two students are running on a circular path. it takes the first student 25 minutes to complete one lap, and it takes the second student 30 minutes to complete one lap. if they both start at the same time and run in the same direction, when will they meet each other at the starting point? 175 minutes 150 minutes 25 minutes 5 minutes

Answer:

y = - 2x² + 8x + 5

Step-by-step explanation:

the equation of a quadratic function in standard form is

y = ax² + bx + c ( a ≠ 0 )

to find a, b and c use ordered pairs from the table

(0, 5 )

5 = a(0)² + b(0) + c = 0 + 0 + c = 5 ⇒ c = 5 , then

y = ax² + bx + 5

(1, 11 )

11 = a(1)² + b(1) + 5 = a + b + 5 ( subtract 5 from both sides )

a + b = 6 → (1)

(2, 13 )

13 = a(2)² + b(2) + 5 = 4a + 2b + 5 ( subtract 5 from both sides )

4a + 2b = 8 → (2)

solve the 2 equations simultaneously to find a and b

multiplying (1) by - 2 and adding to (2) will eliminate b

- 2a - 2b = - 12 → (3)

add (2) and (3) term by term to eliminate b

2a + 0 = - 4

2a = - 4 ( divide both sides by 2 )

a = - 2

substitute a = - 2 into (1) and solve for b

- 2 + b = 6 ( add 2 to both sides )

b = 8

then a = - 2, b = 8 and c = 5 gives the standard quadratic function

y = - 2x² + 8x + 5

Step-by-step explanation:

standard equation would be

y = ax² + bx + c

out of that we know already from (0, 5) that c = 5, as

a×0² + b×0 + c = 5.

because of (-1, -5) we see

-5 = a×1 + b×-1 + 5 = a - b + 5

-10 = a - b

or

a = b - 10

because of (1, 11) we see

11 = a×1 + b×1 + 5 = a + b + 5

6 = a + b

now we use the previous equation :

6 = (b - 10) + b = 2b - 10

16 = 2b

b = 8

.

a = b - 10 = 8 - 10 = -2

so, our standard equation is

y = -2x² + 8x + 5

Answer:

Sally is 12 years old.

Step-by-step explanation:

[tex]2x+3=27\\2x+3-3=27-3\\2x=24\\\frac{2x}{2}=\frac{24}{2}\\x=12[/tex]

Answer:

1. 15.17ft          2. 18.57ft           3. 22.41%

Step-by-step explanation:

1. What was the length of one side of the garage originally?

Area of a square = s × s which is also equal to s²

s means one side of the square, as it is a square, all sides are equal.

so

230 = s²

s = √230 = 15.17

2. What is the length of one side of the garage now?

The original area of the garage was 230ft²

But now, the area has increased by 50%

Increased Area = 230 × 50% = 115ft²

Total Area = 230 + 115 = 345ft²

In the question, they are saying that after the area is increased, the garage is still a square which means that the side lengths have equal values.

Area = s²

345 = s²

s = √345 = 18.57

3. What was the percentage increase of the length of one side?

  Length : Percentage

    15.17   :      100

   18.57   :         x

When the length of one side was 15.17, the percentage was 100% as that is what the original length was, we can use ratio and proportion to find what the percentage will be when the length is 18.57.

Now cross multiply

18.57 × 100 = 15.17x

1857 = 15.17x

1857/15.17 = x

x = 122. 41

The new percentage is 122.41%

The difference between both percentages is:

122.41 - 100 = 22.41

And 22.41 is the percentage increase.

Answer:

h(-6) = 1

Step-by-step explanation:

Hello!

Substitute -6 for x in the equation.

h(-6) is 1.

Answer:

Ama is an elephant so she is 2 years old

Step-by-step explanation:

Answer:

baby help you with what? All i can do is pray for you,

Step-by-step explanation:

matter of fact bow yo head..............Amen

Answer:

19

Step-by-step explanation:

5w+3°=98°

5w=98°-3°

5w=95°

therefore w=95/5=19

one on right is 2,-2 and one on left is -1,1

Answer:

The absolute value inequality will be |x| ≥ -2.

