a ladder touches a wall 15ft off the ground, and the base of the ladder is 8 feet from the base of the wall. how long is the ladder

Answer:

When combining like terms the given expression turned to the simplest form of expression 3(x+z)+5

That is  4x+7z-x+5-(4z)=3(x+z)+5

Step-by-step explanation:

Given expression is 4x+7z-x+5-(4z)

To combining the given expression to solve it as below :

4x+7z-x+5-(4z)

=4x+7z-x+5-4z

=4x-x+7z-4z+5  ( combining the like terms of x and z )

=3x+3z+5 ( here adding the like terms )

=3(x+z)+5 ( taking the common factor )

Therefore 4x+7z-x+5-(4z)=3(x+z)+5

When combining like terms the given expression turned to the simplest form of expression 3(x+z)+5

That is  4x+7z-x+5-(4z)=3(x+z)+5

Answer:

Step-by-step explanation:

1. reg pay: 8.96,week days: 1.5 overtime pay, sat: double pay, sun: triple pay

38 hrs regular pay : 38 * 8.96 = 340.48

15 hrs overtime during week : 15 * 1.5(8.96) = 15 * 13.44 = 201.60

3 hrs overtime on saturday: 3 * 2(8.96) = 3 * 17.92 = 53.76

2 hrs overtime on sunday: 2 * 3(8.96) = 2 * 26.88 = 53.76

Gross wage = (340.48 + 201.60 + 2(53.76) = 649.60 <====

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

2. reg pay : 14.60, weekday pay: 1.25,sat pay: 1.5 , sun pay: double

(a) basic wage = 40(14.60) = 584 <==

(b) overtime wage : 15 * 1.25(14.60) + 6 * 1.5(14.60) + 5 * 2(14.60) = (15 * 18.25) + (6 * 21.9) + (5 * 29.2) = 273.75 + 131.40 + 146 = 551.15 <==

(c) gross wage : 584 + 551.15 = 1135.15 <==

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

3. basic work wk: 40 hrs...earned 518...overtime 148

(a) basic pay rate : (518 - 148) / 40 = 370/40 = 9.25 per hr <==

(b) if overtime is paid for at double time.....so overtime pay is (2 * 9.25) = 18.50 per hr....and he got paid 148....148/18.5 = 8 hrs <==

The gross wage of the man who worked overtime from Monday to Friday, on Saturday, and on Sunday is $582.40.

In order to determine the gross wage of the man, we need to calculate the wages for each type of overtime worked. Let's start with the basic wage calculation for each scenario:

The man worked 15 hours overtime on week-days, so he will receive 15 x 8.96 = $134.40 for week-day overtime.

He also worked 3 hours overtime on Saturday, so he will receive 3 x (2 x 8.96) = $53.76 for Saturday overtime.

Lastly, he worked 2 hours overtime on Sunday, so he will receive 2 x (3 x 8.96) = $53.76 for Sunday overtime.

Now let's calculate the gross wage by adding the basic wage and the overtime wages together:

Gross Wage = Basic Wage + Week-day Overtime Wage + Saturday Overtime Wage + Sunday Overtime Wage

= (38 x 8.96) + 134.40 + 53.76 + 53.76

= $340.48 + $134.40 + $53.76 + $53.76

= $582.40

https://brainly.com/question/19799429

#SPJ2

The two numbers are 15 and 6

Solution:

Let the two number be "a" and "b"

Let the first number be "a" and second number be "b"

Given that,

The difference between two numbers is 9

a - b = 9 -------- eqn 1

The first number plus twice the other number is 27

First number + twice the second number = 27

a + 2b = 27 ---------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

a = 9 + b ------ eqn 3

Substitute eqn 3 in eqn 2

9 + b + 2b = 27

3b = 27 - 9

3b = 18

Divide both sides of equation by 3

Substitute b = 6 in eqn 3

a = 9 + 6

Thus the two numbers are 15 and 6

Answer:

25 feet

Step-by-step explanation:

In this problem, you would need to use the pythagorean theorem, a^2 + b^2 = c^2.

It doesn't matter which you decide to be a and which you decide to be b, but the diagonal line, or hypotenuse, must be c. In this case, that is the ladder.

Now you plug numbers into the equation. 20^2 + 15^2 = c^2.

Simplify the left side of the equation. 400 + 225 = c^2, 625 = c^2.

Now, since c is still squared, take the square root of both sides. c = 25.

