At 10:00 a.m., two boys start out on their bikes to meet each other from towns located
68 miles apart. They meet at 1:00 p.m. If one boy traveled 3 miles per hour faster than
the other, what was the speed of each boy?

sjdffdghddffffdbdbbfbdhdbdbfbd

The sum of ages of P & Q before 4 years is 42 years.

Let present age of P is 4x years and the present age of Q is 6x years.

According to the problem, the sum of the present ages of P and Q is 50 years, so we have:

4x + 6x = 50

10x = 50

then, x = 5

So the present age of P is 4 * 5 = 20 years and the present age of Q is 6 * 5 = 30 years.

To find the sum of their ages before 4 years, we subtract 4 from each of their present ages:

20 - 4 = 16 years (for P)

30 - 4 = 26 years (for Q)

hence, sum of their ages before 4 years is 16 + 26 = 42 years.

Learn more about ratio:

https://brainly.in/question/14982256

The graph of the given quadratic function, y = -0.5(x + 5)(x - 3), is shown below

From the question, we are to draw the graph of the given quadratic function.

The given quadratic function is

y = -0.5(x + 5)(x - 3)

To plot the graph of the given quadratic function, we will determine the value pairs that satisfy the equation

When x = -5

y = -0.5(-5 + 5)(-5 - 3)

y = -0.5(0)(-8)

y = 0

When x = -2

y = -0.5(-2 + 5)(-2 - 3)

y = -0.5(3)(-5)

y = 7.5

When x = 0

y = -0.5(0 + 5)(0 - 3)

y = -0.5(5)(-3)

y = 7.5

When x = 2

y = -0.5(2 + 5)(2 - 3)

y = -0.5(7)(-1)

y = 3.5

When x = 3

y = -0.5(3 + 5)(3 - 3)

y = -0.5(8)(0)

y = 0

When x = -5

y = -0.5(5 + 5)(5 - 3)

y = -0.5(10)(2)

y = -10

Using the value pairs above, the graph of the given function is shown below

Learn more on Graph of Quadratic function here: https://brainly.com/question/14477557

#SPJ1

The function f(8)=4 defines that it will take x/2 hrs to complete the work and "x being No of workers".

The given data is as follows:

There are x people working in the crew at the racetrack, it takes f(x) hrs to get the track ready.

Let us assume that there is x worker at the racetrack,

f(x) is the function that is going to define the working hours required to get the track ready,

The function will depend on workers as it is mentioned as "f(x)".

Now,

function f(x)=?

But given that f(8)=4

It means when  x=8 that means when are there 8 workers working at the racetrack and it took  4 hours to complete the work.

Now,

we have written a function that gives the relation between a given worker as 8 and time as 4 hrs.

so 8 workers complete work in 4 hrs,

then x worker will complete in y hrs i.e.f(x).

=4x=8*f(x)

=4x/8

=x/2.

Hence the function will be f(x)=x/2

To learn more about functions problems,

https://brainly.com/question/12108704

#SPJ4

The complete question is -

max works as a groundskeeper at a racetrack, where he is part of a bigger crew. when x people are working on the crew, it takes them f(x) hours to get the track ready for a day of racing. what does f(8)=4 tells us?

The probability of a female student studying abroad is 9.5%. 60% of those who study abroad are female, while 49% of those who do not study abroad are female.

P(Female studying abroad) = P(Female and Studying Abroad) / P(Female)

P(Female and Studying Abroad) = 0.095 × 0.60 = 0.057

P(Female) = 0.095 × 0.60 + 0.905 × 0.49 = 0.902

P(Female studying abroad) = 0.057 / 0.902 = 0.063

Therefore, the probability of a female student studying abroad is 0.063.

The probability of a female student studying abroad is 9.5%. This means that out of all the undergraduate students, 9.5% of them are female and are studying abroad. It is also important to note that out of those who study abroad, 60% are female, while 49% of those who do not study abroad are female. This means that more female students are likely to study abroad than male students, as the percentage of female students studying abroad is higher than the percentage of male students studying abroad. It is also important to note that the overall percentage of female students studying abroad is lower than the overall percentage of male students studying abroad, as the number of female students who study abroad is lower than the number of male students who study abroad. Therefore, the probability of a female student studying abroad is 9.5%.