Step-by-step explanation:

The solution of the given equation are (1/2 , 17/2) and (-3 , 12)

The two equation that we have been given are :

    y = 9 – x            (1)

    y = 2x² + 4x + 6       (2)

We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get

       9 – x = 2x² + 4x + 6

        3 = 2x² + 5x

2x² + 5x – 3 = 0

Now to find the factors of the value x we will use quadratic formula.

   x = (-b±√b² – 4ac)/2a

   x = [ -5 ± √25 + 24 ]/4

   x = [ -5 ± 7 ]/4

x = (-5 + 7)/4              and                 x = (-5 – 7)/4

x = 1/2     and    x= -3

putting the required value of x in equation (1) we get

y = 9 – 1/2            and             y = 9 – (-3)

y = 17/2      and    y = 12

Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)

Learn more about equation here : https://brainly.com/question/22688504

#SPJ9  

Answer: a, 9x10^9, largest number 900000000

Answer: greatest is A.

Step-by-step explanation:

The value of x from the given diagram is 64 degrees

A line is defined as the shortest distance between two points. From the given diagram, we have that the line AB bisects FAB, hence;

<FAB = <CAB = 58 degrees

Also since the sum of angles on a straight line is 180 degrees, hence;

58 + 58 + x = 180

116 + x = 180

x = 180 - 116

x = 64 degrees

Hence the value of x from the given diagram is 64 degrees

Learn more on line and angles here: https://brainly.com/question/16810065

#SPJ1

Based on the length of the subway sandwich, the length of the larger pieces is 11 feet.

Assume that the length of the shorter pieces is x.

The length of the larger pieces is therefore 5 + x.

The relevant equation to find the length is:

52 = x + x + x + x +x + 5 + x + 5 + x

52 = 7x + 10

x = (52 - 10) / 7

= 6 foot

The length of the larger pieces is:

= 5 + x

= 5 + 6

= 11 foot

Find out more on solving for length at https://brainly.com/question/10703621

#SPJ1

Answer: Left 10 Units

Step-by-step explanation: hope this helps

In step 1 mistake has been made because negative multiplication gives a positive result but is written negative.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given that,

−4(6−y) + 4 = −4

By using distribution property

-24 + 4y + 4 = -4

But in the question +4y is written as -4y which is wrong.

Hence In step 1 negative multiplication gives a positive result but is written negative so in step 1 mistake has been made".

To learn more about an equation from the given link:

https://brainly.com/question/15332858

#SPJ4

The given question is not complete.

Consider this solution to a problem.

Problem: −4(6−y)+4=−4

Step 1: −24−4y+4=−4

Step 2: −20−4y=−4

Step 3: −4y=16

Step 4: y=−4

In the first response box, enter the number of the step where the mistake is made.

The value of the underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.

As given in the question,

Given number = 2.439 , 1.987 ,  6.175 , and 0.618

Value of underlined digit :

2.439 = Tenth or 4 / 10

1.987 = Thousandth or 7/1000

6.175 = Ones or 6

0.618 = Hundredth or 1/100

Therefore, the value of the underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 is equal to tenth, thousandth, Ones and tenth.

The complete question is :

How do i write the value of this underlined digit 2.439 , 1.987 ,  6.175 , and 0.618 ?

Learn more about digit here

brainly.com/question/10913044

#SPJ4

7) No, y has two different values when x = -1.

8) Yes, each value of x maps onto only one value of y.

9) Yes, each value of x maps onto only one value of y.

Given x is Complimentary angle

Also, line1 is parallel to line2

Thus,
x [tex]+[/tex]  139° [tex]=[/tex] 132° [Alternate angle]

x [tex]=[/tex] 132°[tex]_[/tex][tex]_[/tex]- 139°

x[tex]=[/tex] -7°

What is Complimentary angle?

When two angles are added together, complementary angles are defined. When the total of the two angles is 90 degrees, we get a pair of complimentary angles. In other terms, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complimentary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the illustration below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

Leran more about complimentary angles https://brainly.com/question/14368155

#SPJ9

The like terms are -xy, 1/2xy and 2xy

Like terms are expressions that have the same variable factor

Take for instance, 2x and 5x are like terms because their variable factors are x

Also, 5x and 2xy are not like terms

Using the above as a guide, the like terms are -xy, 1/2xy and 2xy

Read more about like terms at:

https://brainly.com/question/11361920

#SPJ!

The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

Slope of the line:

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given,

The point (9,10) that cuts off the least area from the first quadrant

Here we need to find the slope and y intercept of the line.

A line is passing through a point (9,10) cuts off least area in first quadrant.

