A 40 ​-inch board is to be cut into three pieces so that the second piece is 4 as long as the first piece and the third piece is 5 times as long as the first piece. If x represents the length of the first​ piece, find the lengths of all three pieces.

Answers

Answer 1

Answer:

4*4=16 INCHES FOR THE SECOND PIECE. 5*4=20 INCHES FOR THE LONGEST PIECE.

Step-by-step explanation:

Answer 2

x = 20 inch, the length of the first piece

What is mathematical expression?

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

given,

Total length = 40 inch

let first piece be = x inch

second piece = 4 times of first piece = 4x inch

third piece = 5 times of first piece = 5x inch

So,

x + 4x + 5x = 200

10x = 200

x = 200/10

x = 20

Therefore, the length of the first piece is 20 inch

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Related Questions

You have $150 in a savings account and you have some cash. The tape diagram represents the ratio of the amounts of money. You want to have twice the amount of money in your savings account as you have in cash. How much of your cash should you deposit into your savings account?

Answers

Answer: $200

Step-by-step explanation:

We know that:

You have $150 in a savings account.

This is represented with two tiles.

Then each tile represents:

$150/2 = $75

And in cash you have 5 tiles, then in cash you have:

5*$75 = $375.

Then the problem is:

You have $150 in the savings account

You have $375 in cash.

You want to deposit a quantity such that you have twice the amount of money in your savings account as you have in cash.

Suppose that you move a quantity X from cash to the savings account, then now we have the situation:

Sav. Acc. = $150 + X

Cash = $375 - X

And we want that:

Sav. Acc. = 2*Cash

($150 + X) = 2*($375 - X)

Let's solve this for X.

$150 + X = $750 - 2*X

3*X = $750 - $150 = $600

X = $600/3 = $200

You should deposit $200 in the Savings acount.

Tape diagrams are used to represent numbers as a ratio

$200 from the cash should be deposited into the savings account

Represent the amount in the savings account with s, and the cash with c.

So, we have the following ratio from the tape diagram

[tex]\mathbf{s : c = 2 : 5}[/tex]

You have $150 in the savings account.

So, the ratio becomes

[tex]\mathbf{150 : c = 2 : 5}[/tex]

Express as fractions

[tex]\mathbf{\frac c{150}= \frac 52}[/tex]

Multiply both sides by 150

[tex]\mathbf{c= \frac 52 \times 150}[/tex]

[tex]\mathbf{c= 375}[/tex]

Let the deposited amount be x.

Twice the amount in the savings account as cash means that:

[tex]\mathbf{150 + x = 2 \times (375 - x)}[/tex]

Open brackets

[tex]\mathbf{150 + x = 750 - 2x}[/tex]

Collect like terms

[tex]\mathbf{2x + x = 750 - 150}[/tex]

[tex]\mathbf{3x = 600}[/tex]

Divide both sides by 3

[tex]\mathbf{x = 200}[/tex]

Hence, $200 from the cash should be deposited into the savings account

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Write the decimal represented by each shaded square.

Answers

that’s a 100 mode and there 53 squares shaded so it’s gonna be 0.53 :))

Question 1
1 pts
The function f(x) = 4x + 10 models the amount of money Francis makes when babysitting
for x hours. How much money will he make for 2 hours of babysitting work?
2.
0-2
O-3
O 18

Answers

Answer:

18 would be yr answer

Step-by-step explanation:

Find the equation of a line passing through the point (6,9) and (0,0)

Answers

Answer:

y=3/2x

Step-by-step explanation:

The equation of the required line as per slope-intercept form is 3x - 2y = 0.

What is the equation of a line passing through two points?

The equation of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:  

m = (y₂ - y₁)/(x₂ - x₁)

Here, 'm' is the slope and 'c' is the y-intercept of the given line.

Therefore, the slope of a line that passes through (6, 9) and (0, 0) is

= (0 - 9)/(0 - 6)

= 3/2

Now, the general form of a line is y = mx + c. Here, 'm' is the slope and 'c' is the y-intercept of the line.

The line passes through the point (0, 0).

Therefore, 0 = (3/2) × 0 + c

⇒ c = 0

Now, the equation of the straight line is

y = (3/2)x + 0

⇒ 2y = 3x

⇒ 3x - 2y = 0

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the mass of earth is approximately 5.9×10^24 kg,and the mass of venus is approximately 4.9×10^24 kg. a. find the combined mass b. given that mass of the sun is approximately 1.9 × 10^30 kg how many venues and earths would it take to equal the mass of the sun.​

Answers

a) Combined mass of earth and venues is 10.8 × 10²⁴. b) There are total 18989.2 kg taking earth and venue to equal to the sun.