Learn more about probability here

https://brainly.com/question/11234923

#SPJ4

Step-by-step explanation:

To find the velocity of the particle, we need to take the derivative of the position vector with respect to time.

r(θ) = (a + b * cos(θ)) * i + (b * sin(θ)) * j

d/dt[r(θ)] = d/dt[(a + b * cos(θ)) * i + (b * sin(θ)) * j]

d/dt[r(θ)] = (-b * sin(θ)) * i + (b * cos(θ)) * j

So, the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

Answer:

Step-by-step explanation:

the velocity of the particle at a given value of θ is:

v(θ) = (-b * sin(θ)) * i + (b * cos(θ)) * j.

he value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

According to the trigonometry identity

tan Ф = opposite/adjacent

sin Ф = opposite/hypotenuse

cos Ф = adjacent/hypotenuse

From the given triangle;

AC = 7

AB = 17

BC = 4√15

Determine the following trigonometry given

cos B = BC/AB

cos B = 4√15/17

sinB = AC/AB

sin B = 7/17

sinA = cos B = 4√15/17

tan B = AC/BC

tan B = 7/4√15

tan A = BC/AC

tan A = 4√15/7

The value of the expression cosB, sinB, sinA, tanB, tan A 4√15/17, 7/17, 4√15/17, 7/4√15 and 4√15/7

Learn more on trigonometry identity here: https://brainly.com/question/20094605

#SPJ1

The factored form of the polynomial is x³( x + 2 ) - 1 ( 2x + 1 ).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given that the polynomial is (x⁴)+(2x³)-2x-1. The expression will be factorized as below:-

E =  (x⁴)+(2x³)-2x-1.

E = x² ( x² + 2 ) -1 ( 2x + 1 )

Hence, the factorized form of the polynomial is x² ( x² + 2 ) -1 ( 2x + 1 ).

To know more about polynomials follow

https://brainly.com/question/26147255

#SPJ1

Answer:

69.

im not kidding, haha, good luck!

The boy can wear 720 different outfits to school if he must wear one of each item, we need to find the number of combinations of one pair of pants, one shirt, one tie, and one jacket. The number of different combinations of pants he can wear is 8.

The number of different combinations of shirts he can wear is 5.

The number of different combinations of ties he can wear is 3.

The number of different combinations of jackets he can wear is 6.

To find the total number of different outfits, we multiply the number of combinations of each item:

8 * 5 * 3 * 6 = 8 * 90 = 720

To know more about Combinations

https://brainly.com/question/28065038

#SPJ4

When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

Any points on a parabola is situated at a equal distance from both focus, a fixed point, and the hardware platform, a fixed vertical line. A parabola is a U-shaped plane curve.  Three different parabolas exist. Vertex form, leading to the formation, and intercept form seem to be the three forms. You can access a unique major element for the graph on each submission. There are two different methods to write a parabola's calculation: Form 1: y=a(x-h)2 + k. Form 2 is as wants to follow: x = a(y - k)2 + h.

given

( x-3)^2 > 0 , so -1/20(x-3)^2 < 0

when x>3 , it is decrease , when x<3 it is increase so the equation of the directrix is x =3

When the parabola y = -1/20(x-3)2 + 6 has a focus of (3,1), the directrix equation is x=3.

To know more about parabola visit :-

https://brainly.com/question/4074088

#SPJ1

The number of cakes (x) and cookies (y) are 15 and 60 respectively.

Given the system of equation in the question;

To solve for x and y, plug y = 4x into the first equation and solve for x.

x + y = 75

Plug in y = 4x

x + 4x = 75

5x = 75

Divide both sides by 5

5x/5 = 75/5

x = 75/5

x = 15

Now, plug x = 15 into the second equation and solve for y.

y = 4x

Plug in x = 15

y = 4( 15 )

y = 60.

Therefore, the value of x and y are 15 and 60 respectively.

Learn more about simultaneous equation here: https://brainly.com/question/16763389

#SPJ1

Answer: 12

Step-by-step explanation: by the end of 12 weeks shell have 200 dollars left

An old book was bought for Rs 1520 and sold for Rs 1444. The loss percent is 5.263%

Given,

Cost price = 1520

Selling price = 1444

Loss = C.P - S.P

        = 1520 - 1444

        = 76

Now, percentage of loss = [tex]\frac{Loss}{C.P}[/tex] × 100

                                         = [tex]\frac{76}{1444}[/tex] × 100

                                         = 5.263

Hence, the loss percent is 5.263%  

Learn more about book

https://brainly.com/question/13997839

Answer:

Step-by-step explanation:

To solve for x in the equation 3x + 2 = 11, we'll start by subtracting 2 from both sides:

3x + 2 - 2 = 11 - 2

Simplifying the left-hand side:

3x = 9

Finally, divide both sides of the equation by 3 to find x:

(3x) / 3 = 9 / 3

x = 3

The situations when you might want to estimate the answer to a division problem are listed below.

