Solve the word problems
1) There are 45 red balloons, 85 blue balloons and
120 yellow balloons. How many red and blue
balloons are there altogether?
(Show your work)

Answer:

5/6

Step-by-step explanation:

Get LCD of 30 and add

9/30 + 16/30

25/30

Reduce

5/6

The sum of finite arithmetic series 1+4+7+ . . . . . .+31 is S(11) = 176

The given  arithmetic series is:

      1+4+7+ . . . . . .+31

From the above series, we know that:

The first term, a(1) = 1

The last term, a(n) = 31

The common difference, d = 4 - 1 = 3

Recall the formula to find the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

Substitute a(1) = 1, a(n) = 31, and d = 3:

31 = 1 + (n-1) . 3

31 = 3n - 2

3n = 33

n = 11

In an arithmetic series, the sum of the first n terms is given by:

S(n) = n/2 [ a(1) + a(n) ]

Substitute n = 11, a(1) = 1, and a(n) = 31:

S(n) = 11/2 (1 + 31)

S(11) = 11. 16 = 176

Learn more about arithmetic series here:

https://brainly.com/question/14792255

#SPJ4

Answer:

55 sq ft

Step-by-step explanation:

okay so the are of the lil square is 9 sq ft and the area of the big square is 64 sq ft so j subtract the small from the big

Answer: 55cm ^2

Step-by-step explanation:

Area of a square is A=a^2

Area of small square is 3cm^2 = 9cm^2

Large square has an area of 8cm^2 = 64cm^2

64 - 9 = 55 cm^2

Therefore the remaining area is 55 centimeters squared

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -1 , [tex]y_{1}[/tex] = -5 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = -3 .

On substituting the values of variables in equation1, we will get

m = ( (-1)-(-5) ) / ( (-3)-(3) ) = (4/0) = Infinity.

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

To know more about Slope of Straight Line refer to the link:

https://brainly.com/question/21203777

#SPJ4

Natalie’s current available balance is $116.07.

To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.

Account Balance = Pending deposits / credits – Pending Withdrawals /debits

= $126.02- $97.68 = $28.34

Available Balance = Account Balance + Current Posted Balance

= $28.34 +$87.73 = $116.07

Current Available Balance = $116.07

The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.

Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.

Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.

Hence Natalie’s current available balance is $116.07.

To learn more about Bank Balance, visit:

brainly.com/question/24385637

#SPJ1

Bounce 2 is 2

Bounce 4 is 1/2

Bounce 5 is 1/4

Bounce 6 is 1/8

all of your equivalent heights are correct.

The dimensions of the decks increased by the 11 feet.

According to the statement

We have to find that the length by which we increase the dimensions.

So, For this purpose, we know that the

The Area is the amount of space occupied by a two-dimensional figure.

From the given information:

Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled.

Then

The shape of the deck is the rectangle then dimensions is 22 feet by 11 feet.

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  22* 11

Area of the deck with the given dimensions =  242.

Then the dimensions increased by the x

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  (22+x)* (11+x)

Area of the deck with the given dimensions =  242 + 22x+11x+x^2

Area of the deck with the given dimensions =  242 + 33x+x^2

Then according to given details:

x^2 + 33x + 242 = 3*242

x^2 + 33x + 242 = 726

x^2 + 33x = 726 - 242

x^2 + 33x = 484

x^2 + 33x - 484 = 0

After solving

The value of the x become

x = 11 and x = -44

Then second option be neglected.

Then the length increased by the 11 feet.

So, The dimensions of the decks increased by the 11 feet.

Learn more about Area here

https://brainly.com/question/25292087

#SPJ1

The product of  -2.1. (-3.5) is  7.35

The product of  (-2.1 ) and (-3.5) =  [tex]-2.1\times-3.5[/tex]

                                                    =  7.35

So, the product of (-2.1) and (-3.5) is 7.35.

The quotient is the number which is produced when we perform division operations on two numbers. Fundamentally, it is the result of the division method. There are four primary wordings utilized within the arithmetic division such as divisor, dividend, quotient and remainder.

To learn more about quotient, visit;

https://brainly.com/question/16134410

#SPJ4

Answer:

The y-value is 1 less than the square of the x-value,

Step-by-step explanation:

if we follow the letters and convert them into numbers we will get:

y-value=y

1 less than=-1

square of x value=x^2

so

we put the number in order according to the words:

y value=1 less than the square of x

so

y=x^2-1

hope this helps!

8 × 10⁻⁷   is 0.00000008 in scientific notation .

What does a scientific symbol mean?

A frequently used floating-point system where values are expressed as the product of a number between 1 and 10 with the appropriate power of 10 (for example, 1.591 1020).