What is the arithmetic operator?

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Given that,

Mass of earth = 5.9 × 10²⁴ kg

Mass of venus = 4.9 ×  10²⁴ kg

a) Combined mass of earth and venus

5.9 × 10²⁴ +  4.9 ×  10²⁴ = 10.8 × 10²⁴

b) If the mass of the sun =  1.9 × 10³⁰

Let's say the total gain of earth and venus combined x so it will equal the mass.

Then,

10.8 × 10²⁴ + x = 1.9 × 10³⁰

x = 18989.2 kg

Hence "Combined mass of earth and venues is 10.8 × 10²⁴ and there are a total of 18989.2 kg taking earth and venue to equal to the sun.

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If we double the sum of the numbers x and -21, we get the number -100. What is x?​

Answers

Step-by-step explanation:

2{x + (-21) }= –100

= 2x – 42 = –100

= 2x= –100 + 42

= 2x= –58

= x = –58/2

x= –29

Jonae gets paid $16.50 an hour working at a furniture store. She also gets paid 20% of all of the store's furniture sales each week. This week, the store made $600 on a table and $400 on chairs. If Jonae worked 40 hours this week, how much will she be paid?

Answers

Answer:

$860

Step-by-step explanation:

Jonae makes $16.50 an hour and worked 40 hours.  Multiply the hours worked by the amount of money she earned.

$16.50 × 40 = $660

The stored made $600 on a table and $400 on chairs, which, in total, is $1000.  Since Jonae gets paid 20% of all of the furniture sales, multiply the total sales by the percentage.

$1000 × 0.2 = $200

Add together the earnings she made per hour and the earnings she made from the furniture store's sales.

$660 + $200 = $860

1. Diane's Sweet Treats can make 24 cupcakes using 16 ounces of whipped
icing. How much icing is used on each cupcake?
a. 1/6 ounce of icing per cupcake.
b. 2/3 ounce of icing per cupcake.
c. 1/2 ounce of icing per cupcake.
d. 3/4 ounce of icing per cupcake.

Answers

Answer:

b. 2/3 ounce of icing per cupcake.

Step-by-step explanation:

 Given parameters:

       Number of cupcakes = 24 cupcakes

        Ounces of whipped icing = 16 ounces

Unknown:

How much icing was used in each cupcake  = ?

Solution:

 To find the number icing used per cupcake;

                             = [tex]\frac{number of ounces of whipped icing}{Number of cupckakes}[/tex]

  Input the parameters;

                              = [tex]\frac{16 ounce of icing }{24 cupcake}[/tex]

                             = [tex]\frac{2}{3}[/tex] ounce of icing per cupcake

Barb’s Grandma is always creating math problems for her to solve. In one problem she gave Barb a store receipt that listed 72 identical items, each the same price, for a total cost of $*67.9* Barb’s grandma covered the first and last digits of the total price on the receipt with stars. Determine the value of the digits that Barb’s Grandma covered.

Answers

9514 1404 393

Answer:

  367.92

Step-by-step explanation:

72 = 9·8

In order for the total cost to be divisible by both 8 and 9, it must meet a couple of requirements:

The sum of the digits must be divisible by 9. The last three digits must be divisible by 8.

In order for the sum of digits to be divisible by 9, the first and last digits must total 5 or 14. (The total of existing digits is 22. The sum needs to be 27 or 36.)

In order for the last three digits to be divisible by 8, the last digit must be 2*. So, the first digit must be 5-2=3.

The first digit is 3; the last digit is 2.

The total cost is 367.92. Each item price is 367.92/72 = $5.11.

_____

* 790/8 = 98.75, so (790 + 2)/8 will be 99. 792 is the only number starting with 79 that is divisible by 8.

A triangle has side links of 16 cm, 63 cm, and 64 cm. Classify it as acute, obtuse, or right

Answers

Answer:

acute

Step-by-step explanation:

All sides are smaller than 90 degrees

Write the equation of the line that passes through the given points.
(0,5) and (-2,-4)

Answers

Answer:

[tex]y=\frac{9}{2}x+5[/tex]

Step-by-step explanation:

To find the equation of the a line that passes through the two given points, we must first find the slope between the two points. We can do this by using the slope formula. The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.

