Darius was walking from one class to the other during the passing period when he realized his shoes were untied. He stopped to tie his shoes and then glanced at the clock. The clock read 11:52 AM. He had to get to his classroom by 11:55 or he would be counted tardy to class. His class is 30 feet away. How fast will Darius have to move to make it to class on time?

The distance between the points where the points are given as [tex](5\frac 78, -\frac 12)[/tex] and [tex](9\frac 34, -\frac 12)[/tex] is 3.875 units

The points are given as

[tex](5\frac 78, -\frac 12)[/tex] and [tex](9\frac 34, -\frac 12)[/tex]

The distance between the points is calculated as

d  = √(x₁ - x₂)² + (y₁ - y₂)²

Where x and y are the coordinate points and d is the distance

Substitute the known values in the above equation

So, we have

[tex]d = \sqrt{(5\frac 78 - 9\frac 34)\² + (-1/2 + 1/2)\²[/tex]

Evaluate the sum in the above equation

So, we have

[tex]d = \sqrt{(5\frac 78 - 9\frac 34)\²[/tex]

Evaluate the exponents in the above equation

So, we have

[tex]d = (-5\frac 78 + 9\frac 34)[/tex]

Evaluate the difference  in the above equation

So, we have

d  = 3.875

Hence, the distance between the points is 3.875 units

Read more about distance at

brainly.com/question/7243416

#SPJ1

Since the lines a and b are parallel, the corresponding angles <1 and <5 are congruent, therefore angle <5 measures 80°.

Angles <6 and <7 are supplementary angles to angle <5, so we have:

So the sum of <6 and <7 is:

Therefore the answer is 200.

The value of cos (A - B) will be 33/65.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The values are;

cos A = 24/25

And, sin B = 63/65

Now,

cos (A - B) = cos A cos B + sin A sin B

Since, cos A = 24/25

So, sin A = 7/25

And, sin B = 63/65

So, cos B = 16/65

Substitute all the values, we get;

cos (A - B) = cos A cos B + sin A sin B

               = 24/25 x 16/65 + 7/25 x 63/65

              = 384/1625 + 441 / 1625

              = 825 / 1625

              = 33/65

Thus, The value of cos (A - B) will be 33/65.

Learn more about the mathematical expression visit:

https://brainly.com/question/1859113

#SPJ1

The number of cheeseburgers sold was three times the number of hamburgers sold then 79 hamburgers and 237 cheeseburgers were sold on Sunday.

Let h be the number of hamburgers

c be the number of cheeseburgers

A local hamburger shop sold a combined total of 316 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.  

h + c = 316

c = 3h

h + 3h = 316

simplifying the above equation, we get

⇒ 4h = 316

Dividing both sides of the equation by 4, we get

⇒ 4h / 4 = 316 / 4

⇒ h = 79

Therefore, hamburgers were sold on Saturday is 79.

The number of cheeseburgers sold was three times the number of hamburgers sold then

c = 3h

substitute the value of h in the above equation, we get

⇒ c = 237

Therefore, 79 hamburgers and 237 cheeseburgers were sold on Sunday.

To learn more about equations refer to:

https://brainly.com/question/22688504

#SPJ9

Out of 30 students, the probability of one student winning the top prize is 1/30.

Since the student who won the top prize cannot be the student who wins the second prize, then the probability of a student winning the second prize is 1/29.

So, the probability that you will win the top prize and your best friend wins the second prize is:

Answer:

The probability that you will win the top prize and your best friend wins the second prize is 1/870.

In decimal form, this is 0.001149.

In percent form, this is approximately 0.11%.

the length of th diagonal is 10√2

side length = 10 inches

We need an illustration to solve the question:

Using pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = diagonal

opposite = 10 in, adjacent = 10 in

diagonal² = 10² + 10²

diagonal² = 100 + 100

diagonal² = 200

diagonal = √200

diagonal = 10√2

Hence, the length of th diagonal is 10√2

F(x) = K• (b)^x

then find K, and b

6 = K• (b^0) = K

also

42= K•(b^1) = K• b

then

b= 42/K= 42/6= 7

Then answer formula is

F (x) = K• (b)^x

. = 6• (7^x)

The value of x in the equation is 4

Algebraic expressions are seen as expressions that consist of factors, variables, terms, coefficients, and certain constants.