Example: 700. Why is 700 written as 7 × 102 in Scientific Notation

Example: 4,900,000,000. 1,000,000,000 = 109

Example: 0.0055 is written 5.5 × 10-3

Example: 3.2 is written 3.2 × 100

Why is it employed in scientific notation?

 scientific notation of 0.00000008 = 8 × 10⁻⁷

Learn more about scientific notation

brainly.com/question/18073768

#SPJ9

  955°C is  temperature (in celsius) is the rate constant equal to 0.08857 sec-1.

What is the short definition of activation energy?

The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .

K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]

logk = logA = Eq/RT

log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1  -  [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]

                   = log5.57  + [tex]log 10^{10}[/tex]  - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]

                   = log5.57  + 10log10 - 15.10 * 10³ J/T

   -1.5483 = 0.7458 + 10 - 15.10 * 10³/ T

  -1.5483 = 10.7458 - 15.10 * 10²/T

 - 15.10 * 10³/ T   = -1.5483 - 10.7458

   15.10 * 10³ /T = 12.2941

 T = 15.10 * 10³/ 12.2941

       = 1228K

       = 955°C

Learn more about activation energy

brainly.com/question/11334504

#SPJ4

Answer:

slope = -4

Step-by-step explanation:

slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4

Step-by-step explanation:

[tex](x+4)(2x+5)\\\\2x^2+5x+8x+20\\\large\boxed{2x^2+13x+20}[/tex]

2 packages of bacon would have to buy for both stores to cost the same.

Given that,
At a store, a carton of eggs costs $2.25 and a package of bacon costs $4.25. At another store, eggs cost $2.75, and bacon costs $4.00. If you were to buy one carton of eggs, how many packages of bacon would you have to buy for both stores to cost the same is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to question
WIth the help of arithmetic operators
2.25 + 4.25y = 2.75 + 4.00y
0.25y = 0.50
y = 2

Thus, 2 packages of bacon would have to buy for both stores to cost the same.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ1

The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   We write the given equation

b = 3x + 4a

 and we have the values of the coefficients a and b, and these are:

  We substitute these values in the equation:

b = 3x + 4a

(12) = 3x + 4(-9)     :::: We solve the equation

12 = 3x -36

3x = 12 + 36

3x = 48

x = 48/3

x = 16

Learn more about equations at:

https://brainly.com/question/28562414

#SPJ4

Answer:

Step-by-step explanation:

simplify

6/7x + 7= 31

6/7x+7-7=31-7

6/7x=24

6/7x=24/6/7

28

6/7(28)+15-8=31

24+15-8=31

39-8=31

The inequality that represents the number of nights he can stay in Dallas is 155n+ 99 ≤ 850 (option d).

Here are inequality signs and what they mean:

Since his budget is $850, he can spent a total of $850 or less than $850 on the trip. The sign that would be used to represent this is ≤.

(Total hotel stay cost) + cost of flight ≤. budget

(cost per night x number of hotel stays) + $99 ≤ $850

155n + $99 ≤ 850

To learn more about inequality, please check: https://brainly.com/question/5031619

#SPJ1

Answer:

Answer is D

Step-by-step explanation:

Measure of angle 3 i.e. m∠3 = 130°

The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.

In the question,

Let given angle is ∠8.

Given, ∠8 = 50°

Now, according to supplementary angle property

∠8 + ∠6 = 180

50° + ∠6 = 180

∠6 = 130°

As, ∠6 and ∠2 are corresponding angles,

therefore, ∠6 = ∠2 = 130°

Also, ∠2 and ∠3 are vertical opposite angles,

thus, ∠2 = ∠3 = 130°

therefore, ∠3 = 130°

To know more about measurement of angle, visit :

brainly.com/question/27243531

#SPJ4

The complete question is :

Find measures of numbered angle.

a. ∠2

b. ∠3

c. ∠4

By SSS (Side, side, side) congruency;

⇒ Δ T J D ≅ ΔS E K

Given that;

The vertices of ΔT J D  are;

T (-4, -2) , J (0, 5),  and D (1, -1),

The vertices of  ΔS E K  are;

S (-1, 3), E (3, 10) , and K (4, 4)

We have to prove that  Δ T J D ≅ΔS E K.

What is congruency in triangle?

If all three corresponding sides are equal and all the three corresponding angles are equal in measure, then Two triangles are said to be congruent.

Now,

The vertices of ΔT J D  are;

T (-4, -2) , J (0, 5),  and D (1, -1),

The vertices of  ΔS E K  are;

S (-1, 3), E (3, 10) , and K (4, 4)

To prove Δ T J D ≅ΔS E K we use distance formula and prove all sides are equal.