By plugging in (-2, -4) and (0, 5) for (x₁, y₁) and (x₂, y₂) respectively, we get:

[tex]y=\frac{5-(-4)}{0-(-2)}=\frac{9}{2}[/tex]

So the slope is 9/2. Now we that we have found the slope, we can write an equation. Normally, when we are given two points, we would pick one of the points and plug it into the point-slope form and then solve for slope-intercept form. Here, notice that one of the points give, (0, 5), is the y-intercept. Knowing this, we can plug in 5 for the y-intercept into the slope-intercept form to get our equation. Remember, slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Pugging in 9/2 for m and 5 for b we get:

[tex]y=\frac{9}{2}x+5[/tex]

which would be our equation.

I hope this helps. Happy studying.

How many solutions does this system of equations have? Exactly one None Infinitely many Exactly two

Answers

None because they are parallel and not equal.

A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Answers

Answer and Step-by-step explanation:

Given:

Charges includes 10 hour per month = $50

Charges for additional hour = $9

Piecewise definition of cost F(x) for a month in which a member use a car for  hours.

Find limits?

Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Lim x → 10- F(x) = 50$

Lim x → 10 [ 9x – 70] = 9( 10) – 70  

                                = 90 – 70

                                = 20 > 10

Limit does not exist.

Lim x → 10+ F(x) = 50$

Lim x → 10+  F(x) = Lim x → 10+   [90x – 70]

                         = 90 – 70

                          = 20 > 10

Limit does not exist.

Lim x → 10 F(x) = 50$

An integer or an decimal.

The limit does not exist.

The piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

Given,

Membership plan is [tex]\$50[/tex] per month.

We have to write a piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours.

Here, [tex]\$[/tex][tex]$50[/tex] per month fees includes 10 hours of driving each month, so the cost for a month is given as,

[tex]f(x)= 50+9(x-10)[/tex]

Here [tex]x[/tex] is the no. of additional hours for the month.

Further,

[tex]f(x)= 9x-40[/tex].

Now at,

[tex]lim _{x \to 10^+}f(x) = 9\times 10-40\\[/tex]

Or,

[tex]f(x)= 90-40\\f(x)=50[/tex]

Similarly, at left limit,

[tex]lim _{x \to 10^-}f(x) = 9\times (-10)-40[/tex]

Or,

[tex]f(x)=-90-40[/tex]

[tex]f(x)=-130[/tex]

Finally at [tex]x=10[/tex], [tex]f(x)=9\times10-40[/tex]

[tex]f(x)=90-40\\f(x)=50[/tex]

Since [tex]lim{x \to}10^+[/tex] [tex]\neq limx\to 10^-\neq f(x) (at x= 10)[/tex]

So the required function [tex]f(x)[/tex] is discontinuous at [tex]x=10[/tex]

Hence the piece wise definition of the cost [tex]f(x)[/tex] for a month in which a member uses a car for [tex]x[/tex] hours is given by the equation,[tex]f(x)= 50+9(x-10)[/tex].

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HELP ON #15 PLEASE GIVE ME ANSWER!

Answers

Answer: so it’s 85?

Step-by-step explanation:

Swedish researchers concluded that viewing and discussing art soothes the soul and helps relieve medical conditions such as high blood pressure and constipation. This conclusion was based on a study in which 20 elderly women gathered once a week to discuss different works of art. The study also included a control group of 20 elderly women who met once a week to discuss their hobbies and interests. At the end of 4 months, the art discussion group was found to have a more positive attitude, to have lower blood pressure, and to use fewer laxatives than the control group.

Required:
a. Why would it be important to determine if the researchers assigned the women participating in the study at random to one of the two groups?
b. Explain why you think that the researchers included a control group in this study.

Answers

Step-by-step explanation:

1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.

2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.

Find The Difference.
1) 8.5-7.6=
2) 2.5-17.8=
3)-2.9-(7.5)-
4) 3.5-1.9=

Answers

Answer:

0.9

-15.3

-10.4

1.6

Step-by-step explanation:

Let me know if I messed up I think I went to fast

Answer:

1. 0.9

2. -15.3

3. -10.4

4. 1.6

mass and weight math​

Answers

Answer: There is 10,000 ug in 1 cg

What is the value of sin-1(cos(2pi/3))?

