MATHEMATICS HIGH SCHOOL

A construction manager needs 12 workers to complete a building project in 54 days. Find in terms of T the number of workers needed to complete the same project in T days

Answers

Answer 1

Answer:

Answer:

2T/9

Step-by-step explanation:

A construction manager needs 12 workers to complete a building project in 54 days, we can write;

12 workers = 54 days

T find the number of workers needed to complete the same project in T days, we will write;

x workers = T days

Divide both equations

12/x = 54/T

Cross multiply

12T = 54x

x = 12T/54

x = 2T/9

Hence the number of workers needed to complete the same project in T days is 2T/9 workers

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3-2r+5=2-8/3 is simplified to what?
Hi there,Can you solve this task?You see seven sisters standing around the kitchen table. Every sister has her own backpack. In each backpack there are seven large cats. And guess what! For every big cat there are also seven small kittens. The question is – how many legs are in the room?

The Drama Club is showing a video of their recent play. The first showing begins at 4:35 p.M. The second showing is scheduled at 7:15 p.M. With a 1 2 −hour break between the showings. How long is the video in hours and minutes? The video is hours and minutes. Complete the explanation of how you can use a number line to find the answer. You can work backward from the start time of the second showing at : . You count back 1 2 hour, which is minutes, for the break between showings to : . The second showing started 20 minutes late. Will the second showing be over by 9:35 p.M.? Complete the explanation why your answer is reasonable. The second showing started at : p.M. The movie lasts hours minutes, so it ends at :45 p.M. So, ? The second showing ? Be over by 9:35 p.M.

Answers

Answer:

Part A

2 hours 10 minutes

Part B;

Please find attached a number line created with MS Visio

Part C

The completed explanation is given as follows

The second showing starts at 7:35 p.m. The movie lasts 2 hours 10 minutes so it ends 9:45 p.m. So the second sowing be over by 9:45 p.m

Step-by-step explanation:

Part A

The given parameters are;

The time the first showing starts, t₁ = 4:35 p.m.

The time the first showing starts, t₂ = 7:15 p.m.

The time interval between shows, $t_(interval)$ = 1/2 hours = 30 minutes

Let 'x' represent the video in minutes, we have;

x = 7:15 - 4:35 - 30 = 2 hours 40 minutes - 30 minutes = 2 hours 10 minutes

The length of the video = 2 hours 10 minutes

Part B;

Using the number line, we have;

1) Plotting the points for the starting and points for the two showing points which are 4:35 pm. and 7:15 p.m.

2) Plot the point 30 minutes before the start of the second movie which is 6:45 p.m and find the time difference between the start of the first showing and the point 6:45 p.m. which gives the length of the movie which is 2 hours and 10 minutes

3) Given that the second showing starts 20 minutes late, the second showing will start at 7:15 p.m. + 20 min = 7:35 p.m.

4) The second showing ends at 7:35 p.m. + 2 hours 10 minutes = 9:45 p.m.

Therefore, the second showing will be over 9:35 p.m.

Part C

The second showing starts at 7:35 p.m. The movie lasts 2 hours 10 minutes so it ends 9:45 p.m. So the second sowing be over by 9:45 p.m.

What is the simplified expression for 5ab+9ab-ab?

Answers

Answer:

The simplified form of the given expression is $13ab$ .

Step-by-step explanation:

We are given the expression,

$5ab+9ab-ab$

Using the order of operations rule, we have,

First we will add the terms 5ab and 9ab.

So, the expression is $14ab-ab$

Now, we will subtract the terms to get the final answer,

That is, $5ab+9ab-ab$ = $13ab$

Hence, the simplified form of the given expression is $13ab$ .

Remember the order of operations, pemdas, add 5ab and 9ab to get 14ab, then subtract to get 13ab

The area of a sector of a circle with a radius of 4 centimeters is 2.512 square centimeters. The estimated value of π is 3.14. The measure of the angle defining the sector is °.'

Answers

Area = (theta/360)* pi * r^2
where theta is the angle of the sector
subs by your givens in the above equation
2.512 = (theta/360) * pi * (4)^2
theta = (2.512 * 360) /(pi*(4)^2)
theta = 18 degree

I would love the help!(Geometry S2).

Answers

Answer:

Step-by-step explanation:

a² + a² = c²
2a² = c², this is the step you are at
a√2 = c

This proves the hypotenuse is √2 times the side.

The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Answers

Answer-

The line equation is,

$\boxed{\boxed{6x+15y-10=0}}$

Solution-

The line $y =3x-5$ meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

$\Rightarrow 0 =3x-5$

$\Rightarrow 3x=5$

$\Rightarrow x=(5)/(3)$

So, coordinate of M is $((5)/(3),\ 0)$

The line $3y+2x=2$ meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

$\Rightarrow 3y+2(0)=2$

$\Rightarrow 3y=2$

$\Rightarrow y=(2)/(3)$

So, coordinate of N is $(0,\ (2)/(3))$

The line joining M and N can be found out by applying two point formula of straight line,

$\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$

$\Rightarrow (y-0)/((2)/(3)-0)=(x-(5)/(3))/(0-(5)/(3))$

$\Rightarrow (y)/((2)/(3))=(x-(5)/(3))/(-(5)/(3))$

$\Rightarrow -(5)/(3)y=(2)/(3)(x-(5)/(3))$

$\Rightarrow -5y=2(x-(5)/(3))$

$\Rightarrow -5y=2x-(10)/(3)$

$\Rightarrow 2x+5y-(10)/(3)=0$

As it is given that all the coefficients are integers, so multiplying with 3

$\Rightarrow 6x+15y-10=0$

Solution: As given line y =3x-5 meet x-axis at the point M.

On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given by

→ $(y-b)/(x-a) =(q-b)/(p-a)$

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is → $(x)/(a) + (y)/(b) =1$ , where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→ $(x)/((5)/(3)) + (y)/((2)/(3))=1$

→ $(3x)/(5) + (3y)/(2) =1$

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Which of the following is an equivalent form of the compound inequality −22 > −5x − 7 ≥ −3?A) −5x − 7 < −22 and −5x − 7 ≥ −3
B) −5x − 7 > −22 and −5x − 7 ≥ −3
C) −5x > −22 and −7 ≥ −3
D) −5x − 7 < −22 and −5x − 7 ≤ −3

Answers

The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

Then a Set of such values is called solution set to the considered equation or inequality.

The equivalent form of the given inequality can be obtained by dividing the inequality into two parts.

In this case, we are given -22 > -5x - 7 > -3.

The two parts are; -22 > -5x - 7 and -5x - 7 > -3.

Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.

For part two, we have −5x − 7 ≥ −3 remains unchanged.

Therefore, The choice that reflects these parts is A)-5x - 7 < -22 and -5x - 7 -3

Hence, The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 are A) −5x − 7 < −22 and −5x − 7 ≥ −3

Learn more about inequalities here:

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A) −5x − 7 < −22 and −5x − 7 ≥ −3

Working;
Since the −5x − 7 and −22 have interchanged sides, the inequality sign also changes direction.

For part two, −5x − 7 ≥ −3 remains unchanged.

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