mph$ .

4 0

3 years ago

What is one of the solutions to the following system of equations? y2 x2 = 53 y − x = 5 (−10, −5) (−7, −2) (7, 2) (5, 10).

Aliun [14]

The solution of the system of equation is (-7, -2).

<h2>Given</h2>

The system of the equations;

$\rm y^2 + x^2 = 53 \\\\y -x = 5$

From equation 1

$\rm y -x=5\\\\y = 5+x$

Substitute the value of y in equation 1

$\rm y^2+x^2=53\\\\(5+x)^2+x^2=53\\\\25+x^2+10x+x^2=53\\\\2x^2+10x+25-53=0\\\\2 x^2 + 10x - 28 = 0 \\\\Divide \ by \ 2 \ both \ side \ the \ equation\\\\x^2 + 5x - 14 = 0\\\\x^2-7x+2x-14=0\\\\x(x-7) + 2(x-7) =0\\\\(x-7) \ (x+2)=0\\\\x-7=0 \ \ x = 7\\\\x +2 =0 \ \ x=-2$

The value of x= 2 is rejected because x = 2 not satisfy the equation.

Substitute 2 for the value of x in equation II

y − x = 5

y – 2 = 5

y = 5 +2

y = 7 (x =2, y =7) … Not included in the options

If x = -7

Substitute the value of x = -7 in the equation

$\rm y -x=5\\\\y - (-7)=5\\\\y +7= 5\\\\y = 5-7\\\\y = -2$

Hence, the solution of the system of equation is (-7, -2).

To know more about System of Equation click the link given below.

brainly.com/question/1495351

6 0

2 years ago

Eric rented a truck for one day the base fee was 16.95 for additional charge of .76 cents for each mile driven eric had to pay 1

goldenfox [79]

Answer:

178 miles

Step-by-step explanation:

Let Eric has driven d miles.

As the rate of charge of driving the truck = 76 cents /mile

So, the charge of driving the truck for d miles = 76d cents= $0.76d

The base fee of the truck was $16.95.

Total money paid at the time of returning the truck = $152.23

So, 16.95+0.76d=152.23

0.76d= 152.23-16.95=135.28

d=135.28/0.76

d=178

Hence, he drives 178 miles.

8 0

2 years ago

Please help me asap

schepotkina [342]

3.) A *the first one*
4.) C *the last one*

6 0

2 years ago

Read 2 more answers

Peter is wants to lose weight. He is105Kg. His aim is to lose 500 g Per week. If he managed this, how many weeks will it be unti

natali 33 [55]

105 - 90 = 15kg

500g = 1/2 kg

Peter is 15kg overweight.

15 x 2 = 30

It will take him 30 weeks for this.

8 0

3 years ago