Answers

Answer:

-pi/6

Step-by-step explanation:

Answer:

-pi/6 c

Step-by-step explanation:

1. Mrs. Wendt called Drano Plumbing Company to fix a leak. Their fee is $35 for the
service call, and $42 per hour.
a) Build a table.
b) Write an equation for the amount she would pay for ‘x’ hours:
_________________________
c) Write and solve an equation to find out how long they worked if her bill was $140.
Equation:_________________________
Solution:_______________

Answers

Answer:

the equation is 140÷42 and the answer is 4

Which is one of the transformations applied to the graph of f(x) = x2 to produce the graph of p(x) = –50 + 14x – x2? a shift down 1 unit a shift left 7 units a shift right 1 unit a shift up 7 units

Answers

Answer:

Shift down one unit

Step-by-step explanation:

Correct for e2020

The transformation applied to the graph of f(x) to produce the graph of p(x) is:

A). a shift down 1 unit and a shift left 7 units.

What is transformation on the graphs?

Let the functions f(x) and g(x) be two real functions.

And g (x) = f (x) + k, where k is real numbers.

The function can be sketched by shifting f (x), k units vertically.

The direction of shift can be found by the value of k:

if k > 0, the base graph shifts k units up, and

if k < 0, the base graph shifts k units down.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

To determine the transformation applied to the graph of f(x) = x² to produce the graph of p(x) = –50 + 14x – x², we can compare the general forms of the two functions:

f(x) = x²

p(x) = –x² + 14x - 50

The function p(x) can be written as,

p(x) = –(x² - 14x + 49) - 1

p(x) = -(x - 7)² - 1

Therefore, the transformation applied to the graph of f(x) to produce the graph of p(x) is:

A). a shift down 1 unit and a shift left 7 units.

So, the correct answer is A).

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What is y = -2/9x + 2 written in standard form?

Answers

Answer:2x+9y=18

Explanation:Move the expression to the left-hand side and change its sign.(y+2/9x=2)Next,multiply both sides of the equation by 9.(9y+2x=18)Lastly,use commutative property to reorder the terms.(2x+9y=18)

help ASAP plz and Thankyou

Answers

Answer: B

Step-by-step explanation:

PLEASE HELP ASAP I GIVE YOU BRAINLIEST AND 20 POINTS

can a system of linear equations be inconsistent and dependent? explain.

Answers

Answer:

No

Step-by-step explanation:

Inconsistent means it has no solution, which means they do not intersect

Dependent means it is the same line

You cannot have both the same line and not intersecting.

Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying a scarves what do the parts of the expression 48s represents

Answers

The expression 48s represents the cost of the scarves.

Given

Emiko makes Shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves.

Let s represent the price of the scarves.

The cost of each scarves is 48.

Therefore,

The cost of scarves = Number of scarves × cost of each scarves.

The cost of scarves = s × 48

The cost of scarves = 48s

Hence, the expression 48s represents the cost of the scarves.

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Answer:In the expression 48s ,represents the number of scarves and 48 represents  the price per scarf

Step-by-step explanation:

Help plz this is due at 11:59

Answers

Answer:

A

Hope this helps ;)

A ITS A HOPE IT HELPED

Write the ordered pair for point H.

1. 3, -5
2. 5, -3
3. -5, 3
4. -3, 5
5. -3, -5

Answers

Answer:

Number 4 is the correct answer: (-3, 5)

The graphed line can be expressed by which equation?

1. y+2=2/3(x×2)
2. y-2=3/4(x-1)
3. y-1=-3/4(x-2)
4. y-2=3/4(x-2)​

Answers

The points are (-2,-2) and (4,2). So the slope is gonna be 2/3. So the answer is number 1. Let me know if I got wrong.

How do you Graph: -3x – 2y = -8

Answers

Answer:

I hope this helps!

Answer:

y = -2/3x +4 --> y = mx+b form

Step-by-step explanation:

-3x-2y = -8 --> add 3x to both side

-2y = 3x-8 --> divide by -2 on both side

y = -2/3x +4 --> y = mx+b form

the y intercept is 4 and the slope is -2/3, down 2, right 3.

therefore, the graph would contain a y intercept point of (0,4) and then from there u would start plotting down 2, going right 3 unit or up 2 and left 3 units. Then when u plotted at least 2/3/4 points, use a straightedge to draw the line.

Vincent is selling candy bars to raise money for his soccer team. He started with a full box of 20 candy bars and has sold 3/10 of them so far. If each candy bar costs $1.25, how much money has vincent raised?

Answers

Answer:

$7.25

Step-by-step explanation:

6*1.25

Answer:

7.50

Step-by-step explanation:

Pls I need help ASAP

Answers

Answer:

the answer is 1/8

thank you

if you loved my answer then please like it and mark as brainliest

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