The equation of the line passing through point (9,10) and has slope m can be expressed as,

=> y - 10 = m (x - 9)

=> y = m(x - 9) + 10

=> y - mx = - 9m + 10

Divide the terms by - 9m + 10, then we get,

=> (y/- 9m+10) - (mx/ - 9m+10) = 1

=> (mx/9m+10) - (y/9m+10) = 1

It can be rewritten as,

[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]

We know that,

The equation of straight line in intercept form is

=> x/a + y/b = 1

So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:

a = 9m-10/m

b =  10 - 9m

The area of the triangle made by the line in first quadrant can be expressed as,

=> A = 1/2 x (9m-10/m) x (10 - 9m)

=> A = -1/2 (9m-10)²/m-----------------------(1)

Differentiate the equation (1) with respect to m.

[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]

when we simplify it,

=> dA/dm = -(9m-10)/2m² [9m-10]

Let dA/dm = 0, then

=> 0 = -1/2m² (9m-10)(9m-10)

=> 0 = 1/m² (10-9m)(9m-10)

=> 0 = (10 - 9m) (9m -10)

Therefore, the value of m is,

=> 10 - 9m = 0

=> -9m = -10

=> m = 10/9

And

=> 9m - 10 =0

=> 9m = 10

=> m = 10/9

The line will be in first quadrant and forms a triangle with axes if the slope is negative.

Substitute m = -10/9

Then, b = 10-9m

Then,

=> y = 10 - 6(-10/9)

=> y = 10 + 20/3

=> y = 50/3

So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

To know more about Slope of the Line here.

https://brainly.com/question/14511992

#SPJ4

The greatest angle in the given triangle is 104 degrees.

Given:

So,

As a result, the second angle has a measurement of 26 degrees.

The first angle's measurement is now 24 degrees greater than the second angle's measurement.

Now,

As a result, the first angle has a measure of 50 degrees.

The third angle is now four times the size of the second angle.

So,

Therefore, the greatest angle in the given triangle is 104 degrees.

Know more about triangles here:

https://brainly.com/question/17335144

#SPJ4

Answer:

240 miles

Step-by-step explanation:

Because it took 5 hours going 48 miles per hour, therefore 5 x 48 =240

Answer:

Step-by-step explanation:

See the attached file below it will help to understand this problem and it will improve your grade and score.

Answer:

B

Step-by-step explanation:

5x + 4y >= 2

4y >= -5x + 2

y >= -5/4x + 1/2

Since the equation is >=, everything on or above the line y = -5/4x + 1/2 should be shaded.

The equation can be summarized as; p = $50 + 3($100 ). Hence William was paid $350.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

Let p represents the paycheck.

William  paid her parents $50 for rent. After paying the rent he evenly divided the rest of the amount into three parts.

He puts $ 100 into her savings account. It means that he also puts $100 into checking account and $ 100 into retirement fund

If we put the parts together, the equation we get is;

p = $50 +$100 +$100 +$100

The equation can be summarized as;

p = $50 + 3($100 )

Now we can easily find how much was William  paid;

p = $50 + 3($100)

p = $50 +$300

p = $350

Hence William was paid $350.

Learn more about linear equations;

https://brainly.com/question/10413253

#SPJ4

Answer:

Option a 340 cm²

Area= bxh

20x17=340 cm²

If the boy is riding a bicycle and gets stuck or got accident by a car, 440ml of IV fluid will be administered.

To avoid further injury, place the victim on the ground very gently and slowly without handling vigorously. In one direction, tilt the sufferer. Dress loosely around the waist, chest, and neck. So that the tongue can fall forward and allow blood and vomit to drain out, tilt your head back and slightly downward. When you come across an accident victim, the first thing you need to determine is whether the victim's body has sustained any physical wounds. Depending on how severe the collision was, you might not be able to see any inside injuries, but you will see a few exterior ones.

In a car accident, spine injuries and head trauma are common. Therefore, be aware that rough handling of the sufferer will result in additional injuries while opting to assist the victim in moving to a safer location on the road. Therefore, request any onlookers to carefully assist in moving the sufferer to a location near the road where it will be safer.

To learn more about accident, click here:

https://brainly.com/question/1235714

#SPJ4

Answer:

====================

Total number of outcomes is 16, count of all outcomes.

Number of outcomes with 3 or more tiles is 5:

The probability is:

Correct choice is D.