In ΔT J D;

Distance between T and J;

[tex]D_{TJ} = \sqrt{(0-(-4))^2 + (5 -(-2))^2} = \sqrt{65}[/tex]

Distance between J and D;

[tex]D_{JD} = \sqrt{(1-0)^2 + (-1 -5)^2} = \sqrt{37}[/tex]

Distance between D and T;

[tex]D_{DT} = \sqrt{(1-(-4))^2 + (-1 -(-2))^2} = \sqrt{26}[/tex]

In ΔS E K;

Distance between S and E;

[tex]D_{SE} = \sqrt{(3-(-1))^2 + (10-3)^2} = \sqrt{65}[/tex]

Distance between E and K;

[tex]D_{EK} = \sqrt{(4-3)^2 + (4 -10)^2} = \sqrt{37}[/tex]

Distance between K and S;

Clearly, Distance between sides of  Δ T J D and ΔS E K are equal as;

[tex]D_{SE} = D_{TJ} \\\\D_{EK} = D_{JD}\\\\D_{KS} = D_{DT}[/tex]

Hence, By SSS congruency;

⇒ Δ T J D ≅ ΔS E K

Learn more about the congruency in triangle visit:

https://brainly.com/question/3999145

#SPJ4

The system of equations, -x + y = -2 and 2x - 2y = 0, has no solution.

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

Given two equations in x and y,

-x + y = -2     (equation 1)

2x - 2y = 0     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -x + y = -2     ⇒     y = x - 2

2x - 2y = 0     (equation 2)

2x - 2(x - 2) = 0

2x - 2x + 4 = 0

4 = 0

Since we do not have a definite value for x, and neither will be for y, the system of equation has no solution.

Checking the slope,

(equation 1) -x + y = -2     ⇒     y = x - 2

m = 1

(equation 2) 2x - 2y = 0     ⇒     y = x

m = 1

Since the two equations has the same slopes but different y-intercepts, then these two equations must be parallel with each other.

To learn more about solving systems of equations: https://brainly.com/question/13729904

#SPJ4

The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

According to the statement

We have to find that the value of the tenth digit.

So, For this purpose, we know that the

Tenth digit  is the first digit to the right of the decimal point; one out of 10 equal parts of a whole.

From the given information:

14 plus cube root of 81 to the nearest tenth.

Then

the statement become is

[tex]14+(81)^\frac{1}{3}[/tex]

Firstly we have to find the cube root of the number 8 and then have to add 14 number in the out coming answer.

Then

14+ Cube root of 81

Then

14+ 4.32

Then after adding it

18.32

In the nearest tenth value it will become 18.3.

So, The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

Learn more about Tenth digit here

https://brainly.com/question/1753036

#SPJ1

Answer: 7

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

The constant of variation in  y = (3/2)x is (3/2)

y = kx                           (Where k is the constant)

Here, y = (3/2)x

so k = (3/2)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

The function g(x)  whose graph is the horizontal shrink of the given graph of  f(x) =5x-6 by a factor (horizontal shrink factor) of 1/4 is  g(x)=5/4 x-6.

As per the question statement, we are supposed to find a function g(x) whose graph is a horizontal shrink of the given graph of f(x) =5x-6 by a factor of 1/4.

Before solving it lets assume f(x)=y

so y =5x-6

Comparing with y= mx+c  where m is the slope

so in y =5x-6  slope is m=5

For applying horizontal shrink by a factor of 1/4 we need to multiply the slope by a factor of 1/4

so new slope [tex]m_{1} =5*\frac{1}{4} =\frac{5}{4}[/tex]

Therefore [tex]g(x) = \frac{5}{4} x -6[/tex]

Therefore the function [tex]g(x)[/tex] whose graph is a horizontal shrink of the given graph of  [tex]f(x) = 5x-6[/tex]  by a horizontal shrink factor of  1/4  is [tex]g(x) = \frac{5}{4} x -6[/tex]

To learn more about such questions, click on the link given below:

https://brainly.com/question/17827171

#SPJ1

The value of the inequality is x > 6

Inequalities are defined as mathematical relations that makes a non-equal comparison between two numbers , elements or expressions.

They are also used to compare two numbers on the number line by their size.

It is an order relationship showing —greater than, greater than or equal to, less than, or less than or equal to

Given the expression;

|1.3x + 7.8| > 0

collect like terms

1. 3x > 0 + 7. 8

1.3x > 7. 8

Make 'x' the subject

Divide both sides by 1. 3

1. x/ 1. 3 > 7. 8/ 1. 3

x > 6

Thus, the value of the inequality is x > 6

Learn more about inequalities here:

https://brainly.com/question/25275758

#SPJ1

Answer:

44 °

Step-by-step explanation:

In a right triangle such as this

  sin B = opposite leg / hypotenuse

  sin B =   20 / 29

   B = arcsin (20/29) = 44 degrees