Another way to solve this is using the special triangles. One of the easiest to remember is the 3-4-5 triangle. That is what this triangle is, once you factor out a 5 from all of the numbers (15/5=3, 20/5=4, 25/5=5). Them you just multiply whatever missing number you are looking for by the factor you took out (5 × 5 = 25).

Answer:

x=0 or x=6/10

Step-by-step explanation:

10x^2=6x ⇔ 10x^2 - 6x = 0 ⇔ x(10x-6)=0 ⇔ x=0 or x= 6/10

Answer:  38.46

Step-by-step explanation:

400/10.4= 38.46

The slope is always rise/run and has a variable. In this case, 2/3x is the slope.

The y-intercept is always the number at the end, which is the y-value. This would mean that 5 is the y-intercept.

Answer:

Step-by-step explanation:

Y = ⅔X + 5

Comparing with y = mx + c

Where m is the slope and c is the intercept

m = ⅔ and c = 5

Answer:

13

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

44+4=48

48/3=16

To simplify, remove the parentheses and combine like terms:

( y + 22) + 3

Y + 22 + 3

Answer: Y + 25

Answer:

an equal number of students chosen at random from each grade level

In statistics, a sample is a little amount that reveals how the remainder is or should be.

Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.

A middle school contains sixth, seventh, and eighth graders each grade level contains approximately the same number of students the principal wants to find the answer to a survey question affecting each student in the school.

An equal number of pupils from each grade level were chosen at random.

We could simply collect the information of all the pupils by randomly picking some students such that there are an equal number of students from each grade.

More about the statistics link is given below.

https://brainly.com/question/10951564

#SPJ2

Greater than bc the pieces is bigger

Answer:

His Age is 4 years old

Step-by-step explanation:

His brother is 7

Answer: 4

Step-by-step explanation:

If Tyler is 4 years old then his brother would be 7 and 7+4=11

Answer: 4000

Step-by-step explanation:

40(43+57)

40(100)

4000

Answer:

3600

Step-by-step explanation:

(43+47)*40

=90*40

=3600

There are a couple different dates that people say WW2 started but the main start of the war was when the Nazi’s invaded Poland September 1, 1939

Answer: [tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Step-by-step explanation:

To find the inverse , all we need do is to make x the subject of the formula.

y = 7x - 10

Add 10 to both sides

y + 10 = 7x

divide both sides by 7

Therefore:

x = y + 10 / 7 , that is

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Answer:

Step-by-step explanation:

y=7x-10  calculate x :  7x-10 =y

7x = y+10

x = 1/7 y +10/7

the inverse of y=7x-10 is ; y = 1/7 x +10/7

Answer:

14 cm

Step-by-step explanation:

10 plus 8 plus 6

perimeter means add up the sides

The solution is (-4,4)

Step-by-step explanation:

Given equations are:

[tex]4x-9y = 20\ \ \ \ Eqn1\\2x-6x = 16\ \ \ \ Eqn2[/tex]

In linear combination method, we have to make coefficients of any one variable opposites by multiplying with an integer

So multiplying 2nd equation by -2

[tex]-2(2x-6y=16)\\-4x+6y=-32\ \ \ \ Eqn3[/tex]

Adding Equation 1 and Equation 3:

[tex]4x-9y-4x+12y = 20-32\\3y = -12[/tex]

Dividing both sides by 3

[tex]\frac{3y}{3} = \frac{-12}{3}\\y = -4[/tex]

Putting y=-4 in equation 1

[tex]4x-9(-4) = 20\\4x +36= 20\\4x = 20-36\\4x = -16[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4} = \frac{-16}{4}\\x = -4[/tex]

Hence,

The solution is (-4,4)

Keywords: Linear combination, linear equations

Learn more about linear combination method at:

#LearnwithBrainly

Answer:

The equation y = 3x represents a proportional relationship, where y represents distance in miles, and x represents time in hours. The point (3, 9) represents that Alonso walks 9 miles in 3 hours. The point (5, 15) represents that Alonso walks 15 miles in 5 hours.

The graph of line y = 3x represents how much distance is covered in how much time.

Here x is the time and y represents distance traveled. So, for points (3, 9) and (5, 15), it represents that Alonso covered 9 units of distance in 3 units of time and 15 units of distance in 5 units of time.

The general equation of line is,

y = mx + c

where m is the slope and c is the intercept.