There are several situations when you might want to estimate the answer to a division problem:

Large numbers: When dividing large numbers, estimation can be quicker and provide a close enough answer.

Complex decimals: Estimating can help when the answer is a complex decimal and you only need a rough idea.

Time constraints: When you're short on time and need a quick answer, estimation can be useful.

Cost calculations: In budgeting or finance, you may need to estimate the cost of an item, which can be done by dividing the total cost by the number of items.

Determining proportions: In many real-world scenarios, you may need to determine the proportion of a certain characteristic, which involves dividing the number of occurrences of that characteristic by the total number of observations.

Quick analysis: In some cases, you might want a quick and rough estimate of the answer to a division problem to see if it falls within a certain range.

Learn more about estimation on:

https://brainly.com/question/107747

#SPJ1

Answer:

see below

Step-by-step explanation:

enter the values of -1 & -2 into the equation

so you'll get 2 equations for 2 variables: m & n

when x = -1

1-(m-2)*(-1)-3+n=0 ==> 1+m-2-3+n =0 so m+n=5

when x = -2

4-(m-2)*(-2)-3+n=0 ==> 4+2m-4-3+n =0 so 2m+n=3

use equation 2 subtract equation 1

2m=-2, so m = -1

n= 6

Answer:

Step-by-step explanation:

Given roots of x² -(m -2)x -(3 -n) = 0 are -1 and -2, you want the values of m and n.

Given roots -1 and -2 for a quadratic equation, we know its factored form is ...

  (x -(-1))(x -(-2)) = 0

  (x +1)(x +2) = 0

Then the standard form is ...

  x² +3x +2 = 0

Comparing this to the given equation, we find ...

  -(m-2) = 3   ⇒   m = -1

  -(3 -n) = 2   ⇒   n = 5

Use the rules of exponents to divide variables with the same base when dividing monomials. According to this rule, the base should remain in the position (numerator or denominator) where the greater exponent was when dividing variables with the same base after the exponents have been subtracted.

In order to divide a polynomial by a monomial, let's first divide a monomial by another monomial. The monomial should be divided into numerical and variable factors. By deducting the exponents of each y term, divide the coefficients and variables.

Let's go over the three steps that must be completed in order to divide a polynomial by a monomial. Rewrite the issue and divide each polynomial term by the monomial as a first step. Dividing the numbers is the next step. Divide the variables is the third and last stage.

To know more about exponents visit:-

brainly.com/question/5497425

#SPJ1

Volume= l*b*h

=7*5*3

=105 cubic inches

Answer: 5<x

Step-by-step explanation:

Answer: x>5

Isolate the variable

Answer:

x=5

Step-by-step explanation:

distribute: 6x-12=4x-2

subtract 4x and add 12 on both sides: 2x=10

Answer:

a) The measure of the angle created by the car's turning would be 75°. This is because 4th Street is parallel to 3rd Street, thus the angle formed when the car turns onto King Avenue heading northeast would be a 90° angle, which is the same as the angle between 4th Street and 3rd Street.

b) The measure of the angle created by the car's turning would be 180°. This is because when the car is traveling southwest on King Avenue and turns left onto 3rd Street, it is essentially making a full turn to face the opposite direction.

c) The measure of the angle created by the car's turning would be 90°. This is because when the car is traveling northeast on King Avenue and turns right onto 3rd Street, it is essentially making a right angle turn as it transitions from one street to the other.

The value of 'd' in the expression 2-16 = 12d is 168.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 2016 = 12d.

Now, To solve for 'd' we have to move the coefficient of 'd' to the other side also it will sit on the denominator now.

Therefore, 2016 = 12d.

2016/12= d.

d = 168.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ1

Converting the value from meters/second to kilometers/hour is 105 m/s =378 km/h

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used

We have to convert the meters per second into kilometers per hour.

1m /sec = (1/1000)/ (1/3600) km/h = 3600/1000 km /h

So, we have to divide 105 by 1000, and multiply it by 3600.

Mathematically speaking

Hence, converting One kilometer is equal to 1,000 meters, and 1 hour is equal to 3,600 seconds is 378 km/h

Learn more about conversion at:https://brainly.com/question/97386

#SPJ1

Answer:0.625

Step-by-step explanation:

Answer:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Step-by-step explanation:

1) -11/180

2) 52/15

3) -43/72

4) 347/70

5) 11/12

6) 75/8

Explanation: You can simplify the numbers to smaller numbers and make the denominator the same, or else just use a calculator.