These expressions are also known to be composed of some arithmetic operations, which includes;

Given the expression;

(2x-4)^2=16

√(2x-4)^2 = 16

Find the square root of the expression, we have;

√(2x -4)^2= √16

Find the values

2x - 4 = 4

collect like terms

2x = 4 + 4

Add like terms

2x = 8

Make 'x' the subject of formula

x = 8/2

x = 4

Hence, the value is 4

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

Answer: bot eleum got it right

Step-by-step explanation:

If a bus use 40 litres of fuel to travel 100km  27.2 liters fuel will be used on a journey of 68km​.

simplification to the amount of fuel needed-

Amount of fuel bus use to travel 100km = 40 liters

How much distance will travel with 1Liter of fuel  =

To find that  divide 100 by 40

That is total distance travelled by 40 liters of fuel

= 100/40 = 2.5

Bus will travel 2.5 km with 1L fuel.

The amount of fuel for 68KM = 68km /2.5km  = 27.2 Liter

To learn more about fuel efficiency here-

https://brainly.com/question/13347135    

#SPJ9                  

First we need to look at the change of signal of the function (it changes from √x to -√x).

This change of signal means the function was reflected over the x-axis.

Then, the value of -3 was added to the function.

An addition of -3 in the function means a translation of 3 units down.

So the transformations from m(x) to p(x) are:

A reflection over the x-axis followed by a translation of 3 units down.

Answer:

your answer is C

Step-by-step explanation:

by elimination B is not possible as the graph shows a cubic shape B has no cubic terms, D is not possible because the graph shows a translation on X axis and D represents a translation in Y axis, and A is not possible because when X=0 the value of Y must be -64 and A doesn't comply to that.

Answer:

C

Step-by-step explanation:

the graph has 3 zero solutions (values of x with y = 0).

therefore it has to be of 3rd degree (3 is the max. exponent of x).

that eliminates B, because it is only of 2nd degree.

when x = 0, y is a little bit below -60 but above -80.

but y is negative.

that eliminates A, because when x = 0, y = +64.

for x = -8, y has to be 0 too.

that eliminates D, because for x = -8, y = -8³ - 64 = -512 - 64 = -576

and not 0.

so, C must be correct.

for x = 0, y = -64

for x = -8, y = -8³ + 6×-8² - 24×-8 - 64 =

= -512 + 6×64 + 192 - 64 =

= -512 + 384 + 192 - 64 = 0

for x = -2, y = -2³ + 6×-2² - 24×-2 - 64 =

= -8 + 6×4 + 48 - 64 =

= -8 + 24 + 48 - 64 = 0

for x = 4, y = 4³ + 6×4² - 24×4 - 64 =

= 64 + 6×16 - 96 - 64 =

= 64 + 96 - 96 - 64 = 0

all fits.

Answer:

Step-by-step explanation:

g

u

The equations given are,

Isolate 'x' in equation 1

Substitute 'x' is equal to (5-8y)/2 into equation 2

Substitute y = 3/4 into equation 3 and solve for x

Hence,

Answer:

196 = y

Step-by-step explanation:

If o is 140, the value of y is what? 28 ✕ o = 20 ✕ y

28 ✕ o = 20 ✕ y

28 ✕ 140 = 20 ✕ y

3,920 = 20✕ y

right side: 20 is multiplied by y and can be written back to back:

3,920 = 20y

divide both sides by 20:

3,920/20 = 20y/20

196 = y

ANSWER :

0.529

EXPLANATION :

From the problem, Carl made 37 out of 70 free throws attempt.

Divide the number of free throws made by the total number of free throws attempt

When z = 9 and x = 4, and y = 360. then, with x = 4 and z = 9, we obtain the value of y = 600.

According to question, given that

x = 4, z = 9 , y = 360

The value of y varies jointly with the values of x and z then

Joint variation ⇒ y = k. x. z , where k is constant. In all cases when k ≠ 0

360 = k (4) (9)

360 = 36 k

k = 360/36

k = 10

y = k. x. z

y = 10 .x . z

when x = 5 and z = 12 then

y = 10 .x . z

y = 10 (5) (12)

y = 600

Therefore,  When x=4 and z=9, and the value of y is 360. then we get the value of y = 600, when x=4 and z=9 using joint variation.

Any number of issues involving rates, times, and work can be resolved rationally. Rational formulas include direct, inverse, and joint variation equations. In direct variation, the variables are directly related to one another; as one quantity rises, the other will as well.

To learn more about  joint variation visit here :brainly.com/question/12250735

#SPJ1

Given:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {1,2,3,4,5}

B = {4, 5, 6, 7}

C = {5, 6, 7, 8, 9}

D= {1, 3, 5, 7, 9}

E= {2, 4, 6, 8}

F = {1, 5, 9}

What is the question: Find AUC'.

Recall the following:

A ∩ C (read as A intersection C) - are members that are common to both set A and set C.

A ∪ C (read as A union C) - are members that are in set A or set C or both, combining the members of all sets.