Now the given equation is,

y = 3x

This represents Alonso's walking speed.

So it is explained that y distance is covered in x time.

Hence for points (3,9),

x = 3

y = 9

So,

Alonso covered 9 units of distance in 3 units of time.

For point (5,15)

x = 5

y = 15

So,

Alonso covered 15 units of distance in 5 units of time.

Thus,for points (3, 9) and (5, 15), it represents that Alonso covered 9 units of distance in 3 units of time and 15 units of distance in 5 units of time.

To learn more about line:

https://brainly.com/question/1553538

#SPJ2

Volume of a rectangular prism is V = L x W x H

The length for the small prism is 6

The width for the small prism is 4

The height for the small prism is 3

So 6 x 4 x 3 = 72

The length for the large prism is 16

The width for the large prism is 9

The height for the large prism is 2

So 16 x 9 x 2 = 288

Now you add the two volumes together: 288 + 72 = 360 ft cubed.

Answer:

E

Step-by-step explanation:

The pattern is 3 letters before.

[tex]\frac{5x-20}{14x^{2}-7x }[/tex]

Answer:

b

Step-by-step explanation:

Answer:

The answer is spinner B. There are 8 sections on the spinner and 4 of them have letter A, so P(A)= 1/2.

Answer:

Step-by-step explanation:

28.80 = 360x%

28.80 / 360 = x%

0.08 = x%

8% = x <====

To find the sales tax rate, divide the sales tax amount ($28.80) by the cost of the item before tax ($360) to get 0.08. Multiplying this by 100 converts it to a percentage, thus, the sales tax rate is 8%.

The subject of your question is related to sales tax calculations, a topic under mathematics. To find the sales tax rate, we should divide the amount of sales tax by the original cost of the item, then multiply the result by 100 to get the percentage.

Here are step by step calculations:

Therefore, the sales tax rate is 8%.

https://brainly.com/question/29442509

#SPJ2

Answer:

It could be -111 and -173

Step-by-step explanation:

-111 is 62 more than -173 and together they are -284.

Answer:

4+5x<50

Step-by-step explanation:

5n < 50 <--- subtracts 4 from both sides

n < 10 <--- divides both sides by 5

Check: testing n=0, we have 4 + 5(0) = 4 + 0 = 4 < 54, so yes it works

testing n=10, 4 + 5(10) = 4 + 50 = 54.

testing n=11, 4 + 5(11) = 4 + 55 = 59 <--- fails as expected.

X < 10, proven, verified, correct

The inequality 'Four more than 5 times the number x is less than 50' translates to '5x + 4 < 50'. By solving, we find the solution is 'x < 9.2', indicating that x must be less than 9.2.

The question "Four more than 5 times the number x is less than 50" can be translated into a mathematical inequality. The 'four more than' suggests addition, and '5 times the number x' indicates multiplication.

Therefore, we have the inequality 5x + 4 < 50. To find the range of values for x, we need to solve the inequality for x.

Step 1: Subtract 4 from both sides to isolate the term with x on one side of the inequality. 5x < 46.

Step 2: Divide both sides by 5 to solve for x. x < 9.2.

So, the solution to the inequality is that x must be less than 9.2. This inequality does not require the quadratic formula as suggested in some parts of the provided information.

The assumption that 'The value of x is not less than 5% of 0.50' is also not relevant to solving this particular inequality.

Answer:

Option B.) 3 inches

Step-by-step explanation:

Let us first express some principles that we can use to solve our problem. Generally, the Volume of a Box is given by:

[tex]V=h*w*l[/tex]

where

[tex]V[/tex] : is the volume

[tex]h[/tex]   : is the height

[tex]w[/tex]   : is the width

[tex]l[/tex]   : is the length

Now we know that:

Volume of Box A ( [tex]V_{A}[/tex] )  is Equal to Volume of Box B ( [tex]V_{B}[/tex] ) so we have:

[tex]V_{A}=(2in)(3in)(6in)\\V_{A}=36 in[/tex]

So now we can find the Length ( [tex]l_{B}[/tex] ) of Box B easily, as we now the volume along with the height and the width, as follow:

[tex]V_{A}=V_{B}=36in\\\\36in = (3in)(4in)l_{B}\\\\36in=(12in)l_{B}\\\\l_{B}=\frac{36in}{12in}\\ \\l_{B}=3in[/tex]

So the Length of Box B is 3 inches, thus Option B. is correct.