C' (read as C complement) - are members that are not in the universal set.

Since what we are about to find is A ∪ C', let's first determine the members of C'.

We get,

C' = {1, 2, 3, 4}

A = {1,2,3,4,5}

Therefore, AUC' = {1,2,3,4,5}.

The linear equation that passes through (-2, 11) and (1, -4) is:

y = -5*x + 1

The general linear equation is:

y = a*x +b

Where a is the slope and b is the y-intercept.

If the line passes through points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through the points (-2, 11) and (1, -4), then the slope is:

a = (-4 - 11)/(1 + 2) = -15/3 = -5

y = -5*x + b

To find the value of b, we use one of the two given points, here i will use (1, -4), it gives:

-4 = -5*1 + b

-4 + 5 = b

1 = b

So the linear equation is:

y = -5*x + 1

Learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Therefore the answer is C.

We need to write an equation relating x (leg CD) to the given data.

The image shows the right triangle ACD, with legs, in ft, given by:

Also, angle DAC is 25.4º. Since CD is the opposite leg, and AC is the adjacent leg to this angle, we have:

Thus, option A is correct.

Also, we can multiply both sides of the above equation by 1600, to find the equivalent equation:

Thus, option C is also correct.

Notice that:

Therefore, only options A and C are correct.

Given:

The scale is 15 ft = 1 in

Height = 80 ft

Length = 200 ft

Find-:

The required dimensions of the paper

Explanation-:

The scale is:

The required dimension of paper is:

The length is:

So the demission is height 5.33 in and length 13.33 in

The sheet demission is

So, Adoncia's drawing will not fit on the sheet of paper.

Answer:

the answer to your question is that of 17 1/4

To find how much di the stock gain or lose in value after 5 days, we just have to sum the values of the Gain/Loss column from the first row to the fifth one, like this:

Total gain or loss = -2.25 + (-1.5) + 1.25 + (-0.75) + 2.25 = -1

Then, the stock lose $1 in value ($-1)

The total amount of security deposits and other deposits received by or on behalf of the Obligors and retained by their originators and affiliates as of any date is referred to as the Deposit Balance (or any agent thereof on their behalf).

The written checks would be deducted from the balance and the paycheck would be added to it. Hand-doing the math for the realistic quantities in the question would take a lot of time, but the values may be typed into the calculator in a single continuous string as they are shown in the equation.

New Balance Deposited = Old Balance + Paycheck deposited - Check written  

New Balance = 1219.17 + 2425.66 + 235.89 - 418.37.

New Balance = 2140.57 .

To Learn more About Deposit Balance, Refer:

https://brainly.com/question/2261596

#SPJ9

Given that the buffet is to have 19 desserts for every 16 people.

Let's find the number of desserts they should have if they plan for 320 people.

19 desserts = 16 people

x desserts = 320 people

Therefore, we have:

Divide both sides by 16:

Thereore, they should have 380 desserts if they plan for 320 people.

ANSWER:

380 desserts

Given:

The graph shows the XY plane where x shows the number of T shirts bought and Y shows the number of stickers received.

The plotted points on the graph have the coordinates:

Clearly, we can see the y coordinate is double of x coordinate here, so the equation of graph shown will be : y = 2x

Now we will check the points given in tables in the options if they satisfy this equation or not.

Check option (F),we get:

Which doesnot satisfy the equation y=2x hence, option F is wrong.

Now chcek option G ,

These points clearly satisfy y= 2x, hence,

Option (G) is correct.

Similarly, if we check option (H) and (I) they will not satisfy the equation, Hence , option (G) is only correct.

Answer: x^2+4x-45

Step-by-step explanation:

Multiply (x-5)(x+9)

Using the FOIL Method.

Multiply

x and x

x and -5

x and 9

-5 and 9

You should get x^2-5x+9x-45

Subtract -5x and 9 and you get your answer

x^2+4x-45

Answer

Angle A = 19°

Explanation

Vertical angles are angles that are directly opposite each other at a point where two lines intersect or cross each other. Vertical angles are known to be equal to each other.

So, Angle A = Angle B

Angle A = 3x + 13

Angle B = 5x + 9

3x + 13 = 5x + 9

We can rewrite this as

5x + 9 = 3x + 13

5x - 3x = 13 - 9

2x = 4

Divide both sides by 2

(2x/2) = (4/2)

x = 2

Angle A = 3x + 13 = 3(2) + 13 = 6 + 13 = 19°

Hope this Helps!!!

Since:

(8,3200) is a viable point

---------------------------

Since w is the number of copies of the school newsletter, the values of w must be whole numbers